Research ArticleA Fatigue Life Prediction Method for the Drive System of WindTurbine Using Internet of Things

Hang Zhou Shi-Jun Yi Ya-Fei Liu Yong-Quan Hu and Yong Xiang

School of Computer Engineering Chengdu Technological University Chengdu 611731 China

Correspondence should be addressed to Yong Xiang zhouchcdsc163com

Received 24 June 2020 Revised 4 August 2020 Accepted 6 August 2020 Published 27 August 2020

Guest Editor Shun-Peng Zhu

Copyright copy 2020 Hang Zhou et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-e wind turbine drive system is one of the key components in converting wind energy into electrical energy-e life prediction ofdrive system is very important for themaintenance of wind turbineWith increasing capacity the wind turbine system has becomemore complicated Consequently for the life prediction of drive system it is necessary to consider the problems of multi-information fusion of big data quantification of time-varying dynamic loads and analysis of multiple-damage coupling In orderto solve the above challenges the fatigue life analysis and evaluation method considering the interaction of coupled multipledamages are proposed in this study -e hierarchical Bayesian theory with fault physics technology is introduced to deal with theuncertainty of wind turbine drive system -en a time-varying performance analysis model is established based on the multiple-damage coupling competition failure mechanism Moreover the Internet of-ings (IoT) technology is introduced and combinedwith the proposed model -rough the data collection by IoT the time-stress curve of drive system can be obtained A case studyabout the remaining fatigue life estimation of drive system is utilized to illustrate the effectiveness of the proposed method

1 Introduction

Wind energy is a common clean and renewable energy -eeffective utilization of wind energy can reduce the energycrisis and protect the environment-e early development ofwind energy is mainly carried out on land Engineers havesuccessfully built many onshore wind turbines Comparedwith offshore wind farms onshore wind farms are moremature in technology and management [1] Generally theoffshore wind farms are located on the ocean and have verylittle impact on humans-erefore offshore wind power willaccount for more proportion in the future wind powerindustry

Uncertain environment has restricted the developmentof offshore wind turbines and threatened the wind turbinedrive system security [2] -e design requirements for off-shore wind farms are more difficult than those for onshorewind farms [3ndash6] Risk assessment can improve the reli-ability of systems [7ndash11] For wind turbine drive system it isimportant to study the failure mechanism fault diagnosisand life prediction of key components Accordingly recent

research involves multiple subjects like dynamics materialmechanics fatigue reliability and signal analysis [12 13]

Taking the wind turbine planetary gearbox as an ex-ample the dynamic analysis mainly focuses on the char-acteristics of gears and bearings -e gear dynamics modelmainly analyzes the gear mesh stiffness characteristics [14]the tooth surface contact force [15 16] and the influence ofassembly and machining errors [17] -e bearing dynamicsmodel mainly analyzes the interaction force between therolling element and the cage [18 19] and the influence of thecage parameters on the bearing characteristics [20] Duringthe operation of the gearbox the tooth surfaces and roots aresubjected to alternating and impact loads which leads tofatigue damage of the gears Many uncertainties also causethe failure of the bearing -us the dynamic model isproposed for failure mechanism analysis fault diagnosisand life prediction

-e research of gear failure mechanism starts from thetooth root crack [21] the tooth surface pitting [15] and therelationship between crack change and meshing stiffnesschange [14] -e research of bearing failure mechanism

HindawiAdvances in Materials Science and EngineeringVolume 2020 Article ID 9048508 8 pageshttpsdoiorg10115520209048508

starts from the change of bearing rolling element clearance[22 23] the number of pressure rolling elements [24] thelubrication characteristics [25] and the cage flexibilitycharacteristics [26] Recent research results include rollingbearing-rotor systems [27] gear transmission systems [28]gear-rotor-bearing system [29] and gearbox bearing system[30]

-e main working mode of wind turbine planetarygearbox is that the load changes with the wind speed-erefore the fault diagnosis is the core technology in re-search process Many methods have been proposed such asusing instantaneous power spectrum and genetic pro-gramming methods to identify fault feature parameters [31]fault diagnosis of rotating machinery under variable oper-ating conditions based on wavelet packet coefficients andentropy information indicators [32] and fault informationextraction based on the VoldndashKalman method [33]

In the process of fault diagnosis it is necessary to analyzethe internal and external load characteristics However thecurrent research mainly focuses on the relationship betweena certain fault state and system dynamics -ese researchworks are short on developing dynamic fault responsemechanism -is paper proposes the coupling fault diag-nosis mechanism and the fatigue life prediction methodbased on wind farm complex conditions

Many scholars have carried out research on productremaining life prediction methods such as model-basedmethods data-driven methods and hybrid methods[34ndash37] -e product monitoring data have the character-istics of large quantity and variety Consequently it isnecessary to achieve automatic real-time analysis of productmonitoring data by the Internet of -ings (IoT) Deeplearning methods are also effective ways to solve thisproblem However most of them cannot solve the productremaining life prediction problems Hence the productremaining life prediction based on the Internet of-ings hasa good research prospect

In this paper a remaining life prediction method basedon deep learning is proposed and it can be operated undermultiple failure models -is method can integrate themultisensor monitoring data with the dynamic workingcondition data into the fusion data -rough the usage ofbidirectional neural network in the deep learning the timecorrelation model of the fusion data can be obtained -enthis method can achieve nonlinear regression analysis of thefusion data and product remaining life under multiplefailure models-is paper takes the remaining life predictionof wind turbine drive system as a case to prove the effec-tiveness of the method

2 The Construction of Internet of Things(IoT) in the Drive System of Wind Turbine

-e working environment of wind turbine drive system ishard so it is necessary to monitor working conditions andenvironmental information -erefore a sensor is used tocollect information as data support for the system -esensor can convert physical signals into electrical signals soas to satisfy the actual demand [38] Its accuracy affects the

performance of the system so the selection of sensors shouldtake the system requirements and environment factors intoconsideration

-e state monitoring and life prediction system of thewind turbine drive system based on the Internet of-ings canbe divided into three functional levels (a) Perception layer-e perception layer includes transmission equipment sen-sors and wireless sensor nodes Its function is to perceive theworking conditions of the transmission system (b) Trans-mission layer -e transmission layer uses the CAN com-munication protocol to achieve wired communicationbetween devices and uses the ZigBee communication protocolto build a wireless sensor network Its function is to deliver theworking condition information of the transmission system(c) Application layer -e application layer is composed ofPC104 operating system software and life prediction al-gorithm Its function is to achieve acceptance storage displayand intelligent processing of the working condition infor-mation and manage the entire life cycle of the wind turbine

Figure 1 shows the system hardware framework -ewireless sensor network collects speed and temperature in-formation of the transmission system and delivers them to thePC104 for processing At the same time the ARM processorcollects fault signals status signals current signals and vi-bration signals of the transmission system and delivers them tothe PC104 for processing -e PC104 processes the collectedinformation and displays the results and status monitoringinformation on the LCD screen -e PC104 can share theinformation with the centralized control center through theEthernet communication module -en the centralized con-trol center can monitor the transmission system in real time

3 Data-Driven Fatigue Life PredictionBased on IoT

A large amount of data has been accumulated during thesensor operation After being processed the data stillcontain unused information -e data-driven multivariatestatistical algorithm can use these data to carry out processmonitoring fault monitoring and diagnosis and quality andlife prediction [39ndash41]

-e product remaining life is the time interval betweenthe current moment and the failure moment Specificallythe product monitoring information at this moment iscompared with the historical information to get the com-parison conclusion and predict the product remaining life

31 Data Collection -e degradation status information ofproducts during operation is monitored by multiple sensors-en the data is defined as online measurement data -emonitoring data of training products are recorded untilfailure and saved to si yi1113864 1113865

L

i1 si isin RMtimesp represents theonline monitoring data of the i-th training product-e dataare monitored by p sensors Each sensor employs M datapoints L is the total number of training products yi rep-resents the degradation state of the i-th training product andneeds to be detected offline -e monitoring data of textingproducts are recorded and saved to sj1113864 1113865

C

j1 sj isin RMtimesp

2 Advances in Materials Science and Engineering

represents the online real-time monitoring data of the j-thtesting product C is the total number of testing products-e information about the degradation status and remaininglife of the testing product is unknown and it needs to befurther estimated based on sj1113864 1113865

C

j1

32 Data Preprocessing -e data preprocessing can be di-vided into three sections namely feature extraction dataregularization processing and sliding time window processing

-e feature extraction of the monitoring data can reducethe data size and increase work efficiency -e noisy andabnormal data points will affect prediction accuracy of themethod -e feature extraction can reduce the above-mentioned adverse effects First the time domain features ofthe monitoring data can be extracted such as mean stan-dard deviation root mean square skewness and kurtosisSecond the frequency domain features of the monitoringdata can be extracted by the fast Fourier transform tech-nique such as average frequency spectral skewness spectralkurtosis and spectral power -ird the time-frequencydomain features can be extracted by the empirical modedecomposition and wavelet change technique

After the above steps the monitoring data si1113864 1113865L

i1 andsj1113864 1113865

C

j1 can be converted into set xi1113864 1113865L

i1 and xj1113864 1113865C

j1xi isin R1timesN and xj isin R1timesN represent the initial features of thei-th training product si and the j-th testing product sj Nrepresents the number of initial features However theextracted features have different data size so the z-scoreregularization method is used to normalize data as follows

x

kd

xkd minus μd

σd

(1)

where xkd represents the d-th feature quantity for the k-th

sample xkd represents the result after normalization and

μd and σd represent the mean and standard deviation ofthe d-th feature in set

33 Life PredictionMethod Based on Particle Filter Algorithm-e network structure based on the bidirectional long short-term memory (Bi-LSTM) model can be divided into two

sections (1) extracting the time-dependent features ofnormalized data by the Bi-LSTM network (2) processing thetime-dependent features and outputting the prediction re-sult of product degradation indicators A schematic diagramof the correlation between the two sections is shown inFigure 2

More details can be found as follows

Step 1 the training set Xk yk1113864 1113865K

k1 can be obtained byprocessing monitoring data Xk [xk

1 xk2 xk

t

xktTW

] represents the data of the k-th training fea-ture tTW represents the length of the data xk

t isin R1timesN

represents the normalized feature data at time t yk

represents the product degradation state of Xk -evalue of yk is the data of the offline degradation stateXk is normalized and its time-dependent features areextracted by the Bi-LSTM network as follows

h1 h2 ht htTW1113960 1113961 f1 X

k Θrarr

BIminusLSTM Θlarr

BIminusLSTM1113874 1113875

(2)

where f1 represents the hidden layer function of the Bi-LSTM network -e parameter set of the Bi-LSTMnetwork is described by (Θ

rarrBIminusLSTM Θ

larrBIminusLSTM)

All output features of the Bi-LSTM network are givenin (2) However only the output features of the last timepoint of the second layer are used for the fully con-nected layer the calculation process is as follows

htTW h

rarrtTWoplus h

larrtTW

(3)

where hrarr

tTWand h

larrtTW

represent the output features of theforward and reverse Bi-LSTM networks at the last mo-ment andoplus represents the sum operation point-by-pointStep 2 -e output feature htTW

of the Bi-LSTM networkis used in the fully connected layer to further extract theadvanced features -e calculation process is as follows

Speed information

Temperature information

Fault signal

Status signal

Motor current signal

Motor and gearbox vibration

Wirelesssensor

network

ARMprocessor

PC104embeddedcomputer

LCD

Newsreport

module

Centralizedcontrolcenter

Figure 1 -e frame diagram of system hardware

Advances in Materials Science and Engineering 3

ok

f2 htTWΘFC1113872 1113873 WFhtTW

+ bF (4)

where ok is the output features of the fully connected layerand ΘFC is the parameter set of the fully connected layerincluding the weight matrix WF and the bias vector bF-enok is used to predict the degradation state of the product-eprocess can be described by the following equation

1113954yk f3 okΘR1113872 1113873 WRo

k (5)

where 1113954yk is the prediction of the product degradation indexand WR is the weight vector of the last linear regressionlayer

Step 1 and Step 2 both use single-layer bidirectional longshort-term memory neural network expression and fullyconnected neural network expression In actual engineeringmore layers can be stacked to form a deep structureHowever the deep neural network structure has a morecomplex model and needs more training data

-e calculation process of the model forward propa-gation has been given earlier -en the model loss functionbased on mean variance can be defined as follows

L(Θ) 1K

1113944

K

k1y

kminus fΘ X

k1113872 11138731113872 1113873

2 (6)

where yk represents the normalized value of the degradationindicators in the shutdown state yk fΘ(Xk) representsthe prediction of the product degradation indicators Xk andfΘ(bull) is defined by (2)ndash(5)

For some complex products the degradation state data isdifficult to obtain online directly because of actual engi-neering limitations Hence online monitoring techniquesare used as auxiliary means to obtain indirect data andcomplete the estimation of the degradation state In order todefine the problem of product degradation state estimationfirstly the relationship between the degradation state andtime is given as follows

yk f ykminus1 vkminus1( 1113857⟺p yk

1113868111386811138681113868 ykminus11113872 1113873 (7)

where k represents the time point f(bull) represents theproduct state transition model ykminus1 represents the internaldegradation state of the product at time k-1 and vkminus1represents an independent and identically distributed pro-cess noise At any time point k the online measurement datask isin RMtimesp of the product can be obtained and the nonlinearrelationship between sk and yk is given as follows

sk h yk wk( 1113857⟺p sk

1113868111386811138681113868 yk1113872 1113873 (8)

where h(middot) is the observation model and wk is an inde-pendent and identically distributed measurement noise

-e online measurement data is collected by multiplesensors at very high sampling frequency and its signal tonoise ratio is low so it is difficult to obtain the displayanalytical model between the onlinemonitoring data and theinternal degradation state -erefore the online measure-ment data is processed earlier including feature extractionnormalization and serialization -en the online moni-toring data can be converted into a set of normalized dataxk [xk

1 xk2 xk

t xktTW

] fPreminusprocessing(sk) Finallythe model between the extracted feature xk and the internaldegradation state yk is established based on the Bi-LSTMnetwork and is given as follows

zk hBIminusLSTM yk xk wk( 1113857⟺p zk

1113868111386811138681113868 yk1113872 1113873 (9)

where zk represents the predicted output value of theproduct degradation index yk represents the internaldegradation state of the product in the shutdown state andwk is the measurement noise and follows a normaldistribution

In the framework of Bayesian learning the main task isto calculate the posterior probability distributionp(yk+1 | sk+1) of the product degradation state when the real-time online measurement data sk+1 is known [42ndash47] sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index predicted output value

LSTMLL

LSTMLR

Xk rarrΘBI-LSTM

larrΘBI-LSTM

rarrhtTW

ΘFC

okf2

f3 yk

Section one Section twoBI-LSTM

larrhtTW

htTW

ΘR

f1

f1

Figure 2 -e diagram of the correlation between the two sections

4 Advances in Materials Science and Engineering

zk+1 -us the posterior probability distributionp(yk+1 | zk+1) is actually obtained If p(yk | zk) is known attime k the probability density function p(yk+1 | zk) based onthe ChapmanndashKolmogorov equation is given as follows

p yk+11113868111386811138681113868 zk1113872 1113873 1113946 p yk+1 yk

11138681113868111386811138681113872 1113873 yk zk

11138681113868111386811138681113872 1113873dyk (10)

At time k+ 1 the new online measurement data sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index prediction outputzk+1 -en the posterior probability distributionp(yk+1 | zk+1) can be updated based on the Bayesian crite-rion as follows

p yk+1 zk+111138681113868111386811138681113872 1113873

p zk+1 yk+111138681113868111386811138681113872 1113873p yk+1 zk

11138681113868111386811138681113872 1113873

p zk+1 zk

11138681113868111386811138681113872 1113873 (11)

where p(zk+1 | yk+1) represents the likelihood function attime k+ 1 and can be defined by (9) the probability densitydistribution p(yk+1 | zk) can be calculated through theprediction and p(zk+1 | zk) represents the normalizationfactor -e calculation process is as follows

p zk+1 zk

11138681113868111386811138681113872 1113873 1113946 p zk+1 yk+111138681113868111386811138681113872 1113873 yk+1 zk

11138681113868111386811138681113872 1113873dyk+1 (12)

Because of the nonlinear features it is difficult to obtainexact solutions of above equations so particle filtering isintroduced to solve these problems -e structure of particlefiltering is actually the Monte Carlo method (which refers tothe probability of the event by the frequency of occurrence ata certain time) with a layer of importance sampling proposedin it -e basic idea of this method is to use a set of samples(or particles) to approximate the posterior probability dis-tribution of the system and then use this approximaterepresentation to estimate the state of the nonlinear systemUsing this idea particle filtering can handle any form ofprobability in the filtering process At the same timep(yk+1 | zk+1) is approximated by Bayesian filtering methodbased on Monte Carlo simulation If p(yk | zk) is known attime k and can be described by discrete valuesy1

k yik yN

k and their weights ω1k ωi

k ωNk the

calculation process is given as follows

p yk zk

11138681113868111386811138681113872 1113873 asymp 1113944N

i1ωi

kδ yk minus yik1113872 1113873 (13)

where 1113936Ni1 ω

ik 1 δ(middot) represents the Dirac δ function

Equation (10) can be rewritten as follows

p yk+11113868111386811138681113868 zk1113872 1113873 asymp 1113944

N

i1ωi

kδ yk minus yik1113872 1113873p yk+1

1113868111386811138681113868 yk1113872 1113873

1113944

N

i1ωi

kp yk+11113868111386811138681113868 yk1113872 1113873

(14)

where i represents the i-th particle N represents the totalnumber of particles and p(yk+1 | yk) can be calculated basedon the state transition model

-e weight value ωik of (9) can be updated by the im-

portance sampling method and the update process is givenas follows

ωik+1propω

ikp zk+1

1113868111386811138681113868 yik1113872 1113873 (15)

where p(zk+1 | yik) represents the likelihood function of the

predicted output zk+1In order to avoid the particle degradation during the

operation of the particle filtering algorithm the resamplingmethod based on the inverse cumulative function is used toobtain particles with equal weights -e steps are as followsStep 1 Construct the cumulative density function based onthe likelihood function p(zk+1 | yi

k) Step 2 Sample a ran-dom value from the uniform distribution U (0 1) and use itas the input of the cumulative density function in Step 1 Step3 Take out the particle whose value is most similar to theoutput of CDF in Step 2 and consider it as the result afterresampling Step 4 Repeat the calculation process of Steps1ndash3 N times and obtain N equal weight resampling particles-en use these particles to approximate the posteriorprobability density distribution p(yk+1 | zk+1)

4 Case Study

41 Doubly Fed Wind Turbine Drive System -e windturbine drive system can transmit torque and changerotating speed Its structure has a great influence on thelayout of wind turbine At present the wind turbine hastwo types doubly fed and direct-drive -e differencebetween them is the structure of the drive system -edrive system of the doubly fed wind turbine has a speed-increasing gearbox while the drive system of the direct-drive wind turbine does not have one -e object of thispaper is the doubly fed wind turbine drive system

-e wheel hub of the doubly fed wind turbine isconnected to one side of the low-speed main shaft -eother side is connected to the input of the speed-increasinggearbox -e output of the gearbox (high-speed shaft) isconnected to the generator rotor through the flexiblecoupling -e hydraulic brake disc is installed on the high-speed shaft -e entire drive system is installed on the mainframe -e thrust and radial load generated by the windwheel are transmitted to the main frame first and then tothe tower

Because of the speed-increasing gearbox the generatorrotor can reach a high rotating speed and the requirementfor magnetic poles is low-e gearbox calls for a high speed-increasing ratio and use multistage planetary gears com-bined with fixed-shaft gears -e characteristics of thedoubly fed wind turbine drive system are as follows (1) -eoperating conditions change with the wind speed and lead toconstant change of vibration signal amplitude and fre-quency As a result the signal contains a large number ofuncertainties (2)-e drive system is located in the top of thetower Strong wind will cause the body shake Hence thesignal will contain noise interference (3) -e mechanicalstructure of wind turbine drive system is complex It calls forhigh standard of related technologies (4) Wind turbines are

Advances in Materials Science and Engineering 5

severely affected by environmental conditions and have highrequirements for the reliability and anti-interference abilityof the test system

42 Dynamic Modeling of Wind Turbine Drive System-is paper uses the dynamic analysis process of the windturbine gearbox drive system as shown in Figure 3

First of all the external and internal incentives of thegearbox are obtained through the monitoring of the Internetof -ings technology -ey are transmitted as dynamicincentives to the analysis model of gearbox system Secondthe analysis model of gearbox system processes the inputdynamic incentives through centralized parameter methodfinite element method hybrid modeling method and bonggraph theory After processing the inherent features anddynamic responses are output and they are used as thedynamic responses of the analysis system Finally theparticle filter algorithm is used for conditionmonitoring andlife prediction applications -e above is the main appli-cation process of the method proposed in this paper for thewind turbine drive system

-e external excitation of the gearbox mainly includesthe dynamic input torque the nontorsional loads thegenerator feedback torque the braking torque and theimpact load -e internal excitation includes time-varyingstiffness excitation time-varying error excitation meshingshocks and tooth backlash -is paper uses dynamic re-sponse analysis method dynamic stability analysis methodand inherent characteristic analysis method to optimize thesystem structure Based on the IoT technology the dynamicmodel has been proposed to monitor the gearbox status andprovide theoretical basis of fault diagnosis and lifeprediction

43MethodValidation -e gearbox wear tests are recordedas A1 A2 and A3 Each test includes online monitoring datafrom six signal channels and each test collected 600 sets of

online monitoring data during transmission process Inorder to describe the online monitoring data clearly 50equidistant data monitoring points are used for each onlinemonitoring data group

In order to reduce the data size and improve predictionefficiency the method extracts the time domain featurefirst and then the frequency domain feature -e BL-STMmodel has been used to simplify the feature processingflow

During the experiment A1 is used as the test sample andA2 and A3 are used as the training samples -e predictionresult of the final transmission pair loss is shown in Table 1According to the experiment results the top five featureswith the highest scores can achieve the best predictionperformance

-e influence of the feature fusion step on the finaltransmission pair loss prediction result is shown in Table 2-e optimal feature set used in Table 2 is composed of thetop eight features with the highest scores It can be inferredfrom Table 2 that the fusion feature with the highest scorescan bring the best prediction performance

Combined with the state transfer model of transmissionpair wear and its observation model based on Bi-LSTM theparticle filter algorithm is used to predict the evolution of thetransmission pair degradation index When the index ex-ceeds the failure threshold the remaining useful life (RUL)of transmission pair can be obtained

Dynamic incentive(system input)

Analysis model ofgearbox system

Dynamic response(system output) Application

External incentive

Internal incentive

Centralizedparameter method

Finite elementmethod

Hybrid modelingmethod

Bond graph theory

Inherent features

Dynamic response

Evaluation andprevention of

vibration and noise

Conditionmonitoring andfault diagnosis

Load identificationand dynamic

design

Figure 3 Dynamic modeling and analysis process of wind turbine gearbox

Table 1 Influence of feature selection steps on prediction resultsOptimal feature set 20 15 13 10 5Root mean square error 714 578 524 509 497Mean absolute error 689 568 587 502 475

Table 2 Influence of feature selection steps on prediction resultsNumber of principal components retained () 95 97 99Root mean square error 317 423 524Mean absolute error 307 348 435

6 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

represents the online real-time monitoring data of the j-thtesting product C is the total number of testing products-e information about the degradation status and remaininglife of the testing product is unknown and it needs to befurther estimated based on sj1113864 1113865

C

j1

32 Data Preprocessing -e data preprocessing can be di-vided into three sections namely feature extraction dataregularization processing and sliding time window processing

-e feature extraction of the monitoring data can reducethe data size and increase work efficiency -e noisy andabnormal data points will affect prediction accuracy of themethod -e feature extraction can reduce the above-mentioned adverse effects First the time domain features ofthe monitoring data can be extracted such as mean stan-dard deviation root mean square skewness and kurtosisSecond the frequency domain features of the monitoringdata can be extracted by the fast Fourier transform tech-nique such as average frequency spectral skewness spectralkurtosis and spectral power -ird the time-frequencydomain features can be extracted by the empirical modedecomposition and wavelet change technique

After the above steps the monitoring data si1113864 1113865L

i1 andsj1113864 1113865

C

j1 can be converted into set xi1113864 1113865L

i1 and xj1113864 1113865C

j1xi isin R1timesN and xj isin R1timesN represent the initial features of thei-th training product si and the j-th testing product sj Nrepresents the number of initial features However theextracted features have different data size so the z-scoreregularization method is used to normalize data as follows

x

kd

xkd minus μd

σd

(1)

where xkd represents the d-th feature quantity for the k-th

sample xkd represents the result after normalization and

μd and σd represent the mean and standard deviation ofthe d-th feature in set

33 Life PredictionMethod Based on Particle Filter Algorithm-e network structure based on the bidirectional long short-term memory (Bi-LSTM) model can be divided into two

sections (1) extracting the time-dependent features ofnormalized data by the Bi-LSTM network (2) processing thetime-dependent features and outputting the prediction re-sult of product degradation indicators A schematic diagramof the correlation between the two sections is shown inFigure 2

More details can be found as follows

Step 1 the training set Xk yk1113864 1113865K

k1 can be obtained byprocessing monitoring data Xk [xk

1 xk2 xk

t

xktTW

] represents the data of the k-th training fea-ture tTW represents the length of the data xk

t isin R1timesN

represents the normalized feature data at time t yk

represents the product degradation state of Xk -evalue of yk is the data of the offline degradation stateXk is normalized and its time-dependent features areextracted by the Bi-LSTM network as follows

h1 h2 ht htTW1113960 1113961 f1 X

k Θrarr

BIminusLSTM Θlarr

BIminusLSTM1113874 1113875

(2)

where f1 represents the hidden layer function of the Bi-LSTM network -e parameter set of the Bi-LSTMnetwork is described by (Θ

rarrBIminusLSTM Θ

larrBIminusLSTM)

All output features of the Bi-LSTM network are givenin (2) However only the output features of the last timepoint of the second layer are used for the fully con-nected layer the calculation process is as follows

htTW h

rarrtTWoplus h

larrtTW

(3)

where hrarr

tTWand h

larrtTW

represent the output features of theforward and reverse Bi-LSTM networks at the last mo-ment andoplus represents the sum operation point-by-pointStep 2 -e output feature htTW

of the Bi-LSTM networkis used in the fully connected layer to further extract theadvanced features -e calculation process is as follows

Speed information

Temperature information

Fault signal

Status signal

Motor current signal

Motor and gearbox vibration

Wirelesssensor

network

ARMprocessor

PC104embeddedcomputer

LCD

Newsreport

module

Centralizedcontrolcenter

Figure 1 -e frame diagram of system hardware

Advances in Materials Science and Engineering 3

ok

f2 htTWΘFC1113872 1113873 WFhtTW

+ bF (4)

where ok is the output features of the fully connected layerand ΘFC is the parameter set of the fully connected layerincluding the weight matrix WF and the bias vector bF-enok is used to predict the degradation state of the product-eprocess can be described by the following equation

1113954yk f3 okΘR1113872 1113873 WRo

k (5)

where 1113954yk is the prediction of the product degradation indexand WR is the weight vector of the last linear regressionlayer

Step 1 and Step 2 both use single-layer bidirectional longshort-term memory neural network expression and fullyconnected neural network expression In actual engineeringmore layers can be stacked to form a deep structureHowever the deep neural network structure has a morecomplex model and needs more training data

-e calculation process of the model forward propa-gation has been given earlier -en the model loss functionbased on mean variance can be defined as follows

L(Θ) 1K

1113944

K

k1y

kminus fΘ X

k1113872 11138731113872 1113873

2 (6)

where yk represents the normalized value of the degradationindicators in the shutdown state yk fΘ(Xk) representsthe prediction of the product degradation indicators Xk andfΘ(bull) is defined by (2)ndash(5)

For some complex products the degradation state data isdifficult to obtain online directly because of actual engi-neering limitations Hence online monitoring techniquesare used as auxiliary means to obtain indirect data andcomplete the estimation of the degradation state In order todefine the problem of product degradation state estimationfirstly the relationship between the degradation state andtime is given as follows

yk f ykminus1 vkminus1( 1113857⟺p yk

1113868111386811138681113868 ykminus11113872 1113873 (7)

where k represents the time point f(bull) represents theproduct state transition model ykminus1 represents the internaldegradation state of the product at time k-1 and vkminus1represents an independent and identically distributed pro-cess noise At any time point k the online measurement datask isin RMtimesp of the product can be obtained and the nonlinearrelationship between sk and yk is given as follows

sk h yk wk( 1113857⟺p sk

1113868111386811138681113868 yk1113872 1113873 (8)

where h(middot) is the observation model and wk is an inde-pendent and identically distributed measurement noise

-e online measurement data is collected by multiplesensors at very high sampling frequency and its signal tonoise ratio is low so it is difficult to obtain the displayanalytical model between the onlinemonitoring data and theinternal degradation state -erefore the online measure-ment data is processed earlier including feature extractionnormalization and serialization -en the online moni-toring data can be converted into a set of normalized dataxk [xk

1 xk2 xk

t xktTW

] fPreminusprocessing(sk) Finallythe model between the extracted feature xk and the internaldegradation state yk is established based on the Bi-LSTMnetwork and is given as follows

zk hBIminusLSTM yk xk wk( 1113857⟺p zk

1113868111386811138681113868 yk1113872 1113873 (9)

where zk represents the predicted output value of theproduct degradation index yk represents the internaldegradation state of the product in the shutdown state andwk is the measurement noise and follows a normaldistribution

In the framework of Bayesian learning the main task isto calculate the posterior probability distributionp(yk+1 | sk+1) of the product degradation state when the real-time online measurement data sk+1 is known [42ndash47] sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index predicted output value

LSTMLL

LSTMLR

Xk rarrΘBI-LSTM

larrΘBI-LSTM

rarrhtTW

ΘFC

okf2

f3 yk

Section one Section twoBI-LSTM

larrhtTW

htTW

ΘR

f1

f1

Figure 2 -e diagram of the correlation between the two sections

4 Advances in Materials Science and Engineering

zk+1 -us the posterior probability distributionp(yk+1 | zk+1) is actually obtained If p(yk | zk) is known attime k the probability density function p(yk+1 | zk) based onthe ChapmanndashKolmogorov equation is given as follows

p yk+11113868111386811138681113868 zk1113872 1113873 1113946 p yk+1 yk

11138681113868111386811138681113872 1113873 yk zk

11138681113868111386811138681113872 1113873dyk (10)

At time k+ 1 the new online measurement data sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index prediction outputzk+1 -en the posterior probability distributionp(yk+1 | zk+1) can be updated based on the Bayesian crite-rion as follows

p yk+1 zk+111138681113868111386811138681113872 1113873

p zk+1 yk+111138681113868111386811138681113872 1113873p yk+1 zk

11138681113868111386811138681113872 1113873

p zk+1 zk

11138681113868111386811138681113872 1113873 (11)

where p(zk+1 | yk+1) represents the likelihood function attime k+ 1 and can be defined by (9) the probability densitydistribution p(yk+1 | zk) can be calculated through theprediction and p(zk+1 | zk) represents the normalizationfactor -e calculation process is as follows

p zk+1 zk

11138681113868111386811138681113872 1113873 1113946 p zk+1 yk+111138681113868111386811138681113872 1113873 yk+1 zk

11138681113868111386811138681113872 1113873dyk+1 (12)

Because of the nonlinear features it is difficult to obtainexact solutions of above equations so particle filtering isintroduced to solve these problems -e structure of particlefiltering is actually the Monte Carlo method (which refers tothe probability of the event by the frequency of occurrence ata certain time) with a layer of importance sampling proposedin it -e basic idea of this method is to use a set of samples(or particles) to approximate the posterior probability dis-tribution of the system and then use this approximaterepresentation to estimate the state of the nonlinear systemUsing this idea particle filtering can handle any form ofprobability in the filtering process At the same timep(yk+1 | zk+1) is approximated by Bayesian filtering methodbased on Monte Carlo simulation If p(yk | zk) is known attime k and can be described by discrete valuesy1

k yik yN

k and their weights ω1k ωi

k ωNk the

calculation process is given as follows

p yk zk

11138681113868111386811138681113872 1113873 asymp 1113944N

i1ωi

kδ yk minus yik1113872 1113873 (13)

where 1113936Ni1 ω

ik 1 δ(middot) represents the Dirac δ function

Equation (10) can be rewritten as follows

p yk+11113868111386811138681113868 zk1113872 1113873 asymp 1113944

N

i1ωi

kδ yk minus yik1113872 1113873p yk+1

1113868111386811138681113868 yk1113872 1113873

1113944

N

i1ωi

kp yk+11113868111386811138681113868 yk1113872 1113873

(14)

where i represents the i-th particle N represents the totalnumber of particles and p(yk+1 | yk) can be calculated basedon the state transition model

-e weight value ωik of (9) can be updated by the im-

portance sampling method and the update process is givenas follows

ωik+1propω

ikp zk+1

1113868111386811138681113868 yik1113872 1113873 (15)

where p(zk+1 | yik) represents the likelihood function of the

predicted output zk+1In order to avoid the particle degradation during the

operation of the particle filtering algorithm the resamplingmethod based on the inverse cumulative function is used toobtain particles with equal weights -e steps are as followsStep 1 Construct the cumulative density function based onthe likelihood function p(zk+1 | yi

k) Step 2 Sample a ran-dom value from the uniform distribution U (0 1) and use itas the input of the cumulative density function in Step 1 Step3 Take out the particle whose value is most similar to theoutput of CDF in Step 2 and consider it as the result afterresampling Step 4 Repeat the calculation process of Steps1ndash3 N times and obtain N equal weight resampling particles-en use these particles to approximate the posteriorprobability density distribution p(yk+1 | zk+1)

4 Case Study

41 Doubly Fed Wind Turbine Drive System -e windturbine drive system can transmit torque and changerotating speed Its structure has a great influence on thelayout of wind turbine At present the wind turbine hastwo types doubly fed and direct-drive -e differencebetween them is the structure of the drive system -edrive system of the doubly fed wind turbine has a speed-increasing gearbox while the drive system of the direct-drive wind turbine does not have one -e object of thispaper is the doubly fed wind turbine drive system

-e wheel hub of the doubly fed wind turbine isconnected to one side of the low-speed main shaft -eother side is connected to the input of the speed-increasinggearbox -e output of the gearbox (high-speed shaft) isconnected to the generator rotor through the flexiblecoupling -e hydraulic brake disc is installed on the high-speed shaft -e entire drive system is installed on the mainframe -e thrust and radial load generated by the windwheel are transmitted to the main frame first and then tothe tower

Because of the speed-increasing gearbox the generatorrotor can reach a high rotating speed and the requirementfor magnetic poles is low-e gearbox calls for a high speed-increasing ratio and use multistage planetary gears com-bined with fixed-shaft gears -e characteristics of thedoubly fed wind turbine drive system are as follows (1) -eoperating conditions change with the wind speed and lead toconstant change of vibration signal amplitude and fre-quency As a result the signal contains a large number ofuncertainties (2)-e drive system is located in the top of thetower Strong wind will cause the body shake Hence thesignal will contain noise interference (3) -e mechanicalstructure of wind turbine drive system is complex It calls forhigh standard of related technologies (4) Wind turbines are

Advances in Materials Science and Engineering 5

severely affected by environmental conditions and have highrequirements for the reliability and anti-interference abilityof the test system

42 Dynamic Modeling of Wind Turbine Drive System-is paper uses the dynamic analysis process of the windturbine gearbox drive system as shown in Figure 3

First of all the external and internal incentives of thegearbox are obtained through the monitoring of the Internetof -ings technology -ey are transmitted as dynamicincentives to the analysis model of gearbox system Secondthe analysis model of gearbox system processes the inputdynamic incentives through centralized parameter methodfinite element method hybrid modeling method and bonggraph theory After processing the inherent features anddynamic responses are output and they are used as thedynamic responses of the analysis system Finally theparticle filter algorithm is used for conditionmonitoring andlife prediction applications -e above is the main appli-cation process of the method proposed in this paper for thewind turbine drive system

-e external excitation of the gearbox mainly includesthe dynamic input torque the nontorsional loads thegenerator feedback torque the braking torque and theimpact load -e internal excitation includes time-varyingstiffness excitation time-varying error excitation meshingshocks and tooth backlash -is paper uses dynamic re-sponse analysis method dynamic stability analysis methodand inherent characteristic analysis method to optimize thesystem structure Based on the IoT technology the dynamicmodel has been proposed to monitor the gearbox status andprovide theoretical basis of fault diagnosis and lifeprediction

43MethodValidation -e gearbox wear tests are recordedas A1 A2 and A3 Each test includes online monitoring datafrom six signal channels and each test collected 600 sets of

online monitoring data during transmission process Inorder to describe the online monitoring data clearly 50equidistant data monitoring points are used for each onlinemonitoring data group

In order to reduce the data size and improve predictionefficiency the method extracts the time domain featurefirst and then the frequency domain feature -e BL-STMmodel has been used to simplify the feature processingflow

During the experiment A1 is used as the test sample andA2 and A3 are used as the training samples -e predictionresult of the final transmission pair loss is shown in Table 1According to the experiment results the top five featureswith the highest scores can achieve the best predictionperformance

-e influence of the feature fusion step on the finaltransmission pair loss prediction result is shown in Table 2-e optimal feature set used in Table 2 is composed of thetop eight features with the highest scores It can be inferredfrom Table 2 that the fusion feature with the highest scorescan bring the best prediction performance

Combined with the state transfer model of transmissionpair wear and its observation model based on Bi-LSTM theparticle filter algorithm is used to predict the evolution of thetransmission pair degradation index When the index ex-ceeds the failure threshold the remaining useful life (RUL)of transmission pair can be obtained

Dynamic incentive(system input)

Analysis model ofgearbox system

Dynamic response(system output) Application

External incentive

Internal incentive

Centralizedparameter method

Finite elementmethod

Hybrid modelingmethod

Bond graph theory

Inherent features

Dynamic response

Evaluation andprevention of

vibration and noise

Conditionmonitoring andfault diagnosis

Load identificationand dynamic

design

Figure 3 Dynamic modeling and analysis process of wind turbine gearbox

Table 1 Influence of feature selection steps on prediction resultsOptimal feature set 20 15 13 10 5Root mean square error 714 578 524 509 497Mean absolute error 689 568 587 502 475

Table 2 Influence of feature selection steps on prediction resultsNumber of principal components retained () 95 97 99Root mean square error 317 423 524Mean absolute error 307 348 435

6 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

ok

f2 htTWΘFC1113872 1113873 WFhtTW

+ bF (4)

where ok is the output features of the fully connected layerand ΘFC is the parameter set of the fully connected layerincluding the weight matrix WF and the bias vector bF-enok is used to predict the degradation state of the product-eprocess can be described by the following equation

1113954yk f3 okΘR1113872 1113873 WRo

k (5)

where 1113954yk is the prediction of the product degradation indexand WR is the weight vector of the last linear regressionlayer

Step 1 and Step 2 both use single-layer bidirectional longshort-term memory neural network expression and fullyconnected neural network expression In actual engineeringmore layers can be stacked to form a deep structureHowever the deep neural network structure has a morecomplex model and needs more training data

-e calculation process of the model forward propa-gation has been given earlier -en the model loss functionbased on mean variance can be defined as follows

L(Θ) 1K

1113944

K

k1y

kminus fΘ X

k1113872 11138731113872 1113873

2 (6)

where yk represents the normalized value of the degradationindicators in the shutdown state yk fΘ(Xk) representsthe prediction of the product degradation indicators Xk andfΘ(bull) is defined by (2)ndash(5)

For some complex products the degradation state data isdifficult to obtain online directly because of actual engi-neering limitations Hence online monitoring techniquesare used as auxiliary means to obtain indirect data andcomplete the estimation of the degradation state In order todefine the problem of product degradation state estimationfirstly the relationship between the degradation state andtime is given as follows

yk f ykminus1 vkminus1( 1113857⟺p yk

1113868111386811138681113868 ykminus11113872 1113873 (7)

where k represents the time point f(bull) represents theproduct state transition model ykminus1 represents the internaldegradation state of the product at time k-1 and vkminus1represents an independent and identically distributed pro-cess noise At any time point k the online measurement datask isin RMtimesp of the product can be obtained and the nonlinearrelationship between sk and yk is given as follows

sk h yk wk( 1113857⟺p sk

1113868111386811138681113868 yk1113872 1113873 (8)

where h(middot) is the observation model and wk is an inde-pendent and identically distributed measurement noise

-e online measurement data is collected by multiplesensors at very high sampling frequency and its signal tonoise ratio is low so it is difficult to obtain the displayanalytical model between the onlinemonitoring data and theinternal degradation state -erefore the online measure-ment data is processed earlier including feature extractionnormalization and serialization -en the online moni-toring data can be converted into a set of normalized dataxk [xk

1 xk2 xk

t xktTW

] fPreminusprocessing(sk) Finallythe model between the extracted feature xk and the internaldegradation state yk is established based on the Bi-LSTMnetwork and is given as follows

zk hBIminusLSTM yk xk wk( 1113857⟺p zk

1113868111386811138681113868 yk1113872 1113873 (9)

where zk represents the predicted output value of theproduct degradation index yk represents the internaldegradation state of the product in the shutdown state andwk is the measurement noise and follows a normaldistribution

In the framework of Bayesian learning the main task isto calculate the posterior probability distributionp(yk+1 | sk+1) of the product degradation state when the real-time online measurement data sk+1 is known [42ndash47] sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index predicted output value

LSTMLL

LSTMLR

Xk rarrΘBI-LSTM

larrΘBI-LSTM

rarrhtTW

ΘFC

okf2

f3 yk

Section one Section twoBI-LSTM

larrhtTW

htTW

ΘR

f1

f1

Figure 2 -e diagram of the correlation between the two sections

4 Advances in Materials Science and Engineering

zk+1 -us the posterior probability distributionp(yk+1 | zk+1) is actually obtained If p(yk | zk) is known attime k the probability density function p(yk+1 | zk) based onthe ChapmanndashKolmogorov equation is given as follows

p yk+11113868111386811138681113868 zk1113872 1113873 1113946 p yk+1 yk

11138681113868111386811138681113872 1113873 yk zk

11138681113868111386811138681113872 1113873dyk (10)

At time k+ 1 the new online measurement data sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index prediction outputzk+1 -en the posterior probability distributionp(yk+1 | zk+1) can be updated based on the Bayesian crite-rion as follows

p yk+1 zk+111138681113868111386811138681113872 1113873

p zk+1 yk+111138681113868111386811138681113872 1113873p yk+1 zk

11138681113868111386811138681113872 1113873

p zk+1 zk

11138681113868111386811138681113872 1113873 (11)

where p(zk+1 | yk+1) represents the likelihood function attime k+ 1 and can be defined by (9) the probability densitydistribution p(yk+1 | zk) can be calculated through theprediction and p(zk+1 | zk) represents the normalizationfactor -e calculation process is as follows

p zk+1 zk

11138681113868111386811138681113872 1113873 1113946 p zk+1 yk+111138681113868111386811138681113872 1113873 yk+1 zk

11138681113868111386811138681113872 1113873dyk+1 (12)

Because of the nonlinear features it is difficult to obtainexact solutions of above equations so particle filtering isintroduced to solve these problems -e structure of particlefiltering is actually the Monte Carlo method (which refers tothe probability of the event by the frequency of occurrence ata certain time) with a layer of importance sampling proposedin it -e basic idea of this method is to use a set of samples(or particles) to approximate the posterior probability dis-tribution of the system and then use this approximaterepresentation to estimate the state of the nonlinear systemUsing this idea particle filtering can handle any form ofprobability in the filtering process At the same timep(yk+1 | zk+1) is approximated by Bayesian filtering methodbased on Monte Carlo simulation If p(yk | zk) is known attime k and can be described by discrete valuesy1

k yik yN

k and their weights ω1k ωi

k ωNk the

calculation process is given as follows

p yk zk

11138681113868111386811138681113872 1113873 asymp 1113944N

i1ωi

kδ yk minus yik1113872 1113873 (13)

where 1113936Ni1 ω

ik 1 δ(middot) represents the Dirac δ function

Equation (10) can be rewritten as follows

p yk+11113868111386811138681113868 zk1113872 1113873 asymp 1113944

N

i1ωi

kδ yk minus yik1113872 1113873p yk+1

1113868111386811138681113868 yk1113872 1113873

1113944

N

i1ωi

kp yk+11113868111386811138681113868 yk1113872 1113873

(14)

where i represents the i-th particle N represents the totalnumber of particles and p(yk+1 | yk) can be calculated basedon the state transition model

-e weight value ωik of (9) can be updated by the im-

portance sampling method and the update process is givenas follows

ωik+1propω

ikp zk+1

1113868111386811138681113868 yik1113872 1113873 (15)

where p(zk+1 | yik) represents the likelihood function of the

predicted output zk+1In order to avoid the particle degradation during the

operation of the particle filtering algorithm the resamplingmethod based on the inverse cumulative function is used toobtain particles with equal weights -e steps are as followsStep 1 Construct the cumulative density function based onthe likelihood function p(zk+1 | yi

k) Step 2 Sample a ran-dom value from the uniform distribution U (0 1) and use itas the input of the cumulative density function in Step 1 Step3 Take out the particle whose value is most similar to theoutput of CDF in Step 2 and consider it as the result afterresampling Step 4 Repeat the calculation process of Steps1ndash3 N times and obtain N equal weight resampling particles-en use these particles to approximate the posteriorprobability density distribution p(yk+1 | zk+1)

4 Case Study

41 Doubly Fed Wind Turbine Drive System -e windturbine drive system can transmit torque and changerotating speed Its structure has a great influence on thelayout of wind turbine At present the wind turbine hastwo types doubly fed and direct-drive -e differencebetween them is the structure of the drive system -edrive system of the doubly fed wind turbine has a speed-increasing gearbox while the drive system of the direct-drive wind turbine does not have one -e object of thispaper is the doubly fed wind turbine drive system

-e wheel hub of the doubly fed wind turbine isconnected to one side of the low-speed main shaft -eother side is connected to the input of the speed-increasinggearbox -e output of the gearbox (high-speed shaft) isconnected to the generator rotor through the flexiblecoupling -e hydraulic brake disc is installed on the high-speed shaft -e entire drive system is installed on the mainframe -e thrust and radial load generated by the windwheel are transmitted to the main frame first and then tothe tower

Because of the speed-increasing gearbox the generatorrotor can reach a high rotating speed and the requirementfor magnetic poles is low-e gearbox calls for a high speed-increasing ratio and use multistage planetary gears com-bined with fixed-shaft gears -e characteristics of thedoubly fed wind turbine drive system are as follows (1) -eoperating conditions change with the wind speed and lead toconstant change of vibration signal amplitude and fre-quency As a result the signal contains a large number ofuncertainties (2)-e drive system is located in the top of thetower Strong wind will cause the body shake Hence thesignal will contain noise interference (3) -e mechanicalstructure of wind turbine drive system is complex It calls forhigh standard of related technologies (4) Wind turbines are

Advances in Materials Science and Engineering 5

severely affected by environmental conditions and have highrequirements for the reliability and anti-interference abilityof the test system

42 Dynamic Modeling of Wind Turbine Drive System-is paper uses the dynamic analysis process of the windturbine gearbox drive system as shown in Figure 3

First of all the external and internal incentives of thegearbox are obtained through the monitoring of the Internetof -ings technology -ey are transmitted as dynamicincentives to the analysis model of gearbox system Secondthe analysis model of gearbox system processes the inputdynamic incentives through centralized parameter methodfinite element method hybrid modeling method and bonggraph theory After processing the inherent features anddynamic responses are output and they are used as thedynamic responses of the analysis system Finally theparticle filter algorithm is used for conditionmonitoring andlife prediction applications -e above is the main appli-cation process of the method proposed in this paper for thewind turbine drive system

-e external excitation of the gearbox mainly includesthe dynamic input torque the nontorsional loads thegenerator feedback torque the braking torque and theimpact load -e internal excitation includes time-varyingstiffness excitation time-varying error excitation meshingshocks and tooth backlash -is paper uses dynamic re-sponse analysis method dynamic stability analysis methodand inherent characteristic analysis method to optimize thesystem structure Based on the IoT technology the dynamicmodel has been proposed to monitor the gearbox status andprovide theoretical basis of fault diagnosis and lifeprediction

43MethodValidation -e gearbox wear tests are recordedas A1 A2 and A3 Each test includes online monitoring datafrom six signal channels and each test collected 600 sets of

online monitoring data during transmission process Inorder to describe the online monitoring data clearly 50equidistant data monitoring points are used for each onlinemonitoring data group

In order to reduce the data size and improve predictionefficiency the method extracts the time domain featurefirst and then the frequency domain feature -e BL-STMmodel has been used to simplify the feature processingflow

During the experiment A1 is used as the test sample andA2 and A3 are used as the training samples -e predictionresult of the final transmission pair loss is shown in Table 1According to the experiment results the top five featureswith the highest scores can achieve the best predictionperformance

-e influence of the feature fusion step on the finaltransmission pair loss prediction result is shown in Table 2-e optimal feature set used in Table 2 is composed of thetop eight features with the highest scores It can be inferredfrom Table 2 that the fusion feature with the highest scorescan bring the best prediction performance

Combined with the state transfer model of transmissionpair wear and its observation model based on Bi-LSTM theparticle filter algorithm is used to predict the evolution of thetransmission pair degradation index When the index ex-ceeds the failure threshold the remaining useful life (RUL)of transmission pair can be obtained

Dynamic incentive(system input)

Analysis model ofgearbox system

Dynamic response(system output) Application

External incentive

Internal incentive

Centralizedparameter method

Finite elementmethod

Hybrid modelingmethod

Bond graph theory

Inherent features

Dynamic response

Evaluation andprevention of

vibration and noise

Conditionmonitoring andfault diagnosis

Load identificationand dynamic

design

Figure 3 Dynamic modeling and analysis process of wind turbine gearbox

Table 1 Influence of feature selection steps on prediction resultsOptimal feature set 20 15 13 10 5Root mean square error 714 578 524 509 497Mean absolute error 689 568 587 502 475

Table 2 Influence of feature selection steps on prediction resultsNumber of principal components retained () 95 97 99Root mean square error 317 423 524Mean absolute error 307 348 435

6 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

zk+1 -us the posterior probability distributionp(yk+1 | zk+1) is actually obtained If p(yk | zk) is known attime k the probability density function p(yk+1 | zk) based onthe ChapmanndashKolmogorov equation is given as follows

p yk+11113868111386811138681113868 zk1113872 1113873 1113946 p yk+1 yk

11138681113868111386811138681113872 1113873 yk zk

11138681113868111386811138681113872 1113873dyk (10)

At time k+ 1 the new online measurement data sk+1 isprocessed and transmitted to the Bi-LSTM network toobtain the product degradation index prediction outputzk+1 -en the posterior probability distributionp(yk+1 | zk+1) can be updated based on the Bayesian crite-rion as follows

p yk+1 zk+111138681113868111386811138681113872 1113873

p zk+1 yk+111138681113868111386811138681113872 1113873p yk+1 zk

11138681113868111386811138681113872 1113873

p zk+1 zk

11138681113868111386811138681113872 1113873 (11)

where p(zk+1 | yk+1) represents the likelihood function attime k+ 1 and can be defined by (9) the probability densitydistribution p(yk+1 | zk) can be calculated through theprediction and p(zk+1 | zk) represents the normalizationfactor -e calculation process is as follows

p zk+1 zk

11138681113868111386811138681113872 1113873 1113946 p zk+1 yk+111138681113868111386811138681113872 1113873 yk+1 zk

11138681113868111386811138681113872 1113873dyk+1 (12)

Because of the nonlinear features it is difficult to obtainexact solutions of above equations so particle filtering isintroduced to solve these problems -e structure of particlefiltering is actually the Monte Carlo method (which refers tothe probability of the event by the frequency of occurrence ata certain time) with a layer of importance sampling proposedin it -e basic idea of this method is to use a set of samples(or particles) to approximate the posterior probability dis-tribution of the system and then use this approximaterepresentation to estimate the state of the nonlinear systemUsing this idea particle filtering can handle any form ofprobability in the filtering process At the same timep(yk+1 | zk+1) is approximated by Bayesian filtering methodbased on Monte Carlo simulation If p(yk | zk) is known attime k and can be described by discrete valuesy1

k yik yN

k and their weights ω1k ωi

k ωNk the

calculation process is given as follows

p yk zk

11138681113868111386811138681113872 1113873 asymp 1113944N

i1ωi

kδ yk minus yik1113872 1113873 (13)

where 1113936Ni1 ω

ik 1 δ(middot) represents the Dirac δ function

Equation (10) can be rewritten as follows

p yk+11113868111386811138681113868 zk1113872 1113873 asymp 1113944

N

i1ωi

kδ yk minus yik1113872 1113873p yk+1

1113868111386811138681113868 yk1113872 1113873

1113944

N

i1ωi

kp yk+11113868111386811138681113868 yk1113872 1113873

(14)

where i represents the i-th particle N represents the totalnumber of particles and p(yk+1 | yk) can be calculated basedon the state transition model

-e weight value ωik of (9) can be updated by the im-

portance sampling method and the update process is givenas follows

ωik+1propω

ikp zk+1

1113868111386811138681113868 yik1113872 1113873 (15)

where p(zk+1 | yik) represents the likelihood function of the

predicted output zk+1In order to avoid the particle degradation during the

operation of the particle filtering algorithm the resamplingmethod based on the inverse cumulative function is used toobtain particles with equal weights -e steps are as followsStep 1 Construct the cumulative density function based onthe likelihood function p(zk+1 | yi

k) Step 2 Sample a ran-dom value from the uniform distribution U (0 1) and use itas the input of the cumulative density function in Step 1 Step3 Take out the particle whose value is most similar to theoutput of CDF in Step 2 and consider it as the result afterresampling Step 4 Repeat the calculation process of Steps1ndash3 N times and obtain N equal weight resampling particles-en use these particles to approximate the posteriorprobability density distribution p(yk+1 | zk+1)

4 Case Study

41 Doubly Fed Wind Turbine Drive System -e windturbine drive system can transmit torque and changerotating speed Its structure has a great influence on thelayout of wind turbine At present the wind turbine hastwo types doubly fed and direct-drive -e differencebetween them is the structure of the drive system -edrive system of the doubly fed wind turbine has a speed-increasing gearbox while the drive system of the direct-drive wind turbine does not have one -e object of thispaper is the doubly fed wind turbine drive system

-e wheel hub of the doubly fed wind turbine isconnected to one side of the low-speed main shaft -eother side is connected to the input of the speed-increasinggearbox -e output of the gearbox (high-speed shaft) isconnected to the generator rotor through the flexiblecoupling -e hydraulic brake disc is installed on the high-speed shaft -e entire drive system is installed on the mainframe -e thrust and radial load generated by the windwheel are transmitted to the main frame first and then tothe tower

Because of the speed-increasing gearbox the generatorrotor can reach a high rotating speed and the requirementfor magnetic poles is low-e gearbox calls for a high speed-increasing ratio and use multistage planetary gears com-bined with fixed-shaft gears -e characteristics of thedoubly fed wind turbine drive system are as follows (1) -eoperating conditions change with the wind speed and lead toconstant change of vibration signal amplitude and fre-quency As a result the signal contains a large number ofuncertainties (2)-e drive system is located in the top of thetower Strong wind will cause the body shake Hence thesignal will contain noise interference (3) -e mechanicalstructure of wind turbine drive system is complex It calls forhigh standard of related technologies (4) Wind turbines are

Advances in Materials Science and Engineering 5

severely affected by environmental conditions and have highrequirements for the reliability and anti-interference abilityof the test system

42 Dynamic Modeling of Wind Turbine Drive System-is paper uses the dynamic analysis process of the windturbine gearbox drive system as shown in Figure 3

First of all the external and internal incentives of thegearbox are obtained through the monitoring of the Internetof -ings technology -ey are transmitted as dynamicincentives to the analysis model of gearbox system Secondthe analysis model of gearbox system processes the inputdynamic incentives through centralized parameter methodfinite element method hybrid modeling method and bonggraph theory After processing the inherent features anddynamic responses are output and they are used as thedynamic responses of the analysis system Finally theparticle filter algorithm is used for conditionmonitoring andlife prediction applications -e above is the main appli-cation process of the method proposed in this paper for thewind turbine drive system

-e external excitation of the gearbox mainly includesthe dynamic input torque the nontorsional loads thegenerator feedback torque the braking torque and theimpact load -e internal excitation includes time-varyingstiffness excitation time-varying error excitation meshingshocks and tooth backlash -is paper uses dynamic re-sponse analysis method dynamic stability analysis methodand inherent characteristic analysis method to optimize thesystem structure Based on the IoT technology the dynamicmodel has been proposed to monitor the gearbox status andprovide theoretical basis of fault diagnosis and lifeprediction

43MethodValidation -e gearbox wear tests are recordedas A1 A2 and A3 Each test includes online monitoring datafrom six signal channels and each test collected 600 sets of

online monitoring data during transmission process Inorder to describe the online monitoring data clearly 50equidistant data monitoring points are used for each onlinemonitoring data group

In order to reduce the data size and improve predictionefficiency the method extracts the time domain featurefirst and then the frequency domain feature -e BL-STMmodel has been used to simplify the feature processingflow

During the experiment A1 is used as the test sample andA2 and A3 are used as the training samples -e predictionresult of the final transmission pair loss is shown in Table 1According to the experiment results the top five featureswith the highest scores can achieve the best predictionperformance

-e influence of the feature fusion step on the finaltransmission pair loss prediction result is shown in Table 2-e optimal feature set used in Table 2 is composed of thetop eight features with the highest scores It can be inferredfrom Table 2 that the fusion feature with the highest scorescan bring the best prediction performance

Combined with the state transfer model of transmissionpair wear and its observation model based on Bi-LSTM theparticle filter algorithm is used to predict the evolution of thetransmission pair degradation index When the index ex-ceeds the failure threshold the remaining useful life (RUL)of transmission pair can be obtained

Dynamic incentive(system input)

Analysis model ofgearbox system

Dynamic response(system output) Application

External incentive

Internal incentive

Centralizedparameter method

Finite elementmethod

Hybrid modelingmethod

Bond graph theory

Inherent features

Dynamic response

Evaluation andprevention of

vibration and noise

Conditionmonitoring andfault diagnosis

Load identificationand dynamic

design

Figure 3 Dynamic modeling and analysis process of wind turbine gearbox

Table 1 Influence of feature selection steps on prediction resultsOptimal feature set 20 15 13 10 5Root mean square error 714 578 524 509 497Mean absolute error 689 568 587 502 475

Table 2 Influence of feature selection steps on prediction resultsNumber of principal components retained () 95 97 99Root mean square error 317 423 524Mean absolute error 307 348 435

6 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

severely affected by environmental conditions and have highrequirements for the reliability and anti-interference abilityof the test system

42 Dynamic Modeling of Wind Turbine Drive System-is paper uses the dynamic analysis process of the windturbine gearbox drive system as shown in Figure 3

First of all the external and internal incentives of thegearbox are obtained through the monitoring of the Internetof -ings technology -ey are transmitted as dynamicincentives to the analysis model of gearbox system Secondthe analysis model of gearbox system processes the inputdynamic incentives through centralized parameter methodfinite element method hybrid modeling method and bonggraph theory After processing the inherent features anddynamic responses are output and they are used as thedynamic responses of the analysis system Finally theparticle filter algorithm is used for conditionmonitoring andlife prediction applications -e above is the main appli-cation process of the method proposed in this paper for thewind turbine drive system

-e external excitation of the gearbox mainly includesthe dynamic input torque the nontorsional loads thegenerator feedback torque the braking torque and theimpact load -e internal excitation includes time-varyingstiffness excitation time-varying error excitation meshingshocks and tooth backlash -is paper uses dynamic re-sponse analysis method dynamic stability analysis methodand inherent characteristic analysis method to optimize thesystem structure Based on the IoT technology the dynamicmodel has been proposed to monitor the gearbox status andprovide theoretical basis of fault diagnosis and lifeprediction

43MethodValidation -e gearbox wear tests are recordedas A1 A2 and A3 Each test includes online monitoring datafrom six signal channels and each test collected 600 sets of

online monitoring data during transmission process Inorder to describe the online monitoring data clearly 50equidistant data monitoring points are used for each onlinemonitoring data group

In order to reduce the data size and improve predictionefficiency the method extracts the time domain featurefirst and then the frequency domain feature -e BL-STMmodel has been used to simplify the feature processingflow

During the experiment A1 is used as the test sample andA2 and A3 are used as the training samples -e predictionresult of the final transmission pair loss is shown in Table 1According to the experiment results the top five featureswith the highest scores can achieve the best predictionperformance

-e influence of the feature fusion step on the finaltransmission pair loss prediction result is shown in Table 2-e optimal feature set used in Table 2 is composed of thetop eight features with the highest scores It can be inferredfrom Table 2 that the fusion feature with the highest scorescan bring the best prediction performance

Combined with the state transfer model of transmissionpair wear and its observation model based on Bi-LSTM theparticle filter algorithm is used to predict the evolution of thetransmission pair degradation index When the index ex-ceeds the failure threshold the remaining useful life (RUL)of transmission pair can be obtained

Dynamic incentive(system input)

Analysis model ofgearbox system

Dynamic response(system output) Application

External incentive

Internal incentive

Centralizedparameter method

Finite elementmethod

Hybrid modelingmethod

Bond graph theory

Inherent features

Dynamic response

Evaluation andprevention of

vibration and noise

Conditionmonitoring andfault diagnosis

Load identificationand dynamic

design

Figure 3 Dynamic modeling and analysis process of wind turbine gearbox

Table 1 Influence of feature selection steps on prediction resultsOptimal feature set 20 15 13 10 5Root mean square error 714 578 524 509 497Mean absolute error 689 568 587 502 475

Table 2 Influence of feature selection steps on prediction resultsNumber of principal components retained () 95 97 99Root mean square error 317 423 524Mean absolute error 307 348 435

6 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

5 Conclusions

Based on the bidirectional long short-term memory neuralnetwork and particle filter technology the remaining lifeprediction method for wind turbine drive system is pro-posed Compared with the traditional method it simplifiesthe feature processing flow by using deep learning tech-nology -rough the engineering examples the effectivenessof the method proposed in this paper has been proved -eresearch results in this paper will further promote the en-gineering application of deep learning technology to theproduct fatigue life prediction higher safety requirements

Data Availability

All data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

-is research was supported by the National Key ResearchDevelopment Plan Funds under contract no2018YFB1702804

References

[1] D Meng Z Hu P Wu S-P Zhu J A F O Correia andA M P De Jesus ldquoReliability-based optimisation for offshorestructures using saddlepoint approximationrdquo Proceedings ofthe Institution of Civil EngineersmdashMaritime Engineeringvol 173 no 2 pp 33ndash42 2020

[2] D Meng Y Li S-P Zhu Z Hu T Xie and Z Fan ldquoCol-laborative maritime design using sequential optimisation andreliability assessmentrdquo Proceedings of the Institution of CivilEngineersmdashMaritime Engineering vol 173 no 1 pp 3ndash122020

[3] R Yuan H Li and Q Wang ldquoAn enhanced genetic algo-rithm-based multi-objective design optimization strategyrdquoAdvances in Mechanical Engineering vol 10 no 7 pp 1ndash62018

[4] R Yuan H Li Z Gong et al ldquoAn enhanced Monte Carlosimulation-based design and optimization method and itsapplication in the speed reducer designrdquo Advances in Me-chanical Engineering vol 9 no 9 pp 1ndash7 2017

[5] R Yuan and H Li ldquoA multidisciplinary coupling relationshipcoordination algorithm using the hierarchical controlmethods of complex systems and its application in multi-disciplinary design optimizationrdquo Advances in MechanicalEngineering vol 9 no 1 pp 1ndash11 2017

[6] D Meng Y Li S-P Zhu G Lv J Correia and A De JesusldquoAn enhanced reliability index method and its application inreliability-based collaborative design and optimizationrdquoMathematical Problems in Engineering vol 2019 Article ID4536906 10 pages 2019

[7] B Liu and Y Deng ldquoRisk evaluation in failure mode andeffects analysis based on D numbers theoryrdquo International

Journal of Computers Communications amp Control vol 14no 5 pp 672ndash691 2019

[8] H Wang Y P Fang and E Zio ldquoRisk assessment of anelectrical power system considering the influence of trafficcongestion on a hypothetical scenario of electrified trans-portation system in New York staterdquo IEEE Transactions onIntelligent Transportation Systems pp 1ndash14 2019

[9] L Pan and Y Deng ldquoProbability transform based on theordered weighted averaging and entropy differencerdquo Inter-national Journal of Computers Communications amp Controlvol 15 no 4 p 3743 2020

[10] C Sun S Li and Y Deng ldquoDetermining weights in multi-criteria decision making based on negation of probabilitydistribution under uncertain environmentrdquo Mathematicsvol 8 no 2 p 191 2020

[11] R Liu P Chen X Zhang and S Zhu ldquoNon-shock ignitionprobability of octahydro-1357-tetranitro-tetrazocine-basedpolymer bonded explosives based on microcrack stochasticdistributionrdquo Propellants Explosives Pyrotechnics vol 45no 4 pp 568ndash580 2020

[12] D Liao S-P Zhu B Keshtegar G Qian and Q WangldquoProbabilistic framework for fatigue life assessment ofnotched components under size effectsrdquo International Journalof Mechanical Sciences vol 181 Article ID 105685 2020

[13] S-P Zhu B Keshtegar S Chakraborty and N-T TrungldquoNovel probabilistic model for searching most probable pointin structural reliability analysisrdquo Computer Methods in AppliedMechanics and Engineering vol 366 Article ID 113027 2020

[14] X Liang M J Zuo and M Pandey ldquoAnalytically evaluatingthe influence of crack on the mesh stiffness of a planetary gearsetrdquoMechanism andMachine9eory vol 76 pp 20ndash38 2014

[15] S Li and A Kahraman ldquoA micro-pitting model for spur gearcontactsrdquo International Journal of Fatigue vol 59 pp 224ndash233 2014

[16] R Yuan H Li and Q Wang ldquoSimulation-based design andoptimization and fatigue characteristics for high-speedbackplane connectorrdquo Advances in Mechanical Engineeringvol 11 no 6 pp 1ndash10 2019

[17] H Dong C Zhang X Wang and D Wang ldquoA precise FEmodel of a spur gear set considering eccentric error for quasi-static analysisrdquo in Mechanism and Machine Sciencepp 1263ndash1274 Springer Singapore 2017

[18] G Dong M Jing and H Liu ldquo-e study of elastohy-drodynamic lubrication for the dynamic analysis of rollingbearingrdquo in Proceedings of the 2013 IEEE InternationalSymposium on Assembly and Manufacturing (ISAM)pp 297ndash299 Xirsquoan China July 2013

[19] A Leblanc D Nelias and C Defaye ldquoNonlinear dynamicanalysis of cylindrical roller bearing with flexible ringsrdquoJournal of Sound amp Vibration vol 325 no 1-2 pp 145ndash1602009

[20] L Cui and Z Qian ldquoStudy on dynamic properties of rollerbearing with nonlinear vibrationrdquo in Proceedings of the 2010International Conference on Mechanic Automation andControl Engineering pp 2723ndash2726 Wuhan China June2010

[21] O D Mohammed M Rantatalo and J-O Aidanpaa ldquoDy-namic modelling of a one-stage spur gear system and vi-bration-based tooth crack detection analysisrdquo MechanicalSystems and Signal Processing vol 54-55 pp 293ndash305 2015

[22] X Li Y Zhu Z Zhou and N Wang ldquoFault diagnosis basedon nonlinear dynamic modeling in rolling element bearingsystemsrdquo in Proceedings of the 2013 IEEE International

Advances in Materials Science and Engineering 7

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering

Symposium on Assembly and Manufacturing (ISAM)pp 12ndash15 Xirsquoan China July 2013

[23] J Liu Z Shi and Y Shao ldquoAn analytical model to predictvibrations of a cylindrical roller bearing with a localizedsurface defectrdquo Nonlinear Dynamics vol 89 no 3pp 2085ndash2102 2017

[24] A Rafsanjani S Abbasion A Farshidianfar andH Moeenfard ldquoNonlinear dynamic modeling of surfacedefects in rolling element bearing systemsrdquo Journal of Soundand Vibration vol 319 no 3ndash5 pp 1150ndash1174 2009

[25] L Niu H Cao H Hou B Wu Y Lan and X XiongldquoExperimental observations and dynamic modeling of vi-bration characteristics of a cylindrical roller bearing withroller defectsrdquo Mechanical Systems and Signal Processingvol 138 Article ID 106553 2020

[26] Y Cui S Deng W Zhang and G Chen ldquo-e impact of rollerdynamic unbalance of high-speed cylindrical roller bearing onthe cage nonlinear dynamic characteristicsrdquo Mechanism andMachine 9eory vol 118 pp 65ndash83 2017

[27] S E Deng J H Fu Y S Wang and H S Yang ldquoAnalysis ondynamic characteristics of aero-engine rolling bearingdual-rotor systemrdquo Journal of Aerospace Power vol 28 no 1pp 195ndash204 2013

[28] L Xiang Y Zhang N Gao A Hu and J Xing ldquoNonlineardynamics of a multistage gear transmission system withmulti-clearancerdquo International Journal of Bifurcation andChaos vol 28 no 3 Article ID 1850034 2018

[29] X Liang M J Zuo and Z Feng ldquoDynamic modeling ofgearbox faults a reviewrdquo Mechanical Systems and SignalProcessing vol 98 pp 852ndash876 2018

[30] M A Ghaffari Y Zhang and S Xiao ldquoMultiscale modelingand simulation of rolling contact fatiguerdquo InternationalJournal of Fatigue vol 108 pp 9ndash17 2018

[31] J D Martınez-Morales E R Palacios-Hernandez andD U Campos-Delgado ldquoMultiple-fault diagnosis in induc-tion motors through support vector machine classification atvariable operating conditionsrdquo Electrical Engineeringvol 100 no 1 pp 59ndash73 2018

[32] P Boskoski and ETH Juricic ldquoFault detection of mechanicaldrives under variable operating conditions based on waveletpacket Renyi entropy signaturesrdquo Mechanical Systems ampSignal Processing vol 31 pp 369ndash381 2012

[33] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using Kalman tracking filtersrdquo Shock ampVibration vol 2 no 6 pp 507ndash515 1995

[34] D Meng S Yang Y Zhang and S P Zhu ldquoStructural re-liability analysis and uncertainties-based collaborative designand optimization of turbine blades using surrogate modelrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 42 no 6 pp 1219ndash1227 2019

[35] S-P Zhu Z-Y Yu Q Liu and A Ince ldquoStrain energy-basedmultiaxial fatigue life prediction under normalshear stressinteractionrdquo International Journal of Damage Mechanicsvol 28 no 5 pp 708ndash739 2019

[36] D Meng T Xie P Wu et al ldquoUncertainty-based design andoptimization using first order saddlepoint approximationmethod for multidisciplinary engineering systemsrdquo ASCE-ASME Journal of Risk and Uncertainty in Engineering SystemsPart A Civil Engineering vol 6 no 3 Article ID 040200282020

[37] D Meng Y F Li H Z Huang Z Wang and Y Liu ldquoRe-liability-based multidisciplinary design optimization usingsubset simulation analysis and its application in the hydraulic

transmission mechanism designrdquo Journal of MechanicalDesign vol 137 no 5 Article ID 051402 2015

[38] C Durager A Heinzelmann and D Riederer ldquoA wirelesssensor system for structural health monitoring with guidedultrasonic waves and piezoelectric transducersrdquo Structure andInfrastructure Engineering vol 9 no 11 pp 1177ndash1186 2013

[39] S P Zhu Q Liu Q Lei and Q Wang ldquoProbabilistic fatiguelife prediction and reliability assessment of a high pressureturbine disc considering load variationsrdquo InternationalJournal of Damage Mechanics vol 27 no 10 pp 1569ndash15882018

[40] S-P Zhu Q Liu W Peng and X-C Zhang ldquoComputa-tional-experimental approaches for fatigue reliability assess-ment of turbine bladed disksrdquo International Journal ofMechanical Sciences vol 142-143 pp 502ndash517 2018

[41] S P Zhu Q Liu J Zhou and Z Y Yu ldquoFatigue reliabilityassessment of turbine discs under multi-source uncertaintiesrdquoFatigue amp Fracture of Engineering Materials amp Structuresvol 41 no 6 pp 1291ndash1305 2018

[42] J Dai and Y Deng ldquoA newmethod to predict the interferenceeffect in quantum-like Bayesian networksrdquo Soft Computingvol 24 no 14 pp 10287ndash10294 2020

[43] Q Cai and Y Deng ldquoA fast Bayesian iterative rule in amoebaalgorithmrdquo International Journal of Unconventional Com-puting vol 5 no 19 pp 449ndash466 2019

[44] S-P Zhu H-Z Huang W Peng H-K Wang andS Mahadevan ldquoProbabilistic Physics of Failure-basedframework for fatigue life prediction of aircraft gas turbinediscs under uncertaintyrdquo Reliability Engineering amp SystemSafety vol 146 pp 1ndash12 2016

[45] S-P Zhu H-Z Huang R Smith V Ontiveros L-P He andM Modarres ldquoBayesian framework for probabilistic low cyclefatigue life prediction and uncertainty modeling of aircraftturbine disk alloysrdquo Probabilistic Engineering Mechanicsvol 34 pp 114ndash122 2013

[46] R Yuan M Tang H Wang and H Li ldquoA reliability analysismethod of accelerated performance degradation based onbayesian strategyrdquo IEEE Access vol 7 pp 169047ndash1690542019

[47] H Li R Yuan and J Fu ldquoA reliability modeling for multi-component systems considering random shocks and multi-state degradationrdquo IEEE Access vol 7 pp 168805ndash1688142019

8 Advances in Materials Science and Engineering