research article model-based water wall fault detection

Research ArticleModel-Based Water Wall Fault Detection and Diagnosis ofFBC Boiler Using Strong Tracking Filter

Li Sun, Junyi Dong, Donghai Li, and Yuqiong Zhang

State Key Lab of Power System, Department of Thermal Engineering, Tsinghua University, Beijing 100083, China

Correspondence should be addressed to Donghai Li; [email protected]

Received 21 February 2014; Accepted 17 March 2014; Published 28 April 2014

Academic Editor: Zhijun Zhang

Copyright © 2014 Li Sun et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fluidized bed combustion (FBC) boilers have received increasing attention in recent decades. The erosion issue on the water wallis one of the most common and serious faults for FBC boilers. Unlike direct measurement of tube thickness used by ultrasonicmethods, the wastage of water wall is reconsidered equally as the variation of the overall heat transfer coefficient in the furnace.In this paper, a model-based approach is presented to estimate internal states and heat transfer coefficient dually from the noisymeasurable outputs.The estimated parameter is compared with the normal value.Then themodified Bayesian algorithm is adoptedfor fault detection and diagnosis (FDD). The simulation results demonstrate that the approach is feasible and effective.

1. Introduction

Fluidized bed combustion (FBC) boiler, the most popularclean coal combustion technology in power and chemicalindustries [1], facilitates burning a wide variety of fuels withhigh combustion efficiency, especially for the low-gradingcoal. The technology burns fuel at temperatures from 800to 950∘C, a range where nitrogen oxide (NOx) formation ismuch lower than that in traditional pulverized coal boiler [2].The fluidized bed has several potential advantages in CO

2

capture from flue gas [3]. In addition, water-wall slaggingis significantly eliminated due to the combustion conditionof lower temperature. Furthermore, soot formation can beattenuatedwith the appropriate distributor plate layout.How-ever, wastage of tube materials, both refractory and metallic,is more prominent than pulverized coal boiler because theparticulates in the fluidization state strike and rub the tubemore fiercely and frequently. It has become a source ofconcern for FBC boilers because it is responsible for water-wall burst and even undesired shutdowns.

A great deal of research has been done in an effort to fur-ther understand metal wastage in fluidized bed combustionenvironments and to find solutions to ease it. It is generallyacknowledged that tube wastage is caused by simultaneous

corrosion and erosion. In [4, 5], the erosion-prone areaswere identified in circulating and bubbling fluidized bedboilers anddescribed currentmethods for erosion protection.The wastage rate was most significant in the water wallaround the bed region, decreasing with increasing height [6].The rate of tube erosion is usually a complex function ofcharacteristics of the coal particulates, that is, shape, strength,size, composition, and ash content, such as SiO

2, Al2O3,and

Fe2O3[7]. Most researches [4–8] of tube wear have been

conducted for exploration of erosion mechanism to improveboiler design. However, there have been few reports on onlinemonitoring of erosion occurring during runtime. In [9],the method by ultrasonic thickness gauge was introducedto investigate tube wastage patterns successfully. But theincreased equipment cost and integration difficulties limit itsbroad application in industry.

An alternative monitoring method based on boilerdynamic model and optimal estimation theory was intro-duced in this paper. By delving into the performance char-acteristics of FBC boiler, we can deduce that the globalwastage or deposition rate of water wall could be expressedequally as the variation of the overall heat transfer coefficientregardless of its cause. Hence the problem of thicknessmeasurement anddetectionwas reconstructed as a parameter

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 504086, 8 pageshttp://dx.doi.org/10.1155/2014/504086

2 Mathematical Problems in Engineering

estimation issue. This critical parameter can be assumed asan extended state, which would be estimated with other statevariables simultaneously in an augmented nonlinear model.Specifically, the observability of augmented system should beexamined, which serves as a necessary precondition of theproposed software redundancymethod other than hardware-based measurement method.

The conventional linear estimation theory was proposedby Kalman [10] and then developed into nonlinear versionin NASA, named “extended Kalman filter” (EKF) whichwas widely applied in the aerospace and navigation areas.However, in most industrial cases, the EKFmethod is of poorrobustness against model mismatches [11], which can onlygive a biased state estimation and even may quickly diverge,owing to its linearization. We propose to adopt a new filter,called a strong tracking filter (STF) [12], which can overcomethe above-mentioned flaws of EKF. In STF, themean square ofestimated residues is minimized based on the orthogonalityprincipal. Thus the Kalman gain can be adjusted in real timeto track the actual states. This approach is applicable to jointstates and parameters estimation with unknown changinglaws.

In the current paper, Section 2 is devoted to a briefintroduction to the structure and model of a bubblingfluidized bed combustor. The outline of STF is presentedin Section 3. After introducing an FDD strategy based onmodified Bayes’ classification algorithm, computer simula-tion results are given in Section 4 to show the effectivenessof the proposed approach. Section 5 is the conclusions andfuture work. The strategy in this paper is also applicable forcirculating fluidized bed (CFB) boiler if the correspondingdynamic model can be provided with acceptable accuracy.

2. System Description andAnalysis of FBC Boiler

2.1. Overview of Fluidized Bed Combustion Technology. Flu-idized beds find widespread application in industrial applica-tions because of their favorable heat transfer properties.Withappropriate upward-blowing primary air velocity to suspendsolid fuels, there are tumbling action and bubble formation,which provides more effective combustion and heat transfer.The bed of solid particles exhibits the properties of a boilingliquid and assumes the appearance of a fluid—“bubblingfluidized bed.” The schematic of a FBC boiler is shown inFigure 1.

As shown in Figure 1, a mixture of inert/sorbent bedmaterial and solid fuel is fluidized by the primary air enteringfrom below. Secondary air is injected above the fuel bed toensure complete gas burning out. But the total amount shouldbe limited due to economic efficiency. The heat released incombustion is captured by heat exchangers and used for thegeneration of steam.

2.2. Global Dynamic Model of Bubbling FBC Boiler. The full-order dynamic model of FBC has been set up for mechanismstudy, but it is not suitable for fault detection and stateestimation because of the complexity. The classical bubbling

Throat temperature

Freeboard temperature

Secondary air flow

Primary air flow

Bed temperature

Freeboard

Bed

Fuel feed

Heat exchanges

Stack

Throat

CO2

CNO𝑥

Figure 1: A schematic of a typical FBC plant.

FBC model was originally formulated in [13] based on massand energy balances, which was verified by experimentaldata. To strike a balance between fidelity and simplicity, themodel was further modified as follows [14].

Dynamics of fuel inventory𝑊𝐶[kg]:

𝑑𝑊𝐶(𝑡)

𝑑𝑡= (1 − 𝑉)𝑄

𝐶(𝑡) − 𝑄

𝐵(𝑡) . (1)

Dynamics of bed oxygen content 𝐶𝐵[Nm3/Nm3]:

𝑑𝐶𝐵(𝑡)

𝑑𝑡=

1

𝑉𝐵

[𝐶1𝐹1(𝑡) − 𝑄

𝐵(𝑡) 𝑋𝐶− 𝐶𝐵(𝑡) 𝐹1(𝑡)] . (2)

Dynamics of freeboard oxygen content 𝐶𝐹[Nm3/Nm3]:

𝑑𝐶𝐹(𝑡)

𝑑 (𝑡)=

1

𝑉𝐹

{𝐶𝐵(𝑡) 𝐹1(𝑡) + 𝐶

2𝐹2(𝑡)

−𝑉𝑄𝐶(𝑡) 𝑋𝑉− 𝐶𝐹(𝑡) [𝐹1(𝑡) + 𝐹

2(𝑡)]} .

(3)

Dynamics of bed temperature 𝑇𝐵[K]:

𝑑𝑇𝐵(𝑡)

𝑑𝑡=

1

𝐶𝐼𝑊𝐼

{𝐻𝐶𝑄𝐵(𝑡) + 𝑐

1𝐹1(𝑡) 𝑇1

−𝛼𝐵𝑡𝐴𝐵𝑡

[𝑇𝐵(𝑡) − 𝑇

𝐵𝑡] − 𝑐𝐹𝐹1(𝑡) 𝑇𝐵(𝑡)} .

(4)

Dynamics of freeboard temperature 𝑇𝐹[K]:

𝑑𝑇𝐹(𝑡)

𝑑𝑡=

1

𝐶𝐹𝑉𝐹

{𝑉𝑄𝐶(𝑡) + 𝑐

1𝐹1(𝑡) 𝑇1

−𝛼𝐵𝑡𝐴𝐵𝑡

[𝑇𝐵(𝑡) − 𝑇

𝐵𝑡] − 𝑐𝐹𝐹1(𝑡) 𝑇𝐵(𝑡)} .

(5)

Mathematical Problems in Engineering 3

Dynamics of thermal power 𝑃 [MW]:

𝑑𝑃 (𝑡)

𝑑𝑡=

1

𝜏mix[𝑃𝐶(𝑡) − 𝑃 (𝑡)] , (6)

where the combustion rate in bed 𝑄𝐵[kg/s] is 𝑄

𝐵(𝑡) =

(𝑊𝐶(𝑡)/𝑡𝐶)(𝐶𝐵(𝑡)/𝐶1) and the combustion power 𝑃

𝐶[MW]

is 𝑃𝐶(𝑡) = 10

−6

[𝐻𝐶𝑄𝐵(𝑡) + 𝐻

𝑉𝑉𝑄𝐶(𝑡)]. Here, other detailed

variable nomenclatures and fine-tuned model parametervalues have been given in [14]. In this FBC process, themanipulated inputs u are fuel feed𝑄

𝐶[kg/s], primary air flow

𝐹1[Nm3/s], and secondary air flow𝐹

2[Nm3/s]; the controlled

variables are power 𝑃, bed temperature 𝑇𝐵, and freeboard

oxygen content 𝐶𝐹; freeboard temperature 𝑇

𝐹is also a

measurable output in addition to the 3 controlled variables.Hereby a canonical nonlinear model can be established from(1)–(6):

x = 𝑓 (x, u) ,

y = ℎ (x) ,(7)

where x = [𝑊𝐶

𝐶𝐵𝐶𝐹𝑇𝐵𝑇𝐹𝑃]𝑇

, u = [𝑄𝐶

𝐹1𝐹2]𝑇, and

y = [𝑇𝐵𝑃 𝑇𝐹𝐶𝐹]𝑇.

3. Strong Tracking Filter BasedState Estimation

3.1. Extension andDiscretization. If soot formation or erosionoccurs in water wall tube, the corresponding heat transfercoefficient will change due to variation of thermal conductionresistance. However, it is impossible to obtain the heattransfer coefficient ℎ

𝐵by measurement. We can estimate the

variation of ℎ𝐵by using methods based on joint state and

parameter estimation. Considering the influence of noise,and assuming ℎ

𝐵as an extended state, the augmented model

can be discretized as

z (𝑘 + 1) = 𝑓𝑒(z (𝑘) , u (𝑘)) + w

𝑘,

y (𝑘 + 1) = ℎ𝑒(z (𝑘 + 1)) + k

𝑘+1,

(8)

where z(𝑘) = [x(𝑘) ℎ𝐵(𝑘)]𝑇 is the augmented state by

assuming ℎ𝐵(𝑘 + 1) = ℎ

𝐵(𝑘). Thereby, functions 𝑓

𝑒and ℎ

𝑒

can be derived from (7) by Euler methods. w𝑘and v𝑘are the

process and observation noises which are both assumed to bezero mean multivariate Gaussian noises with covariances 𝑄

𝑘

and 𝑅𝑘, respectively.

3.2. Basic Principals of STF. It is well known that the extendedKalman filter (EKF) can be used [15] for the joint estimationof the systems described by (8), which can be summarized asthe following formulas.

Predicted state:

z−𝑘

= 𝑓𝑒(z+𝑘−1

, u𝑘−1

) . (9)

Predicted covariance:

𝑃−

𝑘

= 𝐹𝑘−1

𝑃+

𝑘−1

𝐹𝑇

𝑘−1

+ 𝑄𝑘−1

. (10)

Measurement residual:

𝛾𝑘

= y𝑘− ℎ𝑒(z−𝑘

) . (11)

Kalman gain:

𝐾𝑘= 𝑃−

𝑘

𝐻𝑇

𝑘

(𝐻𝑘𝑃−

𝑘

𝐻𝑇

𝑘

+ 𝑅𝑘)−1

. (12)

Updated state:

z+𝑘

= z−𝑘

+ 𝐾𝑘𝛾𝑘

. (13)

Updated covariance:

𝑃+

𝑘

= (𝐼 − 𝐾𝑘𝐻𝑘) 𝑃−

𝑘

, (14)

where the superscripts − and + represent the values beforeand aftermeasurement correction, respectively.𝐹

𝑘and𝐻

𝑘are

the state transition and observationmatrices by linearizing𝑓𝑒

and ℎ𝑒at each time step.

However, in most cases, especially for industrial faultdiagnostics, the EKF has the following flaws:

(i) poor robustness against model mismatches;(ii) sensitivity to the statistics of the initial states and

noise;(iii) weak tracking ability to the suddenly changing states.

All these drawbacks will be more prominent especiallywhen filter approaches steady, as shown in the next subsec-tion. The essential reason accounting for the phenomenonis that the optimal Kalman gain is actually calculated byopen-loop method in spite of updating process in statecorrection. According to the original paper [10] regardinglinear filtering, the predicted covariance and Kalman gainboth depend on the model and initial parameter settings of𝑃0, 𝑄𝑘, and 𝑅

𝑘. The Kalman gain 𝐾

𝑘will approach zero after

long-time steadiness and then EKF will lose tracking abilitywhen process uncertainty occurs.

For this reason, Zhou and Frank proposed a strongtracking filter (STF) in [12]. By introducing a diagonal matrixΛ𝑘to (10),

𝑃−

𝑘

= Λ𝑘𝐹𝑘−1

𝑃+

𝑘−1

𝐹𝑇

𝑘−1

+ 𝑄𝑘−1

; (15)

the Kalman gain can be adjusted online to maintain thestrong tracking ability of filters.The suboptimal fading factorsΛ𝑘can be obtained recursively by solving the following

equations:

𝐸 [(z𝑘+1

− z+𝑘+1

)𝑇

(z𝑘+1

− z+𝑘+1

)] = min,

𝐸 [𝛾𝑇

𝑘+1

𝛾𝑘+1+𝑗

] = 0; 𝑗 = 1, 2, . . . .

(16)

The second equation of (16) is named orthogonality principle,whose physical meaning is that the residual error seriesshould be made mutually orthogonal at each step, so thatthe rich information in the residual error series could beextracted. For deduction details, see [12].


0

20

40

60

80

100

120

140

160

180

200

220

(kg)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000(s)

(a) Fuel inventory [kg]

0

0.05

0.1

Nm

(

)3

3/N

m

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000(s)

(b) Bed O2content [Nm3/Nm3]

800

850

900

950

1000

1050

1100

(K)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000(s)

(c) Bed temperature [K]

Nm

(

)3

3/N

m

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.04

0.045

0.05

0.055

0.06

0.065

0.07

(s)

(d) Freeboard O2content [Nm3/Nm3]

STFEKF

StateMeasurement

(K)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000910

915

920

925

930

935

940

945

950

(s)

(e) Freeboard temperature [K]

STFEKF

StateMeasurement

(MW

)

(s)0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

22

22.5

23

23.5

24

24.5

25

25.5

26

(f) Thermal power [MW]

Figure 2: Simulation comparison of estimated states.


Actuator FBC plant Sensor

Reference

MBAFault detection Fault diagnosis

STF

Soot formation

Erosion

MultivariableMPC

PI

P

TB

QC

F1

F2 CB

Figure 3:The structure of closed-loop fault detection and diagnosis.

3.3. Open-Loop Simulation and Comparison. In this part,an open-loop simulation on FBC plant (7) was conductedwithout joint estimation. In the simulation, EKF and STFshared the same set of filter parameters with initial statesdeviating from the actual value. The simulation results areshown in Figure 2. In simulating process, the input variable(fuel feed 𝑄

𝐶) increased by 25% at 𝑡 = 1000 s; the state

variable (fuel inventory𝑊𝐶) dropped suddenly at 𝑡 = 2000 s.

In addition, there is a mutation in heat transfer coefficient ℎ𝐵

at 𝑡 = 3500 s.As shown in Figure 2, the adjective “strong” in STF

implies (i) faster rate of convergence in the presence of initialerror (see Figure 2(a)), (ii) stronger tracking ability to theabrupt changing states regardless of dynamic or stationaryfashion, and (iii) better robustness tomodeling error (Figures2(c), 2(d), and 2(e), titles: “freeboard” and “temperature”).

4. FDD of Water Wall

4.1. Strategy of Fault Detection. Once the erosion or sootformation occurs, it will growmore andmore serious. Hence,it is necessary to detect the fault in time. Assume the fault is adrift-type process.While the boiler is running at normal state,the heat transfer parameter is

ℎ𝐵(𝑘) ∼ 𝑁 (ℎ

0

𝐵

, 𝜎2

0

) , (17)

where ℎ0

𝐵

is the normal operating value and 𝜎2

0

is thereasonable variation which is acceptable for engineering.Themodified Bayes’ algorithm is adopted for fault detection.

Define

𝜇ℎ𝐵

(𝑘) =1

𝑁

𝑁

∑

𝑗=1

ℎ+

𝐵

(𝑘 − 𝑗) ,

𝜎2

ℎ𝐵1(𝑘) =

1

𝑁 − 1

𝑁

∑

𝑗=1

[ℎ+

𝐵

(𝑘 − 𝑗) − ℎ0

𝐵

]2

,

𝜎2

ℎ𝐵2(𝑘) =

1

𝑁 − 1

𝑁

∑

𝑗=1

[ℎ+

𝐵

(𝑘 − 𝑗) − 𝜇ℎ𝐵

(𝑘)]2

,

𝑑 (𝑘) =

𝜎2

ℎ𝐵1(𝑘)

𝜎2

0

− ln𝜎2

ℎ𝐵2(𝑘)

𝜎2

0

− 1,

(18)

where 𝑁 is the preselected data window and 𝑑 is nameddetection parameter. When the boiler operates well, 𝑑 isclose to zero. As soon as the fault occurs, 𝑑 will be soaringsensitively. When a threshold 𝛽

0is defined, the strategy of

fault detection is, thus, obtained:

𝑑 (𝑘) > 𝛽0, (19)

where 𝛽0can be selected by operating experience. With

smaller 𝛽0, smaller faults can be detected, but more false

alarms occur. On the other hand, with larger 𝛽0, only relative

larger fault can be detected, and missing alarms will increase.

4.2. Closed-Loop Structure of Fault Diagnosis. In [16],the authors proposed a multivariable coordinated controlmethod of FBC boiler based on LSSVM-GPC, which cancontrol output power and bed temperature well by regulatingfuel feed and primary air flow. Here, a PI controller wasapplied in the secondary air flow-freeboard oxygen contentloop. Based on the above discussion, a closed-loop faultdetection and diagnosis strategy was developed under thecontrol framework, as shown in Figure 3, where the strongtracking filter was used to estimate state variables and heattransfer coefficient dually based on (8).

4.3. Numerical Simulation. The simulation time is 14000 s. Aload-up commandwas givenwith setpoints of𝑃 and𝑇

𝐵rising

to 30MW and 850∘C, respectively, while the setpoint of 𝐶𝐵

was kept constant.Suppose soot was deposited gradually in water wall at

𝑡 = 2000 s and then was cleaned up by soot blower at𝑡 = 7000 s. After 1000 seconds, tube erosion of water walloccurred due to severe attrition. Let Λ

𝑘= 𝜆𝑘𝐼7; that is, the

STF based on multiple fading factors deteriorates to a singlefading factor which also has good tracking ability.The closed-loop simulation results were shown in Figures 4–6.

It can be seen from Figure 4 that STF can track all thestate variables with almost no errors under the conditionof joint estimation while EKF is more sensitive to modelmismatch (see Figures 4(a) and 4(b)). Figure 5(a) shows theoverwhelming superiority of STF in tracking time-varyingheat transfer coefficient with unknown changing laws whilethe EKF can be used to estimate constant parameters only.Figure 5(b) shows that the fading factor 𝜆

𝑘can be increased

rapidly oncemodelmismatch happens.Thus theKalman gaincan be adjusted in real time, which accounts for the strongtracking ability essentially.

As shown in Figure 6, the detection parameter 𝑑 ishypersensitive to water wall fault, which grows exponentiallyonce fault happens. The incipient fault can be detected at anearly stage. For example, the soot formation fault is detected at


100

200

300

400

500

600

700

800

0 2000 4000 6000 8000 10000 12000 14000

(kg)

(s)

(a) Fuel inventory [kg]

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

Nm

(

)3

3/N

m

0 2000 4000 6000 8000 10000 12000 14000(s)

(b) Bed O2content [Nm3/Nm3]

900

950

1000

1050

1100

1150

1200

1250

1300

(K)

0 2000 4000 6000 8000 10000 12000 14000(s)

(c) Bed temperature [K]

−0.01

0

0.01

0.02

0.03

0.04

0.05

0 2000 4000 6000 8000 10000 12000 14000(s)

Nm

(

)3

3/N

m

(d) Freeboard O2content [Nm3/Nm3]

STFEKF

StateMeasurement

900

950

1000

1050

1100

1150

1200

(K)

0 2000 4000 6000 8000 10000 12000 14000(s)

(e) Freeboard temperature [K]

STFEKF

StateMeasurement

20

25

30

35

(MW

)

0 2000 4000 6000 8000 10000 12000 14000(s)

(f) Thermal power [MW]

Figure 4: States estimation of closed-loop simulation.


0 2000 4000 6000 8000 10000 12000 14000

180

200

220

240

ActualEKFSTF

Tube attrition

Soot deposition Soot blowing

W/(

m2

·K)

(s)

(a) Heat transfer coefficient estimation [W/(m2⋅K)]

2000 4000 6000 8000 10000 12000 140000

20

40

60

(s)

𝜆

(b) Fading factor

Figure 5: Heat transfer coefficient estimation.

0 2000 4000 6000 8000 10000 12000 14000t (s)

Threshold 𝛽0

104

103

102

101

100

d

Figure 6: A semilog graph of detection parameter 𝑑.

𝑡 = 5493 s with estimated fault amplitude, −19.9. The erosionfault is detected at 𝑡 = 10006 s with estimated fault amplitude,19.8 (see Figure 5(a)). The estimation accuracy of the faultamplitude is 66.4% and 99.3%, respectively. It is possible todetect a fault earlier if we select a lower threshold, but the rateof false alarm will correspondingly increase.

5. Conclusion and Future Work

Because the security and reliability of FBC boiler are becom-ing more and more important, and the erosion is one of themost common faults of FBC boiler, it is urgent to investigatefurther the erosion fault of FBC. The STF is adopted forjoint estimation due to the virtue of strong robustness againstmodel mismatch and strong tracking of drifting states, as wellas jumping states even when the filter is stable. Accordingto the estimated heat transfer coefficient, the soot formationand erosion can be detected based on the modified Bayes’algorithm. At last, the simulation results demonstrate that theapproach is feasible and effective. The line of research willlead to the future work in comprehensive fault detection and

diagnosis and fault-tolerant control by incorporating othercommon faults, such as sensor and actuator faults.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

This work has been supported by the National NaturalScience Foundation of China (nos. 51176086 and 51076071).

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