overview of reliability engineering and my current … workshop - harvard may 16... · overview of...

Overview of Reliability Engineering and My Current Research Mohammad ModarresDepartment of Mechanical Engineering

Presented at the Workshop on:Aging and Failure in Biological, Physical and Engineered Systems

Harvard University, Cambridge MA

May 15-17, 2016

COPYRIGHT © 2016, M. Modarres

Outline

PART 1:– A Quick Overview of Reliability Engineering– Current Leading Researches in Reliability

Engineering

PART 2:– My Current Research:

• Reliability Based on Entropy• Damage Precursors and Uses in Prognosis and Health Management (PHM)

– ConclusionsCOPYRIGHT © 2016, M. Modarres

ReliabilityEngineeringOverview

• Reliability engineering measures and improvesresistance to failure of an item over time

• Two Overlapping Frameworks for Modeling Life andPerformance of Engineered Systems Have Emerged:– Data or Evidence View: Statistical / Probabilistic– Physics-View

• Empirical: Physics of Failure• Physical Laws

• Areas of Applications– Design (Assuring Reliability, Testing, Safety, Human-

Software-Machine, Warranty)– Operation (Repair, Maintenance, Risks, Obsolescence,

Root Cause Evaluations)COPYRIGHT © 2016, M. Modarres

DataorEvidenceView:Statistical/ProbabilisticMetric

– Post WWII Initiatives due to unreliability of electronics andfatigue issues

• Inspired by the weakest link, statistical process control, insurance anddemographic mortality data analysis methods

• Defined reliability on an item as the likelihood of failures based on lifedistribution models

• Systems analysis methods– Based on the topology of components of the system– Based on the logical connections of the components (fault trees, etc.)

– Common Assumptions• Use of historical failure data or reliability test data are the truth and every

items have the same resistance to failure as the historical failures indicate• Maintenance and repair contribute to renewal of the item• Degradation trend can be measured by the hazard rate . In this case𝑅" 𝑡 = 𝑒&' ( , 𝑤ℎ𝑒𝑟𝑒H . = cumulativehazard, andh . = hazardrate

– Issues• Results rarely match field experience

)tTPr()t(R ≥=


Physics-BasedViewofReliability

– Failures occur due to failure mechanisms– This view started in the 1960’s and revived in the 1990’s.– Referred to physics-of-failure, time to failures are

empirically modeled:• Inspired by advances in fracture mechanics• Accelerated life and degradation testing provide data• Probabilistic empirical models of time to failure (PPoF models) developed and

simulations

• Benefits• No or very little dependence on historical failure data• Easily connected to all physical models• Address the underlying causes of failure (failure mechanisms)• Specific to the items and the condition of operation of that item

• Drawbacks• Hard to model interacting failure mechanisms• Models markers of degradation not the total damage• Based of small experimental evidences and more on subjective judgments

So = Operational StressesSe= Environmental Stressesg = Geometry related factors𝜽= material propertiesd = defects, flaws, etc.

𝑡? = 𝑓(𝑆C,𝑆D, 𝑔, 𝑑", 𝜽G


Physics-Based View (Cont.)

• Modern Areas of Research– Hybrid Models Combined Logic Models, Physical Models

(PoF) and Probabilistic Models• Tremendous emphasis on

– PHM methods in support of resilience, replacement, repair andmaintenance

– Reliability of autonomous systems and cyber-physical safety security• Applications of Data science

– Sensors– Data / information fusion– Simulation tools (MCMC, Recursive Bayes and Bayesian filtering)– Machine learning

– Search for fundamental sciences of reliability• Thermodynamics• Information theory• Statistical mechanics COPYRIGHT © 2016, M. Modarres

ReliabilitySummary

Endurance toDamage

Dam

age

/Deg

rada

tion

Life

InitialDamage

Time-to-Failure Distribution

t1 t2

SummaryofReliabilityOverviewD

ata

Driv

en

Futu

reEm

piric

al P

oF

Why Entropy?

ü Entropy can modelmultiple competingdegradation processesleading to damage

ü Entropy is independentof the path to failureending at similar totalentropy at failure

ü Entropy accounts forcomplex synergisticeffects of interactingdegradation processes

ü Entropy is scaleindependent


• My Recent Research on Damage,Degradation and Failure


AnEntropicTheoryofDamage

• Failure mechanisms are irreversible processes leading todegradation and share a common feature at a deeper level:Dissipation of Energy

• Dissipation (or equivalently entropy generation)≅DamageDissipation energies Damage Entropy generation Degradation mechanisms

Failure1 occurs when the accumulated total entropy generated exceeds the entropic-endurance of the unit

• Entropic-endurance describes the capacity of the unit towithstand entropy

• Entropic-endurance of identical units is equal• Entropic-endurance of different units is different• Entropic-endurance to failure can be measured

(experimentally) and involves stochastic variability

1. Defined as the state or condition of not meeting a requirement, desirable behavior or intended functionCOPYRIGHT © 2016, M. Modarres

AnEntropicTheoryofDamage(Cont.)

[1] Anahita Imanian and Mohammad Modarres, A Thermodynamic Entropy Approach to Reliability Assessment with Application to Corrosion Fatigue, Entropy 17.10 (2015): 6995-7020[2] M. Naderi et al., On the Thermodynamic Entropy of Fatigue Fracture, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 466.2114 (2009): 1-16[3] D. Kondepudi and I. Prigogine, “Modern Thermodynamics: From Heat Engines to Dissipative Structures, ” Wiley, England, 1998.[4] J. Lemaitre and J. L. Chaboche, “Mechanics of Solid Materials, ” 3rd edition; Cambridge University Press: Cambridge, UK, 2000.

[1, 3,4]

Product of thermodynamic forces and fluxes

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Entro

py to

Fai

lure

(MJ/m

3 K)

Time (Cycle) × 104

F=330 MPa

F=365 MPa

F=405 MPa

F=260 MPa

F=290 MPa

[1]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

500 5000

Frac

ture

Fati

gue F

ailu

re (M

J m-3

K-1)

Number of Cycles to Failure

[2]

𝜎 =1𝑇K 𝐽M N 𝛻𝑇 −Q 𝛻

𝜇S𝑇

T

SUV+1𝑇𝜏: 𝜖\̇ +

1𝑇Q 𝑣 𝐴^

`

^UV+1𝑇Q 𝑐b𝐽b −𝛻𝜓

d

bUVThermal

Diffusion Chemical External field energyMechanical

𝑱T(𝑛 = 𝑞, 𝑘, 𝑎𝑛𝑑 𝑚) = thermodynamic fluxes due to heat conduction, diffusion and external f ields, T = temperature, 𝜇S = chemicalpotential, 𝑣" = chemical reaction rate, 𝝉 = stress tensor, 𝝐\̇ = plastic strain rate, 𝐴^ = chemical affinity, 𝜓 = potential of the externalfield , and 𝑐b = coupling constant [3, 4].


EntropyasanIndexofDamage

• The evolution trend of the damage, 𝐷, according to our theory is dominatedby the entropy generated:

𝐷 =𝛾p − 𝛾pq𝛾pr − 𝛾pq

, 𝛾=𝜌𝑠volumetric entropy generation

𝐷~𝛾p|𝑡~w [𝜎|𝑋" 𝑢 , 𝑱" 𝑢 ]𝑑𝑢(

|

• The reliability expressed in termsof entropic damage :

𝑅 𝑡 = ∫ 𝑔 𝑡 𝑑𝑡~(�

=1- ∫ 𝑓(𝐷|𝑡)𝑑𝐷~��


ReliabilityofStructuresSubjecttoCorrosion-Fatigue(CF)


EntropyGenerationinCF

• Contribution from corrosion activation over-potential, diffusion over-potential, corrosion reaction chemicalpotential, plastic and elastic deformation and hydrogen embrittlement to the rate of entropy generation:

𝜎 =1𝑇 𝑱�,�𝑧�𝐹𝐸��,�

+ 𝑱�,�𝑧�𝐹𝐸��,�+ 𝑱�,�𝑧�𝐹𝐸��,� + 𝑱�,�𝑧�𝐹𝐸��,�

+1𝑇 𝑱�,�𝑧�𝐹𝐸��,�

+ 𝑧�𝐹𝑱�,�𝐸��,�

+1𝑇 𝑱�,�𝛼�𝐴� + 𝐽�,� 1 −𝛼� 𝐴� + 𝑱�,�𝛼�𝐴� + 𝑱�,� 1 −𝛼� 𝐴�

+1𝑇 �̇�\ : 𝝉 +

1𝑇 𝑌�̇�

+𝜎'

𝑇 = temperature, 𝑧� =number of moles of electrons exchanged in the oxidation process, 𝐹 =Farady number, 𝐽�,� and 𝐽�,� = irreversible anodic and cathodic activationcurrents for oxidation reaction, 𝐽� ,� and 𝐽� ,� =anodic and cathodic activation currents for reduction reaction, 𝐸��,� and 𝐸��,� =anodic and cathodic over-potentials foroxidation reaction, 𝐸��,� and 𝐸��,� =anodic and cathodic over-potentials for reduction reaction, 𝐸��,� and 𝐸��,� =concentration over-potentials for the cathodicoxidation and cathodic reduction reactions, 𝛼� and 𝛼� =charge transport coefficient for the oxidation and reduction reactions, 𝐴� and 𝐴� = chemical affinity for theoxidation and reductions, �̇�\ =plastic deformation rate, 𝜏 =plastic stress, �̇� =dimensionless damage flux, 𝑌 the elastic energy, and 𝜎' =entropy generation due tohydrogen embrittlement.

[1] Imanian, A. and Modarres. M, “A Thermodynamic Entropy Based Approach for Prognosis and Health Management withApplication to Corrosion-Fatigue,” 2015 IEEE International Conference on Prognostics and Health Management, 22-25 June, 2015, Austin, USA.

Diffusion dissipations

Chemical reaction dissipations

Mechanicaldissipations

Hydrogen embrittlement dissipation


CFExperimentalSetup

• Fatigue tests of Al 7075-T651 performed in 3.5% wt. NaCl aqueous solutionacidified with a 1 molar solution of HCl, with the pH of about 3, under axial loadcontrolled and free corrosion potential

• Specimens electrochemically monitored via a potentiostat using Ag/AgClreference electrode maintained at a constant distance (2 mm) from the specimen,a platinum counter electrode, and specimen as the working electrode

• Digital image correlation (DIC) technique used to measure strain

Electrochemical corrosion cell made of plexiglass

Entropic-BasedReliabilityResultsforCF

0 2000 4000 6000 8000 10000 12000 14000 160000

0.2

0.4

0.6

0.8

1

Time(Cycle)

Damage

P=405 MPaP=365MPaP=330MPaP=290MPaP=260MPaP=190MPaP=215MPa

0.8 1 1.2 1.4 1.6 1.8 2

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized Entropic Damage to Failure ED

TF P

DF

(f(D))

0.4 0.6 0.8 1 1.2 1.4 1.6

x 104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

-4

Cycle to Failure

CTF P

DF (g(K))

True CTF PDFDerived PDF of CTF

4.055 4.06 4.065 4.07 4.075 4.08 4.085 4.09 4.095 4.1 4.105

x 104

-0.766

-0.765

-0.764

-0.763

Cycle

Poten

tial (

V)

4.055 4.06 4.065 4.07 4.075 4.08 4.085 4.09 4.095 4.1 4.105

x 104

0

100

200

300

Cycle

Stre

ss (M

Pa)

• In a mechano-chemical effectin CF, an enhanced anodicdissolution flux is induced bythe dynamic surfacedeformation

1. Imanian, A. and Modarres, M, “A Thermodynamic Entropy Approach to ReliabilityAssessment with Applications to Corrosion-Fatigue”, vol., 17. 10, 6995-7020, Journal ofEntropy.


StatisticalMechanicsEntropyMeasureofDamage

Δ𝑈 = 𝑄 +𝑊 𝑈� −𝑈� = 𝑄 +𝑊

𝐹 = 𝑈− 𝑆𝑇 Δ𝐹 = F� − 𝐹� = 𝑈� − 𝑈� − 𝑆� − 𝑆� 𝑇

Δ𝐹 = Δ𝑈 − 𝑇Δ𝑆Δ𝐹 = 𝑊+𝑄 − 𝑇Δ𝑆

𝜋� +𝑊𝜋�(−𝑊)

= 𝑒�&��S��

�&��

= Δ𝑆− ��

=Δ𝑆(C(

Internal energyFlow of energy into the system

Applied work on the system by the work

protocol

First law of thermodynamics

From Helmholtz free energy

[1,2] Δ𝑆(C(� = 𝑘� log𝜋� +𝑊𝜋�(−𝑊)

[1] Crooks, Gavin E. "Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences." Physical Review E60.3 (1999): 2721.[2] Jarzynski, C., Nonequilibrium Equality for Free Energy Differences, Phys. Rev. Lett. (1997), 78, 2690-2693.


EntropyComputationinFatigueDegradation/Damage

Test 1 strai

n

cycle

… …

Test 2 strai

n

cycle

… …

strai

n

cycle

… …Test n

…

Cycle 1 Cycle 2 Cycle i Cycle f

F R F R R F R F R F R

∆𝑆" = 𝑘�𝑙𝑜𝑔𝜋�,"(+𝑊)𝜋�,"(−𝑊)

𝑊",K�

ρ

W

𝜋𝜌�,"

𝜋𝜌�,"

𝑊" ,K�

InformationEntropy:AcousticEmissionAsaDamageSignal

Discrete approaches

𝑆¦ = −∑ 𝑝" 𝑙𝑜𝑔K(𝑝")T"UV

Acoustic emission waveforms

Histogram of the AE signals

Shannon Entropy

Probability distribution ( 𝒑𝒊)

Calculation of 𝒑𝒊 each waveform

Acoustic emission waveforms

Assigning a set of trial probability density function to the acoustic waveform

Shannon Entropy

Model selection based on the Maximum Entropy obtained

𝑆 = −∫ 𝑓 𝑥 log[𝑓 𝑥 ]𝑑𝑥¬~&~

Parametric approach

Entropic-based PHM Framework

RUL Estimation

Design Data

Critical Components

Dissipative Processes

Operating Data Entropy Quantification Diagnostics Anomaly

Entropy MonitoringEndurance ThresholdHistorical Data

Prognostics


Intersection of Data Science and Reliability: PHM Applications

– Damage Precursors: Any recognizable variation ofmaterials/physical properties influenced by theevolution of the hidden/ inaccessible/ unmeasurabledamage during the degradation process

– Heterogeneous Big Data / Information Sources• Online and Offline Sensor Values• Human Inspections• Physical Model Predictions / Simulations


Information Entropy: Parametric Results

Trend of evolution of the cumulative entropy of the acoustic signals (parametric approach)

Trend of Degradation of the modulus of elasticity in the course of the fatigue

Damage parameter based on the degradation of the modulus of elasticity

The acoustic entropy evolution trend reveals the trend of evolution of the fatigue damage


A Two-Stage Hybrid-ModelPHM Approach

Machine Learning:

Characterizing Precursor Indicator

Stage 1: Damage Precursor Model

PPoF ModelsInitial Damage

Model Parameters

Failure Agents

Stage 2: PPoF Models

Current State of Health

Future State of Health

RUL Estimation

Sensor-Based Monitoring

Extract Damage Indicators

Microstructural Damage Mechanisms

Damage Precursors

Measurements

NDI Data

FeatureExtraction

Built-in Sensors

Measurement Errors

Expert Judgments

Partially Relevant Information

Measurement Errors

Probability of Detection (POD)

Probability of Detection (POD)

Conclusions• Reliability engineering traditionally relied on historical evidences of

failures which provide limited and often inaccurate perspective on aging• Physics of failure and simulation methods offer improvement in

reliability assessment, but the models are judgmental or at based onlimited empirical evidence.

• Entropic damage provides a more fundamental approach todegradation, damage and aging assessment in reliability engineering

• Applications to reliability and PHM are explored• The proposed theory offers a consistent framework to account for the

underlying dissipative processes• Entropic fatigue and corrosion-fatigue degradation model

experimentally studied and supported the proposed theory• Expansions to statistical mechanics definition of entropy and

applications to the information theory is underway• Applications of the entropic-damage in reliability assessment in PHM is

promising


Thank you for your attention!

Funding From the Office of Naval Research (ONR) Under

Grant N000141410005 Is Acknowledged


Literature:EntropyforDamageCharacterization

Entropy for damage characterization

Statistical mechanicsmicroscopic interpretation

Macroscopic interpretation within the second law of thermodynamics

Ø Basaran et al. (1998, 2002, 2004, 2007)Ø Tucker et al. (2012)Ø Chen et al. (2012)Ø Temfeck et al. (2015)

Ø Feinberg and Widom (1996, 2000)Ø Bryant et al.(2008)

DamageEntropy 𝑆 = 𝐾�ln𝑊


EntropyGenerationforDamageCharacterization

Dissipation energies

Damage

Entropy generation

Degradation mechanisms

ØFatigue

ØWear

ØCorrosion

• Whaley et al. (1983)• Ital’yantsev (1984)• Naderi et al. (2010)• Amiri et al. (2012)• Ontiveros (2013)

• Klamecki et al. (1984)• Doelling (2000)

• Gutman (1998)

ExamplesofThermodynamicForcesandFluxes

Primary mechanism Thermodynamic force,𝑿 Thermodynamic flow, 𝑱 Examples

Heat conduction Temperature gradient, 𝛻(1/𝑇) Heat flux, 𝑞 Fatigue, creep, wear

Plastic deformation of solids Stress, 𝜏/T Plastic strain, �̇�\

Fatigue, creep, wear

Chemical reaction Reaction affinity, 𝐴S/𝑇 Reaction rate, 𝜈SCorrosion, wear

Mass diffusion Chemical potential, −𝛻(±²�)

Diffusion flux, 𝑗S Wear, creep

Electrochemical reaction Electrochemical potential, 𝐴/𝑇 Corrosion current density, 𝑖�C`̀ Corrosion

Irradiation Particle flux density, 𝐴`/𝑇 Velocity of target atoms after collision, �̇̀� Irradiation damage

Annihilation of lattice sites Creep driving force, 𝜏 − ω· /𝑇 Creep deformation rate, R Creep


overview of reliability engineering and my current … workshop - harvard may 16... · overview of...

Documents