Overview of Reliability Engineering and My Current Research - - PowerPoint PPT Presentation

Overview of Reliability Engineering and My Current Research

Mohammad Modarres Department 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

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)

– Conclusions

Reliability Engineering Overview

• Reliability engineering measures and improves

resistance to failure of an item over time

• Two Overlapping Frameworks for Modeling Life and

Performance 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)

Data or Evidence View: Statistical / Probabilistic Metric

– Post WWII Initiatives due to unreliability of electronics and fatigue issues

• Inspired by the weakest link, statistical process control, insurance and

demographic mortality data analysis methods

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

distribution 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 case

𝑆" 𝑢 = 𝑓&' ( , 𝑥ℎ𝑓𝑠𝑓 H . = cumulative hazard,and h . = hazard rate

– Issues

• Results rarely match field experience

) t T Pr( ) t ( R ≥ =

Physics-Based View of Reliability

– 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 Stresses Se= Environmental Stresses g = Geometry related factors 𝜾 = material properties d = defects, flaws, etc.

𝑢? = 𝑔(𝑇C,𝑇D,𝑕,𝑒",𝜾G

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 and maintenance – 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

Reliability Summary

Endurance to Damage

Damage /Degradation Life

Initial Damage

Time-to-Failure Distribution t1 t2

Summary of Reliability Overview

Data Driven

Future

Empirical PoF Why Entropy? ü Entropy can model multiple competing degradation processes leading to damage ü Entropy is independent

• f the path to failure

ending at similar total entropy at failure ü Entropy accounts for complex synergistic effects of interacting degradation processes ü Entropy is scale independent

• My Recent Research on Damage,

Degradation and Failure

An Entropic Theory of Damage

• Failure mechanisms are irreversible processes leading to

degradation and share a common feature at a deeper level: Dissipation of Energy

• Dissipation (or equivalently entropy generation)≅Damage

Dissipation 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 to

withstand 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 function

An Entropic Theory of Damage(Cont.)

[1] Anahita Imanian and Mohammad Modarres, A Thermodynamic Entropy Approach to Reliability Assessm ent 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

0.5 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

Entropy to Failure (MJ/m3K) Time (Cycle) × 104

F=330 MPa F=365 MPa F=405 MPa F=260 MPa F=290 MPa

[1]

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 500 5000

Fracture Fatigue Failure (MJ m-3 K-1) Number of Cycles to Failure

[2]

𝜏 = 1 𝑈K 𝐾M N 𝛼𝑈 − Q 𝛼 𝜈S 𝑈

T SUV

+ 1 𝑈 𝜐:𝜗̇\ + 1 𝑈 Q 𝑤^𝐵^

` ^UV

+ 1 𝑈 Q 𝑑b𝐾

b −𝛼𝜔 d bUV

Thermal Diffusion Chemical External field energy Mechanical

𝑲T (𝑜 = 𝑟, 𝑙, 𝑏𝑜𝑒 𝑛) = thermodynamic fluxes due to heat conduction, diffusion and external fields, T = temperature, 𝜈S = chemical potential, 𝑤" = chemical reaction rate, 𝝊 = stress tensor, 𝝑\ ̇ = plastic strain rate, 𝐵^ = chemical affinity, 𝜔 = potential of the external field , and 𝑑b = coupling constant [3, 4].

Entropy as an Index of Damage

• The evolution trend of the damage, 𝐸, according to our theory is dominated

by the entropy generated: 𝐸 = 𝛿p − 𝛿pq 𝛿pr − 𝛿pq , 𝛿=𝜍𝑡 volumetric entropy generation 𝐸~𝛿p|𝑢~ w [𝜏|𝑌" 𝑣 , 𝑲" 𝑣 ]𝑒𝑣

( |

• The reliability expressed in terms
• f entropic damage :

𝑆 𝑢 = ∫ 𝑕 𝑢 𝑒𝑢

~ (•

=1- ∫ 𝑔(𝐸|𝑢)𝑒𝐸

~ ۥ

Reliability of Structures Subject to Corrosion-Fatigue (CF)

Entropy Generation in CF

• Contribution from corrosion activation over-potential, diffusion over-potential, corrosion reaction chemical

potential, plastic and elastic deformation and hydrogen embrittlement to the rate of entropy generation:

𝜏 = 1 𝑈 𝑲‚,ƒ𝑨‚𝐺𝐹‚‡•ˆ,‡ + 𝑲‚,‰𝑨‚𝐺𝐹‚‡•ˆ,• + 𝑲Š,ƒ𝑨Š𝐺𝐹Š‡•ˆ,‡ + 𝑲Š,‰𝑨Š𝐺𝐹Š‡•ˆ,• + 1 𝑈 𝑲‚,‰𝑨‚𝐺𝐹‚•‹Œ•,• + 𝑨Š𝐺𝑲Š,‰𝐹Š•‹Œ•,• + 1 𝑈 𝑲‚,ƒ𝛽‚𝐵‚ + 𝐾‚,‰ 1 − 𝛽‚ 𝐵‚ + 𝑲Š,ƒ𝛽Š𝐵Š + 𝑲‚,ƒ 1 − 𝛽Š 𝐵Š + 1 𝑈 𝝑̇\: 𝝊 + 1 𝑈 𝑍𝑬 ̇ +𝜏'

𝑈 = temperature, 𝑨‚ =number of moles of electrons exchanged in the oxidation process, 𝐺 =Farady number, 𝐾

‚,ƒ and 𝐾 ‚,‰ = irreversible anodic and cathodic activation

currents for oxidation reaction, 𝐾

Š ,ƒ and 𝐾 Š ,‰ =anodic and cathodic activation currents for reduction reaction, 𝐹‚‡•ˆ,‡ and 𝐹‚‡•ˆ,• =anodic and cathodic over-potentials for

• xidation reaction, 𝐹Š

‡•ˆ,‡ and 𝐹Š ‡•ˆ,• =anodic and cathodic over-potentials for reduction reaction, 𝐹‚•‹Œ•,• and 𝐹Š•‹Œ•,• =concentration over-potentials for the cathodic

• xidation and cathodic reduction reactions, 𝛽‚ and 𝛽Š =charge transport coefficient for the oxidation and reduction reactions, 𝐵‚ and 𝐵Š = chemical affinity for the
• xidation and reductions, 𝜗̇\ =plastic deformation rate, 𝜐 =plastic stress, 𝐸

̇ =dimensionless damage flux, 𝑍 the elastic energy, and 𝜏

' =entropy generation due to

hydrogen embrittlement.

[1] Imanian, A. and Modarres. M, “A Thermodynamic Entropy Based Approach for Prognosis and Health Management with Application to Corrosion-Fatigue,” 2015 IEEE International Conference on Prognostics and Health Management, 22-25 June, 2015, Austin, USA. Diffusion dissipations Chemical reaction dissipations Mechanical dissipations Hydrogen embrittlement dissipation

CF Experimental Set up

• Fatigue tests of Al 7075-T651 performed in 3.5% wt. NaCl aqueous solution

acidified with a 1 molar solution of HCl, with the pH of about 3, under axial load controlled and free corrosion potential

• Specimens electrochemically monitored

via a potentiostat using Ag/AgCl reference 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-Based Reliability Results for CF

2000 4000 6000 8000 10000 12000 14000 16000 0.2 0.4 0.6 0.8 1 Time(Cycle) Damage

P=405 MPa P=365MPa P=330MPa P=290MPa P=260MPa P=190MPa P=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 EDTF PDF ( f(D))

0.4 0.6 0.8 1 1.2 1.4 1.6 x 10

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10

• 4

Cycle to Failure CTF PDF (g(K))

True CTF PDF Derived 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 10

• 0.766
• 0.765
• 0.764
• 0.763

Cycle Potential (V)

4.055 4.06 4.065 4.07 4.075 4.08 4.085 4.09 4.095 4.1 4.105 x 10

100 200 300

Cycle Stress (MPa)

• In a mechano-chemical effect

in CF, an enhanced anodic dissolution flux is induced by the dynamic surface deformation

• 1. Imanian, A. and Modarres, M, “A Thermodynamic Entropy Approach to Reliability

Assessment with Applications to Corrosion-Fatigue”, vol., 17. 10, 6995-7020, Journal of Entropy.

Statistical Mechanics Entropy Measure of Damage

Δ𝑉 = 𝑅 + 𝑋 𝑉” − 𝑉

• = 𝑅 + 𝑋

𝐺 = 𝑉 − 𝑇𝑈

Δ𝐺 = F— − 𝐺

• = 𝑉” − 𝑉• − 𝑇” − 𝑇• 𝑈

Δ 𝐺 = Δ𝑉 − 𝑈Δ𝑇 Δ𝐺 = 𝑋 + 𝑅 − 𝑈Δ𝑇 𝜌™ +𝑋 𝜌š(−𝑋) = 𝑓

›&œ™ S•ž

›&œ™ ž

= Δ𝑇 −

Ÿ ž =Δ𝑇(C(

Internal energy Flow of energy into the system Applied work on the system by the work protocol

First law of thermodynamics From Helmholtz free energy

[1,2]

Δ𝑇(C(ƒ = 𝑙” log𝜌™ +𝑋 𝜌š(−𝑋)

[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.

Entropy Computation in Fatigue Degradation / Damage

Test 1

strain cycle

… …

Test 2

strain cycle

… …

strain cycle

… …

Test n

…

Cycle 1 Cycle 2 Cycle i Cycle f

F R F R R F R F R F R

∆𝑇" = 𝑙”𝑚𝑝𝑕𝜌™,"(+𝑋) 𝜌š,"(−𝑋)

𝑋

",K ™ ρ W

𝜌𝜍™," 𝜌𝜍š,"

𝑋

",K š

Information Entropy: Acoustic Emission As a Damage Signal

Discrete approaches 𝑇¦ = − ∑ 𝑞" 𝑚𝑝𝑕K(𝑞")

T "UV

Acoustic emission waveforms Histogram of the AE signals Shannon Entropy Probability distribution ( 𝒒𝒋) Calculation of 𝒒𝒋 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

𝑇 = − ∫ 𝑔 𝑦 log[𝑔 𝑦 ]𝑒𝑦

¬~ &~

Parametric approach

Entropic-based PHM Framework

RUL Estimation Design Data Critical Components Dissipative Processes Operating Data Entropy Quantification Diagnostics Anomaly Entropy Monitoring Endurance Threshold Historical Data Prognostics

Intersection of Data Science and Reliability: PHM Applications

– Damage Precursors: Any recognizable variation of materials/physical properties influenced by the evolution of the hidden/ inaccessible/ unmeasurable damage 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-Model PHM Approach

Machine Learning: Characterizing Precursor Indicator

Stage 1: Damage Precursor Model

PPoF Models

Initial 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

Feature Extraction

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 on limited empirical evidence.

• Entropic damage provides a more fundamental approach to

degradation, 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: Entropy for Damage Characterization

Entropy for damage characterization Statistical mechanics microscopic 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)

Damage Entropy 𝑇 = 𝐿” ln𝑋

Entropy Generation for Damage Characterization

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)

Examples of Thermodynamic Forces and Fluxes

Primary mechanism Thermodynamic force, 𝒀 Thermodynamic flow, 𝑲 Examples Heat conduction

T emperature gradient, 𝛼(1/𝑈) Heat flux, 𝑟 Fatigue, creep, wear

Plastic deformation of solids

Stress, 𝜐/T Plastic strain, 𝜗̇\ Fatigue, creep, wear

Chemical reaction

Reaction affinity, 𝐵S/𝑈 Reaction rate, 𝜉S Corrosion, wear

Mass diffusion

Chemical potential, −𝛼(±²

ž )

Diffusion flux, 𝑘

S

Wear, creep

Electrochemical reaction

Electrochemical potential, 𝐵 ´/𝑈 Corrosion current density, 𝑗‰C`` Corrosion

Irradiation

Particle flux density, 𝐵`/𝑈 Velocity of target atoms after collision, 𝑤̇` Irradiation damage

Annihilation of lattice sites

Creep driving force, 𝜐 − ω· /𝑈 Creep deformation rate, R Creep