Prognostics and Health Management

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Prognostics and Health Management (PHM) is being widely applied in many industrial systems to ensure high system availability over their life cycle. This web seminar will present key steps of PHM: data processing, feature extraction, fault diagnostics, and failure prognostics. The fundamental algorithms, models and techniques for each step will be discussed. Time domain, frequency domain and time frequency data analysis are introduced, and the corresponding feature extraction technologies presented. Mode-based and data-driven-based approaches are described in fault diagnostics and failure prognostics.

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Prognostics and Health Management

  1. 1. Prognostics and Health  Management  (故障预测和健康管理) Dr. Chaochao Chen  (陈超超博士) ©2012 ASQ & Presentation Chen Presented live on Oct 14th, 2012http://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_liability Calendar/Webinars ‐_Chinese/Webinars_‐_Chinese.html
  2. 2. ASQ Reliability Division  ASQ Reliability Division Chinese Webinar Series Chinese Webinar Series One of the monthly webinars  One of the monthly webinars on topics of interest to  reliability engineers. To view recorded webinar (available to ASQ Reliability  Division members only) visit asq.org/reliability ) / To sign up for the free and available to anyone live  webinars visit reliabilitycalendar.org and select English  Webinars to find links to register for upcoming eventshttp://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_liability Calendar/Webinars ‐_Chinese/Webinars_‐_Chinese.html
  3. 3. Prognostics TM Prognostics and Health Management Fundamentals Chaochao Chen, Ph.D. Center for Advanced Life Cycle Engineering University of Maryland College Park, MD 20742 chaochao@calce.umd.edu www.calce.umd.educalce Center for Advanced Life Cycle Engineering 1 University of Maryland TM Copyright © 2012 CALCE
  4. 4. CALCE Overview • The Center for Advanced Life Cycle Engineering (CALCE) formally started in 1984, as a NSF Center of Excellence in systems reliability. • One of the world’s most advanced and comprehensive testing and failure analysis laboratories • Funded at $4M by over 150 of the world’s leading companies • Supported by over 100 faculty, visiting scientists and research assistants • Received NSF innovation award in 2009calce Center for Advanced Life Cycle Engineering 2 University of Maryland TM Copyright © 2012 CALCE
  5. 5. CALCE Research Funding (over $6M): 2012 Emerson Appliance Controls • Motorola • S.C. Johnson Wax• Alcatel-Lucent • Emerson Appliance Solutions • Mobile Digital Systems, Inc. • Sandia National Labs• Aero Contol Systes • Emerson Network Power • NASA • SanDisk• Agilent Technologies • Emerson Process Management • National Oilwell Varco • Schlumberger• American Competitiveness Inst. • Engent, Inc. • NAVAIR • Schweitzer Engineering Labs• Amkor • Ericsson AB • NetApp • Selex-SAS• Arbitron • Essex Corporation • nCode International • Sensors for Medicine and Science Arcelik • • Consumer and mobile products• Ethicon Endo-Surgery, Inc. • Nokia Siemens • SiliconExpert• ASC Capacitors • Exponent, Inc. • Nortel Networks • Silicon Power• ASE • • Telecommunications and computer systems Fairchild Controls Corp. • Nordostschweizerische Kraftwerke • Space Systems Loral• Astronautics • Filtronic Comtek AG (NOK) • SolarEdge Technologies• Atlantic Inertial Systems • Northrop Grumman • Starkey Laboratories, Inc • Energy systems (generation/storage/distr)• AVI-Inc • GE Healthcare • General Dynamics, AIS & Land Sys. • NTSB • Sun Microsystems• Axsys Engineering • General Motors • NXP Semiconductors • Symbol Technologies, Inc• BAE Systems ••• Benchmark Electronics Boeing • Industrial systems •• • • Guideline Hamlin Electronics Europe Ortho-Clinical Diagnostics Park Advanced Product Dev. • • SymCom Team Corp • Tech Film•• Branson Ultrasonics Brooks Instruments • Transportation systems • • Hamilton Sundstrand • Harris Corp • Penn State University PEO Integrated Warfare • • Tekelec Teradyne Buehler • Henkel Technologies • Petra Solar • Aerospace systems ••• Honda Philips • The Bergquist Company• Capricorn Pharma • Honeywell Philips Lighting • The M&T Company• Cascade Engineering • • Medical systems Howrey, LLP • Pole Zero Corporation • The University of Michigan• Celestical International • Intel • Pressure Biosciences • Tin Technology Inc.• Channel One International • Qualmark • TÜB TAK Space Technologies • Military systems• Cisco Systems, Inc. • Instituto Nokia de Technologia • Juniper Networks • Quanterion Solutions Inc • U.K. Ministry of Defence• Crane Aerospace & Electronics • Johnson and Johnson • Quinby & Rundle Law • U.S. Air Force Research Lab• Curtiss-Wright Corp ••• CDI • Equipment manufacturers De Brauw Blackstone Westbroek • • Johns Hopkins University • Kimball Electronics • Raytheon Company Rendell Sales Company • • U.S. AMSAA U.S. ARL • U.S. Naval Surface Warfare Center•• Dell Computer Corp. DMEA • Government Labs and Agencies • • L-3 Communication Systems • LaBarge, Inc • Research in Motion Resin Designs LLC • • U.S. Army Picatinney/UTRS U.S. Army RDECOM/ARDEC• Dow Solar • Lansmont Corporation • RNT, Inc. Laird Technologies • Roadtrack • Vectron International, LLC• DRS EW Network Systems, Inc. • LG, Korea • Rolls Royce • Vestas Wind System AS• EIT, Inc. • Liebert Power and Cooling • Rockwell Automation • Virginia Tech• Embedded Computing & Power • Lockheed Martin Aerospace • Rockwell Collins • Weil, Gotshal & Manges LLP• EMCORE Corporation • Lutron Electronics • Saab Avitronics • WesternGeco AS• EMC • Maxion Technologies, Inc. • Samsung Mechtronics • Whirlpool Corporation• EADS - France • Microsoft • Samsung Memory • WiSpry, Inc.• Emerson Advanced Design Ctr • • Woodward Governor calce Center for Advanced Life Cycle Engineering 3 University of Maryland TM Copyright © 2012 CALCE
  6. 6. CALCE Mission and Thrust AreasProvide a knowledge and resource base to support the development and sustainment of competitive electronic products Physics of Failure, Failure Mechanisms and Material Behavior Design for Reliability and Virtual Qualification Life Cycle Risk, Cost Analysis and Management Strategies for Risk Assessment, Mitigation and Management Accelerated Testing, Screening and Quality Supply Chain Assessment Assurance and Management Diagnostic and Prognostic Health Managementcalce Center for Advanced Life Cycle Engineering 4 University of Maryland TM Copyright © 2012 CALCE
  7. 7. CALCE PHM Team • Professors and Research Staff: • Students: – Prof. Michael Pecht – Hyunseok Oh (PhD) – Moon-Hwan Chang (PhD) – Dr. Chaochao Chen – Wei He (PhD) – Dr. Michael Osterman – Yunhan Huang (PhD) – Dr. Michael Azarian – Anto Peter (PhD) – Dr. Diganta Das – Ranjith Kumar (PhD) – Prof. Peter Sandborn – Arvind Vasan (PhD) – Preeti Chauhan (PhD) – Prof. Abhijit Dasgupta – Qingguo Fan (PhD) – Prof. Donald Barker – Nick Williard (PhD) – Jing Tian (PhD) – Yan Ning (PhD) – Sony Mathew (PhD) – Surya Kunche (MS) – Edwin Sutrisno (MS)calce Center for Advanced Life Cycle Engineering 5 University of Maryland TM Copyright © 2012 CALCE
  8. 8. What is PHM? Prognostics is the process of monitoring the health of a product and predicting its remaining useful life (RUL) by assessing the extent of deviation or degradation from its expected state of health in its expected usage conditions. Health Management utilizes prognostic information to make decisions related to safety, condition-based maintenance, ensuring adequate inventory, and product life extension. PHM permits the evaluation of a system’s reliability in its actual life-cycle conditions.calce Center for Advanced Life Cycle Engineering 6 University of Maryland TM Copyright © 2012 CALCE
  9. 9. Some Benefits of PHM • Improved understanding of application conditions – knowing the customer • Extension of maintenance cycles through condition-based maintenance – enhanced system availability • Reduced life cycle costs by decreasing inspections, repairs, downtime, and inventory – product support cost avoidance • Proactive maintenance to forestall failures – reduced failure rate • Extension of operational life • Improved product/system design • Improved warranty managementcalce Center for Advanced Life Cycle Engineering 7 University of Maryland TM Copyright © 2012 CALCE
  10. 10. PHM in Industry • Apple said: If an iPhone or iPod has been damaged by liquid (for example, coffee or a soft drink), the service for such liquid damage is not covered by the Apple one (1) year limited warranty or an AppleCare Protection Plan (APP) • Liquid Contact Indicators are being used by Apple and other large cell phone manufacturers for condition monitoring. Inside the headphone jack Inside the dock connectorcalce Center for Advanced Life Cycle Engineering 8 University of Maryland TM Copyright © 2012 CALCE
  11. 11. PHM in Military The U.S. Department of Defense’s 5000.2 policy document on defense acquisition states that program managers should utilize diagnostics and prognostics to optimize the operational readiness of defense-related systems. F-35 Joint Strike Fighter Multifunction Utility/Logistics and Equipmentcalce Center for Advanced Life Cycle Engineering 9 University of Maryland TM Copyright © 2012 CALCE
  12. 12. F-35 PHM Architecturecalce Center for Advanced Life Cycle Engineering 10 University of Maryland TM Copyright © 2012 CALCE
  13. 13. PHM in New Energy Electric Vehicle (Nissan Leaf) Wind Turbinecalce Center for Advanced Life Cycle Engineering 11 University of Maryland TM Copyright © 2012 CALCE
  14. 14. PHM Modules Data Processingcalce Center for Advanced Life Cycle Engineering 12 University of Maryland TM Copyright © 2012 CALCE
  15. 15. Data Processing-Time Domain Analysis Processing- Statistical Measures Estimated Mean N ∑x i =1 i µ= N The mean is the most probable event within the distribution. For some distributions, the mean may not convey much information (i.e. uniform distributions). The estimated means of two distributions can be simply compared through subtraction of the means. Estimated Variance N ∑ (x − µ) i 2 σ2 = i =1 N The variance measures the confidence in the mean and the spread of the distribution.calce Center for Advanced Life Cycle Engineering 13 University of Maryland TM Copyright © 2012 CALCE
  16. 16. Data Processing-Time Domain Analysis Processing- Statistical Measures Estimated Skewness N ∑ (x − µ) i =1 i 3 γ= Nσ 3 Skewness vanishes for symmetric distributions and is positive (negative) if the distribution develops a longer tail to the right (left) of the mean E(x). It measures the amount of spread of the distribution in either direction from the mean. Estimated Kurtosis N ∑ (x − µ) i =1 i 4 kurtosis = Nσ 4 Kurtosis measures the contribution of the tails of the distribution. It is possible for a distribution to have the same mean, variance, and skew, and not have the same kurtosis measurement.calce Center for Advanced Life Cycle Engineering 14 University of Maryland TM Copyright © 2012 CALCE
  17. 17. Data Processing-Frequency Domain Analysis Processing- Fourier Series: Periodic functions and signals may be expanded into a series of sine and cosine functions Fourier Transform: A mathematical operation that decomposes a signal into its constituent frequenciescalce Center for Advanced Life Cycle Engineering 15 University of Maryland TM Copyright © 2012 CALCE
  18. 18. Data Processing-Frequency Domain Analysis Processing- Continuous Fourier Transform: Forward Transform: Inverse Transform:calce Center for Advanced Life Cycle Engineering 16 University of Maryland TM Copyright © 2012 CALCE
  19. 19. Data Processing-Frequency Domain Analysis Processing- An example using MATLAB functions 15 Nosiy Data Raw data MATLAB Code: 10 fs = 100; % Sample frequency (Hz) t = 0:1/fs:10-1/fs; % 10 sec sample 5 Amplitude x = (1.3)*sin(2*pi*15*t) ... % 15 Hz component 0 + (1.7)*sin(2*pi*40*(t-2)) ... % 40 Hz component −5 + (2.5)*randn(size(t)); % Gaussian noise; −10 0 2 4 6 8 10 Time (Sec)calce Center for Advanced Life Cycle Engineering 17 University of Maryland TM Copyright © 2012 CALCE
  20. 20. Data Processing-Frequency Domain Analysis Processing- An example using MATLAB functions (FFT) 700 40 Hz MATLAB Code: 600 15 Hz m = length(x); % Window length 500 n = pow2(nextpow2(m)); % Absolute Amplitude 400 Transform length y = fft(x,n); % DFT 300 f = (0:n-1)*(fs/n); % Frequency 200 range 100 y1 = abs(y) 0 0 20 40 60 80 100 Frequency (Hz)calce Center for Advanced Life Cycle Engineering 18 University of Maryland TM Copyright © 2012 CALCE
  21. 21. Data Processing-Frequency Domain Analysis Processing- An example using MATLAB functions (Power Spectrum) 450 40 Hz 400 MATLAB Code: 350 m = length(x); % Window length 300 n = pow2(nextpow2(m)); % 15 Hz Transform length 250 Power y = fft(x,n); % DFT 200 f = (0:n-1)*(fs/n); % Frequency 150 range 100 power = y.*conj(y)/n; 50 0 0 20 40 60 80 100 Frequency (Hz)calce Center for Advanced Life Cycle Engineering 19 University of Maryland TM Copyright © 2012 CALCE
  22. 22. Data Processing-Wavelet Analysis Processing- • Stationary Signal – Signals whose frequency content unchanged in time – All frequency components exist all time • Non-stationary Signal – Frequency changes in timecalce Center for Advanced Life Cycle Engineering 20 University of Maryland TM Copyright © 2012 CALCE
  23. 23. Data Processing-Wavelet Analysis Processing- Frequency: 2 Hz to 20 Hz Different in Time Domain Frequency: 20 Hz to 2 Hz 1 150 1 150 0.8 0.8 0.6 0.6 0.4 0.4 100 100 0.2 0.2Magnitude Magnitude Magnitude Magnitude 0 0 -0.2 -0.2 50 50 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -1 0 -1 0 0 0.5 1 0 5 10 15 20 25 0 0.5 1 0 5 10 15 20 25 Time Frequency (Hz) Time Frequency (Hz) Same in Frequency Domain Bhushan D Patil, Introduction to Wavelet FT cannot tell where in time the spectral components of the signal appear ! calce Center for Advanced Life Cycle Engineering 21 University of Maryland TM Copyright © 2012 CALCE
  24. 24. Data Processing-Wavelet Analysis Processing- Continuous Wavelet Transform (CWT): x (t ) • ψ *  1 t− τ (τ , s ) = Ψ xψ (τ , s ) = ∫ ψ CWT x   dt s  s  Translation (The location of the window) Scale (inverse of Mother Wavelet frequency) Energy Normalization • Wavelet – Small wave – Means the window function is of finite length • Mother Wavelet – A prototype for generating the other window functions – All the used windows are its dilated or compressed and shifted versionscalce Center for Advanced Life Cycle Engineering 22 University of Maryland TM Copyright © 2012 CALCE
  25. 25. Data Processing-Wavelet Analysis Processing- Discrete Wavelet Transform (DWT): One-Stage Filtering: Approximations and Details Approximations: high-scale, low-frequency Details: low-scale, high-frequency components componentscalce Center for Advanced Life Cycle Engineering 23 University of Maryland TM Copyright © 2012 CALCE
  26. 26. Data Processing-Wavelet Analysis Processing- Discrete Wavelet Transform (DWT): Multiple-Level Decomposition f=0~1000Hz f=0~500Hz f=500~1000Hz f=0~250Hz f=250~500Hz f=0~125Hz f=125~250Hzcalce Center for Advanced Life Cycle Engineering 24 University of Maryland TM Copyright © 2012 CALCE
  27. 27. Feature Extraction Feature Extraction is to obtain suitable parameters or indicators that reveal whether an interesting pattern is emerging Failure Feature/Precursor/Indicator is a data event or trend that signifies impending failure Attributes of good features: • Computationally inexpensive to measure • Mathematically definable • Explainable in physical terms • Insensitive to extraneous variables • Uncorrelated with other featurescalce Center for Advanced Life Cycle Engineering 25 University of Maryland TM Copyright © 2012 CALCE
  28. 28. Feature Extraction Select the life-cycle parameters to be monitored • safety • mission completeness • long downtimes • past experience • field failure data on similar products • qualification testing • failure modes mechanisms and effects analysis (FMMEA) Select the failure feature based on physics of failure Select the failure feature based on statistics and machine learningcalce Center for Advanced Life Cycle Engineering 26 University of Maryland TM Copyright © 2012 CALCE
  29. 29. Diagnostic and Prognostic Approaches There are numerous methodologies that can be used to conduct diagnostics and prognostics, but each of these falls into three main categories : • The Physics-of-Failure(PoF)/Model-based Approach PoF is the root cause of where, how and why materials fail. It provides a methodology for building-in reliability, based on assessing the hardware configuration and life-cycle stresses to identify root-cause failure mechanisms in the materials used at potential failure sites. • The Data-Driven Approach Data-driven methods use current and historical data to statistically and probabilistically obtain estimates, decisions, and predictions about the health and reliability of a product • Fusion Approachcalce Center for Advanced Life Cycle Engineering 27 University of Maryland TM Copyright © 2012 CALCE
  30. 30. The Physics-of-Failure(PoF)/Model- based Approachcalce Center for Advanced Life Cycle Engineering 28 University of Maryland TM Copyright © 2012 CALCE
  31. 31. Physics of Failure Based PHM Methodology FMMEA Define system and (1): life consumption monitoring Material identify elements and (2): canary properties and functions to be analyzed product geometries Identify potential failure modes Identify life Identify potential failure Monitor life cycle Data processing cycle profile causes environment and and load feature operating loading (1) extraction Identify potential failure mechanisms Damage assessment Identify failure models (2) Choose critical Remaining failure Use fuse useful life Maintenance Prioritize the failure mechanisms or canary estimation records mechanisms and failure site devicescalce Center for Advanced Life Cycle Engineering 29 University of Maryland TM Copyright © 2012 CALCE
  32. 32. Failure Modes, Mechanisms, and Effects Analysis • Failure Modes, Mechanisms and Effects Analysis (FMMEA) is an approach that uses the life cycle profile of a product along with the design information to identify the critical failure mechanisms affecting a product. • Failure mechanism: The processes by which physical, electrical, chemical and mechanical conditions induce failure. • Failure mode: The effect by which a failure is observed to occur • Failure site: The location of the failure. • Failure cause: The specific process, design and/or environmental condition that initiated the failure, whose removal will eliminate the failure.calce Center for Advanced Life Cycle Engineering 30 University of Maryland TM Copyright © 2012 CALCE
  33. 33. Types of Failure Mechanisms Overstress Mechanisms Wearout Mechanisms Stress exceeds item strength; failure sudden Accumulation of damage with repeated stress Yield, Fracture, Mechanical Interfacial delamination Mechanical Fatigue, Creep, Wear Glass transition (Tg) Thermal Phase transition Thermal Stress driven diffusion voiding (SDDV) Dielectric breakdown, TDDB, Electromigration, Electrical Electrical overstress, Electrostatic discharge, Electrical Surface charge spreading, Hot electrons, Second breakdown CFF, Slow trapping Radiation embrittlement, Radiation Single event upset Radiation Charge trapping in oxides Corrosion, Chemical Contamination Chemical Dendrite growth, Depolymerization, Intermetallic Growthcalce Center for Advanced Life Cycle Engineering 31 University of Maryland TM Copyright © 2012 CALCE
  34. 34. Identify Life Cycle Profile (LCP) • A life cycle profile (LCP) is a forecast of events and associated environmental and usage conditions a product will experience from manufacture to end of life. • The phases in a product life cycle includes manufacturing/assembly, test, rework, storage, transportation and handling, operation, repair and maintenance. • The description of life cycle profile needs to include the occurrences and duration of these conditions. • Life cycle loads include conditions such as temperature, humidity, pressure, vibration, shock, chemical environments, radiation, contaminants, current, voltage, power and the rates of change of these conditions.calce Center for Advanced Life Cycle Engineering 32 University of Maryland TM Copyright © 2012 CALCE
  35. 35. Canary • The use of canary devices is a PoF based approach for implementing PHM in products. • Canary is a structure that will fail faster than the actual product when subjected to the life cycle conditions. • Canary is designed to fail by the same failure mechanism as the actual product. • The acceleration factor by which the canary device is designed to fail can be used to estimate the time to failure for the actual product. • Failure of a canary device serves as an advance warning of impending failure of the product. • Canary device is integrated into the electronic assembly just like other components.calce Center for Advanced Life Cycle Engineering 33 University of Maryland TM Copyright © 2012 CALCE
  36. 36. Estimation of Remaining Useful Lifecalce Center for Advanced Life Cycle Engineering 34 University of Maryland TM Copyright © 2012 CALCE
  37. 37. PoF Simulation Based Life Assessmentcalce Center for Advanced Life Cycle Engineering 35 University of Maryland TM Copyright © 2012 CALCE
  38. 38. The Data-Driven Approachcalce Center for Advanced Life Cycle Engineering 36 University of Maryland TM Copyright © 2012 CALCE
  39. 39. Statistical Analysis-SPRT Analysis- Sequential probability ratio test (SPRT) is a statistical binary hypothesis test for anomaly detection • detect statistical changes at the earliest possible time using in- situ monitoring data • include one null hypothesis (healthy condition) and one or more alternative hypotheses (faulty conditions) -M 0 +M σ2/V σ2 Vσ2 σ Shift in mean Shift in variance (positive/negative mean test) (Normal/Inverse variance test)calce Center for Advanced Life Cycle Engineering 37 University of Maryland TM Copyright © 2012 CALCE
  40. 40. Statistical Analysis-SPRT Analysis-calce Center for Advanced Life Cycle Engineering 38 University of Maryland TM Copyright © 2012 CALCE
  41. 41. Statistical Analysis-PCA Analysis- As a multivariate statistical analysis method, Principal Component Analysis (PCA) is a simple, non-parametric method of extracting relevant information from confusing data sets. • minimize signal redundancy, measured by covariance • maximize the signal, measured by variancecalce Center for Advanced Life Cycle Engineering 39 University of Maryland TM Copyright © 2012 CALCE
  42. 42. Statistical Analysis-PCA Analysis- Solve PCA: • Find an orthonormal matrix P where Y = PX such that CY ≡ 1/ T n−1YY is diagonalized, then the rows of P are the principal components of X • The principal components of X are the eigenvectors of XXT or the rows of P • The ith diagonal value of CY is the variance of X along Picalce Center for Advanced Life Cycle Engineering 40 University of Maryland TM Copyright © 2012 CALCE
  43. 43. Statistical Analysis-MD Analysis- Mahalanobis distance (MD) is able to reduce a multivariate system to a univariate system, and is sensitive to inter-variable changes in a multivariate system • In statistics we prefer a distance that takes variability of each variable into account • Variables with high variability should receive less weight than components with low variability • Considering the full covariance structure yields the following general form for the statistical distance of two points • Def. The statistical distance or Mahalanobis distance between two points x=(x1,…,xp)T and y=(y1,…,yp)T in the p-dimensional space Rp is defined as d MD ( x, y ) = (x − y )T Σ −1 (x − y )calce Center for Advanced Life Cycle Engineering 41 University of Maryland TM Copyright © 2012 CALCE
  44. 44. Statistical Analysis-MD Analysis- MD calculation for anomaly detection: • Healthy performance parameter normalization where • Healthy MD can be calculated by where is the correlation matrix • MD is calculated using the normalized test data with the mean and standard deviation of healthy data • When the value of test MD is larger than a threshold defined in the healthy MD, an anomaly is detected.calce Center for Advanced Life Cycle Engineering 42 University of Maryland TM Copyright © 2012 CALCE
  45. 45. Statistical Analysis-SVM Analysis- Support vector machine (SVM) can perform as a classifier for diagnostics to determine the decision boundaries among different classes • map the input data to a higher dimension feature space, where the transformed data become linearly separable • does not suffer from multiple local minima and its solution is global and unique; it also does not have the problem of the curse of dimensionalitycalce Center for Advanced Life Cycle Engineering 43 University of Maryland TM Copyright © 2012 CALCE
  46. 46. Statistical Analysis-SVM Analysis- • The optimal hyperplane is determined through support hyperplanes. x2 r w Negative group data x1 x9 x4 ( y = -1 ) Positive group data x5 x7 ( y = +1 ) 2 x3 Margin Maximize Margin x6 f (x) = k w ; B x2 x8 f (x) = 0 1 2 1 T f (x) = − k min! w = w w x1 2 2 • The supporting hyperplanes can be expressed as: f ( x) = w T x + b = k w T xi + b ≥ 1 for yi = +1 f (x) = w T x + b = − k w T x i + b ≤ −1 for yi = −1, i = 1,..., n or yi (wT xi + b) − 1 ≥ 0 for i = 1,..., n constraintscalce Center for Advanced Life Cycle Engineering 44 University of Maryland TM Copyright © 2012 CALCE
  47. 47. Statistical Analysis-HMM Analysis- Hidden Markov models (HMMs) are fully probabilistic models to describe the signal evolution through a finite number of states. • HMMs have been successfully employed in speech processing • HMMs have been applied in machine health diagnostics and prognostics due to their similarities to speech processing problems • They are all related to the quasi-stationary signals that are the functions of operational and environmental conditionscalce Center for Advanced Life Cycle Engineering 45 University of Maryland TM Copyright © 2012 CALCE
  48. 48. Statistical Analysis-HMM Analysis- • Transition probabilities: ∂ k ,l = P(st = l st −1 = k ), k , l = 1,..., M . • Initial probabilities: π k = P(s1 = k ), k = 1,..., M • Observation probabilities: bk (u ) = P(u t = u st = k ), k = 1,..., M . 1  1  exp − (u − u k ) ∑ −1 (u − u k ) Gaussian = k Distribution (2π )d ∑ k  2  46calce 46 University of Maryland TM Center for Advanced Life Cycle Engineering Copyright © 2012 CALCE
  49. 49. Statistical Analysis-PF Analysis- Particle filtering (PF) is a sequential Monte Carlo method, which uses a mathematical process model to estimate a state vector in a recursive Bayesian framework • The output of the PF is a posterior probability density function (PDF) approximated by a set of particles with their associated weights • Through the PDF, many statistical measures of the estimated states become available, such as the estimation confidence, which are not possible with scalar datacalce Center for Advanced Life Cycle Engineering 47 University of Maryland TM Copyright © 2012 CALCE
  50. 50. Statistical Analysis-PF Analysis- Sequential Importance Sampling For i=1,…,N: 1. Particle generation xki ) ~ p ( xk | xki−)1 ) ( ( 2a. Weight computation wk i ) = wk −i1) p ( z k | xki ) ) *( *( ( (i ) wk i ) *( 2b. Weight normalization w = k N ∑ wk i ) *( i =1 N 3. Estimate computation E ( g ( xk | z1:k )) = ∑ g ( xki ) ) wki ) ( ( i =1 ENDcalce Center for Advanced Life Cycle Engineering 48 University of Maryland TM Copyright © 2012 CALCE
  51. 51. Machine Learning-FFNN Learning- Feedforward neural network (FFNN) is considered as one of the most widely used machine learning method in the fault diagnosis and failure prognosis L 1 M x = ∑ x Wli i H l L yiH = 1 + exp (− xiH ) y = ∑ y m C mi O i H l =1 m =1calce Center for Advanced Life Cycle Engineering 49 University of Maryland TM Copyright © 2012 CALCE
  52. 52. Machine Learning-RBFNN Learning- A radial basis function neural network (RBFNN) contains radial basis functions in its hidden nodes L ∑ (x − Wli ) L 2 M y = ∑ y m C mi l O H H l =1 y = exp( − i 2 ) i 2σ m =1calce Center for Advanced Life Cycle Engineering 50 University of Maryland TM Copyright © 2012 CALCE
  53. 53. Machine Learning-RNN Learning- A recurrent neural network (RNN) has feedback links in the model structure, they are capable of dealing with dynamic processes L 1 M x = ∑ x Wli H L yiH (t ) = y = ∑ y m C mi O H i l 1 + exp (− ( xiH (t ) + yiH (t − 1)) i l =1 m =1calce Center for Advanced Life Cycle Engineering 51 University of Maryland TM Copyright © 2012 CALCE
  54. 54. Machine Learning-SOM NN Learning- A self-organizing map (SOM) neural network does not need supervised training and the input data can be automatically clustered in different groups Weight update W (t + 1) = W (t ) + θ (t )L(t )( x(t ) − W (t )) Neighborhood of BMU  Dist 2  θ (t ) = exp − 2   2σ (t )    Similarity L ∑ (x − Wli ) L 2 Dist = l l =1calce Center for Advanced Life Cycle Engineering 52 University of Maryland TM Copyright © 2012 CALCE
  55. 55. Machine Learning-NFS Learning- A neuro-fuzzy system (NFS) combines advantages of fuzzy inference systems and neural networksxt +r= ∑ y(j4) (c1j xt −3r + c2j xt −2r + c3j xt−r + c4j xt + c5j ), j ( 4) y (j3) y = , ∑ y (j3) j j y (j3) = ∏ uA2j) (xi(1) ), ( i i 1u A2j) (xi(1) ) = ( , i 1 + exp(− bij2 ) (xi(1) − mij2 ) )) ( ( yi(1) = xi(1) , i = 1,2, K ,4. Wang, W et al.,“Prognosis of Machine Health Condition Using Neuro-Fuzzy Systems,” Mechanical System and Signal Processing, 2004, Vol. 18, pp.813-831. calce Center for Advanced Life Cycle Engineering 53 University of Maryland TM Copyright © 2012 CALCE
  56. 56. The Fusion Approachcalce Center for Advanced Life Cycle Engineering 54 University of Maryland TM Copyright © 2012 CALCE
  57. 57. Fusion: Data Driven and Physics of Failure Healthy Baseline Identify parameters Continuous Yes Anomaly? Alarm Monitoring No Physics of Database and Parameter Failure Standards Isolation Models Failure Data Driven Definition Algorithms Remaining Useful Life Estimationcalce Center for Advanced Life Cycle Engineering 55 University of Maryland TM Copyright © 2012 CALCE
  58. 58. Fusion: Data Driven and Physics of Failure InitialPerformance Model Parameter Parameters Updated Parameters Degradation Performance Model Threshold Prediction Estimation Errors Tuned Moving Model Nonlinear Degradation Window Adaptation Filtering Model Parameter Identification Loop Prediction Loop Remaining Useful Performancecalce Center for Advanced Life Cycle Engineering 56 University of Maryland TM Copyright © 2012 CALCE
  59. 59. Fusion: Multiple Data Drivencalce Center for Advanced Life Cycle Engineering 57 University of Maryland TM Copyright © 2012 CALCE

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