Intelligent Fault Diagnosis & Prognosis

Transcription

1 F.L. Lewis, IEEE Fellow Moncrief-O Donnell Endowed Chair Head, Controls & Sensors Group Automation & Robotics Research Institute (ARRI) The University of Texas at Arlington Intelligent Fault Diagnosis & Prognosis

2 John Wiley, New York, 2006 John Wiley, New York, 2003

3 Outline Why Intelligent Diagnostics & Prognostics? Diagnostics Intelligent Decision Making Prognostics Condition-Based Maintenance Signal Processing Machinery Monitoring using Wireless Sensor Networks

4 Dr. George Vachtsevanos Who is the Customer The maintainer Maintenance, Repair and Overhaul of Critical Systems The operator/pilot Awareness and corrective action under safety critical conditions The operations manager/field commander What is my confidence that I can deploy a particular asset for a specific mission/task? The system designer How do I take advantage of CBM/PHM technologies to design highconfidence, fault-tolerant systems?

5 New Business Models for Machinery Maintenance Dr. Jay Lee Original Equipment Manufacturer Becomes the Service Provider Integrate Manufacturing, Service, and Maintenance Lifetime Machine Service Contract Guaranteed Up-Time for User Guaranteed Lifetime Revenue Stream for OEM Subcontracted Maintenance Service Providers MSP provides and maintains the wireless sensor network MSP monitors equipment, schedules & provides maintenance Like current Security Systems- Brinks, etc. Internet-Based E-Maintenance Integrate Internet with Machine On-Board Diagnostics Centralized Service Scheduling and Dispatching Reduced Service Costs

6 Old Paradigm- open loop, no feedback of machine condition Two Extremes of Manpower & Resource Waste Preventive Maintenance Periodic, whether needed or not Run-to-Failure No maintenance Imperatives for New Automated Maintenance Paradigms Breakdowns, Unscheduled Maintenance, and Temporary Repairs- add Billions to Manufacturing Costs destroy throughput and Due Date schedules Reduced manning levels in Factory Of The Future, Military, Navies Complexity of new machinery makes maintenance more complex Reduced failure tolerance of Just-in-Time systems Small companies cannot afford full-time maintenance technicians Ready availability of on-board sensors used for control purposes Ease of remote information access over the internet

7 Condition-Based Maintenance (CBM) Prognostics & Health Management (PHM) Objectives Extend equipment lifetime Reduce down time Keep throughput and due dates on track mission criticality Use minimum of maintenance personnel Maximum uptime for minimum effective maintenance costs CBM should be transparent to the user No extra maintenance for the CBM network! Determine the best time to do maintenance Efficiently use maintenance & repair resources Do not interfere with machine usage requirements Allow planning for maintenance costs No unexpected last-minute costs!

8 CBM+: Maintenance-Centric Logistics Support for the Future Dr. George Vachtsevanos

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10 Machine User Group- CBM Data

11 Condition Monitoring and Diagnostics of Machines

12 Dr. George Vachtsevanos The Systems Approach to CBM/PHM Trade Studies Failure Modes and Effects Criticality Analysis (FMECA) System Test Plan Design Comparison of Data Distributions/Statistical Measures Performance Metrics Verification and Validation (V&V) of PHM Systems

13 The CBM/PHM Cycle Select Sensors! Machine Sensors Required Background Studies Identify important features Fault Mode Analysis Machine legacy failure data Available resources RUL Mission due dates Data Pre- Processing Feature Extraction Fault Classification Prediction of Fault Evolution Schedule Required Maintenance Systems & Signal processing Diagnostics Prognostics Maintenance Scheduling CBM PHM

14 Three Stages of CBM/PHM Diagnostics Prognostics Maintenance Scheduling Two Phases of CBM Diagnostics Off Line- Background Studies, Fault Mode Analysis On Line- Perform real-time Fault Monitoring & Diagnosis

15 Diagnostics Exception Fault Failure Fault (Failure) Detection Fault (Failure) Isolation Fault (Failure) Identification

16 Phase I- Preliminary Off Line Studies CBM Fault Diagnosis Background Studies Fault Mode Analysis (FMA) - Identify Failure and Fault Modes Identify the best Features to track for effective diagnosis Identify measured sensor outputs needed to compute the features Build Fault Pattern Library Deal with FAULTS Need to identify Faults before they become Failures

17 Fault Mode Analysis Why Motors Fail? Bearing Failures: Root cause of ~ 50%Motor Failures Effect: Motor burn out Sources: Improper Lubrication, Shaft Voltages, Excessive Loadings Excessive Vibrations: Effect: bearing failures, metal fatigue of parts and windings Sources: Usually caused by improper balance of rotating part Electrical Problems: Effect: Higher than normal current, overheating Sources: Low Voltages, Unbalanced 3-Phase Voltages Mechanical Problems: Effect: Bearing failures, overheating Sources: Excessive Load and Load Fluctuations result in more current Maintenance issues: Sources: Inadequate regular maintenance, lack of preventive maintenance, lack of Root Cause Analysis

18 Fault Mode Analysis Dr. George Vachtsevanos Ex. - Navy Centrifugal Chiller Failure Modes Condenser Tube Fouling Condenser Water Control Valve Failure Tube Leakage Decreased Sea Water Flow Compressor Pre-rotation Vane Compressor Stall & Surge Shaft Seal Leakage Oil Level High/Low Aux. Pump Fail Oil Cooler Fail PRV/VGD Mechanical Failure SW in/out temp. SW flow Cond. press. Cond. PD press. Cond. liquid out temp. Condenser Comp. suct. press./temp. Comp. disch. press./temp. Comp. oil press./flow (at required points) Comp. bearing oil temp Comp. suct. super-heat Shaft seal interface temp. PRV Position Evaporator Target Flow Meter Failure Decreased Chilled Water Flow Evaporator Tube Freezing CW in/out temp./flow Eva. temp./press. Eva. PD press. Liquid line temp. (Refrigerant weight) Non Condensable Gas in Refrigerant Contaminated Refrigerant Refrigerant Charge High Refrigerant Charge Low

19 Fault Mode: Refrigerant Charge Low Symptoms:. Low Evaporator Liquid Temperature 2. Low Evaporator Suction pressure 3. Increasing difference (D-ELT-CWDT) between Chilled Water Discharge Temperature and Evaporator Liquid Temperature Sensors:. Evaporator Liquid Temperature (ELT) 2. Evaporator Suction Pressure (ESP) 3. Chilled Water Discharge Temperature (CWDT)

20 Failure Modes and Effects Criticality Analysis Dr. George Vachtsevanos Failure Modes and Effects Criticality Analysis New systematic approach based on fuzzy Petri networks and efficient search techniques to define failure effect root cause relationships Not ok (0.) Check Pressure Meter Not ok (0.) Large Leak Detected (0.9) Ok (0.9) Check Vacuum Pump Not ok (0.2) Large Leak While Meter Reading is Correct (0.8) Ok (0.9) Check for Overheating (0.8) Ok (0.8) Not ok (0.9) Check for Dirty Fluid Ok (0.)

21 Dr. George Vachtsevanos Helicopter Fault Tree Helicopter Failure Motor Failures Actuator Failures Power Failures Sensor Failures Computer System Failures Main Rotor Failures Tail Rotor Failures

22 Motor Fault Tree Motor Failure Local Power Lines Fail Gear Box Failure Internal Motor Failure Gears Slip Wear On Gears

23 Feature Selection What to measure to get information about the fault? Sensor Selection Existing OEM sensors Used e.g. for Control Add extra DSP Virtual Sensors Add additional sensors for CBM/PHM

24 Dr. George Vachtsevanos SENSOR SELECTION AND PLACEMENT Objective: Determine the optimum type and placement of sensors Current Status: Ad hoc;heuristic methods; Mostly an art Future Direction: Put some science into the problem

25 Diagnostics Model-Based Methods Non-Model-Based Data-Based Statistical Analysis Methods

26 Fault Mode Analysis V. Skormin, 994 SUNY Binghamton Fault Modes of an Electro-Hydraulic Flight Actuator bearing control surface Fault Modes Control surface loss Excessive bearing friction hydraulic cylinder Hydraulic system leakage Air in hydraulic system Excessive cylinder friction Malfunction of pump control valve Rotor mechanical damage Motor magnetism loss pump motor power amplifier

27 Select Fault ID Feature Vector The Fault Feature Vector is a sufficient statistic for identifying existing fault modes and conditions Use Physics of Failure and Failure Models to select failure features to include in feature vectors Method - Dynamical System Diagnostic Models motor dynamics ω( s) T ( s) = Js + B V. Skormin, 994 SUNY Binghamton pump/piston dynamics X ( s) F( s) = ( M p s + B p ) s actuator system dynamics P( s) R( s) = ( A 2 ) s K + L Physical parameters are J, B, M p, B p, K, L

28 Select Feature Vector Relate physical parameters J, B, M p, B p, K, L to fault modes Get expert opinion (from manufacturer or from user group) Get actual fault/failure legacy data from recorded machine histories Or run system testbed under induced faults Result - V. Skormin, 994 SUNY Binghamton IF (leakage coeff. L is large) IF (motor damping coeff. B is large) AND (piston damping coeff. B p is large) IF (actuator stiffness K is small) AND (piston damping coeff. B p is small) Etc. Condition Fault Mode THEN (fault is hydraulic system leakage) THEN (fault is excess cylinder friction) THEN (fault is air in hydraulic system) Etc. Therefore, select the physical parameters as the feature vector φ( t ) = [ J B M B K L] p p T

29 V. Skormin, 994 SUNY Binghamton Select Sensors for the Best Outputs to Measure Cannot directly measure the feature vector φ( t ) = [ J B M B K L] Can measure the inputs and outputs of the dynamical blocks, e.g. p p T armature current I(t) pressure difference P(t) ω( s) T( s) Js+ B motor speed D T ( t) = CI ( t) P( t) = ω(t) 2π Therefore, use system identification techniques to estimate the features Virtual Sensors = physical sensors + signal processing signals from machine sensors DSP Fault ID features

30 Select Fault ID Feature Vector Method 2- Non-Model-Based Techniques Get expert opinion (from manufacturer or from user group) Get actual fault/failure legacy data from recorded machine histories Or run system testbed under induced faults IF (base mount vibration energy is large) IF (shaft vibration second mode is large) AND (motor vibration RMS value is large) IF (third harmonic of shaft speed is present) AND (kurtosis of load vibration is large) Etc. Condition Fault Mode THEN (fault is unbalance) THEN (fault is gear tooth wear) THEN (fault is worn outer ball bearing) Etc. Therefore, include vibration moments and frequencies in the feature vector φ (t) = [ time signals frequency signals ] T

31 Select Fault ID Feature Vector Method 3- Statistical Regression Techniques Drive train gear tooth wear Fault Fault 2 Pearson s correlation Nonlinear correlation techniques Multivariable regression Fault 3 Vibration magnitude Clustering techniques Neural networks Statistical outliers

32 Fault Pattern Library IF (leakage coeff. L is large) IF (motor damping coeff. B is large) AND (piston damping coeff. B p is large) IF (actuator stiffness K is small) AND (piston damping coeff. B p is small) Etc. Condition Fault Mode THEN (fault is hydraulic system leakage) THEN (fault is excess cylinder friction) THEN (fault is air in hydraulic system) Etc. IF (base mount vibration energy is large) IF (shaft vibration second mode is large) AND (motor vibration RMS value is large) IF (third harmonic of shaft speed is present) AND (kurtosis of load vibration is large) Etc. Condition Fault Mode THEN (fault is unbalance) THEN (fault is gear tooth wear) THEN (fault is worn outer ball bearing) Etc.

33 Phase II- On Line Fault Monitoring and Diagnostics CBM Fault DIAGNOSTICS Procedure Sensing Inject probe test signals for refined diagnosis machines Math models x = f ( x, u, π) y = h( x, u, π) Sensor outputs Physics of failure System dynamics Physical params. π Model-Based Diagnosis Systems, DSP & Data Fusion Dig. Signal Processing System Identification- Kalman filter NN system ID RLS, LSE Sensor Fusion Vibration Moments, FFT πˆ Fault Feature Extraction Physical Parameter estimates & Aero. coeff. estimates Feature Vectors- Sufficient statistics Feature vectors Feature fusion φ(t) Feature extraction - determine inputs for Fault Classification Reasoning & Diagnosis Fault Classification Feature patterns for faults Decision fusion could use: Fuzzy Logic Expert Systems NN classifier Stored Fault Pattern Library Identify Faults/ Failures yes More info needed? Set Decision Thresholds Manuf. variability data Usage variability Mission history Minimize Pr{false alarm} Baseline perf. requirements Stored Legacy Failure data Statistics analysis Inform pilot yes Serious? no Inform pilot Request Maintenance

34 Stored Fault Pattern Library Fault Classification Feature Vectors φ(t) Decision-Making Fault Classification Diagnosed Faults Neural networks Fuzzy logic Expert system rulebase Bayesian Dempster-Shafer Model-Based Reasoning Model-Based Reasoning (MBR) vs. Case-Based Reasoning Faults depend on Operating conditions Too complex!

35 Decision-Making Bayes Probability P( π / δ ) i = Dempster-Shafer Rules of Evidence Expert & Rule-Based systems i P( δ / π ) P( π ) i P( δ / π ) P( π ) i i S j Bel( π i ) = i = π S j i = 0 m j m ( S j j ( S ) j ) IF (BM is negative medium) and (LC is negative small) IF (BM is positive) and (LC is normal) IF (BM is normal) and (LC is positive medium) THEN (fault is air contamination) THEN (fault is water contamination) THEN (fault is excessive leakage) Fuzzy Logic f ( x) N n i z i= j= = N n i= j= μ ( x ij ij μ ( x j j ) ) Model-Based Reasoning

36 Bayesian Classifier Performance normal spec abnormal FN spec FN FP decision criterion False negative False positive Prob. of False Alarm

37 = = = j i j i B A j i C B A j i B m A m B m A m C m m ) ( ) ( ) ( ) ( ) ( Dempster-Shafer If m and m 2 are two pieces of Evidence, the combined Evidence is given by Conflict between two pieces of evidence Based on this, can compute: Belief C is definitely true. Bel(C)= Plausibility C may be true. Pl(C)= D C D m ) ( 0 ) ( C D D m In Bayes, Bel= Pl

38 Dempster-Shafer Example Suppose there are 00 cars in a parking lot consisting of type A (red) and B (green). Two policemen count the type of cars in the lot. First policeman m says that there are 30 A cars and 20 B cars. Second policeman m2 says that there are 20 A cars and 20 cars that could A or B. m2(a) 0.2 m2(ab) 0.2 m2(θ) 0.6 Using the formulas above: m(a) m(b) (0 intersection) CONFLICT m(θ) Bel(A)=m2(A)=0.42. (42 A cars) Bel(B)=m2(B)=0.7. (7 B cars) So there are between 42 and 83 cars of type A between 7 and 58 cars of type B Pl(A)= m2(a)+m2(ab)+m2(θ)=0.83. (83 A cars) Pl(B)= m2(b)+m2(ab)+m2(θ)=0.58. (58 B cars)

39 Fuzzy Logic Fault Classification Fault conditions one two three Unifies expert systems statistical neural network approaches Drive train gear tooth wear Vibration magnitude small medium large Sideband component I 2 one incip. none one or two incip. Sideband component I small medium large Fig FL rulebase to diagnose broken bars in motor drives using sideband components of vibration signature FFT [Filippetti 2000]. Number of broken bars = none, one, two. Incip. = incipient fault one two one or two one low med severe Fig 5 Clustering of statistical fault data 2-D FL system c.f. neural network

40 FL Decision Thresholds Based on Legacy fault data histories Manuf. variability data Usage variability Mission history Minimize Pr{false alarm} Baseline perf. requirements Can be tuned using adaptive learning techniques From Chestnut

41 Neural Networks V T σ(.) W T 2-layer NN y = W T σ T ( V x) x x 2 2 σ(.) y y 2 RVFL NN has V= random 3 σ(.) -layer NN has W= I T y = σ ( V x) x n inputs L σ(.) outputs y m Training hidden layer Two-Layer Neural Network -layer Gradient Descent V ( k + ) = V ( k) +ηe T X Where X= input pattern vectors Y= output target vectors e = Y y(k) = training error Multilayer- backpropagation (Paul Werbos)

42 Neural Networks - Classification Group : o (,), (,2) Group 2: x (2,-), (2, -2) Group 3: + (-,2), (-2,) Group 4: # (-,-), (-2,-2) Classify 8 points into two groups o o x x + + # # Represent the 4 groups as 00, 0, 0, Then, the input pattern vector and target vector are = X = Y I. Training

43 MATLAB Code R=[-2 2;-2 2]; % define 2-D input space netp=newp(r,2); % define 2-neuron NN p=[ ]'; p2=[ 2]'; p3=[2 -]'; p4=[2-2]'; p5=[- 2]'; p6=[-2 ]'; p7=[- -]'; p8=[-2-2] ; t=[0 0]'; t2=[0 0]'; t3=[0 ]'; t4=[0 ]'; t5=[ 0]'; t6=[ 0]'; t7=[ ]'; t8=[ ] ; P=[p p2 p3 p4 p5 p6 p7 p8]; T=[t t2 t3 t4 t5 t6 t7 t8]; netp.trainparam.epochs = 20; % train for max 20 epochs netp = train(netp,p,t); result y = T σ 3 2 x + 0 Defines 2 lines in (x, x 2 ) plane II. Classification (simulation) All points are classified into one of the 4 regions Y=sim(netp,P) Result after training

44 Clustering Using NN Competitive NN I. Training & Clustering Given 80 data points Make 2 x 80 matrix P of the 80 points MATLAB code % make new competitive NN with 8 neurons net = newc([0 ;0 ],8,.); % train NN with Kohonen learning net.trainparam.epochs = 7; net = train(net,p); w = net.iw{}; %plot plot(p(,:),p(2,:),'+r'); xlabel('p()'); ylabel('p(2)'); hold on; circles = plot(w(:,),w(:,2),'ob'); II. Classification (simulation) p = [0; 0.2]; a = sim(net,p) Activates neuron number

45 Model-Based Reasoning MBR Dr. George Vachtsevanos Possible failures depend on current operating mode

46 Model-Based Reasoning (MBR) Provides a Significant Part of PHM Design Solution MBR Approach Provides Multiple Benefits and Functions: Intuitive, Multi-Level Modeling Inherent Cross Checking for False Alarm Mitigation Multi-Level Correlation for Failure Isolation Advantage Michael Gandy and Kevin Line Lockheed Martin Aeronautics Model Legend - Condition Function Chains of Functions Indicate Functional Flows. Components Link to the Functions They Support. Sensors Link to the Functions They Monitor. Conditions Link to the Functions They Control. Component Sensor Block Diagram MBR Model

47 Four Stages of CBM/PHM Diagnostics Prognostics & RUL Maintenance Prescription Maintenance Scheduling Two Phases of Prognostics & RUL Off Line- Background Studies, RUL Analysis On Line- Perform real-time Prognostics & RUL

48 Prognostics The CBM/PHM Cycle PHM Machine Sensors Required Background Studies Machine legacy failure data Available resources RUL Mission due dates Data Pre- Processing Feature Extraction Fault Classification Prediction of Fault Evolution Prescribe Maintenance Schedule Required Maintenance Systems & Signal processing Diagnostics Prognostics Prescription Maintenance Scheduling Current fault condition

49 PHM Maintenance Prescription and Scheduling Procedure Prescription-Based Health Management System (PBHMS) Diagnostic Fault condition Stored Prescription Library Prescription Library failure modes trends side effects Rulebase expert system Fuzzy/Neural System Prescription decision tree Bayesian Dempster-Shafer Adaptive integration of new prescriptions Medical Health Prescriptions Prescription Maint. Request RUL Estimated time of failure Mission criticality and due date requirements Maintenance Requirements Planning Maint. Planning & Scheduling weight maint. Requests Computer machine planners HTN, etc. Scheduling Maintenance Priorities Mission Due Dates Guaranteed QoS Performance Priority Measures earliest mission date least slack repair time due date safety risk cost User interfaces for Decision assistance Decision Support Manufacturing MRP Priority Costs Automatically generated work orders. Maintenance plan with maint. Rankings Manufacturing On-Line Resource Dispatching Resource assignment and dispatching priority dispatching maximum % utilization minimize bottlenecks resources Dispatching opportunity convenience Prioritized Work Orders assigned to Maint. Units Generate: optimized maint. tasks (c.f. PMS cards) Communications System Scheduling & Routing

50 Prognostics- Why? I. Fault Propagation & Progression II. Time of Failure & Remaining Useful Life (RUL) Replace subsystem 0% fault failure Replace entire system RUL Estimated time of Failure (ETF) Mission due date 4% fault Fault detection threshold Replace Component Fault development trend: Progressive escalation of required maintenance N. Viswanadham Progressive Escalation Impacts the Prescription Present time Remove from service Repair time Start repair Scheduling Removal From Service and Start of Repair in terms of ETF and Mission Due Date Mission Criticality Impacts the Scheduling

51 Four Stages of CBM/PHM Diagnostics Prognostics & RUL Maintenance Prescription Maintenance Scheduling Two Phases of Prognostics & RUL Off Line- Background Studies, RUL Analysis On Line- Perform real-time Prognostics & RUL

52 Phase I- Preliminary Off-Line Studies PHM Fault Prognostics & RUL Background Studies Fault Mode Time Analysis- Identify MTTF in each fault condition Identify the best Feature Combinations to track for effective prognosis & RUL Identify Best Decision Schemes to compute the feature combinations Build Failure Time Pattern Library Deal with Mean Time to Failure in each Fault condition. ALSO require Confidence Limits

53 PROGNOSTICS Legacy Data Statistics gives MTBF, MTTF etc. Estimate Remaining Useful Life with Confidence Intervals Hazard Function- Probability of failure at current time -H. Chestnut Wearin- Early mortality t Wearout Based on legacy failure data φ(t) Fault tolerance limits Trend Analysis & Prediction- Track Feature vector trends Study φ (t) and φ(t) t Normal operating region Fault tolerance limits found by legacy data statistics

54 Stored Legacy Failure data Statistics analysis Statistical Regression Clustering Neural network classification Drive train gear tooth wear.....failure Vibration magnitude Sample of legacy statistical fault data Useful Remaing Life Vibration magnitude Sample of legacy statistical RUL data Find MTTF for given fault condition and find confidence limits

55 Dr. George Vachtsevanos OR- Physical Modeling e.g. Deterministic Crack Propagation Models Variations of available empirical and deterministic fatigue crack propagation models are based on Paris formula: da Where: dn = C ( ) n o Δ K α = instantaneous length of dominant crack Ν = running cycles C o, n = material dependent constants ΔК = range of stress intensity factor over one loading cycle

56 Andy Hess, US Naval Air Estimation of Failure Probability Density Functions Gives best estimate of RUL (conditional mean) as well as confidence limits A priori failure PDF A posteriori conditional failure PDF given no failure through present time Present time Expected remaining life tt RUL confidence limits JITP Remaining life PDF Removal From Service- Just In Time Point (JITP) avoids 95% of failures Lead-time interval Present time 5% 95% Expected remaining life t

57 Andy Hess, US Naval Air RUL PDFs as a Function of Time a priori RUL PDF RUL estimates become more accurate and precise as RUL decreases Expected failure time Current time First indication Expected RUL 95% confidence limits time

58 Fault Trend Analysis φ(t) Fault tolerance limits alarm failure Confidence limits Normal operating region Estimated feature Minimize Pr{false alarm} Pr{miss} Model-Based Predictive Methods - Mike Grimble t Kalman Filter is the optimal estimator for the conditional PDF for linear Gaussian case -gives estimate plus covariance

59 Dr. George Vachtsevanos The Confidence Prediction Neural Network (CPNN) For CPNN, each node assigns a weight (degree of confidence) for an input X and a candidate output Y i. Final output is the weighted sum of all candidate outputs. In addition to the final output, the confidence distribution of that output can be computed as Pattern layer Numerator Summation layer output Denominator Confidence distribution approximator l 2 ( Y Y) CD( X, Y) = C( X, Yi )exp[ ] (2 πσ ) l 2σ CD i= i 2 CD Input layer CPNN

60 Dr. George Vachtsevanos 6 Prognostic Results Without reinforcement learning 5 4 historical data prediction real failure time dist of prognostic failure time

61 Dr. George Vachtsevanos Prognostic Results 6 With reinforcement learning More accurate prediction

62 Prescription of Maintenance Stored Prescription Library Fault condition Decision-Making Prescription Maintenance Prescription Fault Trend?? Neural networks Fuzzy logic Expert system rulebase Bayesian Dempster-Shafer Prescription may change if fault worsens Model-Based Reasoning (MBR) for Fault Progression?

63 Prescription Library Diagnosis IF (leakage coefficient is excessive) IF (piston friction is excessive) IF (excessive bearing wear) IF(exc. piston friction) AND (exc. bearing wear) Prescription THEN (Replace hydraulic pump) THEN (Replace hydraulic pump) THEN (replace motor) THEN (replace hydraulic pump/motor assembly) Side Effects? Equipment down time Impact on related systems Mission failure Use of critical maintenance resources or parts

64 Dr. George Vachtsevanos A Maintenance Management Architecture Time-Directed Tasks Trend Data Logs Real-time Diagnostics / Prognostics and Trend Analysis Technical Doc Ref Preplanned Work Corrective Tasks Emergent Work Case Library Work Order Backlog Material Required Labor Required Work Procedures Maintenance Schedule Actions Taken Conditions Found Cost Collector Other Process Management Component (ERP) Enabling Technologies Genetic Algorithms for Optimum Maintenance Scheduling Case-Based Reasoning and Induction Cost-Benefit Analysis Studies

65 Signal Processing and Decision-Making Time domain - Moments, statistics, correlation, moving averages Frequency Domain - Discrete Fourier Transform Dynamical System Theory State Estimation- Kalman Filter System Identification- Recursive Least Squares (RLS) Statistical Techniques Regression PDF estimation Decision-Making Techniques Bayesian Dempster-Shafer Rule-Based & Expert Systems Fuzzy Logic Neural Networks Classification Clustering

66 Aircraft Nose Wheel Shimmy Dr. George Vachtsevanos Nose wheel can vibrate during landing Divergent vibration is more likely when nose gear free play is high and tire is worn Two approaches Monitor and trend free play before taxi Monitor and trend vibration on landing θ Shimmy Vibration Measurement Force Good Nose Gear Measured Free Play Landing Gear with Possible Divergent Shimmy

67 Dr. George Vachtsevanos Data Pre-Processing is OFTEN REQUIRED Task of massaging raw input data and extracting desired information noise removal signal enhancement removal of artifacts data format transformation, sampling, digitization, etc. feature extraction filtering and data compression Improving signal-to-noise ratio

68 Time Domain- Moments, Statistics, Correlation p th moment of RV x(t) with PDF f(x) is E( x p p ) = x f ( x) dx If the RV is ergodic, then its ensemble averages can be approximated by time averages. p th moment of time series x k over time interval [,N] is given by first moment is the (sample) mean value x = N N k = x k N N k = x k p second moment is the moment of inertia energy root-mean-square (RMS) value N 2 x k N k = N k = 2 x k N 2 x k N k =

69 third moment about the mean is the skew contains symmetry information N 3 ( x k x) 3 Nσ k = A measure of unbalance kurtosis is a measure of the size of the sidelobes of a distribution N 4 ( ) 4 x k x Nσ k = 3 A measure of banging

70 SECOND ORDER STATISTICS Correlation, Covariance, Convolution = + = N k n k k x x x N n R ) ( (auto)correlation = + = N k n k k x x x x x N n P ) )( ( ) ( (auto)covariance = + = N k n k k xy y x N n R ) ( Cross-correlation of two series = + = N k n k k xy y y x x N n P ) )( ( ) ( Cross-covariance = = 0 ) ( * N k k x k y n n y x discrete-time convolution for N point sequences Needed for Confidence Limits

71 Statistical Tools for Estimating the PDF Given statistical data Parzen estimator for PDF failure Drive train gear tooth wear Consistent estimator for the joint PDF is N i T i i..... ( x x ) ( x x ) ( z z ) P( x, z) =..... exp exp ( n+ ) / 2 n (2π ) σ N i= 2σ 2σ (x i,y i ) = sum of Gaussians. Conditional expected value formula Vibration magnitude Sample of legacy statistical fault data E[ z / x] = zp( x, z) dz p( x, z) dz 2 This also gives error covariance or Confidence measure yields estimate for x given z E[ z / x] N i= = N i= i T i ( x x ) ( x z exp 2 2σ i T ( x x ) ( x x exp 2 2σ i x ) i )

72 Parzen pdf Estimator- Example Legacy Historcial Failure data Gaussian pdf centered at data points Sum of Gaussians pdf SoG pdf contours

73 Discrete Fourier Transform (DFT) Given time series x(n), DFT is X ( k) = 2π Scale the frequency axis - w = ( k N N n= x( n) e j 2π ( k )( n ) / N ; k=,2, N DFT is periodic with period N )

74 Using DFT to Extract Frequency Component Information Emulation- manufacture signals with prescribed freq. components. Time signal with frequency components at 50 Hz and 20 Hz + random noise is >> t=0:0.00:0.6; >> x=sin(2*pi*50*t) + sin(2*pi*20*t); >> y=x + 2*randn(size(t)); >> plot(y(:50)) % signal w/ noise

75 dft of the first 52 samples given by >> Y=fft(y,52); >> plot(abs(y)) % mag spectrum of signal with noise Scale frequency. Sample time is T=0.00 sec. Sampling freq. is f s Therefore, scale using f = ( k ) = ( k ) N NT f s = T mag spectrum With noise PSD with noise

76 Discrete Fourier Transform- Time-varying DFT using window (using MATLAB FFT) frequency time

77 Onset of gear tooth wear 0.5 sec buffer DFT at a refreshing rate of 0.25 sec Resulting load imbalance DFT (Hz) frequency time (sec) Intermittent incipient bearing outer race fault One second buffer DFT of the speech at a refreshing rate of one second 8 DFT for CBM DFT (Hz) 50 frequency time 3 (sec)

78 Dr. George Vachtsevanos Planetary Gear Transmission McFadden s Method

79 Dr. George Vachtsevanos Effect of angular shift of the planets on the model spectrum Ideal system presents sidebands only at frequencies that are integer multiples of the number of planets By Ideal meaning that the Sample planets spectrum are of evenly ideal system spaced with zero tolerance Amplitude Fourier Coefficients at frequencies that are integer multiples of the number of planets are non-zero All other coefficients are zero First Harmonic of the Meshing Frequency Zero and non-zero phenomenon is true for any harmonic Frequency = k * fc (k:integer, fc: carrier rotation freq.)

80 Dr. George Vachtsevanos UH-60A Blackhawk Helicopter Main Transmission Planetary Carrier Fault Diagnostics

81 Frequency Domain Plot Dr. George Vachtsevanos Pattern changes in the SIDEBANDS are useful for diagnostics & prognostics Sample spectrum at Harmonic High shift of one planet (.3 deg) Small shift of one planet (. deg) Planetary gear analysis Amplitude Medium shift of one planet (.5 deg) Healthy system with tolerance of +/- 0.0 degrees in planet angles Frequency = k * fc (k: integer, fc: carrier rotation freq.)

82 Helicopter Gearbox VMEP Accelerometer Locations Dr. George Vachtsevanos VMEP Sensor Locations View of Engine Illustrations Courtesy of Keller, Johnathan, Grabill, Paul, Vibration Monitoring of a UH-60A Main Transmission Planetary Carrier Fault.

83 Dr. George Vachtsevanos Accelerometer Data Analysis UH-60A Helicopter Planetary Carrier Fault Prognosis Seeded fault test (with an initial crack of.344 in.) provides accelerometer data and crack measurements The carrier plate was stressed with a loading spectrum consisting of Ground Air Ground (GAG), P geometric vibratory, 980Hz gear vibratory, and transverse shaft bending. EDM Notch Crack Gages Strain Gages

84 Dr. George Vachtsevanos Spectrum of the TSA data TSA data in the frequency domain The scale on the x axis is the integer multiple of the shaft frequency Meshing Components clearly visible up to 7 th harmonic

85 Dr. George Vachtsevanos Spectrum Changes as Test Progresses Spectrum content around the fundamental meshing frequency Dominant Frequency Green for data at GAG #9 Blue for GAG #260 Red for GAG #639 Apparent Frequency The decrease of the dominant frequency as well as the other apparent frequencies and the increase of the rest may be a good sign of the crack growth, and may be quantified as features for fault diagnosis and prognosis purposes.

86 Dr. George Vachtsevanos Statistical Distribution of Features Amplitude Sum around the 5 th Mesh Harmonic (Raw Data) A) Test Cell, raw data (PortRing) B) On-aircraft, Asynchronous data (PortRing) red X is for faulted data.

87 Kalman Filter (Discrete Time) Stochastic Dynamical System x = Ax + Bu + Gw k + k z = Hx + v k k k k k Dynamics plus process noise Sensor outputs plus measurement noise Dynamics A, B, G, H are known. Internal state x k is unknown Find the full state x k given only a few sensor measurements z k Time-Varying KF Estimate update Kalman gain Covariance update k+ k k k k k xˆ = Axˆ + Bu + AK ( z Hxˆ ), T k k k T ( ) K = P H HP H + R P A P P H HP H R HP A GQG T T T T k+ = k k ( k + ) k +,. Steady-State KF T T T T T ( ). P = APA APH HPH + R HPA + GQG

88 MU MU MU KF Also Gives Error Covariance - a measure of accuracy and confidence in the estimate error covariance a priori error covariance P P 2 P 3 time update (TU) a posteriori error covariance P 0 P P 2 P 3 meas. update TU TU time Error covariance update timing diagram

89 F.L. Lewis Moncrief-O Donnell Endowed Chair Head, Controls & Sensors Group Automation & Robotics Research Institute (ARRI) The University of Texas at Arlington CBM- ARRI Testbed

90 h+ Wireless Sensor Networks Contact Contact Frank Frank Lewis Lewis Machinery monitoring & Condition-Based Maintenance (CBM / PHM / RUL) Personnel monitoring and secure area denial Machine Monitoring Wireless Sensor Security Personnel and Vehicle Monitoring C&C User Interface for wireless networks- Wireless Data Collection Networks Environmental Monitoring H C O O H H H C C C O O O O O O H 2O H h + H C H 2O h + C h O O + h + H H H O O e - C H O O C C C O O O O O O H C O O e - TiO 2 e - TiO 2 e - Ni Biochemical Monitoring

91 Crossbow Berkeley Motes Berkeley Crossbow Sensor Crossbow transceiver MICA mote has 5 sensors- temp, sound, light, seismic, magnetic Tiny OS operating system allows programming each mote $2000 for Dev. Kit

92 Microstrain Wireless Sensors Microstrain G-Sensor Microstrain V-Link Transceiver Microstrain Transceiver Connect to PC V-link 4 voltage inputs for any sensors that vary voltage G-link accelerometer S-link strain gauge sensor

93 User Interface, Monitoring, & Decision Assistance Wireless Access over the Internet LabVIEW Real-time Signaling & Processing CBM Database and real time Monitoring PDA access Failure Data from anytime and anywhere

94 ARRI CBM Machinery Testbed

95

96 Network Configuration Wizard On Clicking, Current/default settings for that node appear in the next screen

97 Real-Time Plots LabVIEW User Display Internet Access

98 Dr. George Vachtsevanos Wireless Aircraft Health Monitoring actual Navy application Proposed Sensor Locations Marine H53 Helicopter (Pax( River)