On Line- Perform real-time Fault Monitoring & Diagnosis. Two Phases of CBM ...
Fault Mode Analysis (FMA) - Identify Failure and Fault Modes. • Identify the best ...
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
http://ARRI.uta.edu/acs
[email protected]
John Wiley, New York, 2006
John Wiley, New York, 2003
Outline ¾ Why Intelligent Diagnostics & Prognostics? ¾ Diagnostics ¾ Intelligent Decision Making ¾ Prognostics ¾ Condition-Based Maintenance ¾ Signal Processing ¾ Machinery Monitoring using Wireless Sensor Networks
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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?
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
Old Paradigm- open loop, no feedback of machine condition Two Extremes of Manpower & Resource Waste Run-to-Failure Preventive Maintenance No maintenance Periodic, whether needed or not
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
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!
CBM+: Maintenance-Centric Logistics Support for the Future
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
www.MIMOSA.org Machine User Group- CBM Data
Condition Monitoring and Diagnostics of Machines
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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
The CBM/PHM Cycle Select Sensors! Machine Sensors
Data
Required Background Studies Identify important features
Available resources RUL Mission due dates
Fault Mode Analysis
Machine legacy failure data
PreProcessing
Feature Extraction
Systems & Signal processing
CBM
Fault Classification
Diagnostics
Prediction of Fault Evolution
Prognostics
PHM
Schedule Required Maintenance
Maintenance Scheduling
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
Diagnostics Exception
Fault
• Fault (Failure) Detection • Fault (Failure) Isolation • Fault (Failure) Identification
Failure
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
Fault Mode Analysis
Why Motors Fail? z Bearing Failures: – Root cause of ~ 50%Motor Failures – Effect: Motor burn out – Sources: Improper Lubrication, Shaft Voltages, Excessive Loadings z Excessive Vibrations: – Effect: bearing failures, metal fatigue of parts and windings – Sources: Usually caused by improper balance of rotating part z Electrical Problems: – Effect: Higher than normal current, overheating – Sources: Low Voltages, Unbalanced 3-Phase Voltages z Mechanical Problems: – Effect: Bearing failures, overheating – Sources: Excessive Load and Load Fluctuations result in more current z Maintenance issues: – Sources: Inadequate regular maintenance, lack of preventive maintenance, lack of Root Cause Analysis
Fault Mode Analysis
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Ex. - Navy Centrifugal Chiller Failure Modes •Condenser Tube Fouling •Condenser Water Control Valve Failure •Tube Leakage •Decreased Sea Water Flow
•SW in/out temp. •SW flow •Cond. press. •Cond. PD press. •Cond. liquid out temp.
Compressor
Pre-rotation Vane
•Compressor Stall & Surge •Shaft Seal Leakage •Oil Level High/Low •Aux. Pump Fail •Oil Cooler Fail •PRV/VGD Mechanical Failure •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
Condenser
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
Fault Mode:
Refrigerant Charge Low
Symptoms:
1. 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:
1. Evaporator Liquid Temperature (ELT) 2. Evaporator Suction Pressure (ESP) 3. Chilled Water Discharge Temperature (CWDT)
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Failure Modes and Effects Criticality Analysis Failure Modes and Effects Criticality Analysis
Large Leak Detected (0.9) Not ok (0.1)
Ok (0.9) Check Pressure Meter
New systematic approach based on fuzzy Petri networks and efficient search techniques to define failure effect – root cause relationships
Large Leak While Meter Reading is Correct (0.81) Ok (0.9)
Not ok (0.1) Check Vacuum Pump
(0.81) Ok (0.8)
Not ok (0.2) Check for Overheating
Ok (0.1)
Not ok (0.9) Check for Dirty Fluid
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Helicopter Fault Tree
Helicopter Failure
Motor Failures
Actuator Failures
Power Failures
Main Rotor Failures
Sensor Failures
Tail Rotor Failures
Computer System Failures
Motor Fault Tree Motor Failure
Gear Box Failure
Local Power Lines Fail
Gears Slip
Internal Motor Failure
Wear On Gears
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
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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
Diagnostics • Model-Based Methods • Non-Model-Based – Data-Based • Statistical Analysis Methods
V. Skormin, 1994 SUNY Binghamton
Fault Mode Analysis
Fault Modes of an Electro-Hydraulic Flight Actuator bearing control surface
Fault Modes Control surface loss Excessive bearing friction
hydraulic cylinder pump
Hydraulic system leakage Air in hydraulic system Excessive cylinder friction Malfunction of pump control valve Rotor mechanical damage Motor magnetism loss
motor
power amplifier
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 1- Dynamical System Diagnostic Models motor dynamics
ω (s)
1 = T ( s) Js + B
pump/piston dynamics
X (s) 1 = F (s) (M p s + B p )s
actuator system dynamics
P( s) 1 = 2 R( s) ( A ) s + L K
Physical parameters are J, B, Mp, Bp, K, L
V. Skormin, 1994 SUNY Binghamton
V. Skormin, 1994 SUNY Binghamton
Select Feature Vector
Relate physical parameters J, B, Mp, Bp, 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 Condition
Fault Mode
IF (leakage coeff. L is large)
THEN (fault is hydraulic system leakage)
IF (motor damping coeff. B is large) AND (piston damping coeff. Bp is large)
THEN (fault is excess cylinder friction)
IF (actuator stiffness K is small) AND (piston damping coeff. Bp is small)
THEN (fault is air in hydraulic system)
Etc.
Etc.
Therefore, select the physical parameters as the feature vector
φ (t ) = [ J B M p B p K L]
T
V. Skormin, 1994 SUNY Binghamton
Select Sensors for the Best Outputs to Measure Cannot directly measure the feature vector
φ (t ) = [ J B M p B p K L]
T
Can measure the inputs and outputs of the dynamical blocks, e.g. armature current I(t) pressure difference P(t)
D T (t ) = CI (t ) − P (t ) 2π
ω(s)
1 = T (s) Js + B
motor speed
ω(t)
Virtual Sensors = physical sensors + signal processing
signals from machine
sensors
Therefore, use system identification techniques to estimate the features
DSP
Fault ID features
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 Condition
Fault Mode
IF (base mount vibration energy is large)
THEN (fault is unbalance)
IF (shaft vibration second mode is large) AND (motor vibration RMS value is large)
THEN (fault is gear tooth wear)
IF (third harmonic of shaft speed is present) THEN (fault is worn outer ball bearing) AND (kurtosis of load vibration is large) Etc.
Etc.
Therefore, include vibration moments and frequencies in the feature vector
φ (t ) = [ time signals
… frequency signals ]T
Select Fault ID Feature Vector
Drive train gear tooth wear
Method 3- Statistical Regression Techniques Fault 3 Fault 2
Clustering techniques Neural networks Statistical
Fault 1 outliers
Vibration magnitude Pearson’s correlation Nonlinear correlation techniques Multivariable regression
Fault Pattern Library Condition
Fault Mode
IF (leakage coeff. L is large)
THEN (fault is hydraulic system leakage)
IF (motor damping coeff. B is large) AND (piston damping coeff. Bp is large)
THEN (fault is excess cylinder friction)
IF (actuator stiffness K is small) AND (piston damping coeff. Bp is small)
THEN (fault is air in hydraulic system)
Etc.
Etc. Condition
Fault Mode
IF (base mount vibration energy is large)
THEN (fault is unbalance)
IF (shaft vibration second mode is large) AND (motor vibration RMS value is large)
THEN (fault is gear tooth wear)
IF (third harmonic of shaft speed is present) THEN (fault is worn outer ball bearing) AND (kurtosis of load vibration is large) Etc.
Etc.
Phase II- On Line Fault Monitoring and Diagnostics Stored Legacy Failure data Statistics analysis
CBM Fault DIAGNOSTICS Procedure Systems, DSP & Data Fusion
Sensing
Fault Feature Extraction
Reasoning & Diagnosis
Stored Fault Pattern Library
Inject probe test signals for refined diagnosis Sensor outputs machines
Dig. Signal Processing System IdentificationKalman filter NN system ID RLS, LSE Sensor Fusion
Math models
x = f ( x, u,π ) y = h(x, u,π ) Physics of failure System dynamics Physical params.
π
Model-Based Diagnosis
Vibration Moments, FFT
πˆ
Feature vectors Feature VectorsSufficient statistics
Physical Parameter estimates & Aero. coeff. estimates
φ(t)
Fault Classification Feature patterns for faults Decision fusion could use: Fuzzy Logic Expert Systems NN classifier
Identify Faults/ Failures
yes
Inform pilot
yes More info needed?
Serious? no
Request Maintenance
Feature fusion
Feature extraction determine inputs for Fault Classification
Inform pilot
Set Decision Thresholds Manuf. variability data Usage variability Mission history Minimize Pr{false alarm} Baseline perf. requirements
Fault Classification Stored Fault Pattern Library
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!
Decision-Making P (δ / π i ) P (π i ) Bayes Probability P (π i / δ ) = ∑ P(δ / π i ) P(π i ) i
Dempster-Shafer Rules of Evidence
Bel (π i ) =
Expert & Rule-Based systems
∑∏ m
j
(S j )
∩ S j =π i 1 − ∑∏ m j ( S j ) ∩ S j =0
IF (BM is negative medium) and (LC is negative small)
THEN (fault is air contamination)
IF (BM is positive) and (LC is normal)
THEN (fault is water contamination)
IF (BM is normal) and (LC is positive medium)
THEN (fault is excessive leakage)
n
N
∑ z ∏μ i
Fuzzy Logic
f ( x) =
i =1 N
(x j )
j =1 n
∑∏ μ i =1 j =1
Model-Based Reasoning
ij
ij
(x j )
Bayesian Classifier Performance
spec normal
FNspec
False negative
abnormal
FN
decision criterion
FP
False positive Prob. of False Alarm
Dempster-Shafer • If m1 and m2 are two pieces of Evidence, the combined Evidence is given by
∑ m ( A )m ( B )
m1 ⊗ m2 (C ) =
Ai ∩ B j =C
1−
1
2
i
j
∑ m ( A )m ( B )
Ai ∩ B j =∅
1
i
2
j
Conflict between two pieces of evidence
• Based on this, can compute:
In Bayes, Bel= Pl
m( D ) • Belief – C is definitely true. Bel(C)= D∑ ⊂C
• Plausibility – C may be true.
Pl(C)= D∩∑C ≠m0 ( D)
Dempster-Shafer Example Suppose there are 100 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 m1 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. m1(A) 0.3
m1(B) 0.2
m1(θ) 0.5
m2(A) 0.2
0.06
0.04 (0 intersection) CONFLICT
0.1
m2(AB) 0.2
0.06
0.04
0.1
m2(θ) 0.6
0.18
0.12
0.3
Using the formulas above:
Bel(A)=m12(A)=0.42. (42 A cars) Bel(B)=m12(B)=0.17. (17 B cars) Pl(A)= m12(A)+m12(AB)+m12(θ)=0.83. (83 A cars) Pl(B)= m12(B)+m12(AB)+m12(θ)=0.58. (58 B cars)
So there are between 42 and 83 cars of type A between 17 and 58 cars of type B
.
Drive train gear tooth wear
two one
Fault conditions
three
. .. . .... . . .. . ..... ... .. . ... . ............. .. . . . . .... . .. .
one or two
one
small
Unifies expert systems statistical neural network approaches
large medium Sideband component I2
Fuzzy Logic Fault Classification
two
incip.
one
one or two
none
incip.
one
Sideband component I1
small
medium
large
Fig 1 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
Vibration magnitude
low
med
severe
Fig 5 Clustering of statistical fault data
2-D FL system c.f. neural network
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
Neural Networks 2-layer NN
x1
y = W σ (V x) T
VT
σ(.)
T
y = σ (V x) T
1
WT
2
x2 σ(.)
3
xn
ym L
inputs
σ(.)
hidden layer
Training
y1 y2
RVFL NN has V= random 1-layer NN has W= I
σ(.)
Two-Layer Neural Network
1-layer – Gradient Descent V (k + 1) = V (k ) + ηe T X Where X= input pattern vectors Y= output target vectors e = Y − y (k ) = training error Multilayer- backpropagation (Paul Werbos)
outputs
Neural Networks - Classification Classify 8 points into two groups
Group 1: o Group 2: x Group 3: + Group 4: #
(1,1), (1,2) (2,-1), (2, -2) (-1,2), (-2,1) (-1,-1), (-2,-2) 3
I. Training
1
o o
+
2
+
0
Represent the 4 groups as 00, 01, 10, 11 Then, the input pattern vector and target vector are 2 − 1 − 2 − 1 − 2⎤ ⎡1 1 2 X =⎢ ⎥ ⎣1 2 − 1 − 2 2 1 − 1 − 2 ⎦
⎡0 0 0 0 1 1 1 1⎤ Y =⎢ ⎥ 0 0 1 1 0 0 1 1 ⎣ ⎦
#
-1
-2
-3 -3
x x
# -2
-1
0
1
2
3
MATLAB Code R=[-2 2;-2 2]; % define 2-D input space netp=newp(R,2); % define 2-neuron NN p1=[1 1]'; p2=[1 2]'; p3=[2 -1]'; p4=[2 -2]'; p5=[-1 2]'; p6=[-2 1]'; p7=[-1 -1]'; p8=[-2 -2]‘; t1=[0 0]'; t2=[0 0]'; t3=[0 1]'; t4=[0 1]'; t5=[1 0]'; t6=[1 0]'; t7=[1 1]'; t8=[1 1]‘; P=[p1 p2 p3 p4 p5 p6 p7 p8]; T=[t1 t2 t3 t4 t5 t6 t7 t8]; netp.trainParam.epochs = 20; % train for max 20 epochs netp = train(netp,P,T);
result
⎛ ⎡− 3 − 1 ⎤ ⎡− 1⎤ ⎞ y = σ ⎜⎜ ⎢ x + ⎢ ⎥ ⎟⎟ ⎥ ⎣ 0 ⎦⎠ ⎝ ⎣ 1 − 2⎦ T
Defines 2 lines in (x1, x2) plane
II. Classification (simulation) All points are classified into one of the 4 regions Y1=sim(netp,P1)
Result after training
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 1;0 1],8,.1); % train NN with Kohonen learning net.trainParam.epochs = 7; net = train(net,P); w = net.IW{1}; %plot plot(P(1,:),P(2,:),'+r'); xlabel('p(1)'); ylabel('p(2)'); hold on; circles = plot(w(:,1),w(:,2),'ob');
II. Classification (simulation) p = [0; 0.2]; a = sim(net,p)
Activates neuron number 1
Model-Based Reasoning MBR
Possible failures depend on current operating mode
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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 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.
Block Diagram
MBR Model
Michael Gandy and Kevin Line Lockheed Martin Aeronautics
Model Model Legend Legend -Condition
Function Sensor
Component
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
Prognostics PHM
The CBM/PHM Cycle
Required Background Studies Machine Sensors
Data
Available resources RUL Mission due dates Machine legacy failure data
PreProcessing
Feature Extraction
Systems & Signal processing
Fault Classification
Diagnostics
Prediction of Fault Evolution
Prescribe Maintenance
Prognostics Prescription
Current fault condition
Schedule Required Maintenance
Maintenance Scheduling
PHM Maintenance Prescription and Scheduling Procedure Prescription-Based Health Management System (PBHMS) Stored Prescription Library
User interfaces for Decision assistance Decision Support
Medical Health Prescriptions Prescription Diagnostic Prescription Library Fault failure modes condition trends side effects Rulebase expert system Fuzzy/Neural System Prescription decision tree Bayesian Dempster-Shafer
Adaptive integration of new prescriptions
Maint. Request
Manufacturing On-Line Resource Dispatching
Manufacturing MRP
Dispatching
Maintenance Requirements Planning
Resource assignment
Maint. Planning & Scheduling weight maint. Requests Computer machine planners HTN, etc.
and dispatching priority dispatching maximum % utilization minimize bottlenecks
Scheduling
Automatically generated work orders. Maintenance plan with maint. Rankings
Maintenance Priorities Mission Due Dates Guaranteed QoS
resources
RUL Performance Priority Measures Estimated time earliest mission date least slack repair time of failure due date
Mission criticality and due date requirements
safety risk cost
opportunity convenience
Prioritized Work Orders assigned to Maint. Units
Generate: optimized maint. tasks (c.f. PMS cards)
Priority Costs Communications System
Scheduling & Routing
Prognostics- Why? I. Fault Propagation & Progression Replace subsystem
II. Time of Failure & Remaining Useful Life (RUL)
Replace entire system failure
10% fault 4% fault
RUL
Estimated time of Failure (ETF)
Replace Component
Repair time Present time
Fault detection threshold
Fault development trend: Progressive escalation of required maintenance N. Viswanadham
Progressive Escalation
Impacts the Prescription
Mission due date
Remove from service
Start repair
Scheduling Removal From Service and Start of Repair in terms of ETF and Mission Due Date
Mission Criticality
Impacts the Scheduling
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
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
PROGNOSTICS Legacy Data Statistics gives MTBF, MTTF etc. Estimate Remaining Useful Life with Confidence Intervals Fault tolerance limits
φ(t) WearinEarly mortality
t
Normal operating region
Wearout
Hazard FunctionProbability of failure at current time - H. Chestnut
Based on legacy failure data
t
Trend Analysis & PredictionTrack Feature vector trends Study φ(t) and φ(t) Fault tolerance limits found by legacy data statistics
Vibration magnitude Sample of legacy statistical fault data
Useful Remaing Life
failure
. . .. .. . . .. . ... .. . . . . . ..... ... . . . . . .. .... ..... .. ...... ... . . . ........ . . . .. .. . ...... . . . .. . . . . . . ... . . ..... . . .. . .. . .. . . . . .. . . .
Statistical Regression Clustering Neural network classification . . . . . ... .. . . ... . . . ... ... .. . . . .... . . ..... . . . . . . .. . .. .. . .. . . .
Drive train gear tooth wear
Stored Legacy Failure data Statistics analysis
0 Vibration magnitude Sample of legacy statistical RUL data
Find MTTF for given fault condition and find confidence limits
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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 = C o (Δ K )n dN
Where: α = instantaneous length of dominant crack Ν = running cycles Co, n = material dependent constants ΔК = range of stress intensity factor over one cycle
loading
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
tt RUL confidence limits
Present time Expected remaining life
Remaining life PDF JITP Lead-time interval
Removal From ServiceJust In Time Point (JITP) avoids 95% of failures
5%
95% t
Present time
Expected remaining life
Andy Hess, US Naval Air
RUL PDFs as a Function of Time RUL estimates become more accurate and precise as RUL decreases
a priori RUL PDF
Expected failure time Expected RUL
Cu
st Fir
rr en t
time tim
e
95% confidence limits
ind n tio ica
Fault Trend Analysis
φ(t)
Confidence limits
Fault tolerance limits
failure
alarm Normal operating region
Estimated feature t
Minimize Pr{false alarm} Pr{miss}
Model-Based Predictive Methods - Mike Grimble
Kalman Filter is the optimal estimator for the conditional PDF for linear Gaussian case -gives estimate plus covariance
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
The Confidence Prediction Neural Network (CPNN) •
• •
For CPNN, each node assigns a weight (degree of confidence) for an input X and a candidate output Yi. 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 (Y − Yi ) 2 1 1 l CD ( X , Y ) = ⋅ ∑ C ( X , Yi ) exp[− ] 2 (2π )σ CD l i =1 2σ CD
output Numerator
Denominator Confidence distribution approximator
Summation layer
Pattern layer
Input layer
CPNN
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Prognostic Results Without reinforcement learning
6
5
4
historical data
prediction
3 real failure time
2
0.9 0.8 0.7 0.6 0.5 0.4
1
0.3 0.2 0.1 0
95
96
97
98
99
100
101
dist of prognostic failure time
0
0
20
40
60
80
100
120
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Prognostic Results With reinforcement learning
6
5
4
More accurate prediction
3
2
0.9 0.8 0.7 0.6 0.5
1
0.4 0.3 0.2 0.1 0
0
0
20
40
60
80
96
100
97
98
99
100
120
101
Prescription of Maintenance Stored Prescription Library
Fault condition
Fault Trend??
Decision-Making Prescription
Maintenance Prescription
Neural networks Fuzzy logic Expert system rulebase Bayesian Dempster-Shafer
Prescription may change if fault worsens Model-Based Reasoning (MBR) for Fault Progression?
Prescription Library Diagnosis
Prescription
IF (leakage coefficient is excessive)
THEN (Replace hydraulic pump)
IF (piston friction is excessive)
THEN (Replace hydraulic pump)
IF (excessive bearing wear)
THEN (replace motor)
IF(exc. piston friction) AND (exc. bearing wear)
THEN (replace hydraulic pump/motor assembly)
Side Effects? Equipment down time Impact on related systems Mission failure Use of critical maintenance resources or parts
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
A Maintenance Management Architecture Time-Directed Tasks •• Trend Trend Data Data •• Logs Logs
Real-time Real-time Diagnostics Diagnostics // Prognostics Prognostics and and Trend Trend Analysis Analysis
•• Technical Technical Doc Doc Ref Ref •• Preplanned Work Preplanned Work Corrective Tasks •• Emergent Emergent Work Work
Case Case Library Library
Work Work Order Order Backlog Backlog •• Material Material Required Required •• Labor Required Labor Required •• Work Work Procedures Procedures
Maintenance Schedule
•• Actions Actions Taken Taken •• Conditions Conditions Found Found •• Cost Collector Cost Collector
Enabling Technologies Genetic Algorithms for Optimum Maintenance Scheduling Case-Based Reasoning and Induction Cost-Benefit Analysis Studies
Other Other Process Process Management Management Component Component (ERP) (ERP)
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
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Aircraft Nose Wheel Shimmy • 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 Shimmy Vibration Measurement θ
Good Nose Gear Force
Measured Free Play
Landing Gear with Possible Divergent Shimmy
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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
Time Domain- Moments, Statistics, Correlation pth moment of RV x(t) with PDF f(x) is
E ( x p ) = ∫ x p f ( x ) dx
If the RV is ergodic, then its ensemble averages can be approximated by time averages.
1 pth moment of time series xk over time interval [1,N] is given by N first moment is the (sample) mean value
second moment is the moment of inertia
1 x= N
1 N
root-mean-square (RMS) value
∑x k =1
N
∑ xk k =1
N
energy
N
∑ xk
2
k =1
1 N
N
∑x k =1
2 k
2
k
N
∑ xk k =1
p
third moment about the mean is the skew – contains symmetry information 1 Nσ
N
3
∑ (x k =1
k
− x)3
A measure of unbalance
kurtosis is a measure of the size of the sidelobes of a distribution 1 Nσ
N
4
∑ (x k =1
k
− x)4 − 3
A measure of ‘banging’
SECOND ORDER STATISTICS Correlation, Covariance, Convolution (auto)correlation (auto)covariance
1 R x ( n) = N 1 Px (n) = N
N
∑ (x k =1
k
Cross-covariance
N
∑ (x k =1
k
∑x k =1
k
xk +n
− x )( x k + n − x )
1 Cross-correlation of two series R xy (n) = N 1 Pxy (n) = N
N
N
∑x k =1
k
y k +n
− x )( y k + n − y )
N −1
discrete-time convolution for N point sequences x * y (n) = ∑ x k y n − k k =0
Needed for Confidence Limits
Statistical Tools for Estimating the PDF Drive train gear tooth wear
Given statistical data failure
Parzen estimator for PDF
. . .. Consistent estimator for the joint PDF is . .. ... . . . .. . .. . . .. ..... ... . . . . .. ⎡ (x − xi ) T (x − xi ) ⎤ ⎡ (z − zi )2 ⎤ 1 1 N .... ..... .. ...... ... . P( x, z ) = exp ⎢− ∑ . . ........ . ⎥ exp ⎢− ⎥ ( n +1) / 2 2 2 n +1 . N ( 2 π ) σ 2 σ 2 σ . . . . . = 1 i . . ⎣ ⎦ ⎣ ⎦ . . . . ... ... .. . . . .... . . ..... . . = sum of Gaussians (xi,yi) .. . .. . .. .. . . .. . . Conditional expected value formula .
Vibration magnitude Sample of legacy statistical fault data
zp( x, z ) dz ∫ E[ z / x] = ∫ p( x, z ) dz yields estimate for x given z ⎡ (x − xi ) T (x − xi ) ⎤ z exp ⎢− ∑ ⎥ 2σ 2 i =1 ⎣ ⎦ E[ z / x] = N i T i ⎡ (x − x ) (x − x ) ⎤ exp ∑ ⎢− ⎥ 2σ 2 i =1 ⎣ ⎦ N
i
This also gives error covariance or Confidence measure
Parzen pdf Estimator- Example
Legacy Historcial Failure data
Sum of Gaussians pdf
Gaussian pdf centered at data points
SoG pdf contours
Discrete Fourier Transform (DFT) N
Given time series x(n), DFT is
X (k ) = ∑ x(n) e − j 2π ( k −1)( n −1) / N
; k= 1,2,…N
n =1
DFT is periodic with period N Scale the frequency axis -
w=
2π (k − 1) N
Using DFT to Extract Frequency Component Information Emulation- manufacture signals with prescribed freq. components. Time signal with frequency components at 50 Hz and 120 Hz + random noise is >> t=0:0.001:0.6; >> x=sin(2*pi*50*t) + sin(2*pi*120*t); >> y=x + 2*randn(size(t));
>> plot(y(1:50)) % signal w/ noise
dft of the first 512 samples given by >> Y=fft(y,512); >> plot(abs(Y)) % mag spectrum of signal with noise
Scale frequency. Sample time is T=0.001 sec. Sampling freq. is f s = Therefore, scale using
f =
fs 1 (k − 1) = (k − 1) N NT
mag spectrum With noise PSD with noise
1 T
Discrete Fourier TransformTime-varying DFT using window (using MATLAB FFT)
frequen
tim cy
e
0.5 sec buffer DFT at a refreshing rate of 0.25 sec
Resulting load imbalance
Onset of gear tooth wear 6
5
4
Intermittent incipient bearing outer race fault
1000
tim e
3
2 0 500
450
400
350
1 300
250
(sec) 200
150
(Hz)
100
50
0
One second buffer DFT of the speech at a refreshing rate of one second
0
frequency 8
7
DFT for CBM
6
5 1000 4
500 0 500
3 450
400
350
300
2 250
200
150
freque(Hz) ncy
100
50
1 0
tim e
DFT
DFT
2000
(sec)
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Planetary Gear Transmission
McFadden’s Method
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
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 spectrum ideal system By “Ideal” meaning that theSample planets areofevenly spaced with zero tolerance 1.2
1
Fourier Coefficients at frequencies that are integer multiples of the number of planets are non-zero
0.8 Amplitude
•
0.6
First Harmonic of the Meshing Frequency Zero and non-zero phenomenon is true for any harmonic
All other coefficients are zero
0.4
0.2
0
210
215
220 225 230 235 240 Frequency = k * fc (k:integer, fc: carrier rotation freq.)
245
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
UH-60A Blackhawk Helicopter Main Transmission Planetary Carrier Fault Diagnostics
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Frequency Domain Plot Pattern changes in the SIDEBANDS are useful for diagnostics & prognostics
Sample spectrum at Harmonic 1 0.35 High shift of one planet (.3 deg)
0.3
Planetary gear analysis
Amplitude
0.25 0.2
Medium shift of one planet (.15 deg)
Small shift of one planet (.1 deg)
Healthy system with tolerance of +/- 0.01 degreesin planet angles
0.15 0.1 0.05
210
215
220 225 230 235 240 Frequency = k * fc (k: integer, fc: carrier rotation freq.)
245
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Helicopter Gearbox VMEP Accelerometer Locations
VMEP Sensor Locations
View of Engine
Illustrations Courtesy of Keller, Johnathan, Grabill, Paul, “Vibration Monitoring of a UH-60A Main Transmission Planetary Carrier Fault.”
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Accelerometer Data Analysis UH-60A Helicopter Planetary Carrier Fault Prognosis Seeded fault test (with an initial crack of 1.344 in.) provides accelerometer data and crack measurements The carrier plate was stressed with a loading spectrum consisting of Ground Air Ground (GAG), 1P geometric vibratory, 980Hz gear vibratory, and transverse shaft bending.
EDM Notch
Crack Gages
Strain Gages
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Spectrum of the TSA data TSA data in the frequency domain 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
200
400
600
800
1000 1200 1400 1600 1800 2000
• The scale on the x axis is the integer multiple of the shaft frequency • Meshing Components clearly visible up to 7th harmonic
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Spectrum Changes as Test Progresses Spectrum content around the fundamental meshing frequency 2.5
Dominant Frequency
Green for data at GAG #9 Blue for GAG #260 Red for GAG #639
2
1.5
1
Apparent Frequency
0.5
0 215
220
225
230
235
240
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.
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Statistical Distribution of Features Amplitude Sum around the 5th Mesh Harmonic (Raw Data)
A) Test Cell, raw data (PortRing)
red X is for faulted data.
B) On-aircraft, Asynchronous data (PortRing)
Kalman Filter (Discrete Time) Stochastic Dynamical System
x k +1 = Ax k + Bu k + Gwk z k = Hx k + v k
Dynamics plus process noise Sensor outputs plus measurement noise
Dynamics A, B, G, H are known.
Internal state xk is unknown
Find the full state xk given only a few sensor measurements zk Time-Varying KF Estimate update Kalman gain Covariance update
xˆk−+1 = Axˆk− + Buk + AK k ( z k − Hxˆk− ), −1
K k = Pk−H T ( HPk−H T + R ) , −1 Pk−+1 = A ⎢⎡ Pk− − Pk−H T ( HPk−H T + R ) HPk− ⎤⎥ AT + GQGT . ⎣ ⎦
Steady-State KF −1
P = APAT − APH T ( HPH T + R )
HPAT + GQGT .
KF Also Gives Error Covariance - a measure of accuracy and confidence in the estimate
error covariance a priori error covariance
1
2
3
MU
0
TU
P3
MU
P2
TU
P1
ate
meas. update MU
P3
P0
eu pd
a posteriori error covariance
P2
ti m
(T U)
P1
Error covariance update timing diagram
time
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
http://ARRI.uta.edu/acs
[email protected]
Wireless Sensor Networks
Contact ContactFrank FrankLewis Lewis
[email protected] [email protected] http://arri.uta.edu/acs http://arri.uta.edu/acs
• Machinery monitoring & Condition-Based Maintenance (CBM / PHM / RUL) • Personnel monitoring and secure area denial Security Personnel and Vehicle Monitoring
Machine Monitoring
C&C User Interface for wireless networks-
Wireless Sensor Wireless Data Collection Networks
Environmental Monitoring H 2O
H
O
H
H
C
C
C
O
O
O
O
H
h+
C O H
O
H
H
h+
eO
C
C
C O
O
H
H
H
C
C
C
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TiO2
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H2 O
h+ h+
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e-
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Biochemical Monitoring
O
Crossbow Berkeley Motes
http://www.xbow.com/
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
Microstrain Wireless Sensors
http://www.microstrain.com/index.cfm
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
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
ARRI CBM Machinery Testbed
Network Configuration Wizard…
On Clicking, Current/default settings for that node appear in the next screen
Real-Time Plots – LabVIEW User Display Internet Access
Dr. George Vachtsevanos http://icsl.gatech.edu/icsl
Wireless Aircraft Health Monitoring Æ actual Navy application
Proposed Sensor Locations
Marine H53 Helicopter (Pax River)