intelligent fault diagnosis & prognosis - uta prog 08.pdf · 2017-12-14 · • model-based...
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F.L. LewisAutomation & Robotics Research Institute (ARRI)
The University of Texas at Arlington
Intelligent Fault Diagnosis & Prognosis
Organized and invited by
John GanMing Mao Wong
Automation & Robotics Research Institute (ARRI)The University of Texas at Arlington
F.L. Lewis, Fellow IEEE, Fellow IFAC, Fellow UK InstMCMoncrief-O’Donnell Endowed Chair
Head, Controls & Sensors Group
http://ARRI.uta.edu/[email protected]
Intelligent Fault Diagnosis & Prognosis
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
ProfessorSystems and Controls, and Bioengineering
Phone: 404.894.6252 Fax: 404.894.7583 Office: VL E392
Email [email protected] Control Systems Laboratory
Great Minds Think Differently
John Wiley, New York, 2006 John Wiley, New York, 2003
New Business Models for Machinery Maintenance
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
• Internet-Based E-Maintenance• Integrate Internet with Machine On-Board Diagnostics• Centralized Service Scheduling and Dispatching• Reduced Service Costs
Subcontracted Maintenance Service Providers MSP provides and maintains the wireless sensor network MSP monitors equipment, schedules & provides maintenance Like current Security Systems- Brinks, etc.
Dr. Jay LeeUniv Cincinnati
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 resourcesDo not interfere with machine usage requirements
Allow planning for maintenance costsNo unexpected last-minute costs!
Condition-Based Maintenance (CBM)Prognostics & Health Management (PHM)
CBM+: Maintenance-CentricLogistics Support for the Future
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
www.MIMOSA.org
www.MIMOSA.org
Machine User Group- CBM Data
Condition Monitoring and Diagnostics of Machines
The CBM/PHM Cycle
MachineSensors
Pre-Processing
FeatureExtraction
FaultClassification
Predictionof Fault
EvolutionData
ScheduleRequired
Maintenance
Systems &Signal processing
Diagnostics PrognosticsMaintenanceScheduling
Identify importantfeatures
Fault Mode Analysis
Machine legacy failure data
Available resourcesRULMission due dates
Required Background Studies
PHM CBM
SelectSensors!
Systems Approach to Intelligent Diagnosis & Prognosis
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Off Line- Background Studies, Fault Mode Analysis On Line- Perform real-time Fault Monitoring & Diagnosis
Two Phases of CBM Diagnostics
Three Stages of CBM/PHM
Diagnostics Prognostics Maintenance Scheduling
Diagnostics
• Fault (Failure) Detection
• Fault (Failure) Isolation
• Fault (Failure) Identification
Exception Fault Failure
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 FAULTSNeed to identify Faults before they become Failures
Phase I- Preliminary Off Line Studies
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
Fault Mode AnalysisDr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Compressor Pre-rotation Vane
Condenser
Evaporator
•Compressor Stall & Surge•Shaft Seal Leakage•Oil Level High/Low•Aux. Pump Fail•Oil Cooler Fail•PRV/VGD Mechanical Failure
•Condenser Tube Fouling•Condenser Water Control Valve Failure•Tube Leakage•Decreased Sea Water Flow
•Target Flow Meter Failure•Decreased Chilled Water Flow•Evaporator Tube Freezing
•Non Condensable Gas in Refrigerant•Contaminated Refrigerant•Refrigerant Charge High•Refrigerant Charge Low
•SW in/out temp.•SW flow•Cond. press.•Cond. PD press.•Cond. liquid out temp.
•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
•Liquid line temp.•(Refrigerant weight)
•CW in/out temp./flow•Eva. temp./press.•Eva. PD press.
Ex. - Navy Centrifugal Chiller Failure Modes
Fault Mode AnalysisDr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
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 Vachtsevanoshttp://icsl.gatech.edu/icsl
Failure Modes and Effects Criticality Analysis
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
Large LeakDetected (0.9)
Ok (0.9)Not ok (0.1)
CheckPressure Meter
CheckVacuum Pump
Check forOverheating
Check forDirty Fluid
(0.81)
Ok (0.9)
Ok (0.8)
Ok (0.1)
Not ok (0.1)
Not ok (0.2)
Not ok (0.9)
Large Leak While Meter Readingis Correct (0.81)
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Helicopter Fault Tree
HelicopterFailure
MotorFailures
ActuatorFailures
PowerFailures
SensorFailures
Computer SystemFailures
Main RotorFailures
Tail RotorFailures
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Motor Fault Tree
MotorFailure
Gear BoxFailure
InternalMotorFailure
LocalPower Lines
Fail
GearsSlip
WearOn
Gears
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Sensor Selection
• Existing OEM sensors
• Used e.g. for Control
• Add extra DSP – Virtual Sensors
• Add additional sensors for CBM/PHM
Feature Selection
• What to measure to get information about the fault?
Example- Jay Lee, Unic CincinnatiXerox machine- paper jam sensorUse Door open switch !!
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
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Diagnostics
• Model-Based Methods
• Non-Model-Based – Data-Based
• Statistical Analysis Methods
Fault Modes of an Electro-Hydraulic Flight Actuator
V. Skormin, 1994SUNY Binghamton
bearing
control surface
hydrauliccylinder
pump
poweramplifier
Fault Modes
Control surface lossExcessive bearing friction
Hydraulic system leakageAir in hydraulic systemExcessive cylinder frictionMalfunction of pump control valve
Rotor mechanical damageMotor magnetism loss
motor
Fault Mode Analysis
Use Physics of Failure and Failure Models to select failure features to include in feature vectors
Select Fault ID Feature Vector
Method 1- Dynamical System Diagnostic Models
The Fault Feature Vector is a sufficient statistic for identifying existing fault modes and conditions
BJssT
s
1
)(
)(motor dynamics
sBsMsF
sX
pp )(
1
)(
)(
pump/piston dynamics
LsKAsR
sP
)(
1
)(
)(2
actuator system dynamics
Physical parameters are J, B, Mp, Bp, K, L
V. Skormin, 1994SUNY Binghamton
Select Feature VectorRelate 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 vectorT
pp LKBMBJt ][)(
V. Skormin, 1994SUNY Binghamton
Select Sensors for the Best Outputs to Measure
V. Skormin, 1994SUNY Binghamton
Tpp LKBMBJt ][)(
Cannot directly measure the feature vector
Can measure the inputs and outputs of the dynamical blocks, e.g.
BJssT
s
1
)(
)()(
2)()( tP
DtCItT
(t)
motor speed
armaturecurrent I(t)
pressuredifference P(t)
Therefore, use system identification techniques to estimate the features
Virtual Sensors = physical sensors + signal processing se
nso
rs
DSPsignals from machine
Fault IDfeatures
BUT- There Ain’t no such thing as a Physical Parameter Meter
Method 2- Non-Model-Based Techniques
Select Fault ID Feature Vector
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)AND (kurtosis of load vibration is large)
THEN (fault is worn outer ball bearing)
Etc. Etc.
Therefore, include vibration moments and frequencies in the feature vector
)(t [ time signals … frequency signals ]T
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
More about DSP later
Method 3- Statistical Regression Techniques
Select Fault ID Feature Vector
Vibration magnitude
Driv
e tr
ain
gear
too
th w
ear
Principal Component AnalysisPearson’s correlationNonlinear correlation techniquesMultivariable regression
Clustering techniquesNeural networksStatistical
Fault 1
Fault 2
Fault 3
outliers
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.
Fault Pattern Library
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)AND (kurtosis of load vibration is large)
THEN (fault is worn outer ball bearing)
Etc. Etc.
)(t [ time signals … frequency signals ]T
Jay LeeUniv. Cincinnati
Bearing 1
Bearing 2
shaft
Base mount rear
Base mount front
0
1
Health status0= failure1= healthy
Multidimensional feature vector visualization-- Failure Radar Screen
Indicates correlated faults
Bearing 1
Bearing 2
shaft
Base mount rear
Base mount front
0
1
CBM Fault DIAGNOSTICS Procedure
machines
Math models
),,(
),,(
uxhy
uxfx
System Identification-Kalman filterNN system ID
RLS, LSE
Dig. Signal Processing
PhysicalParameterestimates &Aero. coeff.estimates
Sensoroutputs
VibrationMoments, FFT
FeatureVectors-
Sufficientstatistics
)(tFault ClassificationFeature patterns for faultsDecision fusion could use:
Fuzzy LogicExpert SystemsNN classifier
Stored Legacy Failure dataStatistics analysis
Feature extraction -determine inputs for Fault Classification
Physics of failureSystem dynamicsPhysical params.
Identify Faults/Failures
More info needed?
Inject probe test signals for refined diagnosisInformpilotyes
Serious?
Informpilot
yes
SensingFault Feature Extraction
Reasoning& Diagnosis
Systems, DSP& Data Fusion
SensorFusion
Featurevectors
Featurefusion
StoredFault Pattern
Library
Model-BasedDiagnosis
Set Decision ThresholdsManuf. variability dataUsage variabilityMission historyMinimize Pr{false alarm}Baseline perf. requirements
Phase II- On Line Fault Monitoring and Diagnostics
no
Request Maintenance
Fault Classification
Decision-MakingFault Classification
StoredFault Pattern
Library
Feature Vectors
)(t
Diagnosed Faults
Model-Based Reasoning (MBR) vs. Case-Based Reasoning
Too complex!Faults depend on Operating conditions
Neural networksFuzzy logicExpert system rulebaseBayesianDempster-ShaferModel-Based Reasoning
Decision-Making
N
i
n
jjij
N
i
n
jjij
i
x
xz
xf
1 1
1 1
)(
)(
)(
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)
iii
iii PP
PPP
)()/(
)()/()/(
0
)(1
)(
)(
j
ij
Sjj
Sjj
i Sm
Sm
Bel
Bayes Probability
Dempster-Shafer Rules of Evidence
Expert & Rule-Based systems
Fuzzy LogicFuzzy logic unifies ALL these approaches
Bayesian Classifier Performance
normal abnormal
FN FPdecision criterion
False positiveFalse negative
Prob. of False Alarm
Decision threshold
Hypothesistesting
ji
ji
BAji
CBAji
BmAm
BmAm
Cmm)()(1
)()(
)(21
21
21
Dempster-Shafer
• If m1 and m2 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)=
CD
Dm )(
0
)(CD
Dm
In Bayes, Bel= Pl
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
So there are between 42 and 83 cars of type Abetween 17 and 58 cars of type B
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)
Using the formulas above:
Fuzzy Logic Fault Classification
Unifiesexpert systemsstatisticalneural network approaches
2-D FL system c.f. neural network
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
small medium large
smal
lm
ediu
mla
rge
Sideband component I1
Sid
eban
d co
mpo
nent
I2
none incip.
incip.
one
one
one
oneortwo
oneortwo
two
.
..
.......
.
..
......
...............
..........
. . . ...... ..
. ..
.
. ..
Fig 5 Clustering of statistical fault data
Vibration magnitude
Dri
ve tr
ain
gear
toot
h w
ear
Fau
lt c
ondi
tion
s
one
two
thre
e
lowmed severe
FL Decision Thresholds
From Harold Chestnut
Based onLegacy fault data historiesManuf. variability dataUsage variabilityMission historyMinimize Pr{false alarm}Baseline perf. requirements
Can be tuned using adaptive learning techniques
Two-Layer Neural Network
(.)
(.)
(.)
(.)
x1
x2
y1
y2
VT WT
inputs
hidden layer
outputs
xn ym
1
2
3
L
Neural Networks
)( xVWy TT
1-layer NN has W= I
)( xVy T
2-layer NN
RVFL NN has V= random
Training
1-layer – Gradient Descent XekVkV T )()1(
Where X= input pattern vectorsY= output target vectors
)(kyYe = training error
Multilayer- backpropagation (Paul Werbos)
Neural Networks - ClassificationGroup 1: o (1,1), (1,2)Group 2: x (2,-1), (2, -2)Group 3: + (-1,2), (-2,1)Group 4: # (-1,-1), (-2,-2)
Classify 8 points into two groups
-3 -2 -1 0 1 2 3-3
-2
-1
0
1
2
3
oo
xx
++
##
Represent the 4 groups as 00, 01, 10, 11Then, the input pattern vector and target vector are
21122121
21212211X
11001100
11110000Y
I. Training
MATLAB CodeR=[-2 2;-2 2]; % define 2-D input spacenetp=newp(R,2); % define 2-neuron NNp1=[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 epochsnetp = train(netp,P,T);
0
1
21
13xy T
result
Result after training
Defines 2 lines in (x1, x2) plane
II. Classification (simulation)
All points are classified into one of the 4 regions
Y1=sim(netp,P1)
Clustering Using NN
Competitive NN
Make 2 x 80 matrix P of the 80 points
Given80 datapoints
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};
%plotplot(P(1,:),P(2,:),'+r');xlabel('p(1)');ylabel('p(2)');hold on;circles = plot(w(:,1),w(:,2),'ob');
I. Training & Clustering
II. Classification (simulation)p = [0; 0.2];a = sim(net,p)
Activates neuron number 1
Possible failures depend on current operating mode
Model-Based ReasoningMBR
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Model Legend -
Condition Function
SensorComponent
BlockDiagram
MBRModel
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.
Michael Gandy and Kevin LineLockheed Martin AeronauticsModel-Based Reasoning (MBR) Provides a
Significant Part of PHM Design Solution
Off Line- Background Studies, RUL Analysis On Line- Perform real-time Prognostics & RUL
Two Phases of Prognostics & RUL
Four Stages of CBM/PHM
Diagnostics Prognostics & RUL Maintenance Prescription Maintenance Scheduling
The CBM/PHM Cycle
MachineSensors
Pre-Processing
FeatureExtraction
FaultClassi-fication
Predictionof Fault
EvolutionData
ScheduleRequired
Maintenance
Systems &Signal processing
DiagnosticsPrescription
MaintenanceScheduling
PrescribeMaintenance
Prognostics
Current fault condition
Required Background Studies
Machine legacy failure data
Available resourcesRULMission due dates
PHM
Prognostics
Prescription Libraryfailure modestrendsside effects
Rulebase expert systemFuzzy/Neural SystemPrescription decision treeBayesianDempster-Shafer
DiagnosticFaultcondition
Maint. Request
Maint. Planning & Schedulingweight maint. Requests
Computer machine plannersHTN, etc.
Performance Priority Measuresearliest mission dateleast slack repair timedue date
RULEstimated time of failure
Mission criticality and due date requirements
Maintenance Requirements Planning
Maintenance PrioritiesMission Due Dates
safetyriskcost
opportunityconvenience
Automatically generated work orders.Maintenance plan with maint. Rankings
Resource assignmentand dispatching
priority dispatchingmaximum % utilizationminimize bottlenecks
resources
PrioritizedWork Ordersassigned toMaint. Units
Guaranteed QoS
User interfaces forDecision assistanceDecision Support
Adaptiveintegrationof newprescriptions
PHM Maintenance Prescription and Scheduling Procedure
StoredPrescription
Library
Medical HealthPrescriptions
Manufacturing MRP
Communications SystemScheduling & Routing
ManufacturingOn-Line ResourceDispatching
Prescription-Based Health Management System (PBHMS)
Generate:optimized maint. tasks(c.f. PMS cards)
Prescription
Scheduling
Priority Costs
Dispatching
Fault detection threshold
4%fault
10%fault
failure
ReplaceComponent
Replacesubsystem Replace entire
system
Fault development trend:Progressive escalation of required maintenance
Repair time
Missiondue date
Startrepair
Removefromservice
Estimatedtime of Failure (ETF)
Scheduling Removal From Service and Start of Repair in terms of ETF and Mission Due Date
Prognostics- Why?
I. Fault Propagation & Progression
II. Time of Failure &Remaining Useful Life (RUL)
Impacts the Prescription Impacts the Scheduling
N. Viswanadham
RUL
Presenttime
Progressive Escalation Mission Criticality
Extension of manufacturing MRP
Off Line- Background Studies, RUL Analysis On Line- Perform real-time Prognostics & RUL
Two Phases of Prognostics & RUL
Four Stages of CBM/PHM
Diagnostics Prognostics & RUL Maintenance Prescription Maintenance Scheduling
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
Phase I- Preliminary Off-Line Studies
PROGNOSTICS
Hazard Function-Probability of failure at current time
tWearin-Earlymortality
Wearout
Trend Analysis & Prediction-Track Feature vector trendsStudy and)(t )(t
t
)(tNormal operatingregion
Fault tolerance limits
Fault tolerance limits found by legacy data statistics
Estimate Remaining Useful Life with Confidence Intervals
Legacy Data Statistics gives MTBF, MTTF etc.
Based on legacy failure data
- H. Chestnut
.
..
. ....
. .....
.. . ..
.
...
...........
..
...... .. .
. . .......
.. .
.
.
. ..
Sample of legacy statistical fault data
Vibration magnitude
Dri
ve tr
ain
gear
toot
h w
ear
failure .
.
. ..
. . ..
.... . . . . . . .. ..
.......
.. .. .
..
. . .. . . . .. .
.. .
....
. ..
.
.
..
.
Sample of legacy statistical RUL data
Vibration magnitude
Use
ful R
emai
ng L
ife
0
Stored Legacy Failure data Statistics analysis
Find MTTF for given fault conditionand find confidence limits
. . ..
.
...
.
.. . ....
...
.. .
.
... . .
.
...
... .
. . .......
.. .
.
..
. . ..
.
...
.
.. . ....
...
..
..
Statistical RegressionClusteringNeural network classification
• Variations of available empirical and deterministic fatigue crack propagation models are based on Paris’ formula:
Where:α = instantaneous length of dominant crackΝ = running cyclesCo, n = material dependent constantsΔК = range of stress intensity factor over one loading cycle
no KCdN
da
e.g. Deterministic Crack Propagation Models
OR- Physical Modeling
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Andy Hess, US Naval Air
Estimation of Failure Probability Density FunctionsGives best estimate of RUL (conditional mean) as well as confidence limits
A priori failure PDF A posteriori conditional failure PDFgiven no failure through present time
Present time
Expected remaining life
RUL confidence limits
t
Remaining life PDF
Expected remaining life
Present time
5%95%
t
t
Lead-timeinterval
JITP
Removal From Service-Just In Time Point (JITP) avoids 95% of failures
Andy Hess, US Naval Air
RUL PDFs as a Function of Time
timeExpected RUL
RUL estimates become more accurate and precise as RUL decreases
a priori RUL PDF
Expected failure time
95% confidencelimits
Kalman Filter is the optimal estimator for the conditional PDF for linear Gaussian case-gives estimate plus
covariance
t
)(tNormal operatingregion
Fault tolerance limits
Confidence limits
Estimated feature
alarm
failure
Minimize Pr{false alarm}Pr{miss}
Model-Based Predictive Methods- Mike Grimble
Fault Trend Analysis
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
2
21
( )1 1( , ) ( , ) exp[ ]
(2 ) 2
li
iiCD CD
Y YCD Y C Y
l
X X
Input layer
Patternlayer
Summationlayer
output
Numerator Denominator
Confidencedistribution
approximator
CPNN
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
CBM- Prescription of Maintenance
Decision-MakingPrescription
StoredPrescription
Library
Fault condition Maintenance Prescription
Neural networksFuzzy logicExpert system rulebaseBayesianDempster-Shafer
Model-Based Reasoning (MBR) for Fault Progression?
Prescription may change if fault worsens
FaultTrend??
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)
Prescription Library
Side Effects?
Equipment down timeImpact on related systemsMission failureUse of critical maintenance resources or parts
Wireless Sensor Networks
• Machinery monitoring & Condition-Based Maintenance (CBM / PHM / RUL)
• Personnel monitoring and secure area denial
$180K in ARO/ UTA/ Texas funding to set up ARRI WSN lab $240K in MEMS & Network related Grants from NSF and ARO
Contact Frank [email protected]
http://arri.uta.edu/acs
C&C UserInterface forwireless networks-
Wireless
Data Collection Networks
Wireless Sensor
Machine Monitoring
Security Personnel and Vehicle Monitoring
C
O O
HH2O
h+
h+
h+
H2OC
O O
H
C
O O
H
C
O O
HC
O O
H h+
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
e-
e-
e-
e-
TiO2TiO2
Ni
C
O O
H
C
O O
HH2O
h+
h+h+
h+
H2OC
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
HC
O O
H
C
O O
H h+
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
e-
e-
e-
e-
TiO2TiO2
Ni
Biochemical Monitoring
EnvironmentalMonitoring
Wireless
Data Collection Networks
Wireless Sensor
Machine Monitoring
Security Personnel and Vehicle Monitoring
C
O O
HH2O
h+
h+
h+
H2OC
O O
H
C
O O
H
C
O O
HC
O O
H h+
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
e-
e-
e-
e-
TiO2TiO2
Ni
C
O O
H
C
O O
HH2O
h+
h+h+
h+
H2OC
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
HC
O O
H
C
O O
H h+
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
C
O O
H
e-
e-
e-
e-
TiO2TiO2
Ni
Biochemical Monitoring
EnvironmentalMonitoring
Microstrain V-Link
Transceiver
MicrostrainTransceiver
Connect to PC
MicrostrainG-Sensor
Microstrain Wireless Sensorshttp://www.microstrain.com/index.cfm
V-link – 4 voltage inputs for any sensors that vary voltageG-link – accelerometerS-link – strain gauge sensor
LabVIEW Real-time Signaling & Processing
CBM Database and real time Monitoring
PDA access Failure Data from anytime and
anywhere
User Interface, Monitoring, & Decision AssistanceWireless Access over the Internet
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 DisplayInternet Access
Time-varying DFT using window (using MATLAB FFT)
Discrete Fourier Transform-
1
2
3
4
5
6
7
8
050
100150
200250
300350
400450
500
0
500
1000
(sec)
One second buffer DFT of the speech at a refreshing rate of one second
(Hz)
DF
T
0
1
2
3
4
5
6
050
100150
200250
300350
400450
500
0
1000
2000
(sec)
0.5 sec buffer DFT at a refreshing rate of 0.25 sec
(Hz)
DF
T
0
1
2
3
4
5
6
050
100150
200250
300350
400450
500
0
1000
2000
(sec)
0.5 sec buffer DFT at a refreshing rate of 0.25 sec
(Hz)
DF
T
Intermittentincipient bearingouter race fault
Onset of geartooth wear
Resulting load imbalance
DFT for CBM
Planetary Gear Transmission
McFadden’s Method
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
UH-60A Blackhawk HelicopterMain Transmission Planetary Carrier Fault Diagnostics
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
210 215 220 225 230 235 240 245
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Frequency = k * fc (k: integer, fc: carrier rotation freq.)
Am
plitu
de
Sample spectrum at Harmonic 1
Small shift ofone planet (.1 deg)
Healthy system withtolerance of +/- 0.01degrees in planet anglesMedium shift
of one planet(.15 deg)
High shiftof one planet(.3 deg)
Frequency Domain Plot Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Pattern changes in the SIDEBANDS are useful for diagnostics & prognostics
Planetary gear analysis
Time domain - Moments, statistics, correlation, moving averagesFrequency Domain - Discrete Fourier TransformDynamical System Theory
State Estimation- Kalman Filter System Identification- Recursive Least Squares (RLS)
Statistical TechniquesRegressionPDF estimation
Decision-Making TechniquesBayesianDempster-ShaferRule-Based & Expert SystemsFuzzy Logic
Neural NetworksClassificationClustering
Signal Processing and Decision-Making
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
Good Nose Gear
Landing Gear with Possible Divergent Shimmy
Shimmy Vibration Measurement
Force
Measured Free Play
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Data Pre-Processing is USUALLY 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
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Time Domain- Moments, Statistics, Correlation
dxxfxxE pp )()(pth moment of RV x(t) with PDF f(x) is
If the RV is ergodic, then its ensemble averages can be approximated by time averages.
N
k
pkx
N 1
1pth moment of time series xk over time interval [1,N] is given by
first moment is the (sample) mean value
N
kkx
Nx
1
1
second moment is the moment of inertia
N
kkx
N 1
21
N
kkx
1
2
energy
root-mean-square (RMS) value
N
kkx
N 1
21
third moment about the mean is the skew – contains symmetry information
N
kk xx
N 1
33
)(1
kurtosis is a measure of the size of the sidelobes of a distribution
3)(1
1
44
N
kk xx
N
A measure of unbalance
A measure of ‘banging’
SECOND ORDER STATISTICSCorrelation, Covariance, Convolution
N
knkkx xx
NnR
1
1)((auto)correlation
N
knkkx xxxx
NnP
1
))((1
)((auto)covariance
N
knkkxy yx
NnR
1
1)(Cross-correlation of two series
N
knkkxy yyxx
NnP
1
))((1
)(Cross-covariance
1
0
)(*N
kknk yxnyxdiscrete-time convolution for N point sequences
Needed for Confidence Limits
Statistical Tools for Estimating the PDF
.
..
. ....
. .....
.. . ..
.
...
...........
..
...... .. .
. . .......
.. .
.
.
. ..
Sample of legacy statistical fault data
Vibration magnitude
Dri
ve tr
ain
gear
toot
h w
ear
failure
. . ..
.
...
.
.. . ....
...
.. .
.
... . .
.
...
... .
. . .......
.. .
.
..
. . ..
.
...
.
.. . ....
...
..
..
Consistent estimator for the joint PDF is
2
2
1212/)1( 2
)(exp
2
)()(exp
1
)2(
1),(
iN
i
iTi
nn
zzxxxx
NzxP
dzzxp
dzzxzpxzE
),(
),(]/[
Conditional expected value formula
yields estimate for x given z
N
i
iTi
N
i
iTii
xxxx
xxxxz
xzE
12
12
2
)()(exp
2
)()(exp
]/[
Given statistical data
This also gives error covariance or Confidence measure
(xi,yi)
Parzen estimator for PDF
= sum of Gaussians
Parzen pdf Estimator- Example
Legacy Historcial Failure data Gaussian pdf centered at data points
Sum of Gaussians pdf SoG pdf contours
Discrete Fourier Transform (DFT)
N
n
NnkjenxkX1
/)1)(1(2)()( Given time series x(n), DFT is ; k= 1,2,…N
DFT is periodic with period N
)1(2
kN
w
Scale the frequency axis -
Time-varying DFT using window (using MATLAB FFT)
Discrete Fourier Transform-
1
2
3
4
5
6
7
8
050
100150
200250
300350
400450
500
0
500
1000
(sec)
One second buffer DFT of the speech at a refreshing rate of one second
(Hz)
DF
T
0
1
2
3
4
5
6
050
100150
200250
300350
400450
500
0
1000
2000
(sec)
0.5 sec buffer DFT at a refreshing rate of 0.25 sec
(Hz)
DF
T
0
1
2
3
4
5
6
050
100150
200250
300350
400450
500
0
1000
2000
(sec)
0.5 sec buffer DFT at a refreshing rate of 0.25 sec
(Hz)
DF
T
Intermittentincipient bearingouter race fault
Onset of geartooth wear
Resulting load imbalance
DFT for CBM
Planetary Gear Transmission
McFadden’s Method
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
UH-60A Blackhawk HelicopterMain Transmission Planetary Carrier Fault Diagnostics
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
210 215 220 225 230 235 240 245
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Frequency = k * fc (k: integer, fc: carrier rotation freq.)
Am
plitu
de
Sample spectrum at Harmonic 1
Small shift ofone planet (.1 deg)
Healthy system withtolerance of +/- 0.01degrees in planet anglesMedium shift
of one planet(.15 deg)
High shiftof one planet(.3 deg)
Frequency Domain Plot Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Pattern changes in the SIDEBANDS are useful for diagnostics & prognostics
Planetary gear analysis
Wireless Aircraft Health Monitoring actual Navy application
ProposedSensor Locations
Marine H53 Helicopter (Pax River)
Dr. George Vachtsevanoshttp://icsl.gatech.edu/icsl
Kalman Filter – for noise removal, signal enhancement, trend prediction
( )
( )
( )
1
1
11
ˆ ˆ ˆ ,
,
.
k k k k k k
T Tk k k
T T T Tk k k k k
x Ax Bu AK z Hx
K P H HP H R
P A P P H HP H R HP A GQG
- - -+
-- -
-- - - - -+
= + + -
= +
é ù= - + +ê úë û
Kalman Filter (Discrete Time)
Estimate update
Kalman gain
Covariance update
( ) 1.T T T T TP APA APH HPH R HPA GQG
-= - + +
Steady-State KF
Time-Varying KF
kkkk GwBuAxx 1
kkk vHxz
Stochastic Dynamical System
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
KF Also Gives Error Covariance- a measure of accuracy and
confidence in the estimate
0 1 2 3
errorcovariancea priorierror covariance
a posteriorierror covariance P0 P1 P2 P3
time
P1 P2 P3
Error covariance update timing diagram