Intelligent Fault Diagnosis & Prognosis - The University of Texas at ...

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


www.MIMOSA.org Machine User Group- CBM Data

Condition Monitoring and Diagnostics of Machines


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


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)


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


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


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



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


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

.


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


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 . . . . . ... .. . . ... . . . ... ... .. . . . .... . . ..... . . . . . . .. . .. .. . .. . . .


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


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


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


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


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


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


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


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)


Planetary Gear Transmission

McFadden’s Method


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


UH-60A Blackhawk Helicopter Main Transmission Planetary Carrier Fault Diagnostics


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


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.”


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


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


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.


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

O

TiO2

O O

O

O

O

O

H2 O

h+ h+

H C

O

O

e-

e-

O O

TiO2

e-

Ni

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


Wireless Aircraft Health Monitoring Æ actual Navy application

Proposed Sensor Locations

Marine H53 Helicopter (Pax River)