Prognostics and Health Management

Prognostics and Health
Management
（故障预测和健康管理）

Dr. Chaochao Chen
(陈超超博士)
©2012 ASQ & Presentation Chen
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Prognostics
TM

Prognostics and Health Management
Fundamentals

Chaochao Chen, Ph.D.
Center for Advanced Life Cycle Engineering
University of Maryland
College Park, MD 20742
chaochao@calce.umd.edu
www.calce.umd.edu

calce Center for Advanced Life Cycle Engineering 1 University of Maryland
TM

Copyright © 2012 CALCE

CALCE Overview
• The Center for Advanced Life Cycle Engineering (CALCE)
formally started in 1984, as a NSF Center of Excellence in
systems reliability.
• One of the world’s most advanced and comprehensive testing and
failure analysis laboratories
• Funded at $4M by over 150 of the world’s leading companies
• Supported by over 100 faculty, visiting scientists and research
assistants
• Received NSF
innovation
award in 2009

TM


CALCE Research Funding (over $6M): 2012
Emerson Appliance Controls • Motorola • S.C. Johnson Wax
• Alcatel-Lucent •
Emerson Appliance Solutions • Mobile Digital Systems, Inc. • Sandia National Labs
• Aero Contol Systes •
Emerson Network Power • NASA • SanDisk
• Agilent Technologies •
Emerson Process Management • National Oilwell Varco • Schlumberger
• American Competitiveness Inst. •
Engent, Inc. • NAVAIR • Schweitzer Engineering Labs
• Amkor •
Ericsson AB • NetApp • Selex-SAS
• Arbitron •
Essex Corporation • nCode International • Sensors for Medicine and Science
Arcelik •
• Consumer and mobile products
•
Ethicon Endo-Surgery, Inc. • Nokia Siemens • SiliconExpert
• ASC Capacitors •
Exponent, Inc. • Nortel Networks • Silicon Power
• ASE •
• Telecommunications and computer systems
Fairchild Controls Corp. • Nordostschweizerische Kraftwerke • Space Systems Loral
• Astronautics •
Filtronic Comtek AG (NOK) • SolarEdge Technologies
• Atlantic Inertial Systems •
Northrop Grumman • Starkey Laboratories, Inc
• Energy systems (generation/storage/distr)
• AVI-Inc • GE Healthcare
•
General Dynamics, AIS & Land Sys.
• NTSB • Sun Microsystems
• Axsys Engineering •
General Motors
• NXP Semiconductors • Symbol Technologies, Inc
• BAE Systems •
•
•
Benchmark Electronics
Boeing
• Industrial systems ••
•
•
Guideline
Hamlin Electronics Europe
Ortho-Clinical Diagnostics
Park Advanced Product Dev.
•
•
SymCom
Team Corp
• Tech Film
•
•
Branson Ultrasonics
Brooks Instruments • Transportation systems
•
•
Hamilton Sundstrand
•
Harris Corp
•
Penn State University
PEO Integrated Warfare •
•
Tekelec
Teradyne
Buehler • Henkel Technologies
• Petra Solar
• Aerospace systems ••
•
Honda Philips • The Bergquist Company
• Capricorn Pharma •
Honeywell Philips Lighting • The M&T Company
• Cascade Engineering •
• Medical systems
Howrey, LLP
• Pole Zero Corporation • The University of Michigan
• Celestical International •
Intel • Pressure Biosciences • Tin Technology Inc.
• Channel One International •
Qualmark • TÜB TAK Space Technologies
• Military systems
• Cisco Systems, Inc. • Instituto Nokia de Technologia
•
Juniper Networks
• Quanterion Solutions Inc • U.K. Ministry of Defence
• Crane Aerospace & Electronics •
Johnson and Johnson
• Quinby & Rundle Law • U.S. Air Force Research Lab
• Curtiss-Wright Corp •
•
•
CDI • Equipment manufacturers
De Brauw Blackstone Westbroek
•
•
Johns Hopkins University
•
Kimball Electronics
•
Raytheon Company
Rendell Sales Company
•
•
U.S. AMSAA
U.S. ARL
• U.S. Naval Surface Warfare Center
•
•
Dell Computer Corp.
DMEA • Government Labs and Agencies
•
•
L-3 Communication Systems
•
LaBarge, Inc
•
Research in Motion
Resin Designs LLC •
•
U.S. Army Picatinney/UTRS
U.S. Army RDECOM/ARDEC
• Dow Solar • Lansmont Corporation • RNT, Inc.
Laird Technologies • Roadtrack • Vectron International, LLC
• DRS EW Network Systems, Inc. •
LG, Korea • Rolls Royce • Vestas Wind System AS
• EIT, Inc. •
Liebert Power and Cooling • Rockwell Automation • Virginia Tech
• Embedded Computing & Power •
Lockheed Martin Aerospace • Rockwell Collins • Weil, Gotshal & Manges LLP
• EMCORE Corporation •
Lutron Electronics • Saab Avitronics • WesternGeco AS
• EMC •
Maxion Technologies, Inc. • Samsung Mechtronics • Whirlpool Corporation
• EADS - France •
Microsoft • Samsung Memory • WiSpry, Inc.
• Emerson Advanced Design Ctr •
• Woodward Governor

TM


CALCE Mission and Thrust Areas
Provide a knowledge and resource base to support the development
and sustainment of competitive electronic products

Physics of Failure, Failure
Mechanisms and Material
Behavior
Design for Reliability and
Virtual Qualification Life Cycle Risk, Cost Analysis and
Management

Strategies for
Risk Assessment, Mitigation and
Management

Accelerated Testing,
Screening and Quality Supply Chain Assessment
Assurance and Management

Diagnostic and Prognostic
Health Management

TM


CALCE PHM Team
• Professors and Research Staff: • Students:
– Prof. Michael Pecht – Hyunseok Oh (PhD)
– Moon-Hwan Chang (PhD)
– Dr. Chaochao Chen
– Wei He (PhD)
– Dr. Michael Osterman – Yunhan Huang (PhD)
– Dr. Michael Azarian – Anto Peter (PhD)
– Dr. Diganta Das – Ranjith Kumar (PhD)
– Prof. Peter Sandborn – Arvind Vasan (PhD)
– Preeti Chauhan (PhD)
– Prof. Abhijit Dasgupta
– Qingguo Fan (PhD)
– Prof. Donald Barker – Nick Williard (PhD)
– Jing Tian (PhD)
– Yan Ning (PhD)
– Sony Mathew (PhD)
– Surya Kunche (MS)
– Edwin Sutrisno (MS)

TM


What is PHM?
Prognostics is the process of monitoring the health of a
product and predicting its remaining useful life (RUL) by
assessing the extent of deviation or degradation from its
expected state of health in its expected usage conditions.

Health Management utilizes prognostic information to
make decisions related to safety, condition-based
maintenance, ensuring adequate inventory, and product
life extension.

PHM permits the evaluation of a system’s reliability in its
actual life-cycle conditions.

TM


Some Benefits of PHM

• Improved understanding of application conditions – knowing the customer
• Extension of maintenance cycles through condition-based maintenance –
enhanced system availability
• Reduced life cycle costs by decreasing inspections, repairs, downtime, and
inventory – product support cost avoidance
• Proactive maintenance to forestall failures – reduced failure rate
• Extension of operational life
• Improved product/system design
• Improved warranty management

TM


PHM in Industry
• Apple said:
If an iPhone or iPod has been damaged by liquid (for
example, coffee or a soft drink), the service for such liquid
damage is not covered by the Apple one (1) year limited
warranty or an AppleCare Protection Plan (APP)
• Liquid Contact Indicators are being used by Apple and other
large cell phone manufacturers for condition monitoring.

Inside the headphone jack Inside the dock
connector

TM


PHM in Military
The U.S. Department of Defense’s 5000.2 policy document on
defense acquisition states that program managers should utilize
diagnostics and prognostics to optimize the operational readiness
of defense-related systems.
F-35 Joint Strike Fighter Multifunction Utility/Logistics and Equipment

TM


F-35 PHM Architecture

TM


PHM in New Energy

Electric Vehicle (Nissan Leaf) Wind Turbine

TM


PHM Modules

Data
Processing

TM


Data Processing-Time Domain Analysis
Processing-
Statistical Measures
Estimated Mean
N

∑x
i =1
i
µ=
N
The mean is the most probable event within the distribution. For some distributions, the
mean may not convey much information (i.e. uniform distributions). The estimated means
of two distributions can be simply compared through subtraction of the means.

Estimated Variance
N

∑ (x − µ) i
2

σ2 = i =1

N
The variance measures the confidence in the mean and the spread of the distribution.

TM


Data Processing-Time Domain Analysis
Processing-
Statistical Measures
Estimated Skewness
N

∑ (x − µ)
i =1
i
3

γ=
Nσ 3
Skewness vanishes for symmetric distributions and is positive (negative) if the distribution
develops a longer tail to the right (left) of the mean E(x). It measures the amount of spread
of the distribution in either direction from the mean.

Estimated Kurtosis
N

∑ (x − µ)
i =1
i
4

kurtosis =
Nσ 4
Kurtosis measures the contribution of the tails of the distribution. It is possible for a
distribution to have the same mean, variance, and skew, and not have the same kurtosis
measurement.

TM


Data Processing-Frequency Domain Analysis
Processing-

Fourier Series:
Periodic functions and signals may be expanded
into a series of sine and cosine functions
Fourier Transform:
A mathematical operation that decomposes a
signal into its constituent frequencies

TM


Processing-

Continuous Fourier Transform:

Forward Transform:

Inverse Transform:

TM


Processing-

An example using MATLAB functions
15

Nosiy Data
Raw data MATLAB Code:
10
fs = 100; % Sample frequency (Hz)
t = 0:1/fs:10-1/fs; % 10 sec sample
5
Amplitude

x = (1.3)*sin(2*pi*15*t) ... % 15 Hz
component
0
+ (1.7)*sin(2*pi*40*(t-2)) ... % 40 Hz
component
−5
+ (2.5)*randn(size(t)); % Gaussian
noise;
−10
0 2 4 6 8 10
Time (Sec)

TM


Processing-

An example using MATLAB functions (FFT)
700
40 Hz
MATLAB Code:
600

15 Hz m = length(x); % Window length
500
n = pow2(nextpow2(m)); %
Absolute Amplitude

400
Transform length
y = fft(x,n); % DFT
300
f = (0:n-1)*(fs/n); % Frequency
200 range

100 y1 = abs(y)

0
0 20 40 60 80 100
Frequency (Hz)

TM


Processing-

An example using MATLAB functions (Power Spectrum)
450
40 Hz
400 MATLAB Code:

350 m = length(x); % Window length
300 n = pow2(nextpow2(m)); %
15 Hz Transform length
250
Power

y = fft(x,n); % DFT
200
f = (0:n-1)*(fs/n); % Frequency
150
range
100
power = y.*conj(y)/n;
50

0
0 20 40 60 80 100
Frequency (Hz)

TM


Data Processing-Wavelet Analysis
Processing-

• Stationary Signal
– Signals whose frequency content unchanged in
time
– All frequency components exist all time

• Non-stationary Signal
– Frequency changes in time

TM


Processing-

Frequency: 2 Hz to 20 Hz Different in Time Domain Frequency: 20 Hz to 2 Hz
1 150 1 150

0.8 0.8

0.6 0.6

0.4 0.4
100 100
0.2 0.2
Magnitude

Magnitude

Magnitude
Magnitude
0 0

-0.2 -0.2
50 50
-0.4 -0.4

-0.6 -0.6

-0.8 -0.8

-1 0 -1 0
0 0.5 1 0 5 10 15 20 25 0 0.5 1 0 5 10 15 20 25
Time Frequency (Hz) Time Frequency (Hz)

Same in Frequency Domain Bhushan D Patil, Introduction to Wavelet

FT cannot tell where in time the spectral components of the signal appear !

TM


Processing-
Continuous Wavelet Transform (CWT):

x (t ) • ψ * 
1 t− τ
(τ , s ) = Ψ xψ (τ , s ) = ∫
ψ
CWT x   dt
s  s 
Translation (The location of
the window) Scale (inverse of Mother Wavelet
frequency) Energy Normalization

• Wavelet
– Small wave
– Means the window function is of finite length
• Mother Wavelet
– A prototype for generating the other window functions
– All the used windows are its dilated or compressed and shifted
versions

TM


Processing-

Discrete Wavelet Transform (DWT):
One-Stage Filtering: Approximations and Details

Approximations: high-scale, low-frequency Details: low-scale, high-frequency
components components

TM


Processing-
Discrete Wavelet Transform (DWT):
Multiple-Level Decomposition

f=0~1000Hz

f=0~500Hz f=500~1000Hz

f=0~250Hz f=250~500Hz

f=0~125Hz f=125~250Hz

TM


Feature Extraction
Feature Extraction is to obtain suitable parameters or
indicators that reveal whether an interesting pattern is
emerging

Failure Feature/Precursor/Indicator is a data event or trend
that signifies impending failure

Attributes of good features:
• Computationally inexpensive to measure
• Mathematically definable
• Explainable in physical terms
• Insensitive to extraneous variables
• Uncorrelated with other features

TM


Feature Extraction
Select the life-cycle parameters to be monitored
• safety
• mission completeness
• long downtimes
• past experience
• field failure data on similar products
• qualification testing
• failure modes mechanisms and effects analysis (FMMEA)

Select the failure feature based on physics of failure

Select the failure feature based on statistics and machine
learning

TM


Diagnostic and Prognostic Approaches
There are numerous methodologies that can be used to conduct
diagnostics and prognostics, but each of these falls into three
main categories :
• The Physics-of-Failure(PoF)/Model-based Approach
PoF is the root cause of where, how and why materials fail. It provides a
methodology for building-in reliability, based on assessing the hardware
configuration and life-cycle stresses to identify root-cause failure
mechanisms in the materials used at potential failure sites.
• The Data-Driven Approach
Data-driven methods use current and historical data to statistically and
probabilistically obtain estimates, decisions, and predictions about the
health and reliability of a product
• Fusion Approach

TM


The Physics-of-Failure(PoF)/Model-
based Approach

TM


Physics of Failure Based PHM Methodology
FMMEA

Define system and (1): life consumption monitoring
Material
identify elements and (2): canary
properties and
functions to be analyzed
product
geometries
Identify potential failure
modes

Identify life Identify potential failure Monitor life cycle Data processing
cycle profile causes environment and and load feature
operating loading (1) extraction

Identify potential failure
mechanisms
Damage
assessment
Identify failure models
(2)
Choose critical Remaining
failure Use fuse useful life
Maintenance Prioritize the failure
mechanisms or canary estimation
records mechanisms
and failure site devices

TM


Failure Modes, Mechanisms, and Effects Analysis

• Failure Modes, Mechanisms and Effects Analysis (FMMEA) is
an approach that uses the life cycle profile of a product along
with the design information to identify the critical failure
mechanisms affecting a product.
• Failure mechanism: The processes by which physical, electrical,
chemical and mechanical conditions induce failure.
• Failure mode: The effect by which a failure is observed to occur
• Failure site: The location of the failure.
• Failure cause: The specific process, design and/or environmental
condition that initiated the failure, whose removal will eliminate
the failure.

TM


Types of Failure Mechanisms

Overstress Mechanisms Wearout Mechanisms
Stress exceeds item strength; failure sudden Accumulation of damage with repeated
stress
Yield, Fracture,
Mechanical Interfacial delamination Mechanical Fatigue,
Creep, Wear

Glass transition (Tg)
Thermal Phase transition Thermal
Stress driven diffusion
voiding (SDDV)
Dielectric breakdown, TDDB, Electromigration,
Electrical Electrical overstress,
Electrostatic discharge, Electrical
Surface charge
spreading, Hot electrons,
Second breakdown CFF, Slow trapping

Radiation embrittlement,
Radiation Single event upset
Radiation Charge trapping in oxides

Corrosion,
Chemical Contamination Chemical Dendrite growth,
Depolymerization,
Intermetallic Growth

TM


Identify Life Cycle Profile (LCP)
• A life cycle profile (LCP) is a forecast of events and associated
environmental and usage conditions a product will experience from
manufacture to end of life.
• The phases in a product life cycle includes manufacturing/assembly,
test, rework, storage, transportation and handling, operation, repair
and maintenance.
• The description of life cycle profile needs to include the occurrences
and duration of these conditions.
• Life cycle loads include conditions such as temperature, humidity,
pressure, vibration, shock, chemical environments, radiation,
contaminants, current, voltage, power and the rates of change of
these conditions.

TM


Canary
• The use of canary devices is a PoF based approach for
implementing PHM in products.
• Canary is a structure that will fail faster than the actual product
when subjected to the life cycle conditions.
• Canary is designed to fail by the same failure mechanism as the
actual product.
• The acceleration factor by which the canary device is designed
to fail can be used to estimate the time to failure for the actual
product.
• Failure of a canary device serves as an advance warning of
impending failure of the product.
• Canary device is integrated into the electronic
assembly just like other components.

TM


Estimation of Remaining Useful Life

TM


PoF Simulation Based Life Assessment

TM


The Data-Driven Approach

TM


Statistical Analysis-SPRT
Analysis-

Sequential probability ratio test (SPRT) is a statistical binary
hypothesis test for anomaly detection
• detect statistical changes at the earliest possible time using in-
situ monitoring data
• include one null hypothesis (healthy condition) and one or
more alternative hypotheses (faulty conditions)

-M 0 +M σ2/V
σ2
Vσ2
σ

Shift in mean Shift in variance
(positive/negative mean test) (Normal/Inverse variance test)

TM


Statistical Analysis-SPRT
Analysis-

TM


Statistical Analysis-PCA
Analysis-
As a multivariate statistical analysis method, Principal
Component Analysis (PCA) is a simple, non-parametric
method of extracting relevant information from confusing data
sets.
• minimize signal redundancy, measured by covariance
• maximize the signal, measured by variance

TM


Statistical Analysis-PCA
Analysis-

Solve PCA:
• Find an orthonormal matrix P where Y = PX such that CY ≡
1/ T
n−1YY is diagonalized, then the rows of P are the principal
components of X
• The principal components of X are the eigenvectors of XXT or
the rows of P
• The ith diagonal value of CY is the variance of X along Pi

TM


Statistical Analysis-MD
Analysis-
Mahalanobis distance (MD) is able to reduce a multivariate
system to a univariate system, and is sensitive to inter-variable
changes in a multivariate system
• In statistics we prefer a distance that takes variability of each
variable into account
• Variables with high variability should receive less weight than
components with low variability
• Considering the full covariance structure yields the following
general form for the statistical distance of two points
• Def. The statistical distance or Mahalanobis distance between
two points x=(x1,…,xp)T and y=(y1,…,yp)T in the p-dimensional
space Rp is defined as
d MD ( x, y ) = (x − y )T Σ −1 (x − y )
TM


Statistical Analysis-MD
Analysis-
MD calculation for anomaly detection:
• Healthy performance parameter normalization

where

• Healthy MD can be calculated by
where is the correlation matrix

• MD is calculated using the normalized test data with the mean
and standard deviation of healthy data
• When the value of test MD is larger than a threshold defined in
the healthy MD, an anomaly is detected.
TM


Statistical Analysis-SVM
Analysis-
Support vector machine (SVM) can perform as a classifier for
diagnostics to determine the decision boundaries among
different classes
• map the input data to a higher dimension feature space, where
the transformed data become linearly separable
• does not suffer from multiple local minima and its solution is
global and unique; it also does not have the problem of the
curse of dimensionality

TM


Statistical Analysis-SVM
Analysis-
• The optimal hyperplane is determined through support hyperplanes.
x2 r
w
Negative group data
x1 x9 x4 ( y = -1 )

Positive group data
x5 x7 ( y = +1 )

2
x3 Margin
Maximize Margin
x6 f (x) = k w
; B
x2 x8 f (x) = 0
1 2 1 T
f (x) = − k min! w = w w
x1 2 2

• The supporting hyperplanes can be expressed as:
f ( x) = w T x + b = k w T xi + b ≥ 1 for yi = +1

f (x) = w T x + b = − k w T x i + b ≤ −1 for yi = −1, i = 1,..., n

or yi (wT xi + b) − 1 ≥ 0 for i = 1,..., n
constraints

TM


Statistical Analysis-HMM
Analysis-
Hidden Markov models (HMMs) are fully probabilistic
models to describe the signal evolution through a finite number
of states.
• HMMs have been successfully employed in speech processing
• HMMs have been applied in machine health diagnostics and
prognostics due to their similarities to speech processing
problems
• They are all related to the quasi-stationary signals that are the
functions of operational and environmental conditions

TM


Statistical Analysis-HMM
Analysis-

• Transition probabilities:
∂ k ,l = P(st = l st −1 = k ), k , l = 1,..., M .

• Initial probabilities:

π k = P(s1 = k ), k = 1,..., M
• Observation probabilities:
bk (u ) = P(u t = u st = k ), k = 1,..., M .
1  1 
exp − (u − u k ) ∑ −1 (u − u k )
'
Gaussian = k
Distribution (2π )d ∑ k  2 

46
calce 46 University of Maryland
TM

Center for Advanced Life Cycle Engineering

Statistical Analysis-PF
Analysis-
Particle filtering (PF) is a sequential Monte Carlo method,
which uses a mathematical process model to estimate a state
vector in a recursive Bayesian framework
• The output of the PF is a posterior probability density function
(PDF) approximated by a set of particles with their associated
weights
• Through the PDF, many statistical measures of the estimated
states become available, such as the estimation confidence,
which are not possible with scalar data

TM


Statistical Analysis-PF
Analysis-

Sequential Importance Sampling
For i=1,…,N:

1. Particle generation xki ) ~ p ( xk | xki−)1 )
( (

2a. Weight computation wk i ) = wk −i1) p ( z k | xki ) )
*( *( (

(i ) wk i )
*(

2b. Weight normalization w =
k N

∑ wk i )
*(

i =1
N
3. Estimate computation E ( g ( xk | z1:k )) = ∑ g ( xki ) ) wki )
( (

i =1

END
TM


Machine Learning-FFNN
Learning-
Feedforward neural network (FFNN) is considered as one of
the most widely used machine learning method in the fault
diagnosis and failure prognosis

L 1 M
x = ∑ x Wli
i
H
l
L yiH =
1 + exp (− xiH )
y = ∑ y m C mi
O
i
H

l =1 m =1

TM


Machine Learning-RBFNN
Learning-
A radial basis function neural network (RBFNN) contains
radial basis functions in its hidden nodes

L

∑ (x − Wli )
L 2
M
y = ∑ y m C mi
l O H
H l =1
y = exp( −
i 2
) i
2σ m =1

TM


Machine Learning-RNN
Learning-
A recurrent neural network (RNN) has feedback links in the
model structure, they are capable of dealing with dynamic
processes

L 1 M
x = ∑ x Wli
H L yiH (t ) = y = ∑ y m C mi
O H
i l 1 + exp (− ( xiH (t ) + yiH (t − 1)) i
l =1 m =1

TM


Machine Learning-SOM NN
Learning-
A self-organizing map (SOM) neural network does not need
supervised training and the input data can be automatically
clustered in different groups
Weight update

W (t + 1) = W (t ) + θ (t )L(t )( x(t ) − W (t ))

Neighborhood of BMU
 Dist 2 
θ (t ) = exp − 2 
 2σ (t ) 
 
Similarity
L

∑ (x − Wli )
L 2
Dist = l
l =1

TM


Machine Learning-NFS
Learning-
A neuro-fuzzy system (NFS) combines advantages of fuzzy
inference systems and neural networks
xt +r
= ∑ y(j4) (c1j xt −3r + c2j xt −2r + c3j xt−r + c4j xt + c5j ),
j

( 4) y (j3)
y = ,
∑ y (j3)
j

j

y (j3) = ∏ uA2j) (xi(1) ),
(
i i

1
u A2j) (xi(1) ) =
(
,
i
1 + exp(− bij2 ) (xi(1) − mij2 ) ))
( (

yi(1) = xi(1) , i = 1,2, K ,4.

Wang, W et al.,“Prognosis of Machine Health Condition Using Neuro-Fuzzy Systems,” Mechanical System and Signal Processing, 2004, Vol. 18, pp.813-831.

TM


The Fusion Approach

TM


Fusion: Data Driven and Physics of Failure

Healthy
Baseline
Identify
parameters
Continuous Yes
Anomaly? Alarm
Monitoring
No
Physics of
Database and Parameter
Failure
Standards Isolation
Models

Failure Data Driven
Definition Algorithms
Remaining Useful Life
Estimation

TM


Fusion: Data Driven and Physics of Failure
Initial
Performance
Model
Parameter
Parameters

Updated Parameters
Degradation Performance
Model Threshold
Prediction
Estimation Errors
Tuned
Moving Model Nonlinear
Degradation
Window Adaptation Filtering
Model
Parameter Identification Loop Prediction Loop

Remaining
Useful
Performance

TM


Fusion: Multiple Data Driven

TM


Prognostics and Health Management

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