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Transcript of NASA Prognostics[1]
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 112/09/2009
Prognostics
Prognostics Center of Excellence
NASA Ames Research Center, Moffett Field CA 94035
Kai Goebel
April 27, 2010
http://prognostics.nasa.gov
TEAM MEMBERS
Kai Goebel Ph.D. (Center Lead)
Vadim Smelianskyi, Ph.D.
(Center Co-Director)
Scott Poll (ADAPT)
Edward Balaban
Jose Celaya, Ph.D.
Matt Daigle, Ph.D.
Bhaskar Saha, Ph.D.
Sankalita Saha, Ph.D.
Abhinav Saxena, Ph.D.
Phil Wysocki
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 2
Prognostics CoE
“The Prognostics Center of Excellence
(PCoE) at Ames Research Center provides
an umbrella for prognostic technology
development, specifically addressing
technology gaps within the application
areas of aeronautics and space
exploration.”
• En route to becoming a national asset
• Expertise in prediction technology and
uncertainty management for systems
health monitoring
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 3
Prognostics
0 500 1000 1500 2000 2500 3000 3500
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
time (secs)
voltage (
V)
EEOD
E (measured)
E (from PF)
Prediction points
tEOD
EOD pdfs
Definition: Predict damage progression of a fault based on current
and future operational and environmental conditions to estimate the
time at which a component no longer fulfils its intended function within
desired bounds (“Remaining Useful Life”)
health
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 4
Key Ingredients for Prognostics• Run-to-failure data
– Measurement data
– Ground truth data
– Operational conditions
• Load profiles
• Environmental conditions
– Failure threshold
• Physics of Failure models
– For each fault in the fault catalogue
• Uncertainty information
– Sources of uncertainty
– Uncertainty characterization
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 5
Prognostics Algorithms• Data Driven Algorithms
– Gaussian Process Regression
– Relevance Vector Machine
– Neural Networks
– Polynomial Regression
• Model Based Algorithms
• Hybrid Algorithms
– Particle Filters
• Classical PF
• Rao-Blackwellized PF
• Risk Sensitive PF
– Kalman Filters
• Classical KF
• Extended KF
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 6
30 35 40 45 50 55 60 650
5
10
15
20
25
30
35
40
- Metric ( = 0.2, = 0.5)
Time (weeks)
RU
L
End of Life (EOL)
80% accuracy zone
actual RUL
RVM-PF RUL
GRP RUL
Baseline Statistics RUL
Metrics Example• Establishing a common ground to compare different prognostic efforts
• Metrics must not only measure accuracy and precision but also the convergence of both properties
• Data/time requirement of algorithms (prognostic horizon) before they produce consistent predictions is also important
0 10 20 30 40 50 60 700.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1Particle Filter Prediction
Time (weeks)
C/1
ca
pa
city (
mA
h);
R
UL
pd
f (b
iase
d b
y 0
.7)
Real data
RUL threshold
RUL pdfs
PredictionSpread (weeks)
PredictionHorizon (weeks)
——l—— 4.23 32
——l—— 3.25 16
——l—— 5.34 32
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 7
Sources of
Uncertainty
Uncertainty
Management
• Model
• System complexity
• Insufficient knowledge
• Usage
• Load profile
• Temperature
• Noise
• Internal, external
• Electrical, mechanical, thermal
• Sensors
• Training data based extrapolation
• Probabilistic state space model
• Online model adaptation
• Noise modeling
• Probabilistic regression
• Hyperparameters to prevent overfitting
Uncertainty Management
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 8
Ames Research Center
Application Example: ValvesModeling, Algorithms, Metrics
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 9
Valve Prognostics• Apply model-based prognostics to
pneumatic valves
• Develop high-fidelity simulation model– Progressive damage models include seal wear
(internal and external leaks), spring degradation,
and increase in friction.
• Investigate performance under different
circumstances using prognostic
performance metrics for comparison– Impact of using different filters
– Effects of increased sensor noise
– Effects of increased process noise and model
uncertainty
– Feasibility of different sensor sets (e.g. continuous
position sensor vs. discrete open/closed indicators)
Computational Architecture
Source: M. Daigle and K. Goebel, "Model-based Prognostics with Fixed-lag Particle Filters“ Accepted for publication
at PHM09
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 10
Problem Formulation
• Prognostics goal– Compute EOL = time point at which component no longer meets specified
performance criteria– Compute RUL = time remaining until EOL
• System model
• Define condition that determines if EOL has been reached
• EOL and RUL defined as
5/
26
Compute and/or
State Input Process Noise
Output Sensor Noise
Parameters
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 11
Fault Detection
Isolation &
Identification
Damage
EstimationPrediction
uk yk F p(EOLk|y0:k)System
yk
p(xk,θk|y0:k)
p(RULk|y0:k)
Prognostics Architecture
5/
26
System receives inputs, produces
outputs
Identify active damage mechanisms
Estimate current state and parameter
values
Predict EOL and RUL as probability
distributions
1
2
3
4
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 12
Return Spring
Piston
Plug
Top
Pneumatic Port
Bottom
Pneumatic Port
Fluid Flow
Case Study• Apply framework to pneumatic valve
– Complex mechanical devices used in many domains including aerospace
– Failures of critical valves can cause significant effects on system function
• Pneumatic valve operation– Valve opened by opening bottom
port to supply pressure and top port to atmosphere
– Valve closed by opening bottom port to atmosphere and top port to supply pressure
– Return spring ensures valve will close upon loss of supply pressure
5/
26
/2
01
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 13
Case Study• Faults
– External leaks at ports & internal leaks across piston– Friction buildup due to lubrication breakdown, sliding wear, buildup of
particulate matter– Spring degradation
• Defining EOL– Limits defined for open and close
times of valves• E.g., main fill valve opens in 20 seconds
(26 req.), closes in 15 (20 req.)
– Limits placed on valve leakage rates (pneumatic gas)
– Valve must be able to fully close upon fail-safe
– Valve is at EOL when any of above conditions violated (defines CEOL)• Function of amount of damage, parameterized
in model
5/
26
Return Spring
Piston
Plug
Top
Pneumatic Port
Bottom
Pneumatic Port
Fluid Flow
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 14
Physics-based Modeling
• Valve state defined by
• State derivatives given by
• Inputs given by
5/
26
Valve positionValve velocityGas mass above pistonGas mass below piston
VelocityAccelerationGas flow above pistonGas flow below piston
Fluid pressure (left)Fluid pressure (right)Input pressure at top portInput pressure at bottom port
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 15
Physics-based Modeling: Forces
• Piston movement governed by sum of forces, including– Pneumatic gas:
– Process fluid:
– Weight:
– Spring:
– Friction:
– Contact forces:
5/
26
Valve Stroke Length
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 16
Physics-based Modeling: Flows
• Gas flows determined by choked/non-choked orifice flow equations:
• Fluid flow determined by orifice flow equation:
5/
26
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 17
Pneumatic Valve Modeling
• Possible sensors include
where,
5/
26
Valve positionGas pressure (top)Gas pressure (bottom)Fluid flowOpen indicatorClosed Indicator
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 18
Modeling Damage
Increase in friction
• Based on sliding wear equation
• Describes how friction coefficient changes as function of friction force, piston velocity, and wear coefficient
Degradation of spring
• Assume form similar to sliding wear equation
• Describes how spring constant changes as function of spring force, piston velocity, and wear coefficient
Growth of internal leak
• Based on sliding wear equation
• Describes how leak size changes as function of friction force, piston velocity, and wear coefficient
Growth of external leak
• Based on environmental factors such as corrosion
• Assume a linear change in absence of known model
5/
26
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 19
Damage Progression
5/
26
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
3.5
4x 10
6
Time (cycles)
Friction C
oeff
icie
nt
(Ns/m
)
Damage Progression of Friction Coefficient
40 411.05
1.1
x 106
0 20 40 60 80 1004
5
6
7
8
9
10x 10
4
Time (cycles)
Spring C
onsta
nt
(N/m
)
Damage Progression of Spring Constant
40 41
6.846.866.886.9
6.926.94
x 104
0 20 40 60 80 1000
0.5
1
1.5
2x 10
-6
Time (cycles)
Inte
rnal Leak A
rea (
m2)
Damage Progression of Internal Leak
40 41
6.8
6.9
7
x 10-7
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3x 10
-5
Time (cycles)
Top E
xte
rnal Leak A
rea (
m2)
Damage Progression of Top External Leak
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 20
Damage Estimation
• Wear parameters are unknown, and must be estimated along with system state
5/
26
PositionVelocityGas mass above pistonGas mass below pistonFriction coefficientSpring rateInternal leak areaExternal leak area (top)External leak area (bottom)
Friction wearSpring wearInternal leak wearExternal leak wear (top)External leak wear (bottom)
Augment system state with unknown parameters and use
state observer
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 21
Particle Filters
• Employ particle filters for joint state-parameter estimation– Represent probability
distributions using set of weighted samples
– Help manage uncertainty (e.g., sensor noise, process noise, etc.)
– Similar approaches have been applied successfully to actuators, batteries, and other prognostics applications
5/
26
w
x
t
Distribution evolves in time
State represented with discrete probability
distribution
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 22
Damage Estimation with PF
• Particle filters (PFs) are state observers that can be applied to general nonlinear processes with non-Gaussian noise– Approximate state distribution by set of discrete weighted samples:
– Suboptimal, but approach optimality as N∞
• Parameter evolution described by random walk:
– Selection of variance of random walk noise is important– Variance must be large enough to ensure convergence, but small enough
to ensure precise tracking
• PF approximates posterior as
5/
26
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 23
Sampling Importance Resampling
• Begin with initial particle population• Predict evolution of particles one step ahead• Compute particle weights based on likelihood of given observations• Resample to avoid degeneracy issues
– Degeneracy is when small number of particles have high weight and the rest have very low weight– Avoid wasting computation on particles that do not contribute to the approximation
5/
26
w
x
Initial Particle Population
w
x
Predict Evolution
w
x
Compute Weights
w
x
Resample
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 24
• Particle filter computes
• Prediction n steps ahead approximated as
• Similarly, EOL prediction approximated as
• General idea– Propagate each particle forward until EOL reached (condition on
EOL evaluates to true)
– Use particle weights for EOL weights
Prediction
5/
26
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 25
Prediction
5/
26
25
Friction progression EOL prediction
Hypothesized inputs
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 26
Validation of Methodology
5/
26
26
EOL predictions all contain true EOL, andget more accurate and precise as EOL isapproached.
Estimate of wear parameter convergesafter a few cycles, after this, leak area canbe tracked well.
Internal Leak EOL
Predictions
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 27
α-λ Performance
• Plot summarizes performance of internal leak prognosis
• Over 50% of probability mass concentrated within the bounds at all prediction points except at 20 and 30 cycles– Mean RULs are
within the bounds at these points
• For α=0.122, metric is satisfied at all points
5/
26
27
α=0.1, β=0.5
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 28
Prediction Performance
5/
26
28
α-λ metric for spring damage prediction, where α =0.1, β=0.4, M={x,f,pt,pb}
α-λ metric for spring damage prediction, where α =0.1, β=0.4, M={open,closed}
Both cases have similar accuracy, but the case with continuous measurementshas much better precision, as the metric evaluates to true for all but one λ point.
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 29
Discussion• Different sensor sets have comparable estimation and prediction accuracy,
but some differences are observed
• Wide differences observed in precision of estimation and prediction
• Results reveal that some sensors are more useful for certain faults than others
– Flow measurement can be dropped with little effect
– For friction and spring faults, sensor sets with position measurement perform best
– For leak faults, sensor sets with pressure measurements perform best
– Helps decide importance of sensors based on which faults are most important
• Overall performance still reasonable with higher levels of noise
– Sensor sets with continuous measurements impacted most
5/
26
29
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 30
Ames Research Center
Application Example: Electronics
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 31
Prognostics for Electronics
Component:
Power Transistor
Line Replaceable Unit:
Power Controller
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 32
Motivation• Electronic components have increasingly critical role in on-
board, autonomous functions for – Vehicle controls, Communications, Navigation, Radar systems
• Future aircraft systems will rely more on electric & electronic components– More electric aircraft
– Next Generation Air Traffic System (NGATS)
• Move toward lead-free electronics and microelectromechanical devices (MEMS)
• Assumption of new functionality increases number of electronics faults with perhaps unanticipated fault modes
• Needed– Understanding of behavior of deteriorated components to
– develop capability to anticipate failures/predict remaining RUL
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 33
Current Research Efforts
• Thermal overstress aging of MOSFETs and IGBTs• Electrical overstress aging testbed (isothermal)• Modeling of MOSFETs• Identification of precursors of failure for different IGBT
technologies*• Prognostics for output capacitor in power supplies+
• Effects of lightning events of MOSFETS• Effects of ESD events of MOSFETS and IGBTs• Effects of radiation on MOSFETS and IGBTs
• In collaboration with* University of Maryland+ Vanderbilt University
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 34
Accelerated aging system
• A platform for aging, characterization, and scenario simulation of gate controlled power transistors.
• The platform supports:– Thermal cycling
– Simulation of operation conditions
– Isothermal aging
• In situ state monitoring is supported at varying gate and drain voltage levels.
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 35
4.15 4.2 4.25 4.3 4.35
x 10-5
0
5
10
time (s)Colle
cto
r-E
mm
iter
and G
ate
(V
)
4.22 4.222 4.224 4.226 4.228 4.23 4.232
x 10-5
7.4
7.6
7.8
8
8.2
time (s)
Colle
cto
r-E
mm
iter
Voltage (
V)
180 min
150 min
110 min
65 min
30 min
T = ~ 330C
Vd = 4v
Vg = 10vVg
Vce
Experiment on IGBT
• Collector-emitter voltage turn-OFF transient
Potential degradation Indicator
326 326.5 327 327.5 328 328.5 329 329.5 330 330.5 3317
7.5
8
8.5
9
9.5
10
10.5
11
11.5
temperature (C)S
witchin
g T
ransie
nt
peak(V
)
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000Degradation time (s)
• Turn-OFF collector-emitter voltage transient decreased significantly with both increases in temperature and thermal overstress aging time
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 36
Electronics Aging
5.07 5.08 5.09 5.1 5.11 5.12 5.13 5.14 5.15 5.16
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Offstate ICE
Time (min)
measurements
curve fit
85.44 85.45 85.46 85.47 85.48 85.49
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Offstate ICE
Time (min)
measurements
curve fit
86.88 86.89 86.9 86.91 86.92 86.93
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Offstate ICE
Time (min)
measurements
curve fit
86.94 86.96 86.98 87 87.02 87.04 87.06 87.08 87.1 87.120
1
2
3
4
5
6
7
8
Time (mins)
IGBT Waveforms
ICE
VGE
33.82 33.84 33.86 33.88 33.9 33.92 33.94 33.96 33.98 34 34.02
0
1
2
3
4
5
6
7
8
Time (mins)
IGBT Waveforms
ICE
VGE
0 10 20 30 40 50 60 70 80 90-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0x 10
5 Coeff of Polyfit Term P1t3
Time (mins)
0 10 20 30 40 50 60 70 80 90-2
0
2
4
6
8x 10
7 Coeff of Polyfit Term P2t2
Time (mins)
0 10 20 30 40 50 60 70 80 90-6
-5
-4
-3
-2
-1
0
1x 10
9 Coeff of Polyfit Term P3t
Time (mins)
0 10 20 30 40 50 60 70 80 90-5
0
5
10
15
20x 10
10 Coeff of Polyfit Term P4
Time (mins)
0 10 20 30 40 50 60 70 80-2.5
-2
-1.5
-1
-0.5
0
0.5
1Particle Filter Parameter Estimation
Time (mins)
P
1
Pre
dic
tion @
51.8
75 m
ins
0 10 20 30 40 50 60 70 80-2.5
-2
-1.5
-1
-0.5
0
0.5
1Particle Filter Parameter Estimation
Time (mins)
P
1
Pre
dic
tion @
51.8
75 m
ins
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 37
Ames Research Center
Application Example: EMA
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 38
Electro-Mechanical Actuators
Mission Statement0 500 1000 1500 2000 2500 3000 3500 4000
299
301.5
304
306.5
309
Time (s)
Tem
pera
ture
(K
)
Temperature Plot: Baseline Run 2
0 500 1000 1500 2000 2500 3000 3500 4000-1
-0.5
0
0.5
1
Err
or
(K)
Motor TCTsurf (Model)
EMA
Data collection in laboratory…
…and flight conditions
Model Verification
Physical Modeling
5 metric ton load capacity
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 39
Flyable Electro-mechanical Actuator (FLEA) Testbed
• One load actuator and two test actuators (nominal and faulty), switcheable in flight
• Sensor suite includes accelerometers, current sensors, position sensors, temperature sensors and a load cell
• Real-time flight surface loads
simulation and data recording
• Data collection flights performed on
C-17 (DFRC) and planned on UH-60
(ARC)
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 40
Ames Research Center
Application Example: Energy Storage Devices
Demonstration
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 41
Prognostics HIL Testbed
• Demonstrate prognostic algorithm performance– Fast
– Inexpensive
– Control of several run-to-failure parameters
– Interesting dynamics
• Evaluate different prediction algorithms and uncertainty management schemes
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 42
Modeling Batteries
Concentration
polarization
IR drop
Activation polarization
Eo
Increasing Current I
Incre
asin
g V
olta
ge
E
Polarization Curve
1/
C
re re+rct
-> oo
m=1/(rctCnf)
re+2S2Cnf
Re(Z)
Im(Z
)
Increasing Ohmic Resistance
0
0
Increasing Ohmic Resistance
Electrolyte Weakening
Re(Z)
Im(Z
)
Increasing Charge Transfer Resistance
0
0
Increasing Charge Transfer Resistance
Plate Sulphation
Freq.
Domain
Time
Domain
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 43
• Objective: Predict when Li-ion battery voltage will dip below 2.7V indicating end-of-discharge (EOD)
• Approach
– Model non-linear electro-chemical phenomena that explain the discharge process
– Learn model parameters from training data
– Let the PF framework fine tune the model during the tracking phase
– Use the tuned model to predict EOD
time
voltage
Eo
Eo-E
sd
Eo-E
rd
Eo-E
mt
E=Eo-E
sd-E
rd-E
mt
mt: mass transfersd: self dischargerd: reactant depletion
Modeling SOC
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 44
• Objective: Predict when Li-ion battery capacity will fade by 30% indicating life (EOL)
• Approach
– Model self-recharge and Coulombic efficiency that explain the aging process
– Learn model parameters from training data
– Let the PF framework fine tune the model during a few initial cycles
– Use the tuned model to predict EOL
time
voltage
discharge self-recharge
from measurements from modelR. Huggins, Advanced Batteries: Materials Science
Aspects, 1st ed., Springer, 2008.
Modeling SOL
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 45
Battery Testbed• Cells are cycled through charge and
discharge under different load and
environmental conditions set by the
electronic load and environmental chamber
respectively
• Periodically EIS measurements are taken to
monitor the internal condition of the
battery
• DAQ system collects externally observable
parameters from the sensors
• Switching circuitry enables cells to be in the
charge, discharge or EIS health monitoring
state as dictated by the aging regimeBHM
EIS: Electro-chemical Impedance Spectroscopy
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 46
Prognostics in Action
12/09/2009 D I A G N O S T I C S & P R O G N O S T I C S 47
References• A. Saxena, J. Celaya, B. Saha, S. Saha, K. Goebel, “Metrics for Offline Evaluation of Prognostic
Performance”, International Journal of Prognostics and Health Management, 001, 2010
• M. Daigle and K. Goebel, “Model-based Prognostics under Limited Sensing”, Proceeding of IEEE Aerospace conference 2010, 2010
• A. Saxena, K. Goebel, “Requirements Specification for Prognostics Performance - An Overview”, Proceedings of AIAA@Infotech 2010, 2010
• B. Saha, K. Goebel, and J. Christophersen, “Comparison of Prognostic Algorithms for Estimating Remaining Useful Life of Batteries”, Transactions of the Royal UK Institute on Measurement & Control, special issue on Intelligent Fault Diagnosis & Prognosis for Engineering Systems, pp. 293-308, 2009
• B. Saha, K. Goebel, S. Poll and J. Christophersen, “Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework”, IEEE Transactions on Instrumentation and Measurement, Vol. 58, No. 2, pp. 291-296, 2009
• J. Celaya, N. Patil, S. Saha, P. Wysocki, and K. Goebel, “Towards Accelerated Aging Methodologies and Health Management of Power MOSFETs”, Proceedings of Annual Conference of the PHM Society 2009, 2009
• B. Saha, K. Goebel, “Modeling Li-ion Battery Capacity Depletion in a Particle Filtering Framework”, Proceedings of Annual Conference of the PHM Society 2009, 2009
• K. Goebel, B. Saha, A. Saxena, J. Celaya, and J. Christophersen, “Prognostics in Battery Health Management”, I&M Magazine, Vol. 11, No. 4, pp. 33-40, 2008
• K. Goebel, B. Saha, and A. Saxena, “A Comparison of Three Data-driven Techniques for Prognostics”, Proceedings of MFPT 2008 2008