Reservoir Computing Methods for Prognostics and Health ... · •260 run-to-failure trajectories...
Transcript of Reservoir Computing Methods for Prognostics and Health ... · •260 run-to-failure trajectories...
Reservoir Computing Methods for
Prognostics and Health Management (PHM)
Piero Baraldi, Mingjing Xu
Energy Department
Politecnico di Milano
Italy
In this presentaton
• Recurrent Neural Network (RNN)
• Reservoir Computing
• Echo State Network
• Application 1: Prediction of Turbofan Engine RUL
• Application 2: Prediction of ALSTOM Fast Train Brake system RUL
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Recurrent NN: General Idea 3
𝑅𝑈𝐿 𝑡𝑝𝒖 1: 𝑡𝑝
𝑢1
𝑢𝑁Time
trajectory
𝑡 = 1
𝑡 = 𝑡𝑝
PROGNOSTIC MODEL
𝒖 1: 𝑡𝑝
Recurrent NN: General Idea 4
𝑥2
𝑥1
𝑥𝑀
Linear
Regression
Non Linear
Expansion
𝑅𝑈𝐿 𝑡𝑝 = 𝑾𝒐𝒖𝒕𝒙(𝑡𝑝)𝒖 1: 𝑡𝑝
𝑢1
𝑢𝑁Time
trajectory
𝑡 = 1
𝑡 = 𝑡𝑝𝑟𝑢𝑙
𝑀 ≫ 𝑁
𝒙 𝑡𝑝 = 𝑓 𝒖 1: 𝑡𝑝
𝒖 1: 𝑡𝑝
𝒙 𝑡𝑝
𝑅𝑈𝐿 𝑡𝑝
Recurrent NN: General Idea 5
𝑥2
𝑥1
𝑥𝑀
Linear
Regression
Non Linear
Expansion
𝑅𝑈𝐿 𝑡𝑝 = 𝑾𝒐𝒖𝒕𝒙(𝑡𝑝)𝒖 1: 𝑡𝑝
𝑢1
𝑢𝑁Time
trajectory
𝑡 = 1
𝑡 = 𝑡𝑝𝑟𝑢𝑙
𝑀 ≫ 𝑁
𝒙 𝑡𝑝 = 𝑓 𝒖 1: 𝑡𝑝 = 𝑓 𝒖 1: 𝑡𝑝 − 1 , 𝒖 𝑡𝑝
𝑥 𝑡𝑝 − 1 = 𝑓 𝒖 1: 𝑡𝑝 − 1
𝒙 𝑡𝑝 = 𝑓 𝒙(𝑡𝑝 − 1), 𝒖 𝑡𝑝
𝒖 1: 𝑡𝑝
𝒙 𝑡𝑝
𝑅𝑈𝐿 𝑡𝑝
Recurrent NN 6
𝒖 1: 𝑡𝑝 𝑥1(𝑡𝑝) = 𝑓
𝑖=1
𝑁
𝑤𝑖1𝑖𝑛 𝑢𝑖(𝑡𝑝) +
𝑖=1
𝑀
𝑤𝑖1 𝑥𝑖 (𝑡𝑝 − 1)
𝑾𝒊𝒏
𝑾Non Linear Expansion
𝑢3(𝑡𝑝)
𝑢2(𝑡𝑝)
𝑢1(𝑡𝑝)
Recurrent NN 7
𝒖 1: 𝑡𝑝 𝒙(𝑡𝑝) = 𝑓 𝑾𝒊𝒏𝒖(𝑡𝑝) +𝑾𝒙(𝑡𝑝 − 1) 𝑅𝑈𝐿 𝑡𝑝 = 𝑊𝑜𝑢𝑡𝒙(𝑡𝑝)
𝑾Linear RegresionNon Linear Expansion
𝑢3(𝑡𝑝)
𝑢2(𝑡𝑝)
𝑢1(𝑡𝑝)
𝑾𝒊𝒏
𝑾𝒐𝒖𝒕
𝑅𝑈𝐿 𝑡𝑝
RNN: Training 8
𝑊𝑖𝑛,𝑊,𝑊𝑜𝑢𝑡
TRAINING SET
𝒖 1 , 𝑅𝑈𝐿𝐺𝑇 1 = 𝑡𝑓 − 1
…𝒖 5 , 𝑅𝑈𝐿𝐺𝑇 5 = 𝑡𝑓 − 5
…
𝒖 𝑡𝑓 − 1 , 𝑅𝑈𝐿𝐺𝑇 𝑡𝑓 − 1 = 1
Run-to-failure
degradation trajectory
t
𝒖
5 𝑡𝑓
𝒖(5)
𝑅𝑈𝐿𝐺𝑇 5 = 𝑡𝑓 − 5
RNN: Training 9
𝑊𝑖𝑛,𝑊,𝑊𝑜𝑢𝑡
Training Objective: minimize the error function
𝐸 𝑅𝑈𝐿, 𝑅𝑈𝐿𝐺𝑇 =RMSE=
𝑡=1
𝑡𝑓−11
𝑡𝑓 − 1𝑅𝑈𝐿(𝑡) − 𝑅𝑈𝐿𝐺𝑇(𝑡) 2
TRAINING SET
𝒖 1 , 𝑅𝑈𝐿𝐺𝑇 1 = 𝑡𝑓 − 1
𝒖 2 , 𝑅𝑈𝐿𝐺𝑇 2 = 𝑡𝑓 − 2
…
𝒖 𝑡𝑓 − 1 , 𝑅𝑈𝐿𝐺𝑇 𝑡𝑓 − 1 = 1
RNN: Training 10
𝑊𝑖𝑛,𝑊,𝑊𝑜𝑢𝑡
Training Objective: minimize the error function
𝐸 𝑅𝑈𝐿, 𝑅𝑈𝐿𝐺𝑇 =RMSE=
𝑡=1
𝑡𝑓−11
𝑡𝑓 − 1𝑅𝑈𝐿(𝑡) − 𝑅𝑈𝐿𝐺𝑇(𝑡) 2
TRAINING SET
𝒖 1 , 𝑅𝑈𝐿𝐺𝑇 1 = 𝑡𝑓 − 1
𝒖 2 , 𝑅𝑈𝐿𝐺𝑇 2 = 𝑡𝑓 − 2
…
𝒖 𝑡𝑓 − 1 , 𝑅𝑈𝐿𝐺𝑇 𝑡𝑓 − 1 = 1
Training Methods:
• Gradient-descent-based methods
• Reservoir Computing
Gradient-descent-based methods for RNN
RNN are difficult to train using gradient-descent-based methods:
• Bifurcations
• Many updating cycles → Too long training times
• Hard to obtain long range memory
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𝑾𝒊𝒏 𝑾𝒐𝒖𝒕
𝑾
-
𝑅𝑈𝐿𝐺𝑇(𝑡)𝑅𝑈𝐿(𝑡)
Error(t)
𝒖(𝑡)
In this presentaton
• Recurrent Neural Network (RNN)
• Reservoir Computing
• Echo State Network
• Application 1: Prediction of Turbofan Engine RUL
• Application 2: Prediction of ALSTOM Fast Train Brake system RUL
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Reservoir Computing (RC): Terminology
What is it? Purpose
ReservoirNon-linear temporal
expansion function
Expand the input history 𝒖 1: 𝑡𝑝 into a rich-enough
reservoir space 𝒙(𝑡𝑝)
readout Linear function
Combine the neuron signals 𝒙(𝑡𝑝) into the desired output
signal target 𝑅𝑈𝐿 𝑡𝑝
Reservoir Computing (RC): Basic Idea 14
What is it? Purpose
ReservoirNon-linear temporal
expansion function
Expand the input hystory 𝒖 1: 𝑡𝑝 into a rich-enough
reservoir space 𝒙(𝑡𝑝)
readout Linear function
Combine the neuron signals 𝒙(𝑡𝑝) into the desired output
signal target 𝑅𝑈𝐿 𝑡𝑝
Reservoir and readout
serve different purposes
They can be separately
trained
In this presentaton
• Recurrent Neural Network (RNN)
• Reservoir Computing
• Echo State Network
• Application 1: Prediction of Turbofan Engine RUL
• Application 2: Prediction of ALSTOM Fast Train Brake system RUL
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Generate the reservoir
...
...
Readout
Readout
Linear regression
Traditional RNN ESN
-
Training: Traditional RNN VS ESN 18
error
-
error
random
The Echo State Property
In this presentaton
• Recurrent Neural Network (RNN)
• Reservoir Computing
• Echo State Network
• Application 1: Prediction of Turbofan Engine RUL
• Application 2: Prediction of ALSTOM Fast Train Brake system RUL
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Prognostics: What is the Problem?
Aircraft Turbofan Engine
N Monitored Signals
• Signal 1
• Signal 2
• ………..
• Signal N
Aircraft Engine
RUL Prediction
TimeR
UL
Prognostic
Model
Tem
per
atu
re
Time
• 260 run-to-failure trajectories
• 21 measured signals + 3 signals representative of the operating
conditions
• 6 different operating conditions
Data
Preprocessing**
The C-MAPPS dataset*
* A. Saxena, K. Goebel, D. Simon, N. Eklund, Damage propagation modeling for aircraft engine run-to-failure simulation, PHM2008
**M. Rigamonti, P. Baraldi, E. Zio, I. Roychoudhury, K. Goebel, S. Poll, Echo State Network for Remaining Useful Life Prediction of a
Turbofan Engine, PHM 2016, Bilbao
ESN Architecture Optimization
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Output Scaling
RUL(t)
Network Architecture Optimization: Parameters
ESN Architecture Optimization
RUL(t)
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Output Scaling
RUL(t)
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling/Shifting
5) Output Scaling/Shifting
6) Output Feedback
ESN Architecture Optimization
RUL(t)
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Output Scaling
ESN Architecture Optimization
RUL(t)
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Input Shifting
ESN Architecture Optimization
RUL(t)
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Input Shifting
ESN Architecture Optimization
Sigmoidal Activation Function
ESN Architecture Optimization
• Optimization Algorithm
• Population-based:
• Evolutionary-based
CHROMOSOME
Network
DimensionsConnectivity
Spectral
Radius
Input
Scaling
Inout
Shifting
Initialization Mutation Crossover Selection
• Experience + trial & errors→ difficult, good performance not guaranteed
• Differential evolution
Objective function: 𝑅𝐴 =σ 𝑅𝑈𝐿𝐺𝑇−𝑅𝑈𝐿
𝑅𝑈𝐿𝐺𝑇
Optimal Architecture
Network Architecture Optimization: Parameters
1) Network Dimensions
2) Spectral Radius
3) Connectivity
4) Input Scaling
5) Input Shifting
RUL(t)
Network
DimensionsConnectivity
Spectral
Radius
Input
Scaling
Output
Scaling
385 0.17 0.67 0.45 -0.05
ESN for Prognostics: Results (I)
0 20 40 60 80 100 1200
20
40
60
80
100
120
Time (Cycle)
RU
L (
Cyc
le)
RUL Prediction for Tansient 157
True RUL
ESN
FS
ELM
ESN = Echo State Network
FS = Fuzzy Similarity-based Prognosti Method
ELM = Extreme Learning Machine
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Cumulative Relative Accuracy Steadiness
Extreme
Learning
Machine
0.42 ± 0.03 15.3 ± 2.2
Fuzzy
Similarity-based
Method
Echo State
Network
➢ Results – Prognostic Metrics (70 test trajectories)
RUL
RULLURRA
GT−=
ˆ,)var( :)( tttt TSI −=
ESN for Prognostics: Results (II)
In this presentaton
• Recurrent Neural Network (RNN)
• Reservoir Computing
• Echo State Network
• Application 1: Prediction of Turbofan Engine RUL
• Application 2: Prediction of ALSTOM Fast Train Brake system RUL
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What is the problem?
Problem: Use Prognostic model to predict RUL of Fast Train Brake System
Fast Train Brake System
Fast Train Brake System
Brake systems of Fast Train
Component 1 Component 2 Component 3 Component 4
Case Study
Run-to-Fail Trajectory 170
Signals 6
➢ Available Dataset
Artificial data that mimic the complexity of the industrial data.
Brake systems of Fast Train
0 2000 4000 6000 8000 10000 12000 14000
time
350
360
370
380
390
Tem
pe
ratu
re [
K]
0 2000 4000 6000 8000 10000 12000 14000
time
0
2
4
6
8
10
Op
era
tio
n M
od
e
Case Study
Run-to-Fail Trajectory 170
Signals 6
Brake systems of Fast Train
0 5000 10000 15000
time
0.09
0.1
0.11
0.12
0.13
Degra
da
tion I
nde
x
Component 1
0 5000 10000 15000
time
0.08
0.1
0.12
0.14
0.16
0.18
Degra
da
tion I
nde
x
Component 2
0 5000 10000 15000
time
0.08
0.1
0.12
0.14
0.16
0.18D
egra
da
tion I
nde
x
Component 3
0 5000 10000 15000
time
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Degra
da
tion I
nde
x
Component 4
➢ Available Dataset
Artificial data that mimic the complexity of the industrial data.
Case Study
Simulated Data
Acquisition
➢ Animation: Data Collection Process
Case Study
Simulated Data
Acquisition
➢ Difficulty
• Signals acquisition only when
event occurs
• If no Event occurs, no measurement signals will be collected.
Case Study
Simulated Data
Acquisition
➢ Difficulty
• Signals acquisition only when
event occurs
Case Study
Simulated Data
Acquisition
➢ Difficulty
• Signals acquisition only when
event occurs
Stop
data acquisition
Stop
data acquisition
Stop
data acquisition
Stop
data acquisition
Stop
data acquisition
Stop
data acquisition
Case Study 42
➢ i) incomplete data
➢ ii) dynamic and non stationary signal behavouir
➢ iii) continuous modification of industrial equipment operating conditions
Dataset Characteristic
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➢ RUL prediction result
• prognostic metrics computed on 100 test
trajectories
Metrics CRA [-inf,1] 𝛼 − 𝜆 [0,1]
0.711±0.140 0.635±0.276
• RUL prediction examples
0 1 2 3 4
time 104
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
RU
L
104
true RUL vs. predicted RUL-- trajectory #120
CRA=0.89778 - =0.92581 SI=95.3245
0 1 2 3 4
time 104
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
RU
L
104
true RUL vs. predicted RUL-- trajectory #99
CRA=0.75715 - =0.45984 SI=86.79
Events
Events
ESN for Prognostics: Results
Conclusions
Recurrent Neural Network
Training: Reservoir Computing
Echo State Network
• Accurate RUL prediction
• Short Training Time
• Able to catch the system dynamics
Time
RU
L
Dynamic problem
Thank you very much
for your attention!
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