Reservoir Computing Methods for Prognostics and Health Management (PHM) Piero Baraldi Energy Department Politecnico di Milano Italy

Transcription

1 Reservoir Computing Methods for Prognostics and Health Management (PHM) Piero Baraldi Energy Department Politecnico di Milano Italy

2 2 Piero Baraldi Data Industry Digitalization 2.8 Trillion GD (ZD) generated in 2016 Available data Analytics Time Data Analytics

3 3 Piero Baraldi Data Industry Digitalization 2.8 Trillion GD (ZD) generated in 2016 Available data Analytics Time Data Analytics Predictive Maintenance

4 4 Piero Baraldi Predictive Maintenance 4 Ambient & Operating Conditions u 1 Monitored Signals Analytics Industry 4.0 u 2 u N Prognostic Model Remaining Useful Life (RUL) t p Present time Failure time

5 5 Piero Baraldi Predictive Maintenance 5 Ambient & Operating Conditions u 1 Monitored Signals Analytics Industry 4.0 u 2 u N Prognostic Model Remaining Useful Life (RUL) t p Present time Failure time Safety improvement, Cost Saving, New Business Maximum Availability Business continuity Warehouse savings Zero-defect production Zero-waste production Optimal Maintenance Decisions Future demand Logistics options

6 In this Presentaton 6 Prognostics Recurrent Neural Network (RNN) Reservoir Computing Echo State Network Application to the Prediction of Turbofan Engine RUL 6 Piero Baraldi

7 Temperature Prognostics: What is the Problem? Aircraft Turbofan Engine N Monitored Signals Signal 1 Signal 2.. Signal N 7 Time

8 Temperature Prognostics: What is the Problem? RUL Aircraft Turbofan Engine N Monitored Signals Signal 1 Signal 2.. Signal N Prognostic Model Aircraft Engine RUL Prediction 8 Time Time

9 9 Piero Baraldi Prognostics: the Challenge 9 System evolution depends on present and past signal values (the memory of the history) 2 identical components Monitored Signal u Same measurements at time t p : u t p u(t p ) t p 0 t p Monitored Signal u t f t p t p t f

10 10 Prognostics: Methods Feedforward Neural Network Connection: RUL t p u 1 w 11 w 11 u 1 Computational unit (neurons): u 1 w 11 u 2 w 21 f 3 u i w i1 i=1 u 3 w 31

11 11 Prognostics: Methods Feedforward Neural Network RUL t p connections only "from left to right", no connection cycle no memory

12 Prognostics: Methods Feedforward Neural Network Recurrent Neural Network RUL t p RUL t p 12 connections only "from left to right", no connection cycle no memory at least one connection cycle activation can "reverberate", persist even with no input system with memory

13 In this presentaton 13 Prognostics Recurrent Neural Network (RNN) Reservoir Computing Echo State Network Application to the Prediction of Turbofan Engine RUL 13 Piero Baraldi

14 14 Piero Baraldi Recurrent NN: General Idea 14 Time trajectory u N t = 1 u 1: t p t = t p u 1 u 1: t p PROGNOSTIC MODEL RUL t p

15 15 Piero Baraldi Recurrent NN: General Idea 15 Non Linear Expansion M N Time trajectory u N x 2 Linear Regression x t p t = 1 u 1: t p u 1 x 1 RUL t p rul t = t p x M x t p = f u 1: t p u 1: t p Recursive definition RUL t p = W out x(t p ) x t p = f x(t p 1), u t p

16 16 Piero Baraldi Recurrent NN 16 Non Linear Expansion W W in u 1 (t p ) u 2 (t p ) u 3 (t p ) u 1: t p x 1 (t p ) = f N i=1 M w in i1 u i (t p ) + i=1 w i1 x i (t p 1)

17 17 Piero Baraldi Recurrent NN 17 Non Linear Expansion W Linear Regresion u 1 (t p ) W in W out u 2 (t p ) u 3 (t p ) RUL t p u 1: t p x(t p ) = f W in u(t p ) + Wx(t p 1) RUL t p = W out x(t p )

18 18 RNN: Training TRAINING SET u 1, RUL GT 1 = t f 1 u 5, RUL GT 5 = t f 5 u t f 1, RUL GT t f 1 = 1 W in, W, W out u Run-to-failure degradation trajectory u(5) 5 t f t RUL GT 5 = t f 5

19 19 19 RNN: Training TRAINING SET u 1, RUL GT 1 = t f 1 u 2, RUL GT 2 = t f 2 u t f 1, RUL GT t f 1 = 1 W in, W, W out Training Objective: minimize the error function t f 1 E RUL, RUL GT =RMSE= t=1 1 t f 1 RUL(t) RULGT (t) 2

20 20 20 RNN: Training TRAINING SET u 1, RUL GT 1 = t f 1 u 2, RUL GT 2 = t f 2 u t f 1, RUL GT t f 1 = 1 W in, W, W out Training Objective: minimize the error function t f 1 E RUL, RUL GT =RMSE= t=1 1 t f 1 RUL(t) RULGT (t) 2 Training Methods: Gradient-descent-based methods Reservoir Computing

21 21 21 Gradient-descent-based methods for RNN W W in W out RUL GT (t) u(t) RUL(t) - Error(t) RNN are difficult to train using gradient-descent-based methods: Bifurcations Many updating cycles Too long training times Hard to obtain long range memory

22 In this presentaton 22 Prognostics Recurrent Neural Network (RNN) Reservoir Computing Echo State Network Application to the Prediction of Turbofan Engine RUL 22 Piero Baraldi

23 23 Piero Baraldi Reservoir Computing (RC): Terminology Reservoir readout What is it? Non-linear temporal expansion function Linear function Purpose Expand the input history u 1: t p into a rich-enough reservoir space x(t p ) Combine the neuron signals x(t p ) into the desired output signal target RUL t p

24 24 Piero Baraldi Reservoir Computing (RC): Basic Idea 24 Reservoir and readout serve different purposes They can be separately trained Reservoir readout What is it? Non-linear temporal expansion function Linear function Purpose Expand the input hystory u 1: t p into a rich-enough reservoir space x(t p ) Combine the neuron signals x(t p ) into the desired output signal target RUL t p

25 Reservoir Methods 25 Echo State Networks Liquid State Machines Evolino Backpropagation-Decorrelation Temporal Recurrent Networks 25 Piero Baraldi

26 In this presentaton 26 Prognostics Recurrent Neural Network (RNN) Reservoir Computing Echo State Network Application to the Prediction of Turbofan Engine RUL 26 Piero Baraldi

27 Generate the reservoir Purpose: obtain a rich enough reservoir space x(n) Recipe: Big reservoir (M up to 10 4 ) rich enough reservoir space Sparsely connected W is sparse (no more than 20% of possible connections) Randomly connected weights of the connections are randomly generated from a uniform distribution symmetric around the zero value W

28 28 Readout Purpose: learn the weights W out which minimize: E RUL, RUL GT t f 1 =RMSE= t=1 1 t f 1 W outx(t) RUL GT (t) 2 u 1 (t) u 2 (t) W in W W out x t = RUL GT (t) Readout Linear regression W out RUL(t p t ) = W out x(t) u N (t)

29 29 29 Training: Traditional RNN VS ESN Traditional RNN ESN W RUL GT random W RUL GT u W in W out RUL - u W in W out RUL - error error

30 30 The Echo State Property The effect of x t and u t on a future state x t + k should vanish gradually as time passes (i.e., k ) and not persist or even get amplified. For most practical purposes: ρ W : spectral radius of W = largest absolute eigenvalue of W < 1 Echo State Property is satisfied

31 31 31 In this presentaton Prognostics: Recurrent Neural Networks (RNN) Reservoir Computing Echo State Network Application to the prediction of Turbofan Engine RULs

32 Temperature Prognostics: What is the Problem? RUL Aircraft Turbofan Engine N Monitored Signals Signal 1 Signal 2.. Signal N Prognostic Model Aircraft Engine RUL Prediction 32 Time Time

33 The C-MAPPS dataset* 260 run-to-failure trajectories 21 measured signals + 3 signals representative of the operating conditions 6 different operating conditions Data Preprocessing** 33 * 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

34 34 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Output Scaling

35 35 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Output Scaling

36 36 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling/Shifting 5) Output Scaling/Shifting 6) Output Feedback

37 37 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Output Scaling

38 38 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Input Shifting

39 39 ESN Architecture Optimization Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Input Shifting Sigmoidal Activation Function

40 40 ESN Architecture Optimization Experience + trial & errors difficult, good performance not guaranteed Differential evolution Optimization Algorithm Population-based: Objective function: RA = σ RULGT R UL RUL GT CHROMOSOME Network Dimensions Connectivity Spectral Radius Input Scaling Inout Shifting Evolutionary-based Initialization Mutation Crossover Selection

41 41 Optimal Architecture Network Architecture Optimization: Parameters RUL(t) 1) Network Dimensions 2) Spectral Radius 3) Connectivity 4) Input Scaling 5) Input Shifting Network Dimensions Connectivity Spectral Radius Input Scaling Output Scaling

42 42 RUL (Cycle) ESN for Prognostics: Results (I) RUL Prediction for Tansient 157 True RUL ESN FS ELM Time (Cycle) ESN = Echo State Network FS = Fuzzy Similarity-based Prognosti Method ELM = Extreme Learning Machine

43 43 43 ESN for Prognostics: Results (II) Results Prognostic Metrics (70 test trajectories) Cumulative Relative Accuracy RA RUL ˆ RUL RUL GT Alpha-Lambda α = 0. 2 SI t Steadiness var( T t t) : ), ( t Extreme Learning Machine Fuzzy Similarity-based Method 0.42 ± ± ± ± ± ± 0.7 Echo State Network 0.37 ± ± ± 1.2

44 44 RUL Conclusions Recurrent Neural Network Dynamic problem Time Training: Reservoir Computing Echo State Network Accurate RUL prediction Short Training Time Able to catch the system dynamics

45 45 45 Acknowledgments Dr. Sameer Al-Dahidi Francesco Cannarile Dr. Michele Compare Dr. Francesco Di Maio Dr. Marco Rigamonti Mingjing Xu Zhe Yang Prof. Enrico Zio

46 46 Thank You!