Nonlinear System Identification using Support Vector Regression
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1 Nonlinear System Identification using Support Vector Regression Saneej B.C. PhD Student Department of Chemical and Materials Engineering University of Alberta
2 Outline 2 1. Objectives 2. Nonlinearity in Process Industry 3. Support Vector Regression 4. Nonlinear System Identification: Case studies a. Melt Index Soft Sensor b. Nonlinear Dynamic System Identification of a ph neutralization process 5. Concluding Remarks
3 Objectives 3 Development of soft sensors based on the theory of Support Vector Regression (SVR) for application to nonlinear plants Development of a methodology for nonlinear system identification from dynamic data using SVR
4 Nonlinearity in Process Industry 4 Many industrial processes pushed to nonlinear operation windows Increasingly tight product specifications Higher Environmental & Safety considerations Economic pressures Nonlinear Model Predictive control (NMPC) is becoming popular in the chemical industry due to increasing process nonlinearities 125 NMPC applications reported in chemical industries in the past decade* Breakdown of NMPC applications in Chemical Industry *Courtesy: Nonlinear Model Predictive Control: From Chemical Industry to Microelectronics,Zoltán K. Nagy and Frank Allgöwer, 43rd IEEE Conference on Decision and Control,2004 SVR can be used to build data based nonlinear models
5 Support Vector Regression 5 Support Vector Regression Machines proposed in 1996 by Vapnik, Harris Drucker, Chris Burges, Linda Kaufman and Alex Smola (Advances in Neural Information Processing Systems 9, NIPS 1996, , MIT Press) f(x ) + ε f(x ) f(x) - ε y ξ * ξ x
6 Support Vector Regression Support vectors 6 ( ) Support Vectors f(x)+ε f(x) ξ f(x)- ε y ξ x
7 Support Vector Regression Nonlinear regression by Kernels 7 Examples: Linear <x i, x j > Polynomial (<x i, x j >+c) p Sigmoid tanh(c+γ <x i, x j >) Radial Basis function /Gaussian kernel exp(-γ x i -x j 2 ) Choosing a Kernel depends on application
8 8 MI Soft Sensor
9 What is a Soft Sensor? 9 Online Analyzer Expensive High Maintenance Cost
10 10 MI Soft Sensor Nonlinear SVR can be used to build a soft sensor where the output has nonlinear relationship with the input Eg: Melt Index of polymer is observed to be nonlinearly related to variables monitored in the extruder (Sharmin et al (2006), Alleyne et al (2006)) Extruder Schematic Online Analyzer Unreliable Head Flange Screen Pack
11 MI Soft Sensor (contd..) 11 Application to MI data from EVA polymerization plant Empirical Soft sensor previously implemented MI = exp(a + b.s S + c( P 2 T α ) + d.p ) α Nonlinear Least square Regression (slow training, local minima, results highly dependent on initial guesses) Soft sensor required bias update every 30 mins using the online rheometer readings Extruder Schematic Online Analyzer 30 mins bias updating Soft Sensor Head Flange Screen Pack
12 MI Soft Sensor (contd..) 12 SVR based soft sensor Implementation in MATLAB: LIBSVM Toolbox Based on 10 variables measured at the extruder upstream of the online MI measurement Input variables : 6 Pressures, 3 Temperatures, Extruder speed Target variable : Y i = log(mi) Kernel choice : RBF kernel All parameters tuned by trial and error method C=100, ε=0.3,γ =1e-6 Extruder Schematic Online Analyzer bias updating (>30 mins)? Head Flange Screen Pack SVR Soft Sensor
13 MI Soft Sensor (contd..) 13 MI data from EVA polymerization unit (AT Plastics, Edmonton) ~ 10 grades Challenge: Single Model!
14 MI Soft Sensor (contd..) 14 Comparing the two models (without bias update):
15 MI Soft Sensor (contd..) 15 Comparing 2 hrs-bias values of the two models
16 MI Soft Sensor (contd..) 16 Comparing 2 hrs-bias values of the two models Higher bias fluctuation within grades
17 MI Soft Sensor (contd..) 17 Comparing the two models (with 2hrs bias update): Lower MSE (~ 4-fold better)
18 MI Soft Sensor (contd..) 18 Comparing the two models (with 2hrs bias update): Zooming
19 MI Soft Sensor (contd..) 19 Comparing the two models (with 2hrs bias update): Better predictions Higher variance in the predictions (undesirable for control)
20 Nonlinear Dynamic System Identification 20 ph neutralization process Highly Nonlinear dynamic system Inputs: Acid, Base flow rates Output: ph of mixture Acetic Acid Sodium Hydroxide (Base) ph TRAINING Tim e(secs) DaISy: Database for the Identification of Systems Department of Electrical Engineering, ESAT/SISTA, K.U.Leuven, Belgium, URL: VALIDATION
21 Nonlinear Dynamic System Identification (contd..) 21 SVR based system identification Assume Nonlinear ARX structure (NARX) y( t) = f ([ y( t 1: t na), u ( t d : t d nb + 1), u ( t d : t d nb + 1)]) + ε RBF Kernel Model order selection (na, nbs), delay selection, SVR parameter tuning: By trial and error based on the validation data fit Validation: Infinite horizon prediction on validation data set SELECT SVR Parameters (Kernel, Loss function, C) Model Order Training Validation Good? Y Use it! Redo N
22 Nonlinear Dynamic System Identification Results 22 Validation results:
23 Concluding Remarks SVR is an efficient tool for non-linear regression 2. Case studies discussed: a. Soft sensor development based on SVR MI Soft sensor: Accurately captures wide operating ranges of a nonlinear EVA polymerization plant b. Nonlinear Dynamic System Identification using SVR ph neutralization: Illustrates effectiveness of SVR for developing nonlinear dynamic models based on process data
24 Acknowledgements Dr. Sirish L. Shah 2. CPC Group Members 3. NSERC-Matrikon-Suncor-iCORE for financial support
Support Vector Regression (SVR) Descriptions of SVR in this discussion follow that in Refs. (2, 6, 7, 8, 9). The literature
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