Nonlinear LFR Block-Oriented Model: Potential Benefits and Improved, User-Friendly Identification Method

Nowadays, there is a high need for accurate, parsimonious nonlinear dynamic models. Block-oriented nonlinear model structures are known to be excellent candidates for this task. The nonlinear linear fractional representation model, composed of a static nonlinearity (SNL) and a multiple-input-multiple-output (MIMO) linear time-invariant (LTI) part, is highly flexible since it creates an arbitrary MIMO-LTI interconnection between the model's input and output and the SNL's input and output. First of all, it can cope with the nonlinear feedback (which is very important in oscillators and mechanical applications). Secondly, it incorporates certain classical block-oriented models as special cases. Finally, it does not postulate the SNL's location prior to the identification. Starting from two classical frequency response measurements of the system, the method generates the best possible MIMO-LTI configuration and estimates the SNL in an automated, user-friendly, and efficient (noniterative) way. The method will be illustrated on simulation examples and experimental data.

[1]  H. Craighead.  Nanoelectromechanical systems. , 2000, Science.

[2]  K. E. -A. Van Den Abeele,et al.  Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part II: Single-Mode Nonlinear Resonance Acoustic Spectroscopy , 2000, Research in Nondestructive Evaluation.

[3]  Jan Swevers,et al.  Identification of nonlinear systems using Polynomial Nonlinear State Space models , 2010, Autom..

[4]  Y. Ben‐Zion,et al.  Non-linear damage rheology and wave resonance in rocks , 2009 .

[5]  Fabio Filicori,et al.  A nonlinear dynamic model for performance analysis of large-signal amplifiers in communication systems , 2004, IEEE Transactions on Instrumentation and Measurement.

[6]  Julian J. Bussgang,et al.  Crosscorrelation functions of amplitude-distorted gaussian signals , 1952 .

[7]  Gerd Vandersteen,et al.  Measurement and identification of nonlinear systems consisting of linear dynamic blocks and one static nonlinearity , 1999, IEEE Trans. Autom. Control..

[8]  J. Potter.  Matrix Quadratic Solutions , 1966 .

[9]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[10]  Johan Schoukens,et al.  Identification of systems with localised nonlinearity: From state-space to block-structured models , 2013, Autom..

[11]  D. Rees,et al.  System modelling in the presence of nonlinear distortions , 2004, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510).

[12]  Rik Pintelon,et al.  Estimation of the risk for an unstable behaviour of feedback systems in the presence of nonlinear distortions , 2004, Autom..

[13]  L. Ljung,et al.  Subspace-based multivariable system identification from frequency response data , 1996, IEEE Trans. Autom. Control..

[14]  Georgios B. Giannakis,et al.  A bibliography on nonlinear system identification , 2001, Signal Process..

[15]  Stephen A. Billings,et al.  Identification of systems containing linear dynamic and static nonlinear elements , 1982, Autom..

[16]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.

[17]  Yves Rolain,et al.  Identification of a Block-Structured Nonlinear Feedback System, Applied to a Microwave Crystal Detector , 2008, IEEE Transactions on Instrumentation and Measurement.

[18]  Ana Paula Rocha,et al.  Linear and nonlinear heart-rate analysis in a rat model of acute anoxia , 2008, Physiological measurement.

[19]  Lennart Ljung,et al.  Perspectives on system identification , 2010, Annu. Rev. Control..

[20]  Yves Rolain,et al.  Mastering System Identification in 100 Exercises: Schoukens/Mastering , 2012 .

[21]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[22]  V. Verdult.  Non linear system identification : a state-space approach , 2002 .

[23]  Henry Shu-Hung Chung,et al.  Nonlinear high-intensity discharge lamp model including a dynamic electrode voltage drop , 2003 .

[24]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..

[25]  J. Schoukens,et al.  Estimation of nonparametric noise and FRF models for multivariable systems—Part I: Theory , 2010 .

[26]  M. Hamilton,et al.  Linear and nonlinear frequency shifts in acoustical resonators with varying cross sections , 2001 .

[27]  Grigorios N. Beligiannis,et al.  Nonlinear model structure identification of complex biomedical data using a genetic-programming-based technique , 2005, IEEE Transactions on Instrumentation and Measurement.

[28]  Johan A. K. Suykens,et al.  Artificial neural networks for modelling and control of non-linear systems , 1995 .

[29]  J. Schoukens,et al.  Nonparametric initial estimates for Wiener-Hammerstein systems , 2006 .

[30]  K. Mårtensson,et al.  On the matrix riccati equation , 1971, Inf. Sci..

[31]  Yves Rolain,et al.  Mastering System Identification in 100 Exercises , 2012 .

[32]  Yves Rolain,et al.  Fast approximate identification of nonlinear systems , 2003, Autom..

[33]  Lennart Ljung,et al.  Linear approximations of nonlinear FIR systems for separable input processes , 2005, Autom..

[34]  Raúl Rojas,et al.  Neural Networks - A Systematic Introduction , 1996 .

[35]  K. Mrtensson.  On the matrix riccati equation , 1971 .

[36]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[37]  L. Vanbeylen.  From two frequency response measurements to the powerful nonlinear LFR model , 2012, 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings.