Mathematical Methods for Modelling and Identification of Nonlinear Systems

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.

Multidimensional membership functions in T–S fuzzy models for modelling and identification of nonlinear multivariable systems using genetic algorithms

Teaching Aids for Modeling and Control of Hybrid Systems (CAMCHS)

A state‐of‐the‐art review on various identification schemes proposed for the Hammerstein, Wiener, and Volterra systems is presented with respect to the special problems arising in the identification of unknown nonlinear systems. Past and recent developments in the field of nonlinear system identification, parameter estimation, and nonlinear control schemes along with the nonlinearity issues are also deeply investigated. A comprehensive analysis on various parameter estimation approaches and nonlinear control laws are made adding credit to the noteworthy contributions, constructive arguments, and remarkable breakthroughs of researchers in various research fields. The application of most popular nonlinear control strategies for many nonlinear systems in the existing literature are presented spotlighting their merits and major shortcomings. The challenges faced in the nonlinear control field and their emergences to future directions are projected.

Identification of nonlinear systems using NARMAX model

Identification of nonlinear systems is one of the important problems in engineering. Chaotic systems are among those nonlinear systems that have been in the center of attention of many researchers because of their complex and unpredictable behaviors. This paper proposes an algorithm for optimally estimating the parameters of system by minimizing the mean of squared errors (MSE) index. In this paper, Teaching Learning Based Optimization (TLBO) algorithm is used for solving both offline and online parameter estimation problems for chaotic systems. The validity of this algorithm in terms of convergence speed and parameter accuracy in comparison to other popular optimization algorithms such as Standard PSO (PSO), Differential Evolution (DE), Adaptive Particle Swarm Optimization (APSO) and Genetic Algorithm (GA) is shown through an illustrative example for the modeling of chaotic systems. Furthermore, in order to demonstrate the feasibility of this algorithm, it is applied to the problem of parameter identification of a well-known nonlinear Lorenz chaotic system. According to simulation results, the proposed algorithm is a very suitable algorithm for online parameter identification for a class of nonlinear chaotic systems.

A method for identifying nonlinear dynamic systems with noise is proposed by using probabilistic universal learning networks (PrULNs). PrULNs are extensions of universal learning networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.

Nonlinear dynamic systems are characterized with uncertainties in terms of structure and parameters. These uncertainties cannot be described by deterministic models. The modelling and identification of nonlinear dynamic systems through the measured experimental data is a problem in engineering and technical processes. Therefore, field of system identification have become an important area of research. Fuzzy technology is an effective tool for dealing with complex nonlinear processes that are characterized with uncertain factors. In this paper, a novel approach based on Local Linear method learning in dynamical filter weights neurons for the identification of non-linear dynamic systems is presented. The fuzzy wavelet neural network combines wavelet theory with fuzzy logic and neural networks. Learning fuzzy rules and parameter update in fuzzy wavelet neural network is based on gradient decent method. The proposed approach is said to be Fuzzy Local Linear Wavelet Neural Network based model. It has been explained through examples. The structure is tested for the identification with both wavelet neural network and Fuzzy Local Linear Wavelet Neural Network that shows the comparative performance.KeywordsSystem IdentificationNon-linear SystemWavelet Neural NetworkFuzzy Wavelet Neural NetworkLocal Linear Wavelet Neural NetworkFuzzy Local Linear Wavelet Neural Network

Identification of nonlinear cascade systems with output hysteresis based on the key term separation principle

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

The identification and modeling of linear and nonlinear dynamic systems through the use of measured experimental data is a problem of considerable importance in engineering. Among the identification methods, the artificial neural network is a newly developed technique. Due to its attributes, such as parallelism, adaptability, robustness, and the inherent ability to handle nonlinearity, artificial neural networks have shown great promise in function mapping, pattern recognition, image processing, and so on. However, dynamic function mapping, including the structural dynamic model identification, is still a challenging topic in neural network applications. A neural network approach for structural dynamic model identification is presented in this paper. The neural network is trained, tested, and verified by using the responses recorded in a real apartment building during earthquakes. The results show that the dynamic behaviors of the building can be very well modeled by the trained neural network. The results also indicate the great potential of using neural networks in structural dynamic model identification.

Identification of nonlinear systems by use of nonstationary white-noise inputs

Publication in the conference proceedings of EUSIPCO, Trieste, Italy, 1996

A new algorithm is presented for the identification of non-linear lumped time-invariant SISO systems. The method is based on differentiation properties of the exponential Fourier series and can be used to identify a wide class of systems. Identification of two specific systems is studied. An illustrative example is provided which shows that the algorithm gives accurate parameter estimates

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics