Support vector machines for system identification

This article presents a theoretical framework for the identification of nonlinear dynamic MISO systems with orthonormal base function models on fundamental basics of the Volterra theory. In the past the Volterra theory was used for the identification of nonlinear dynamic SISO systems (e.g. Hammerstein and Wiener models). In principle it is possible to extend these approaches to systems with more than one input (i.e. MISO systems). In former times this failed due to a lack of computational performance. In this paper an approach is presented which allows the identification of arbitrary coupled Hammerstein and Wiener models with multiple inputs. Some fundamental considerations for the identification of MISO systems based on arbitrary coupled Hammerstein models are made and extended to MISO systems based on arbitrary coupled Wiener models. This extended Volterra theory results in equations where the unknown parameters can be separated of the input values in a linear manner. In order to approximate the truncated impulse responses of the linear dynamic systems and to reduce the number of unknown parameters orthonormal base functions (OBFs) are introduced. As an example the proposed identification method is applied to a MISO system based on forward and backward coupled Hammerstein and Wiener models.

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

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

This paper describes the development of a self-feedback Sigma-Pi-linked (/spl Sigma/-/spl Pi/) backpropagation neural network and its applications to dynamical system identification. A self-feedback path is added to each neuron to generate the recursive effect. Each neuron output is recursively related by current input and its preceding output. The introduction of this self-feedback path enables the network to exhibit a dynamic characteristic. Using this complex /spl Sigma/-/spl Pi/-linked architecture, the developed network is capable of performing a system identification for a highly non-linear plant. In the last section of this paper, the function approximation property of this modified network is applied to system identification for different linear and non-linear dynamical systems. This paper also compares the modified network with the conventional backpropagation neural network. Simulation results show that the function approximation property of the modified network is encouraging and can be successfully applied to nonlinear dynamical system identification. >

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.

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.

The paper proposes a general framework for modelling non-linear dynamic systems based on a support vector machine (SVM): it first provides a short introduction to regression SVMs, then uses a standard SVM to model a non-linear auto-regressive and moving average (NARMAX) model, and contains a theoretical discussion about its robustness under low and high noise by its properties. The simulation results indicate that the SVM method can reduce the effect of samples and noise for modelling, and its performance is better than that of the neural network modelling method.

In this study, nonlinear dynamic systems are identified by using artificial bee colony (ABC) algorithm and adaptive neuro fuzzy inference system (ANFIS). ABC algorithm is used in training and updating of ANFIS. The most appropriate model is formed by optimizing the antecedent and conclusion parameters that are found in the structure of ANFIS. The dynamic systems that consist of one input and one output (SISO) are used for the identification of nonlinear dynamic systems. The obtained results are compared with fuzzy neural network, neural network and ANFIS-based methods such as RSONFIN, DFNN, RSEFNN-LF, WRFNN and RFNN. The simulation results show that the proposed method is successful in the identification of considered nonlinear dynamic systems.

In this paper, nonlinear dynamic system identification by using multiobjectively selected RBF network is considered. RBF networks are widely used as a model structure for nonlinear systems. The determination of its structure that is the number of basis functions is prior important step in system identification, and the tradeoff between model complexity and accuracy exists in this problem. By using multiobjective evolutionary algorithms, the candidates of the RBF network structure are obtained in the sense of Pareto optimality. We discuss an application to system identification by using such RBF networks having Pareto optimal structures. Some numerical simulations for nonlinear dynamic systems are carried out to show the applicability of the proposed approach.

This paper illustrates how the Muntz neural networks can be used effectively for identification of linear and nonlinear dynamic systems. A neuron is utilized to build the Muntz networks with locally distributed dynamics to identify input/output models of dynamic processes. For static neural network design, the orthogonal Muntz polynomials are used; for dynamic part, the orthogonal Muntz-Legendre rational functions are used

The paper demonstrates that radial basis function network (RBFN) with adaptive centers and width can be used effectively for identification of nonlinear dynamic system. The proposed RBFN is trained by hybrid learning algorithm, which uses conjugate gradient optimization algorithm to obtain the center and width of each radial basis function and the least squares method to obtain the weights. To avoid capturing a local optimum, regularization error energy function is used and the centers of basis functions are initialized using a fuzzy C-means clustering method. Simulation results reveal that the identification schemes based on RBFN gives considerably better performance and show faster learning in comparison to previous methods

Discovering nonlinear PDEs with sparse identification of nonlinear dynamical systems (SINDy) is hindered by high dimensionality, noise, and expensive data acquisition. We propose the greedy sampling neural network for sparse identification of nonlinear PDEs (GN-SINDy), a three–stage framework that integrates strategic sampling, differentiable surrogate modelling, and sparse equation discovery. First, a two–way Q-DEIM–based greedy strategy selects maximally informative space–time samples from snapshot data, drastically reducing data requirements. Second, a deep neural network (DNN) is trained as a differentiable surrogate of the solution field, enabling noise–robust analytic derivatives via automatic differentiation. Third, sparse regression with sparsity–promoting estimators [Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016a). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932–3937; Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017). Data-driven discovery of partial differential equations. Science Advances, 3(4), e1602614.] is applied to recover the governing PDE. Building on the DeepMoD paradigm, GN-SINDy embeds greedy sampling into data acquisition and stabilises coefficient estimation through neural–enhanced differentiation. We analyze noise robustness, structural stability, and QR–based sampling strategies to guide sampler and hyperparameter selection. Experiments on Burgers', Allen–Cahn, and Korteweg–de Vries equations show that GN-SINDy reliably recovers governing PDEs using under 1 % of the data, outperforming DeepMoD in efficiency, support recovery, and robustness to noise.

A procedure based on the use of artificial neural networks for the identification of nonlinear dynamic systems is developed and applied to the damped Duffing oscillator under deterministic excitation. The “generalization” ability of neural networks is invoked to predict the response of the same nonlinear oscillator under stochastic excitations of differing magnitude. The analogy between the neural network approach and a qualitatively similar nonparametric identification technique previously developed by the authors is illustrated. Some of the computational aspects of identification by neural networks, as well as their fault-tolerant nature, are discussed. It is shown that neural networks provide high-fidelity mathematical models of structure-unknown nonlinear systems encountered in the applied mechanics field.

This paper presents developed engineering software tools used for nonparametric identification of nonlinear dynamical systems based on Volterra models. The polyharmonic test sequences with different amplitudes are used for test procedures in frequency domain. The wavelets application allowed enlarging computational stability of the identification method for measurement noises filtering of received responses and characteristics of the system being identified. The methodology proposed in pervious works and developed software tools applied for construction communication channel models of different orders.

This article addresses parameter convergence problem in identification of nonlinear dynamic systems using fuzzy models. We first establish persistent excitation conditions and then propose several detailed algorithms to generate input signals that guarantee the convergence of the parameter estimates in the fuzzy system models to the true values in identifications of second-order nonlinear moving-average and auto-regressive-moving-average systems. Numerical example is given to illustrate the ideas and results.