Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Genetic least squares for system identification

The recursive least-squares algorithm with a forgetting factor has been extensively applied and studied for the on-line parameter estimation of linear dynamic systems. This paper explores the use of genetic algorithms to improve the performance of the recursive least-squares algorithm in the parameter estimation of time-varying systems. Simulation results show that the hybrid recursive algorithm (GARLS), combining recursive least-squares with genetic algorithms, can achieve better results than the standard recursive least-squares algorithm using only a forgetting factor.

Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

System identification using partitioned least squares

A novel partitioned least squares (PLS) algorithm is presented, in which estimates from several simple system models are combined by means of a Bayesian methodology of pooling partial knowledge. The method has the added advantage that, when the simple models are of a similar structure, it lends itself directly to parallel processing procedures, thereby speeding up the entire parameter estimation process by several factors.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

An introduction to radial basis functions for system identification: a comparison with other neural network methods

A look is taken at the use of radial basis functions (RBFs), for nonlinear system identification. RBFs are firstly considered in detail themselves and are subsequently compared with a multi-layered perceptron (MLP), in terms of performance and usage.

Wiener System identification using B-spline functions with De Boor recursion

A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

System identification of Wiener systems with B-spline functions using De Boor recursion

In this article a simple and effective algorithm is introduced for the system identification of the Wiener system using observational input/output data. The nonlinear static function in the Wiener system is modelled using a B-spline neural network. The Gauss–Newton algorithm is combined with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialisation scheme. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.