Unsupervised Learning Methods for Identification of Complex 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.

In this paper, advanced concepts for the identification of complex nonlinear systems are discussed. Three major problems are addressed: The nonlinearity of the system, noise in the data upon which the model has to be built, and the potential to incorporate qualitative and quantitative prior knowledge about the system. As an integrated solution approach, local model networks (LMNs) with appropriate parameter estimation schemes are proposed. LMNs generally offer a versatile structure for the identification of nonlinear dynamic systems. In order to account for a realistic situation when noise is present both in input and output data, an equality constrained generalised total least squares algorithm for the local model parameter estimation of the LMN is presented; the incorporation of equality constraints allows to mathematically enforce desired system properties. As an application and benchmark problem, the vertical dynamics of a vehicle is considered. After training the LMN on a rough road, excellent predictions of the behaviour of the vehicle at crossing a single obstacle are obtained, thus proving the effectiveness of the proposed algorithm. It is illustrated how both the application of a proper parameter estimation scheme and the integration of system constraints systematically improve the performance of the model.

Detection and classification of non-linearities based on Volterra kernels processing

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)

To improve the parameter identification accuracy of vessel steering machine (VSM), a multivariate evidential reasoning-based particle swarm optimisation (MER-PSO) method is proposed. Firstly, multivariate evidential reasoning (MER), a framework designed to directly model multiple-input multiple-output (MIMO) problems without cascading multiple MISO models, is proposed and applied to the joint dynamic modelling and collaborative inference of multiple PSO hyperparameters, which overcomes the inherent limitations of traditional ER in handling MIMO scenarios. Subsequently, the integrated MER-PSO is proposed and used for VSM parameter identification, which provides a new adaptive optimisation framework for parameter identification of complex nonlinear systems. Finally, the significant advantages of MER-PSO (with a 53.7% reduction in mean square error compared to PSO) are demonstrated via the VSM parameter identification experiments, which include the simulation/actual data-based parameter identification experiments and provide a new paradigm for fine-grained modelling.

The joint robots are used in kinds of production processes. A fast time work load identification is the premise to ensure the safe operation of robots. However, in some special application scenarios, the work load can not be measured directly, which is often identified indirectly by dynamic methods. Because of the obvious nonlinearity and the uncertainty of model parameters, the accuracy and efficiency of load identification are not enough. Therefore, based on Fourier neural network, this paper proposes an improved model to realize load identification, in order to improve the prediction accuracy and timeliness of system load parameters. Compared with the dynamic model solution method, the proposed method has higher accuracy and faster calculation speed. It only needs to learn several alternate sample sets in the prediction range, and any results in the prediction range can be accurately identified with good generalization ability. The sensitive parameters of the network are also analyzed, and the performance is compared with that of mature neural network algorithm. In this method, two neural network models are combined to effectively identify different feature sets in high-dimensional data, so as to realize efficient load parameter identification and provide reference for parameter identification of complex nonlinear systems.

This paper presents an intelligent system identification methodology for the identification of a realistic model of an ultrasonic position estimation system that uses the difference in the time of arrivals of waves from a transmitter to various receivers. Even though a linearized formulation for the 3D system exists and is currently being used to estimate the position of the transmitter, its accuracy can still be improved further. A neural network approach is developed to train the system based on training sets obtained from the actual system, and it is proposed to use the final trained system to estimate the 3D position in real time. The weights of the neural network are obtained from an innovative procedure using genetic algorithms. Results for a simplified 1D system are presented as proof of concept. The performance of the identified 1D system using genetic algorithms is shown to be comparable to the one using the analytical model. Further, the identified system using genetic algorithms is also shown to be superior to the one using the traditional back propagation method for finding the weights for the neural networks. This work has significant applications in the identification of complex non-linear systems.

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.

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 systems using NARMAX model

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.

Mathematical Methods for Modelling and Identification of Nonlinear Systems

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