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

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.

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.

In this chapter we deal with learning (optimization) methods used in modeling and identification of complex nonlinear systems. We treat methods that enable estimation of model parameters and, possibly, identification of the structure of the models from the measured data (samples).

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.

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener kernels and operators. Also, the problem of a best approximation of large-scale nonlinear systems using Volterra operators in weighted Fock spaces is described. Examples of applications considered are the following: Volterra series use in description of nonlinear distortions in satellite systems and their equalization or compensation, exploiting Wiener kernels to modelling of biological systems, the use of both Volterra and Wiener theories in description of ocean waves and in magnetic resonance spectroscopy. Moreover, connections between Volterra series and neural network models, and also input-output descriptions of quantum systems by Volterra series are discussed. Finally, we consider application of Volterra series to solving some nonlinear problems occurring in hydrology, navigation, and transportation.

Identification of nonlinear systems using NARMAX model

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

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.

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)

Theory of nonlinear systems

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

Nonlinear model identification of an experimental ball-and-tube system using a genetic programming approach

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.

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.