Structure detection and model validity tests in the identification of nonlinear systems

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

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.

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

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.

Applications of the shifted Legendre polynomials expansion to the analysis and identification of the nonlinear time-delayed system, described by a memoryless nonlinear element followed by a linear plant with time delay, are studied. The system described here is assumed both controllable and observable. For analysis, by using the shifted Legendre polynomials expansion, the solution of a nonlinear state equation is reduced to the solution of a linear algebraic matrix equation. For identification, through the shifted Legendre expansions of the measured input/output data, the unknown parameters of both the linear delayed plant and the characterisation of the nonlinear element are estimated by using the least-squares method. Algorithms are presented. Numerical examples are given to illustrate the use of this approach.

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

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

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.

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

The Genetic Algorithm was used to estimate the hydraulic compliance of the hydraulic system on the UBC teleoperated heavy duty excavator. Using real recorded and simulation data from the excavator, the Genetic Algorithm has successfully identified the compliance of single link and multi-link hydraulic system of the excavator. A Parallel GA ( PGA ) was implemented with 16 T800 Transputers. It achieved a speedup factor of 12 over a traditional GA. With such a high speedup factor, real-time monitoring of hydraulic compliance and other hydraulic parameters is becoming possible. New mechanisms such as the distributed fitness function, the active error analysis were used to enhance the performance of a PGA. A PGA which incorporated these mechanisms actually outperformed a traditional GA in key areas such as variance of the estimated parameter and parameter tracking ability. Finally, a physical model that explains the fundamental properties of GAs was introduced. The physical model ( a hypercube ) not only provides an excellent explanation of GAs searching power, but also gives insight to GAs users ways to improve and to predict the performance of GAs in most applications.

ABSTRACTThis paper addresses the identification of Nonlinear (NL) systems using a linearization approach, introducing a combined estimator to tackle this challenge. We assume that the unknown NL system operates around a stable, slowly varying (nominal) operating point. The system trajectory is then perturbed slightly via small input perturbations. While the system's operating point evolves slowly over time, the small (broadband) input signal excites the system dynamics. We demonstrate that the NL system's response to these small perturbations can be approximated by a Linear Parameter‐Varying (LPV) system model. Furthermore, we show that this LPV model represents the linearized version of the unknown NL system around the operating point. A new parametrization for the LPV model coefficients, referred to as “gradient‐parameterized” LPV coefficients, is introduced, establishing a structural relationship between the coefficients. This structural relationship reduces the number of parameters to be estimated and ensures that the LPV model always corresponds to the linearized form of the NL system. Additionally, we demonstrate that this LPV model structure allows for the unique reconstruction of the NL system model through symbolic integration, resulting in a closed‐form nonlinear Ordinary Differential Equation (ODE). This integration introduces a second structural relationship, linking the LPV model to the NL model. By leveraging these two structural relationships, we reformulate the problem of NL system identification via linearization as a combined estimation problem, leading to a unified LPV‐NL estimation framework. This approach utilizes all available data, including perturbation data (linear response) and the varying operating point (NL response). The proposed approach employs a combined estimator to locally identify the joint LPV‐NL model within the neighborhood of the system's operating point. Although the estimated NL model is localized around this nominal trajectory, an experimental approach is proposed to reduce the linear approximation error, thereby enlarging the validity region of the final model. Finally, we present a numerical example to illustrate the performance of the proposed method.

Rapid parameter identification system for linear time-invariant plant with only input and output measurable

Identification of nonlinear systems using NARMAX model

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

International audience