Adaptive nonlinear system identification of separation unit for raw materials

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.

Local model (LM) networks are applied to the identification of the global nonlinear dynamics of a turbogenerator excitation loop. A hybrid algorithm is used in conjunction with prior plant information to optimise the learning process. The resulting model was then used to devise a nonlinear generalised minimum variance (GMV) controller. This controller was found to outperform linear GMV controllers tuned at each generator operating point.

This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.

Local Model Networks (LMNs) provide a global representation of a nonlinear dynamical system by interpolating between a set of locally valid sub-models distributed across the operating range. Training such networks typically involves heuristic selection of the number of sub-models and their structure followed by the combined estimation of the free sub-model and interpolation function parameters. This paper describes a new genetic learning approach to the construction of LMNs comprising ARX local models and normalised Gaussian interpolation functions. In addition to allowing the simultaneous optimisation of the number of sub-models, model parameters arid interpolation function parameters, the approach provides a flexible framework for targeting transparency and generalisation. Fuzzy logic is used with special features to provide a directional and dynamic search for the genetic algorithm. Several modifications of the classical genetic algorithm are adopted to optimise each local model separately within the overall global model. A linear direct feedback control scheme is derived from the LMN representation of the nonlinear plant and local stability analysis is discussed. Simulation studies on a pH neutralisation process confirm the excellent nonlinear modelling properties of LM networks and illustrate the potential of the proposed control scheme.

In this paper, a new control parameter adaptation scheme is introduced into the classical differential evolution (DE) algorithm. Then, a method for nonlinear system identification is proposed. The method combines modified differential evolution (MDE) and radial basis function (RBF) neural networks, which can auto-configure the structure of RBF networks and obtain the model parameters. The RBF network structure and parameters could be determined simultaneously based on input-output data without a priori knowledge. Finally, an example of nonlinear function identification is given to illustrate the effectiveness of the proposed approach.

Nonlinear identification via connected neural networks for unsteady aerodynamic analysis

Local Model Networks (LMNs) provide a global representation of a nonlinear dynamical system by interpolating between a set of locally valid sub-models distributed across the operating range. Training such networks typically involves heuristic selection of the number of sub-model and their structure followed by the combined estimation of the free sub-model and interpolation function parameters. This paper describes a new genetic learning approach to the construction of LMNs comprising ARX local models and normalised Gaussian interpolation functions. In addition to allowing the simultaneous optimisation of the number of sub-models, model orders, model parameters and interpolation function parameters, the approach provides a flexible framework for targeting transparency and generalisation. Fuzzy logic is used with special features to provide a directional and dynamic search for the genetic algorithm. Several modifications of the classical genetic algorithm are adopted to optimise each local model separately within the overall global model. Studies on actual data from a pH neutralisation process confirm the potential of the proposed scheme.

Theory of nonlinear systems

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

An extended self-organizing map (ESOM) network, which consists of a self-organization phase and an optimization phase, was recently developed to construct a local model network (LMN) automatically using the plant data. However, this previous result suffers two drawbacks: (1) increased computation time in the self-organization phase as the number of local models increases, (2) lack of checking stability conditions for both local models and LMN. To overcome these problems, an improved algorithm for the ESOM network is developed in this paper by employing a competitive learning algorithm for data clustering in the self-organization phase and parametric constraints are formulated in the optimization phase to handle the stability of local models. In addition, the global stability of LMN is addressed. With LMN constructed by the ESOM network, it serves as a basis for building a nonlinear controller that combines several local controllers through the weighting functions obtained by the ESOM algorithm. Literature examples are used to illustrate the proposed ESOM-based modeling and controller design method.

Two-motor variable frequency speed-regulating synchronous system is a multivariable nonlinear coupling system. In order to estimate speed and tension of this system more effectively, a method of modeling based on local model networks (LMN) is given. Through using correlative testing signal to drive two-motor synchronous system firstly, series of output response about speed and tension are obtained.Then fuzzy C-means clustering algorithm is used to cluster the data of input-output according to the satisfactory performance index. Finally ,the sum of linear local model identification model for speed and tension is built . The simulation results are presented to demonstrate the validity of the proposed the method.

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics

Most of the existing SHM damage detection methodologies are based on the changes in the system parameters estimated by the linear model fitted to the structure. However, real-life structures exhibit nonlinearity even in their healthy state due to complex joints, interfaces, etc. Nonlinear identification and damage identification are very challenging inverse engineering problems. In this paper, a nonlinear system identification methodology using empirical Slow-Flow Model has been presented. A dynamical system described by slowly varying amplitudes and phases is obtained through performing partition between slow and flow dynamics of the system using the well known complexification-averaging technique. By using the theoretical link between the measured instantaneous parameters through Hilbert transform and slow-flow equations of a system, the system parameters are identified using the classical least square procedure. A numerical simulation study has been conducted on a beam with breathing crack to demonstrate the effectiveness of the proposed algorithm.

The identification of nonlinear systems with artificial neural networks models has been successfully used in many applications. Most processes in industry are characterized by nonlinear and time-varying behavior. In this context, the identification of mathematical models for nonlinear systems is vital in many fields of engineering. The Radial Basis Function Neural Network (RBF-NN) is a powerful approach for nonlinear identification and can be improved using Particle Swarm Optimization (PSO) approaches. This paper presents a multivariable nonlinear system identification using RBF-NN combined with standard PSO and Constriction Factor PSO (CFPSO) approaches in order to determine the RBF-NN parameters. RBF-NN is considered to be a good choice for black-box modeling problems due to its rapid learning capacity and, therefore, has been applied successfully to nonlinear time series modeling and nonlinear identification. On the other hand, PSO was inspired by the choreography of bird flocks and fish schools and can be seen as a distributed behavior algorithm that performs multidimensional search. Furthermore, promising simulation results from performance analysis of the proposed RBF-NN with PSO training approaches are presented and discussed in this paper showing promising results.

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.