Identification of Nonlinear Systems Using Radial Basis Function Neural Network

This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function

DEEP LEARNING OF NONLINEAR DYNAMICAL SYSTEM

A data-driven approach, such as neural networks, is an alternative to traditional parametric-model methods for nonlinear system identification. Recently, long Short- Term Memory (LSTM) neural networks have been studied to model nonlinear dynamical systems. However, many of these contributions are made considering that the input to the system is known or measurable, which often may not be the case. This thesis presents a method based on LSTM for output-only modeling, identification, and prediction of nonlinear systems. A numerical study is performed and discussed on Duffing systems with various cubic nonlinearity

Parameter reduction in nonlinear state-space identification of hysteresis

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree, as well as the connections with neural network modeling. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50\%, while maintaining a comparable output error level.Comment: 24 pages, 8 figure

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

A Nonlinear Model for Online Identifying a High-Speed Bidirectional DC Motor

The modeling system is a process to define the real physical system mathematically, and the input/output data are responsible for configuring the relation between them as a mathematical model. Most ofthe actual systems have nonlinear performance, and this nonlinear behavior is the inherent feature for thosesystems; Mechatronic systems are not an exception. Transforming the electrical energy to mechanical one orvice versa has not been done entirely. There are usually losses as heat, or due to reverse mechanical, electrical,or magnetic energy, takes irregular shapes, and they are concerned as the significant resource of that nonlinearbehavior. The article introduces a nonlinear online Identification of a high-speed bidirectional DC motor withdead zone and Coulomb friction effect, which represent a primary nonlinear source, as well as viscosity forces.The Wiener block-oriented nonlinear system with neural networks are implemented to identify the nonlin-ear dynamic, mechatronic system. Online identification is adopted using the recursive weighted least squares(RWLS) method, which depends on the current and (to some extent) previous data. The identification fitnessis found for various configurations with different polynomial orders, and the best model fitness is obtainedabout 98% according to normalized root mean square criterion for a third order polynomial

Neural Network Based System Identification of an Axis of Car Suspension System

Neural networks system identification have been widely used for estimate the nonlinear model of system. In this paper, multilayer perceptron neural network is used for identifying the Nonlinear AutoRegressive with eXogenous input (NARX) model of a quarter car passive suspension system. Input output data are acquired by driving a car on a special road event. The networks structure is developed based on system model. The Networks learning algorithm is derived using Fisher's scoring method. Then the Fisher information is given as a weighted covariance matrix of inputs and outputs the network hidden layer. Unitwise Fisher's scoring method reduces to the algorithm in which each unit estimate its own weights by a weighted least square method. The results show that the method uses suitable for modeling a quarter car passive suspension systems

Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example