Research On Nonlinear System Identification Methods And Applications Based On Neural Networks

Nonlinear system identification has become one of the fundamental problems in control science and engineering applications,which covers the fields of industry,human bioinformatics,ecosystems and economic systems.In order to analyze the operation of a system and to design its control laws,it is necessary to obtain an accurate mathematical model of the system.However,in the absence of a priori knowledge,it is difficult to obtain a mathematical model of a system.The system identification methods proposed in this paper are based on neural networks.With the help of the powerful nonlinear approximation capability of neural networks,it is used to determine the quantitative dependence of system characteristics.This paper can be divided into three aspects.Firstly,we use the Raised Cosine Radial Basis Function Neural Networks(RCRBFNN)to approximate the unknown continuous periodic nonlinear dynamical function and analyze the persistent excitation condition of the rising cosine function.Applying the error conversion function in updated equation can ensure the identification algorithm has strong stability.Secondly,a multiscale wavelet neural networks(MWNN)is proposed for the identification of discrete chaotic systems and electrocardiography dynamic systems.In order to guarantee the stability of discrete iteration,Z-transform is used to determine the range of the gains.Finally,an improved Zhang neural networks(ZNN)algorithm is proposed by integrating the chord slope method and the downhill method,which is applied to the identification of the nonlinear filter system of diaphragmatic electromyography(EMGdi)signals.The details can be described as follows:1)The RC function has the property of 1-D constant value approximation that been proved by other scholars.Based on this property,we demonstrate that the RC function also has a constant-value approximation result in multidimensional space.With the help of the Taylor expansion,we proves that the RC function using the lattice points as the center point of the mapping has the property of arbitrary accuracy approximation for the continuous function in the multidimensional space.When the periodic or quasi periodic trajectories generated by the nonlinear dynamical system pass through lattice points,the RC function that is close to the trajectories will be activated to generate a regression matrix according to the distance between the trajectories and each lattice point.Based on the property of the diagonal dominance matrix,we prove that the RC function satisfies the persistent excitation condition.In order to ensure that the identification error has fast convergence,the conversion function is used for shrinking the gain in the error differential equation.Taylor expansion is used to determine the range of gain to satisfy the stability of identification process.Constructing a Lyapunov function to determine the differential equation of the weights of neural networks,it is shown that the weights of the neural networks will converge to the neighborhood of its true value and the identification error will converge to neighborhood of zero in a periodic or period-like nonlinear dynamical system.Thus,we solve the problem of accurate identification of nonlinear dynamical system.2)The MWNN,combining with the wavelet approximation theory and the characteristics of neural networks learning,makes the neural nodes have the ability of local perception and multi-scale perception.MWNN,designed by a three-layer RBF neural networks structure,lattice points,wavelet functions and discrete model,is proposed to identify chaotic nonlinear dynamical system.The distribution of lattice points and three-layer can be regarded as the as scale transformation and time translation respectively in the mechanism of MWNN.In practical engineering applications,due to the limitations of hardware equipment,continuous differential equations are usually replaced by discrete ones.In this paper,the Z-transform theory is applied to prove the selection interval of the iteration gains and stability of the discrete-time difference equation.After discrete-time Lyapunov analysis,the identification error will converge to neighborhood of zero in a first-order manner with sampling time.In this paper,the validity of the method is verified by using the 3-D Electrocardiograph(ECG)signal from the PTB database and the Lorenz chaotic system.That also develops a new research method for the identification of ECG dynamical systems.3)In this paper,an improved ZNN algorithm is proposed and applied to the identification of nonlinear filter system for EMGdi signals.After determining the interfering interval and the undisturbed interval,the system is modeled by adding the wavelet energy coefficients filtered by the nonlinear filter in interfering interval.The application precondition of the traditional ZNN iterative algorithm is that the target functions have the property of well-defined expression and continuously derivability.The traditional ZNN iterative algorithm is not suitable to identify the nonlinear filter system for biomedical signals denoising,as the biomedical signals do not have expressions,not to mention the continuous derivability.Although the EMGdi signal does not have any expression,we demonstrates that the energy function located in interference interval has monotonically increasing characteristics with the value of threshold.To establish the loss function of the identification mechanism by using energy error,we use the chord intercept method to replace the derivative of the ZNN algorithm.In order to avoid the divergence of the iterative process,the downhill factor is used for regulating gain in iterative equation.Then an improved ZNN algorithm is formed.In order to ensure that the threshold parameters have the convergence characteristics,we use Z-transform theory to prove that the threshold parameter of nonlinear filter will gradually converge to the neighborhood of their true values.Simulation and clinical EMGdi signal are used to verify the effectiveness of new ZNN in practical application,which also provides more accurate clinical EMGdi signal for subsequent medical diagnosis and analysis.