Recursive Parameter Estimation For Radial Basis Function-Based Nonlinear Models

The theory of linear system identification is relatively mature,while nonlinear system identification is very difficult and also a research hot spot in the field.Radial basis functions have the features of simple form and flexible node configuration,which allow them to form networks to identify complex nonlinear systems.In machine learning,the network weight parameters are trained by fitting the observed samples.In system identification,this kind of weight training is actually an iterative parameter estimation computation process.The networks composed of radial basis functions can describe the nonlinear model mapping relationships between input and output,and this thesis studies the recursive parameter estimation methods of the radial basis function-based nonlinear models.The selected topic has important theoretical significance and application prospects.The main research contents are as follows.1.For the radial basis function-based nonlinear autoregressive model,a convergence factor determination method is proposed by using the Taylor expansion and approximation,which solves the problem that the analytical solution of the optimal convergence factor cannot be obtained when the parameters are optimized by the negative gradient search.On this basis,through the innovation extension,a multi-innovation stochastic gradient estimation algorithm is proposed.Further,a two-stage multi-innovation stochastic gradient estimation algorithm and a least squares multi-innovation stochastic gradient estimation algorithm are proposed by utilizing the global nonlinearity and local linearity of the model,which improve the parameter estimation accuracy.2.For the radial basis function-based nonlinear autoregressive moving average model,in order to reduce the influence of the colored noise on parameter estimation,the data filtering technique is used to construct a filter to filter the observed data,and a filtered identification model and a noise identification model are derived,which realizes the white noise processing of the model.On this basis,using the gradient search and combining the multi-innovation identification theory,a filtered multi-innovation extended stochastic gradient estimation algorithm and a decomposition-based filtered extended recursive estimation algorithm are proposed,which solve the problem of the low accuracy of the traditional parameter estimation algorithms under the interference of colored noise.3.For the radial basis function-based multivariate nonlinear autoregressive moving average model,in order to solve the problem of a large computational effort in the estimation process caused by its high dimension and large number of parameters,the original multivariate identification model is decomposed into several low-dimensional subidentification models according to the dimension of the model output vector.On this basis,a partially-coupled extended stochastic gradient estimation algorithm is proposed by using the coupled identification method,which reduces the computational complexity of the algorithm.To further improve the parameter estimation accuracy,a multi-stage coupled average extended recursive estimation algorithm is proposed by combining the coupled average method with the interactive identification.4.For the radial basis function-based nonlinear controlled autoregressive model,in order to improve the efficiency of the observed data using and fully mine the useful information in the data,the dynamical criterion functions are constructed by using the observed data with increasing data length.On this basis,an increasing data-based recursive gradient estimation algorithm is proposed by using the recursive search technique.Considering the different characteristics of the model parameters,an increasing databased hierarchical recursive gradient estimation algorithm and an increasing data-based hierarchical Newton recursive estimation algorithm are further developed,which realize the separable and interactive estimation of different types of parameters.The thesis verifies the effectiveness of the proposed algorithms through a series of simulation examples,and the simulation results show that the proposed algorithms have high parameter estimation accuracy.In addition,the computational efficiency of some algorithms are analyzed and compared,and the results show that the proposed coupling algorithms have high computational efficiency.