Parameter Identification Of Complex Nonlinear System Based On Gradient Algorithm

In industrial environments,it is necessary to build complex nonlinear models.The key is to construct dynamical behaviors in complex systems that are difficult to explain by conventional science.Therefore,the identification of unknown quantities such as parameters,structures,and time delays in the models is of great theoretical and practical value.In this paper,based on gradient algorithm,the identification of parameter,structure and time delay for several types of complex nonlinear systems is mainly studied.The corresponding system identification methods are proposed,and the details of the research are as follows:1.An adaptive gradient algorithm is proposed for nonlinear systems(rational models)with unknown time delays,based on the redundant rules,self-organizing map algorithm and bias compensation methods.The algorithm uses redundant rules to construct a set of models from sampled data,and an accurate time delay estimate is obtained by comparing the residuals between different models.Then,the adaptive gradient algorithm is used to obtain the parameter estimates.Finally,the biased parameter estimates are converted into unbiased parameter estimates by using bias compensation method,which improves the accuracy of estimates.Moreover,based on the different data sampling methods,offline and online adaptive gradient algorithms are proposed respectively.The effectiveness of the proposed methods is verified in simulation experiments.2.A regularized gradient algorithm with an improved kernel matrix is proposed for time-delayed nonlinear systems with unknown structure based on Volterra series and kernel methods.The algorithm first approximates the time-delay nonlinear model with unknown structure using the Volterra model,and then constructs a set of model pools for different time-delay cases using redundant rule and self-organizing map algorithm.Then,a kernel matrix that can identify the unknown time delay is proposed,and the estimates of the time delay are obtained by adjusting the diagonal elements in the kernel matrix.Finally,the model parameters are identified using the adaptive momentum gradient algorithm(Adam).In addition,the estimation method of the hyper-parameters in the kernel matrix is also proposed.The simulation results illustrate the effectiveness of the algorithm.3.For the identification state of charge(SOC)in battery management systems,two identification methods for SOC are proposed based on bidirectional gated recurrent neural networks and adaptive kernel extreme learning machine identification methods.In the battery management system,the system cannot be modeled accurately due to its complex physicochemical structure,a black box model is used to construct it.The first method uses Nadam gradient algorithm to update the parameters of the weight matrix in the network by building a neural network based on attention mechanism.Finally,the updated network model is used to predict the SOC.The second method combines the kernel method with the regularized extreme learning machine,and constructs an adaptive kernel matrix by the greedy algorithm,which can avoid the selection of hyper-parameters in the regularized extreme learning machine.The experimental results demonstrate the excellent performance of these two types of methods for SOC identification.In summary,this paper studies the parameter identification of complex nonlinear systems.Based on the traditional gradient algorithm,several improved gradient algorithms for different systems is proposed,and the specific flow and derivation of each algorithm are given.The effectiveness of the proposed method is verified by simulation experiments and practical examples.Conclusions and future directions are given in the last of the paper.