Research Of Interval Neural Networks And Application Study On Unknown-But-Bounded Errors Modeling

With the advancement of science and technology,the systems in control engineering have become more and more complex.The uncertainty caused by complex systems has become more and more prominent.The classical certain description is no longer applicable,so how to express uncertain information and modeling effectively is an important issue in control research.The creation of the granularity concept opens up a new approach for the description of uncertain information.There are many methods derived from granularity,such as fuzzy sets,rough sets,entropy spaces,interval analysis,etc.,have been proved to have a good application effect and extensively studying.Interval neural network is an effective method to solve the inaccurate data modeling.The interval is used to express uncertainty and the neural network is utilized to accomplish modeling tasks.In this paper,two kinds of interval neural network are proposed.The validity of the models is verified by simulations,and it has been applied in solving the unknown-but-bounded errors modeling.The specific research work of this paper is as follows.Discrete wavelet neural network utilizes the wavelet analysis theory,which can effectively guide the design of structure and parameters,and then overcome the blindness of BP neural network structure.Using a single-scale radial wavelet framework avoids the curse of dimensionality in multidimensional spaces.The learning algorithm based on the least squares method makes the network converge fast and avoids the local optimization.After a large number of references and books are reviewed,two types of interval multidimensional discrete wavelet neural network model are designed based on the discrete wavelet network.The structure and parameters design are given based on wavelet analysis.The learning algorithm is derived based on the least squares method.A simulation experiment is carried out to verify the advantages of two types networks in structure and convergence speed.Aiming at the recurrent neural network,a typical Elman network is selected.The Elman neural network is a globally feed-forward partially recurrent network model.Thus,it has dynamic characteristic with short-time memory,which makes it realize the modeling for high-order dynamic systems.Combining the interval theory,a modified Elman neural network with interval parameters is proposed in this paper to solve the high-order dynamic interval system modeling with uncertainty.The justifiability of the network is proved by numerical simulation experiments.Finally,combining with the two kinds of interval neural networks proposed in this paper,we put forward an application study on unknown-but-bounded(UBB)errors modeling.When the error bound is known,the interval is used to describe the boundness.When the error bound is unknown,a penalty factor is introduced to improve the learning algorithm,thereby predicting the output interval effectively.The two networks have the same solution to the problem.On the one hand,this paper uses the interval multidimensional discrete wavelet network as a tool to model linear and nonlinear systems.On the other hand,taking a modeling process of first-order linear system as an example,the dynamic characteristics of the interval Elman network and the advantages of the network structure are illustrated.The effectiveness of the proposed method is verified by the simulation results,which provides a new way to solve the UBB problem.