Global Characteristics Of The Numerical Solution Of Nonlinear Stochastic Systems Based On Figure Cell Mapping Method Gear Research

The ultimate of this study is global character analysis of nonlinear stochastic gear system based on the digraph cell mapping method. The key points of the research are digraph cell mapping method, precise integration method and the model of the non-linear stochastic gear system.The digraph cell mapping method is researched mainly in the second and third chapters. The basic principles, the basic concepts and the application of cell mapping method are introduced based on improved simple cell mapping algorithm firstly. Then the digraph cell mapping method based on generalized cell mapping method is studied systematically, and it is found that digraph cell mapping method can response more characteristic information of nonlinear system and have more applications. Finally, the digraph cell mapping method is used for studying the global features of single degree of freedom nonlinear gear system and good results are achieved.The random response process of nonlinear stochastic gear system with random excitation is studied based on precise integration method in the fourth chapter. In the model of nonlinear gear system with a stationary random excitation, the response will be also a random process. The values of the expectation and the correlation matrix can be got by use of precise integration in every discrete time points.The structure randomness of nonlinear gear system is existent commonly. The precise integration method can't solve this kind of problems, but the digraph cell mapping method has a natural advantage for solving it. Therefore, the digraph cell mapping method is tried to solve these problems with structure randomness in the fifth chapter. Obtaining the sample of random parameters by using Monte Carlo simulation, and then obtaining the mapping relation with different sampling parameters between cell and other cell by using numerical integration method, the global characteristics map of stochastic nonlinear gear system also can be obtained by using digraph cell mapping algorithm at last. In the previous study, two types of stochastic system model have been established. One is the random model with stochastic excitation, the other one is the random model with stochastic parameters. A simple comparison of the experiment is worked out in the sixth chapter.