No abstract

The forward displacement analysis of parallel mechanism can be transformed into solving complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of damp least square method, all the solutions of equations can be found and the solving efficiency is related to modeling methods. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the chaos sequences-based damp least square method. Based on the connection topology of chaotic neural network composed of the four chaotic neurons, hyper-chaos exists in the chaotic neural network system. Combining hyper-chaos with damp least square method, a new method to find all solutions of nonlinear questions was proposed, in which initial points are generated by utilizing hyper-chaotic neural network. For the first time, based on quaternion, the model of the forward displacements of 6-SPS parallel mechanism is built up. The result is verified by a numerical example.

For the problem of lower precision as well as lower adaptability in non-equidistant GM(1,1) model, applying the new information principle, modeling method of Grey system and accumulated generating operation of reciprocal number, a non-equidistant new information GRM(1,1) model generated by accumulated generating operation of reciprocal number was put forward which was taken the nth component as the initialization. Based on index characteristic of grey model and the definition of integral, the background value in non-equidistant GRM(1,1) was researched and the discrete function with non-homogeneous exponential law was used to fit the accumulated sequence and optimum formula was given. The formula of background value of new information GRM(1,1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.

The discovery of dynamical chaos is one of the main achievements in the modern science and how to expand its application has important significance to the development of modern science. Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. To improve solving efficiency, the demand to chaos sequences is uniform distribution in every interval. The probability characteristics of three kinds of chaos were investigated. The simulations were work out with Matlab software. For the first time, a new　method to find all solutions based on utilizing　equal probability chaos sequences to obtain initial points to find all solutions of the nonlinear questions was proposed　and it has higher solving efficiency compared with unequal probability chaos sequences to find all solutions. The numerical example in linkage synthesis shows that the method is correct and effective. And, different equal probability chaos sequences has different solving efficiency, so, for the same kind of question to be solved we can find the best equal probability chaos sequences to be used. This provides a simple realization method for mechanics design.

Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1,1) model’s background value of non-equal distance sequence was put forward and a kind of non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed. The mean relative error is taken as the optimum objective function. The power mutation particle swarm optimization program PMPSO1.0 was compiled with Matlab 7.6 software to make optimization. Two examples were given, their results were compared with the results based other Grey models, respectively. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.