Papers by Keyword: Cusp Catastrophe

Abstract: This paper deals with the statistical catastrophe theory method for the optimal design of machine components. A short introduction to the catastrophe theory is presented, the statement of optimal design problem is given in the first part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is focused on probability approach. Manage variables are viewed as random stationary processes, statistical linearization method and Pearson moment method are used for the reliability function evaluation.

Abstract: The purpose of this paper is to present the catastrophe theory method for the optimal design of machine components. A brief description of the cusp catastrophe is presented in the introduction. The statement of optimal design problem is given in the second part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is devoted to probability approach. Manage variables are viewed as stochastic quantities, analytical and statistical linearization methods are used for the reliability function evaluation.

Abstract: The development of new catastrophe theory methods, coupled with probability theory is opening new possibilities to estimate the reliability measures. A brief review of the cusp catastrophe is presented in the introduction. The second part is devoted to probability approach. Manage variables are viewed as stationary random processes (functions) and a problem of overshoot of random function is formulated. Mean number of zero crossings by Gaussian random stationary process is evaluated; analytical equations to estimate the reliability function are obtained.

Abstract: According to acoustic emission mechanism of the material stress process, establish the gray cusp catastrophe model of acoustic emission parameters based on the grey theory and catastrophe theory. Using the model, carried out mutation analysis of the acoustic emission parameters of the coal mining face supporting pressure, then realized to face discrimination and prediction of rock burst. Point mutations in the roof sandstone acoustic emission rate of this parameter, has important significance for fracture mechanics study of working face roof sandstone.

Abstract: Seeking for a scientific and reasonable predict model is the key point to ensure accurate and reliable prediction results for the land subsidence. In this paper, the research of subsidence area pointed out by picks the process of land subsidence which causes by the water reservoir that conforms to the characteristic of nonlinear dynamics, thus, a new model is established to solve the combinatorial weighted coefficients by using the predict precision, and a simple method is introduced to solve the grey model and neural network combination forecast model. Based on many examples, the new cusp catastrophe land subsidence model is proved to be very effective and much more accurate.