An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mend...An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function（PDF） of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not itemtive circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.展开更多
This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MAR...This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MARS is an adaptive regression process,which fits in with the multidimensional problems.It adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller highly accurate models.MLS for moving and resizing the search sub-regions is employed in the space of design variables.The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS.The disadvantages of the conventional response surface method（RSM） have been avoided,specifically,highly nonlinear high-dimensional problems.The GRS/MARS with MLS is applied to a high-dimensional test function and an engineering problem to demonstrate its feasibility and convergence,and compared with quadratic response surface（QRS） models in terms of computational efficiency and accuracy.展开更多
基金Project(50378036) supported by the National Natural Science Foundation of China Project (200503) supported by the Foundation ofCommunications Department of Hunan Province, China
文摘An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function（PDF） of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not itemtive circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.
基金Project supported by the National Natural Science Foundation of China (Grant No.50775084)the National Hightechnology Research and Development Program of China (Grant No.2006AA04Z121)
文摘This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MARS is an adaptive regression process,which fits in with the multidimensional problems.It adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller highly accurate models.MLS for moving and resizing the search sub-regions is employed in the space of design variables.The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS.The disadvantages of the conventional response surface method（RSM） have been avoided,specifically,highly nonlinear high-dimensional problems.The GRS/MARS with MLS is applied to a high-dimensional test function and an engineering problem to demonstrate its feasibility and convergence,and compared with quadratic response surface（QRS） models in terms of computational efficiency and accuracy.
