A New Difference Scheme and Convergence Criterion for Gradient Optimization Method for Slope Stability
Abstract: It is necessary to use optimization methods to find the most dangerous sliding surface for the safety factor of slope stability calculated by the limit equilibrium method. Gradient method is an accurate optimization method, however there may fail to find accurately the most dangerous sliding surface. An improved gradient optimization method with a descent difference scheme for the calculation of the direction vector is proposed. The descent difference scheme is superior to the central difference scheme both in accuracy and consuming time. The problem of wrong search direction occurring in the central difference scheme is dissolved in this scheme. The problem of convergence criterion used in the classical optimization method based on the gradient of the objective function is pointed out. A new convergence criterion for single variable optimization or for multivariable optimization along the gradient direction is proposed. The stability of three test examples is analyzed with a two-stage search method for circular slip surface. The gradient method combined with the descent difference scheme is an accurate and efficient method with an ability of avoiding to fall to a local minimum in a search process. The errors of search results in the test examples are less than the given convergence error. The proposed convergence criterion is appropriate.
文章引用: 吴梦喜 , 何蕃民 , 湛正刚 , 范福平 (2015) 边坡稳定梯度法优化计算中新的差分格式与收敛准则。 应用数学进展， 4， 343-356. doi: 10.12677/AAM.2015.44043
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