基于最大伪梯度搜索的多样复合形法及其在边坡稳定分析中的应用

The diverse complex method based on the maximum quasi-gradient and its application to the slope stability analysis

摒弃了基本复合形法中最坏点替换策略,在每个顶点及其对应剩余顶点的几何中心点之间构造一个伪梯度,在最大伪梯度值对应的顶点及其剩余顶点的几何中心点的连线上寻找比该顶点有所改善的两个新点分别位于几何中心点的两侧,根据最大复合形中心距准则选择一新点替换掉该顶点构成新复形并不断迭代,形成一种新的复合形法,利用新复合形法对一复杂土坡的最小安全系数进行了搜索,与基本复合形法的比较说明了新复合形法的全局搜索能力。

The bad design point is abandoned in the basic complex method. A quasi-gradient between each design point and the centroid of the remaining design points could be generated by the new complex method. One design point is called improved design point, whose quasi-gradient is the maximum, and its corresponding centroid is used to find two better design points outside and inside the centroid of the improved design point. One of two better design points is chosen to replace the improved design point based on the maximum complex central distance and forms a new complex. The new complex method is applied to search for the minimum factor of safety of soil slopes. The comparison of computing results between the new and the basic complex method shows that the new complex method is much more likely to locate the true minimum factor of safety than the basic complex method.