滑坡模糊可靠性评价的改进响应面法及优化研究

提出过无差点的改进响应面模型，并结合模糊随机理论求解滑坡的可靠性指标。首先，考虑到滑带土力学参数的模糊随机性，非线性程度较高，采用正态模糊隶属函数对参数样本进行模糊—随机处理，并作为优化模型的约束函数；然后，采用过无差点的改进响应面法将功能函数显式化为二阶近似函数，黏聚力和内摩擦角约束函数显式化为线性函数，基于二次规则方法，采用理性运动极限计算方法，寻找合理、有效而稳定的优化策略求解滑坡的目标功能函数；最后，采用一次二阶矩法计算滑坡的可靠性指标。改进的响应面法在迭代过程中通过中心展开点，优化过程可以收敛到精确的局部最优点，同时理性运动把每次寻优的空间缩小，在建立近似显函数展开点或构造点的怜域进行寻优，避免了优化迭代振荡、收敛速度缓慢或不收敛的缺陷，提升了优化速度并保证求解的有效性和准确性。计算方法保证了改进响应面法的精度，求得的可靠性指标考虑了参数模糊不确定性的影响，研究成果为拓展响应法的改进并应用于滑坡工程的可靠性评价领域起到一定的推动作用。

Landslide fuzzy reliability evaluation based on improved response surface method and optimization research

This paper aims at proposing a improved response surface model (PRSM), which pass centers expansion point, and combining the fuzzy random theory to calculate the reliability index of the landslides. First of all, considering the fuzzy randomness character of the soil mechanics parameters ,the nonlinear degree is much higher, the normal fuzzy membership function is to used to dispose the soil sample, and put them as constraint functions of optimization model ;Then, the transfer the explicit function into second order approximation function using PRSM method, the constraint function of cohesion and Angle of internal friction function are transferred to linear function, based on the quadratic programming method, the rational motion limit calculation method is used, so as to look for a reasonable, effective and stable optimization strategy to obtain the performance function, then using JC method to calculate the reliability index of landslides. PSRM method passes the center expansion point, the optimization process can be exactly converged to local points, and at the same time, the optimal space is becoming narrower every time in establishing approximate explicit function expansion point or structure point, which avoiding the drawbacks of iteration vibration and slow speed in convergence, promoting the optimizing speed and ensuring the effectiveness and accuracy of the result. The precision of PSRM method is ensured, obtained considering the fuzzy uncertainty of parameters are considered in the process of obtaining the reliability indexes, These results can provide a basis for extending the application of the PRSM to reliability analysis of rock slope stability.