深埋隧道衬砌稳定可靠度的Kriging插值法与遗传算法协同优化求解法

首先利用遗传算法(GA)的全局优化能力，解决了Kriging插值预测算法中相关参数的精确求解问题。针对衬砌结构力学状态表征量与基本参数是高度非线性关系而无法明晰表达的难题，建立了基于Kriging插值预测法的状态表征量等代显式通用模型。以抗拉强度控制参量为例，提出了采用拉丁抽样等代显式通用模型的具体隧道工程衬砌结构力学状态方程构造程序。基于以状态方程为约束条件建立的可靠度指标计算模式，构建起Kriging与GA协同优化的隧道衬砌稳定可靠度求解方法。实例应用对比表明，该方法与精确解的相对误差为4.8%，计算工作量仅为其2.5%。与目前已有的同类方法相比，具有明显的优越性。

Calculation for reliability of deep tunnel lining through optimization method of Kriging interpolation in collaboration with genetic algorithm

Countermeasure to solve unknown parameters for Gauss correlation function in Kriging interpolation accurately is presented by means of global optimization ability of genetic algorithm. A universal equivalent explicit formulation for state equation is established by Kriging interpolation to solve a problem that mechanical state equation for lining structure can’t be expressed through basic parameters explicitly because of a highly nonlinear relation between state quantity and basic parameters. A state equation for stretch resistance is taken as an example, construction procedure of mechanical state equation for one tunnel’s lining structure through the universal equivalent explicit formulation in connection with Latin sample way is presented. An analysis approach for stability reliability degree of tunnel’s lining structure based on optimization method for Kriging interpolation in collaboration with genetic algorithm (GA) is founded through calculation mode of reliability degree index established based on constraint condition for the state equation. Some practical examples are given to illustrate the application, which manifests that the relative error between the present approach and the accurate one is found to be 4.8%; and the computational burden of this approach is only 2.5% of that when employing the precise one. The present approach is excellent over existing analogous approaches on computational burden and accuracy.