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Adaptive surrogate model with active refinement combining Kriging and a trust region method

机译：结合克里格法和信任域方法的主动细化自适应代理模型

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摘要

The reliability analysis of engineering structural systems with limit state functions defined implicitly by time-consuming numerical models (e.g. finite element analysis structural models) requires the use of efficient solution strategies in order to keep the required computational costs at acceptable levels. In this paper, an adaptive Kriging surrogate model with active refinement is proposed to solve component reliability assessment problems (i.e. involving one single design point) with nonlinear and time-consuming implicit limit state functions with a moderate number of input basic random variables. The proposed model, in the first stage, uses an adaptive Kriging-based trust region method to search for the design point in the standard Gaussian space and predict an initial failure probability based on the first-order reliability method as well as sensitivity factors for the input basic random variables. This initial prediction is then verified or improved efficiently in a second stage using Monte Carlo simulation with importance sampling based on a Kriging surrogate model defined iteratively around the design point using an active refinement algorithm. A convergence criterion that detects the stabilization of the failure probability prediction during the active refinement process is also proposed and implemented. The usefulness of the proposed adaptive Kriging surrogate model in terms of accuracy and efficiency for reliability assessment of engineering structural systems is shown in the paper with two relevant numerical examples, involving a highly nonlinear analytical limit state function in two-dimensions and an advanced nonlinear finite element analysis structural model in a larger dimensional space.
机译：具有耗时的数值模型（例如，有限元分析结构模型）隐式定义的极限状态函数的工程结构系统的可靠性分析需要使用有效的求解策略，以将所需的计算成本保持在可接受的水平上。在本文中，提出了一种具有主动细化的自适应Kriging替代模型，以解决具有中等数量输入基本随机变量的非线性且耗时的隐式极限状态函数的组件可靠性评估问题（即，涉及一个设计点）。所提出的模型在第一阶段使用自适应的基于Kriging的信赖域方法来搜索标准高斯空间中的设计点，并基于一阶可靠性方法以及该模型的敏感性因子来预测初始失效概率。输入基本随机变量。然后，在第二阶段中使用蒙特卡洛模拟对这一初始预测进行有效地验证或改进，并使用基于主动克里特算法在设计点周围迭代定义的Kriging替代模型的重要性采样进行重要性采样。还提出并实现了一种收敛准则，该准则可检测主动优化过程中故障概率预测的稳定性。本文通过两个相关的数值示例展示了所提出的自适应Kriging替代模型在精度和效率上对工程结构系统可靠性评估的有用性，其中包括二维的高度非线性分析极限状态函数和高级非线性有限元较大空间中的元素分析结构模型。

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