Purpose

The collocation-based stochastic response surface method (CSRSM) is widely used in geotechnical reliability analyses due to its efficiency and accuracy. Determining the optimal truncated order of the associated polynomial chaos expansion (PCE) is important, as it may strongly affect the practical applicability of CSRSM.

Design/methodology/approach

This study investigates the performance of different optimal order selection strategies used in the CSRSM and proposes a new cross-order validation method. First, several methods commonly used for optimal order selection are briefly reviewed, and their merits and limitations for reliability analyses are discussed. Then, an improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed.

Findings

In total, ten simple mathematical examples from the literature are employed to perform a preliminary test on the proposed method, and a comparative study is conducted to demonstrate its advantages with respect to some other existing methods.

Practical implications

A total of three typical geotechnical problems are employed to demonstrate the performance of the proposed method in geotechnical practice.

Originality/value

An improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed. The threshold value of the deterministic coefficient used for the proposed method is discussed.

中文翻译：

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基于配置的SRSM在可靠性分析中优化截断PCE阶的新方法及其在岩土工程中的应用

目的

基于搭配的随机响应面法（CSRSM）因其高效和准确而广泛应用于岩土可靠性分析。确定相关多项式混沌展开 (PCE) 的最佳截断阶数很重要，因为它可能会强烈影响 CSRSM 的实际适用性。

设计/方法/方法

本研究调查了 CSRSM 中使用的不同最优顺序选择策略的性能，并提出了一种新的交叉顺序验证方法。首先，简要回顾了几种常用的最优阶数选择方法，并讨论了它们在可靠性分析中的优点和局限性。然后，提出了一种改进的最优顺序选择方法，可以在效率和准确度之间取得更好的平衡。

发现

总共使用了文献中的十个简单数学示例对所提出的方法进行了初步测试，并进行了比较研究以证明其相对于其他一些现有方法的优势。

实际影响

共采用三个典型的岩土工程问题来证明所提出的方法在岩土工程实践中的性能。

原创性/价值

提出了一种改进的最优顺序选择方法，可以在效率和准确性之间取得更好的平衡。讨论了用于所提出方法的确定性系数的阈值。