Optimal maximum entropy quantile function for fractional probability weighted moments and its applications in reliability analysis

Optimal maximum entropy quantile function for fractional probability weighted moments and its applications in reliability analysis

The maximum entropy principle (MEP) under the constraint of fractional probability weighted moments (FPWM) is a well-developed method for a direct estimation of the quantile function of a random variable. The accuracy, unbiasedness, and efficiency of max-imum entropy quantile functions (MEQFs) have been demonstrated in the literature. How-ever, the issue of how to select an optimal order of FPWMs given a sample of data is not fully solved, and the application of this approach to reliability analysis in civil engineering has not been fully investigated. This paper presents a FPWM-based MEP with a new nondi-mensional analysis and proposes the Akaike information criterion to determine the optimal order of FPWM in MEP analysis. To illustrate this approach, two examples of the estimation of optimal quantile functions for soil undrained shear strength and annual maximum daily discharge are presented. The paper presents a novel approach to use the quantile function for the First Order Reliability Method, a widely used method in civil engineering. As a case study of this approach, the reliability analysis of a rock slope is included. The FPWM-based MEQFs are compared with common empirical distributions and MEQFs based on integral probability weighted moments to demonstrate the advantages and disadvantages of the developed method.(c) 2022 Elsevier Inc. All rights reserved.

在分数概率加权矩（FPWM）约束下的最大熵原理（MEP）是一种用于直接估计随机变量分位数函数的成熟方法。最大熵分位数函数（MEQFs）的准确性、无偏性和有效性已在文献中得到证明。然而，给定一组数据样本时如何选择FPWM的最优阶数这一问题尚未完全解决，并且这种方法在土木工程可靠性分析中的应用也未得到充分研究。本文提出了一种基于FPWM的MEP，并进行了一种新的无量纲分析，还提出了赤池信息准则来确定MEP分析中FPWM的最优阶数。为了说明这种方法，给出了两个估计土的不排水抗剪强度和年最大日流量的最优分位数函数的实例。本文提出了一种将分位数函数用于一阶可靠性方法（土木工程中广泛使用的一种方法）的新方法。作为这种方法的一个案例研究，包含了一个岩质边坡的可靠性分析。将基于FPWM的MEQFs与常见的经验分布以及基于积分概率加权矩的MEQFs进行了比较，以展示所提出方法的优缺点。（c）2022爱思唯尔公司。保留所有权利。