利用矩求积设计点自动生成高维替代模型

Xuefei Guan

doi:10.1088/3050-2454/ae5966

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利用矩求积设计点自动生成高维替代模型

Papers | 更新时间：2026-05-08

- 利用矩求积设计点自动生成高维替代模型
- Automatic generation of high-dimensional surrogate models using moment quadrature design points
- 可靠性科学与工程学报（英文） 2026年页码：1-25
- 作者机构：
  
  Graduate School of China Academy of Engineering Physics, Beijing 100193, People's Republic of China
- 作者简介：
  
  [ "Xuefei Guan is currently a Professor at Graduate School of China Academy of Engineering Physics. His research interests include ultrasonic nondestructive evaluation, fatigue and fracture, and uncertainty quantification methods applied to reliability engineering." ]
- 基金信息：
- DOI：10.1088/3050-2454/ae5966
  中图分类号：
- 收稿：2025-11-20，
  
  修回：2026-02-26，
  
  录用：2026-03-31，
  
  网络首发：2026-04-10，
  
  纸质出版：2026-06
- 稿件说明：
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Xuefei Guan. 利用矩求积设计点自动生成高维替代模型[J]. 可靠性科学与工程学报（英文）, 2026, 2: 025002.

Xuefei Guan. Automatic generation of high-dimensional surrogate models using moment quadrature design points[J]. Journal of Reliability Science and Engineering, 2026, 2: 025002.
Xuefei Guan. 利用矩求积设计点自动生成高维替代模型[J]. 可靠性科学与工程学报（英文）, 2026, 2: 025002. DOI： 10.1088/3050-2454/ae5966.

Xuefei Guan. Automatic generation of high-dimensional surrogate models using moment quadrature design points[J]. Journal of Reliability Science and Engineering, 2026, 2: 025002. DOI： 10.1088/3050-2454/ae5966.

摘要

本研究提出了一种基于矩求积设计点的确定且明确的代理模型构建方法。与自适应或随机采样方法不同，该框架直接从输入概率密度函数的统计矩中推导出设计点，确保了可重复性、最优多项式精度，以及对涉及任意分布（包括非均匀分布，原则上也包括经验分布）的低维和高维问题的广泛适用性。该方法具备用于基生成、系数回归以及可选项剪枝的自动化流程，避免了依情况而定的参数调整。此外，它允许直接基于同一组模型评估结果来获取不确定性度量和全局灵敏度指数。大量的数值算例，包括标准基准测试函数以及涉及多达100个随机变量的工程应用，表明与传统代理建模方法相比，该方法具有高精度和高计算效率。

Abstract

This study proposes a deterministic and definitive methodology for surrogate model construction based on moment quadrature design points. Different from adaptive or randomly sampling approaches

the proposed framework derives design points directly from the statistical moments of the input probability density functions

ensuring reproducibility

optimal polynomial exactness

and broad applicability to low- and high-dimensional problems involving arbitrary distributions

including nonuniform distributions and

in principle

empirical ones. It features an automatic pipeline for basis generation

coefficient regression

and optional term pruning

avoiding case-dependent tuning. Moreover

it allows direct evaluation of uncertainty metrics and global sensitivity indices to be obtained using the same set of model evaluations. Extensive numerical examples

including standard benchmark functions and engineering applications involving up to 100 random variables

demonstrate that the proposed method achieves high accuracy and computational efficiency compared with conventional surrogate modeling approaches.

关键词

Keywords

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