Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region of China 999077, People’s Republic of China
School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, People’s Republic of China
Department of Civil and Environmental Engineering, Engineering Research Center for Advanced Technology for Large Structural Systems (ATLSS Center), Lehigh University, Bethlehem, PA, United States of America
School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, People’s Republic of China
[ "Tao Wang is currently a Post-Doctoral Fellow with the Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, China. His current research interests include uncertainty quantification, structural and system reliability, wind-induced risk and resilience assessment of power transmission structures and amphibious robots for power facility maintenance." ]
[ "Da-Gang Lu is a professor with the School of Civil Engineering, Harbin Institute of Technology, China. His current research interests include structural reliability, seismic fragility, analysis of multi-disaster safety, risk and resilience in civil engineering, as well as seismic design methods." ]
[ "You Dong is an associate professor with the Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, China. His current research interests include life-cycle performance, intelligent maintenance and resilience assessment of infrastructure, climate change adaptation, and the application of AI in civil engineering." ]
[ "Dan M Frangopol is a Fazlur R. Khan chair professor with the Department of Civil and Environmental Engineering, Lehigh University, USA. His current research interests include structural reliability, life-cycle management of engineering structures, multi-disaster risk analysis, and theories and engineering applications of infrastructure resilience." ]
[ "Yi-Qiu Tan is a professor with the School of Transportation Science and Engineering, Harbin Institute of Technology, China. Her current research interests include the durability and safety of asphalt roads in cold regions, prevention of ice and snow disasters, integrated design method of structure and material, and intelligent maintenance of transportation infrastructure." ]
收稿:2025-07-15,
修回:2025-10-20,
录用:2025-11-11,
网络首发:2025-12-02,
纸质出版:2025
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Tao Wang, Da-Gang Lu, You Dong, 等. 随机系统不确定性量化的降维积分法:矩估计研究现状综述[J]. 可靠性科学与工程学报(英文), 2025,(4):1-25.
Tao Wang, Da-Gang Lu, You Dong, et al. Dimension-reduction integration methods for uncertainty quantification of stochastic systems: a state-of-the-art review on moments estimation[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-25.
Tao Wang, Da-Gang Lu, You Dong, 等. 随机系统不确定性量化的降维积分法:矩估计研究现状综述[J]. 可靠性科学与工程学报(英文), 2025,(4):1-25. DOI: 10.1088/3050-2454/ae1df9.
Tao Wang, Da-Gang Lu, You Dong, et al. Dimension-reduction integration methods for uncertainty quantification of stochastic systems: a state-of-the-art review on moments estimation[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-25. DOI: 10.1088/3050-2454/ae1df9.
随机系统矩估计是工程不确定性量化与可靠性分析中较为常见的问题。降维积分法(dimension-reduction integration methods,DRIMs)源于降维模型,其理论基础在于将随机系统矩估计中涉及的高维积分转化为关于各组成函数的一组低维积分,现已成为矩估计的重要方法。本文系统综述了现有应用于随机系统矩估计的降维积分法,涵盖降维模型、矩估计的降维积分法,以及这些积分方法与先进数值积分算法的结合。最后,展望与结论部分指出了降维积分法面临的挑战与未来潜在研究方向,从而为该领域的研究人员和工程实践者提供基础性参考。
Estimating the moments of stochastic systems is a relatively common problem in engineering uncertainty quantification and reliability analysis. Dimension-reduction integration methods (DRIMs)
derived from dimension-reduction models
provide the theoretical foundation for converting the high-dimensional integrals involved in stochastic system moment estimation into sets of low-dimensional integrals over component functions. These methods have emerged as important approaches for moment estimation. This paper provides a comprehensive review of existing DRIMs for stochastic system moment estimation
including a review of dimension-reduction models
DRIMs for moment estimation
and the combination of these integration methods with advanced numerical integration algorithms. Finally
the outlook and conclusion section identifies challenges and promising future research directions for DRIMs
thereby providing a foundational reference for researchers and practitioners in the field.
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