Probabilistic Engineering Mechanics最新文献_第7页

Gaussian processes-based Bayesian updating framework for time-dependent reliability assessment of aging bridges with limited inspection data 基于高斯过程的老化桥梁时变可靠性评估贝叶斯更新框架

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103820

Yi Chen , Hui Yang , Wenwei Fu , Yaozhi Luo , Zhi Ma , Biran Zheng

Accurate time-varying reliability assessment of aging infrastructure is essential for informed maintenance and operational decisions but is often limited by uncertainties in available data, complicating decision-making under budget constraints. This highlights the need for advanced uncertainty quantification methods in reliability analysis. This study presents a Gaussian processes-based Bayesian updating for evaluating the time-varying reliability of aging bridges under the uncertainty of limited field inspections and sparse traffic survey data. The approach integrates Monte Carlo simulation, vehicle-bridge interaction (VBI) analysis, and progressive deterioration modeling to iteratively update key parameters and improve the reliability assessment of aging infrastructure. Stochastic vehicle flows (SVF) are simulated using Monte Carlo methods, with Bayesian inference employed to progressively update parameters such as vehicle speed distributions, axle weights, and spacing based on newly available traffic data. This iterative updating process ensures the simulations reflect the dynamic characteristics of real-world traffic, providing a robust foundation for the subsequent reliability analysis. VBI analysis is used to model the maximum load induced by traffic, resulting in a probability-based load model that characterizes load distribution for further reliability assessment. The temporal evolution of random variables related to resistance deterioration, such as material degradation, is monitored using an integrated approach combining conditional random fields with Bayesian inference, enabling the development of a progressive deterioration model. An active learning reliability assessment framework is developed to prioritize evaluating high-risk failure modes, enabling a dynamic assessment of the bridge's failure probability and reliability indices over time. This framework reduces prior epistemic uncertainties and provides a more accurate and comprehensive reliability analysis for aging infrastructure under limited inspection data.

对老化基础设施进行准确的时变可靠性评估对于明智的维护和运营决策至关重要，但往往受到可用数据的不确定性的限制，使预算约束下的决策复杂化。这突出了在可靠性分析中需要先进的不确定性量化方法。本文提出了一种基于高斯过程的贝叶斯更新方法，用于有限现场检验和稀疏交通调查数据不确定性下的老化桥梁时变可靠度评估。该方法将蒙特卡罗仿真、车桥相互作用（VBI）分析和渐进式劣化建模相结合，迭代更新关键参数，提高老化基础设施的可靠性评估。采用蒙特卡罗方法模拟随机车辆流（SVF），并利用贝叶斯推理逐步更新车辆速度分布、轴重和间距等参数。这种迭代更新过程保证了仿真结果能够反映真实流量的动态特性，为后续的可靠性分析提供了坚实的基础。利用VBI分析对交通引起的最大负荷进行建模，得到基于概率的负荷模型，该模型表征了负荷分布，为进一步的可靠性评估提供了依据。使用将条件随机场与贝叶斯推理相结合的综合方法来监测与电阻退化（如材料退化）相关的随机变量的时间演变，从而开发出渐进退化模型。开发了主动学习可靠性评估框架，优先评估高风险失效模式，实现了桥梁失效概率和可靠性指标随时间的动态评估。该框架减少了先验认知的不确定性，在有限的检测数据下为老化基础设施提供了更准确、更全面的可靠性分析。

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引用次数: 0

Constraint interval model updating with Chebyshev inclusion functions Chebyshev包含函数对约束区间模型的更新

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103821

Jinyan Li, Zhiyu Shi, Xujun Peng, Zheng Yang

Finite element model updating techniques for uncertain parameters have been extensively developed in recent years. Due to the limited information available on the probability distributions of parameters in practical engineering applications, interval analysis has emerged as a prominent research approach. Traditional interval algorithms, as a fundamental component of interval analysis, commonly assume parameter independence, which often results in significant and unavoidable interval overestimation. To address this issue in interval finite element model updating, this paper proposes a novel methodology that introduces the Chebyshev inclusion function based on cut high-dimensional model representations (Cut-HDMR), combined with a constraint interval algorithm(CIA), into the updating process. First, the Chebyshev inclusion function is used to approximate the modal frequencies decomposed by the Cut-HDMR method, forming a constraint interval representation. Then, a constraint interval finite element model updating method is developed, in which both modal frequencies and the parameters to be updated are described within the same constraint interval model. To demonstrate the practicality of the proposed approach, an interval finite element model updating toolbox is established. The effectiveness of the method in reducing interval overestimation is validated through several numerical examples, including a spring–mass system, the Garteur aircraft model, and a double-deck bridge model.

针对不确定参数的有限元模型修正技术近年来得到了广泛的发展。由于实际工程应用中有关参数概率分布的信息有限，区间分析已成为一种重要的研究方法。传统的区间算法作为区间分析的基本组成部分，通常假设参数无关，这往往导致不可避免的区间高估。为了解决区间有限元模型更新中的这一问题，本文提出了一种新的方法，将基于切高维模型表示的切比雪夫包含函数（cut - hdmr）与约束区间算法（CIA）相结合，引入到区间有限元模型更新过程中。首先，利用Chebyshev包含函数对Cut-HDMR方法分解的模态频率进行近似，形成约束区间表示；然后，提出了一种约束区间有限元模型更新方法，该方法将模态频率和需要更新的参数都描述在同一约束区间模型中。为了验证该方法的实用性，建立了区间有限元模型更新工具箱。通过弹簧-质量系统、Garteur飞机模型和双层桥模型的数值算例验证了该方法在减少区间高估方面的有效性。

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引用次数: 0

Enhancements and benchmarking of MCMC algorithms for subset simulation in structural reliability 结构可靠性子集仿真中MCMC算法的改进和基准测试

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103809

Juan G. Sepúlveda , Sebastian T. Glavind , Michael H. Faber

This paper contributes to identifying the most suitable reliability analysis techniques for different types of engineering applications by benchmarking recent and promising approaches, including Subset Simulation, the Probability Density Evolution Method (PDEM), and Polynomial Chaos Expansion (PCE). Particular focus is placed on Subset Simulation due to its robustness and efficiency in computing small failure probabilities, making it highly relevant for applications involving extreme loading conditions. Enhancements to the Markov Chain Monte Carlo (MCMC) algorithms used within Subset Simulation are proposed to address inefficiencies when applied in cloud computing environments. Benchmarking results reveal that the enhancements significantly improve efficiency by balancing variance reduction and runtime of the algorithm. While metamodels are advantageous in specific scenarios, their limitations in scalability and accuracy for large random spaces are highlighted. These findings provide valuable insights for practitioners and researchers in selecting appropriate reliability analysis techniques for complex structural applications.

本文通过对包括子集仿真、概率密度演化法（PDEM）和多项式混沌展开（PCE）在内的最新和有前途的方法进行基准测试，有助于确定最适合不同类型工程应用的可靠性分析技术。由于其在计算小故障概率方面的鲁棒性和效率，因此特别关注子集模拟，使其与涉及极端负载条件的应用高度相关。提出了子集仿真中使用的马尔可夫链蒙特卡罗（MCMC）算法的增强，以解决在云计算环境中应用时的低效率问题。基准测试结果表明，通过平衡方差减少和算法运行时间，改进后的算法显著提高了效率。虽然元模型在特定场景中是有利的，但它们在大型随机空间的可伸缩性和准确性方面的局限性是突出的。这些发现为从业者和研究人员在复杂结构应用中选择合适的可靠性分析技术提供了有价值的见解。

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引用次数: 0

Reduced-order equivalent linearization based on explicit time-domain method for nonstationary random vibration analysis of nonlinear systems 基于显式时域法的降阶等效线性化非线性系统非平稳随机振动分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103825

Xiaoxiang Lin , Jianhua Xian , Cheng Su

Equivalent linearization method (ELM) is among the most promising techniques for analyzing large-scale nonlinear systems under random excitations, involving repetitive random vibration analyses of the series of linearized systems. The existing linear random vibration methods can be directly incorporated into ELM to conduct these analyses. However, their efficiency is still far from satisfactory when it comes to the nonstationary problems of large-scale systems. In this study, a reduced-order equivalent linearization method based on the explicit time-domain method (EL-ETDM) is proposed for the nonstationary random vibration analysis of systems with local nonlinearity. For a specific time instant, the explicit expression of dynamic responses of the equivalent linear system is first established, and a reduced-order iteration scheme is then developed for the statistical moment responses of the nonlinear degrees of freedom, without the need for repeated analyses of the entire linearized systems involved in the iteration process. This feature enables the efficiency of the iteration process of EL-ETDM to be independent of the system scale. The reduced-order EL-ETDM is further developed for the sensitivity analysis of nonstationary random vibration of nonlinear systems. The energy-dissipation structure with nonlinear eddy current dampers is adopted for mathematical formulation of the proposed method. A two-story shear-type structure with a nonlinear eddy current damper is studied to demonstrate the accuracy of the present approach, and a 1148m long suspension bridge with 8 nonlinear eddy current dampers is investigated to illustrate the feasibility of the present approach for stochastic optimization of large-scale structures.

等效线性化方法（ELM）是分析随机激励下的大规模非线性系统最有前途的技术之一，涉及对一系列线性化系统的重复随机振动进行分析。现有的线性随机振动方法可以直接纳入ELM进行这些分析。然而，当涉及到大型系统的非平稳问题时，它们的效率还远远不能令人满意。本文提出了一种基于显式时域法（EL-ETDM）的降阶等效线性化方法，用于具有局部非线性的系统的非平稳随机振动分析。首先建立等效线性系统在特定时刻的动力响应的显式表达式，然后建立非线性自由度的统计力矩响应的降阶迭代格式，而无需在迭代过程中对整个线性化系统进行重复分析。这一特性使得EL-ETDM迭代过程的效率与系统规模无关。进一步发展了用于非线性系统非平稳随机振动灵敏度分析的降阶EL-ETDM。采用带非线性涡流阻尼器的耗能结构作为该方法的数学公式。以两层剪力型非线性涡流阻尼器结构为例，验证了该方法的准确性；以1148m长悬索桥为例，验证了该方法在大型结构随机优化中的可行性。

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引用次数: 0

Stochastic dynamics and first-passage failure of wind turbine transmission system with time-varying stiffness under harmonic excitations using path integral methods 用路径积分法研究谐波激励下时变刚度风力发电机组传动系统的随机动力学及首次失效

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103815

Jiankang Liu , Meilin Lu , Chen Jin , Bao Sun , Wei Xu

To reveal the dynamical behaviors of wind power transmission systems under complex external environments, this paper establishes a two-mass drivetrain model of the mechanical transmission chain with the time-varying stiffness under a combination of harmonic and Gaussian white noise excitations. Then the evolution of the stationary and transient probability density functions of the system is computed using the improved path integral method. Furthermore, the path integral results are used to evaluate the stability of the wind power transmission system with the first-passage failure theory. Meanwhile, the results of the improved path integral method are compared with those of the Monte Carlo simulations to verify its accuracy in predicting periodic behavior as well as tail peak values. Studies show that the damping coefficients and the time-varying stiffness amplitude can induce stochastic P-bifurcation, and larger damping coefficients, smaller time-varying stiffness amplitude, harmonic excitation and noise intensity are more favorable for the stability of the wind turbine drive shaft system.

为了揭示复杂外部环境下风电传动系统的动力学行为，建立了谐波和高斯白噪声联合激励下具有时变刚度的机械传动链双质量传动系统模型。然后利用改进的路径积分法计算系统的平稳和暂态概率密度函数的演化。利用路径积分的结果，应用首道失效理论对风电系统的稳定性进行了评价。同时，将改进的路径积分方法与蒙特卡罗模拟结果进行了比较，验证了其在预测周期行为和尾峰值方面的准确性。研究表明，阻尼系数和时变刚度幅值会诱发随机p分岔，阻尼系数越大，时变刚度幅值越小，谐波激励和噪声强度越有利于风力机传动轴系统的稳定性。

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引用次数: 0

Seismic reliability assessment of in-service water distribution networks 在役配水管网抗震可靠性评价

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103826

Wei Liu , Zhiyin Xie , Jiankang Xie

Most existing studies on the seismic reliability of water distribution networks (WDNs) neglect pipe deterioration over service life, including increased pipe roughness and elevated daily failure rates such as leaks. This neglect of pipe deterioration essentially treats in-service WDNs as new systems, which may lead to overestimated seismic reliability. This study proposes a novel framework that integrates established deterioration models to comprehensively assess the seismic reliability of in-service WDNs. First, the daily pipe failure probability, predicted using a deep learning algorithm, is incorporated into a pipe fragility model based on pipe reliability. A seismic risk assessment model is simultaneously applied to evaluate damage to pumping stations and water plants. Second, nodal heads following seismic events are derived via hydraulic analysis, accounting for multiple component types, including pipes, nodes, pumping stations, and water plants. Pipe roughness is modeled using a time-dependent function that reflects the progressive decline in hydraulic performance. Third, a probability density evolution method is employed to account for uncertainties in the characteristics of pipes, pumping stations, and water plants, enabling the derivation of nodal head distributions and calculation of seismic reliability. Finally, the proposed framework is applied to a real large-scale WDN in China, demonstrating the compounded effects of integrated deterioration mechanisms and highlighting the importance of such considerations for realistic seismic reliability assessment.

大多数关于配水网络（wdn）地震可靠性的现有研究都忽略了管道在使用寿命期间的劣化，包括管道粗糙度的增加和泄漏等日常故障率的增加。这种对管道劣化的忽视本质上是将正在使用的wdn视为新系统，这可能导致高估地震可靠性。本研究提出了一个新的框架，该框架集成了已建立的退化模型，以全面评估在役wdn的地震可靠性。首先，利用深度学习算法预测管道的每日失效概率，并将其纳入基于管道可靠性的管道易损性模型。同时应用地震风险评估模型对泵站和水厂的震害进行评估。其次，通过水力分析得出地震事件后的节点水头，考虑到多种组件类型，包括管道，节点，泵站和水厂。管道粗糙度是用一个时间相关的函数来建模的，该函数反映了水力性能的逐渐下降。第三，采用概率密度演化方法，考虑管道、泵站和水厂特征的不确定性，推导节点水头分布，计算地震可靠度。最后，将所提出的框架应用于中国实际的大型WDN，展示了综合退化机制的复合效应，并强调了这些考虑因素在实际地震可靠性评估中的重要性。

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引用次数: 0

Moment Lyapunov exponents and stochastic stability of non-linear systems under white-noise excitation 白噪声激励下非线性系统的矩Lyapunov指数与随机稳定性

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103824

Maral Ghaedi, Jian Deng

The moment Lyapunov exponent (MLE) is a critical index for assessing the stochastic stability of structures and has been widely applied to linear systems. However, its application to strongly nonlinear systems remains limited due to the inadequacy of traditional methods, such as the method of stochastic averaging. This paper addresses this gap by analyzing the stochastic stability of strongly nonlinear structural systems subjected to parametric excitations modeled as white noise, using MLEs. The analysis begins with the formulation of a strongly nonlinear system. A stochastic averaging method based on a transformed energy envelope is developed to derive a system of Itô stochastic differential equations. Unlike conventional approaches that rely on the Euclidean norm of the state vector, a modified Khasminskii-type transformation is employed, using the square root of the system's Hamiltonian to study stability. To validate the analytical findings, Monte Carlo simulations are conducted to independently compute the MLE. Additionally, the largest Lyapunov exponents and a stability index are evaluated to further characterize the system's stochastic behavior. The effects of key parameters on stability are systematically investigated. This study offers novel insights into the stochastic dynamics of strongly nonlinear structural systems.

矩Lyapunov指数（MLE）是评价结构随机稳定性的一个重要指标，在线性系统中得到了广泛的应用。然而，由于传统方法如随机平均方法的不足，其在强非线性系统中的应用仍然受到限制。本文通过分析强非线性结构系统在白噪声参数激励下的随机稳定性来解决这一问题。分析从一个强非线性系统的公式开始。提出了一种基于变换能量包络的随机平均方法，导出了一个Itô随机微分方程组。与依赖于状态向量欧几里得范数的传统方法不同，采用了一种改进的哈斯明斯基型变换，使用系统哈密顿量的平方根来研究稳定性。为了验证分析结果，进行了蒙特卡罗模拟来独立计算MLE。此外，评估了最大Lyapunov指数和稳定性指数，以进一步表征系统的随机行为。系统地研究了关键参数对稳定性的影响。这项研究为强非线性结构系统的随机动力学提供了新的见解。

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引用次数: 0

Harnessing physics-informed operators for high-dimensional reliability analysis problems 利用物理知识的操作员进行高维可靠性分析问题

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103807

Navaneeth N. , Tushar , Souvik Chakraborty

Quantifying the reliability of complex engineering systems under uncertainty is a computationally demanding task, particularly when the system response depends on a large number of stochastic parameters. Traditional reliability analysis techniques, anchored in repeated high-fidelity simulations or experimental evaluations, become prohibitively expensive in high-dimensional settings, especially for systems governed by partial differential equations (PDEs) that require discretization-based solvers such as the finite element or finite volume methods. Surrogate modeling offers a viable alternative by approximating the input–output mapping of such systems with reduced computational overhead. Among these, neural operators have recently gained attention for their ability to learn solution operators of PDEs from limited data. In this work, we investigate the utility of the physics-informed wavelet neural operator (PI-WNO) for high-dimensional reliability analysis. We demonstrate that PI-WNO can accurately learn the stochastic input-to-solution map without resorting to repeated numerical simulations, thereby enabling efficient and scalable reliability estimation. Through benchmark problems, we illustrate the effectiveness of the proposed framework in handling high-dimensional uncertainty while preserving accuracy. Furthermore, we extend this approach to systems governed by coupled PDEs, highlighting the broad applicability and potential of physics-informed neural operators for reliability analysis in complex physical systems.

对不确定条件下复杂工程系统的可靠性进行量化是一项计算要求很高的任务，特别是当系统响应依赖于大量随机参数时。传统的可靠性分析技术依赖于重复的高保真度模拟或实验评估，在高维环境中变得非常昂贵，特别是对于需要基于离散化的求解器（如有限元或有限体积方法）的偏微分方程（pde）控制的系统。代理建模提供了一种可行的替代方案，通过减少计算开销来近似此类系统的输入-输出映射。其中，神经算子因其从有限数据中学习偏微分方程解算子的能力而受到关注。在这项工作中，我们研究了物理信息小波神经算子（PI-WNO）在高维可靠性分析中的应用。我们证明PI-WNO可以准确地学习随机输入-解映射，而无需诉诸重复的数值模拟，从而实现高效和可扩展的可靠性估计。通过基准问题，我们证明了该框架在处理高维不确定性的同时保持精度的有效性。此外，我们将这种方法扩展到由耦合偏微分方程控制的系统，强调了物理信息神经算子在复杂物理系统可靠性分析中的广泛适用性和潜力。

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引用次数: 0

AGP-SYS: An adaptive learning and Gaussian process modeling-based system reliability method AGP-SYS：基于自适应学习和高斯过程建模的系统可靠性方法

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103805

K. Wen , W. Zeng , S.Y. Zeng

Various system reliability analysis methods based on surrogate models have recently been developed for problems reliant on costly performance function (PF) evaluation. Existing surrogate-based methods approximate the system performance function (SPF) using the max/min of component performance functions (CPFs), which may introduce errors in failure probability estimation. Through SPF analysis across diverse scenarios, we demonstrate that substituting a certain CPF for SPF may introduce significant errors. Furthermore, SPF distributions exhibit non-Gaussian characteristics in specific contexts. According to these cases, we propose the AGP-SYS method. This approach employs Gaussian process modeling to predict CPFs, then rigorously derives the mean and variance of SPF using all CPF predictions—thereby avoiding errors induced by maximum/minimum approximations. Given that the SPF distribution is non-Gaussian, the probability of misclassification (PMC) is used as the learning function instead of the conventional U-function, whose physical significance is strictly confined to Gaussian-distributed SPF. Furthermore, an adaptive shrinking distance criterion preventing training-point clustering is introduced for enhancing model-updating efficiency. The effectiveness of AGP-SYS is demonstrated through three case studies: a series system, a parallel system, and a column-based independent foundation in civil engineering.

基于代理模型的各种系统可靠性分析方法最近被开发出来用于依赖于昂贵性能函数（PF）评估的问题。现有的基于代理的方法使用部件性能函数（cpf）的最大/最小值来近似系统性能函数（SPF），这可能会在故障概率估计中引入错误。通过不同场景下的SPF分析，我们证明用特定的CPF代替SPF可能会引入显著的误差。此外，SPF分布在特定环境中表现出非高斯特征。针对这些情况，我们提出了AGP-SYS方法。该方法采用高斯过程建模来预测CPF，然后使用所有CPF预测严格推导SPF的均值和方差，从而避免了由最大/最小近似引起的误差。考虑到SPF的非高斯分布，采用误分类概率（probability of misclassification， PMC）代替传统的u函数作为学习函数，其物理意义严格局限于高斯分布的SPF。此外，为了提高模型更新效率，引入了防止训练点聚类的自适应距离缩小准则。通过串联系统、并联系统和柱式独立基础在土木工程中的应用，验证了AGP-SYS的有效性。

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引用次数: 0

A novel double-layer kriging model-based reliability analysis framework for time-dependent structural system with stochastic process 基于双层kriging模型的随机过程时变结构系统可靠度分析框架

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-07-01 DOI: 10.1016/j.probengmech.2025.103812

Nan Ye , Zhenzhou Lu

In the surrogate model-based time-dependent reliability analysis, the discretization of stochastic process may lead to a great increase of input dimensionality, which poses challenges to the construction and training of surrogate model. To address this issue, a novel Double-Layer Kriging model-based Reliability Analysis Framework (nDLK-RAF) is proposed for time-dependent structural system with stochastic process in this paper. The random vector and stochastic process are treated separately in nDLK-RAF. Specifically, the Kriging model of time-dependent performance function under given random vector realization is established in the inner layer of nDLK-RAF, thus the conditional time-dependent failure probability (TDFP) corresponding to given random vector realization can be estimated by the inner convergent Kriging model. On this basis, the relationship between conditional TDFP and random vector is further surrogated by the Kriging model of outer-layer, and the final TDFP can be estimated by the outer convergent Kriging model. Further, aiming at the rare failure problem in engineering, this paper designs the variance reduction strategies of embedding directional sampling and importance sampling in the inner and outer layers, respectively, which improves the training efficiency of double-layer Kriging models in nDLK-RAF. Compared with the existing methods that simultaneously consider random vector and stochastic process, the nDLK-RAF reasonably balances the input dimensionalities of inner and outer Kriging models, which avoids the construction of high-dimensional surrogate models. Meanwhile, the two combined variance reduction sampling methods reduce the required candidate sample pool size for updating Kriging model, ultimately achieving efficient time-dependent reliability analysis. The superiority of nDLK-RAF over existing Kriging model-based methods is demonstrated by the example analysis.

在基于代理模型的时变可靠性分析中，随机过程的离散化可能导致输入维数的大幅增加，这给代理模型的构建和训练带来了挑战。针对这一问题，本文提出了一种基于双层Kriging模型的时变随机结构系统可靠性分析框架（nDLK-RAF）。在nDLK-RAF中，随机向量和随机过程是分开处理的。具体而言，在nDLK-RAF的内层建立了给定随机向量实现下的时变性能函数的Kriging模型，从而可以通过内部收敛的Kriging模型估计给定随机向量实现对应的条件时变失效概率（TDFP）。在此基础上，进一步用外层的Kriging模型代替条件TDFP与随机向量之间的关系，并通过外层收敛Kriging模型估计最终的TDFP。进一步，针对工程中罕见的失效问题，设计了分别在内层和外层嵌入定向采样和重要采样的方差缩减策略，提高了nDLK-RAF中双层Kriging模型的训练效率。与现有同时考虑随机向量和随机过程的方法相比，nDLK-RAF合理平衡了内外克里格模型的输入维数，避免了高维代理模型的构建。同时，两种联合方差缩减抽样方法减少了更新Kriging模型所需的候选样本池大小，最终实现了高效的时变信度分析。通过算例分析，证明了nDLK-RAF相对于现有基于Kriging模型的方法的优越性。

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引用次数: 0