Probabilistic Engineering Mechanics最新文献

Spatial variation of parallel to grain tensile strength in sawn lumber 锯材平行晶粒抗拉强度的空间变异

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-25 DOI: 10.1016/j.probengmech.2026.103906

Fiona A. O'Donnell , Kevin U. Murillo , Sanjay R. Arwade

The natural growth of wood leads to significant variation in the mechanical properties of structural lumber among boards and within a single board. As such, the safe and efficient use of wood in structural applications requires a process to assess the probabilistic nature of wood properties. Current processes for dimension lumber neglect within-member variation and utilize uniform design properties for a given species and grade. This paper presents a framework for considering within-member tensile strength variation to enable higher precision uncertainty characterization of ultimate tensile strength. The spatially varying tensile strength is a function of the correlation structure of the mechanical properties within the lumber and the presence of naturally occurring defects like knots. In this model, the clear wood strength variation is decoupled from the strength reduction associated with the presence of knots. Two strength ratio models for the influence of knots on the clear wood strength are considered. The developed framework can be employed in computational analyses, such as reliability studies, to support improved material efficiency of structural lumber and large engineered wood products, like cross laminated timber. The models were calibrated to Eastern hemlock but could be applied to other softwood species of interest.

木材的自然生长导致结构木材的机械性能在板之间和单个板内发生显著变化。因此，在结构应用中安全有效地使用木材需要一个过程来评估木材性能的概率性质。目前尺寸木材的工艺忽略了构件内部的变化，并对给定的品种和等级使用统一的设计特性。本文提出了一个考虑构件内部抗拉强度变化的框架，以实现更高精度的极限抗拉强度不确定性表征。空间变化的抗拉强度是木材内部机械性能的相关结构和存在自然发生的缺陷（如结）的函数。在这个模型中，清晰的木材强度变化与与结的存在相关的强度降低是分离的。考虑了两种强度比模型对结对透明木强度的影响。开发的框架可用于计算分析，例如可靠性研究，以支持提高结构木材和大型工程木制品（如交叉层压木材）的材料效率。这些模型被校准为东部铁杉，但可以应用于其他感兴趣的软木物种。

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引用次数: 0

Gaussian and non-Gaussian random field simulation on curved surface based on the heat flow method of distance field computation 基于距离场计算的热流法的曲面高斯和非高斯随机场模拟

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-14 DOI: 10.1016/j.probengmech.2026.103902

Ding Wang , Hao Chen

In the field of engineering, certain materials, such as concrete,exhibit spatially uncertain properties. To analyze the reliability of structures composed of these materials, random fields are employed to characterize the spatial variability of material properties. Several methods have been proposed to simulate random fields in Euclidean space. For curved spaces, a conventional approach to simulate random fields involves isometrically mapping the surface onto a plane, simulating the random field on the plane, and mapping it back inversely onto the original surface. However, for surfaces with non-zero Gaussian curvatures, isometric mapping only provides an approximation. This approximation introduces significant errors when the absolute value of the Gaussian curvature is large. The study presented in this paper addresses the challenge of calculating geodesic distance and simulating random fields on curved surfaces. The advantage of the proposed approach lies in its ability to compute geodesic distance and correlation function directly on the curved surface by numerically solving the heat equation and Poisson equation. This eliminates the need to map the surface to a plane and avoids the distance distortion caused by such mapping. The practicality of the proposed approach is verified through two numerical examples. The first example involves simulating Gaussian and non-Gaussian random fields on a spherical surface. The second example focuses on simulating the random field of concrete elastic modulus in the hyperbolic shell of revolution of a large cooling tower and investigating the effect of correlation length on the structural buckling mode.

在工程领域，某些材料，如混凝土，具有空间不确定性。为了分析由这些材料组成的结构的可靠性，采用随机场来表征材料性能的空间变异性。提出了几种模拟欧几里得空间随机场的方法。对于弯曲空间，模拟随机场的传统方法包括将曲面等距映射到平面上，在平面上模拟随机场，然后将其反向映射到原始曲面上。然而，对于具有非零高斯曲率的曲面，等距映射只能提供近似。当高斯曲率的绝对值很大时，这种近似引入了显著的误差。本文提出的研究解决了计算测地线距离和模拟曲面随机场的挑战。该方法的优点在于通过数值求解热方程和泊松方程，可以直接在曲面上计算测地线距离和相关函数。这消除了将表面映射到平面的需要，并避免了由这种映射引起的距离失真。通过两个算例验证了该方法的实用性。第一个例子涉及在球面上模拟高斯和非高斯随机场。第二个算例重点模拟了大型冷却塔旋转双曲壳内混凝土弹性模量随机场，研究了相关长度对结构屈曲模态的影响。

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引用次数: 0

Description of the linear elastic material parameters of short fiber composites using random fields. A comparison of Gaussian and non-Gaussian random fields 利用随机场描述短纤维复合材料的线弹性材料参数。高斯和非高斯随机场的比较

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-02 DOI: 10.1016/j.probengmech.2026.103896

Ilona Małgorzata Widera, Natalie Rauter

Modeling spatially random materials such as short fiber reinforced composites remains a persistent challenge. Existing approaches tend to either oversimplify the inherent heterogeneity and complex character of these materials or demand substantial computational resources and cost. However, as these materials gain increasing relevance across various industries, there is a growing need for efficient yet realistic modeling strategies. One such approach involves representing mechanical properties through random fields. So far the approach is limited to Gaussian random fields, which implies a normal distribution of the underlying material properties. Since this is usually not the case and e.g. negative valued material parameters are inadmissible, the method is extended to non-Gaussian random fields in this work. To assess the necessity of the presented extended approach the non-Gaussian random fields are compared with each other to derive advantages and limitations. It is shown that the numerical approach proposed here provides an effective framework for the realization of non-Gaussian random fields to model the elasticity tensor of short fiber-reinforced composites. The results demonstrate that non-Gaussian random fields in context of finite element simulations don't enhance the representation accuracy of the input data significantly. Therefore, the use of Gaussian random fields is deemed sufficient in the context of finite numerical simulations, provided that the input data are based on a sufficiently large window size or that the negligible number of negative values is appropriately corrected afterward.

空间随机材料（如短纤维增强复合材料）的建模仍然是一个持续的挑战。现有的方法倾向于过度简化这些材料固有的异质性和复杂性，或者需要大量的计算资源和成本。然而，随着这些材料在各个行业中获得越来越多的相关性，对高效而现实的建模策略的需求日益增长。其中一种方法是通过随机场来表示机械性能。到目前为止，该方法仅限于高斯随机场，这意味着底层材料属性的正态分布。由于通常情况并非如此，例如，负值的材料参数是不可接受的，因此本工作将该方法推广到非高斯随机场。为了评估所提出的扩展方法的必要性，对非高斯随机场进行了比较，得出了优点和局限性。结果表明，本文提出的数值方法为实现非高斯随机场对短纤维增强复合材料弹性张量的建模提供了有效的框架。结果表明，非高斯随机场在有限元模拟中不能显著提高输入数据的表示精度。因此，在有限数值模拟的情况下，只要输入数据基于足够大的窗口大小，或者之后适当地纠正了可忽略不计的负值数量，高斯随机场的使用就被认为是足够的。

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引用次数: 0

Seismic fragility analysis of deep sliding stability in gravity dams via vector-valued intensity measures 基于向量值强度测度的重力坝深滑稳定性地震易损性分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-13 DOI: 10.1016/j.probengmech.2026.103904

Xiangjiang Li, Zhiqiang Song, Zhilong Li, Yunhe Liu

To assess the probabilistic risk of deep sliding instability of concrete gravity dams under near-fault ground motion, this study develops a finite element model of a gravity dam–slider–foundation system and conducts fragility analysis. Global damage, displacement, and sliding responses are adopted as engineering demand parameters, and the corresponding damage-state classification criteria are established. Within the framework of probabilistic seismic demand models, the optimal vector-valued intensity measure for the considered system is identified through a systematic comparison, and the probabilistic seismic demand model and fragility surface under the vector-valued intensity measure are constructed accordingly. The results indicate that the optimal vector-valued intensity measure is (PGA, ASI), whose joint constraint on the amplitude and energy characteristics of ground motions can significantly reduce the dispersion in demand predictions and improve model efficiency. Compared with conventional fragility curves based on scalar-valued intensity measures, the fragility surface based on the vector-valued intensity measure can more robustly characterize failure probabilities under different combinations of ground-motion features, thereby enhancing the reliability of the probabilistic seismic performance assessment of gravity dams.

为了评估近断层地震动作用下混凝土重力坝发生深度滑动失稳的概率风险，本文建立了重力坝-滑块-基础系统的有限元模型，并进行了易损性分析。采用整体损伤、位移和滑动响应作为工程需求参数，建立相应的损伤状态分类准则。在概率地震需求模型框架内，通过系统比较，确定了考虑系统的最优向量值烈度测度，并构造了向量值烈度测度下的概率地震需求模型和易损性曲面。结果表明，最优的向量值强度度量是（PGA， ASI），其对地震动振幅和能量特性的联合约束可以显著减少需求预测中的频散，提高模型效率。与基于标度烈度测度的传统易损性曲线相比，基于矢量值烈度测度的易损性面能更稳健地表征不同地震动特征组合下的破坏概率，从而提高了重力坝概率抗震性能评价的可靠性。

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引用次数: 0

Time-variant reliability analysis based on an improved Kriging method for industrial robot joint rotational accuracy subject to temperature 基于改进Kriging方法的温度下工业机器人关节旋转精度时变可靠性分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-24 DOI: 10.1016/j.probengmech.2025.103883

Jia Li , Liang Wang , Jialong He , Yan Liu , Guofa Li , Liyao Yu

Industrial robot joints experience time-varying temperature changes during operation, which directly affect rotational accuracy. However, systematic investigations into how dynamic and cumulative temperature effects lead to accuracy failure within a single work cycle remain limited. Moreover, the difficulty of precisely controlling temperature in practical environments complicates the acquisition of sufficient joint accuracy data under varying thermal conditions. To address these issues, this paper develops a joint rotation simulation model that explicitly incorporates temperature effects, allowing precise temperature control and accurate identification of the maximum rotational accuracy error under different operating conditions. Based on the simulated responses, a time-variant reliability analysis framework is employed to evaluate the probability of accuracy failure over the work cycle. Nevertheless, conventional active Kriging methods often suffer from inefficient sampling strategies. To overcome this limitation, a Rapid Uncertainty Assessment-guided Active Kriging (RUA-AK) method is proposed, in which a rapid uncertainty assessment function is constructed for time trajectories and sampling is adaptively refined according to uncertainty indicators, thereby improving computational efficiency. Numerical examples demonstrate that RUA-AK can substantially reduce the number of model evaluations required to achieve a prescribed accuracy level. Finally, the proposed method is applied to the time-variant reliability analysis of industrial robot joint rotational accuracy, elucidating the influence of temperature variations on reliability evolution throughout the work cycle.

工业机器人关节在工作过程中会经历时变的温度变化，直接影响旋转精度。然而，对动态和累积温度效应如何导致单个工作周期内精度失效的系统调查仍然有限。此外，在实际环境中精确控制温度的难度使得在不同热条件下获得足够的关节精度数据变得复杂。为了解决这些问题，本文开发了一个明确纳入温度影响的关节旋转仿真模型，可以精确控制温度并准确识别不同操作条件下的最大旋转精度误差。基于仿真响应，采用时变可靠性分析框架，对整个工作周期精度失效概率进行评估。然而，传统的主动克里格方法往往存在采样策略效率低下的问题。针对这一局限性，提出了一种基于快速不确定性评估的主动克里格（RUA-AK）方法，该方法对时间轨迹构建快速不确定性评估函数，并根据不确定性指标自适应细化采样，从而提高了计算效率。数值算例表明，RUA-AK可以大大减少达到规定精度水平所需的模型评估次数。最后，将该方法应用于工业机器人关节旋转精度的时变可靠性分析，阐明了温度变化对整个工作周期可靠性演化的影响。

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引用次数: 0

Online POD–Kriging surrogate for efficient uncertainty quantification of dynamical systems 动态系统不确定度定量的在线POD-Kriging代理

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-23 DOI: 10.1016/j.probengmech.2025.103886

Samrul Hoda, Biswarup Bhattacharyya

Surrogate models serve as a pivotal tool in addressing the computational hurdles in analyzing the dynamical systems, especially in the presence of parametric uncertainty. In the context of uncertainty quantification (UQ) for dynamical systems, computing surrogate model parameters at each time step is often challenging, as it necessitates the computation of model parameters at each time step. This paper introduces an online reduced-order surrogate model for UQ in dynamical systems. An online Proper Orthogonal Decomposition (POD) approach is employed to represent stochastic response quantities using a minimal number of POD bases at each time instance. This approach allows for the fast updating of POD bases and coefficients at each time step in an online manner without needing to use all the data for the calculation. Further, the uncertainty propagation is facilitated through the utilization of the Kriging model. The efficacy of the proposed online POD–Kriging model is demonstrated for UQ in both linear and nonlinear dynamical systems, with results compared against a state-of-the-art method and full-scale Monte Carlo simulations. The consistently low predictive epistemic uncertainty observed across all cases confirms that the model achieves high accuracy, thereby establishing its efficiency and reliability for UQ in dynamical systems.

替代模型是解决分析动力系统的计算障碍的关键工具，特别是在参数不确定性存在的情况下。在动态系统不确定性量化（UQ）的背景下，在每个时间步长计算替代模型参数通常具有挑战性，因为它需要在每个时间步长计算模型参数。本文介绍了动态系统中UQ的在线降阶代理模型。采用在线固有正交分解（POD）方法，在每个时间实例中使用最少的POD基数来表示随机响应量。这种方法允许以在线方式在每个时间步快速更新POD基和系数，而无需使用所有数据进行计算。此外，利用Kriging模型促进了不确定性的传播。提出的在线POD-Kriging模型在线性和非线性动力系统中的UQ有效性得到了证明，并将结果与最先进的方法和全尺寸蒙特卡罗模拟进行了比较。在所有情况下观察到的一致的低预测认知不确定性证实了该模型达到了很高的准确性，从而建立了其在动态系统中UQ的效率和可靠性。

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引用次数: 0

A time-dependent reliability analysis method for landing gear retraction mechanism based on truncated β-sphere sampling and improved APCK 基于截断β球采样和改进APCK的起落架收放机构时变可靠性分析方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-13 DOI: 10.1016/j.probengmech.2026.103901

Peng Yang , Xinchen Zhuang , Yongjie Li , Tianxiang Yu

As a key component of the aircraft landing gear system, the retraction mechanism significantly impacts system reliability through its motion capabilities and precision. This study presents a time-dependent reliability analysis of the landing gear retraction mechanism, introducing the APCK-TBS method, which integrates the Adaptive Polynomial-chaos-based Kriging (APCK) surrogate model with the truncated β-sphere sampling (TBS) approach. Initially, a multi-body dynamics simulation model is developed to simulate the retraction mechanism. By accounting for random variables and wear degradation in hinge clearance, reliability models are formulated for blocking, positioning, and motion accuracy failures. An adaptive strategy is then introduced to optimize the polynomial chaos order and basis function, enhancing the PCK surrogate model, and mitigating the risk of overfitting. To further improve adaptability, a multi-point active learning framework is proposed, employing TBS and K-means clustering. Additionally, an enhanced convergence criterion is applied, significantly reducing computational overhead. The effectiveness of the TBS and the APCK-TBS method in terms of both computational efficiency and accuracy is validated through numerical examples. This methodology enables precise and efficient analysis of the time-dependent reliability of the landing gear retraction mechanism, providing a novel approach for the reliability assessment of complex mechanical systems.

收放机构作为飞机起落架系统的关键部件，其运动性能和精度直接影响着起落架系统的可靠性。本文对起落架收放机构进行了时变可靠性分析，引入了APCK-TBS方法，该方法将基于自适应多项式混沌的Kriging （APCK）代理模型与截断β球采样（TBS）方法相结合。首先，建立了一个多体动力学仿真模型来模拟收放机理。通过考虑铰链间隙中的随机变量和磨损退化，建立了阻塞、定位和运动精度故障的可靠性模型。引入自适应策略对多项式混沌阶和基函数进行优化，增强了PCK代理模型，降低了过拟合风险。为了进一步提高自适应性，提出了采用TBS和K-means聚类的多点主动学习框架。此外，应用了增强的收敛准则，显著降低了计算开销。通过算例验证了TBS方法和APCK-TBS方法在计算效率和精度方面的有效性。该方法能够精确有效地分析起落架收放机构的时变可靠性，为复杂机械系统的可靠性评估提供了一种新的方法。

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引用次数: 0

A spectrum-based ductility demand approach for the design of Fluid Viscous Dampers (FVDs) for the improvement of hysteretic framed r.c. structures under seismic excitations 基于延性需求谱的流体粘性阻尼器设计方法，用于改善地震作用下的滞回框架钢筋混凝土结构

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-02-26 DOI: 10.1016/j.probengmech.2026.103905

Anthea Amato, Liborio Cavaleri

Fluid viscous dampers (FVDs) have been widely used due to their capacity to generate dissipative forces (velocity dependent) that are not in phase with the displacements, namely able to exhibit their maximum forces when internal restoring forces are minimum. The possibility of increasing the damping ratio of a structure without significantly altering the inherent stiffness is another reason for the advantaging use of FVDs. For these characteristics, fluid viscous dampers are often preferred over other types of dampers. However, the lack of specific code prescriptions and simple but sufficiently reliable design procedures for structures exhibiting a non-linear plastic behavior is an issue not definitively faced. Deepening this issue could make the use of viscous dampers more diffused than it is. In this frame, here, a novel design procedure for non-linear FVDs to apply to hysteretic r.c. framed structures is proposed and discussed in terms of reliability in practical applications. The novelty of the procedure is that the scope of limiting the structural response is searched considering the contribution of external viscous damping, inherent viscous damping and hysteretic damping that the structure is able to exhibit. Therefore, the dimensioning of the external viscous dampers is carried out taking into account the rate of energy that the structure can dissipate by hysteretic damping differently from the most diffused approaches based on the maintaining of a structural elastic behavior. To this scope, the hypothesis of a simplified dynamic structural response is assumed to be coupled to the equivalent linearization of FVDs. The suitability of this hypothesis is discussed by a comparison between the obtainable results and the design targets in the case of structures that do not satisfy the assumed hypothesis. The results obtainable are analyzed in a statistical sense. Time history analyses of FVDs-equipped (and non) structural non-linear models are performed under appropriate families of base accelerograms. The design procedure is tested on benchmark models and on a case study in order to assess the degree of success of the proposed approach in connection to the assumed target objectives.

流体粘性阻尼器（FVDs）由于其产生与位移不一致的耗散力（速度相关）的能力而被广泛使用，即当内部恢复力最小时能够显示出最大的力。在不显著改变结构固有刚度的情况下增加结构阻尼比的可能性是fvd具有优势的另一个原因。由于这些特性，流体粘性阻尼器通常优于其他类型的阻尼器。然而，对于表现出非线性塑性行为的结构，缺乏具体的规范规定和简单但足够可靠的设计程序是一个没有明确面对的问题。加深这个问题可能会使粘性阻尼器的使用比它更广泛。在此框架下，本文提出了一种适用于迟滞钢筋混凝土框架结构的非线性fvd设计方法，并从实际应用的可靠性方面进行了讨论。该程序的新颖之处在于，考虑结构能够表现出的外部粘性阻尼、固有粘性阻尼和滞后阻尼的贡献，搜索限制结构响应的范围。因此，外部粘性阻尼器的尺寸计算考虑了结构通过滞回阻尼耗散的能量速率，这与基于保持结构弹性行为的最广泛的方法不同。在此范围内，简化的结构动力响应假设与fvd的等效线性化相耦合。在结构不满足假设的情况下，通过将可获得的结果与设计目标进行比较，讨论了该假设的适用性。从统计意义上分析所得的结果。在适当的基本加速度族下，对配备fvds的（和非）结构非线性模型进行了时程分析。设计过程在基准模型和案例研究中进行测试，以评估拟议方法与假设目标目标的成功程度。

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引用次数: 0

A probabilistic framework for predicting hysteresis loops of reinforced concrete columns with different failure modes and cross-section types 不同破坏模式和截面类型钢筋混凝土柱滞回线预测的概率框架

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2025-12-30 DOI: 10.1016/j.probengmech.2025.103889

Ying Ma , Zebin Wu , Dongsheng Wang , Chengqing Liu , Zhiguo Sun

This study develops a comprehensive probabilistic framework for predicting the hysteresis loops of reinforced concrete (RC) columns with different failure modes and cross-section types. A database of cyclic loading tests on 373 rectangular and spiral RC columns is compiled from the PEER-Structural Performance Database. The Bouc-Wen-Baber-Noori (BWBN) model is employed to describe the hysteretic behavior. The twelve BWBN model parameters are probabilistically identified for each specimen using a Bayesian parameter identification approach, yielding their full posterior distributions. Analysis of the identified posterior distributions reveals a systematic dependence of the BWBN parameters on the RC column's failure mode (flexure, flexural-shear, or shear failure) and cross-section type (rectangular or spiral), alongside a weak linear correlation with the RC column parameters. To address this complex nonlinear mapping, separate Bayesian Neural Network (BNN) models are trained for rectangular and spiral RC columns. The proposed probabilistic framework establishes an end-to-end predictive process: given RC column parameters, the BNN predicts the statistical distributions of the BWBN model parameters, which are then used to generate the hysteresis loop and its associated uncertainty bounds. The framework's accuracy is validated against experimental data, demonstrating high fidelity across different failure modes and cross-section types. The framework provides a robust tool for incorporating multifaceted uncertainties into the inelastic seismic analysis of RC columns.

本研究开发了一个综合概率框架，用于预测不同破坏模式和截面类型的钢筋混凝土柱的滞回线。从peer结构性能数据库中编制了373根矩形和螺旋RC柱的循环加载试验数据库。采用Bouc-Wen-Baber-Noori （BWBN）模型来描述滞回行为。使用贝叶斯参数识别方法对每个样本的12个BWBN模型参数进行概率识别，得到它们的完整后验分布。对确定的后验分布的分析表明，BWBN参数与RC柱的破坏模式（弯曲、弯剪或剪切破坏）和截面类型（矩形或螺旋形）有系统的相关性，同时与RC柱参数呈弱线性相关。为了解决这种复杂的非线性映射，分别训练了矩形和螺旋RC柱的贝叶斯神经网络（BNN）模型。提出的概率框架建立了一个端到端的预测过程：给定RC列参数，BNN预测BWBN模型参数的统计分布，然后用于生成滞后环及其相关的不确定性界限。根据实验数据验证了框架的准确性，证明了不同破坏模式和截面类型的高保真度。框架提供了一个强大的工具，将多方面的不确定性纳入RC柱的非弹性地震分析。

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引用次数: 0

Continuously nested moment quadrature for uncertainty quantification of black-box models 黑箱模型不确定性量化的连续嵌套矩正交

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2026-01-01 Epub Date: 2026-01-10 DOI: 10.1016/j.probengmech.2026.103892

Tianci Gong , Jingjing He , Xuefei Guan

This study presents a continuously nested moment quadrature method for uncertainty quantification of stochastic systems with arbitrary random input distributions. The method allows for continuous nesting and convergence testing simultaneously; therefore, existing model evaluation results can fully be reused to obtain a converged result at a minimum incremental computational demand. By incorporating a dynamic precision adjustment strategy and adopting criteria on the allowable number of negative weights, the proposed method overcomes the potential limitations of nesting only once under uniform distributions in the conventional Gauss-Kronrod formula, while achieving the highest possible algebraic precision in terms of polynomial degrees. The proposed method is applied to multiple classical and complex engineering and mathematical cases, including a computationally intensive 3D crack propagation problem. Results show that the proposed method requires less computational effort to achieve the same algebraic precision compared to the regular moment quadrature method and the Monte Carlo method. Notably, for problems with uniform random inputs, the computational demand can be reduced to one-fifth of that required by the regular moment quadrature method.

提出了一种连续嵌套矩正交法，用于任意随机输入分布的随机系统的不确定性量化。该方法允许同时进行连续嵌套和收敛性测试；因此，可以充分重用现有的模型评估结果，以最小的增量计算需求获得收敛的结果。该方法通过引入动态精度调整策略，采用允许负权数的准则，克服了传统高斯-克朗罗德公式在均匀分布下只能嵌套一次的局限性，同时实现了多项式度的最高代数精度。该方法适用于多个经典和复杂的工程和数学案例，包括计算量大的三维裂纹扩展问题。结果表明，与常规矩交法和蒙特卡罗法相比，该方法在达到相同代数精度的情况下，计算量更少。值得注意的是，对于均匀随机输入的问题，计算量可以减少到常规矩正交法的五分之一。

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引用次数: 0