Structural Safety最新文献_第9页

The generalized first-passage probability considering temporal correlation and its application in dynamic reliability analysis 考虑时间相关性的广义首通概率及其在动态可靠度分析中的应用

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-22 DOI: 10.1016/j.strusafe.2024.102547

Xian-Lin Yang , Ming-Ming Jia , Da-Gang Lu

In the traditional up-crossing rate approaches, the absence of consideration for correlation among crossing events often results in significant inaccuracies, particularly in scenarios involving stochastic processes with high autocorrelation and low thresholds. To fundamentally address these issues and limitations, the probability density function of the first passage time represented by the high-dimensional joint probability density function was investigated, and the equiprobable joint Gaussian (E-PHIn) method is proposed to prevent the redundant counting of the same crossing event. The innovation of the developed method is that it accounts for the correlation among different time instances of the stochastic process and allows for direct integration to derive the first-passage probabilities. When dealing with stochastic processes with unknown marginal distributions, the method of moments was introduced, complementing the E-PHIn method. Meanwhile, corresponding dimensionality reduction strategies are offered to improve computational efficiency. Through theoretical analysis and case studies, the results indicate that the conditional up-crossing rate represents the probability density function of the first-passage time. The E-PHIn method effectively addresses the first-passage problem for stochastic processes with either known or unknown marginal probability density functions. It fills the gap in traditional up-crossing rate approaches within the domain of nonlinear dynamic reliability. For the example structures, the E-PHIn method demonstrates higher accuracy compared to traditional point-based PDEM. Compared to MCS, the E-PHIn method significantly improves analytical efficiency while maintaining high precision for low-probability failure events.

在传统的上交叉率方法中，没有考虑交叉事件之间的相关性往往会导致显著的不准确性，特别是在涉及高自相关性和低阈值的随机过程的情况下。为了从根本上解决这些问题和局限性，研究了由高维联合概率密度函数表示的首次通过时间的概率密度函数，并提出了等概率联合高斯（E-PHIn）方法来防止同一交叉事件的重复计数。该方法的创新之处在于，它考虑了随机过程的不同时间实例之间的相关性，并允许直接积分来推导首次通过的概率。在处理边缘分布未知的随机过程时，引入矩量法作为E-PHIn方法的补充。同时，提出了相应的降维策略以提高计算效率。理论分析和实例分析表明，条件上交率是首次通过时间的概率密度函数。E-PHIn方法有效地解决了具有已知或未知边际概率密度函数的随机过程的首次通过问题。它填补了非线性动态可靠度领域中传统上交率方法的空白。对于实例结构，与传统的基于点的PDEM相比，E-PHIn方法具有更高的精度。与MCS相比，E-PHIn方法显著提高了分析效率，同时在低概率故障事件中保持了高精度。

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引用次数: 0

A novel deterministic sampling approach for the reliability analysis of high-dimensional structures 用于高维结构可靠性分析的新型确定性抽样方法

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-20 DOI: 10.1016/j.strusafe.2024.102545

Yang Zhang , Jun Xu , Enrico Zio

Overcoming the “curse of dimensionality” in high-dimensional reliability analysis is still an enduring challenge. This paper proposes an innovative deterministic sampling method designed to overcome this challenge. The approach starts with a two-dimensional uniform point set, generated using the good lattice point method. This set is then refined through the cutting method to produce a specific number of points. A novel generating vector is computed based on this method, enabling the generation of the targeted high-dimensional point set through a strategic dimension-by-dimension mapping. Notably, this method eliminates the need for complex congruence computation and primitive root optimization, enhancing its efficiency for high-dimensional sampling. The resulting point set is deterministic and uniform, greatly reducing variability in reliability analysis. Then, the proposed approach is integrated into the fractional exponential moment-based maximum entropy method with the Box–Cox transform. This integration efficiently recovers the probability distribution for the limit state function (LSF) with high-dimensional inputs, enabling precise assessment of the failure probability. The efficacy of the proposed method is demonstrated through three high-dimensional numerical examples, involving both explicit and implicit LSFs, highlighting its applicability for high-dimensional reliability analysis of structures.

克服高维度可靠性分析中的 "维度诅咒 "仍然是一项持久的挑战。本文提出了一种创新的确定性抽样方法，旨在克服这一难题。该方法以二维均匀点集为起点，该点集是利用良好网格点法生成的。然后通过切割法对该集合进行细化，以产生特定数量的点。在此基础上计算出一个新颖的生成向量，通过策略性的逐维映射生成目标高维点集。值得注意的是，这种方法无需复杂的全等计算和原始根优化，提高了高维采样的效率。所得到的点集具有确定性和均匀性，大大降低了可靠性分析中的变异性。然后，利用 Box-Cox 变换将所提出的方法集成到基于分数指数矩的最大熵方法中。这种集成能有效地恢复具有高维输入的极限状态函数（LSF）的概率分布，从而实现对故障概率的精确评估。通过三个涉及显式和隐式 LSF 的高维数值示例，证明了所提方法的有效性，突出了其在结构高维可靠性分析中的适用性。

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引用次数: 0

A stratified beta-sphere sampling method combined with important sampling and active learning for rare event analysis 用于罕见事件分析的分层贝塔球取样法与重要取样和主动学习相结合

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-20 DOI: 10.1016/j.strusafe.2024.102546

Fangqi Hong , Jingwen Song , Pengfei Wei , Ziteng Huang , Michael Beer

Accurate and efficient estimation of small failure probability subjected to high-dimensional and multiple failure domains is still a challenging task in structural reliability engineering. In this paper, we propose a stratified beta-spheres sampling method (SBSS) to tackle this task. Initially, the whole support space of random input variables is divided into a series of subdomains by using multiple specified beta-spheres, which is a hypersphere centered in the origin in standard normal space, then, the corresponding samples truncated by beta-spheres are generated explicitly and efficiently. Based on the truncated samples, the real failure probability can be estimated by the sum of failure probabilities of these subdomains. Next, we discuss and demonstrate the unbiasedness of the estimation of failure probability. The proposed method stands out for inheriting the advantages of Monte Carlo simulation (MCS) for highly nonlinear, high-dimensional problems, and problems with multiple failure domains, while overcoming the disadvantages of MCS for rare event. Furthermore, the SBSS method equipped with importance sampling technique (SBSS-IS) is also proposed to improve the robustness of estimation. Additionally, we combine the proposed SBSS and SBSS-IS methods with GPR model and active learning strategy so as to further substantially reduce the computational cost under the desired requirement of estimated accuracy. Finally, the superiorities of the proposed methods are demonstrated by six examples with different problem settings.

在结构可靠性工程中，准确有效地估计高维和多失效域的小失效概率仍然是一项具有挑战性的任务。本文提出了一种分层 beta 球体抽样方法（SBSS）来解决这一问题。首先，使用多个指定的贝塔球将随机输入变量的整个支持空间划分为一系列子域。根据截断样本，可以通过这些子域的失效概率之和估算出真正的失效概率。接下来，我们讨论并证明了失效概率估计的无偏性。所提出的方法继承了蒙特卡洛模拟（MCS）在处理高度非线性、高维问题和多失效域问题时的优点，同时克服了蒙特卡洛模拟在处理罕见事件时的缺点。此外，我们还提出了配备重要性抽样技术的 SBSS 方法（SBSS-IS），以提高估计的鲁棒性。此外，我们还将所提出的 SBSS 和 SBSS-IS 方法与 GPR 模型和主动学习策略相结合，从而在保证估计精度的前提下进一步大幅降低计算成本。最后，我们通过六个不同问题设置的实例证明了所提方法的优越性。

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引用次数: 0

An augmented integral method for probability distribution evaluation of performance functions 性能函数概率分布评估的增强积分法

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-06 DOI: 10.1016/j.strusafe.2024.102544

Yan-Gang Zhao, Chang-Xing Zou, Xuan-Yi Zhang, Ye-Yao Weng

The paper proposes an efficient augmented integral method for probability distribution evaluation of performance functions. In the proposed method, the performance function is augmented by adding an auxiliary random variable, whose probability density function (PDF) and cumulative distribution function (CDF) are formulated as the integrations of the original performance function with respect to basic random variables. The optimal auxiliary random variable is determined to provide an accurate estimation of the integrations by investigating the geometric properties of integrands and a distribution parameter optimization approach based on moment analysis. According to the convolution formula, the relationship between the PDFs of the augmented performance function and the original performance function is clarified. Then, the PDF of the original performance function is calculated by solving an unconstrained optimization problem that is established using the convolution formula. Finally, four numerical examples are investigated to demonstrate the efficiency and accuracy of the proposed method for structural reliability analysis. The results indicate that the proposed method can evaluate the probability distribution of performance functions accurately and efficiently, even when the performance functions are strongly nonlinear and implicit.

本文针对性能函数的概率分布评估提出了一种高效的增强积分法。在所提出的方法中，通过添加辅助随机变量来增强性能函数，其概率密度函数（PDF）和累积分布函数（CDF）被表述为原始性能函数相对于基本随机变量的积分。通过研究积分的几何特性和基于矩分析的分布参数优化方法，确定了最佳辅助随机变量，以提供对积分的精确估计。根据卷积公式，明确了增强性能函数和原始性能函数的 PDF 之间的关系。然后，通过解决利用卷积公式建立的无约束优化问题，计算出原始性能函数的 PDF。最后，研究了四个数值实例，以证明所提方法在结构可靠性分析中的效率和准确性。结果表明，即使性能函数是强非线性和隐式的，所提出的方法也能准确有效地评估性能函数的概率分布。

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引用次数: 0

Preface of the special issue: The Joint Committee of Structural Safety: past, present and a perspective on the future 特刊前言：结构安全联合委员会：过去，现在和对未来的展望

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-10-23 DOI: 10.1016/j.strusafe.2024.102542

Jochen Köhler, Ton Vrouwenvelder, Michael Havbro Faber (President, and Past Presidents of the Joint Committee on Structural Safety), Maria Pina Limongelli (JCSS Reporter and Executive Guest Editor of the Special Issue)

引用次数: 0

Bivariate cubic normal distribution for non-Gaussian problems 非高斯问题的二元三次正态分布

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-10-16 DOI: 10.1016/j.strusafe.2024.102541

Xiang-Wei Li, Xuan-Yi Zhang, Yan-Gang Zhao

Probabilistic models play critical role in various engineering fields. Numerous critical issues exist in probabilistic modeling, especially for non-Gaussian correlated random variables. Traditional parameter-based bivariate distribution models are typically developed for specific types of random variables, which limits their flexibility and applicability. In this study, a flexible bivariate distribution model is proposed, in which the joint cumulative distribution function (JCDF) is derived by expressing the probability as the summation of three basic probabilities corresponding to simple functions. These probabilities are computed using a univariate cubic normal distribution, and thus the proposed model is named as bivariate cubic normal (BCN) distribution. The proposed BCN distribution has been applied in modeling several common bivariate distributions and actual engineering datasets. Results show that the BCN distribution accurately fits the JCDFs of both theoretical distributions and practical datasets, offering significant improvement over existing models. Furthermore, the proposed BCN distribution is utilized in seismic reliability assessment and the calculation of the mean recurrence interval and hazard curve of hurricane wind speed and storm size. Results demonstrate that the BCN distribution excels in modeling and matching capabilities, proving its accuracy and effectiveness in civil engineering applications.

概率模型在各个工程领域发挥着至关重要的作用。概率建模中存在许多关键问题，尤其是非高斯相关随机变量。传统的基于参数的双变量分布模型通常是针对特定类型的随机变量开发的，这限制了其灵活性和适用性。本研究提出了一种灵活的双变量分布模型，其中联合累积分布函数（JCDF）是通过将概率表示为对应于简单函数的三个基本概率的求和而得出的。这些概率使用单变量立方正态分布计算，因此所提出的模型被命名为双变量立方正态分布（BCN）。所提出的 BCN 分布已被应用于几种常见的二元分布和实际工程数据集的建模。结果表明，BCN 分布能准确拟合理论分布和实际数据集的 JCDF，与现有模型相比有显著改进。此外，所提出的 BCN 分布还被用于地震可靠性评估，以及飓风风速和风暴规模的平均重现间隔和危害曲线的计算。结果表明，BCN 分布在建模和匹配能力方面表现出色，证明了其在土木工程应用中的准确性和有效性。

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引用次数: 0

The JCSS probabilistic model Code, future developments JCSS概率模型代码，未来发展

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-10-06 DOI: 10.1016/j.strusafe.2024.102540

R.D.J.M. Steenbergen , A.C.W.M. Vrouwenvelder

To assess and verify the reliability of structures, reliability based building codes allow for the application of full-probabilistic methods and semi-probabilistic methods (i.e. the partial factor method). In principle, both methods should be equivalent and lead to (approximately) the same reliability level. Therefore partial factors should be as much as possible determined based on a probabilistic background and calibration exercises. On the other hand, as the probabilistic design method may be considered as more rational and consistent than the partial factor design, there is a tendency to use probabilistic methods directly in the assessment of special of important new structures and also in the assessment of existing structures. In both the calibration exercise and in the full probabilistic assessment of structures, we face the problem that many assumptions have to be made. In particular in regard to the statistical modelling of random variables and in regard to accepted approximative methods of calculation. This often brings the engineer to a challenging position. In the past years the JCSS probabilistic model code (PMC) has served as an often-consulted operational code for this purpose. In the present paper, the JCSS PMC and its future developments are presented and discussed.

为了评估和验证结构的可靠性，基于可靠性的建筑规范允许应用全概率方法和半概率方法（即部分因子方法）。原则上，这两种方法应该是等效的，并且产生（近似）相同的可靠性水平。因此，部分因素应尽可能根据概率背景和校准练习来确定。另一方面，由于概率设计方法比部分因子设计方法更为合理和一致，因此在特殊的重要新结构的评估和既有结构的评估中，有直接使用概率方法的趋势。在校正工作和对结构进行全面概率评估时，我们面临的问题是必须作出许多假设。特别是关于随机变量的统计建模和关于可接受的近似计算方法。这通常会把工程师带到一个具有挑战性的位置。在过去的几年中，JCSS概率模型代码（PMC）一直是为此目的经常参考的操作代码。本文对JCSS PMC及其未来发展进行了介绍和讨论。

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引用次数: 0

Yet another Bayesian active learning reliability analysis method 另一种贝叶斯主动学习可靠性分析方法

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-09-20 DOI: 10.1016/j.strusafe.2024.102539

Chao Dang , Tong Zhou , Marcos A. Valdebenito , Matthias G.R. Faes

The well-established Bayesian failure probability inference (BFPI) framework offers a solid foundation for developing new Bayesian active learning reliability analysis methods. However, there remains an open question regarding how to effectively leverage the posterior statistics of the failure probability to design the two key components for Bayesian active learning: the stopping criterion and learning function. In this study, we present another innovative Bayesian active learning reliability analysis method, called ‘Weakly Bayesian Active Learning Quadrature’ (WBALQ), which builds upon the BFPI framework to evaluate extremely small failure probabilities. Instead of relying on the posterior variance, we propose a more computationally feasible measure of the epistemic uncertainty in the failure probability by examining its posterior first absolute central moment. Based on this measure and the posterior mean of the failure probability, a new stopping criterion is devised. A recently developed numerical integrator is then employed to approximate the two analytically intractable terms inherent in the stopping criterion. Furthermore, a new learning function is proposed, which is partly derived from the epistemic uncertainty measure. The performance of the proposed method is demonstrated by five numerical examples. It is found that our method is able to assess extremely small failure probabilities with satisfactory accuracy and efficiency.

成熟的贝叶斯故障概率推理（BFPI）框架为开发新的贝叶斯主动学习可靠性分析方法奠定了坚实的基础。然而，如何有效利用失效概率的后验统计来设计贝叶斯主动学习的两个关键组成部分：停止准则和学习函数，仍然是一个未决问题。在本研究中，我们提出了另一种创新的贝叶斯主动学习可靠性分析方法，称为 "弱贝叶斯主动学习正交"（WBALQ），它以 BFPI 框架为基础，用于评估极小的故障概率。与依赖后验方差相比，我们提出了一种计算上更可行的方法，即通过检验故障概率的后验第一绝对中心矩来衡量故障概率的认识不确定性。根据这一指标和失败概率的后验均值，我们设计了一种新的停止准则。然后采用最近开发的数值积分器来近似停止准则中固有的两个难以分析的项。此外，还提出了一种新的学习函数，该函数部分来源于认识不确定性度量。我们通过五个数值示例展示了所提方法的性能。结果发现，我们的方法能够以令人满意的精度和效率评估极小的故障概率。

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引用次数: 0

Improved Bayesian model updating of geomaterial parameters for slope reliability assessment considering spatial variability 考虑空间变异性，改进用于斜坡可靠性评估的土工材料参数贝叶斯模型更新

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-09-14 DOI: 10.1016/j.strusafe.2024.102536

Shui-Hua Jiang , Hong-Peng Hu , Ze Zhou Wang

In engineering practice, Bayesian model updating using field data is often conducted to reduce the substantial inherent epistemic uncertainties in geomaterial properties resulting from complex geological processes. The Bayesian Updating with Subset simulation (BUS) method is commonly employed for this purpose. However, the wealth of field data available for engineers to interpret can lead to challenges associated with the “curse of dimensionality”. Specifically, the value of the likelihood function in the BUS method can become extremely small as the volume of field data increases, potentially falling below the accuracy threshold of computer floating-point operations. This undermines both the computational efficiency and accuracy of Bayesian model updating. To effectively address this technical challenge, this paper proposes an improved BUS method developed based on parallel system reliability analysis. Leveraging the Cholesky decomposition-based midpoint method, the total failure domain in the original BUS method, which involves a low acceptance rate, is subdivided into several sub-failure domains with a high acceptance rate. Facilitated with an improved Metropolis-Hastings algorithm, the improved BUS method enables the consideration of a large volume of field data and spatial variability of geomaterial properties in the probabilistic back analysis. The results of an illustrative soil slope, involving spatially variable undrained shear strength, demonstrate that the improved BUS method is effective in simultaneously incorporating a substantial volume of field measurements and observations in the model updating process. Through a comparison with the original BUS method, the improved BUS method is shown to be useful for Bayesian model updating of high-dimensional spatially variable geomaterial properties and slope reliability assessment.

在工程实践中，经常使用现场数据对贝叶斯模型进行更新，以减少复杂地质过程导致的地质材料属性中固有的大量认识不确定性。为此，通常采用子集模拟贝叶斯更新法（BUS）。然而，可供工程师解释的大量野外数据可能会带来与 "维度诅咒 "相关的挑战。具体来说，随着现场数据量的增加，BUS 方法中的似然函数值会变得非常小，有可能低于计算机浮点运算的精度阈值。这既影响了贝叶斯模型更新的计算效率，也影响了其准确性。为有效应对这一技术挑战，本文提出了一种基于并行系统可靠性分析的改进型 BUS 方法。利用基于 Cholesky 分解的中点法，将原 BUS 方法中接受率较低的总故障域细分为几个接受率较高的子故障域。在改进的 Metropolis-Hastings 算法的帮助下，改进的 BUS 方法能够在概率回溯分析中考虑大量的现场数据和土工材料特性的空间变化。一个涉及空间可变排水抗剪强度的示例土坡的结果表明，改进的 BUS 方法能有效地同时将大量实地测量和观测数据纳入模型更新过程。通过与原始 BUS 方法的比较，证明改进的 BUS 方法适用于高维空间可变土工材料属性的贝叶斯模型更新和边坡可靠性评估。

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引用次数: 0

Data-enhanced design charts for efficient reliability-based design of geotechnical systems 数据增强型设计图表，用于基于可靠性的岩土系统高效设计

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-09-10 DOI: 10.1016/j.strusafe.2024.102527

M.K. Lo, Y.F. Leung, M.X. Wang

This paper proposes a new design chart approach for reliability assessment, which enables clear visualization of the representative soil shear strength parameters under various reliability levels and effective stress levels. Utilizing the design charts, reliability assessment or reliability-based design can be performed with significantly reduced numbers of evaluations of the geotechnical system response. The design charts are established solely based on the probability distributions of soil parameters, and are applicable to a variety of geotechnical problems involving the same soil type. For practical illustration of the proposed approach, design charts are produced from the shear strength databases of saprolitic soils and colluvial soils in Hong Kong, and then applied to the reliability-based design of a slope with soil nail reinforcements. The ensuing design solutions require much fewer soil nails compared to the conventional design practice, while also achieving a better system reliability. The same charts are then applied to the reliability-based design of a retaining wall, where a series of design options are identified with equivalent reliability index against overturning failure and pullout failure. Through the proposed approach, the use of design charts promotes efficient reliability-based design of geotechnical systems with rational incorporation of reliability concepts.

本文提出了一种新的可靠性评估设计图表方法，可清晰显示不同可靠性水平和有效应力水平下的代表性土体抗剪强度参数。利用设计图表，可以进行可靠性评估或基于可靠性的设计，大大减少对岩土系统响应的评估次数。设计图表的建立完全基于土体参数的概率分布，适用于涉及相同土体类型的各种岩土工程问题。为实际说明所建议的方法，我们根据香港的边坡土和冲积土的抗剪强度数据库制作了设计图表，然后将其应用于带土钉加固的基于可靠性的斜坡设计。与传统设计方法相比，设计方案所需的土钉数量要少得多，同时还能获得更好的系统可靠性。然后，同样的图表被应用于挡土墙的可靠性设计，确定了一系列针对倾覆破坏和拉拔破坏具有同等可靠性指数的设计方案。通过所提出的方法，设计图表的使用促进了岩土系统基于可靠性的高效设计，并合理地融入了可靠性概念。

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引用次数: 0