Structural Safety最新文献_第9页

Reliability analysis for data-driven noisy models using active learning 基于主动学习的数据驱动噪声模型可靠性分析

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-26 DOI: 10.1016/j.strusafe.2024.102543

Anderson V. Pires, Maliki Moustapha, Stefano Marelli, Bruno Sudret

Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these simulations have been considered deterministic, i.e. running them multiple times for a given set of input parameters always produces the same output. However, this assumption does not always hold, as many studies in the literature report non-deterministic computational simulations (also known as noisy models). In such cases, running the simulations multiple times with the same input will result in different outputs. Similarly, data-driven models that rely on real-world data may also be affected by noise. This characteristic poses a challenge when performing reliability analysis, as many classical methods, such as FORM and SORM, are tailored to deterministic models. To bridge this gap, this paper provides a novel methodology to perform reliability analysis on models contaminated by noise. In such cases, noise introduces latent uncertainty into the reliability estimator, leading to an incorrect estimation of the real underlying reliability index, even when using Monte Carlo simulation. To overcome this challenge, we propose the use of denoising regression-based surrogate models within an active learning reliability analysis framework. Specifically, we combine Gaussian process regression with a noise-aware learning function to efficiently estimate the probability of failure of the underlying noise-free model. We showcase the effectiveness of this methodology on standard benchmark functions and a finite element model of a realistic structural frame.

可靠性分析的目的是估计工程系统的失效概率。它通常需要多次运行一个极限状态函数，这通常依赖于计算密集型的模拟。传统上，这些模拟被认为是确定性的，即对于给定的一组输入参数多次运行它们总是产生相同的输出。然而，这一假设并不总是成立，因为文献中的许多研究报告了非确定性计算模拟（也称为噪声模型）。在这种情况下，使用相同的输入多次运行模拟将导致不同的输出。同样，依赖于真实世界数据的数据驱动模型也可能受到噪声的影响。这一特性在执行可靠性分析时提出了挑战，因为许多经典方法（如FORM和SORM）都是针对确定性模型量身定制的。为了弥补这一差距，本文提供了一种新的方法来对受噪声污染的模型进行可靠性分析。在这种情况下，噪声将潜在的不确定性引入可靠性估计器，导致对真实潜在可靠性指标的不正确估计，即使使用蒙特卡罗模拟也是如此。为了克服这一挑战，我们建议在主动学习可靠性分析框架中使用基于去噪回归的代理模型。具体来说，我们将高斯过程回归与噪声感知学习函数相结合，以有效地估计底层无噪声模型的失效概率。我们展示了这种方法在标准基准函数和现实结构框架的有限元模型上的有效性。

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引用次数: 0

An Adaptive Gaussian Mixture Model for structural reliability analysis using convolution search technique 利用卷积搜索技术进行结构可靠性分析的自适应高斯混合模型

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Structural Safety

Pub Date : 2024-11-24 DOI: 10.1016/j.strusafe.2024.102548

Futai Zhang , Jun Xu , Zhiqiang Wan

Non-parametric probability density estimation has gained popularity due to its flexibility and ease of use without requiring prior assumptions about distribution types. Notable examples include Kernel Density Estimation, Gaussian Mixture Model (GMM), the Mellin transform, and the Generalized Distribution Reconstruction (GDR) method, etc. However, these methods can encounter issues such as tail oscillation and sensitivity to initial guesses, particularly in the context of structural reliability analysis. To improve accuracy, this paper proposes an Adaptive Gaussian Mixture Model method. This method uses the inverse Fourier relationship between the Characteristic Function (CF) and the Probability Density Function (PDF), combined with a convolution search technique for parameter estimation. First, a more accurate expression for the CF is introduced, where the undetermined parameters are specified based on the numerically estimated CF curve. Then, a convolution search domain is developed to determine these parameters, including weight coefficients, mean domain, and standard deviation domain. Compared to the conventional methods for parameter estimation, the proposed convolution search technique can effectively avoid the problems of overfitting and initial parameter sensitivity. Using these parameters, the PDF is reconstructed and evolves into an Adaptive Gaussian Mixture Model. Numerical investigations are conducted to validate the efficacy of the proposed method, with comparisons made to the Mellin transform, GDR, Classic GMM, and other parametric methods.

非参数概率密度估计因其灵活性和易用性，无需事先假设分布类型而广受欢迎。著名的例子包括核密度估计、高斯混杂模型（GMM）、梅林变换和广义分布重构（GDR）方法等。然而，这些方法可能会遇到尾部振荡和对初始猜测敏感等问题，特别是在结构可靠性分析中。为了提高准确性，本文提出了一种自适应高斯混合模型方法。该方法利用特征函数（CF）和概率密度函数（PDF）之间的反傅里叶关系，结合卷积搜索技术进行参数估计。首先，引入更精确的 CF 表达式，根据数值估计的 CF 曲线指定未确定的参数。然后，开发了一个卷积搜索域来确定这些参数，包括权系数、均值域和标准偏差域。与传统的参数估计方法相比，所提出的卷积搜索技术能有效避免过拟合和初始参数敏感性的问题。利用这些参数，PDF 将被重建并演化为自适应高斯混合模型。通过与梅林变换、GDR、经典 GMM 及其他参数方法的比较，我们进行了数值研究以验证所提方法的有效性。

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引用次数: 0

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