基于主动学习Kriging模型的直立锁缝屋面系统抗风揭可靠度分析

直立锁缝屋面系统由于自重轻、柔性大,在强风作用下常发生风揭破坏。为减少风揭破坏的发生,进行直立锁缝屋面系统抗风揭可靠度分析极为必要。鉴于此,该文提出了基于主动学习Kriging模型的Monte Carlo法(AK-MCS)的直立锁缝屋面系统抗风揭可靠度分析方法。建立直立锁缝屋面系统力学模型以分析其破坏模式,并推导其失效准则对应的极限状态函数;结合AK-MCS法和推导的极限状态函数建立了直立锁缝屋面系统抗风揭可靠度分析方法;以典型实际工程的直立锁缝屋面系统为例进行了抗风揭可靠度分析。分析结果表明:该文方法兼顾精度与效率,与拉丁超立方抽样的Monte Carlo法(LHS-MCS)相比,其计算的可靠度指标的相对误差为3.74%,而计算成本仅为LHS-MCS法的25.1%;该文方法计算所得的直立锁缝屋面系统可靠度指标β=2.7703,相比规范要求的可靠度指标偏低,建议在支座与屋面板锁缝处采取相应的加强措施。     

自适应重要抽样方法的改进算法

失效概率的计算是结构可靠度分析的核心问题之一,发展精确高效的失效概率估计方法渐成国际学术与工程界关注的焦点。该文提出了一种基于样本概率密度加权的采样中心确定方法,该方法兼顾了以下2个目标：1) 增加有效抽样中对失效概率贡献大的样本出现的概率;2) 提高有效抽样比例。通过将该方法与基于主动引导技术的自适应抽样方法相集成,得到了一种改进的自适应重要抽样方法。理论分析与数值算例表明：该文提出的自适应重要抽样算法具有精度高、计算量小的优点。     

模糊可靠性灵敏度分析的线抽样方法

依据失效域具有模糊性时模糊失效概率的定义,提出了模糊可靠性灵敏度分析方法。推导了线性功能函数、独立正态基本变量和正态型隶属函数情况下,模糊可靠性灵敏度的解析表达式。给出了模糊可靠性灵敏度的Monte Carlo数字模拟方法,该方法结果在模拟次数趋于无穷时,收敛于真值,但效率较低,尤其是针对高维和小失效概率问题。为解决数字模拟法效率低的问题,提出了模糊可靠性灵敏度分析的线抽样方法。通过离散模糊失效概率积分区域,建立了模糊可靠性灵敏度与离散区域随机可靠性灵敏度的关系,进而利用随机可靠性灵敏度分析的线抽样方法求得模糊可靠性灵敏度。该方法的基本原理、计算公式及实现步骤被详细给出,适用于高维问题和小失效概率、精度高及收敛快等优点则由该文的算例进行验证。     

二维联合概率密度函数构造方法及结构并联系统可靠度分析

该文目的在于研究二维联合概率密度函数构造方法对结构系统可靠度的影响规律。首先简要介绍了2种构造联合分布函数的近似方法：基于Pearson相关系数的近似方法P和基于Spearman相关系数的近似方法S。提出了基于直接积分方法的并联系统失效概率计算方法。算例结果表明2种近似方法计算的系统失效概率误差取决于系统失效概率的大小、功能函数的形式以及功能函数间相关程度。系统失效概率越小,近似方法计算的系统失效概率误差越大。当系统失效概率小于10?3量级时,近似方法计算的系统失效概率误差较大,工程应用中应该引起足够的重视。功能函数间负相关时近似方法的误差明显大于功能函数间正相关时的误差。此外,系统失效概率误差并不是随着功能函数间相关性的增加而单调增加。     

考虑状态模糊性时广义失效概率计算的矩方法

针对失效状态和安全状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的矩方法。所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散化的积分区域中,极限状态函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为一般的随机可靠性问题,进而可以利用近似的矩方法求得广义失效概率。该文给出了所提方法的实现步骤和原理,算例结果表明所提方法对于中低维问题具有很高的精度和效率。     

基于区间与概率的星载网状天线展开可靠性分析

针对大型星载网状天线展开过程的特点,该文采用区间与概率混合可靠性分析方法对星载网状天线的展开过程可靠性进行了分析和评估。首先,建立了星载网状天线的展开失效树模型,并对失效树模型中各底事件进行了归类;其次,将关键底事件中所涉及到的不确定量视其特点描述为随机变量或区间变量,并利用混合可靠性模型分析方法获得了相应底事件的失效概率;再者,制作了2 m口径试验天线与典型试验展开机构样件,通过试验获得了天线展开过程中伸缩杆滑动的失效概率,进而得到了星载网状天线总的展开失效概率和展开可靠度;最后,对基本底事件进行了重要度分析,找出了可能导致星载网状天线展开失效的薄弱环节。     

基于失效概率积分和马尔可夫链模拟的可靠性灵敏度分析

可靠性灵敏度可以被表达为失效概率对基本随机变量分布参数的偏导数的形式,利用失效概率为基本变量的联合概率密度函数在失效域上的积分表达式,并且利用马尔可夫链能够高效模拟感兴趣区域样本的性质,一种针对单个失效模式和系统多个失效模式的可靠性灵敏度分析方法被提出。由于可靠性参数灵敏度可以表达为一个与联合概率密度函数相关的函数在失效域中的数学期望的形式,所提方法采用马尔可夫链来高效模拟失效域中的样本,进而采用样本均值替代总体均值的方法来得到可靠性灵敏度的估计值。与已有的基于Monte-Carlo模拟的可靠性灵敏度分析方法相比,所提方法在保证计算精度的基础上计算效率有显著提高,尤其是针对小失效概率的可靠性灵敏度分析问题。该算例充分说明了所提方法的合理可行性。     

工程结构可靠性分析的高阶矩法研究

提出了工程结构可靠性分析的高阶矩方法。主要是基于数值逼近原理，以切比雪夫正交函数族{Tk(x)}做基，利用功能函数的高阶矩信息，通过计算功能函数概率密度函数的逼近表达式，然后根据工程结构可靠性的一般表达式来计算结构的失效概率，进行可靠性分析。通过经典分布函数的数值检验和结构构件失效概率的计算结果比较，表明了该方法在理论上的正确性和工程中的实用性。     

基于代理模型的通风盘式制动器制动盘结构优化设计

该文提出一种基于代理模型的复杂结构优化设计方法,并用于通风盘式制动器制动盘结构优化设计。提出的优化设计方法集成了CAE分析、实验设计、代理模型构造及非线性优化几部分,实验设计采用拉丁超立方抽样策略,代理模型选用改进的响应面模型,非线性优化算法采用序列二次规划算法。为了解决传统的响应面模型部分预测值与实验值误差较大问题,改进方法认为只有能够确保在每一个抽样点处的预测值与试验值的相对误差均在一定范围内的响应面模型才是一个可行的模型。在保证制动盘质量不变情况下,以寿命最大化为目标,应用设计的集成优化方法对制动盘进行优化设计,优化设计结果较好,其中制动盘疲劳寿命根据Coffin-Manson方法预测,制动过程中制动盘表面最大热应力及最高温度通过热机耦合的有限元模拟紧急制动过程获得。优化结果表明该文提出的方法是一种有效的复杂结构的优化设计方法。     

基于AK-MCS法的主轴系统振动可靠性分析

采用集中质量法对数控车床主轴系统进行了简化,建立了考虑主轴刚度、阻尼、偏心质量和成组滚动轴承非线性接触力的十自由度非线性振动模型,使用Runge-Kutta数值积分法求得了主轴-轴承系统振动微分方程的数值解。考虑影响主轴振动的相关参数的随机性,以轴端轴心的振动幅值作为衡量主轴振动可靠性的指标,采用Kriging和Monte Carlo法相结合的方法(AK-MCS)计算了主轴振动可靠度。研究结果表明:采用AK-MCS算法与直接Monte Carlo法计算的失效概率几乎相等,而AK-MCS算法的运算效率明显更高,说明了该研究采用的AK-MCS算法的准确性与高效性,也验证了该方法适用于强非线性系统的可靠性计算。     

Structural reliability analysis under evidence theory using the active learning kriging model

Structural reliability analysis under evidence theory is investigated. It is rigorously proved that a surrogate model providing only correct sign prediction of the performance function can meet the accuracy requirement of evidence-theory-based reliability analysis. Accordingly, a method based on the active learning kriging model which only correctly predicts the sign of the performance function is proposed. Interval Monte Carlo simulation and a modified optimization method based on Karush–Kuhn–Tucker conditions are introduced to make the method more efficient in estimating the bounds of failure probability based on the kriging model. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.     

Uncertainty analysis of structural output with closed-form expression based on surrogate model

Uncertainty analysis (UA) is the process that quantitatively identifies and characterizes the output uncertainty and has a crucial implication in engineering applications. The research of efficient estimation of structural output moments in probability space plays an important part in the UA and has great engineering significance. Given this point, a new UA method based on the Kriging surrogate model related to closed-form expressions for the perception of the estimation of mean and variance is proposed in this paper. The new proposed method is proven effective because of its direct reflection on the prediction uncertainty of the output moments of metamodel to quantify the accuracy level. The estimation can be completed by directly using the redefined closed-form expressions of the model’s output mean and variance to avoid excess post-processing computational costs and errors. Furthermore, a novel framework of adaptive Kriging estimating mean (AKEM) is demonstrated for more efficiently reducing uncertainty in the estimation of output moment. In the adaptive strategy of AKEM, a new learning function based on the closed-form expression is proposed. Based on the closed-form expression which modifies the computational error caused by the metamodeling uncertainty, the proposed learning function enables the updating of metamodel to reduce prediction uncertainty efficiently and realize the decrease in computational costs. Several applications are introduced to prove the effectiveness and efficiency of the AKEM compared with a universal adaptive Kriging method. Through the good performance of AKEM, its potential in engineering applications can be spotted.     

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Various adaptive reliability analysis methods based on surrogate models have recently been developed. A multi-mode failure boundary exploration and exploitation framework (MFBEEF) was proposed for system reliability assessment using the adaptive kriging model based on sample space partitioning to reduce computational cost and use the characteristics of the failure boundary in multiple failure mode systems. The efficiency of the adaptive construction of kriging model can be improved by using the characteristics of the center sample of the small space to represent the characteristics of all samples in the small space. This method proposes a failure boundary exploration and exploitation strategy and a convergence criterion based on the maximum failure probability error for a system with multiple failure modes to adaptively approximate the failure boundary of a system with multiple failure modes. A multiple-failure-mode learning function was used to identify the optimal training sample to gradually update the kriging model during the failure boundary exploration and exploitation stages. In addition, a complex failure boundary-oriented adaptive hybrid importance sampling method was developed to improve the applicability of the MFBEEF method to small failure probability assessments. Finally, the MFBEEF method was proven to be effective using five system reliability analysis examples: a series system, a parallel system, a series–parallel hybrid system, a multi-dimensional series system with multiple failure modes, and an engineering problem with multiple implicit performance functions.     

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

This study considers an efficient method for the estimation of quantiles associated to very small levels of probability (up to O(10⁻⁹)), where the scalar performance function J is complex (eg, output of an expensive-to-run finite element model), under a probability measure that can be recast as a multivariate standard Gaussian law using an isoprobabilistic transformation. A surrogate-based approach (Gaussian Processes) combined with adaptive experimental designs allows to iteratively increase the accuracy of the surrogate while keeping the overall number of J evaluations low. Direct use of Monte-Carlo simulation even on the surrogate model being too expensive, the key idea consists in using an importance sampling method based on an isotropic-centered Gaussian with large standard deviation permitting a cheap estimation of small quantiles based on the surrogate model. Similar to AK-MCS as presented in the work of Schöbi et al., (2016), the surrogate is adaptively refined using a parallel infill criterion of an algorithm suitable for very small failure probability estimation. Additionally, a multi-quantile selection approach is developed, allowing to further exploit high-performance computing architectures. We illustrate the performances of the proposed method on several two to eight-dimensional cases. Accurate results are obtained with less than 100 evaluations of J on the considered benchmark cases.     

基于结构响应极值前四阶矩的桥墩抗震可靠度

为研究桥墩非线性地震响应下的抗震可靠度,引入随机函数-谱表示模型与高阶矩法,提出了基于结构响应极值前四阶矩的桥墩抗震可靠度分析方法。考虑三线型恢复力模型,建立了桥墩的单墩模型;利用随机函数-谱表示模型生成非平稳地震加速度时程样本并对桥墩进行非线性时程分析,在此基础上,建立了结构响应极值前四阶矩(均值,标准差,偏度和峰度)的计算框架;最后,考虑桥墩位移界限,给出了桥墩位移的功能函数,进而利用高阶矩法计算桥墩抗震可靠指标。通过对桥墩结构分析,验证了该方法的高效性与精确性;计算结果表明:与Monte Carlo模拟结果相比,该方法计算的前四阶矩、抗震可靠指标(失效概率)的最大相对误差分别为0.28%,1.92%(4.92%),该方法为桥墩抗震可靠度评估提供了一种有效的途径。     

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.     

基于FVM数值分析的海工混凝土结构耐久可靠度Monte Carlo模拟

为研究海工混凝土结构耐久性设计及寿命预测的可靠度方法,分析了耐久性设计与寿命预测的半理论、半经验解析模型方法,讨论了截面形状等条件对氯离子扩散传输的影响。该文研究应用有限体积法(FVM)分析求解混凝土中氯离子含量和蒙特卡罗(Monte Carlo)模拟求解耐久失效概率,分析海工混凝土结构耐久可靠度。这种方法可简称FVM-MC方法。在FVM-MC方法中,首先采用FVM方法求解混凝土中的氯离子含量,然后采用Monte Carlo方法对失效概率进行模拟求解。验证分析表明,FVM-MC方法分析模拟精度高,是海工混凝土结构可靠度分析的一种可靠方法。计算结果表明,截面形状等对混凝土结构的耐久可靠度具有显著的影响,采用Fick第二定律解析解的半理论、半经验模型,由于没有考虑截面形状效应,增加了矩形截面构件的耐久失效风险;圆形截面具有近似一维的扩散传输特点,在条件相同情况下,其构件耐久可靠度显著地高于方形或矩形截面的构件。     

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis. This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.     

A double-loop relevant vector machine-based system reliability analysis method with Meta-IS idea and active learning strategy

This paper proposes a double-loop relevant vector machine (RVM) model for system reliability analysis. To reduce the computational load, an adaptive RVM is constructed, which is built by minority initial samples and K-folds clustering. The candidate sample pool constructed by this rough adaptive RVM model improves the computational efficiency. Based on the idea of active learning, another adaptive RVM is established. By combining two adaptive RVMs, the proposed model has the advantages of both active learning and importance sampling, which is called DLRVM. In this model, the failure probability is expressed as a product of the augmented failure probability and the correction factor. From the characteristics of RVM, this model under the Bayesian framework has significant generalization ability which avoids the limitations of many machine learning models. The accuracy and high efficiency are verified via four academic examples and an implicit engineering problem. The results also indicate that RVM is appropriate for system reliability analysis.