Bootstrap与变权重相结合的多模型综合预测方法

为了更好地估计构件的疲劳寿命,一种较好的策略是将几个合适模型进行合并预测,但传统合并预测的权重值为确定值,随着对预测精度要求的提高,变权重模型合并预测方法逐渐受到重视。但在工程中仅估计出预测结果还不足以提供充分的决策信息,进一步得到置信区间显得很有必要。本文提出一种基于Bootstrap与变权重的多模型综合置信区间预测方法,运用Bootstrap对合并数据进行再抽样,依据再抽样样本,采用变权重合并方法得到各项模型的权重函数,将各预测模型合并起来,最后通过百分位数法预测得到预测置信区间。将该方法用于工程算例中进行了验证,说明本文方法的合理性和可行性。国家自然科学基金项目(U1530122,51505398);;航空科学基金项目(20150968003);;中央高校基本科研业务费专项资金项目(XMU,20720180072)资

飞机结构疲劳可靠度贝叶斯组合预测

在实际工程中,常常需要利用模型去描述和分析问题。然而模型亦存在不确定性,即可能存在多个描述同一现象的模型,例如多个疲劳分析的模型。针对飞机结构的疲劳可靠性问题,提出在考虑三种裂纹扩展模型下基于贝叶斯公式的疲劳可靠度组合预测方法。针对不同应力水平下飞机结构试件的裂纹扩展数据建立了三种随机裂纹扩展模型;在考虑模型参数不确定性条件下,采用贝叶斯模型平均方法对三种模型进行组合;基于组合模型分析结构的可靠度。所提方法在分析飞机结构疲劳可靠度上,采用了组合模型,能够最大限度保障结果的稳定性。此外,考虑了模型参数的不确定性,能够得到更为合理的裂纹扩展预测分布和可靠度预测值。给出的实例及分析结果表明所提方法可行。国家自然科学基金资助项目(U1530122,51505398);;中央高校基本科研业务费专项资金资助项目(20720180072

结构可靠性优化求解的解耦融合策略

在工程结构的可靠性优化过程中,求解的效率和精度是优化方法的关键。该文提出一种针对解耦优化的融合策略。所提方法在优化迭代解耦所用的失效概率函数为前几次迭代设计点构建的局部失效概率函数的加权融合形式。在对原可靠性优化问题进行解耦后,结合序列近似优化方法进行迭代求解。相比于常规的仅使用当次局部建立的失效概率函数而言,所提融合策略最大限度利用了各次迭代中产生的信息用于优化解耦求解,能够提高失效概率函数的近似精度,从而间接达到减少迭代次数和计算量的目的。最后给出了屋架和十杆结构的可靠性优化算例,验证该文方法的正确性和可行性。国家自然科学基金委员会-中国工程物理研究院NSAF联合基金项目(U1530122);;国家自然科学基金青年科学基金项目(51505398

Local estimation of failure probability function by weighted approach

Research Grants Council of the Hong Kong Special Administrative Region [9041550, CityU 110210]; National Natural Science Foundation of China [51105309]In the reliability-based design of engineering systems, it is often required to evaluate the failure probability for different values of distribution parameters involved in the specification of design configuration. The failure probability as a function of the distribution parameters is referred as the 'failure probability function (FPF)' in this work. From first principles, this problem requires repeated reliability analyses to estimate the failure probability for different distribution parameter values, which is a computationally expensive task. A "weighted approach" is proposed in this work to locally evaluate the FPF efficiently by means of a single simulation. The basic idea is to rewrite the failure probability estimate for a given set of random samples in simulation as a function of the distribution parameters. It is shown that the FPF can be written as a weighted sum of sample values. The latter must be evaluated by system analysis (the most time-consuming task) but they do not depend on the distribution. Direct Monte Carlo simulation, importance sampling and Subset Simulation are incorporated under the proposed approach. Examples are given to illustrate their application. (C) 2013 Elsevier Ltd. All rights reserved

A decoupling method of reliability optimization based on sensitivity

针对航空结构可靠性优化设计问题,提出了一种基于灵敏度的可靠性优化(rbO)解耦方法。首先将高效求解的可靠性灵敏度用于失效概率函数(fPf)的快速构建,其优点在于仅需要一次可靠性分析即可得到失效概率函数的局部近似,克服了常规求解方法中需要多次可靠性分析的缺点;然后将得出的fPf近似代入rbO模型中,将原问题解耦成确定性优化子问题,可用常规优化方法来求解。另外,采用了序列近似优化策略来保证可靠性优化解的正确性。文中给出了复合材料梁和机翼三盒段结构的优化求解算例来说明本文方法的可行性和正确性。A decoupling method based on reliability sensitivity is proposed for the reliability-based optimization(RBO)design of aeronautic structure.It utilizes reliability sensitivity to construct the explicit approximation of the failure probability function(FPF)with respect to design variables quickly,thus its advantage is that it only needs one reliability analysis and repeated reliability analyses can be avoided.After the approximation of the FPF is established,the target RBO problem can be transformed into a deterministic one which can be solved by conventional optimization strategies.Meanwhile,a sequential approximate optimization framework is adopted to guarantee the accuracy of the solution.Examples of composite beam and three-box simulated flap structure are given to demonstrate the feasibility and validity of the proposed optimization method.国家自然科学基金(51105309)~

Efficient approach for reliability-based optimization based on weighted importance sampling approach

An efficient methodology is presented to perform the reliability-based optimization (RBO). It is based on an efficient weighted approach for constructing an approximation of the failure probability as an explicit function of the design variables which is referred to as the 'failure probability function (FPF)'. It expresses the FPF as a weighted sum of sample values obtained in the simulation-based reliability analysis. The required computational effort for decoupling in each iteration is just single reliability analysis. After the approximation of the FPF is established, the target RBO problem can be decoupled into a deterministic one. Meanwhile, the proposed weighted approach is combined with a decoupling approach and a sequential approximate optimization framework. Engineering examples are given to demonstrate the efficiency and accuracy of the presented methodology. ? 2014 Elsevier Ltd. All rights reserved

Model Updating and Validation for Bearing-Rotor System at Working Speed Considering Model-Form Error

研究考虑模型形式误差的轴承-转子系统工作转速下的动力学模型修正和确认方法.首先,介绍了模型形式误差以及基于复模态特征值灵敏度的模型修正理论;然后; ,在此基础上以轴承-柔性转子系统为仿真算例,考虑模型形式误差,使用系统在恒定工作转速下的涡动频率和阻尼参数,同时对轴承的支承刚度、支承阻尼和转盘; 的直径转动惯量参数进行修正;最后,通过不平衡响应结果对修正模型进行了确认.仿真结果显示,考虑模型形式误差时的修正参数最大误差仍有-10.1%,而; 修正后特征值实部最大误差为0.95%,特征值虚部最大误差为-1.15%,修正后不平衡响应与目标模型基本重合.研究表明,考虑模型形式误差时轴承-转; 子系统的修正方法是稳健的,也是有效可行的.Structure dynamical model updating and validation for bearing-rotor; system at working speed considering model-form error is presented. The; theory of model-form error, model updating based on complex eigenvalue; sensitivity analysis is successfully accomplished in this piece of work.; The updating for simulation example about flexible rotor-bearing system; at working speed,considering model-form error, is performed to bearing; stiffness,bearing damping and diameter moment of inertia parameters; using wheel frequency and damping as objective residues. The updated; model is validated through unbalance response prediction. The simulation; results show that the maximum residual errors of updated parameter is; still 10. 1 % , but the maximum residual errors for the real part of; updated eigenvalue is 0. 95 % and for the imaginary part is 1. 15 % even; taking into 2 % model-form error account in model updating. The; unbalance response prediction of the updated model matches the target; model unbalance response quite well. The results, in no doubt,proved the; effectiveness and robustness of the model updating method considering; model-form error using wheel frequency and damping for bearing-rotor; system at working speed.国家自然科学基金资助项目; 航空科学基金资助项

Use of Relevance Vector Machine in Structural Reliability Analysis

Nature Science Foundation of China [51175425]; Research Fund for the Doctoral Program of Higher Education of China [20116102110003]The applicability of a relevance vector machine to structural reliability analysis is introduced in this work. Samples covering the important domains in the input space are first generated and selected by a modified Metropolis algorithm. Then, the samples are employed to build a surrogate model with the help of a relevance vector machine to approximate the real performance function. The surrogate model is further used for reliability analysis as a substitution of the real one, as calls to the real performance function may be time consuming or cumbersome, especially in engineering cases. In this work, the relevance vector machine and the Metropolis algorithm are combined in an iterated learning process, constantly updating the samples used according to the convergence trend of the failure probabilities. Both numerical and engineering examples have been analyzed and discussed with the proposed method, as well as comparisons to some other classical reliability methods. The research in this work shows that the proposed method based on the relevance vector machine is a viable alternative for structural reliability analysis