基于小波分析和代理模型的结构可靠性分析方法研究

发布时间：2018-06-15 16:13

本文选题：结构可靠性 + 小波密度估计　；参考：《哈尔滨工业大学》2017年博士论文

【摘要】：可靠性分析对于确保工程结构的安全、适用和耐久具有重要意义。现有的结构可靠性分析方法虽然取得了较大进展,但对于实际复杂工程结构问题仍存在困难。本文针对现有结构可靠性分析方法面临的精度与效率难以兼顾的困难,运用小波密度估计、小波框架神经网络和马尔可夫链模拟等数学工具开展深入研究,提出更加高效精确的结构可靠性分析方法,为实际复杂工程结构可靠性分析问题的解决开辟新的途径。本文的主要研究工作如下:(1)针对现有重要抽样法在处理多设计点、噪声、强非线性功能函数问题时面临的设计点求解困难、效率低等缺点,利用自适应马尔可夫链模拟失效域内样本,采用(非)线性小波密度估计构造重要抽样密度,提出基于(非)线性小波密度估计的结构可靠性分析自适应重要抽样法。算例表明所提方法可自适应地搜索失效域重要区域,和现有方法相比,有效减少结构分析次数,大幅提高计算效率。此外,还可扩展重要抽样法在结构可靠性分析中的应用范围。(2)针对现有神经网络方法广泛存在的过学习、网络泛化能力差及局部最优等问题,通过构造单尺度多维小波框架作为神经网络隐层节点,并利用时频分析及匹配追踪算法高效构造自适应小波框架神经网络近似复杂失效边界,提出基于小波框架神经网络的结构可靠性分析法。算例表明所提模型能有效提高网络的泛化能力,克服现有神经网络难以确定网络结构和参数的困难。和现有基于神经网络的可靠性分析方法相比,有效提高计算精度。此外,所提单尺度多维小波框架神经网络可极大扩展小波神经网络在高维问题中的适用范围。(3)针对现有可靠性分析代理模型法普遍存在的难以量化误差的缺点,引入修正系数来量化代理模型的近似误差;通过将失效概率表达为代理模型失效概率与该修正系数之积的形式,构造失效概率无偏估计,提出自适应更新代理模型和修正系数的迭代算法,建立结构可靠性分析无偏代理模型法。算例表明所构造的修正系数可有效量化并消除代理模型法的误差,克服传统代理模型法难以量化误差的缺点,对采用代理模型法解决实际工程问题具有重要意义。(4)上述无偏代理模型法由于难以获取多失效域内样本而使得用于估计修正系数的马氏链的遍历性得不到保证,故限制了该方法在多失效模式问题中的应用。为此分别提出伪马尔可夫链模拟和自适应聚类来识别失效域,模拟失效域内样本,在此基础上提出多失效模式结构可靠性分析无偏代理法。算例分析表明,伪马氏链模拟和自适应聚类均可高效识别多失效域,为获取失效域信息提供新的方法;所提方法可提高多失效模式结构可靠性分析的精度和效率,为实际工程中常见的多失效模式问题提供有效途径。
[Abstract]:Reliability analysis is of great significance to ensure the safety, applicability and durability of engineering structures. Although great progress has been made in the existing structural reliability analysis methods, there are still some difficulties in the practical complex engineering structure problems. Aiming at the difficulty that the accuracy and efficiency of the existing structural reliability analysis methods are difficult to be taken into account, this paper makes a deep research on the mathematical tools such as wavelet density estimation, wavelet frame neural network and Markov chain simulation. A more efficient and accurate method for structural reliability analysis is proposed, which opens up a new way to solve the problem of structural reliability analysis in practical complex engineering. The main research work of this paper is as follows: (1) in view of the disadvantages of the existing important sampling methods in dealing with the problems of multiple design points, noise, and strong nonlinear function, it is difficult to solve the design points and the efficiency is low. Using adaptive Markov chain to simulate samples in failure domain and using (nonlinear) wavelet density estimation to construct important sampling density, an adaptive importance sampling method for structural reliability analysis based on (nonlinear) wavelet density estimation is proposed. Numerical examples show that the proposed method can adaptively search the important areas in the failure region. Compared with the existing methods, the proposed method can effectively reduce the number of structural analysis and greatly improve the computational efficiency. In addition, it is possible to extend the scope of application of the important sampling method in structural reliability analysis. (2) aiming at the problems of overlearning, poor generalization ability and local optimum of existing neural network methods, By constructing a single scale multi-dimensional wavelet framework as a hidden layer node of neural network and using time-frequency analysis and matching tracking algorithm to construct an adaptive wavelet frame neural network approximately complex failure boundary efficiently. A structural reliability analysis method based on wavelet frame neural network is proposed. Numerical examples show that the proposed model can effectively improve the generalization ability of the network and overcome the difficulty of determining the network structure and parameters of the existing neural networks. Compared with the existing reliability analysis methods based on neural network, the calculation accuracy is improved effectively. In addition, the bill of lading scale multi-dimensional wavelet frame neural network can greatly extend the scope of application of wavelet neural network in high-dimensional problems. The approximate error of the agent model is quantified by introducing the correction coefficient, and the unbiased estimation of the failure probability is constructed by expressing the failure probability as the product of the agent model failure probability and the modified coefficient. An adaptive updating agent model and an iterative algorithm with modified coefficients are proposed to establish an unbiased agent model for structural reliability analysis. The numerical examples show that the modified coefficients can be used to quantify and eliminate the errors of the agent model effectively, and overcome the shortcomings of the traditional agent model which is difficult to quantify the error. The above unbiased agent model method can not guarantee the ergodicity of Markov chain used to estimate the modified coefficient because it is difficult to obtain multi-failure domain samples. Therefore, the application of this method in multi-failure mode problem is limited. For this reason, pseudo-Markov chain simulation and adaptive clustering are proposed to identify the failure region and simulate the samples in the failure domain respectively. Based on this, an unbiased agent method for reliability analysis of multi-failure mode structures is proposed. Numerical examples show that pseudo-Markov chain simulation and adaptive clustering can efficiently identify the multi-failure region and provide a new method for obtaining the information of the failure region, and the proposed method can improve the accuracy and efficiency of reliability analysis of multi-failure mode structures. It provides an effective way for the common multi-failure mode problems in practical engineering.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB114.3

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