可靠性和可靠性灵敏度分析的函数替代方法研究及应用

发布时间：2018-05-12 02:18

  本文选题：随机不确定性 + 可靠性分析　； 参考：《西北工业大学》2015年博士论文

【摘要】：函数替代方法是可靠性和可靠性灵敏度分析方法的重要组成部分,在可靠性研究领域有着极其广泛地应用。代理模型的运用在一定程度上实现了计算效率与计算精度的权衡。本文在概率可靠性的研究范畴内,分别结合人工神经网络、Kriging模型和多项式响应面模型探讨了代理模型在可靠性和可靠性灵敏度分析中的应用,研究提出了一系列的分析求解方法,同时编制开发了具有较强通用性的结构机构可靠性分析设计软件系统,并进一步针对某型导弹关键结构和典型机构开展了工程应用研究。论文的主要研究内容及创新点如下:1.结合马尔科夫链对传统人工神经网络的实验设计方法进行了改进,并分别结合重要抽样、截断重要抽样以及多抽样中心重要抽样三种抽样方法进一步提出了用于可靠性分析的结合人工神经网络的数字模拟方法。所提方法充分利用了马尔科夫链的自适应性以及人工神经网络优秀的非线性拟合性能,降低了传统方法对实验设计的依赖,通过人工神经网络模型实现了对数字模拟样本的高精度预测,从而保证了可靠性分析结果的计算精度,同时有效提高了可靠性分析的计算效率。相关算例分析结果表明,所提方法具有较好的适用性,能够用于对多种类型可靠性问题的求解,能够以较高的计算效率得到精度较好的失效概率分析求解结果。2.针对工程实际中大量存在的隐式可靠性问题,提出了基于主动学习Kriging模型的自适应数字模拟方法。所提方法继承了主动学习机制、马尔科夫链以及Kriging代理模型的诸多优点,在保证计算精度的前提下显著提高了可靠性分析的计算效率。马尔科夫链的运用提高了所提方法的自适应性,保证了用于Kriging模型构建的实验设计样本的质量;主动学习机制的引入充分利用了Kriging模型提供的预测方差信息,有效改进了Kriging模型的拟合能力,提高了对数字模拟样本的预测精度;Kriging模型的使用使得所提方法对真实极限状态函数的计算次数大幅降低,从而提高了计算效率。算例分析结果证明了所提方法的计算效率和适用性。3.基于多项式响应面模型提出了分布函数灵敏度和重要性测度分析的半解析方法。分别推导得到了多项式情况下响应量的概率矩和概率矩对分布参数的偏导数,并给出了通过矩估计方法求解分布函数灵敏度的具体公式;推导得到了变量独立和变量相关两种情况下条件期望以及条件方差的求解公式,给出了具体的求解步骤,实现了对重要性测度的求解。所提方法结合多项式响应面模型通过半解析手段求解得到了各个输入变量的分布函数灵敏度和基于方差的重要性测度,实现了对可靠性灵敏度指标的高效求解,给出的输入变量重要程度排序信息能够为改进结构设计提供有效指导。4.提出了基于Kriging模型进行分布函数灵敏度和重要性测度分析的数字模拟方法。考虑到Kriging模型对非线性函数优秀的拟合近似能力,所提方法具有更为广泛的适用性,能够在保证计算精度的前提下大幅提高可靠性灵敏度分析的计算效率。所提方法对数字模拟策略进行了一定改进,减少了用于灵敏度分析的数字模拟样本,进一步降低了计算量。数字模拟的求解策略保证了在Kriging模型基础上所得到的可靠性灵敏度分析结果的正确性。对数值和简单工程算例的分析结果证实了所提方法的适用性。5.编制开发了具有较强通用性的结构机构可靠性分析设计软件系统,实现了可靠性和可靠性灵敏度分析方法的软件化。软件系统集成了多种概率分布模型和多种可靠性及可靠性灵敏度分析方法,能够用于对各类可靠性问题的求解。软件系统能够与其他商用CAE分析软件进行通信,实现了通过商用CAE软件进行可靠性分析的可能,进而实现了对隐式可靠性问题的求解,增强了实用性。软件系统拥有简洁直观的用户界面设计,能够以图表方式给出丰富的分析结果信息,同时支持简单报告的生成,方便用户的使用。众多数值和工程算例的应用结果证明了软件系统的强大功能,展示出良好的工程应用前景。6.针对某型导弹舵翼面结构以及某型滑翔弹弹翼展开机构对所提出的可靠性和灵敏度方法进行了工程应用研究。实现了对舵翼面结构有限元模型和弹翼展开机构虚拟样机模型的参数化处理,得到了对应的参数化仿真模型。构建了能够准确预测舵翼面结构力学性能响应和弹翼展开机构运动特性响应的Kriging代理模型。通过数字模拟手段求解得到了舵翼面结构和弹翼展开机构的失效概率、分布函数灵敏度以及基于方差的重要性测度分析结果。在考虑不确定性因素的前提下得到了舵翼面结构和弹翼展开机构的安全性能评估,并进一步给出了提高性能的具体措施。
[Abstract]:The function substitution method is an important part of the reliability and reliability sensitivity analysis method. It is widely used in the field of reliability research. The application of the agent model has realized the trade-off between the calculation efficiency and the calculation accuracy to a certain extent. In this paper, the artificial neural network (artificial neural network, Kri) is combined in the research category of the probability reliability. The ging model and the polynomial response surface model are used to discuss the application of the agent model in reliability and reliability sensitivity analysis. A series of analytical solutions are proposed. At the same time, a software system for reliability analysis and design of structural mechanisms with strong generality is developed, and the key structure and typical model of a certain type of missile are further studied. The main research contents and innovation points of this paper are as follows: 1. the experimental design method of traditional artificial neural network is improved with the combination of Markoff chain, and three sampling methods, including important sampling, truncating important sampling and multi sampling center sampling, are further proposed to be used for reliability. The proposed method makes full use of the adaptability of the Markov chain and the excellent nonlinear fitting performance of the artificial neural network, reduces the dependence of the traditional method on the experimental design, and realizes the high precision prediction of the digital analog samples by the artificial neural network model. The calculation accuracy of the reliability analysis results is guaranteed and the efficiency of the reliability analysis is effectively improved. The results of the correlation analysis show that the proposed method has good applicability and can be used to solve many types of reliability problems and can get a better result of failure probability analysis with a higher calculation efficiency. .2. has proposed an adaptive digital simulation method based on active learning Kriging model, which inherits the advantages of active learning mechanism, Markov chain and Kriging agent model, which greatly improves the reliability analysis under the premise of ensuring the accuracy of calculation. The application of Markov chain improves the adaptability of the proposed method and guarantees the quality of the experimental design samples used in the Kriging model. The introduction of active learning mechanism makes full use of the predictive variance information provided by the Kriging model, improves the fitting ability of the Kriging model effectively, and improves the preview of the digital analog samples. Measurement accuracy; the use of the Kriging model makes the proposed method greatly reduce the number of calculation times of the real limit state function, thus improving the computational efficiency. The calculation efficiency and applicability of the proposed method are proved by the numerical example..3. based on the polynomial response surface model presents the semi analytic of the sensitivity of the distribution function and the importance measure analysis. The partial derivative of the probability moment and the probability moment of the response quantity under the polynomial condition is derived, and the specific formula for solving the sensitivity of the distribution function by the moment estimation method is given. The formula of the conditional expectation and the conditional variance under two cases of variable independence and variable correlation are derived. The proposed method combines the polynomial response surface model with the polynomial response surface model to obtain the sensitivity of the distribution functions of each input variable and the importance measure based on the variance. The efficient solution to the reliability sensitivity index is realized. The input variables are important to the degree of importance. The sequence information can provide effective guidance for the improvement of the structure design..4. proposed a digital simulation method based on the Kriging model for the sensitivity and importance measure analysis of the distribution function. Considering the excellent fitting approximation ability of the Kriging model to the nonlinear function, the proposed method has more extensive applicability and can ensure the accuracy of the calculation. The computational efficiency of the reliability sensitivity analysis is greatly improved. The proposed method has improved the digital simulation strategy to reduce the numerical simulation samples for sensitivity analysis and further reduce the amount of calculation. The solution strategy of digital simulation guarantees the reliability sensitivity analysis results based on the Kriging model. The results of the numerical and simple engineering examples confirm the applicability of the proposed method.5.. The software system for reliability analysis and design of structural mechanisms with strong generality is developed, and the software of reliability and reliability sensitivity analysis method is realized. The reliability and reliability sensitivity analysis method can be used to solve all kinds of reliability problems. The software system can communicate with other commercial CAE analysis software, realize the possibility of reliability analysis through commercial CAE software, and then realize the solution of the implicit reliability questions and enhance the practicability. The software system owns the software system. The simple and intuitive user interface design can give a rich analysis of the result information on the chart, support the generation of simple reports and facilitate the use of the users. The application results of many numerical and engineering examples demonstrate the powerful function of the software system, and show a good application prospect.6. for a missile rudder wing structure. And a certain type of gliding projectile wing deployment mechanism is applied to the engineering application of the proposed reliability and sensitivity method. The parameterized processing of the finite element model of the rudder wing structure and the virtual prototype model of the wing deployable mechanism is realized, and the corresponding parameterized simulation model is obtained. The mechanical properties of the rudder wing structure can be accurately predicted. The Kriging agent model, which can respond to the response of the wing unfolded mechanism, obtains the failure probability, the sensitivity of the distribution function and the analysis result of the importance measure based on the variance by the numerical simulation method. The rudder wing structure is obtained on the premise of considering the uncertainty. The safety performance evaluation of the missile wing deployment mechanism is given, and the specific measures for improving the performance are given.

【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O213.2;TP183
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本文编号：1876684