复杂产品认知不确定性的混合可靠性分析方法研究

发布时间：2018-02-17 05:17

本文关键词： 复杂产品认知不确定性区间变量耦合区间变量二阶不确定性混合可靠性分析　出处：《浙江工业大学》2016年博士论文　论文类型：学位论文

【摘要】：复杂产品普遍存在试验测试困难、实验成本高、样本数据不足等情况,导致部分不确定性变量信息稀少,无法建立精确的概率分布模型,存在因信息不充分引起的认知不确定性。同时复杂产品往往存在随机变量、区间变量、耦合区间变量和不同置信分布区间变量等多种不确定性变量。这使得仅考虑随机变量的传统可靠性分析方法或无法适用或较低的计算效率。为此,本论文针对复杂产品认知不确定性和随机不确定性共存,研究多种不确定性下的复杂产品可靠性分析方法,建立复杂产品认知不确定性的混合可靠性分析模型,提出混合可靠性分析高效的数值计算方法。主要工作和成果如下:(1)建立了区间和随机变量的混合可靠性分析模型,为解决双层耦合寻优问题引起的计算效率低的问题,将双层耦合问题转化为序列寻优问题,并提出了一种高效的数值计算方法。在序列寻优问题的概率分析中,采用稳健迭代算法;在区间分析中,基于投影梯度算法,提出了一种新的两阶段区间分析算法。第一个阶段用于处理极限状态函数关于区间变量单调的情况,第二阶段采用利用投影梯度法处理非单调情况。分解的序列寻优问题和提出的区间分析算法提高了可靠性分析的计算效率,解决了区间和随机变量的混合可靠性分析效率低的问题。(2)针对耦合区间变量和随机变量共存情况,基于多椭球模型,建立混合可靠性分析模型,提出一种基于高维度模型表示法转换的单层混合可靠性分析方法。在高维度模型表示法中,采用一次二阶矩法最大概率点算法求解参考点,利用多项式近似模型基于提出的抽样方法建立了极限状态函数关于随机变量和耦合区间变量的子模型。基于子模型求解极限状态函数关于耦合区间变量在多椭球模型域内的极限值,最后采用蒙特卡洛法求解失效概率的上下限。转换后的单层求解问题计算失效概率上下限时仅需调用少量的原始极限状态函数次数,提高了混合可靠性分析的计算效率。(3)考虑不同置信区间变量、二阶不确定性和随机变量,基于证据理论建立了三种不确定性变量下的混合可靠性分析模型,提出了一种高效的单层混合可靠性分析方法。为解决双层耦合寻优问题,利用区间分析KKT条件,将双层耦合优化问题转化为单层优化问题。为解决因KKT条件引起的求解不稳定性及收敛困难,单层混合可靠性分析模型采用光滑函数处理KKT约束条件。单层混合可靠性分析模型简化了不同置信度区间变量、随机变量及二阶不确定性下的可靠性分析问题,分解了双层耦合优化问题,提高了计算效率。(4)以复杂产品金属锯切带锯床的从动轮,机床床身和锯切部件为应用研究对象,展示并验证了本论文提出的混合可靠性分析方法的可行性和高效性。根据三个部件的认知不确定性变量和随机不确定性变量共存情况,分别基于本论文提出的区间和随机变量的混合可靠性分析方法、耦合区间和随机变量的混合可靠性分析方法和不同置信区间和随机变量的混合可靠性分析方法实施了可靠性分析计算。与已有混合可靠性分析方法的极限状态函数调用次数比较发现,本论文提出的混合可靠性分析方法的计算效率较高。以蒙特卡洛法计算结果为参照,提出的混合可靠性分析方法的计算精度较高。
[Abstract]:Complex products are testing experimental difficulties, high costs, lack of sample data and so on, lead to some uncertainty variable information is scarce, unable to establish the probability model of the exact distribution, due to insufficient information caused by cognitive uncertainty. At the same time complex products to the random variables, interval variables, coupling interval variables and different confidence distribution interval variables and other variables. This makes the calculation efficiency of the traditional reliability analysis method of random variables or not applicable or lower consideration only. Therefore, this paper based on the complex product cognitive uncertainty and random uncertainty coexist, analysis method of complex product reliability research under uncertainty, a hybrid reliability of complex product cognition the deterministic analysis model, put forward efficient numerical method for hybrid reliability analysis. The results are summarized as follows : (1) mixed reliability interval and random variable analysis model is established to solve the calculation efficiency of double coupled optimization problems caused by the problem of low, the double coupling problem is transformed into a sequence of optimization problems, and puts forward the calculation of an efficient numerical method. The probability sequence analysis of optimization problems. A robust iterative algorithm; in interval analysis, the gradient projection algorithm based on a new two stage algorithm of interval analysis. The first stage for the treatment of the limit state function for interval variables monotonous, second stage by using the gradient projection method with non monotone decomposition sequence. Analysis of interval optimization problems and put forward the algorithm improves the calculation efficiency of reliability analysis, solves the problem of low efficiency and reliability analysis of mixed interval random variables. (2) for coupling interval variables and random variables. Condition, ellipsoid model based on hybrid reliability analysis model, this paper proposed a hybrid method for the reliability analysis method of single layer conversion based on high dimension model. In the high dimensional model representation, using a solution of maximum probability two order moment algorithm reference point, using polynomial approximation model the limit state function of the random variable and the coupling interval variable sub model is established based on the sampling method. To solve the sub model of limit state function on limit coupling interval variables in multi domain ellipsoid model based on the value of the upper and lower limits and finally solve the failure probability by Monte Carlo method. The original number of single solution of limit state function after conversion to calculate failure probability of the upper and lower limit only need to call a little, to improve the computational efficiency and hybrid reliability analysis. (3) consider different confidence interval variables, uncertainty and random order two Variable, evidence theory of three kinds of hybrid reliability uncertainty variable model was established. Based on the analysis put forward an efficient method of single hybrid reliability. In order to solve the double coupled optimization problem, KKT analysis using interval, double coupling optimization problem into a single optimization problem. To solve the conditions caused by KKT stability and convergence difficulties, single hybrid reliability analysis model using a smooth function to handle KKT constraints. The model simplifies the different confidence interval variable analysis of single hybrid reliability, reliability analysis of random variables and two order under uncertainty, double decomposition optimization, improve the computational efficiency. (4) the product of metal complex the driven wheel cutting band sawing machine, sawing machine bed and components for the application of the research object, display and verify the reliability of the proposed hybrid The method is feasible and efficient. According to the three parts of the cognitive uncertainty variables and random uncertainty variables, respectively analysis of hybrid reliability interval is proposed in this paper, and the random variable method based on hybrid reliability analysis method and different confidence intervals and mixed random variable and random variable coupling interval reliability analysis method of the implementation of the reliability analysis and calculation. And the existing hybrid reliability analysis method of the limit state function call number comparison, analysis and calculation method of high efficiency hybrid reliability is proposed in this paper. The calculation results by Monte Carlo method for reference, analysis and calculation method of high precision hybrid reliability is put forward.

【学位授予单位】：浙江工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB114.3

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