复杂机械结构高效静/动态可靠性分析及可靠性优化设计方法研究

Reliability theory and methods are widely employed in industrial sectors of our country. And reliability is one of the most important technical indexes for a mechanical product. Existing reliability methods are not available for the reliability analysis or the reliability based optimization design of complex mechanical structures because they need to call the target performance function too many times to accomplish the reliability analysis or the reliability based optimization design. This project aims to construct effective time-invariant and time-variant reliability analysis methods and reliability based optimization design method for complex mechanical structures. The innovative methods are based on the Kriging model and the improved design of experiments (DoE). To achieve these goals, the main research needed is summarized as follows:The quantitative indexes that quantify how accurate a given Kriging model is for the applications mentioned above are proposed; The quantitative measurements that quantify how much the accuracy of a given Kriging model is able to be improved if adding a point into the current DoE are raised; Then, to construct the innovative DoE strategies, optimization problems for these concerned applications are designed to search the next best point, based on which the effective methods for time-invariant reliability analysis, time-variant reliability analysis and the reliability based optimization design are proposed. In terms of theory and methodology, these innovative methods provide the support of applying reliability analysis and reliability based optimization design to complex mechanical structures in engineering. Finally, to test the accuracy, the efficiency and the engineering value of the proposed methods, they are used to perform the reliability analysis and the reliability based optimization design of an accessory gearbox of aeroengine which is with complex structure, works in poor condition and holds several failure modes.

可靠性理论和方法广泛应用于国民工业各个领域，可靠性已经成为机械产品最重要的指标之一。现有可靠性分析和可靠性优化设计方法需要进行冗繁的极限状态函数运算，因此很难应用于复杂机械结构可靠性分析及优化设计。本项目采用Kriging模型从改进虚拟仿真实验方案入手，提出高效的适用于工程中复杂机械结构的静/态可靠性分析和可靠性优化设计方法。为此展开如下研究工作：分别提出Kriging模型以上应用场合下模型精度定量估计方法；评价结构输入变量空间内各点对Kriging模型精度改善程度；针对不同问题分别提出以最大程度改进Kriging模型精度为目的的虚拟仿真实验方案，进而形成高效的静/动态可靠性分析和优化设计方法。为工程中复杂机械结构的可靠性分析和优化设计提供理论和方法支撑。以结构复杂、工作环境恶劣、存在多种故障模式的某型航空发动机附件机匣为应用对象验证本项目所提方法的精度、效率及其工程应用价值。

随着工业生产与现代科技的发展，机械产品性能日益提高，机械系统和工作环境更加复杂，表征机械结构运行状态的状态函数的计算复杂程度和非线性程度也越来越高。针对功能函数具有复杂非线性和计算难度高等特点的机械结构，开展基于代理模型的静/动态可靠性分析方法以及优化方法的深入研究具有重要的理论意义和工程实用价值。研究工作主要包括如下几个方面：.（1）针对可靠性分析过程中，Kriging模型精度的定量估计进行研究并推导出两种Kriging模型精度的度量标准。.（2）基于Kriging模型最佳样本点的静态可靠性分析方法研究。定义了能够最大程度提高Kriging模型精度的最佳样本点；基于Kriging模型最佳样本点提出了高效的静态可靠性分析方法。并采用所构造的静态可靠性分析方法进行齿轮齿面接触疲劳强度可靠性分析。.（3）基于Copula理论开展了失效模式间具有相关性的串/并联系统可靠性问题的研究给出了确定复合Copula模型结构的算法；基于Copula理论和Kriging模型对考虑3种失效模式的齿轮系统进行可靠性分析。.（4）基于Kriging模型的动态可靠性分析方法研究。推导动态可靠性分析中Kriging模型预测的失效概率函数和结构寿命分布概率密度函数的误差估计方法；构造基于Kriging模型最佳样本点的动态可靠性分析方法，并完成齿轮齿面接触疲劳强度动态可靠性分析。.（5）基于PC-Kriging模型和粒子群算法提出了高效的优化设计方法。.（6）对某型号飞机发动机附件机匣齿轮热静/动态传递误差可靠性进行分析。.（7）进行齿轮加速试验，并根据实验数据拟合不同工况下齿轮磨损量变化趋势，并完成齿轮系统热传递误差的动态可靠性评估。.（8）基于PC-Kriging代理模型和PSO优化算法的齿轮热-动力学修形优化研究。将齿轮热动态传递误差波动范围最小值作为优化算法的目标函数，以主动轮修形长度、主动轮修形量、从动轮修形长度、从动轮修形量为设计变量，最后由PSO优化算法求解出最优修形参数。