基于田口质量损失的误差源重要性测度方法研究

In engineering practice, the deviation of quality characteristic from the target value is inevitable. According to Taguchi’s view point, deviation of quality characteristic will impart loss to society. With respect to High-end Equipment, e.g., advanced machine tools and Aerospace equipment, the deviation of quality characteristic and the resultant quality loss are actually caused by substantial error sources. In addition, because of the complicated system structure and the large number of design variables, optimization of the High-end Equipment is a challenging work in engineering practice. With respect to this problem, study of the importance measure method for error sources is very necessary. Firstly, we construct the quality loss function for dynamic quality characteristic and repairable deteriorating products respectively, and then study the change of quality loss and repairing fees with time. Secondly, we decompose the typical expected quality loss function in to a series of fractions, representing the individual and interaction effects of the error sources. Then importance indices for error sources are defined based on the quality loss function decomposition, and the properties and the physical interpretations are discussed. Thirdly, the importance measure method for static quality characteristic is extended to deteriorating systems, and the action mechanism and the influence of error sources on the quality loss is studied across the whole life cycle of product. At last, the parallel optimization method for design parameters, tolerances and maintenance strategy is proposed based on the importance measure studies, which is valuable for optimization of highly complex products.

在工程实际中，产品质量特征从目标值的不确定性偏差是不可避免的，田口质量损失函数定量描述了由质量特征偏差产生的社会损失。对高档数控机床、航空航天装备等重大装备，质量特征偏差和质量损失是大量误差源综合作用的结果。由于其系统结构复杂、设计变量多，优化设计一直以来是工业部门面临的难题。在此背景下，研究基于田口质量损失的误差源重要性测度方法，探明误差源对质量损失的作用机理和影响规律，对重大装备的高效优化具有重要意义。本项目拟从构建动态质量特征和可修退化系统的质量损失函数模型入手，分析产品质量损失和维护费用随时间的演变规律。通过研究典型平均质量损失函数的分解方法，给出误差源重要度指标的数学定义，并将其扩展到动态质量特征和可修退化系统的情况，在产品全寿命周期范围内研究误差源对产品质量损失的作用机理和影响规律，最后在此基础上给出产品参数、容差和维修策略的并行优化流程和方法，为重大装备的高效优化提供支撑。

本项目针对工程实际中材料性能参数偏差、零部件制造和装配误差、构件变形、运动副磨损、载荷和环境应力波动等多种误差源造成复杂装备系统质量特征偏差和质量损失的问题，在考虑系统不确定性退化和维修的情况下，开展基于田口质量损失的误差源重要性测度方法研究。基于退化过程模型和连续复利的现金流现值原理构建动态质量特征和可修退化系统的质量损失函数模型，提出基于多元函数泰勒展开的非平方型质量损失函数直接分解方法，以及基于混沌多项式分解和多元函数泰勒展开相结合的平方型质量损失函数的分解方法，给出误差源重要度指标的数学定义和物理解释，在机理层面探明底层误差源在平均质量损失函数中的传播机理，以及误差源对平均质量损失的影响规律，可提高设计人员对误差源和设计变量的内在作用机理的感性和理性认知。最后在此基础上研究以质量损失为核心的参数、容差和维护策略的并行优化原理与方法，为大型复杂产品的高效优化设计提供支撑。