稳健设计中不确定性问题的研究及应用

【作者】 张素梅；

【导师】 师义民；

【作者基本信息】 西北工业大学 ， 应用数学， 2005， 硕士

【摘要】 稳健设计方法作为一种保证产品质量的有效设计方法,已经在电子,机械等诸多领域得到重视和应用。但是,目前稳健设计研究主要集中在传统假设、确定性条件下进行;而实际生产中往往很少符合这些条件。因此为满足实际生产需要,有必要进行不满足传统假设或者不确定性条件下的稳健设计研究。本文拟从实验设计方法和工程模型方法两方面对稳健设计进行研究。 论文主要工作有:1)利用统计学里的广义线性模型(GLM)方法将传统的响应面模型推广到方差非齐(Heterogeneity)情况下的响应面模型。利用GLM对包含噪声因子一阶效应的稳健设计响应面和包含噪声因子二阶效应的稳健设计响应面进行了研究,建立了模型并给出了模型的统计分析方法。2)依据上述研究,将包含噪声因子的稳健设计响应面模型推广到动态环境,建立动态特性稳健设计响应面模型。分别就方差相等和方差不等两种情况给出模型的统计分析方法。在方差非齐情况下,对动态特性稳健设计响应面进行了GLM研究,并考察了方差非齐下动态特性稳健设计响应面模型的参数估计及其假设检验。3)以某制动器的稳健设计为例,建立了动态特性的响应面模型,并利用GLM方法对其均值模型和方差模型进行联合估计,通过SAS软件实现了该方法。4)从工程模型角度出发,利用模糊数学知识对基于成本—质量模型的稳健优化设计进行了初步探索,结合实验设计方法和模糊数学知识,提出了一种新的优化设计方法,并通过实例证明了该方法的有效性。更多还原

【Abstract】 Robust design, a valid design technical, which can assure product quality has been being regarded and applied in electronic industry, engineering industry and so on. However most of achievements have been accomplished under traditional hypothesis or certainty. Since production in practice is usually not accord with those condition. So uncertainty researches need studying. This thesis will research two facets to robust design: experiment design approach and engineer model approach.Four aspects of robust design are researched mainly. Firstly, based on traditional response surface approach the thesis researches response surface under heterogeneity by means of General Linear Model (GLM), moreover establishes one-order response surface model in noise factors and second-order response surface model in noise factors under heterogeneity, and provides model’s statistical analysis method. Secondly, based on response surface model in noise factors the thesis researches robust design response surface model with dynamic characteristics, and establishes robust design model with dynamic characteristics, then provides model’s statistical analysis method under homogeneity and heterogeneity. The parameter estimation and hypothesis test of the model under heterogeneity are reviewed. Thirdly, the thesis gives a brake system example to illustrate this method, and establishes robust design model with dynamic characteristics and estimate joint mean-dispersion model by use of GLM by SAS. At last the thesis also researches optimal robust design based on cost-quality model via fuzzy mathematics knowledge and gives an engineer model approach. A new optimal robust design method based on experiment design approach and fuzzy mathematics knowledge is brought forward, and the effectiveness of this method is verified by means of a living example.更多还原