产品设计阶段多响应参数稳健优化方法研究

Generally, many quality characteristics exist in product design process. Several response variables of product or process should be considered together. For multi-response robustness optimization problem, it's difficult to determine a set of process parameters to optimize all responses simultaneously. This study will mainly focus on the robustness of response to the fluctuation of model goodness of fit, and discuss about the robust parameter optimization for multiple responses. Firstly, the measure of multi-response robustness would be brought forward, based on the analysis of model goodness of fit's influnence on robustness. Secondly, multi-response robust optimization would be present by making appropriate tradeoffs between robustness and optimization. Then, the robust optimal process parameters in the experimental region would be determined, with which confidence region could be provided. Thirdly, when the robust optimal solution is found at the border of the experimental region, the experimenter will probably explore outside the original experimental region. The method to determine search direction for robust optimal experiment region would be brought forward, and then the global robust optimal solution would be found. Lastly, the rationality and validity of this study will be testified by its application in actual design process. The expected achievement of this study will be of theoretical significance and application feasibility for the improvement of design quality in product design process.

在产品设计阶段，往往存在多个质量特性，产品或过程的工艺输出需要同时考虑多个响应变量。对于多响应稳健优化问题，通常难以确定一组工艺参数使所有响应同时稳健最优。本项目拟以多响应过程为研究对象，围绕响应对模型拟合优度波动的稳健性，深入探讨其参数稳健优化问题。首先，基于模型拟合优度对稳健性的影响分析，构建多响应稳健性评价指标。其次，权衡响应的最优性和稳健性，提出多响应稳健优化方法，寻找现有试验区域内的稳健优化点，并建立其置信区域。再次，若稳健优化点落在现有试验区域边界附近时，需要进一步对试验区域寻优，提出搜索方向的确定方法，找到稳健优化试验区域，确定全局稳健优化解。最后，将本研究应用于企业产品设计过程，并进行实证分析。本项目的研究成果对于提高产品设计质量，具有重要理论意义和应用价值。

在产品设计阶段，往往存在多个质量特性，产品或过程的工艺输出需要同时考虑多个响应变量。本项目以多响应过程为研究对象，深入探讨其稳健参数优化问题。在自然科学基金青年基金的资助下，课题组完成了如下几个方面的工作：（1）建立了稳健性的评价指标，并考虑多响应之间的相关性及多响应问题的最优性和稳健性，对传统的广义距离函数法进行了改进，引入修正矩阵，提出了稳健广义距离函数法，将多响应稳健优化问题转化为使改进的广义距离最小化问题，从而得到稳健最优的操作条件；（2）基于Bootstrap方法对传统的模型拟合方式进行改进，从而获得更为稳健的参数设计结果。在获得模型拟合结果后，运用结合满意度函数法和双响应曲面的稳健性设计方法来对拟合结果进行稳健性参数优化；（3）对于田口稳健性参数设计方法的研究，针对田口方法中望小特性信噪比做改进研究，提出新的望小特性定义式，对两者进行比较分析，通过实例验证，与传统田口稳健性参数设计方法相比，具有更好的稳健性；（4）将本研究应用于企业产品设计过程，并进行实证分析。本项目的研究成果对于提高产品设计质量，具有重要理论意义和应用价值。