【作者】 王晶；

【导师】 何桢；

【作者基本信息】 天津大学 ， 管理科学与工程， 2009， 博士

【摘要】 本文主要研究了多响应稳健性参数优化方法中响应对可控因子波动的稳健性问题,目的在于通过同时考虑多响应问题的最优性和稳健性,来获得稳健最优的操作条件,从而使优化的响应对可控因子的波动具有稳健性。以此为目标,本文基于响应曲面方法(RSM)构建了多响应稳健优化模型并加以分析。本文首先介绍了响应曲面和稳健性参数设计的一些基本理论和传统方法,在此基础上提出了处理多响应稳健性参数优化的方法,具体从以下几个方面进行了研究:首先,探讨了多响应优化中响应对可控因子波动的稳健性问题。在实际生产过程中,可控因子很难控制在某一特定值上保持恒定不变,总会在设定值附近某一小范围内做微小的波动,同时响应也会相应发生改变。基于此,建立了两种稳健性的评价指标,并提出了实现多响应稳健性参数优化的技术路线。其次,对传统的满意度函数法进行了改进,构建了一个新的稳健满意度函数,用以衡量响应对可控因子波动的稳健性。考虑到过程的最优性和稳健性,通过将传统的满意度函数与前述稳健满意度函数进行权衡,提出了稳健优化满意度函数方法。实例分析表明,该方法可以较好的解决多响应优化的稳健性问题。再次,基于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,并提出了修正的广义距离函数法以及稳健优化总体广义距离函数法,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。实例分析结果验证了上述方法的可行性与有效性。最后,通过选择合适的稳健矩阵构建了一个新的多元稳健函数,并基于过程的经济性及稳定性,将多元损失函数和多元稳健函数进行权衡,提出了一种新的稳健损失函数,以此来实现过程参数优化的低成本和高稳健性。更多还原

【Abstract】 This dissertation mainly studies the robustness of the responses to the fluctuation of controllable factors in multi-response robust parameter optimization. Considering the optimization and robustness for multi-response problem simultaneously, this dissertation mainly focuses on obtaining a compromised robust optimum condition on which multiple responses are simultaneously optimized and insensitive to small changes of input variables. Aiming at this objective, several multi-response robust optimization models are constructed based on Response Surface Methodology (RSM). With the introduction of basic theories and traditional methods of response surface methodology and robust parameter design, robust optimization methods for multi-response are proposed in this dissertation as follows.First, the robustness of responses to the fluctuations of input variables is discussed. Considering that input variables are hard to be fixed, and the responses will change corresponding to the fluctuation of input variables in a small region, two measures of robustness are presented, and the technical approach to the robust parameter optimization of multi-response is proposed in this dissertation.Second, with the improvement of traditional desirability function, a new robustness desirability function is proposed to measure the robustness of responses to the fluctuations of controllable variables. Considering the optimization and robustness of a process, a new robustness optimization desirability function is presented with the tradeoff between traditional optimization desirability function and robustness desirability function mentioned above. Case study shows that the proposed method is feasible to solve the robustness problem of multi-response optimization.Third, considering the correlations among several responses for the robust optimization of multi-response problem, corrected generalized distance function and robustness optimization overall generalized distance function are introduced. A compromised robust optimum can be obtained by finding conditions that minimize the improved generalized distance. Cases study shows the feasibility and effectiveness of these methods.Last, with the selection of appropriate robustness matrix, a new robustness function is constructed. Based on process economy and robustness, a new robustness loss function is proposed to reduce cost and improve robustness of process parameter optimization.更多还原