基于RSM的多响应稳健性设计方法的研究
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摘要
本文主要研究具有多质量特性的产品或过程的稳健性参数设计问题,重点对考虑设计参数波动及噪声时的多响应稳健性参数设计方法进行深入研究,具体从以下几个方面进行研究:
首先,对最常用的多响应优化方法-满意度函数法进行了深入研究,指出了用其进行多响应参数设计时存在的问题,即该方法没有考虑响应的变异性、相关性和参数估计的不确定性,针对这些问题本文提出了改进方法,并通过实例分析证明了改进方法的有效性。
其次,对考虑噪声因子时的多响应均值和方差进行了估计,并对多质量特性的方差估计进行了改进,然后,对多元损失函数法进行了改进,并提出了一个新的满意度函数法,使这两种方法均考虑了噪声因子产生的方差和拟合模型的预测方差,最后,通过一个实例分析了改进的多元损失函数法和新满意度函数法的应用效果,结果表明,这两种方法对噪声因子和参数估计的不确定都具有稳健性。
再次,研究了考虑设计变量波动及噪声时的多响应稳健性参数设计问题。本文将设计变量的波动分为两种情况,即设计变量服从正态分布和设计变量退化两种情况。对于设计变量服从正态分布的情况,给出了考虑噪声因子时的响应均值及方差的估计,并用新的满意度函数法结合了响应的均方差和对可控因子的变化率,然后用该方法对实例进行了分析,结果表明,该方法进行优化得到的响应对设计变量的变化更具稳健性。对于设计变量退化的情况,给出了质量损失的计算方法,并研究了对设计变量进行简单周期性重置、改进的周期性重置及根据使用寿命进行重置或更换时的多响应参数设计方法。
最后,对设计变量服从正态分布的情况,还研究了多响应参数与容差的并行设计方法,构建了总成本模型,通过使容差成本与质量损失最小化,可以同时得到设计参数的最优水平及容差。最后通过一个实例分析了参数与容差并行设计的有效性。此外,还探讨了设计变量退化时的多响应的参数、容差与维修集成设计问题,考虑了制造成本、维修成本与质量损失,通过使这三者的成本之和最小化可以获得设计参数的水平、容差及维修周期。
In this dissertation, the methodologies for Robust Parameter Design (RPD) of the products or processes with multiple characteristics are developed. The objective is to develop methods for mult-iresponse RPD when noise factors and fluctuations of design parameters are considered. The research includes the following aspects.
First, it relates to the improvement of the traditional desirability function method. Desirability function method is the most popular approach for multi-response optimization, however, the variation, correlation and the uncertainty of parameter estimation of the responses are ignored in this approach. Thus an improved desirability function method is presented. The implementation and effectiveness of the proposed method are illustrated by an example from the literature. The result shows, the proposed method which is robust to prediction quality and variant of responses yields better results than traditional desirability function method.
Secondly, it presents a method to multi-response RPD when noise factors are presented. The mean and variances of the responses are estimated, and the variance estimation is improved to avoid the possible nonpositive definiteness of estimated variance. Then the multivariate loss function method is improved to consider the influence of noise factors, and a new desirability function method is proposed to take into account the mean squared error of the responses. Both the mean value and variance models are incorporated into the two methods, in which the variance combines the variance due to the noise factors with the variance due to predictions, which lead to an unbiased estimator of the combined variance. Finally, an example is given where the two methodologies are applied to the data, the results show that the solutions obtained by proposed methods are robust to both noise factors and parameter estimation uncertainty.
Thirdly, it addresses the multi-response RPD issue when both the fluctuations of design parameters and influences of noise factors are considered. When the design parameters follow normal distribution, the mean and variance estimated models are presented, and the new desirability function method which combines variances due to noise factors and the variation of the controllable factors, the sensitivisity of the responses to the fluctuation of controllable factors is given. The effectiveness of the proposed method is illustrated by an example from the literature. The result shows, compared with results from the literature, the robustness to the fluctuation of controllable factors is improved. When the design parameters drift or degraded over operation time, the quality losses are calculated, and the multi-response RPD methodology are explored when the design parameters are reset based on simple block reseeting policy, modified block resetting policy and age resetting policy.
At last, it extends the concurrent optimization of parameter design and tolerance design to the case of multiple responses when the design parameters follow normal distribution. A total cost model is proposed by balancing multivariate losses incurred by parameter design and increased costs caused by tightening the tolerances of design parameter. And the variations of design parameter and economies of the process are considered by the proposed model. The implementation and advantages of the proposed method are illustrated by an example. The result indicates, compared with conventional parameter design, the variances of the responses and the total costs are all reduced dramatically. Furthermore, the integrated optimization of parameter design, tolerance design and maintenance is explored for products or processes with multiple characteristics when the design parameters degraded. The total cost function which consists of quality losses, manufacturing cost and maintenance is minimized to simultaneously obtain the optimal settings and tolerances of design parameter, as well maintenance policy.
首先,对最常用的多响应优化方法-满意度函数法进行了深入研究,指出了用其进行多响应参数设计时存在的问题,即该方法没有考虑响应的变异性、相关性和参数估计的不确定性,针对这些问题本文提出了改进方法,并通过实例分析证明了改进方法的有效性。
其次,对考虑噪声因子时的多响应均值和方差进行了估计,并对多质量特性的方差估计进行了改进,然后,对多元损失函数法进行了改进,并提出了一个新的满意度函数法,使这两种方法均考虑了噪声因子产生的方差和拟合模型的预测方差,最后,通过一个实例分析了改进的多元损失函数法和新满意度函数法的应用效果,结果表明,这两种方法对噪声因子和参数估计的不确定都具有稳健性。
再次,研究了考虑设计变量波动及噪声时的多响应稳健性参数设计问题。本文将设计变量的波动分为两种情况,即设计变量服从正态分布和设计变量退化两种情况。对于设计变量服从正态分布的情况,给出了考虑噪声因子时的响应均值及方差的估计,并用新的满意度函数法结合了响应的均方差和对可控因子的变化率,然后用该方法对实例进行了分析,结果表明,该方法进行优化得到的响应对设计变量的变化更具稳健性。对于设计变量退化的情况,给出了质量损失的计算方法,并研究了对设计变量进行简单周期性重置、改进的周期性重置及根据使用寿命进行重置或更换时的多响应参数设计方法。
最后,对设计变量服从正态分布的情况,还研究了多响应参数与容差的并行设计方法,构建了总成本模型,通过使容差成本与质量损失最小化,可以同时得到设计参数的最优水平及容差。最后通过一个实例分析了参数与容差并行设计的有效性。此外,还探讨了设计变量退化时的多响应的参数、容差与维修集成设计问题,考虑了制造成本、维修成本与质量损失,通过使这三者的成本之和最小化可以获得设计参数的水平、容差及维修周期。
In this dissertation, the methodologies for Robust Parameter Design (RPD) of the products or processes with multiple characteristics are developed. The objective is to develop methods for mult-iresponse RPD when noise factors and fluctuations of design parameters are considered. The research includes the following aspects.
First, it relates to the improvement of the traditional desirability function method. Desirability function method is the most popular approach for multi-response optimization, however, the variation, correlation and the uncertainty of parameter estimation of the responses are ignored in this approach. Thus an improved desirability function method is presented. The implementation and effectiveness of the proposed method are illustrated by an example from the literature. The result shows, the proposed method which is robust to prediction quality and variant of responses yields better results than traditional desirability function method.
Secondly, it presents a method to multi-response RPD when noise factors are presented. The mean and variances of the responses are estimated, and the variance estimation is improved to avoid the possible nonpositive definiteness of estimated variance. Then the multivariate loss function method is improved to consider the influence of noise factors, and a new desirability function method is proposed to take into account the mean squared error of the responses. Both the mean value and variance models are incorporated into the two methods, in which the variance combines the variance due to the noise factors with the variance due to predictions, which lead to an unbiased estimator of the combined variance. Finally, an example is given where the two methodologies are applied to the data, the results show that the solutions obtained by proposed methods are robust to both noise factors and parameter estimation uncertainty.
Thirdly, it addresses the multi-response RPD issue when both the fluctuations of design parameters and influences of noise factors are considered. When the design parameters follow normal distribution, the mean and variance estimated models are presented, and the new desirability function method which combines variances due to noise factors and the variation of the controllable factors, the sensitivisity of the responses to the fluctuation of controllable factors is given. The effectiveness of the proposed method is illustrated by an example from the literature. The result shows, compared with results from the literature, the robustness to the fluctuation of controllable factors is improved. When the design parameters drift or degraded over operation time, the quality losses are calculated, and the multi-response RPD methodology are explored when the design parameters are reset based on simple block reseeting policy, modified block resetting policy and age resetting policy.
At last, it extends the concurrent optimization of parameter design and tolerance design to the case of multiple responses when the design parameters follow normal distribution. A total cost model is proposed by balancing multivariate losses incurred by parameter design and increased costs caused by tightening the tolerances of design parameter. And the variations of design parameter and economies of the process are considered by the proposed model. The implementation and advantages of the proposed method are illustrated by an example. The result indicates, compared with conventional parameter design, the variances of the responses and the total costs are all reduced dramatically. Furthermore, the integrated optimization of parameter design, tolerance design and maintenance is explored for products or processes with multiple characteristics when the design parameters degraded. The total cost function which consists of quality losses, manufacturing cost and maintenance is minimized to simultaneously obtain the optimal settings and tolerances of design parameter, as well maintenance policy.
引文
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