SX公司产品注塑过程多响应优化研究
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摘要
在实际的产品与工艺过程的优化设计中,往往需要考虑多个质量特性,这就是多响应的问题,多响应问题通常不存在一组特定的输入变量使得所有响应变量同时达到最优,多响应优化设计能够有效地提高产品的质量,并产生了巨大的经济效益,因此多响应优化设计在持续性质量改进活动中显示出越来越重要的地位和作用。
本文以SX公司产品注塑过程的多响应问题为研究对象,通过对该公司产品注塑过程多响应问题的现状分析发现,该公司分析人员采取的是传统的多响应曲面方法,即利用最小二乘法(OLS)拟合响应变量与控制变量的模型,然后基于满意度函数确定最佳因子水平组合。同时通过查阅国内外文献发现,最小二乘法在因子个数较多时难以准确的拟合模型,且在优化过程中需要考虑多响应之间的相关性问题。鉴于以上分析,根据注塑过程中因子个数的情况,将注塑过程分为复杂注塑过程和简单注塑过程,由于两类注塑过程在多响应优化方法上存在差异,本文提出了两类注塑过程的多响应优化的思路：
(1)基于ANN(人工神经网络)的复杂注塑过程多响应优化。计算各响应变量满意度值,利用ANN拟合响应变量的满意度值和控制变量的模型,并进行预测；采用PCA(主成分分析)方法将一系列相关的变量转化成不相关的变量,得到主成分序列；在确定主成分的优化方向后,运用TOPSIS方法确定最佳的因子水平组合。
(2)基于SUR(似不相关回归)的简单注塑过程多响应优化。由于SUR方法在较好拟合模型的同时又能解决响应变量之间的相关性问题,因此,采用SUR方法拟合模型,确定各个变量的满意度函数和总体满意度函数,在此基础上,获得最佳因子水平组合。
最后,将上述两种思路得到的最佳因子水平组合进行试验验证,并对优化前后的结果进行理论和实证上的对比分析。本文的第五章提出了一些促进多响应优化的管理建议。
In the design of the actual product and process optimization, often need to consider multiple quality characteristics, which is multi-response problem, this problem usually does not exist a specific set of input variables to make all response variables at the same time to achieve optimal, multi-response optimization design can effectively improve the quality of the products and generate huge economic benefits, so the multi-response optimization design show an increasingly important position and role in the continuous quality improvement activities.
This paper takes multi-response problems of SX company's product molding process as the research object, through the current situation analysis of multi-response problem to find, analysis personnel taken the traditional multiple response optimization method, namely use least squares method (OLS) to fit the model of response variables and the control variables, and then based on the satisfactory degree function to determine the optimal factor level combination. At the same time, via referring to domestic and foreign literatures found, least square method cannot accurately fit the model in the case of more factors, and in the optimal process needs to consider the correlation between responses. In view of the above analysis, in this paper, according to the factor number in the injection molding process, the injection molding process is divided into complex injection molding process and simple injection molding process, at the same time, put forward two kinds of multiple response optimization thought.
(1) Multiple response optimizations for Complex injection molding process based on ANN. Calculate satisfaction value of each response variables, use the ANN to fit the model of response variables satisfaction value and the control variable, and conduct to predict; then use the PCA method transfer a series of related variables into irrelevant variables, and get the principal component sequence; after determining principal components optimization direction, use TOPSIS method to determine the optimal factor level combination.
(2) Multiple response optimizations for simple injection molding process based on SUR. As the SUR method can either accurately fit model, or solve the correlation between the responses, therefore, use SUR method to fit model, then determine the satisfaction function of each variables and overall satisfaction function, on the basis of these, obtain optimal factor level combination.
Finally, conduct test validation for the best combination of factor levels, and compare the response'results on the theory and practice, and then find the response values have been optimized. The fifth chapter proposes management measures and recommendations to promote multi-response optimization.
本文以SX公司产品注塑过程的多响应问题为研究对象,通过对该公司产品注塑过程多响应问题的现状分析发现,该公司分析人员采取的是传统的多响应曲面方法,即利用最小二乘法(OLS)拟合响应变量与控制变量的模型,然后基于满意度函数确定最佳因子水平组合。同时通过查阅国内外文献发现,最小二乘法在因子个数较多时难以准确的拟合模型,且在优化过程中需要考虑多响应之间的相关性问题。鉴于以上分析,根据注塑过程中因子个数的情况,将注塑过程分为复杂注塑过程和简单注塑过程,由于两类注塑过程在多响应优化方法上存在差异,本文提出了两类注塑过程的多响应优化的思路：
(1)基于ANN(人工神经网络)的复杂注塑过程多响应优化。计算各响应变量满意度值,利用ANN拟合响应变量的满意度值和控制变量的模型,并进行预测；采用PCA(主成分分析)方法将一系列相关的变量转化成不相关的变量,得到主成分序列；在确定主成分的优化方向后,运用TOPSIS方法确定最佳的因子水平组合。
(2)基于SUR(似不相关回归)的简单注塑过程多响应优化。由于SUR方法在较好拟合模型的同时又能解决响应变量之间的相关性问题,因此,采用SUR方法拟合模型,确定各个变量的满意度函数和总体满意度函数,在此基础上,获得最佳因子水平组合。
最后,将上述两种思路得到的最佳因子水平组合进行试验验证,并对优化前后的结果进行理论和实证上的对比分析。本文的第五章提出了一些促进多响应优化的管理建议。
In the design of the actual product and process optimization, often need to consider multiple quality characteristics, which is multi-response problem, this problem usually does not exist a specific set of input variables to make all response variables at the same time to achieve optimal, multi-response optimization design can effectively improve the quality of the products and generate huge economic benefits, so the multi-response optimization design show an increasingly important position and role in the continuous quality improvement activities.
This paper takes multi-response problems of SX company's product molding process as the research object, through the current situation analysis of multi-response problem to find, analysis personnel taken the traditional multiple response optimization method, namely use least squares method (OLS) to fit the model of response variables and the control variables, and then based on the satisfactory degree function to determine the optimal factor level combination. At the same time, via referring to domestic and foreign literatures found, least square method cannot accurately fit the model in the case of more factors, and in the optimal process needs to consider the correlation between responses. In view of the above analysis, in this paper, according to the factor number in the injection molding process, the injection molding process is divided into complex injection molding process and simple injection molding process, at the same time, put forward two kinds of multiple response optimization thought.
(1) Multiple response optimizations for Complex injection molding process based on ANN. Calculate satisfaction value of each response variables, use the ANN to fit the model of response variables satisfaction value and the control variable, and conduct to predict; then use the PCA method transfer a series of related variables into irrelevant variables, and get the principal component sequence; after determining principal components optimization direction, use TOPSIS method to determine the optimal factor level combination.
(2) Multiple response optimizations for simple injection molding process based on SUR. As the SUR method can either accurately fit model, or solve the correlation between the responses, therefore, use SUR method to fit model, then determine the satisfaction function of each variables and overall satisfaction function, on the basis of these, obtain optimal factor level combination.
Finally, conduct test validation for the best combination of factor levels, and compare the response'results on the theory and practice, and then find the response values have been optimized. The fifth chapter proposes management measures and recommendations to promote multi-response optimization.
引文
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[17]A.Noorul Haq, P.Marimuthu, R.Jeyapaul. Multi-response optimization of machining parameters of drilling AL\SIC metal matrix composite using grey relational analysis in the Taguchi method [J]. Int J Adv Manuf Technol (2008)37:250-255.
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[28]汪建均,马义中,翟云焕.相关多质量特性的优化设计[J].管理工程学报,2011,2.
[29]汤禹成,周雄辉,陈军.基于神经网络响应曲面的预锻模具形状优化和再设计方法[J].上海交通大学学报,2007,4.
[30]J.L.Lin, K.S.Wang. Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics [J]. Journal of Materials Processing Technology,48-55, 2000.
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[32]Lee-Ing Tong, Chi-Chan Chen, Chung-Ho Wang. Optimization of multi-response process using the VIKOR method [J]. Int J Adv Manuf Technol(2007)31:1049-1057.
[33]Wei-Jaw Deng. Integrating MRSN Ratio and ANPA to Optimization Process Parameter of Multiple-response Injection Molding Process [J]. Int J Adv Manuf Technol,2008.
[34]Surajit Pal, Susanta Kumar Gauri. Multi-Response Optimization Using Multiple Regression-Based Weighted Signal-to-Noise Ratio(MRWSN) [J]. Quality Engineering, 22:336-350,2010.
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[37]Chao-Ton Su, Hsu-Hwa Chang. Optimization of parameter design:an intelligent approach using neural network and simulated annealing [J]. International Journal of System Science, 2000, volume 31, number 12, pages 1543-1549.
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[2]宗志宇,何桢,孔祥芬.产品设计中多响应优化方法的比较研究[J].组合机床与自动化加工技术,2005(12).
[3]宗志宇,何桢,孔祥芬.多响应优化方法的比较和应用研究[J].数理统计与管理,2006,11.
[4]张于轩.多响应问题的稳健性设计优化研究[D].天津大学硕士学位论文,2003.
[5]钟晓芳,韩之俊.利用主成分分析对多质量特性的优化设计[J].南京理工大学学报,2003,6.
[6]苏国进.动态多响应系统的文件设计研究[D].南京理工大学硕士学位论文,2010.
[7]王颖.基于TOPSIS方法的多元质量特性优化方法研究[D].天津大学博士学位论文,2007.
[8]Susanta Kumar Ganri,Shankar Chakraborty. Multi-response optimization of WEDM process using principal component analysis [J]. Int J Adv Manuf Technol (2009)41:741-748.
[9]Abbas Al-Refaie. Optimising correlated QCHs in robust design using principal component analysis and DEA techniques [J]. Production Planning & Control.2011:1-14.
[10]C.L.Lin, J.L.Lin, T.C.Ko. Optimization of EDM process based on the orthogonal array with fuzzy logic and grey relational analysis method [J]. Int J Adv Manuf Technol (2002)19:271-277.
[11]Chi-Ming Hsu. Solving multi-response problems through neural networks and principal component analysis [J]. Journal of the Chinese Institute of Industial Engineers, Vol.18, No.5, pp.47-54,2001.
[12]Hung-Chang Liao. Multi-response optimization using weighted principal component [J]. Int J Adv Manuf Technol (2006)27:720-725.
[13]Lee-Ing Tong,Chung-Ho Wang, Hung-Cheng Chen. Optimization of multiple response using principal component analysis and technique for order preference by similarity to ideal solution [J]. Int J Adv Manuf Technol (2005)27:407-414.
[14]J.L.Lin, C.L.Lin. The use of the orthogonal array with grey relational analysis to oprimize the electrical discharge machining process with multiple performance characteristics [J]. International Journal of Machine Tools & Manufacture,42:237-244,2002.
[15]Lee-Ing Tong, Chung-Ho Wang, Chih-Wei Tsai. Robust Design for Multiple Dynamic Quality Characteristics Using Data Envelopment Analysis [J]. Quality and reliability engineering international,24:557-571,2008.
[16]Lee-Ing Tong, Chung-Ho Wang, Hung-Cheng Chen. Optimization of multiple responses using principal component analysis and technique for order preference by similarity to ideal solution [J]. Int J Adv Manuf Technol,27:407-414,2005.
[17]A.Noorul Haq, P.Marimuthu, R.Jeyapaul. Multi-response optimization of machining parameters of drilling AL\SIC metal matrix composite using grey relational analysis in the Taguchi method [J]. Int J Adv Manuf Technol (2008)37:250-255.
[18]Rui Ding,Dennis K.J.Lin,Duan Wei. Dual-response Surface Optimization [J].QUALITY ENGINEERING, Vol.16, No.3, pp.377-385,2004.
[19]宗志宇.基于RSM的多响应稳健性设计方法的研究[D].天津大学博士学位论文,2007.
[20]何桢,张于轩.多响应试验设计的优化方法研究[J].工业工程,2003,7.
[21]宗志宇,何桢,孔祥芬.噪声因子存在下的多响应参数设计的优化[J].工业工程,2007,11.
[22]马彦辉,何桢,赵有.基于熵权理论和渴求函数法的多响应优化设计研究[J].组合机床与自动化加工技术,2007(2).
[23]何桢,赵有,马彦辉.基于遗传算法的多响应优化方法研究[J].计算机工业与应用,2007,43(31).
[24]耿金花,高齐圣,张嗣瀛.多因素、多指标产品系统的建模与优化[J].系统工程学报,2008,8.
[25]何桢,朱鹏飞.基于模式搜索的渴求函数法在多响应优化中的应用[J].数学的实践与认识,2009,9.
[26]朱鹏飞,何桢.混合模拟退火的多响应参数优化[J].工业工程与管理,2010,8.
[27]李旭.多响应优化方法研究[D].北京工业大学硕士学位论文,2009,5.
[28]汪建均,马义中,翟云焕.相关多质量特性的优化设计[J].管理工程学报,2011,2.
[29]汤禹成,周雄辉,陈军.基于神经网络响应曲面的预锻模具形状优化和再设计方法[J].上海交通大学学报,2007,4.
[30]J.L.Lin, K.S.Wang. Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics [J]. Journal of Materials Processing Technology,48-55, 2000.
[31]Chao-Tao Su, Tai-Lin Chiang. Optimizing the IC wire bonding process using a neural networks\genetic algorithms approach [J]. Journal of Intelligent Manufacturing,14,229-238, 2003.
[32]Lee-Ing Tong, Chi-Chan Chen, Chung-Ho Wang. Optimization of multi-response process using the VIKOR method [J]. Int J Adv Manuf Technol(2007)31:1049-1057.
[33]Wei-Jaw Deng. Integrating MRSN Ratio and ANPA to Optimization Process Parameter of Multiple-response Injection Molding Process [J]. Int J Adv Manuf Technol,2008.
[34]Surajit Pal, Susanta Kumar Gauri. Multi-Response Optimization Using Multiple Regression-Based Weighted Signal-to-Noise Ratio(MRWSN) [J]. Quality Engineering, 22:336-350,2010.
[35]Wen Wan, Jeffrey B.Birch. A Semiparametric Technique for the Multi-response Optimization Problem [J]. Quality and Reliability Engineering International,2010,4,6.
[36]Szu Hui NG. A Bayesian Model-Averaging Approach for Multi-Response Optimization [J]. Journal of Quality Technology,2010.
[37]Chao-Ton Su, Hsu-Hwa Chang. Optimization of parameter design:an intelligent approach using neural network and simulated annealing [J]. International Journal of System Science, 2000, volume 31, number 12, pages 1543-1549.
[38]R.Noorossana, Sam Davanloo Tajbakhsh, A.Saghaei. An artificial neural network approach to multiple-response optimization [J]. Int J Adv Manuf Technol (2009)19:1227-1238.
[39]Susanta Kumar Gauri, Rina Chakranorty,Shankar Chakraborty. Optimization of correlated multiple responses of ultrasonic maching process [J]. Int J Adv Manuf Technol (2011)53:1115-1127.
[40]Harry K.Shah,Douglas C.Montgomery, W.Matthew Carlyle. Response Surface Modeling and Optimization in Multiresponse Experiments Using Seemingly Unrelated Regressions [J]. Quality Engineering,3:387-397,2004.
[41]John J.Peterson, Guillermo Miro-Quesada, Enrique del Castillo. A Bayesian Reliability Approach to Multiple Response Optimization with Seemingly Unrelated Regression Models [J]. Quality Technology & Quantitative Management, Vol.6, No.4, pp.353-369,2009.
[42]Brian P.Weaver, Michael S.Hamada. A Bayesian Approach to the Analysis of Industrial Experiments:An Illustraion with Binomial Count Data [J].Quality Engineering,20:269-280, 2008.
[43]Guillermo Miro-Quesada, Enrique Del Castillo, John J.Peterson. A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variable [J]. Journal of Applied Statistics,2002,1
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