模型参数不确定的多响应参数和容差并行设计
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摘要
针对模型参数不确定性问题,提出了一种考虑质量损失和制造成本的多响应参数和容差并行设计策略。首先,根据模型参数不确定与设计变量容差,构建多响应的质量损失函数;其次,通过试验数据建立容差成本模型,进而构建参数和容差并行设计的优化目标函数;然后,根据多目标优化算法得到最优参数和容差的Pareto解集,并采用单因素多元方差分析进行容差配置;最后,通过实际案例分析表明,该方法不仅改善了模型的预测性和稳健性能,而且获得了质量损失与制造成本之间的最佳平衡点,与传统的方法相比,能够在显著降低总成本的同时提高产品质量。
A multi-response parameters and tolerances concurrent optimization strategy,considering quality loss and manufacturing cost,is proposed to solve the problem of model parameter uncertainty.Firstly,multiresponse quality loss function is developed based on model parameter uncertainty and the tolerances of design variables.Secondly,tolerance cost model is built according to experimental data,and then the concurrent optimization objective function of parameters and tolerance design is proposed.Optimal Pareto solutions for the optimal parameters and tolerances are obtained from multi-objective optimization algorithm,and one-factor multivariate analysis of variance is used to allocate tolerances.Finally,apractical example demonstrates that the proposed method not only can improve robustness and the performance of the model prediction,but also can maintain the optimal tradeoffs between quality loss and manufacturing cost.That is,the proposed method performs better than traditional methods on quality improvement and cost reduction.
A multi-response parameters and tolerances concurrent optimization strategy,considering quality loss and manufacturing cost,is proposed to solve the problem of model parameter uncertainty.Firstly,multiresponse quality loss function is developed based on model parameter uncertainty and the tolerances of design variables.Secondly,tolerance cost model is built according to experimental data,and then the concurrent optimization objective function of parameters and tolerance design is proposed.Optimal Pareto solutions for the optimal parameters and tolerances are obtained from multi-objective optimization algorithm,and one-factor multivariate analysis of variance is used to allocate tolerances.Finally,apractical example demonstrates that the proposed method not only can improve robustness and the performance of the model prediction,but also can maintain the optimal tradeoffs between quality loss and manufacturing cost.That is,the proposed method performs better than traditional methods on quality improvement and cost reduction.
引文
[1]MONTGOMERY D C.Design and analysis of experiments[M].New York:Wiley,2017.
[2]顾晓光,马义中,刘健,等.基于单值数据过程能力指数的多元质量特性稳健参数设计[J].系统工程与电子技术,2017,39(2):362-368.GU X G,MA Y Z,LIU J,et al.Robust parameter design for multivariate quality characteristics based on process capability index with individual observations[J].Systems Engineering and Electronics,2017,39(2):362-368.
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[5]HAN M,TAN M H Y.Optimal robust and tolerance design for computer experiments with mixture proportion inputs[J].Quality and Reliability Engineering International,2017,39(2):2255-2267.
[6]MOSKOWITZ H,PLANTE R,DUFFY J.Multivariate tolerance design using quality loss[J].IIE Transactions,2001,33(6):437-448.
[7]PLANTE R.Multivariate tolerance design for a quadratic design parameter model[J].IIE Transactions,2002,34(6):565-571.
[8]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,2008,23(4):449-454.GENG J H,GAO Q S,ZHANG S Y.Modeling and optimization of multi-factor and multi-index product system[J].Journal of Systems Engineering,2008,23(4):449-454.
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[11]LEE D H,JEONG I J.IP-MRSO:an iterative posterior preference articulation method to multiple response surface optimization[J].Quality and Reliability Engineering International,2017,33(8):1813-1826.
[12]XIE W,NELSON B L,BARTON R R.A Bayesian framework for quantifying uncertainty in stochastic simulation[J].Operations Research,2014,62(6):1439-1452.
[13]NG S H.A Bayesian model-averaging approach for multiple-response optimization[J].Journal of Quality Technology,2010,42(1):52-68.
[14]OUYANG L H,MA Y Z,BYUN J H,et al.An interval approach to robust design with parameter uncertainty[J].International Journal of Production Research,2016,54(11):3201-3215.
[15]OUYANG L H,MA Y Z,WANG J J,et al.A new loss function for multi-response optimization with model parameter uncertainty and implementation errors[J].European Journal of Operational Research,2017,258(2):552-563.
[16]ZHAO Y M,LIU D S,WEN Z J.Optimal tolerance design of product based on service quality loss[J].The International Journal of Advanced Manufacturing Technology,2016,82(9):1715-1724.
[17]SHAH H K,MONTGOMERY D C,CARLYLE W M.Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions[J].Quality Engineering,2004,16(3):387-397.
[18]ZELLNER A.An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias[J].Journal of the American Statistical Association,1962,57(298):348-368.
[19]JR PIGNATIELLO J J.Strategies for robust multiresponse quality engineering[J].IIIE Transactions,1993,25(3):5-15.
[20]VINING G G.A compromise approach to multiresponse optimization[J].Journal of Quality Technology,1998,30(4):309-313.
[21]KO Y H,KIM K J,JUN C H.A new loss function-based method for multiresponse optimization[J].Journal of Quality Technology,2005,37(1):50-59.
[22]CHASE K W,GREENWOOD W H,LOOSLI B G,et al.Least cost tolerance allocation for mechanical assemblies with automated process selection[J].Manufacturing Review,1990,3(1):49-59.
[23]CHIANG J Y,TSAI T R,LIO Y L,et al.An integrated approach for the optimization of tolerance design and quality cost[J].Computers&Industrial Engineering,2015,87:186-192.
[24]LIU S,JIN Q,DONG Y,et al.A closed-form method for statistical tolerance allocation considering quality loss and different kinds of manufacturing cost functions[J].The International Journal of Advanced Manufacturing Technology,2017,93(5):2801-2811.
[25]ALIKAR N,MOUSAVI S M,GHAZILLA R A R,et al.Application of the NSGA-Ⅱalgorithm to a multi-period inventoryredundancy allocation problem in a series-parallel system[J].Reliability Engineering&System Safety,2017,160:1-10.
[26]JOHNSON R A,WICHERN D W.Applied multivariate statistical analysis[M].New Jersey:Prentice-Hall,2014.
[27]HAMIDA I B,SALAH S B,MSAHLI F,et al.Distribution network reconfiguration using SPEA2for power loss minimization and reliability improvement[J].International Journal of Energy Optimization and Engineering,2018,7(1):50-65.
[28]ZHANG Q F,LI H.MOEA/D:a multi-objective evolutionary algorithm based on decomposition[J].IEEE Trans.on Evolutionary Computation,2007,11(6):712-731.
[29]WANG S,ALI S,YUE T,et al.Integrating weight assignment strategies with NSGA-Ⅱfor supporting user preference multi-objective optimization[J].IEEE Trans.on Evolutionary Computation,2018,22(3):378-393.
[30]ZHANG J X,MA Y Z,YANG T H,et al.Estimation of the Pareto front in stochastic simulation through stochastic Kriging[J].Simulation Modelling Practice and Theory,2017,79:69-86.
[2]顾晓光,马义中,刘健,等.基于单值数据过程能力指数的多元质量特性稳健参数设计[J].系统工程与电子技术,2017,39(2):362-368.GU X G,MA Y Z,LIU J,et al.Robust parameter design for multivariate quality characteristics based on process capability index with individual observations[J].Systems Engineering and Electronics,2017,39(2):362-368.
[3]LI W,WU C F J.An integrated method of parameter design and tolerance design[J].Quality Engineering,1999,11(3):417-425.
[4]HAN M,TAN M H Y.Integrated parameter and tolerance de-sign with computer experiments[J].IIE Transactions,2016,48(11):1004-1015.
[5]HAN M,TAN M H Y.Optimal robust and tolerance design for computer experiments with mixture proportion inputs[J].Quality and Reliability Engineering International,2017,39(2):2255-2267.
[6]MOSKOWITZ H,PLANTE R,DUFFY J.Multivariate tolerance design using quality loss[J].IIE Transactions,2001,33(6):437-448.
[7]PLANTE R.Multivariate tolerance design for a quadratic design parameter model[J].IIE Transactions,2002,34(6):565-571.
[8]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,2008,23(4):449-454.GENG J H,GAO Q S,ZHANG S Y.Modeling and optimization of multi-factor and multi-index product system[J].Journal of Systems Engineering,2008,23(4):449-454.
[9]MA B,LEI G,LIU C C,et al.Robust tolerance design optimization of a PM claw pole motor with soft magnetic composite cores[J].IEEE Trans.on Magnetics,2018,54(3):1-4.
[10]HAZRATI-MARANGALOO H,SHAHRIARI H.A novel approach to simultaneous robust design of product parameters and tolerances using quality loss and multivariate ANOVA concepts[J].Quality and Reliability Engineering International,2017,33(1):71-85.
[11]LEE D H,JEONG I J.IP-MRSO:an iterative posterior preference articulation method to multiple response surface optimization[J].Quality and Reliability Engineering International,2017,33(8):1813-1826.
[12]XIE W,NELSON B L,BARTON R R.A Bayesian framework for quantifying uncertainty in stochastic simulation[J].Operations Research,2014,62(6):1439-1452.
[13]NG S H.A Bayesian model-averaging approach for multiple-response optimization[J].Journal of Quality Technology,2010,42(1):52-68.
[14]OUYANG L H,MA Y Z,BYUN J H,et al.An interval approach to robust design with parameter uncertainty[J].International Journal of Production Research,2016,54(11):3201-3215.
[15]OUYANG L H,MA Y Z,WANG J J,et al.A new loss function for multi-response optimization with model parameter uncertainty and implementation errors[J].European Journal of Operational Research,2017,258(2):552-563.
[16]ZHAO Y M,LIU D S,WEN Z J.Optimal tolerance design of product based on service quality loss[J].The International Journal of Advanced Manufacturing Technology,2016,82(9):1715-1724.
[17]SHAH H K,MONTGOMERY D C,CARLYLE W M.Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions[J].Quality Engineering,2004,16(3):387-397.
[18]ZELLNER A.An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias[J].Journal of the American Statistical Association,1962,57(298):348-368.
[19]JR PIGNATIELLO J J.Strategies for robust multiresponse quality engineering[J].IIIE Transactions,1993,25(3):5-15.
[20]VINING G G.A compromise approach to multiresponse optimization[J].Journal of Quality Technology,1998,30(4):309-313.
[21]KO Y H,KIM K J,JUN C H.A new loss function-based method for multiresponse optimization[J].Journal of Quality Technology,2005,37(1):50-59.
[22]CHASE K W,GREENWOOD W H,LOOSLI B G,et al.Least cost tolerance allocation for mechanical assemblies with automated process selection[J].Manufacturing Review,1990,3(1):49-59.
[23]CHIANG J Y,TSAI T R,LIO Y L,et al.An integrated approach for the optimization of tolerance design and quality cost[J].Computers&Industrial Engineering,2015,87:186-192.
[24]LIU S,JIN Q,DONG Y,et al.A closed-form method for statistical tolerance allocation considering quality loss and different kinds of manufacturing cost functions[J].The International Journal of Advanced Manufacturing Technology,2017,93(5):2801-2811.
[25]ALIKAR N,MOUSAVI S M,GHAZILLA R A R,et al.Application of the NSGA-Ⅱalgorithm to a multi-period inventoryredundancy allocation problem in a series-parallel system[J].Reliability Engineering&System Safety,2017,160:1-10.
[26]JOHNSON R A,WICHERN D W.Applied multivariate statistical analysis[M].New Jersey:Prentice-Hall,2014.
[27]HAMIDA I B,SALAH S B,MSAHLI F,et al.Distribution network reconfiguration using SPEA2for power loss minimization and reliability improvement[J].International Journal of Energy Optimization and Engineering,2018,7(1):50-65.
[28]ZHANG Q F,LI H.MOEA/D:a multi-objective evolutionary algorithm based on decomposition[J].IEEE Trans.on Evolutionary Computation,2007,11(6):712-731.
[29]WANG S,ALI S,YUE T,et al.Integrating weight assignment strategies with NSGA-Ⅱfor supporting user preference multi-objective optimization[J].IEEE Trans.on Evolutionary Computation,2018,22(3):378-393.
[30]ZHANG J X,MA Y Z,YANG T H,et al.Estimation of the Pareto front in stochastic simulation through stochastic Kriging[J].Simulation Modelling Practice and Theory,2017,79:69-86.