基于“质量—成本”均衡的车身公差设计博弈模型及求解方法研究
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摘要
轿车车身是具有大批量生产和复杂制造系统特征的典型产品。零件的尺寸偏差对整车性能及制造成本均具有显著影响。盲目提高偏差要求，虽然保证了质量，但将使产品制造成本增加，造成投资浪费和市场竞争力下降；降低偏差要求，虽然减少了成本，但会影响最终产品质量，导致客户投诉和返修率上升。因此，制订合理的车身零部件公差设计方案，是均衡解决产品质量要求和生产成本限制之间矛盾的重要手段。传统车身公差设计主要采用的方法包括试凑与校核调整法、以质量为约束的成本最优法以及质量、成本的加权评价法等。这些方法难以合理、有效地考量不同性能指标之间的相互影响和冲突，从而在质量、成本多目标优化建模与均衡优化方面存在一定的局限性。
为了解决车身产品公差设计中质量与成本综合优化和均衡协调难题，弥补传统方法的不足，本文引入博弈理论，建立一套车身公差设计博弈建模及求解方法。首先，针对车身产品公差设计需求，提出车身公差设计问题及其相应模型的表达形式；其次，将车身公差设计工程问题转化为博弈数学模型；在此基础上，建立基于合作博弈Shapley值理论的公差设计求解方法，并结合典型车身设计案例进行了工程应用。本文的主要研究工作如下：
(1)基于“质量-成本”均衡的车身公差设计问题分类与表达
根据车身产品公差设计需求，将车身公差设计问题分为两类：面向制造工艺信息的车身公差设计问题与面向历史数据信息的车身公差设计问题。针对第一类问题，结合零件偏差传递规律以及不同公差等级所对应的生产消耗及加工条件的变化，提出表达装配产品质量水平的制造偏差模型和表达装配产品成本水平的制造成本模型；针对第二类问题，结合评价车身产品关键区域质量、成本的主要指标，提出零件和装配产品的质量水平和成本水平的表达方法。
(2)车身公差设计博弈模型构建
对于面向制造工艺信息的车身公差设计问题，首先将装配产品的质量、成本需求视为对策环境中的博弈方，其次针对设计变量与各博弈方之间的映射关系，基于模糊聚类方法将设计变量进行分组，并定义各博弈方的策略空间，最后根据制造偏差模型与制造成本模型建立各博弈方的效用函数。通过上述三要素构造完整的博弈模型及相应的博弈效用矩阵；对于面向历史数据信息的车身公差设计问题，首先根据评价车身关键区域质量、成本的主要指标，定义博弈决策方、博弈策略及博弈效用，从而建立初始博弈效用矩阵。根据搜集、整理的历史数据信息，通过多元回归分析的技术手段补充效用矩阵中的缺失数据，从而形成完备的博弈模型。
(3)车身公差设计博弈模型求解方法研究
针对车身公差设计的“质量-成本”均衡需求，提出基于Nash均衡理论的车身公差设计非合作博弈求解方法，用以求解面向个体效用最优下的公差设计方案；提出基于Shapley值理论的车身公差设计合作博弈求解方法，用以求解面向集体效用最优下的公差设计方案。通过对比和分析不同决策环境下的博弈求解方法与传统多目标优化方法的数学本质，研究了各种优化解之间的差异性和关联性，发现在处理车身公差设计多目标优化问题时，合作博弈方法能够根据质量和成本博弈方对“质量、成本综合性能最优”的贡献度评估，给出一种合理协调两者相互影响和冲突的设计方案，优化解不依赖于经验权值，并且稳定性较好。
(4)基于博弈理论的车身公差设计案例应用
在前面研究的基础上，开发基于“质量-成本”均衡的车身公差设计软件分析模块，并在前机舱水箱架总成和前部大灯区域的公差设计中应用。首先根据水箱架与大灯区域的质量、成本函数或数据信息，构建博弈方、策略和效用，形成博弈数学模型，进而通过合作博弈方法计算均衡点，并与传统多目标优化解进行对比分析。优化结果表明，合作博弈方法能够根据实际工程冲突给出一种合理、公平的“质量-成本”均衡方案，该方案不依赖于经验权值，并且具有较好的稳定性。通过案例应用，揭示了从工程问题表达、博弈模型构建到模型优化求解的车身公差设计全过程，验证了应用博弈理论解决车身公差设计问题的有效性和可靠性。
Automotive body is a kind of complex product that has the large-scalemanufacturing characteristics. Part tolerance is a crucial factor affecting productperformance and manufacturing cost. Tight tolerances can ensure good part quality,but simultaneously pose a high investment stress on the manufacturers. On contrary,loose tolerances may cause a series of problems such as the rework rate increase orcustomer complaints. Consequently, it is significant to develop a reasonable tolerancescheme considering the demands and conflicts of quality and cost. Traditionaltolerance design methods for automotive body products consist of the trial-designand revision method, the least cost method under the quality constraint and thecomprehensive evaluating method combining several optimization objectives withdifferent weights. These approaches may not be desirable as it is difficult toeffectively evaluate the interactive influences and the conflict among differentdemands.
Game theory is introduced into this research and a kind of auto-body tolerancedesign method based on game modelling and solving is established. The purpose is tobalance the quality and the cost demand and avoid the disadvantages of the traditionalmethods. This paper first describes the tolerance design problems and proposes thecorresponding theoretical models according to the research on the variation and thecost propagation. Then the engineering problem is converted to the game model.Further, the equilibrium points are calculated by the Shapley value method incooperative game. The solutions are also compared with the traditionalmulti-objective optimization methods. Finally, the feasibility of the procedure isdemonstrated through some engineering examples. Main research contents are shownas bellows.
(1) Classification and description of the tolerance design problems ofautomotive body based on the “quality-cost” trade-off
The tolerance design problems of automotive body are divided into twocategories: the tolerance design problem of automotive body based on the specific process information and the tolerance design problem of automotive body based onthe historical data information. For the first tolerance design problem, themanufacturing variation model and the manufacturing cost model are presentedconsidering the variation propagation rules and the process cost of different tolerancegrades. For the second tolerance design problem, common quality, cost evaluationapproaches of parts&assemblies in the automotive body manufacturing process arepresented.
(2) Establishment of the game models in the automotive body tolerancedesign
For the tolerance design problem of automotive body based on the specificprocess information, the quality and the cost requirement of the assembly product areconsidered as the game players. The corresponding game payoffs are established.Simultaneously, the tolerance design variables are divided into several groups usingthe fuzzy clustering theory. The game strategy belonging to each player is thendesigned. Finally, the game model (also described by a kind of game payoff matrix) isestablished. For the tolerance design problem of automotive body based on thehistorical data information, the game players, the game strategies and the gamepayoffs are defined by the common indicators that are used to evaluate the quality andthe cost level of parts&assemblies. A primary game payoff matrix is established.Then it is further transformed into a complete payoff matrix using the multipleregression analysis theory based on the measuring data.
(3) Solving methods of the game models in the automotive body tolerancedesign
The Nash equilibrium theory is first proposed to solve the game model based onthe optimal individual payoff. Then the Shapley value theory is presented to solve thegame model based on the optimal collective payoff. The game solution is comparedwith the traditional multi-objective optimization solutions in order to show thetheoretical and the engineering advantage of the game method on solving thetolerance design problems of automotive body. It can be considered to be a kind ofimportance evaluation of each player based on their contribution to the profit of thewhole coalition. The game method is not dependent on the weights and has goodstability.
(4) Application of the tolerance design of automotive body with game theory
The software module for the tolerance design of automotive body based on“quality-cost” trade-off is developed and introduced. The water tank supportassembly and the front lamp assembly are analyzed with the game method. First thequality and the cost information that are relevant to the tolerances of parts&assemblies are converted to the game components in order to form the game model.Further, the equilibrium points are calculated by the non-cooperative and thecooperative game method. The solutions are also compared with the traditionalmulti-objective optimization methods. The optimization conclusion indicates that akind of reasonable and fair tolerance scheme is obtained and it is not dependent on theweights and has good stability. The whole process of the game analysis from thedescription of the design problem to the game modeling and solving is shown. It canbe effective and reliable for the tolerance design of automotive body with gametheory.
为了解决车身产品公差设计中质量与成本综合优化和均衡协调难题，弥补传统方法的不足，本文引入博弈理论，建立一套车身公差设计博弈建模及求解方法。首先，针对车身产品公差设计需求，提出车身公差设计问题及其相应模型的表达形式；其次，将车身公差设计工程问题转化为博弈数学模型；在此基础上，建立基于合作博弈Shapley值理论的公差设计求解方法，并结合典型车身设计案例进行了工程应用。本文的主要研究工作如下：
(1)基于“质量-成本”均衡的车身公差设计问题分类与表达
根据车身产品公差设计需求，将车身公差设计问题分为两类：面向制造工艺信息的车身公差设计问题与面向历史数据信息的车身公差设计问题。针对第一类问题，结合零件偏差传递规律以及不同公差等级所对应的生产消耗及加工条件的变化，提出表达装配产品质量水平的制造偏差模型和表达装配产品成本水平的制造成本模型；针对第二类问题，结合评价车身产品关键区域质量、成本的主要指标，提出零件和装配产品的质量水平和成本水平的表达方法。
(2)车身公差设计博弈模型构建
对于面向制造工艺信息的车身公差设计问题，首先将装配产品的质量、成本需求视为对策环境中的博弈方，其次针对设计变量与各博弈方之间的映射关系，基于模糊聚类方法将设计变量进行分组，并定义各博弈方的策略空间，最后根据制造偏差模型与制造成本模型建立各博弈方的效用函数。通过上述三要素构造完整的博弈模型及相应的博弈效用矩阵；对于面向历史数据信息的车身公差设计问题，首先根据评价车身关键区域质量、成本的主要指标，定义博弈决策方、博弈策略及博弈效用，从而建立初始博弈效用矩阵。根据搜集、整理的历史数据信息，通过多元回归分析的技术手段补充效用矩阵中的缺失数据，从而形成完备的博弈模型。
(3)车身公差设计博弈模型求解方法研究
针对车身公差设计的“质量-成本”均衡需求，提出基于Nash均衡理论的车身公差设计非合作博弈求解方法，用以求解面向个体效用最优下的公差设计方案；提出基于Shapley值理论的车身公差设计合作博弈求解方法，用以求解面向集体效用最优下的公差设计方案。通过对比和分析不同决策环境下的博弈求解方法与传统多目标优化方法的数学本质，研究了各种优化解之间的差异性和关联性，发现在处理车身公差设计多目标优化问题时，合作博弈方法能够根据质量和成本博弈方对“质量、成本综合性能最优”的贡献度评估，给出一种合理协调两者相互影响和冲突的设计方案，优化解不依赖于经验权值，并且稳定性较好。
(4)基于博弈理论的车身公差设计案例应用
在前面研究的基础上，开发基于“质量-成本”均衡的车身公差设计软件分析模块，并在前机舱水箱架总成和前部大灯区域的公差设计中应用。首先根据水箱架与大灯区域的质量、成本函数或数据信息，构建博弈方、策略和效用，形成博弈数学模型，进而通过合作博弈方法计算均衡点，并与传统多目标优化解进行对比分析。优化结果表明，合作博弈方法能够根据实际工程冲突给出一种合理、公平的“质量-成本”均衡方案，该方案不依赖于经验权值，并且具有较好的稳定性。通过案例应用，揭示了从工程问题表达、博弈模型构建到模型优化求解的车身公差设计全过程，验证了应用博弈理论解决车身公差设计问题的有效性和可靠性。
Automotive body is a kind of complex product that has the large-scalemanufacturing characteristics. Part tolerance is a crucial factor affecting productperformance and manufacturing cost. Tight tolerances can ensure good part quality,but simultaneously pose a high investment stress on the manufacturers. On contrary,loose tolerances may cause a series of problems such as the rework rate increase orcustomer complaints. Consequently, it is significant to develop a reasonable tolerancescheme considering the demands and conflicts of quality and cost. Traditionaltolerance design methods for automotive body products consist of the trial-designand revision method, the least cost method under the quality constraint and thecomprehensive evaluating method combining several optimization objectives withdifferent weights. These approaches may not be desirable as it is difficult toeffectively evaluate the interactive influences and the conflict among differentdemands.
Game theory is introduced into this research and a kind of auto-body tolerancedesign method based on game modelling and solving is established. The purpose is tobalance the quality and the cost demand and avoid the disadvantages of the traditionalmethods. This paper first describes the tolerance design problems and proposes thecorresponding theoretical models according to the research on the variation and thecost propagation. Then the engineering problem is converted to the game model.Further, the equilibrium points are calculated by the Shapley value method incooperative game. The solutions are also compared with the traditionalmulti-objective optimization methods. Finally, the feasibility of the procedure isdemonstrated through some engineering examples. Main research contents are shownas bellows.
(1) Classification and description of the tolerance design problems ofautomotive body based on the “quality-cost” trade-off
The tolerance design problems of automotive body are divided into twocategories: the tolerance design problem of automotive body based on the specific process information and the tolerance design problem of automotive body based onthe historical data information. For the first tolerance design problem, themanufacturing variation model and the manufacturing cost model are presentedconsidering the variation propagation rules and the process cost of different tolerancegrades. For the second tolerance design problem, common quality, cost evaluationapproaches of parts&assemblies in the automotive body manufacturing process arepresented.
(2) Establishment of the game models in the automotive body tolerancedesign
For the tolerance design problem of automotive body based on the specificprocess information, the quality and the cost requirement of the assembly product areconsidered as the game players. The corresponding game payoffs are established.Simultaneously, the tolerance design variables are divided into several groups usingthe fuzzy clustering theory. The game strategy belonging to each player is thendesigned. Finally, the game model (also described by a kind of game payoff matrix) isestablished. For the tolerance design problem of automotive body based on thehistorical data information, the game players, the game strategies and the gamepayoffs are defined by the common indicators that are used to evaluate the quality andthe cost level of parts&assemblies. A primary game payoff matrix is established.Then it is further transformed into a complete payoff matrix using the multipleregression analysis theory based on the measuring data.
(3) Solving methods of the game models in the automotive body tolerancedesign
The Nash equilibrium theory is first proposed to solve the game model based onthe optimal individual payoff. Then the Shapley value theory is presented to solve thegame model based on the optimal collective payoff. The game solution is comparedwith the traditional multi-objective optimization solutions in order to show thetheoretical and the engineering advantage of the game method on solving thetolerance design problems of automotive body. It can be considered to be a kind ofimportance evaluation of each player based on their contribution to the profit of thewhole coalition. The game method is not dependent on the weights and has goodstability.
(4) Application of the tolerance design of automotive body with game theory
The software module for the tolerance design of automotive body based on“quality-cost” trade-off is developed and introduced. The water tank supportassembly and the front lamp assembly are analyzed with the game method. First thequality and the cost information that are relevant to the tolerances of parts&assemblies are converted to the game components in order to form the game model.Further, the equilibrium points are calculated by the non-cooperative and thecooperative game method. The solutions are also compared with the traditionalmulti-objective optimization methods. The optimization conclusion indicates that akind of reasonable and fair tolerance scheme is obtained and it is not dependent on theweights and has good stability. The whole process of the game analysis from thedescription of the design problem to the game modeling and solving is shown. It canbe effective and reliable for the tolerance design of automotive body with gametheory.
引文
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