稳健设计建模及优化方法研究
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摘要
作为有效降低不确定性因素对产品质量影响的稳健设计理论日益引起诸多学者的关注。近年来随着科学技术以及工程实际的发展,需要对稳健设计理论做进一步的研究,以适应不同的工程问题。本文在国内外稳健设计研究的基础上,对稳健设计理论的建模及多目标优化做了进一步的研究和探讨,主要内容如下:
1)针对产品质量特性与不确定性因素之间关系未知的隐式工程问题,提出了基于混合响应面的稳健设计改进模型。该方法利用多项式响应面形式简单、计算效率高以及神经网络非线性适应程度好的特点,将二者结合研究了在不确定性因素影响下如何建立产品质量特性的显性表达式,从而达到减小计算量并提高计算精度的目的;利用线性物理规划改进了基于响应面的稳健设计模型。改进后稳健设计模型可以灵活的调节质量特性与波动之间的矛盾,得到设计人员对质量特性、波动均满意的设计方案,更符合实际的工程需要。
2)针对产品质量特性与不确定性因素之间关系已知的显式工程问题,提出了稳健设计的最大波动分析法,建立了最大波动分析法的交互式求解流程。提出的稳健设计模型不需要考虑设计变量、设计参数的分布类型,也不要求目标函数以及约束连续、可导等,对工程优化问题的数学模型要求不高,适用面广。交互式求解流程可以让设计者在目标函数值、目标函数波动以及约束的稳健可行程度之间进行自由选择。无论对于凸有效域还是凹有效域,均匀改变各设计目标的满意程度区间,都可以得到有效域中均匀分布的一组有效解。同时可以方便的进行程序化求解,减少人工干预的次数。
3)针对稳健设计目标函数与波动之间的冲突及协调问题,提出了基于改进遗传算法的多目标稳健设计方法。在考虑机械设计中大量存在的非连续性变量的前提下,改进了多目标遗传算法中Pareto解集过滤器,使得采用遗传算法求出的Pareto前沿面更加均匀,最大程度地给出Pareto最优解集,使决策者有更多的选择余地。提出了一种基于改进模糊折衷规划的多目标稳健设计方法,该方法能够分配每个目标的权重从而均衡目标函数值和波动之间的平衡,将决策者的偏好充分体现到决策过程中,进而有效得到决策者所期望的折衷解。
4)利用本文所提出的稳健设计模型研究了1.5MW风力发电齿轮增速器传动系统的优化设计。详细地分析了斜齿轮传动副中的可控及不可控因素;以保证斜齿轮的接触疲劳强度、弯曲疲劳强度的稳健可行性为基础,建立了斜齿轮副的稳健设计模型并进行了优化。设计结果表明利用传统设计方法得到的设计方案的最小安全系数有可能低于设计时规定的最小允许安全系数。而本文所提稳健设计模型则可以保证设计方案的最小安全系数不低于设计时规定的最小允许安全系数。
Robust design which is used to deal with the uncertain factors has been gaining increasing attentions to many researchers and is applied to many fields.Recently with the development of science technology and engineering it is significant to make a farther research about robust design.Based on the existent work in literatures the dissertation further develops the non-probabilistic robust design theory.The main content of this paper include the following aspects:
1)In most of practical engineering optimal problems,the relationships between quality characteristics and uncertain factors are unknown or complicated.A hybrid response surface method is proposed to solve this problem in robust design.By considering the simpleness of polynomial response surface method and compute precision and cost of artificial neural network method,a hybrid strategy of robust design is proposed,the strategy can balance the relationship between compute precision and cost;then use linear physical programming to adjust the values of objective function and variations.
2)Combining the maximal variation analysis and linear physical programming a new mathematic model of non-probabilistic robust design is proposed.In view of robustness of objective function and constraints in robust design,the principle of variations which are generated in objective functions and constraints are particularly analyzed,then estimates the maximal variations of objective function and constraints through the use of maximal variation analysis.A new constraint is added to original optimization problem to ensure the variation of objective function is less than the value which designer sets;the constraints are divided into three types,robustness index is used to adjust robustness of each constraint,and then a bi-level mathematical optimal model is constructed.The top-level optimization is used to solve the original mathematical model;the lower-level optimization is used to judge the robustness of objective function and constraints.The solutions obtained by the approach are feasible and compared with other robust optimal methods our method has the advantages that it is straightforward and doesn't require presumed probability distribution of uncertain factors or gradient information of the original mathematical optimal model.
3)The multiobjective robust design is studied.In view of multi-objective optimization problem in robust design,a method of multiobjective robust design based on improved genetic algorithms is given.The method consider mixed discrete variables in engineering optimization problems,the Pareto front can be more even by improving Pareto set filter in genetic algorithms.The method takes advantage of parallel computation and random search of genetic algorithms,make designers have more choices.A fuzzy compromise programming approach to determine the optimal solution of robust design is proposed.By using fuzzy preferences the proposed approach gives a global evaluation for conflicting objectives,takes into account the decision-maker's preference by his/her assigning weights to the objectives, and then gives a satisfied solution;
4) Using the theories and methods of robust design in this paper a real engineering problem about speed increasing gearbox for wind generator is studied,and the mathematic model about gear-driven system is built.The results show that the theories and methods in this paper are valid and practicable.
1)针对产品质量特性与不确定性因素之间关系未知的隐式工程问题,提出了基于混合响应面的稳健设计改进模型。该方法利用多项式响应面形式简单、计算效率高以及神经网络非线性适应程度好的特点,将二者结合研究了在不确定性因素影响下如何建立产品质量特性的显性表达式,从而达到减小计算量并提高计算精度的目的;利用线性物理规划改进了基于响应面的稳健设计模型。改进后稳健设计模型可以灵活的调节质量特性与波动之间的矛盾,得到设计人员对质量特性、波动均满意的设计方案,更符合实际的工程需要。
2)针对产品质量特性与不确定性因素之间关系已知的显式工程问题,提出了稳健设计的最大波动分析法,建立了最大波动分析法的交互式求解流程。提出的稳健设计模型不需要考虑设计变量、设计参数的分布类型,也不要求目标函数以及约束连续、可导等,对工程优化问题的数学模型要求不高,适用面广。交互式求解流程可以让设计者在目标函数值、目标函数波动以及约束的稳健可行程度之间进行自由选择。无论对于凸有效域还是凹有效域,均匀改变各设计目标的满意程度区间,都可以得到有效域中均匀分布的一组有效解。同时可以方便的进行程序化求解,减少人工干预的次数。
3)针对稳健设计目标函数与波动之间的冲突及协调问题,提出了基于改进遗传算法的多目标稳健设计方法。在考虑机械设计中大量存在的非连续性变量的前提下,改进了多目标遗传算法中Pareto解集过滤器,使得采用遗传算法求出的Pareto前沿面更加均匀,最大程度地给出Pareto最优解集,使决策者有更多的选择余地。提出了一种基于改进模糊折衷规划的多目标稳健设计方法,该方法能够分配每个目标的权重从而均衡目标函数值和波动之间的平衡,将决策者的偏好充分体现到决策过程中,进而有效得到决策者所期望的折衷解。
4)利用本文所提出的稳健设计模型研究了1.5MW风力发电齿轮增速器传动系统的优化设计。详细地分析了斜齿轮传动副中的可控及不可控因素;以保证斜齿轮的接触疲劳强度、弯曲疲劳强度的稳健可行性为基础,建立了斜齿轮副的稳健设计模型并进行了优化。设计结果表明利用传统设计方法得到的设计方案的最小安全系数有可能低于设计时规定的最小允许安全系数。而本文所提稳健设计模型则可以保证设计方案的最小安全系数不低于设计时规定的最小允许安全系数。
Robust design which is used to deal with the uncertain factors has been gaining increasing attentions to many researchers and is applied to many fields.Recently with the development of science technology and engineering it is significant to make a farther research about robust design.Based on the existent work in literatures the dissertation further develops the non-probabilistic robust design theory.The main content of this paper include the following aspects:
1)In most of practical engineering optimal problems,the relationships between quality characteristics and uncertain factors are unknown or complicated.A hybrid response surface method is proposed to solve this problem in robust design.By considering the simpleness of polynomial response surface method and compute precision and cost of artificial neural network method,a hybrid strategy of robust design is proposed,the strategy can balance the relationship between compute precision and cost;then use linear physical programming to adjust the values of objective function and variations.
2)Combining the maximal variation analysis and linear physical programming a new mathematic model of non-probabilistic robust design is proposed.In view of robustness of objective function and constraints in robust design,the principle of variations which are generated in objective functions and constraints are particularly analyzed,then estimates the maximal variations of objective function and constraints through the use of maximal variation analysis.A new constraint is added to original optimization problem to ensure the variation of objective function is less than the value which designer sets;the constraints are divided into three types,robustness index is used to adjust robustness of each constraint,and then a bi-level mathematical optimal model is constructed.The top-level optimization is used to solve the original mathematical model;the lower-level optimization is used to judge the robustness of objective function and constraints.The solutions obtained by the approach are feasible and compared with other robust optimal methods our method has the advantages that it is straightforward and doesn't require presumed probability distribution of uncertain factors or gradient information of the original mathematical optimal model.
3)The multiobjective robust design is studied.In view of multi-objective optimization problem in robust design,a method of multiobjective robust design based on improved genetic algorithms is given.The method consider mixed discrete variables in engineering optimization problems,the Pareto front can be more even by improving Pareto set filter in genetic algorithms.The method takes advantage of parallel computation and random search of genetic algorithms,make designers have more choices.A fuzzy compromise programming approach to determine the optimal solution of robust design is proposed.By using fuzzy preferences the proposed approach gives a global evaluation for conflicting objectives,takes into account the decision-maker's preference by his/her assigning weights to the objectives, and then gives a satisfied solution;
4) Using the theories and methods of robust design in this paper a real engineering problem about speed increasing gearbox for wind generator is studied,and the mathematic model about gear-driven system is built.The results show that the theories and methods in this paper are valid and practicable.
引文
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