高聚物成型工艺的系统优化设计及其并行计算
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摘要
注塑制品已经广泛的应用于通信产品、医疗器械、航空航天等高精尖领域中。而塑料产品的质量如制品的收缩、翘曲、残余应力、熔接线等以及生产过程中的功耗是模具和工艺设计中要考虑的主要指标。传统的模具设计方法主要依照设计者的经验以及反复试模来完成,不但成本很高,耗时长,而且靠试模来优化模具设计也是不现实的。结合计算机模拟技术与优化方法来提高制品质量是当前模具设计研究中的主流方向。然而由于高聚物成型过程复杂,过程参数众多,同时考虑众多的设计参数来对目标函数进行优化无论从精度还是效率都是对优化算法极大的挑战,本文针对高聚物成型优化设计存在的上述问题展开如下工作：
发展了一种高聚物成型优化设计的系统优化模型。通过引入了系统工程理念,根据各个工艺参数与模具设计对制品质量的影响模式,将优化问题划分为4个子系统：填充子系统、冷却子系统、保压子系统和系统层优化,每个子系统有着各自的目标函数与设计变量。与传统的成型工艺优化模型相比,系统优化模型综合考虑了众多成型工艺参数,在系统层内设置主要优化指标,如减少制品翘曲、提高填充率等；在子系统中根据注塑制品的特殊要求兼顾优化其它指标,如残余应力、注射压力和功耗等。数值算例表明该优化模型可以全面的提高制品的质量。基于各子系统模型的特点,设计了分级优化策略,将原有的高维优化问题划分为若干低维优化问题,填充、冷却和保压三个子系统的目标函数分析仅需调用模拟程序的一个分析子模块,因而大大的提高了优化效率。
针对高聚物成型优化特点,发展了相应的优化算法,其中包括改进的高斯过程代理模型加点准则和浇口位置的代理模型优化算法。
基于高斯过程的代理模型优化算法是当前用于求解一类隐函数优化问题的主要手段。在代理模型算法中,如何平衡全局搜索与局部搜索是一个主要的研究方向。本文在期望提高(EI:Expected Improvement)加点准则中引入了权积分函数,发展了一种可以灵活控制搜索尺度的单点加点准则,权积分期望提高(Weighting-Integral Expected Improvement, WIEI)。然后,通过定义等价优化问题,将具有不同搜索尺度的WIEI函数凝聚在一起得到了具有不同搜索尺度特征的新加点准则,该准则可以根据目标函数的复杂程度来自动选择搜索尺度。
针对复杂几何制品的浇口位置优化问题,通过引入流长的概念,建立了浇口位置的高斯过程代理模型,并结合上述加点准则发展了可以适应任何复杂几何制件的浇口位置黑箱优化算法。数值算例表明本文提出的优化算法均具有较高的优化效率和稳定性。
为适应大规模计算的需要,将并行计算技术应用到高聚物成型优化中,分别在优化算法级别和模拟级别上提出了相应的并行算法。
在优化算法级别上,提出了一种并行的代理模型优化算法,通过在单点加点准则中引入交互信息的概念构造惩罚函数,得到了可以同时考虑单个样本的适应度以及样本总体信息量的多点加点准则。另外针对高斯过程模型在处理大规模样本时所存在的计算困难,提出了一种区域分解优化策略,首先通过主成分分析的方法将样本空间划分为若干子空间。然后,在每个子空间内以及距离邻近该空间的区域选择样本建立优化模型并结合多点加点准则来搜索新的样本点。
为克服注塑填充区域随时间变化的困难,提出了一种高聚物填充过程的并行模拟算法。首先基于聚类的思想设计了填充过程的区域分解算法将计算区域划分为若干子区域,通过定义负载平衡模型和边界控制模型来提高并行效率和降低通信量。在区域分解的基础上,各个子区域可以并行的完成控制方程的组集过程。然后,通过对节点的分类,设计一个超松弛迭代算法来求解有限元方程控制方程。
本文工作得到国家自然科学基金重大项目《高聚物成型加工与模具设计中的关键力学和工程问题》(No.10590354)和《国家重点基础研究发展规划》项目“高聚物成型模拟及模具设计制造中的关键问题研究”中“高聚物成型工艺和模具设计优化”课题(No.2012CB025905)的资助。
Plastic injection molding (PIM) has been widely used in high-tech industries, such as the3C (Computer, Communication, and Consumer-Electronics), automotive and medicinal industries. The quality issues of the product (the shrinkage, the warpage, the residual stress and the weld lines) and the energy cost of the productive process are the main concerns in the design of the PIM process. The traditional ways of mold design and selecting the processing parameters are mainly depended on the experience of the designer and engineers. The designing process may be very expensive and time consuming. Optimizing the mold design and molding process with computer aided engineering (CAE) technology has been proved as an effective way to improve the quality of products. However, because of the complexity of the molding process and the design parameters, considering all the design parameters simultaneously in the optimization problem often involves huge computational effort and lead to a highly demand for the optimizing method.
A system-based optimization model of injection process is proposed. The optimization of the mold and molding process is divided into4sub-systems:the filling sub-system, the cooling sub-system, the packing-subsystem and the system-level problem. Each sub-system has its own objective and design parameters, and objectives of the first three sub-systems can be evaluated by only one sub-model of the simulation program. A coupling optimization strategy is used to solve this system-based model. Comparing with the traditional models, the system-based model is able to consider more design parameters and objectives. The numerical results show that the system-based model has much higher computing efficiency.
A modified Gaussian process surrogate-model based optimization method (GPSBOM) is developed to solve the optimization problem in each sub-system, in which a new infill sample criteria (ISC) and a Gaussian process (GP) model for the gate location optimization problem are also involved.
The balancing between the global exploration and local exploitation has been a main concern in GPSBOM. A weighting function is introduced to improve the "expected improvement (EI)" method, and a new ISC named weighting-integral expected improvement (WIEI) is proposed. The WIEI provides a high flexibility to control the search scope. By defining an equivalent optimization problem, the WIEI functions with different search scopes are condensed into one ISC which is able to select a proper search scope based on the complexity of the optimization problem.
For the gate location optimization problem, the "flow path" is introduced to calculate the correlation model between different locations. With this correlation model, the GP surrogate-model of the gate location can be established. The ISC mentioned above can be used in this GP model in the GPSBOM. This proposed gate location optimization method has three advantages:the objectives can be selected based on the demand, it can be applicable to the gate location design with the complexity of the product's geometry, and can be solved by GPSBOM efficiently.
The parallel computing methods for the optimization process are also studied, that a parallel GPSBOM is developed, and the simulation of filling process is also parallelized.
By introducing the concept of "mutual information", a parallel ISC named EI&MI is developed. The EI&MI considers both the El value of each new sample and the total information of them all. Because that establishing the GP model with a large number of samples may lead to huge computational effort, a domain decomposition optimization strategy is proposed in which the design space is divided into several sub-spaces by primary component analysis method. Then in each sub-space the GP model is established based on the inner and neighboring samples, and the new samples can be searched based on the EI&MI. The numerical results show that the proposed parallel optimization method is able to solve the very complex problem efficiently.
The parallel computing method of filling process is studied. First, based on the cluster method, a domain decomposition algorithm is developed to divide the computation domain into several sub-domains. A domain decomposition model of both "load balance" and "boundary control" is proposed to improve the parallel efficiency and reduce the communication amount. The system equations of each sub-domain can be assembled parallelized. Then by classifying the nodes, a parallel successive over relaxation (SOR) algorithm is developed to solve the system equations. Numerical results show that the method gives a high efficiency, and it is suitable for numerically simulating the injection molding filling process.
The author gratefully acknowledges financial support for this work from the Major program (No.10590354) and the National Natural Science Foundation of China and the National Basic Research Program of China (No.2012CB025905).
发展了一种高聚物成型优化设计的系统优化模型。通过引入了系统工程理念,根据各个工艺参数与模具设计对制品质量的影响模式,将优化问题划分为4个子系统：填充子系统、冷却子系统、保压子系统和系统层优化,每个子系统有着各自的目标函数与设计变量。与传统的成型工艺优化模型相比,系统优化模型综合考虑了众多成型工艺参数,在系统层内设置主要优化指标,如减少制品翘曲、提高填充率等；在子系统中根据注塑制品的特殊要求兼顾优化其它指标,如残余应力、注射压力和功耗等。数值算例表明该优化模型可以全面的提高制品的质量。基于各子系统模型的特点,设计了分级优化策略,将原有的高维优化问题划分为若干低维优化问题,填充、冷却和保压三个子系统的目标函数分析仅需调用模拟程序的一个分析子模块,因而大大的提高了优化效率。
针对高聚物成型优化特点,发展了相应的优化算法,其中包括改进的高斯过程代理模型加点准则和浇口位置的代理模型优化算法。
基于高斯过程的代理模型优化算法是当前用于求解一类隐函数优化问题的主要手段。在代理模型算法中,如何平衡全局搜索与局部搜索是一个主要的研究方向。本文在期望提高(EI:Expected Improvement)加点准则中引入了权积分函数,发展了一种可以灵活控制搜索尺度的单点加点准则,权积分期望提高(Weighting-Integral Expected Improvement, WIEI)。然后,通过定义等价优化问题,将具有不同搜索尺度的WIEI函数凝聚在一起得到了具有不同搜索尺度特征的新加点准则,该准则可以根据目标函数的复杂程度来自动选择搜索尺度。
针对复杂几何制品的浇口位置优化问题,通过引入流长的概念,建立了浇口位置的高斯过程代理模型,并结合上述加点准则发展了可以适应任何复杂几何制件的浇口位置黑箱优化算法。数值算例表明本文提出的优化算法均具有较高的优化效率和稳定性。
为适应大规模计算的需要,将并行计算技术应用到高聚物成型优化中,分别在优化算法级别和模拟级别上提出了相应的并行算法。
在优化算法级别上,提出了一种并行的代理模型优化算法,通过在单点加点准则中引入交互信息的概念构造惩罚函数,得到了可以同时考虑单个样本的适应度以及样本总体信息量的多点加点准则。另外针对高斯过程模型在处理大规模样本时所存在的计算困难,提出了一种区域分解优化策略,首先通过主成分分析的方法将样本空间划分为若干子空间。然后,在每个子空间内以及距离邻近该空间的区域选择样本建立优化模型并结合多点加点准则来搜索新的样本点。
为克服注塑填充区域随时间变化的困难,提出了一种高聚物填充过程的并行模拟算法。首先基于聚类的思想设计了填充过程的区域分解算法将计算区域划分为若干子区域,通过定义负载平衡模型和边界控制模型来提高并行效率和降低通信量。在区域分解的基础上,各个子区域可以并行的完成控制方程的组集过程。然后,通过对节点的分类,设计一个超松弛迭代算法来求解有限元方程控制方程。
本文工作得到国家自然科学基金重大项目《高聚物成型加工与模具设计中的关键力学和工程问题》(No.10590354)和《国家重点基础研究发展规划》项目“高聚物成型模拟及模具设计制造中的关键问题研究”中“高聚物成型工艺和模具设计优化”课题(No.2012CB025905)的资助。
Plastic injection molding (PIM) has been widely used in high-tech industries, such as the3C (Computer, Communication, and Consumer-Electronics), automotive and medicinal industries. The quality issues of the product (the shrinkage, the warpage, the residual stress and the weld lines) and the energy cost of the productive process are the main concerns in the design of the PIM process. The traditional ways of mold design and selecting the processing parameters are mainly depended on the experience of the designer and engineers. The designing process may be very expensive and time consuming. Optimizing the mold design and molding process with computer aided engineering (CAE) technology has been proved as an effective way to improve the quality of products. However, because of the complexity of the molding process and the design parameters, considering all the design parameters simultaneously in the optimization problem often involves huge computational effort and lead to a highly demand for the optimizing method.
A system-based optimization model of injection process is proposed. The optimization of the mold and molding process is divided into4sub-systems:the filling sub-system, the cooling sub-system, the packing-subsystem and the system-level problem. Each sub-system has its own objective and design parameters, and objectives of the first three sub-systems can be evaluated by only one sub-model of the simulation program. A coupling optimization strategy is used to solve this system-based model. Comparing with the traditional models, the system-based model is able to consider more design parameters and objectives. The numerical results show that the system-based model has much higher computing efficiency.
A modified Gaussian process surrogate-model based optimization method (GPSBOM) is developed to solve the optimization problem in each sub-system, in which a new infill sample criteria (ISC) and a Gaussian process (GP) model for the gate location optimization problem are also involved.
The balancing between the global exploration and local exploitation has been a main concern in GPSBOM. A weighting function is introduced to improve the "expected improvement (EI)" method, and a new ISC named weighting-integral expected improvement (WIEI) is proposed. The WIEI provides a high flexibility to control the search scope. By defining an equivalent optimization problem, the WIEI functions with different search scopes are condensed into one ISC which is able to select a proper search scope based on the complexity of the optimization problem.
For the gate location optimization problem, the "flow path" is introduced to calculate the correlation model between different locations. With this correlation model, the GP surrogate-model of the gate location can be established. The ISC mentioned above can be used in this GP model in the GPSBOM. This proposed gate location optimization method has three advantages:the objectives can be selected based on the demand, it can be applicable to the gate location design with the complexity of the product's geometry, and can be solved by GPSBOM efficiently.
The parallel computing methods for the optimization process are also studied, that a parallel GPSBOM is developed, and the simulation of filling process is also parallelized.
By introducing the concept of "mutual information", a parallel ISC named EI&MI is developed. The EI&MI considers both the El value of each new sample and the total information of them all. Because that establishing the GP model with a large number of samples may lead to huge computational effort, a domain decomposition optimization strategy is proposed in which the design space is divided into several sub-spaces by primary component analysis method. Then in each sub-space the GP model is established based on the inner and neighboring samples, and the new samples can be searched based on the EI&MI. The numerical results show that the proposed parallel optimization method is able to solve the very complex problem efficiently.
The parallel computing method of filling process is studied. First, based on the cluster method, a domain decomposition algorithm is developed to divide the computation domain into several sub-domains. A domain decomposition model of both "load balance" and "boundary control" is proposed to improve the parallel efficiency and reduce the communication amount. The system equations of each sub-domain can be assembled parallelized. Then by classifying the nodes, a parallel successive over relaxation (SOR) algorithm is developed to solve the system equations. Numerical results show that the method gives a high efficiency, and it is suitable for numerically simulating the injection molding filling process.
The author gratefully acknowledges financial support for this work from the Major program (No.10590354) and the National Natural Science Foundation of China and the National Basic Research Program of China (No.2012CB025905).
引文
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