近似模型优化体系关键技术研究及应用
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摘要
基于近似模型的优化方法是求解大规模非线性问题最有希望的方法之一,鉴于其高效性,广泛应用于工程优化领域。如果能够高效建立可靠的近似模型,很多大规模工程问题便可以迎刃而解。近年来,随着研究的深入,研究对象的规模和复杂度也日益增强。目前该领域的研究现状是:对于大规模非线性问题的求解,
近似模型技术还缺乏有效的手段。因此,虽然目前基于近似模型技术的优化领域非常活跃,基于近似模型技术的优化方法也多种多样,但对于高维非线性的实际工程优化问题,目前的近似模型技术还缺乏快速构建最大限度反映研究对象的特性模型的手段,这也是近似模型技术研究领域面临的最大瓶颈,阻碍了该技术在工业领域的应用和发展。
近似模型优化技术由三个基本阶段构成:实验设计,近似模型构建,基于近似模型的优化。鉴于工程问题的复杂性和多样性,建立一种通用的近似模型构造体系是非常困难的。因此,目前基于近似模型技术的优化方法都具有一定的针对性,当涉及到不同类型的具体工程优化问题,需要根据问题的特殊性,合理构建可行的优化策略。为此,本文将车辆工程优化设计的难点金属板料成形和车辆耐撞性作为主要实际工程应用研究。以近似模型的精度和效率作为算法的主要评价标准,对近似模型的实验设计和构建这两个方面进行了理论研究。本论文的主要创新点包括以下几个方面:
(一)智能实验设计方法
针对目前“离线”实验设计方法的技术瓶颈,建立了两种“在线”实验设计方法。这类布点方法不仅仅是单纯的实验设计方法,实质上也是一个优化过程,通过近似模型的精度和优化结果确定布点的方向,即将布点过程自动化和智能化。其中粒子群智能布点方法是基于粒子群优化理论建立的一种智能布点方法,将修正后的粒子群优化技术用于新样本的定位;而基于边界条件和最优邻域的智能布点方法则是根据初始样本的边界信息以及设计空间中当前样本的邻域内最优样本生成新样本。为了克服初始设计空间的主观因素,建立了相应的设计空间更新和判断机制,使其能够更为客观地确定新样本的位置。此外,为了提高布点效率,提出了并行智能布点方法,通过对初始样本点数目的扩展,达到提高精度,加快速度的目的。随后,将以上研发的算法同主流实验方法进行了性能比较,通过对多维非线性函数的测试来确认算法的可行性。测试数据表明:智能实验设计方法能够控制更新样本空间,优化样本质量,进而提高后续近似模型的精度和构建效率。
(二)基于概率的最小二乘支持向量回归
主流近似模型技术多数建立在经验风险最小化准则之上,但经验风险最小并不一定意味着期望风险最小。这类近似模型技术的瓶颈是:试图用十分复杂的模型去拟合有限的样本,导致丧失了推广能力,难以反映研究目标的实质和特性。为此,本文以泛化性能出色的基于统计学习理论的支持向量机技术构造近似模型,建立基于概率的最小二乘支持向量回归算法,通过权系数对误差带的控制实现对模型精度的控制。实质上是通过赋予异常样本较小的加权系数,将噪声样本对模型的性能的影响减少到最小的策略,算法的稳健性取决于建模过程中对异常样本的检测和剔除效果。通过基于最小二乘支持向量机回归方法和基于概率的最小二乘支持向量机回归方法对非线性函数的拟合测试,两种方法的性能都有显著地提高,能够克服噪声对函数精度的影响。因此,基于概率的最小二乘支持向量机回归方法是一种可行的近似模型设计方法。
(三)基于响应函数的空间映射技术
作为自成体系的一个优化流派,空间映射技术近年来发展迅猛。空间映射技术的最大瓶颈在于其参数提取技术,即如何确定精细模型的初始解在粗糙空间中对应解。通过对主流的空间映射方法的分析和验证,其关系具有较强的随机性,进而导致优化结果的不准确、甚至不收敛。针对这一问题,本文提出了基于响应函数的空间映射技术,同传统的空间映射相比,其最大特点是建立响应函数间的空间映射,并通过反求算法获得最优设计参数。因此,避免了易造成误差和难以收敛的根本因素——参数提取过程,使空间映射方法更为直接。通过对非线性函数的测试结果表明,本文提出的空间映射技术的精度和收敛性均有大幅度提高。
(四)基于近似模型技术的优化方法在金属板料成形中的应用
金属板料成形过程是一种包括几何非线性,材料非线性,边界条件非线性,且变形机制非常复杂的高度非线性问题。利用提出的智能布点方法、近似模型构造技术以及基于响应的空间映射算法,建立了高效精确的板料成形近似模型优化体系,用以提高对板料成形过程的控制能力、板料成形性的优化精度、生产效率及缩短产品开发周期等方面均具有显著的优越性,有积极的现实意义。
(五)基于时序的近似模型构造体系及其在车辆耐撞性优化中的应用
基于时序问题的近似模型技术充分考虑时间和空间因素,将设计空间进行拓展,在考虑样本历史信息的前提下构建时空两重性的近似模型。该技术的最大特点在于可控性,通过对设计变量的修正,进而完成研究对象在敏感时间域内的控制,是一种针对过程的可控优化技术。研究目标主要是与时序相关的物理过程,而汽车CAE设计中的车辆耐撞性研究则是非常典型的问题,为此,本章将其应用于该问题的优化,得到了令人满意的结果。
Metamodel-based optimization is one of the most popular and hopeful methods which can solve large scale engineering problems. According to its efficiency, the metamodel-based optimization method is widely applied for engineering optimization problems. Many large scale engineering problems can be done well if the metamodel-based optimization runs efficiently and stable. With the development of in-depth research, the scale and complexity of engineering problems are increasingly improved correspondingly. Although several kinds of metamodeling techniques have been approached, it is still difficult to solve practical engineering problems by current developed metamodeling technologies, especially for large-scale nonlinear problems. The major bottleneck of current developed metamodeling techniques is that how to construct accurate metamodel efficiently and how to balance the relationship between the accuracy and efficiency.
The metamodel-based optimization frame is composed of three phases: design of experiment (DOE), construction of metamodel and optimization. Due to the complexity and variety of practical engineering problems, it is impossible to develop a general metamodel method. Therefore, existing metamodeling techniques commonly possess special characteristics for different kinds of engineering problems. According to features of an engineering problem, the feasible way is to propose a type-specific strategy.
According to the metamodel-based optimization, the key factors are the accuracy and efficiency of metamodels. As long as a reliable and accurate metamodel is constructed, the corresponding optimum solution should be easy to achieve. Thus, the emphases of this thesis are DOE, metamodeling technique and time-based metamodeling strategy.
The major innovative suggestions are summarized as follows Intelligent DOE
According to the technique of the popular off-line design of experiment, two on-line DOE are suggested. The on-line sampling strategies are not purely DOEs based on statistical theories; these kinds of strategies are learning procedure essentially. The on-line sampling strategies use responses derived from evaluations to generate new samples automatically. Thus, this kind of online sampling strategy is so-called intelligent DOE. One intelligent DOE is particle swarm optimization (PSO)-based intelligent sampling strategy (PSOIS). This scheme is based on the modified PSO method; the other one is to use the boundary and best neighbor samples to generate new samples and so called BBNS (Boundary and best neighbor sampling) strategy. The BBNS cannot only generate new samples automatically but also correct the initial boundary constraints according to responses of evaluations. Furthermore, in order to improve the efficiency of the proposed intelligent sampling strategies, the parallel intelligent sampling strategy is also built. To assess the performance of the proposed strategies, comparisons between the proposed strategies and popular off-line methods are performed. The test results demonstrate that the proposed intelligent sampling strategies can control the initial design space and optimize the quality of the sample, such that the accuracy of the follow-up metamodel should be evaluated accordingly.
Probability-based least square support regression technique
In this study, a least square support vector regression-based (LS-SVR) metamodeling technique is proposed. Compared with widely used metamodeling techniques, such as Kriging, RBF, etc., the notable difference of the LS-SVR is to construct metamodel by considering the empirical risk minimization (ERM) and structure risk minimization (SRM). It means that the ERM-based metamodeling techniques try to use a complex model to approximate finite samples and the robustness property of metamodel might be lost. In order to overcome this defect, a probability-based LS-SVR (PLS-SVR) metamodeling is implemented. The advantage of the suggested method is to use probability-based weight function to filter noise and outliers. Therefore, the PLS-SVR can obtain more robust estimates for regression compared with the LS-SVR. According to the results of benchmark tests, the PLS-SVR is shown to be promising for highly nonlinear problems. However, the proposed scheme might lead to long computational time due to neural network (NN)-based training procedure. To improve the efficiency and accuracy of the optimization and make the suggested approach feasible in practice, the proposed intelligent sampling strategy is integrated to generate training samples in PLS-SVR.
Response-based space mapping method
Space mapping (SM)-based optimization is a self-contained method and developed rapidly recently. Severe differences between the coarse and fine models and non-uniqueness of the parameter extraction procedure may cause the space mapping algorithm to be trapped in local minima and time consuming. According to this bottleneck, response-based space mapping (RBSM) method is proposed in this study. The distinctive feature of the RBSM is to construct space projection of response space instead of design space. A high dimensional problem can be transferred to lower dimensional problem and the parameter extraction procedure is also avoided. Thus, the RBSM is easy to converge compared with popular SM methods. Additionally, to improve the efficiency of the proposed algorithm, the intelligent sampling is also integrated. The mathematical nonlinear test function demonstrates that the convergence and accuracy of the proposed algorithm are easy to achieve. Application of the proposed metamodeling techniques to sheet forming optimization
Deformation mechanism of sheet forming procedure is very complicated, which contains geometry, contact, and material nonlinearity. In this study, the proposed intelligent DOE methods, metamodeling techniques and RBSM strategies are integrated to build a sheet forming optimization system. To verify the feasibility of proposed system, the proposed system is applied to optimize the real-world engineering problems. Compared with other popular metamodeling techniques, such as Kriging, RBF, sequential 2nd PR, the efficiency and accuracy of the built system are well improved.
Time-based metamodeling technique
A time-based metamodeling technique is suggested for vehicle crashworthiness design. The characteristics of the proposed method are the construction of a time-based objective function and the establishment of a metamodel by the PLS-SVR. Compared with other popular metamodel-based optimization methods, the design space of time-based strategy is extended to time space. Therefore, more time features and information can be extracted by considering time-dependent effect. Because the objective function is based on the time history, the design variables is more convenient to control the objective function in entire simulation procedure and the optimization result is also more useful and feasible in practice. To validate performance of the suggested method, cylinder impacting and full vehicle frontal collision are optimized by the time-based strategy. The results demonstrate the capability and potential of this approach in solving the crashworthiness design of vehicles.
近似模型技术还缺乏有效的手段。因此,虽然目前基于近似模型技术的优化领域非常活跃,基于近似模型技术的优化方法也多种多样,但对于高维非线性的实际工程优化问题,目前的近似模型技术还缺乏快速构建最大限度反映研究对象的特性模型的手段,这也是近似模型技术研究领域面临的最大瓶颈,阻碍了该技术在工业领域的应用和发展。
近似模型优化技术由三个基本阶段构成:实验设计,近似模型构建,基于近似模型的优化。鉴于工程问题的复杂性和多样性,建立一种通用的近似模型构造体系是非常困难的。因此,目前基于近似模型技术的优化方法都具有一定的针对性,当涉及到不同类型的具体工程优化问题,需要根据问题的特殊性,合理构建可行的优化策略。为此,本文将车辆工程优化设计的难点金属板料成形和车辆耐撞性作为主要实际工程应用研究。以近似模型的精度和效率作为算法的主要评价标准,对近似模型的实验设计和构建这两个方面进行了理论研究。本论文的主要创新点包括以下几个方面:
(一)智能实验设计方法
针对目前“离线”实验设计方法的技术瓶颈,建立了两种“在线”实验设计方法。这类布点方法不仅仅是单纯的实验设计方法,实质上也是一个优化过程,通过近似模型的精度和优化结果确定布点的方向,即将布点过程自动化和智能化。其中粒子群智能布点方法是基于粒子群优化理论建立的一种智能布点方法,将修正后的粒子群优化技术用于新样本的定位;而基于边界条件和最优邻域的智能布点方法则是根据初始样本的边界信息以及设计空间中当前样本的邻域内最优样本生成新样本。为了克服初始设计空间的主观因素,建立了相应的设计空间更新和判断机制,使其能够更为客观地确定新样本的位置。此外,为了提高布点效率,提出了并行智能布点方法,通过对初始样本点数目的扩展,达到提高精度,加快速度的目的。随后,将以上研发的算法同主流实验方法进行了性能比较,通过对多维非线性函数的测试来确认算法的可行性。测试数据表明:智能实验设计方法能够控制更新样本空间,优化样本质量,进而提高后续近似模型的精度和构建效率。
(二)基于概率的最小二乘支持向量回归
主流近似模型技术多数建立在经验风险最小化准则之上,但经验风险最小并不一定意味着期望风险最小。这类近似模型技术的瓶颈是:试图用十分复杂的模型去拟合有限的样本,导致丧失了推广能力,难以反映研究目标的实质和特性。为此,本文以泛化性能出色的基于统计学习理论的支持向量机技术构造近似模型,建立基于概率的最小二乘支持向量回归算法,通过权系数对误差带的控制实现对模型精度的控制。实质上是通过赋予异常样本较小的加权系数,将噪声样本对模型的性能的影响减少到最小的策略,算法的稳健性取决于建模过程中对异常样本的检测和剔除效果。通过基于最小二乘支持向量机回归方法和基于概率的最小二乘支持向量机回归方法对非线性函数的拟合测试,两种方法的性能都有显著地提高,能够克服噪声对函数精度的影响。因此,基于概率的最小二乘支持向量机回归方法是一种可行的近似模型设计方法。
(三)基于响应函数的空间映射技术
作为自成体系的一个优化流派,空间映射技术近年来发展迅猛。空间映射技术的最大瓶颈在于其参数提取技术,即如何确定精细模型的初始解在粗糙空间中对应解。通过对主流的空间映射方法的分析和验证,其关系具有较强的随机性,进而导致优化结果的不准确、甚至不收敛。针对这一问题,本文提出了基于响应函数的空间映射技术,同传统的空间映射相比,其最大特点是建立响应函数间的空间映射,并通过反求算法获得最优设计参数。因此,避免了易造成误差和难以收敛的根本因素——参数提取过程,使空间映射方法更为直接。通过对非线性函数的测试结果表明,本文提出的空间映射技术的精度和收敛性均有大幅度提高。
(四)基于近似模型技术的优化方法在金属板料成形中的应用
金属板料成形过程是一种包括几何非线性,材料非线性,边界条件非线性,且变形机制非常复杂的高度非线性问题。利用提出的智能布点方法、近似模型构造技术以及基于响应的空间映射算法,建立了高效精确的板料成形近似模型优化体系,用以提高对板料成形过程的控制能力、板料成形性的优化精度、生产效率及缩短产品开发周期等方面均具有显著的优越性,有积极的现实意义。
(五)基于时序的近似模型构造体系及其在车辆耐撞性优化中的应用
基于时序问题的近似模型技术充分考虑时间和空间因素,将设计空间进行拓展,在考虑样本历史信息的前提下构建时空两重性的近似模型。该技术的最大特点在于可控性,通过对设计变量的修正,进而完成研究对象在敏感时间域内的控制,是一种针对过程的可控优化技术。研究目标主要是与时序相关的物理过程,而汽车CAE设计中的车辆耐撞性研究则是非常典型的问题,为此,本章将其应用于该问题的优化,得到了令人满意的结果。
Metamodel-based optimization is one of the most popular and hopeful methods which can solve large scale engineering problems. According to its efficiency, the metamodel-based optimization method is widely applied for engineering optimization problems. Many large scale engineering problems can be done well if the metamodel-based optimization runs efficiently and stable. With the development of in-depth research, the scale and complexity of engineering problems are increasingly improved correspondingly. Although several kinds of metamodeling techniques have been approached, it is still difficult to solve practical engineering problems by current developed metamodeling technologies, especially for large-scale nonlinear problems. The major bottleneck of current developed metamodeling techniques is that how to construct accurate metamodel efficiently and how to balance the relationship between the accuracy and efficiency.
The metamodel-based optimization frame is composed of three phases: design of experiment (DOE), construction of metamodel and optimization. Due to the complexity and variety of practical engineering problems, it is impossible to develop a general metamodel method. Therefore, existing metamodeling techniques commonly possess special characteristics for different kinds of engineering problems. According to features of an engineering problem, the feasible way is to propose a type-specific strategy.
According to the metamodel-based optimization, the key factors are the accuracy and efficiency of metamodels. As long as a reliable and accurate metamodel is constructed, the corresponding optimum solution should be easy to achieve. Thus, the emphases of this thesis are DOE, metamodeling technique and time-based metamodeling strategy.
The major innovative suggestions are summarized as follows Intelligent DOE
According to the technique of the popular off-line design of experiment, two on-line DOE are suggested. The on-line sampling strategies are not purely DOEs based on statistical theories; these kinds of strategies are learning procedure essentially. The on-line sampling strategies use responses derived from evaluations to generate new samples automatically. Thus, this kind of online sampling strategy is so-called intelligent DOE. One intelligent DOE is particle swarm optimization (PSO)-based intelligent sampling strategy (PSOIS). This scheme is based on the modified PSO method; the other one is to use the boundary and best neighbor samples to generate new samples and so called BBNS (Boundary and best neighbor sampling) strategy. The BBNS cannot only generate new samples automatically but also correct the initial boundary constraints according to responses of evaluations. Furthermore, in order to improve the efficiency of the proposed intelligent sampling strategies, the parallel intelligent sampling strategy is also built. To assess the performance of the proposed strategies, comparisons between the proposed strategies and popular off-line methods are performed. The test results demonstrate that the proposed intelligent sampling strategies can control the initial design space and optimize the quality of the sample, such that the accuracy of the follow-up metamodel should be evaluated accordingly.
Probability-based least square support regression technique
In this study, a least square support vector regression-based (LS-SVR) metamodeling technique is proposed. Compared with widely used metamodeling techniques, such as Kriging, RBF, etc., the notable difference of the LS-SVR is to construct metamodel by considering the empirical risk minimization (ERM) and structure risk minimization (SRM). It means that the ERM-based metamodeling techniques try to use a complex model to approximate finite samples and the robustness property of metamodel might be lost. In order to overcome this defect, a probability-based LS-SVR (PLS-SVR) metamodeling is implemented. The advantage of the suggested method is to use probability-based weight function to filter noise and outliers. Therefore, the PLS-SVR can obtain more robust estimates for regression compared with the LS-SVR. According to the results of benchmark tests, the PLS-SVR is shown to be promising for highly nonlinear problems. However, the proposed scheme might lead to long computational time due to neural network (NN)-based training procedure. To improve the efficiency and accuracy of the optimization and make the suggested approach feasible in practice, the proposed intelligent sampling strategy is integrated to generate training samples in PLS-SVR.
Response-based space mapping method
Space mapping (SM)-based optimization is a self-contained method and developed rapidly recently. Severe differences between the coarse and fine models and non-uniqueness of the parameter extraction procedure may cause the space mapping algorithm to be trapped in local minima and time consuming. According to this bottleneck, response-based space mapping (RBSM) method is proposed in this study. The distinctive feature of the RBSM is to construct space projection of response space instead of design space. A high dimensional problem can be transferred to lower dimensional problem and the parameter extraction procedure is also avoided. Thus, the RBSM is easy to converge compared with popular SM methods. Additionally, to improve the efficiency of the proposed algorithm, the intelligent sampling is also integrated. The mathematical nonlinear test function demonstrates that the convergence and accuracy of the proposed algorithm are easy to achieve. Application of the proposed metamodeling techniques to sheet forming optimization
Deformation mechanism of sheet forming procedure is very complicated, which contains geometry, contact, and material nonlinearity. In this study, the proposed intelligent DOE methods, metamodeling techniques and RBSM strategies are integrated to build a sheet forming optimization system. To verify the feasibility of proposed system, the proposed system is applied to optimize the real-world engineering problems. Compared with other popular metamodeling techniques, such as Kriging, RBF, sequential 2nd PR, the efficiency and accuracy of the built system are well improved.
Time-based metamodeling technique
A time-based metamodeling technique is suggested for vehicle crashworthiness design. The characteristics of the proposed method are the construction of a time-based objective function and the establishment of a metamodel by the PLS-SVR. Compared with other popular metamodel-based optimization methods, the design space of time-based strategy is extended to time space. Therefore, more time features and information can be extracted by considering time-dependent effect. Because the objective function is based on the time history, the design variables is more convenient to control the objective function in entire simulation procedure and the optimization result is also more useful and feasible in practice. To validate performance of the suggested method, cylinder impacting and full vehicle frontal collision are optimized by the time-based strategy. The results demonstrate the capability and potential of this approach in solving the crashworthiness design of vehicles.
引文
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