组合近似模型方法研究及其在轿车车身轻量化设计的应用
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摘要
随着有限元技术的迅速发展,基于仿真的工程设计与优化已经广泛地应用到复杂工程产品设计中。以汽车工业为例,减轻汽车重量以实现节能减排是汽车工业发展的核心问题,新能源汽车与传统汽车都迫切需要轻量化。轿车车身轻量化设计必须满足碰撞安全、刚度和模态以及NVH(振动、噪声、舒适性)等要求,是多学科、多参数、多约束的复杂系统优化问题。实际轻量化设计中,针对碰撞安全、振动噪声等结构强非线性能响应,直接通过有限元分析开展优化很难满足现代车身设计与开发的要求,利用近似模型拟合或预测结构性能响应以代替有限元仿真是国内外研究的前沿与热点,可以减少优化过程的计算量,提高优化效率。尽管基于近似模型的优化方法被认为是解决复杂工程设计问题的最有效途径之一,但工程实践中仍存在很多不足,易引起轻量化设计方案失效。本文对近似模型的关键技术进行研究,提出了组合近似模型的构造方法,为车身结构性能响应的拟合提供精度更高的近似模型建模方法;建立了面向组合近似模型的序贯采样策略,进一步改善模型全局精度;分析了约束函数的近似模型修正方法,保证近似解的实际约束可行性;形成了基于组合近似模型的车身轻量化设计方法,将其应用于新能源轿车车身轻量化设计。主要研究工作及结论如下:
(1)组合近似模型建模方法研究
研究单一近似模型(如多项式响应面、径向基函数、Kriging和支持向量回归等)的预测能力,提出了基于交叉验证误差均值和方差的权系数计算方法,通过加权叠加构建组合近似模型,研究了组合近似模型的适用范围,并分析单一近似模型个数对组合近似模型精度的影响。通过大量测试函数和工程算例表明,该权系数计算方法在预测精度方面具有比已有组合近似模型构造方法和单一近似模型更为明显的优势,且当单一近似模型数量保持在3～5个时,组合近似模型的预测能力最好,非常适用于小样本条件下具有高维强非线性特征的车身结构性能响应的近似建模。
(2)组合近似模型的序贯采样策略研究
基于上述组合近似模型,从单一近似模型预测能力的差异性出发,提出了表征组合近似模型拟合不确定的评价指标——加权标准偏差,验证了该指标与组合近似模型实际误差存在较高的相关性。建立了基于加权标准偏差的组合近似模型序贯采样策略,在拟合不确定较大区域增加样本点逐步提高模型全局精度。通过数值算例和汽车耐撞性问题验证该策略的可行性,能有效指导组合近似模型的迭代更新,为后续车身轻量化设计提供高精度的近似模型。
(3)面向约束优化的近似模型修正方法研究
建立了基于安全裕量的约束函数组合近似模型修正方法,利用交叉验证误差的累计分布函数计量化给定保守度水平下的安全裕量值,使近似解满足实际约束可行性。提出了面向自适应循环优化的保守度水平序列更新策略,合理降低安全裕量值。通过基于耐撞性的车身前部结构轻量化案例,证明了结合组合近似模型、安全裕量和保守度水平序列更新策略开展车身轻量化设计可以在少量循环内快速获得能够满足约束条件要求、具有更小目标值的轻量化方案,具有很好的工程应用价值。
(4)基于组合近似模型的轿车车身轻量化方法研究与工程应用
综合组合近似模型及其序贯采样策略、约束函数近似模型修正方法,对轿车车身轻量化设计方法进行研究。提出了基于组合近似模型的车身轻量化设计总体框架及具体流程。以某新能源轿车车身为对象,开展了考虑多种碰撞形式(正面全宽碰撞、正面偏置碰撞、侧面碰撞和追尾碰撞)、车身刚度和模态以及NVH等性能的车身轻量化设计应用研究,验证了基于组合近似模型的车身轻量化设计方法的可靠性。
本文针对轿车车身设计的多学科、多参数、多约束的复杂系统优化问题,对组合近似模型及其序贯采样策略、约束函数近似模型修正方法进行了研究,目的在于建立更适用于车身强非线性结构性能响应的近似模型以及保证近似优化解的实际工程可行性,为开展轿车车身轻量化设计提供准确、可靠的数学模型基础,指导和完善轻量化车身开发流程,促进我国汽车轻量化设计能力的提高。
Simulation-based design optimization is widely used in design of complex systems building upon the successful development of finite element techniques. Take automotive industry for example, it is a critical problem to reduce the weight to improve fuel efficiency and meet the gas emission requirement; this is an urgent problem for both traditional gasoline and fuel cell vehicles. Meanwhile, the lightweight vehicle should maintain, or achieve better performance in crashworthiness, stiffness, modal and noise, vibration, harshness (NVH) performance, etc. The above problem is widely recognized as a multi-disciplinary, multi-variable, and multi-constraint optimization problem. In practice, integrating structural optimization directly with expensive finite element simulations is generally infeasible since optimization search typically requires thousands or even millions of simulations on crashworthiness and NVH performance,. As a consequence, there is a growing interest in using surrogate model or metamodel to approximate the complicated highly nonlinear behaviors to manage the complexity in analysis and optimization for weight reduction of autobody.
Although surrogate based design optimization is considered as one of the efficient approaches to dealing with complex engineering problems, inaccuracy in metamodeling may result in misleading design solutions.The dissertation concentrates on improving the quality of metamodeling techniques. An approach for constructing the ensemble of surrogates is proposed to provide better approximation of autobody structural responses. A strategy for sequential sampling is presented for ensemble of surrogates to improve its accuracy further. As a refinement, conservative prediction for constraints is put forward to ensure the actual constraint feasibility of the approximated solution. A lightweight design method based on ensemble of multiple surrogates is finally presented, followed by an industrial case study for weight reduction of autobody of fuel cell vehicle. The main research tasks and the corresponding conclusions from this dissertation are summarized as follows:
(1) Study on the ensemble of surrogates
Several individual surrogates are investigated in terms of prediction capability, such as polynomial response surface, radial basis function, Kriging and support vector regression. A new scheme for weights selection is proposed based on cross validation error, and the ensemble of surrogates are constructed through the weighted average method. The scope of application for ensemble of surrogates is discussed and the influence of the number of individual surrogates is also researched. By using a large amount of test functions and engineering cases, it is shown that the new weights selection method is more effective when compared with the currently existing weights selection methods and individual surrogates. It is also demonstrated that the prediction capability of the ensembled surrogates is the best when the number of individual surrogates is from 3 to 5. In conclusion, ensemble of surrogates is an effective approach for metamodeling on autobody structural responses, which possesses high dimensionality, high nonlinearity and small sampling points.
(2) Sequential sampling strategy for ensemble of surrogates
Based on the weights of individual surrogates and its prediction errors with ensemble of surrogates, an index of weighted standard deviation is proposed to represent the metamodel uncertainty for ensemble of surrogates. It has been demonstrated that the proposedhe index is highly correlated with the actual errors of ensemble of surrogates. A sequential sampling strategy is proposed to improve the accuracy of the ensembled surrogates by iteratively adding sample points with the maximum weighted standard deviations. We demonstrate the advantages of this strategy using analytical problems and one engineering problem. It is noted that the index of the weighted standard deviation is more useful for a qualitative identification rather than quantitative on the metamodel uncertainty. It is also shown that the sequential sampling strategy can effectively improve the prediction of ensemble of surrogates in the region of high uncertainty, especially for high dimensional and high nonlinear responses.
(3) Conservative prediction of surrogates for constrained optimization
The methodology of conservative prediction of surrogates is proposed by employing the concept of safety margin. An approach for estimating the safety margins under a given conservativeness level is proposed based on the cumulative distribution function obtained in cross validation. The method helps compensate surrogate errors to push the constrain boundary towards the feasible domain. Furthemore, a strategy for sequentially updating the conservativeness level is developed to decrease the safety margins effectively. The ensemble of surrogates, safety margins, and the scheme for updating the safety margin in surrogate based optimization are applied to lightweight design of vehicle structures under crashworthiness. The proposed techniques resulted in more feasible solutions and achieved more weight reduction within a limited number of optimization cycles, showing great potential for surrogate based design optimization in real engineering problems.
(4) Method on lightweight design of autobody and industrial application based on ensemble of surrogates
A method for lightweight design of autobody is proposed by integrating the ensemble of surrogates, sequential sampling strategy, and conservative surrogates for constraint function. The framework and the detail flowchart of ensemble of surrogates-based method for lightweight design of autobody are presented. An industrial application is studied to verify the feasibility of the proposed framework, where multidisciplinary optimization of autobody for a fuel cell vehicle is conducted considering various types of crash scenarios, including full-overlap frontal crash, 40% overlap frontal crash with deformable barrier, side impact, and rear impact, stiffness and modal frequency of body-in-white, and NVH.
Design optimization for autobody is a complex, multi-disciplinary, multi-variable, and multi-constraint problem. This dissertation studies the ensemble of surrogates,its sequential sampling strategy, and conservative surrogates, in an attempt to construct more accurate surrogate models for autobody structural responses with high nonlinearity and to ensure the actual constraint feasibility of the approximate solution. The research aims for providing better surrogate models for lightweight design of autobody, as well as guiding and improving the process of lightweight autobody development, towards the end goal of improving the R&D capability of vehicle lightweight design.
(1)组合近似模型建模方法研究
研究单一近似模型(如多项式响应面、径向基函数、Kriging和支持向量回归等)的预测能力,提出了基于交叉验证误差均值和方差的权系数计算方法,通过加权叠加构建组合近似模型,研究了组合近似模型的适用范围,并分析单一近似模型个数对组合近似模型精度的影响。通过大量测试函数和工程算例表明,该权系数计算方法在预测精度方面具有比已有组合近似模型构造方法和单一近似模型更为明显的优势,且当单一近似模型数量保持在3～5个时,组合近似模型的预测能力最好,非常适用于小样本条件下具有高维强非线性特征的车身结构性能响应的近似建模。
(2)组合近似模型的序贯采样策略研究
基于上述组合近似模型,从单一近似模型预测能力的差异性出发,提出了表征组合近似模型拟合不确定的评价指标——加权标准偏差,验证了该指标与组合近似模型实际误差存在较高的相关性。建立了基于加权标准偏差的组合近似模型序贯采样策略,在拟合不确定较大区域增加样本点逐步提高模型全局精度。通过数值算例和汽车耐撞性问题验证该策略的可行性,能有效指导组合近似模型的迭代更新,为后续车身轻量化设计提供高精度的近似模型。
(3)面向约束优化的近似模型修正方法研究
建立了基于安全裕量的约束函数组合近似模型修正方法,利用交叉验证误差的累计分布函数计量化给定保守度水平下的安全裕量值,使近似解满足实际约束可行性。提出了面向自适应循环优化的保守度水平序列更新策略,合理降低安全裕量值。通过基于耐撞性的车身前部结构轻量化案例,证明了结合组合近似模型、安全裕量和保守度水平序列更新策略开展车身轻量化设计可以在少量循环内快速获得能够满足约束条件要求、具有更小目标值的轻量化方案,具有很好的工程应用价值。
(4)基于组合近似模型的轿车车身轻量化方法研究与工程应用
综合组合近似模型及其序贯采样策略、约束函数近似模型修正方法,对轿车车身轻量化设计方法进行研究。提出了基于组合近似模型的车身轻量化设计总体框架及具体流程。以某新能源轿车车身为对象,开展了考虑多种碰撞形式(正面全宽碰撞、正面偏置碰撞、侧面碰撞和追尾碰撞)、车身刚度和模态以及NVH等性能的车身轻量化设计应用研究,验证了基于组合近似模型的车身轻量化设计方法的可靠性。
本文针对轿车车身设计的多学科、多参数、多约束的复杂系统优化问题,对组合近似模型及其序贯采样策略、约束函数近似模型修正方法进行了研究,目的在于建立更适用于车身强非线性结构性能响应的近似模型以及保证近似优化解的实际工程可行性,为开展轿车车身轻量化设计提供准确、可靠的数学模型基础,指导和完善轻量化车身开发流程,促进我国汽车轻量化设计能力的提高。
Simulation-based design optimization is widely used in design of complex systems building upon the successful development of finite element techniques. Take automotive industry for example, it is a critical problem to reduce the weight to improve fuel efficiency and meet the gas emission requirement; this is an urgent problem for both traditional gasoline and fuel cell vehicles. Meanwhile, the lightweight vehicle should maintain, or achieve better performance in crashworthiness, stiffness, modal and noise, vibration, harshness (NVH) performance, etc. The above problem is widely recognized as a multi-disciplinary, multi-variable, and multi-constraint optimization problem. In practice, integrating structural optimization directly with expensive finite element simulations is generally infeasible since optimization search typically requires thousands or even millions of simulations on crashworthiness and NVH performance,. As a consequence, there is a growing interest in using surrogate model or metamodel to approximate the complicated highly nonlinear behaviors to manage the complexity in analysis and optimization for weight reduction of autobody.
Although surrogate based design optimization is considered as one of the efficient approaches to dealing with complex engineering problems, inaccuracy in metamodeling may result in misleading design solutions.The dissertation concentrates on improving the quality of metamodeling techniques. An approach for constructing the ensemble of surrogates is proposed to provide better approximation of autobody structural responses. A strategy for sequential sampling is presented for ensemble of surrogates to improve its accuracy further. As a refinement, conservative prediction for constraints is put forward to ensure the actual constraint feasibility of the approximated solution. A lightweight design method based on ensemble of multiple surrogates is finally presented, followed by an industrial case study for weight reduction of autobody of fuel cell vehicle. The main research tasks and the corresponding conclusions from this dissertation are summarized as follows:
(1) Study on the ensemble of surrogates
Several individual surrogates are investigated in terms of prediction capability, such as polynomial response surface, radial basis function, Kriging and support vector regression. A new scheme for weights selection is proposed based on cross validation error, and the ensemble of surrogates are constructed through the weighted average method. The scope of application for ensemble of surrogates is discussed and the influence of the number of individual surrogates is also researched. By using a large amount of test functions and engineering cases, it is shown that the new weights selection method is more effective when compared with the currently existing weights selection methods and individual surrogates. It is also demonstrated that the prediction capability of the ensembled surrogates is the best when the number of individual surrogates is from 3 to 5. In conclusion, ensemble of surrogates is an effective approach for metamodeling on autobody structural responses, which possesses high dimensionality, high nonlinearity and small sampling points.
(2) Sequential sampling strategy for ensemble of surrogates
Based on the weights of individual surrogates and its prediction errors with ensemble of surrogates, an index of weighted standard deviation is proposed to represent the metamodel uncertainty for ensemble of surrogates. It has been demonstrated that the proposedhe index is highly correlated with the actual errors of ensemble of surrogates. A sequential sampling strategy is proposed to improve the accuracy of the ensembled surrogates by iteratively adding sample points with the maximum weighted standard deviations. We demonstrate the advantages of this strategy using analytical problems and one engineering problem. It is noted that the index of the weighted standard deviation is more useful for a qualitative identification rather than quantitative on the metamodel uncertainty. It is also shown that the sequential sampling strategy can effectively improve the prediction of ensemble of surrogates in the region of high uncertainty, especially for high dimensional and high nonlinear responses.
(3) Conservative prediction of surrogates for constrained optimization
The methodology of conservative prediction of surrogates is proposed by employing the concept of safety margin. An approach for estimating the safety margins under a given conservativeness level is proposed based on the cumulative distribution function obtained in cross validation. The method helps compensate surrogate errors to push the constrain boundary towards the feasible domain. Furthemore, a strategy for sequentially updating the conservativeness level is developed to decrease the safety margins effectively. The ensemble of surrogates, safety margins, and the scheme for updating the safety margin in surrogate based optimization are applied to lightweight design of vehicle structures under crashworthiness. The proposed techniques resulted in more feasible solutions and achieved more weight reduction within a limited number of optimization cycles, showing great potential for surrogate based design optimization in real engineering problems.
(4) Method on lightweight design of autobody and industrial application based on ensemble of surrogates
A method for lightweight design of autobody is proposed by integrating the ensemble of surrogates, sequential sampling strategy, and conservative surrogates for constraint function. The framework and the detail flowchart of ensemble of surrogates-based method for lightweight design of autobody are presented. An industrial application is studied to verify the feasibility of the proposed framework, where multidisciplinary optimization of autobody for a fuel cell vehicle is conducted considering various types of crash scenarios, including full-overlap frontal crash, 40% overlap frontal crash with deformable barrier, side impact, and rear impact, stiffness and modal frequency of body-in-white, and NVH.
Design optimization for autobody is a complex, multi-disciplinary, multi-variable, and multi-constraint problem. This dissertation studies the ensemble of surrogates,its sequential sampling strategy, and conservative surrogates, in an attempt to construct more accurate surrogate models for autobody structural responses with high nonlinearity and to ensure the actual constraint feasibility of the approximate solution. The research aims for providing better surrogate models for lightweight design of autobody, as well as guiding and improving the process of lightweight autobody development, towards the end goal of improving the R&D capability of vehicle lightweight design.
引文
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