基于近似模型的汽车轻量化优化设计方法
|
摘要
随着汽车工业在国内的蓬勃发展,使得能源日趋紧张、环境压力加剧的问题日益凸显,这必将成为汽车工业可持续发展的绊脚石。作为有效节能手段的汽车轻量化技术已成为汽车产业发展中的一项关键性研究课题,在不久的将来,它必将成为汽车公司的核心竞争力之一。近年来国内外很多学者在汽车轻量化相关方面开展了较为广泛的研究,并已取得诸多成果,但是汽车轻量化的相关研究仍然存在较多问题,研究方法仍然集中在对汽车车身的一些零部件用低密度材料进行替换,如铝、镁合金、复合材料等,这些方法大多数仍是凭经验设计。本文在总结前人的研究基础上,采用了近似模型技术结合数值优化方法对汽车轻量化设计进行了较为系统和深入的研究,在确保汽车综合性能指标的前提下,尽可能的降低汽车产品自身重量,达到减重、降耗、安全的综合指标。
围绕汽车轻量化这一主题,本论文主要开展了以下几方面的研究内容:
1.建立了一种基于移动最小二乘的汽车正面碰撞响应面近似模型,提出了针对不同的优化设计响应采用不同的近似模型技术来达到提高优化效率的目的。通过与目前广泛运用的多项式响应面与Kriging响应面的对比研究可知,多项式响应面只是对空间试验点的逼近,拟合精度不高,故一般适用于替代非线性程度不高的响应,而Kriging模型准确的通过了空间拟合的采样点,拟合精度高,但它容易受到数值噪声的影响且计算成本高。而移动最小二乘拟合的响应面近似模型恰恰兼顾了两者的优点,故它非常适合于具有高度非线性且具有数值噪声的汽车碰撞安全的优化研究。最终把该模型成功运用到汽车轻量化优化设计中来验证了此模型的有效性。
2.提出了一种基于近似模型和多目标遗传算法的高强度钢板选材方法。虽然汽车制造工业中铝合金等轻质材料在逐渐增加,但是由于铝合金等加工难度高,成形性能较差,又由于铝导热性好,导致铝合金的焊接性能差,关键是它的成本还比钢材高。故目前在汽车制造中仅能部分代替钢铁材料。而厚度变薄的高强度钢相对于普通钢来说则具有高强度、质量轻等优点,而且还能提高车辆的安全性能,所以高强度钢已成为普遍采用的汽车原材料。采用高强度钢板代替普通钢板制造的汽车车身,其重量可以得到较大幅度的降低。但是传统的选材设计往往都是根据工程人员的经验来选择车辆各个部分的材料配置,导致车辆各个部分的材料选择具有盲目性而不能最优化,文中采用近似模型和多目标遗传算法相结合的选材方法对整车的正面碰撞和侧面碰撞安全性进行了深入研究,得到了汽车车身驾驶室前部关键部件与侧围的高强度钢板及其板厚的合理配置,并达到使车辆的安全性能提高和车身轻量化的目的。
3.提出了一种基于近似模型和多学科设计优化相结合的整车轻量化优化设计方法。汽车轻量化的首要前提是应保持汽车原有的性能不受影响,既要有目的地减轻汽车自身的重量,又要保证汽车行驶的安全性、耐撞性、抗振性及舒适性等。但是传统的汽车设计模式往往采取的是一种串行设计模式,在不同的设计阶段设计人员将选择不同的重点来对汽车进行设计和优化,这就把影响汽车性能的空气动力学、振动、噪声、耐撞性、安全性以及舒适性等学科人为的割裂开来,并没有利用和考虑到各个学科之间存在的相互耦合而可能产生的协同效应,这样将导致得到的优化结果往往不是系统整体的最优解。同时,如果轻量化设计中一起考虑到的汽车安全性、振动、刚度等各学科的相互作用来进行优化设计,这样势必遭遇优化设计的瓶颈(单次CAE计算仿真时间过长而引起的时间问题)。正是基于上述传统串行设计与CAE仿真时间过长的缺陷,文中提出了汽车的轻量化优化设计过程也必是一个多学科设计优化的过程,并建立了将响应面和多学科设计优化方法相结合的汽车轻量化优化设计近似模型,成功解决了单次优化时间过长的优化瓶颈问题,并将该方法成功运用到某车型的轻量化优化设计中。
4.建立了基于可靠性设计理论的汽车薄壁纵梁轻量化优化设计模型。车身薄壁纵梁不仅是汽车车身设计的基本承载部件,而且也是车身发生正面碰撞时的主要吸能部件。同时,薄壁纵梁的变形模式和吸能特性直接决定了车体在碰撞时的加速度和力的响应,也就直接影响到车内乘员的安全性。此外,由于它的使用环境较为恶劣,这就对它的设计提出了更高的可靠性要求。传统的优化过程往往忽略了工程设计中的不确定性,如几何尺寸、材料属性、载荷和边界条件以及操作环境等相关的多种不确定因素的影响,而使设计目标超出设计界限而失效,从而降低了产品的可靠性。文中提出将薄壁梁设计看着是一个需要考虑安全性、静态承载特性与一阶振动模态等方面的多学科可靠性优化设计过程,并将该方法成功运用到帽型薄壁纵梁的轻量化优化设计中。
Along with the fast development of automotive industry, the energy tense and environment pressure becomes increasingly serious, which will prevent the development of automotive industry. As an effective energy-saving method, automotive lightweight has already become a crucial research topic. In the near future, it must be one of core competence among car companies. In recent years, many research achievements have been made in the automotive lightweight field. However, many lightweight-related issues need to be studied. Research methods still concentrated on replacing some automobile body parts with low-density materials, such as aluminum, magnesium alloy, composite materials, and so on. These methods almost depend on the empirical design. Therefore, in this paper, based on the predecessor's literature research, an in-depth study about the lightweight, using approximate model technology and optimization method, was conducted, so as to reduce the weight of automobile and achieve aggregative objective (reducing weight and consumes and improving vehicle safety) , under the guarantee of comprehensive performances of automobiles.
Main research content and innovation of the paper are as follows:
1. Based on moving least square method, a response surface approximate model of automotive front impact was established, and used the different approximate model technology for the different optimized design response to achieve the goal of enhancing optimization efficiency. By contrasting to Kriging response surface, the polynomial response surface is approaching the sampling points in design space, and the fitting accuracy is not high, so it is generally applied to the responses of low non-linear level, while the Kriging model whose fitting accuracy is high, can pass the spatial sampling point accurately, but it is vulnerable to numerical noise which raise the cost of calculation. However, the moving least square response surface model has both merits above, so it is very suitable for the car crash safety optimization of highly non-linear, and numerical noise. And, the model's validity is confirmed by utilizing the model in the automotive lightweight.
2. A method of high strength steel plate selection which based on the multi-objective genetic algorithm and approximate model was proposed. Although the application of the light quality materials such as aluminum alloy increases gradually in automotive manufacturing industry, due to the difficulty of processing, forming, and welding results from the good thermal conductivity, and even the higher cost than the steel, aluminum can only be used as vehicle body instead of only part of the iron and steel in the automobile manufacture at present. While the thin high-strength steel has merits of lighter quality, higher strength, as compared to the traditional steels. And it also can improve the performance of vehicle safety. Therefore, the high-strength steel has been widely used as automotive raw materials. Using the high-strength steel plate instead of traditional steel plate, the automobile body weight can be reduced to a greater degree. However, the traditional selection of materials often based on the experiences of engineers, which made the choice of materials in every part of vehicles blind and not optimal. In the paper, the safety of front impact and side impact of vehicles are conducted in deep study by combining the approximate model and the multi-objective genetic algorithm, make the high strength steel plate of front key absorbing parts of the automobile cab and the side parts and its thickness reasonable in disposition. And, the safety of vehicles was improved, and the weight of automotive body was reduced.
3. A method of the entire vehicle lightweight optimization design basing on the approximate model and the multi-disciplinary design optimization was proposed. With the most important premise which is to maintain the original performance, the automobile lightweight, not only destinate to reduce the weight, but also ensure the safety, crashworthiness, vibration, comfort, and so on. However, because the traditional model of car design was often taken as a serial design patterns, in which engineers chosed different key points to design and optimize in different stages, the influence of automobile performance was separated about the aerodynamic performance, vibration, noise, crashworthiness, safety, comfort, and the coordination effect which be produced by coupling of various subjects was not used and taken into account. So it always turned out the optimization results were not the overall optimal solution. At the same time, if the lightweight design of automobile takes the effects of safety, vibration, stiffness into account, this is bound to encounter bottleneck of the optimal design (CAE time of single calculation and simulation is too long). It is based on the flaw above-mentioned traditional serial design and CAE simulation time, and the paper propose that the process of the lightweight of automobile is a multi-disciplinary design optimization process, and establish the approximate model of automobile lightweight optimization design by combining the response surface method and multi-disciplinary design optimization method, and solve the problem that the time of optimization is too long one-time. The method was utilized in lightweight design of a certain vehicle successfully.
4. A design model of thin-walled beam for lightweight optimization was established based on the reliability of design theory. Thin-walled beam of the body is not only a basic loading part in the body design, but also a main energy-absorption part in frontal impact. Meantime, impact responses of acceleration and impact force of a vehicle and occupant safety at collision depend on the pattern of deformation and energy absorption characteristic of the thin-walled beam. In addition, the poor environment in use leads to higher design requirement of reliability . The traditional process of optimization often ignore the effects of uncertainty of the engineering design, such as geometry size, material properties, loads and boundary conditions and operating environment and so on, which leads to the design failure beyond the constraints and reduces the reliability of the product. In the paper, the thin-walled beam design was regarded as a multi-disciplinary reliability optimization design process of considering the safety, the static load-bearing characteristics and the first-order vibration mode. And this method has been applied to the lightweight optimization design of cap-thin-walled successfully.
围绕汽车轻量化这一主题,本论文主要开展了以下几方面的研究内容:
1.建立了一种基于移动最小二乘的汽车正面碰撞响应面近似模型,提出了针对不同的优化设计响应采用不同的近似模型技术来达到提高优化效率的目的。通过与目前广泛运用的多项式响应面与Kriging响应面的对比研究可知,多项式响应面只是对空间试验点的逼近,拟合精度不高,故一般适用于替代非线性程度不高的响应,而Kriging模型准确的通过了空间拟合的采样点,拟合精度高,但它容易受到数值噪声的影响且计算成本高。而移动最小二乘拟合的响应面近似模型恰恰兼顾了两者的优点,故它非常适合于具有高度非线性且具有数值噪声的汽车碰撞安全的优化研究。最终把该模型成功运用到汽车轻量化优化设计中来验证了此模型的有效性。
2.提出了一种基于近似模型和多目标遗传算法的高强度钢板选材方法。虽然汽车制造工业中铝合金等轻质材料在逐渐增加,但是由于铝合金等加工难度高,成形性能较差,又由于铝导热性好,导致铝合金的焊接性能差,关键是它的成本还比钢材高。故目前在汽车制造中仅能部分代替钢铁材料。而厚度变薄的高强度钢相对于普通钢来说则具有高强度、质量轻等优点,而且还能提高车辆的安全性能,所以高强度钢已成为普遍采用的汽车原材料。采用高强度钢板代替普通钢板制造的汽车车身,其重量可以得到较大幅度的降低。但是传统的选材设计往往都是根据工程人员的经验来选择车辆各个部分的材料配置,导致车辆各个部分的材料选择具有盲目性而不能最优化,文中采用近似模型和多目标遗传算法相结合的选材方法对整车的正面碰撞和侧面碰撞安全性进行了深入研究,得到了汽车车身驾驶室前部关键部件与侧围的高强度钢板及其板厚的合理配置,并达到使车辆的安全性能提高和车身轻量化的目的。
3.提出了一种基于近似模型和多学科设计优化相结合的整车轻量化优化设计方法。汽车轻量化的首要前提是应保持汽车原有的性能不受影响,既要有目的地减轻汽车自身的重量,又要保证汽车行驶的安全性、耐撞性、抗振性及舒适性等。但是传统的汽车设计模式往往采取的是一种串行设计模式,在不同的设计阶段设计人员将选择不同的重点来对汽车进行设计和优化,这就把影响汽车性能的空气动力学、振动、噪声、耐撞性、安全性以及舒适性等学科人为的割裂开来,并没有利用和考虑到各个学科之间存在的相互耦合而可能产生的协同效应,这样将导致得到的优化结果往往不是系统整体的最优解。同时,如果轻量化设计中一起考虑到的汽车安全性、振动、刚度等各学科的相互作用来进行优化设计,这样势必遭遇优化设计的瓶颈(单次CAE计算仿真时间过长而引起的时间问题)。正是基于上述传统串行设计与CAE仿真时间过长的缺陷,文中提出了汽车的轻量化优化设计过程也必是一个多学科设计优化的过程,并建立了将响应面和多学科设计优化方法相结合的汽车轻量化优化设计近似模型,成功解决了单次优化时间过长的优化瓶颈问题,并将该方法成功运用到某车型的轻量化优化设计中。
4.建立了基于可靠性设计理论的汽车薄壁纵梁轻量化优化设计模型。车身薄壁纵梁不仅是汽车车身设计的基本承载部件,而且也是车身发生正面碰撞时的主要吸能部件。同时,薄壁纵梁的变形模式和吸能特性直接决定了车体在碰撞时的加速度和力的响应,也就直接影响到车内乘员的安全性。此外,由于它的使用环境较为恶劣,这就对它的设计提出了更高的可靠性要求。传统的优化过程往往忽略了工程设计中的不确定性,如几何尺寸、材料属性、载荷和边界条件以及操作环境等相关的多种不确定因素的影响,而使设计目标超出设计界限而失效,从而降低了产品的可靠性。文中提出将薄壁梁设计看着是一个需要考虑安全性、静态承载特性与一阶振动模态等方面的多学科可靠性优化设计过程,并将该方法成功运用到帽型薄壁纵梁的轻量化优化设计中。
Along with the fast development of automotive industry, the energy tense and environment pressure becomes increasingly serious, which will prevent the development of automotive industry. As an effective energy-saving method, automotive lightweight has already become a crucial research topic. In the near future, it must be one of core competence among car companies. In recent years, many research achievements have been made in the automotive lightweight field. However, many lightweight-related issues need to be studied. Research methods still concentrated on replacing some automobile body parts with low-density materials, such as aluminum, magnesium alloy, composite materials, and so on. These methods almost depend on the empirical design. Therefore, in this paper, based on the predecessor's literature research, an in-depth study about the lightweight, using approximate model technology and optimization method, was conducted, so as to reduce the weight of automobile and achieve aggregative objective (reducing weight and consumes and improving vehicle safety) , under the guarantee of comprehensive performances of automobiles.
Main research content and innovation of the paper are as follows:
1. Based on moving least square method, a response surface approximate model of automotive front impact was established, and used the different approximate model technology for the different optimized design response to achieve the goal of enhancing optimization efficiency. By contrasting to Kriging response surface, the polynomial response surface is approaching the sampling points in design space, and the fitting accuracy is not high, so it is generally applied to the responses of low non-linear level, while the Kriging model whose fitting accuracy is high, can pass the spatial sampling point accurately, but it is vulnerable to numerical noise which raise the cost of calculation. However, the moving least square response surface model has both merits above, so it is very suitable for the car crash safety optimization of highly non-linear, and numerical noise. And, the model's validity is confirmed by utilizing the model in the automotive lightweight.
2. A method of high strength steel plate selection which based on the multi-objective genetic algorithm and approximate model was proposed. Although the application of the light quality materials such as aluminum alloy increases gradually in automotive manufacturing industry, due to the difficulty of processing, forming, and welding results from the good thermal conductivity, and even the higher cost than the steel, aluminum can only be used as vehicle body instead of only part of the iron and steel in the automobile manufacture at present. While the thin high-strength steel has merits of lighter quality, higher strength, as compared to the traditional steels. And it also can improve the performance of vehicle safety. Therefore, the high-strength steel has been widely used as automotive raw materials. Using the high-strength steel plate instead of traditional steel plate, the automobile body weight can be reduced to a greater degree. However, the traditional selection of materials often based on the experiences of engineers, which made the choice of materials in every part of vehicles blind and not optimal. In the paper, the safety of front impact and side impact of vehicles are conducted in deep study by combining the approximate model and the multi-objective genetic algorithm, make the high strength steel plate of front key absorbing parts of the automobile cab and the side parts and its thickness reasonable in disposition. And, the safety of vehicles was improved, and the weight of automotive body was reduced.
3. A method of the entire vehicle lightweight optimization design basing on the approximate model and the multi-disciplinary design optimization was proposed. With the most important premise which is to maintain the original performance, the automobile lightweight, not only destinate to reduce the weight, but also ensure the safety, crashworthiness, vibration, comfort, and so on. However, because the traditional model of car design was often taken as a serial design patterns, in which engineers chosed different key points to design and optimize in different stages, the influence of automobile performance was separated about the aerodynamic performance, vibration, noise, crashworthiness, safety, comfort, and the coordination effect which be produced by coupling of various subjects was not used and taken into account. So it always turned out the optimization results were not the overall optimal solution. At the same time, if the lightweight design of automobile takes the effects of safety, vibration, stiffness into account, this is bound to encounter bottleneck of the optimal design (CAE time of single calculation and simulation is too long). It is based on the flaw above-mentioned traditional serial design and CAE simulation time, and the paper propose that the process of the lightweight of automobile is a multi-disciplinary design optimization process, and establish the approximate model of automobile lightweight optimization design by combining the response surface method and multi-disciplinary design optimization method, and solve the problem that the time of optimization is too long one-time. The method was utilized in lightweight design of a certain vehicle successfully.
4. A design model of thin-walled beam for lightweight optimization was established based on the reliability of design theory. Thin-walled beam of the body is not only a basic loading part in the body design, but also a main energy-absorption part in frontal impact. Meantime, impact responses of acceleration and impact force of a vehicle and occupant safety at collision depend on the pattern of deformation and energy absorption characteristic of the thin-walled beam. In addition, the poor environment in use leads to higher design requirement of reliability . The traditional process of optimization often ignore the effects of uncertainty of the engineering design, such as geometry size, material properties, loads and boundary conditions and operating environment and so on, which leads to the design failure beyond the constraints and reduces the reliability of the product. In the paper, the thin-walled beam design was regarded as a multi-disciplinary reliability optimization design process of considering the safety, the static load-bearing characteristics and the first-order vibration mode. And this method has been applied to the lightweight optimization design of cap-thin-walled successfully.
引文
[1]张彦,来新民,朱平,等.基于抗凹性的轿车零件的轻量化设计及耐撞性分析.机械设计与研究,2004,20(5):75-79
[2]田浩彬,林建平,刘瑞同,等.汽车车身轻量化及其相关成形技术综述.汽车工程,2005,27(3):381-384
[3]王宏雁,徐少英.车门的轻量化设计.汽车工程,2004,26(3):350-354
[4]周朝霞,辛志南.铝及其合金在汽车部件中的应用.世界汽车,1998,10:21-22
[5]孙焕军,刁国强,郝晨声.汽车制造材料的轻量化趋势.黑龙江交通科技,2006,3:90-92
[6]许珞萍,邵光杰,李麟,等.汽车轻量化用金属材料及其发展动态.上海金属.2002,24(3):1-6
[7]王利,朱晓东,张丕军,等.汽车轻量化与先进的高强度钢板.宝钢技术.2003,5:53-58
[8]朱平,林忠钦,陈关龙,等.铝合金材料在轿车车身轻量化中的应用研究.计算机仿真,2006,21(8):187-190
[9]叶平,沈建平,王光耀,等.汽车轻量化用高强度钢现状及其发展趋势.机械工程材料.2006,30(3):4-7
[10]冯美斌.汽车轻量化技术中新材料的发展及应用.汽车工程,2006,28(3):213-220
[11]鞠晓锋,陈昌明,吴宪.现代汽车轻量化技术.设计研究2006,9:31-33
[12]钟新农.汽车轻量化与高强度钢板的成形性分析.机电产品开发与创新,2006,19(3):40-41
[13]Junbo Jia,Anders Ulfvarson.A parametric study for the structural behaviour of a lightweight deck.Engineering Structures,2004,26:963-977
[14]Yuxuan Li,Zhongqin Lin,Aiqin Jiang,et al.Use of high strength steel sheet for lightweight and crashworthy car body.Materials and Design,2003,24:177-182
[15]Fremgen C,Mkrtchyan L,Huber U,et al.Modeling and testing of energy absorbing lightweight materials and structures for automotive applications.Science and Technology of Advanced Materials,2005,6:883-888
[16]杨秀芳,张新,常桂秀,等.汽车主动安全技术的发展现状及趋势.重庆工学院学报(自然科学),2008,22(4):15-18
[17]钟志华,张维刚,曹立波,等.汽车碰撞安全技术.北京:机械工业出版社,2003
[18]肖军.现代新技术使汽车更安全、更可靠.CAD/CAM与制造业信息化,2008,5:22-25
[19]Etman L E P.Optimization of multibody systems using approximations concepts.Technical University Eindhoven,Eindhoven,1997
[20]Schramm U,Thomas H.Crashworthiness design using structural optimization.AIAA Paper No.98-4729,1998
[21]Kurtaran H,Eskandarian A,Marzougui D,et al.Crashworthiness design optimization using successive response surface approximations.Computational Mechanics,2002,29:409-421
[22]Lanzi L,Castelletti L M L,Anghileri M.Multi-objective optimization of composite absorber shape under crashworthiness requirements Composite Structures,2004,65:433-441
[23]张峻,柯映林.基于动态序列响应面方法的钣金成形过程参数优化.中国机械工程,2005,16(42):307-310
[24]王海亮,林忠钦,金先龙.基于响应面模型的薄壁构件抗撞性优化设计.应用力学学报,2003,20(3):61-66
[25]张立新,隋允康,高学仕.基于响应面方法的结构碰撞优化.力学与实践,2005,27(3):35-39
[26]李善坡,隋允康.响应面方法在二维连续体形状优化中的应用.力学与实践,2006,28(2):44-47
[27]王永菲,王成国.响应面法的理论与应用.中央民族大学学报,2005,14(3):236-240
[28]隋永康,李善坡.结构优化中的建模方法概述.力学进展,2008,38(2):190-198
[29]窦毅芳,王中伟,张为华.固体火箭发动机内弹道响应面建模方法.研究弹箭与制导学报,2007,27(5):133-135
[30]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究.航空学报,2005,26(1):55-61
[31]王永菲,王成国.响应面法的完全数值方案及其在悬挂参数优化中的应用.中央民族大学学报,2006,15(2):130-135
[32]任旭春,姚振汉.轮胎胎冠形状优化的自适应序列响应面法.清华大学学报,2006,46(5):736-739
[33]李恩颖,李光耀,王琥.混合响应面法对汽车吸能部件优化关键技术.计算 机应用研究,2008,25(2):368.370
[34]张峻,柯映林.序列响应面方法在覆盖件成形过程优化中的应用研究.汽车工程,2005,27(21:246-250
[35]张峻,柯映林.基于响应面和空间映射技术的模面设计优化.计算机辅助设计与图形学学报,2005,17(3):479-485
[36]房加志,焦群英,常崇义,等.响应面法在薄壁结构碰撞吸能上的应用.中国农业大学学报,2005,10(1):81-85
[37]张立新,高学仕,付志远,等.空间映射与响应面法相结合的结构优化.石油大学学报,2005,29(3):92-95
[38]谢延敏,于沪平,陈军,等.基于代理模型的板料成形优化技术进展.塑性工程学报,2006,13(2):20-24
[39]郑刚,李光耀,孙光永,等.基于近似模型的拉延筋几何参数反求.中国机械工程.2006,17(19):1988-1992
[40]廖兴涛,李青,张维刚.基于连续响应表面法的汽车结构耐撞性仿真优化.机械强度,2007,29(6):941-945
[41]Forsberg J,Nilsson L.On polynomial response surface and Kriging for use in structural optimization of crashworthiness.Struct.Multidisc.Optim.,2005,29(3):232-243
[42]Sakata S,Ashida F,Zako M.An efficient algorithm for Kriging approximation and optimization with large-scale sampling data.Computer Methods in Applied Mechanics and Engineering,2004,193:385-404
[43]Sakata S,Ashida F,Zako M.Structural optimization using Kriging approximation.Computer Methods in Applied Mechanics and Engineering,2003,192:923-939
[44]Huang D,Allen T T,Notz W I,et al.Sequential kriging optimization using multiple-fidelity evaluations.Structural and Multidisciplinary Optimization,2006,32:369-382
[45]刘克龙,姚卫星,穆雪峰.基于Kriging代理模型的结构形状优化方法研究.计算力学学报,2006,23(3):344-347
[46]王晓锋,席光.基于Kriging模型的翼型气动性能优化设计.航空学报,2005,26(5):545-549
[47]樊成,栾茂田,黎勇,等.Kriging插值无网格方法及其在力学边值问题中的应用.岩石力学与工程学报,2007,26(1):195-200
[48]徐亚栋,钱林方,陈龙淼.基于Kriging方法的复合材料身管结构近似分析.中国机械工程,2007,18(8):988-900
[49]曹鸿钧,段宝岩.基于Kriging模型的后优化近似研究.机械设计与研究,2004,20(5):10-13
[50]曾怀恩,黄声享.基于Kriging方法的空间数据插值研究.测绘工程,2007,16(5):5-13
[51]李晓斌,金振中,邹汝平,等.基于Kriging函数的序贯近似建模方法.机械设计与研究,2007,23(3):6-10
[52]张崎,李兴斯.基于Kriging模型的结构可靠性分析.计算力学学报,2006,23(2):175-179
[53]韩永志,高行山,李立州,等.基于Kriging模型的涡轮叶片多学科设计优化.航空动力学报,2007,22(7):1055-1059
[54]游海龙,贾新章.基于遗传算法的Kriging模型构造与优化.计算机辅助设计与图形学学报,2007,19(1):64-67
[55]于向军,张利辉,李春然,等.克里金模型及其在全局优化设计中的应用.中国工程机械学报,2006,4(3):259-261
[56]谢延敏,于沪平,陈军,等.基Kriging模型的可靠度计算.上海交通大学学报,2007,41(2):177-180
[57]王晓锋,席光,王尚锦.Kriging与响应面方法在气动优化设计中的应用.工程热物理学报,2005,26(3):423-425
[58]邳薇,崔新涛,王树新.基于Kriging模型的汽车车门抗撞性优化设计.设计与研究,2006,1:29-32
[59]Anthony A G,Layne T W.A comparison of approximation modeling techniques:polynomial versus interpolating models.AIAA Paper No.4758,1998
[60]龙述尧,刘凯远,胡德安.移动最小二乘近似函数中样条权函数的研究.湖南大学学报(自然科学版),2003,30(6):11-15
[61]邵卫云,张雄.水泵水轮机全特性曲线的拟合—移动最小二乘近似.水力发电学报.2004,23(5):102-106
[62]CHOI K K,YOUN B D,YANG R J.Moving Least Square Method for Reliability-Based Design Optimization.In Proceedings of 4th World Congress of Structural and Multidisciplinary Optimization,Dalian,China.June 4-8,2001:1-6
[63]Lancaster P,Salkauskas K.Surfaces Generated by Moving Least-squares Methods.Mathematics of Computation,1981,37(155):141-158
[64]曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合.工程图学学报,2004,1:84-88
[65]周凤佳,汤禹成,周雄辉.基于移动最小二乘响应曲面的挤压件毛坯优化.锻压技术,2007,32(5):77-85
[66]倪培宏,杨仕友.无网格伽辽金法及其在电磁场数值计算中的应用.电机与控制学报.2003,7(1):26-29
[67]Avalle M,Chiandussi G,Belingardi G.Design optimization by response surface methodology:application to crashworthiness design of vehicle structures.Structural and Multidisciplinary Optimization,2002,24:325-332
[68]王海亮.基于耐撞性数值仿真的汽车车身结构优化设计研究:[上海交通大学博士学位论文].上海:上海交通大学,2002
[69]张科施,韩忠华,李为吉,等.基于近似技术的高亚声速运输机机翼气动/结构优化设计.航空学报,2006,27(5):810-815
[70]廖兴涛,张维刚,李青,等.响应表面法在薄壁构件耐撞性优化设计中的应用.研究工程设计学报,2006,13(5):298-302
[71]MYERS R H,MONTGOMERY D C.Response Surface Methodology:Process and Product Optimization Using Designed Experiments.New York:Wiley Publishers,1995
[72]Forsberg J,Nilsson L.Evaluation of response surface methodologies used in crashworthiness optimization.Int.J.of Impact Engineering,2006,32:759-777
[73]REDHE M,FORSBERGE J,JANSSONE T,et al.Using the response surface methodology and the D-optimality criterion in crashworthiness related problems.Structural and Multidisciplinary Optimization,2002,24(3):185-194
[74]张铁茂,丁建国.试验设计与数据处理.北京:兵器工业出版社,1990
[75]栾军.现代试验设计优化方法.上海:上海交通大学出版社,1995
[76]刘文卿.试验设计.北京:清华大学出版社,2005
[77]何桢,潘越,刘子先,等.因子试验、RSM与田口方法的比较研究.机械设计,1999,10:1-4
[78]Lindman H R.Analysis of variance in experimental design.New York:Springer-Verlag,1991
[79]Akira Todoroki,Tetsuya Ishikawa.Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation.Composite Structures,2004,64:349-357
[80]Jack,Kleijnen P C.An overview of the design and analysis of simulation experiments for sensitivity analysis.European Journal of Operational Research,2005,164:287-300
[81]Montgomery D C.Design and analysis of experiments.4th Version,New York: NY Wiley,1997
[82]张维刚,钟志华.汽车正碰吸能部件改进的计算机仿真.汽车工程,2002,24(1):6-10
[83]曹立波,钟志华,白中浩,刘克进.台车碰撞试验用机械缓冲吸能装置研究.汽车工程,2002,24(3):228-231
[84]Redhe M,Nilsson L.Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique.Structural and Multidisciplinary Optimization,2004,27:411-420
[85]黄世霖,张金换,王晓东,等.汽车碰撞与安全.北京:清华大学出版社,2000
[86]Schramm U,Thomas H.Crashworthiness design using structural optimization.AIAA Paper No.98-4729,1998
[87]Kim C H,Arora J S.Nonlinear dynamic system identification for automotive crash using optimization:A review.Structural and Multidisciplinary Optimization,2003,25:2-18
[88]Reid J D.Crashworthiness of automotive steel midrails:thickness and material sensitivity.Thin-walled structure,1996,26(2):83-103
[89]藤田毅.汽车面板用高性能高强度钢板.鞍钢技术,2008,2:59-62
[90]郑晖,李国峰.汽车用钢板的现状和发展趋势.沈阳航空工业学院学报,2006,23(2):29-31
[91]冯祎卿.双相钢在汽车行业中的应用.工艺材料,2008,4:39-41
[92]马鸣图,M.F.Shi.先进的高强度钢及其在汽车工业中的应用.钢铁,2004,39(7):68-72
[93]马艳波,邢卓.复合钢板焊接技术.焊接,2006,12:39-41
[94]张勇,李光耀,钟志华.基于移动最小二乘响应面方法的整车轻量化设计优化.机械工程学报,2008,44(11):192-196
[95]Fang H,Rais-Rohani M,Liu Z,et al.A comparative study ofmetamodeling methods for multiobjective crashworthiness optimization.Computers and Structures,2005,83:2121-2136
[96]Zarei H R,Kroger M.Multiobjective crashworthiness optimization of circular aluminum tubes.Thin-Walled Structures,2006,44:301-308
[97]Shen-Yeh Chen.An approach for impact Structure optimization using the robust genetic algorithm.Finite Elements in Analysis and Design,2001,37:431-446
[98]易国伟.多学科设计优化中的质量工程:[北京航空航天大学硕士学位论文].北京:北京航空航天大学,2004
[99]陈建江.面向飞航导弹的多学科稳健优化设计方法及应用:[华中科技大学博士学位论文].武汉:华中科技大学:2004
[100]穆雪峰,姚卫星,余雄庆,等.多学科设计优化中常用代理模型的研究.计算力学学报,2005,22(5):608-613
[101]蒙文巩,黄俊.基于多学科设计优化的飞航导弹总体设计方法研究.飞航导弹,2006,4:9-11
[102]舒彪,韩前鹏,邓家褆.基于多学科涡轮叶片气动设计优化.南京航空航天大学学报,2005,37(6):714-719
[103]罗世彬,罗文彩,王振国.基于试验设计和响应面近似的高超声速巡航飞行器多学科设计优化.导弹与航天运载技术,2006,6:2-9
[104]张健,李为吉.飞机多学科设计优化中的近似方法分析.航空计算技术,2005,35(3):5-8
[105]吴立强,尹泽勇,蔡显新.航空发动机涡轮叶片的多学科设计优化.航空.动力学报,2005,20(5):795-80
[106]谷良贤,龚春林.多学科设计优化方法比较.弹箭与制导学报,2005,25(1):60-62
[107]李响,李为吉.飞行器多学科设计优化的三种基本类型及协同设计方法.宇航学报,2005,26(6):693-697
[108]吴宝贵,黄洪钟,原薇.汽车设计的多学科设计优化方法.应用科学学报,2005,23(4):420-423
[109]李晓斌,陈小前,张为华.多学科设计优化中搜索策略研究.战术导弹技术,2004,2:01-06.
[110]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中的应用.航空学报,2000,21(1):1-6.
[111]秦东晨,王丽霞,张珂.大型机械结构件的多学科设计优化(MDO)研究.机床与液压,2004,14:64-65
[112]王宝莎,宋保维.多学科设计优化方法及其在水下航行器设计中的应用.机械设计与制造,2006,3:26-28
[113]王爱俊,陈大融.多学科设计优化方法及其在微型飞行器设计中的应用.中国机械工程,2001,12(12):1350-1353
[114]易国伟,邓家裎.多学科设计优化过程初探.航空制造技术,2006,7:94-97
[115]陈炉云,郭维,王德禹.多学科设计优化技术在舰船设计中的应用.船海工程,2001,4:28-30
[116]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中应用.航空学报,2000,21(1):1-5
[117]王奕首,史彦军,滕弘飞.多学科设计优化研究进展.计算机集成制造系统,2005,11(6):751-756
[118]李晓斌,陈小前,张为华.多学科设计优化中搜索策略研究.战术导弹技术,2004,2:1-6
[119]陈仁伍,谷良贤,龚春林.一种基于SORA方法的多学科可靠性设计方法.机械强度,2008,30(1):37-40
[120]李哲.多学科优化设计在航空航天领域的应用及发展.航天返回与遥感,2004,25(3):65-70
[121]龚春林,谷良贤,袁建平.飞航导弹基于响应面近似技术的并行子空间优化设计.西北工业大学学报,2005,23(3):392-395
[122]王书河,何麟书.飞行器多学科设计优化概述.宇航学报,2004,25(6):697-700
[123]颜力,陈小前,王振国.飞行器多学科设计优化中的灵敏度分析方法研究.航空计算技术,2005,35(1):1-6
[124]贾建东,姚卫星,吴德海.飞行器多学科优化设计技术概论.航空科学技术,2005,6:21-25
[125]何麟书,王书河,张玉珠.飞行器多学科综合设计新算法.航空学报,2004,25(5):465-469
[126]夏露,高正红,李天.飞行器外形多目标多学科综合优化设计方法研究.空气动力学学报,2003,21(3):275-281
[127]张勇,李光耀,孙光永,等.汽车车身耐撞性与NVH多学科设计优化研究.中国机械工程,2008,19(14):1760-1763
[128]胡峪,李为吉。飞机多学科设计中的协同优化算法.西北工业大学学报,2001,19(3):357-360
[129]李响,李为吉.基于序列响应面方法的协同优化算法.西北工业大学学报,2003,21(1):79-81
[130]秦东晨,王丽霞,张珂,等.汽车车身的多学科优化设计(MDO)研究.现代机械,2004,5:4-6
[131]张勇,李光耀,孙光永,等.多学科设计优化在整车轻量化设计中的应用研究.中国机械工程,2008,19(7):877-881
[132]胡峪.飞机多学科设计优化及其应用研究:[西北工业大学博士学位论文].西安:西北工业大学,2001
[133]余雄庆.多学科设计优化算法及其在飞机设计中的应用研究:[南京航空航天大学博士学位论文].南京:南京航空航天大学,1999
[134]韩明红.复杂工程系统多学科设计优化方法及技术研究:[北京航空航天大 学博士学位论文].北京:北京航空航天大学,2004
[135]张健.飞机多学科设计优化中的近似方法研究:[西北工业大学硕士学位论文].西安:西北工业大学:2006
[136]穆雪峰.多学科设计优化代理模型技术的研究和应用:[南京航空航天大学硕士学位论文].南京:南京航空航天大学:2004
[137]原薇.基于可靠性的多学科设计优化:[大连理工大学硕士学位论文].大连:大连理工大学:2005
[138]韩明红,邓家裎.多学科设计优化中的不确定性建模.北京航空航天大学学报,2007,33(1):115-118
[139]YANG R J,GU L,THO C H,et al.Reliability-Based Multidisciplinary Design Optimization of a Full Vehicle System.In Proceedings of 43rd AIAA SDM Conference,Denver,CO,AIAA-2002-1758:1-9
[140]Youn B D,Choi K K.A new response surface methodology for reliability-based design optimization.Computers and Structures,2004,82:241-256
[141]Zang C,Friswell M I,Mottershead J E.A review of robust optimal design and its application in dynamics.Computers and Structures,2005,83:315-326
[142]Courteille E,Leotoing L,Mortier F,et al.New analytical method to evaluate the powerplant and chassis coupling in the improvement vehicle NVH European.Journal of Mechanics A/Solids,2005,24:929-943
[143]张义民,王世鹏,解艳彩.广义随机空间内汽车零部件的可靠性优化设计.汽车工程,2008,30(3):268-270
[144]徐小军,陈循,尚建忠,等.波浪补偿系统差动行星传动多目标模糊可靠性优化设计.中国机械工程,2008,19(4):392-395
[145]苏多,张建国,李强多,等.学科优化技术在空间结构锁可靠性设计分析中的应用.航空学报,2008,29(1):95-100
[146]贺向东,张义民,刘巧伶,等.非正态分布参数的梁结构的刚度可靠性稳健设计.固体力学学报,2007,28(4):411-414
[147]孙光永,李光耀,张勇,等.基于鲁棒性的概率优化设计在薄壁构件耐撞性中的应用.中国机械工程,2007,18(4):479-483
[148]吕震宙,赵洁,岳珠峰.机械可靠性分析的高精度响应面法.应用数学和力学,2007,28(1):17-23
[149]桂劲松,康海贵.结构可靠度分析的响应面法及其Matlab实现.计算力学学报,2004,2l(6):683-687
[150]蒋友宝,冯健,孟少平.极限状态响应面法分析结构可靠度的研究.公路交 通科技,2006,23(11):52-55
[151]刘金辉,乔志德,杨旭东,等.基于响应面法的机翼气动/结构一体化优化设计研究空气动力学学报,2006,24(3):300-306
[152]李玉强,崔振山,陈军,等.基于响应面模型的6 σ稳健设计方法.上海交通大学学报,2006,40(2):201-205
[153]曹鸿钧,段宝岩.多学科系统非概率可靠性分析研究.机械科学与技术,2005,24(6):646-649
[154]张为华,李晓斌.飞行器多学科不确定性设计理论概述.宇航学报,2004,25(6):702-706
[155]曹鸿钧,段宝岩.基于凸集模型的多学科耦合系统不确定性分析.西安电子科技大学学报,2005,32(3):335-338
[156]Klepaczko J R.Review on critical impact velocities in tension and shear.International Journal of Impact Engineering,2005,32:188-209
[157]Liefvendahl M,Stocki R.A study on algorithms for optimization of Latin hypercubes.Journal of Statistical Planning and Inference,2006,136:3231-3247
[158]Kenny Q Ye,William Li,Agus Sudjianto.Algorithmic construction of optimal symmetric Latin hypercube designs.Journal of Statistical Planning and Inference,2000,90:145-159
[159]Rodriguez J F,Perez V M,Padmanabhan D,et al.Sequential approximate optimization using variable fidelity response surface approximations.Structural and Multidisciplinary Optimization,2001,22:24-34
[160]Yang R J,Gu L.High performance computing & rapid visualization for design steering in mdo.AIAA 2003-1528:1-6
[161]Yuping He,John McPhee.Multidisciplinary Design Optimization of Mechatronic Vehicleswith Active Suspensions.Journal of Sound and Vibration,2005,283:217-241
[162]Yang R J,Gu L.Experience with Approximate Reliability-Based Optimization Methods.AIAA 2003-1781:1-8
[163]Gu L,Yang R J.Recent Applications on Reliability-Based Optimization of Automotive Structures.SAE,2003,152(1):1-13
[164]Youn B D,Choi K K,Yang R J,et al.Reliability-based design optimization for crashworthiness of vehicle side impact.Structural and Multidisciplinary Optimization,2003,25:1-12
[165]Youn B D,Choi K K.A new response surface methodology for reliability based design optimization. Computers and Structures, 2004, 82: 241-256
[166] By Ren-Jye Yang, Alexander Akkerman, Daniel F A, et al. Robustness Optimization for Vehicular Crash Simulations. Computing in Science and Engineering, 2000, 22: 8-13
[167] Yang R J, Gu L. Application of Descriptive Sampling and Metamodeling Methods for Optimal Design and Robustness of Vehicle Structures. AIAA 2002-1321:1-7
[168] Yang R J, Gu L, Tho C H. Multidisciplinary design optimization of a full vehicle with high performance computing. AIAA Paper No: 2001-1273, 2001
[169] Sobieszczanski-Sobieski J, Kodiyalam S, Yang R J. Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. AIAA Paper No. 2000-1521,2000
[170] Gu L. A comparison of polynomial based regression models in vehicle safety analysis. Proceedings of DETC'01 ASME 2001 Design Engineering Technical Conferences and the Computers and Information in Engineering Conference Pittsburgh, Pennsylvania, September 9-12, 2001, 1-6
[171] Craig K J, Nielen Stander, Dooge D A, et al. Mdo of automotive vehicle for crashworthiness and NVH using response surface methods. AIAA 2002-5607: 1-8
[172] Gu L, Li G, Yang R J. An Excel Based Robust Design Tool for Vehicle Structural Optimization. SAE, 2004, 1124(1): 1-8
[173] Lam K P, Behdinan K, Cleghorn W L. A material and gauge thickness sensitivity analysis on the NVH and crashworthiness of automotive instrument panel support. Thin-Walled Structures, 2003, 41:1005-1018
[174] Chen J, Xiao R, Zhong Y. A response surface based hierarchical approach to multidisciplinary robust optimization design. Journal of Advanced Manufacture Technology, 2004, 41(6): 189-204
[175] Liefvendahla M, Stockib R. A study on algorithms for optimization of Latin hypercubes. Journal of Statistical Planning and Inference, 2006, 136: 3231-3247
[176] Kenny Q Ye, William Li, Agus Sudjianto. Algorithmic construction of optimal symmetric Latin hypercube designs. Journal of Statistical Planning and Inference, 2000, 90: 145-159
[177] Craig K J, Nielen S, Dooge D A, et al. MDO of automotive vehicle for crashworthiness and NVH using response surface methods. 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization 4-6 September 2002, Atlanta, Georgia, AIAA 2002-5607:1-12
[178] Yang R J, Gu L, Tho C H, et al. Reliability-Based Multidisciplinary Design Optimization of a Full Vehicle System. In Proceedings of 43rd AIAA SDM Conference, Denver, CO, AIAA-2002-1758: 1-9
[179] Kodyalam S, Sobieszczanski-sobieski J. Multidisciplinary design optimization some formal methods, framework, requirements, and application to vehicle design. Int. J. Vehicle Design (Special Issue), 2001, 50(3): 1101-1120
[180] Du X, Chen W. Concurrent subsystem uncertainty analysis in multidisciplinary design. In: 8th AIAA/ USAF/ NASA/ ISSMO Symposium on Multi-Disciplinary Analysis and Optimization, Long Beach, California, AIAA-2000-4841: 1-12.
[181] Kaushik, Sinha. Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety. Structural and Multidisciplinary Optimization, 2007, 33: 255-268
[182] SERHAT HOSDER, LAYNE T W, BERNARD GROSSMAN, et al. Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport. Optimization and Engineering, 2001, 2:431-452
[183] Eric Sandgren, Cameron T M. Robust design optimization of structures through consideration of variation. Computers and Structures, 2002, 80: 1605-1613
[184] Alex Shenfield, Peter J F, Muhammad Alkarouri. Computational steering of a multi-objective evolutionary algorithm for engineering design, Engineering Applications of Artificial Intelligence, 2007, 5:1-11
[2]田浩彬,林建平,刘瑞同,等.汽车车身轻量化及其相关成形技术综述.汽车工程,2005,27(3):381-384
[3]王宏雁,徐少英.车门的轻量化设计.汽车工程,2004,26(3):350-354
[4]周朝霞,辛志南.铝及其合金在汽车部件中的应用.世界汽车,1998,10:21-22
[5]孙焕军,刁国强,郝晨声.汽车制造材料的轻量化趋势.黑龙江交通科技,2006,3:90-92
[6]许珞萍,邵光杰,李麟,等.汽车轻量化用金属材料及其发展动态.上海金属.2002,24(3):1-6
[7]王利,朱晓东,张丕军,等.汽车轻量化与先进的高强度钢板.宝钢技术.2003,5:53-58
[8]朱平,林忠钦,陈关龙,等.铝合金材料在轿车车身轻量化中的应用研究.计算机仿真,2006,21(8):187-190
[9]叶平,沈建平,王光耀,等.汽车轻量化用高强度钢现状及其发展趋势.机械工程材料.2006,30(3):4-7
[10]冯美斌.汽车轻量化技术中新材料的发展及应用.汽车工程,2006,28(3):213-220
[11]鞠晓锋,陈昌明,吴宪.现代汽车轻量化技术.设计研究2006,9:31-33
[12]钟新农.汽车轻量化与高强度钢板的成形性分析.机电产品开发与创新,2006,19(3):40-41
[13]Junbo Jia,Anders Ulfvarson.A parametric study for the structural behaviour of a lightweight deck.Engineering Structures,2004,26:963-977
[14]Yuxuan Li,Zhongqin Lin,Aiqin Jiang,et al.Use of high strength steel sheet for lightweight and crashworthy car body.Materials and Design,2003,24:177-182
[15]Fremgen C,Mkrtchyan L,Huber U,et al.Modeling and testing of energy absorbing lightweight materials and structures for automotive applications.Science and Technology of Advanced Materials,2005,6:883-888
[16]杨秀芳,张新,常桂秀,等.汽车主动安全技术的发展现状及趋势.重庆工学院学报(自然科学),2008,22(4):15-18
[17]钟志华,张维刚,曹立波,等.汽车碰撞安全技术.北京:机械工业出版社,2003
[18]肖军.现代新技术使汽车更安全、更可靠.CAD/CAM与制造业信息化,2008,5:22-25
[19]Etman L E P.Optimization of multibody systems using approximations concepts.Technical University Eindhoven,Eindhoven,1997
[20]Schramm U,Thomas H.Crashworthiness design using structural optimization.AIAA Paper No.98-4729,1998
[21]Kurtaran H,Eskandarian A,Marzougui D,et al.Crashworthiness design optimization using successive response surface approximations.Computational Mechanics,2002,29:409-421
[22]Lanzi L,Castelletti L M L,Anghileri M.Multi-objective optimization of composite absorber shape under crashworthiness requirements Composite Structures,2004,65:433-441
[23]张峻,柯映林.基于动态序列响应面方法的钣金成形过程参数优化.中国机械工程,2005,16(42):307-310
[24]王海亮,林忠钦,金先龙.基于响应面模型的薄壁构件抗撞性优化设计.应用力学学报,2003,20(3):61-66
[25]张立新,隋允康,高学仕.基于响应面方法的结构碰撞优化.力学与实践,2005,27(3):35-39
[26]李善坡,隋允康.响应面方法在二维连续体形状优化中的应用.力学与实践,2006,28(2):44-47
[27]王永菲,王成国.响应面法的理论与应用.中央民族大学学报,2005,14(3):236-240
[28]隋永康,李善坡.结构优化中的建模方法概述.力学进展,2008,38(2):190-198
[29]窦毅芳,王中伟,张为华.固体火箭发动机内弹道响应面建模方法.研究弹箭与制导学报,2007,27(5):133-135
[30]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究.航空学报,2005,26(1):55-61
[31]王永菲,王成国.响应面法的完全数值方案及其在悬挂参数优化中的应用.中央民族大学学报,2006,15(2):130-135
[32]任旭春,姚振汉.轮胎胎冠形状优化的自适应序列响应面法.清华大学学报,2006,46(5):736-739
[33]李恩颖,李光耀,王琥.混合响应面法对汽车吸能部件优化关键技术.计算 机应用研究,2008,25(2):368.370
[34]张峻,柯映林.序列响应面方法在覆盖件成形过程优化中的应用研究.汽车工程,2005,27(21:246-250
[35]张峻,柯映林.基于响应面和空间映射技术的模面设计优化.计算机辅助设计与图形学学报,2005,17(3):479-485
[36]房加志,焦群英,常崇义,等.响应面法在薄壁结构碰撞吸能上的应用.中国农业大学学报,2005,10(1):81-85
[37]张立新,高学仕,付志远,等.空间映射与响应面法相结合的结构优化.石油大学学报,2005,29(3):92-95
[38]谢延敏,于沪平,陈军,等.基于代理模型的板料成形优化技术进展.塑性工程学报,2006,13(2):20-24
[39]郑刚,李光耀,孙光永,等.基于近似模型的拉延筋几何参数反求.中国机械工程.2006,17(19):1988-1992
[40]廖兴涛,李青,张维刚.基于连续响应表面法的汽车结构耐撞性仿真优化.机械强度,2007,29(6):941-945
[41]Forsberg J,Nilsson L.On polynomial response surface and Kriging for use in structural optimization of crashworthiness.Struct.Multidisc.Optim.,2005,29(3):232-243
[42]Sakata S,Ashida F,Zako M.An efficient algorithm for Kriging approximation and optimization with large-scale sampling data.Computer Methods in Applied Mechanics and Engineering,2004,193:385-404
[43]Sakata S,Ashida F,Zako M.Structural optimization using Kriging approximation.Computer Methods in Applied Mechanics and Engineering,2003,192:923-939
[44]Huang D,Allen T T,Notz W I,et al.Sequential kriging optimization using multiple-fidelity evaluations.Structural and Multidisciplinary Optimization,2006,32:369-382
[45]刘克龙,姚卫星,穆雪峰.基于Kriging代理模型的结构形状优化方法研究.计算力学学报,2006,23(3):344-347
[46]王晓锋,席光.基于Kriging模型的翼型气动性能优化设计.航空学报,2005,26(5):545-549
[47]樊成,栾茂田,黎勇,等.Kriging插值无网格方法及其在力学边值问题中的应用.岩石力学与工程学报,2007,26(1):195-200
[48]徐亚栋,钱林方,陈龙淼.基于Kriging方法的复合材料身管结构近似分析.中国机械工程,2007,18(8):988-900
[49]曹鸿钧,段宝岩.基于Kriging模型的后优化近似研究.机械设计与研究,2004,20(5):10-13
[50]曾怀恩,黄声享.基于Kriging方法的空间数据插值研究.测绘工程,2007,16(5):5-13
[51]李晓斌,金振中,邹汝平,等.基于Kriging函数的序贯近似建模方法.机械设计与研究,2007,23(3):6-10
[52]张崎,李兴斯.基于Kriging模型的结构可靠性分析.计算力学学报,2006,23(2):175-179
[53]韩永志,高行山,李立州,等.基于Kriging模型的涡轮叶片多学科设计优化.航空动力学报,2007,22(7):1055-1059
[54]游海龙,贾新章.基于遗传算法的Kriging模型构造与优化.计算机辅助设计与图形学学报,2007,19(1):64-67
[55]于向军,张利辉,李春然,等.克里金模型及其在全局优化设计中的应用.中国工程机械学报,2006,4(3):259-261
[56]谢延敏,于沪平,陈军,等.基Kriging模型的可靠度计算.上海交通大学学报,2007,41(2):177-180
[57]王晓锋,席光,王尚锦.Kriging与响应面方法在气动优化设计中的应用.工程热物理学报,2005,26(3):423-425
[58]邳薇,崔新涛,王树新.基于Kriging模型的汽车车门抗撞性优化设计.设计与研究,2006,1:29-32
[59]Anthony A G,Layne T W.A comparison of approximation modeling techniques:polynomial versus interpolating models.AIAA Paper No.4758,1998
[60]龙述尧,刘凯远,胡德安.移动最小二乘近似函数中样条权函数的研究.湖南大学学报(自然科学版),2003,30(6):11-15
[61]邵卫云,张雄.水泵水轮机全特性曲线的拟合—移动最小二乘近似.水力发电学报.2004,23(5):102-106
[62]CHOI K K,YOUN B D,YANG R J.Moving Least Square Method for Reliability-Based Design Optimization.In Proceedings of 4th World Congress of Structural and Multidisciplinary Optimization,Dalian,China.June 4-8,2001:1-6
[63]Lancaster P,Salkauskas K.Surfaces Generated by Moving Least-squares Methods.Mathematics of Computation,1981,37(155):141-158
[64]曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合.工程图学学报,2004,1:84-88
[65]周凤佳,汤禹成,周雄辉.基于移动最小二乘响应曲面的挤压件毛坯优化.锻压技术,2007,32(5):77-85
[66]倪培宏,杨仕友.无网格伽辽金法及其在电磁场数值计算中的应用.电机与控制学报.2003,7(1):26-29
[67]Avalle M,Chiandussi G,Belingardi G.Design optimization by response surface methodology:application to crashworthiness design of vehicle structures.Structural and Multidisciplinary Optimization,2002,24:325-332
[68]王海亮.基于耐撞性数值仿真的汽车车身结构优化设计研究:[上海交通大学博士学位论文].上海:上海交通大学,2002
[69]张科施,韩忠华,李为吉,等.基于近似技术的高亚声速运输机机翼气动/结构优化设计.航空学报,2006,27(5):810-815
[70]廖兴涛,张维刚,李青,等.响应表面法在薄壁构件耐撞性优化设计中的应用.研究工程设计学报,2006,13(5):298-302
[71]MYERS R H,MONTGOMERY D C.Response Surface Methodology:Process and Product Optimization Using Designed Experiments.New York:Wiley Publishers,1995
[72]Forsberg J,Nilsson L.Evaluation of response surface methodologies used in crashworthiness optimization.Int.J.of Impact Engineering,2006,32:759-777
[73]REDHE M,FORSBERGE J,JANSSONE T,et al.Using the response surface methodology and the D-optimality criterion in crashworthiness related problems.Structural and Multidisciplinary Optimization,2002,24(3):185-194
[74]张铁茂,丁建国.试验设计与数据处理.北京:兵器工业出版社,1990
[75]栾军.现代试验设计优化方法.上海:上海交通大学出版社,1995
[76]刘文卿.试验设计.北京:清华大学出版社,2005
[77]何桢,潘越,刘子先,等.因子试验、RSM与田口方法的比较研究.机械设计,1999,10:1-4
[78]Lindman H R.Analysis of variance in experimental design.New York:Springer-Verlag,1991
[79]Akira Todoroki,Tetsuya Ishikawa.Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation.Composite Structures,2004,64:349-357
[80]Jack,Kleijnen P C.An overview of the design and analysis of simulation experiments for sensitivity analysis.European Journal of Operational Research,2005,164:287-300
[81]Montgomery D C.Design and analysis of experiments.4th Version,New York: NY Wiley,1997
[82]张维刚,钟志华.汽车正碰吸能部件改进的计算机仿真.汽车工程,2002,24(1):6-10
[83]曹立波,钟志华,白中浩,刘克进.台车碰撞试验用机械缓冲吸能装置研究.汽车工程,2002,24(3):228-231
[84]Redhe M,Nilsson L.Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique.Structural and Multidisciplinary Optimization,2004,27:411-420
[85]黄世霖,张金换,王晓东,等.汽车碰撞与安全.北京:清华大学出版社,2000
[86]Schramm U,Thomas H.Crashworthiness design using structural optimization.AIAA Paper No.98-4729,1998
[87]Kim C H,Arora J S.Nonlinear dynamic system identification for automotive crash using optimization:A review.Structural and Multidisciplinary Optimization,2003,25:2-18
[88]Reid J D.Crashworthiness of automotive steel midrails:thickness and material sensitivity.Thin-walled structure,1996,26(2):83-103
[89]藤田毅.汽车面板用高性能高强度钢板.鞍钢技术,2008,2:59-62
[90]郑晖,李国峰.汽车用钢板的现状和发展趋势.沈阳航空工业学院学报,2006,23(2):29-31
[91]冯祎卿.双相钢在汽车行业中的应用.工艺材料,2008,4:39-41
[92]马鸣图,M.F.Shi.先进的高强度钢及其在汽车工业中的应用.钢铁,2004,39(7):68-72
[93]马艳波,邢卓.复合钢板焊接技术.焊接,2006,12:39-41
[94]张勇,李光耀,钟志华.基于移动最小二乘响应面方法的整车轻量化设计优化.机械工程学报,2008,44(11):192-196
[95]Fang H,Rais-Rohani M,Liu Z,et al.A comparative study ofmetamodeling methods for multiobjective crashworthiness optimization.Computers and Structures,2005,83:2121-2136
[96]Zarei H R,Kroger M.Multiobjective crashworthiness optimization of circular aluminum tubes.Thin-Walled Structures,2006,44:301-308
[97]Shen-Yeh Chen.An approach for impact Structure optimization using the robust genetic algorithm.Finite Elements in Analysis and Design,2001,37:431-446
[98]易国伟.多学科设计优化中的质量工程:[北京航空航天大学硕士学位论文].北京:北京航空航天大学,2004
[99]陈建江.面向飞航导弹的多学科稳健优化设计方法及应用:[华中科技大学博士学位论文].武汉:华中科技大学:2004
[100]穆雪峰,姚卫星,余雄庆,等.多学科设计优化中常用代理模型的研究.计算力学学报,2005,22(5):608-613
[101]蒙文巩,黄俊.基于多学科设计优化的飞航导弹总体设计方法研究.飞航导弹,2006,4:9-11
[102]舒彪,韩前鹏,邓家褆.基于多学科涡轮叶片气动设计优化.南京航空航天大学学报,2005,37(6):714-719
[103]罗世彬,罗文彩,王振国.基于试验设计和响应面近似的高超声速巡航飞行器多学科设计优化.导弹与航天运载技术,2006,6:2-9
[104]张健,李为吉.飞机多学科设计优化中的近似方法分析.航空计算技术,2005,35(3):5-8
[105]吴立强,尹泽勇,蔡显新.航空发动机涡轮叶片的多学科设计优化.航空.动力学报,2005,20(5):795-80
[106]谷良贤,龚春林.多学科设计优化方法比较.弹箭与制导学报,2005,25(1):60-62
[107]李响,李为吉.飞行器多学科设计优化的三种基本类型及协同设计方法.宇航学报,2005,26(6):693-697
[108]吴宝贵,黄洪钟,原薇.汽车设计的多学科设计优化方法.应用科学学报,2005,23(4):420-423
[109]李晓斌,陈小前,张为华.多学科设计优化中搜索策略研究.战术导弹技术,2004,2:01-06.
[110]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中的应用.航空学报,2000,21(1):1-6.
[111]秦东晨,王丽霞,张珂.大型机械结构件的多学科设计优化(MDO)研究.机床与液压,2004,14:64-65
[112]王宝莎,宋保维.多学科设计优化方法及其在水下航行器设计中的应用.机械设计与制造,2006,3:26-28
[113]王爱俊,陈大融.多学科设计优化方法及其在微型飞行器设计中的应用.中国机械工程,2001,12(12):1350-1353
[114]易国伟,邓家裎.多学科设计优化过程初探.航空制造技术,2006,7:94-97
[115]陈炉云,郭维,王德禹.多学科设计优化技术在舰船设计中的应用.船海工程,2001,4:28-30
[116]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中应用.航空学报,2000,21(1):1-5
[117]王奕首,史彦军,滕弘飞.多学科设计优化研究进展.计算机集成制造系统,2005,11(6):751-756
[118]李晓斌,陈小前,张为华.多学科设计优化中搜索策略研究.战术导弹技术,2004,2:1-6
[119]陈仁伍,谷良贤,龚春林.一种基于SORA方法的多学科可靠性设计方法.机械强度,2008,30(1):37-40
[120]李哲.多学科优化设计在航空航天领域的应用及发展.航天返回与遥感,2004,25(3):65-70
[121]龚春林,谷良贤,袁建平.飞航导弹基于响应面近似技术的并行子空间优化设计.西北工业大学学报,2005,23(3):392-395
[122]王书河,何麟书.飞行器多学科设计优化概述.宇航学报,2004,25(6):697-700
[123]颜力,陈小前,王振国.飞行器多学科设计优化中的灵敏度分析方法研究.航空计算技术,2005,35(1):1-6
[124]贾建东,姚卫星,吴德海.飞行器多学科优化设计技术概论.航空科学技术,2005,6:21-25
[125]何麟书,王书河,张玉珠.飞行器多学科综合设计新算法.航空学报,2004,25(5):465-469
[126]夏露,高正红,李天.飞行器外形多目标多学科综合优化设计方法研究.空气动力学学报,2003,21(3):275-281
[127]张勇,李光耀,孙光永,等.汽车车身耐撞性与NVH多学科设计优化研究.中国机械工程,2008,19(14):1760-1763
[128]胡峪,李为吉。飞机多学科设计中的协同优化算法.西北工业大学学报,2001,19(3):357-360
[129]李响,李为吉.基于序列响应面方法的协同优化算法.西北工业大学学报,2003,21(1):79-81
[130]秦东晨,王丽霞,张珂,等.汽车车身的多学科优化设计(MDO)研究.现代机械,2004,5:4-6
[131]张勇,李光耀,孙光永,等.多学科设计优化在整车轻量化设计中的应用研究.中国机械工程,2008,19(7):877-881
[132]胡峪.飞机多学科设计优化及其应用研究:[西北工业大学博士学位论文].西安:西北工业大学,2001
[133]余雄庆.多学科设计优化算法及其在飞机设计中的应用研究:[南京航空航天大学博士学位论文].南京:南京航空航天大学,1999
[134]韩明红.复杂工程系统多学科设计优化方法及技术研究:[北京航空航天大 学博士学位论文].北京:北京航空航天大学,2004
[135]张健.飞机多学科设计优化中的近似方法研究:[西北工业大学硕士学位论文].西安:西北工业大学:2006
[136]穆雪峰.多学科设计优化代理模型技术的研究和应用:[南京航空航天大学硕士学位论文].南京:南京航空航天大学:2004
[137]原薇.基于可靠性的多学科设计优化:[大连理工大学硕士学位论文].大连:大连理工大学:2005
[138]韩明红,邓家裎.多学科设计优化中的不确定性建模.北京航空航天大学学报,2007,33(1):115-118
[139]YANG R J,GU L,THO C H,et al.Reliability-Based Multidisciplinary Design Optimization of a Full Vehicle System.In Proceedings of 43rd AIAA SDM Conference,Denver,CO,AIAA-2002-1758:1-9
[140]Youn B D,Choi K K.A new response surface methodology for reliability-based design optimization.Computers and Structures,2004,82:241-256
[141]Zang C,Friswell M I,Mottershead J E.A review of robust optimal design and its application in dynamics.Computers and Structures,2005,83:315-326
[142]Courteille E,Leotoing L,Mortier F,et al.New analytical method to evaluate the powerplant and chassis coupling in the improvement vehicle NVH European.Journal of Mechanics A/Solids,2005,24:929-943
[143]张义民,王世鹏,解艳彩.广义随机空间内汽车零部件的可靠性优化设计.汽车工程,2008,30(3):268-270
[144]徐小军,陈循,尚建忠,等.波浪补偿系统差动行星传动多目标模糊可靠性优化设计.中国机械工程,2008,19(4):392-395
[145]苏多,张建国,李强多,等.学科优化技术在空间结构锁可靠性设计分析中的应用.航空学报,2008,29(1):95-100
[146]贺向东,张义民,刘巧伶,等.非正态分布参数的梁结构的刚度可靠性稳健设计.固体力学学报,2007,28(4):411-414
[147]孙光永,李光耀,张勇,等.基于鲁棒性的概率优化设计在薄壁构件耐撞性中的应用.中国机械工程,2007,18(4):479-483
[148]吕震宙,赵洁,岳珠峰.机械可靠性分析的高精度响应面法.应用数学和力学,2007,28(1):17-23
[149]桂劲松,康海贵.结构可靠度分析的响应面法及其Matlab实现.计算力学学报,2004,2l(6):683-687
[150]蒋友宝,冯健,孟少平.极限状态响应面法分析结构可靠度的研究.公路交 通科技,2006,23(11):52-55
[151]刘金辉,乔志德,杨旭东,等.基于响应面法的机翼气动/结构一体化优化设计研究空气动力学学报,2006,24(3):300-306
[152]李玉强,崔振山,陈军,等.基于响应面模型的6 σ稳健设计方法.上海交通大学学报,2006,40(2):201-205
[153]曹鸿钧,段宝岩.多学科系统非概率可靠性分析研究.机械科学与技术,2005,24(6):646-649
[154]张为华,李晓斌.飞行器多学科不确定性设计理论概述.宇航学报,2004,25(6):702-706
[155]曹鸿钧,段宝岩.基于凸集模型的多学科耦合系统不确定性分析.西安电子科技大学学报,2005,32(3):335-338
[156]Klepaczko J R.Review on critical impact velocities in tension and shear.International Journal of Impact Engineering,2005,32:188-209
[157]Liefvendahl M,Stocki R.A study on algorithms for optimization of Latin hypercubes.Journal of Statistical Planning and Inference,2006,136:3231-3247
[158]Kenny Q Ye,William Li,Agus Sudjianto.Algorithmic construction of optimal symmetric Latin hypercube designs.Journal of Statistical Planning and Inference,2000,90:145-159
[159]Rodriguez J F,Perez V M,Padmanabhan D,et al.Sequential approximate optimization using variable fidelity response surface approximations.Structural and Multidisciplinary Optimization,2001,22:24-34
[160]Yang R J,Gu L.High performance computing & rapid visualization for design steering in mdo.AIAA 2003-1528:1-6
[161]Yuping He,John McPhee.Multidisciplinary Design Optimization of Mechatronic Vehicleswith Active Suspensions.Journal of Sound and Vibration,2005,283:217-241
[162]Yang R J,Gu L.Experience with Approximate Reliability-Based Optimization Methods.AIAA 2003-1781:1-8
[163]Gu L,Yang R J.Recent Applications on Reliability-Based Optimization of Automotive Structures.SAE,2003,152(1):1-13
[164]Youn B D,Choi K K,Yang R J,et al.Reliability-based design optimization for crashworthiness of vehicle side impact.Structural and Multidisciplinary Optimization,2003,25:1-12
[165]Youn B D,Choi K K.A new response surface methodology for reliability based design optimization. Computers and Structures, 2004, 82: 241-256
[166] By Ren-Jye Yang, Alexander Akkerman, Daniel F A, et al. Robustness Optimization for Vehicular Crash Simulations. Computing in Science and Engineering, 2000, 22: 8-13
[167] Yang R J, Gu L. Application of Descriptive Sampling and Metamodeling Methods for Optimal Design and Robustness of Vehicle Structures. AIAA 2002-1321:1-7
[168] Yang R J, Gu L, Tho C H. Multidisciplinary design optimization of a full vehicle with high performance computing. AIAA Paper No: 2001-1273, 2001
[169] Sobieszczanski-Sobieski J, Kodiyalam S, Yang R J. Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. AIAA Paper No. 2000-1521,2000
[170] Gu L. A comparison of polynomial based regression models in vehicle safety analysis. Proceedings of DETC'01 ASME 2001 Design Engineering Technical Conferences and the Computers and Information in Engineering Conference Pittsburgh, Pennsylvania, September 9-12, 2001, 1-6
[171] Craig K J, Nielen Stander, Dooge D A, et al. Mdo of automotive vehicle for crashworthiness and NVH using response surface methods. AIAA 2002-5607: 1-8
[172] Gu L, Li G, Yang R J. An Excel Based Robust Design Tool for Vehicle Structural Optimization. SAE, 2004, 1124(1): 1-8
[173] Lam K P, Behdinan K, Cleghorn W L. A material and gauge thickness sensitivity analysis on the NVH and crashworthiness of automotive instrument panel support. Thin-Walled Structures, 2003, 41:1005-1018
[174] Chen J, Xiao R, Zhong Y. A response surface based hierarchical approach to multidisciplinary robust optimization design. Journal of Advanced Manufacture Technology, 2004, 41(6): 189-204
[175] Liefvendahla M, Stockib R. A study on algorithms for optimization of Latin hypercubes. Journal of Statistical Planning and Inference, 2006, 136: 3231-3247
[176] Kenny Q Ye, William Li, Agus Sudjianto. Algorithmic construction of optimal symmetric Latin hypercube designs. Journal of Statistical Planning and Inference, 2000, 90: 145-159
[177] Craig K J, Nielen S, Dooge D A, et al. MDO of automotive vehicle for crashworthiness and NVH using response surface methods. 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization 4-6 September 2002, Atlanta, Georgia, AIAA 2002-5607:1-12
[178] Yang R J, Gu L, Tho C H, et al. Reliability-Based Multidisciplinary Design Optimization of a Full Vehicle System. In Proceedings of 43rd AIAA SDM Conference, Denver, CO, AIAA-2002-1758: 1-9
[179] Kodyalam S, Sobieszczanski-sobieski J. Multidisciplinary design optimization some formal methods, framework, requirements, and application to vehicle design. Int. J. Vehicle Design (Special Issue), 2001, 50(3): 1101-1120
[180] Du X, Chen W. Concurrent subsystem uncertainty analysis in multidisciplinary design. In: 8th AIAA/ USAF/ NASA/ ISSMO Symposium on Multi-Disciplinary Analysis and Optimization, Long Beach, California, AIAA-2000-4841: 1-12.
[181] Kaushik, Sinha. Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety. Structural and Multidisciplinary Optimization, 2007, 33: 255-268
[182] SERHAT HOSDER, LAYNE T W, BERNARD GROSSMAN, et al. Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport. Optimization and Engineering, 2001, 2:431-452
[183] Eric Sandgren, Cameron T M. Robust design optimization of structures through consideration of variation. Computers and Structures, 2002, 80: 1605-1613
[184] Alex Shenfield, Peter J F, Muhammad Alkarouri. Computational steering of a multi-objective evolutionary algorithm for engineering design, Engineering Applications of Artificial Intelligence, 2007, 5:1-11