In the last years, the automotive engineering industry has been deeply influenced by the use of «machine learning» techniques for new design and innovation purposes. However, some specific engineering aspects like numerical optimization study still require the development of suitable high-performance machine learning approaches involving parametrized Finite Elements (FE) structural dynamics simulation data. Weight reduction on a car body is a crucial matter that improves the environmental impact and the cost of the product. The actual optimization process at Renault SA uses numerical Design of Experiments (DOE) to find the right thicknesses and materials for each part of the vehicle that guarantees a reduced weight while keeping a good behavior of the car body, identified by criteria or sensors on the body (maximum displacements, upper bounds of instantaneous acceleration …). The usual DOE methodology generally uses between 3 and 10 times the numbers of parameters of the study (which means, for a 30-parameters study, at least 90 simulations, with typically 10 h per run on a 140-core computer). During the last 2 years, Renault’s teams strived to develop a disruptive methodology to conduct optimization study. By ‘disruptive’, we mean to find a methodology that cuts the cost of computational effort by several orders of magnitude. It is acknowledged that standard DoEs need a number of simulations which is at least proportional to the dimension of the parameter space, leading generally to hundreds of fine simulations for real applications. Comparatively, a disruptive method should require about 10 fine evaluations only. This can be achieved by means of a combination of massive data knowledge extraction of FE crash simulation results and the help of parallel high-performance computing (HPC). For instance, in the recent study presented by Assou et al. (A car crash reduced order model with random forest. In: 4th International workshop on reduced basis, POD and PGD Model Reduction Techniques—MORTech 2017. 2017), it took 10 runs to find a solution of a 34-parameter problem that fulfils the specifications. In order to improve this method, we must extract more knowledge from the simulation results (correlations, spatio-temporal features, explanatory variables) and process them in order to find efficient ways to describe the car crash dynamics and link criteria/quantities of interest with some explanatory variables. One of the improvements made in the last months is the use of the so-called Empirical Interpolation Method (EIM, [Barrault et al.]) to identify the few time instants and spatial nodes of the FE-mesh (referred to as magic points) that “explain” the behavior of the body during the crash, within a dimensionality reduction approach. The EIM method replaces a former K-Means algorithm (Davies et al. in IEEE Trans Pattern Anal Mach Intell, 1(2):224–227, 1979) which was processed online, for each ROM. Instead, the computation of EIM method is done offline, once for all, for each simulation. This new method allows us to compute a ROM quite faster, and to reduce the number of features that we use for the regression step (~ 100). The nonlinear regression step is achieved by a standard Random Forest (RF, [Breiman. Mach Learn 45:5–32, 2001]) algorithm. Another improvement of the method is the characterization of numerical features describing the shape of the body, at a nodal scale. The characteristics of orientation of the elements surrounding a mesh node must be taken into account to describe the behavior of the node during the crash. The actual method integrates some numerical features, computed from the orientation of the elements around each node, to explain the node behavior. The paper is organized as follows: The introduction states the scientific and industrial context of the research. Then, the ReCUR Method is detailed, and the recent improvements are highlighted. Results are presented and discussed before having some concluding remarks on this piece of work.

中文翻译：

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寻求汽车行业优化研究的新方法，包括最近的简化技术

在过去的几年中，汽车工程行业受到“机器学习”技术用于新设计和创新目的的深刻影响。但是，某些特定的工程方面（例如数值优化研究）仍然需要开发包含参数化有限元（FE）结构动力学仿真数据的合适的高性能机器学习方法。减轻车身重量是提高环境影响和产品成本的关键。雷诺汽车公司的实际优化过程使用数值试验设计（DOE）为车辆的每个零件找到合适的厚度和材料，以确保减轻的重量，同时保持车身的良好性能，这由标准或传感器确定。车身（最大位移，瞬时加速度的上限...）。常用的DOE方法通常使用研究参数的3到10倍（这意味着，对于30个参数的研究，至少要进行90次模拟，在140核计算机上每次运行通常需要10个小时）。在过去的两年中，雷诺的团队努力开发一种破坏性的方法来进行优化研究。“破坏性”是指找到一种方法，可以将计算工作量的成本降低几个数量级。公认的是，标准DoE需要大量模拟，这些模拟至少与参数空间的大小成比例，通常会为实际应用带来数百种精细模拟。相比之下，破坏性方法仅需要进行约10次精细评估。这可以通过将FE碰撞模拟结果的大量数据知识提取与并行高性能计算（HPC）的帮助相结合来实现。例如，在Assou等人最近提出的研究中。（具有随机森林的车祸减少订单模型。在：第4届国际减少研讨会，POD和PGD模型减少技术— MORTech 2017. 2017）中，花了10次奔跑才能找到满足以下条件的34参数问题的解决方案：规格。为了改进此方法，我们必须从仿真结果（相关性，时空特征，解释变量）中提取更多知识，并对它们进行处理，以找到描述车祸动力学的有效方法，并关联感兴趣的标准/数量。一些解释性变量。最近几个月进行的一项改进是使用所谓的经验插值方法（EIM，[Barrault等人]）来识别有限元网格的几个瞬时点和空间节点（称为魔点） ）以降维方法“解释”了碰撞过程中人体的行为。EIM方法替代了以前的K-Means算法（Davies等人，在IEEE Trans Pattern Anal Mach Intell，1（2）：224-227，1979）中为每个ROM在线处理。相反，对于每次仿真，EIM方法的计算都是脱机完成的。这种新方法使我们可以更快地计算ROM，并减少用于回归步骤的功能数量（〜100）。非线性回归步骤通过标准随机森林算法（RF，[Breiman。Mach Learn 45：5–32，2001]）算法实现。该方法的另一个改进是在节点规模上表征了描述身体形状的数字特征。必须考虑网格节点周围元素的定向特性，以描述崩溃期间节点的行为。实际方法集成了一些数字特征，这些数字特征是根据每个节点周围元素的方向计算得出的，以解释节点行为。论文组织如下：引言阐明了研究的科学和工业背景。然后，详细介绍了ReCUR方法，并重点介绍了最近的改进。在对本文进行总结之前，先对结果进行介绍和讨论。必须考虑网格节点周围元素的定向特性，以描述崩溃期间节点的行为。实际方法集成了一些数字特征，这些数字特征是根据每个节点周围元素的方向计算得出的，以解释节点行为。论文组织如下：引言阐明了研究的科学和工业背景。然后，详细介绍了ReCUR方法，并重点介绍了最近的改进。在对本文进行总结之前，先对结果进行介绍和讨论。必须考虑网格节点周围元素的定向特性，以描述崩溃期间节点的行为。实际方法集成了一些数字特征，这些数字特征是根据每个节点周围元素的方向计算得出的，以解释节点行为。论文组织如下：引言阐明了研究的科学和工业背景。然后，详细介绍了ReCUR方法，并重点介绍了最近的改进。在对本文进行总结之前，先对结果进行介绍和讨论。根据每个节点周围元素的方向计算得出，以解释节点行为。论文组织如下：引言阐明了研究的科学和工业背景。然后，详细介绍了ReCUR方法，并重点介绍了最近的改进。在对本文进行总结之前，先对结果进行介绍和讨论。根据每个节点周围元素的方向计算得出，以解释节点行为。论文组织如下：引言阐明了研究的科学和工业背景。然后，详细介绍了ReCUR方法，并重点介绍了最近的改进。在对本文进行总结之前，先对结果进行介绍和讨论。