Robust Design of Energy-Absorbing Crumple-Zone Structures Considering Uncertainties

现代计算机的性能和存储容量不断提高，导致用于数值模拟的模型的复杂性相对稳定地增加。然而，对于要执行的计算成本非常高的优化过程，例如在结构优化的框架中，复杂的高维模型是不合适的，特别是如果要考虑不确定性以确保稳健的优化设计。在现代汽车设计中，乘客安全起着至关重要的作用，在此背景下，本研究项目的总体目标是开发一种新的模糊算法设计策略，以优化具有不确定性鲁棒性的吸能屈曲区结构。由于所涉及的不确定性的多态性，对该结构的鲁棒性提出了两方面的要求：首先，优化后的结构必须对实际碰撞场景中不可预测的、随机的条件和环境影响所引入的任意类型的不确定性具有鲁棒性。其次，该结构应考虑到由于建模的简化、物理假设的理想化和模型降阶技术的应用而导致的信息丢失所带来的认知类型的不确定性，这是实现低维模型以进行有效优化所需要的。为实现项目总体目标，将完成三大工作任务：在推导出汽车全尺寸结构的不同简化碰撞模型后，将简化模型的具体参数考虑为模糊值，以参数不确定性来覆盖模型整体的固有不确定性。然后，这些参数的值将在逆模糊算法策略的基础上进行识别，该策略对高维仿真模型的实现将代表本项目的核心特征。利用申请人开发的一种新的模糊参数化模型质量评估准则，将选择最合适的简化模糊参数化模型，最终形成有效的设计优化基础，并具有抗不确定性的鲁棒性。在本项目中开发的这种新策略，明确地包括了工业设计早期阶段的模糊量形式的任意不确定性和认知不确定性，可以极大地帮助避免在原型测试和认证的最后阶段由忽视的不确定性引起的昂贵和耗时的重新设计周期。

The continually increasing performance and memory capacity of modern computers induces a comparably steady increase of complexity in the models used for numerical simulation. However, with regard to the computationally very costly optimization procedures to be performed, for example, in the framework of structural optimization, complex, high-dimensional models are not suitable, in particular if, additionally, uncertainties are to be taken into account to assure a robust optimized design. Against the background of passenger safety, which plays a vital role in modern automotive design, the overall objective of this research project is to develop a new, fuzzy arithmetical design strategy for an optimized energy-absorbing crumple-zone structure with robustness against uncertainties. The demands made on the robustness of this structure are twofold with respect to the polymorphic property of the uncertainties involved: First, the optimized structure shall be robust against the uncertainties of aleatoric type, introduced by the unpredictable, random conditions and environmental influences in real crash scenarios. Second, the structure shall account for the uncertainties of epistemic type, introduced by the loss of information due to the simplifications in modeling, the idealization of physical assumptions and the application of model order reduction techniques which are needed to achieve lower-dimensional models for an efficient optimization. To achieve the overall project objective, three major work tasks will be performed: After the derivation of different simplified crash models for the full-scale car structure, specific parameters of the simplified models will be considered as fuzzy-valued, for the purpose of covering the overall inherent uncertainty of the model in terms of parametric uncertainties. The values of these parameters will then be identified on the basis of an inverse fuzzy arithmetical strategy, whose implementation for high-dimensional simulation models will represent a core feature of this project. Using a novel criterion, developed by the applicant, for the quality assessment of fuzzy-parameterized models, the most appropriate simplified fuzzy-parameterized model will be selected, forming finally the basis for an effective design optimization of the crumple-zone structure with robustness against uncertainties. This new strategy of explicitly including both aleatoric and epistemic uncertainties in form of fuzzy-valued quantities already in the early stages of industrial design, as to be developed in this project, can significantly help to avoid costly and time-consuming re-engineering cycles, induced by disregarded uncertainties, in the final phases of prototype testing and certification.