New Methods for Reliability-Based Design Optimization of Multiphase Steel Components under Polymorphic Uncertainties

对多种不确定性的影响进行建模是优化定制的碰撞相关汽车零件及其数值结构分析本身的一个基本问题。这些不确定性与材料特性（主要是较小规模的不确定性）、生产过程以及部件使用寿命期间预期的负载情况有关。特别是由于诸如拼焊板或局部激光硬化概念等定制策略的结果，由于正常操作条件下的循环载荷，碰撞安全的重要材料特性会随着时间的推移而变化，这导致碰撞场景的分析存在相当大的额外不确定性。因此，该项目的主要目标是开发在多态不确定性下对定制的碰撞相关汽车部件进行基于可靠性的设计优化的方法。其中的主要目标是最大限度地提高性能指标，同时规定故障概率 (PoF) 上限的最大可接受值。这些方法将基于认知不确定性的狄拉克质量离散化，因此不需要对这些不确定性的分布函数类型做出假设。利用改进的蒙特卡罗方法和专门的代理模型，通过嵌套方法包含任意不确定性。狄拉克质量离散化将在以下方面进行扩展：（i）与模糊变量相结合来描述认知设计参数，（ii）纳入α级离散化的概念，以及（iii）增强以考虑与要优化的性能测量相关的传播不确定性的最佳界限。为了计算性能指标和定义失效的感兴趣数量，将构建一个现实的计算模型，其中包括生产过程的相关部分，例如考虑金属成形过程引起的特征应力。除此之外，还将开发一种新方法，通过使用基于随机场实现的神经网络的代理模型来合并材料属性的局部变化。这些将通过基于数据的房地产地图识别以及与房地产分布和相关性相匹配的实现的构建来获得。通过包含双嵌套蒙特卡罗分析，用于神经网络训练的模型本身的不确定性将得到控制。所开发的方法将在碰撞载荷下汽车零件的实际优化问题以及 SPP 1886 中定义的基准问题的背景下进行分析。

Modeling the influence of multiple uncertainties is a fundamental problem for the optimization of tailored, crash-relevant car parts, and also for their numerical structural analysis itself. These uncertainties are associated with the material properties, which are dominated by uncertainties on a lower scale, with the production process, and with the loading scenarios to be expected during the lifetime of the component. Especially as a result of the tailoring strategies such as the concept of tailored blanks or local laser hardening, important material properties for the crash safety vary over time due to cyclic loading under normal operation conditions, which leads to rather large additional uncertainties for the analysis of the crash scenario. Therefore, in this project the main goal is to develop methods for the reliability-based design optimization of tailored, crash-relevant car components under polymorphic uncertainties. The major target therein is to maximize performance measures while prescribing maximally acceptable values of upper bounds on the probability of failure (PoF). The methods will be based on a Dirac mass discretization of the epistemic uncertainties and thereby, no assumptions regarding the type of distribution functions for these uncertainties need to be made. The aleatoric uncertainties are included through a nested approach taking advantage of improved Monte-Carlo methods and specialized surrogate models. The Dirac mass discretization will be extended with respect to the following aspects: (i) Combination with fuzzy variables to describe epistemic design parameters, (ii) incorporation into the concept of alpha-level discretizations, and (iii) enhancement to account for optimal bounds on propagated uncertainties related with the performance measures to be optimized. For the computation of the performance measures and the quantity of interest defining failure, a realistic computational model will be constructed which includes the relevant parts of the production process, for instance to account for the eigenstresses induced by the metal forming procedure. In addition to that, a new method will be developed to incorporate the local variation of material properties by surrogate models using neural networks based on random field realizations. These will be obtained by the data-based identification of real property maps and the construction of realizations which match the real property distributions and correlations. By including a double-nested Monte-Carlo analysis, the uncertainties of the model itself used for the training of the neural network will be controlled. The developed methods will be analyzed in the context of realistic optimization problems of car parts under crash loads as well as benchmark problems defined in SPP 1886.