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

对多个不确定性的影响进行建模是汽车零部件优化设计的基本问题，也是汽车零部件数值结构分析的基本问题。这些不确定因素与材料性质有关，而材料性质主要受较低规模的不确定因素影响，与生产工艺有关，也与部件寿命期间预期的加载情况有关。特别是，由于定制毛坯或局部激光硬化的概念等定制策略的结果，由于正常运行条件下的循环载荷，碰撞安全性的重要材料特性随着时间的变化而变化，这导致了碰撞场景分析的相当大的附加不确定性。因此，该项目的主要目标是开发基于可靠性的设计优化方法，在多态不确定性下对与碰撞相关的定制汽车部件进行优化设计。它的主要目标是最大化性能指标，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的类型做出假设。利用改进的蒙特卡罗方法和专门的替代模型，通过嵌套方法包括了任意的不确定性。Dirac质量离散化将在以下方面进行扩展：(I)结合模糊变量来描述认知设计参数，(Ii)纳入阿尔法水平离散化的概念，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优界。为了计算性能指标和定义故障的关注量，将建立一个现实的计算模型，其中包括生产过程的相关部分，例如考虑到金属成形过程产生的本征应力。此外，还将开发一种新的方法，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性质的局部变化。这些将通过房地产地图的基于数据的识别和与房地产分布和相关性相匹配的实现来获得。通过引入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。所开发的方法将在汽车零部件在碰撞载荷下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.