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

建模多重不确定性的影响是一个基本问题，优化定制，碰撞相关的汽车零部件，也是其数值结构分析本身。这些不确定性与材料特性有关，而材料特性主要受较小规模的不确定性、生产过程以及部件寿命期间预期的加载情况的影响。特别是由于定制毛坯概念或局部激光硬化等定制策略，在正常工作条件下，由于循环载荷的影响，对碰撞安全至关重要的材料性能会随着时间的推移而变化，这给碰撞场景分析带来了相当大的额外不确定性。因此，本项目的主要目标是开发基于可靠性的多态不确定性下定制的碰撞相关汽车部件的设计优化方法。其主要目标是在规定故障概率（PoF）上界的最大可接受值的同时，使性能指标最大化。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进行假设。通过利用改进的蒙特卡罗方法和专门的代理模型的嵌套方法包括任意不确定性。狄拉克质量离散化将在以下方面得到扩展：(i)与模糊变量的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度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兴趣量，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，例如考虑由金属成形过程引起的特征应力。除此之外，还将开发一种新的方法，通过基于随机场实现的神经网络替代模型来结合材料特性的局部变化。这些将通过基于数据的不动产地图识别和构建与不动产分布和相关性匹配的实现来获得。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spp1886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.