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优化定制的、与碰撞相关的汽车部件的基本问题，也是其数值结构分析本身的基本问题。这些不确定性与材料特性、生产工艺以及部件寿命期内预期的载荷情况有关，材料特性主要受较低尺度的不确定性影响。特别是由于定制策略（例如定制坯料或局部激光硬化的概念），用于碰撞安全性的重要材料特性由于在正常操作条件下的循环载荷而随时间变化，这导致碰撞情景分析的相当大的附加不确定性。因此，在这个项目中的主要目标是开发基于可靠性的设计优化的定制，碰撞相关的汽车部件多态不确定性的方法。其中的主要目标是最大限度地提高性能指标，同时规定最大可接受的值的上限上的故障概率（PoF）。该方法将基于狄拉克质量离散化的认知不确定性，因此，没有假设这些不确定性的分布函数的类型需要作出。任意的不确定性，包括通过一个嵌套的方法，利用改进的蒙特-卡罗方法和专门的代理模型。狄拉克质量离散化将扩展到以下几个方面：（i）与模糊变量相结合，以描述认知设计参数，（ii）纳入α级离散化的概念，以及（iii）增强考虑传播的不确定性与性能措施进行优化的最佳界限。为了计算性能指标和确定故障的相关数量，将构建一个实际的计算模型，该模型包括生产过程的相关部分，例如，用于解释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，通过使用基于随机场实现的神经网络的代理模型来结合材料特性的局部变化。这些将通过基于数据的真实的属性映射的识别和匹配真实的属性分布和相关性的实现的构造来获得。通过包括双重嵌套的蒙特-卡罗分析，将控制用于神经网络训练的模型本身的不确定性。所开发的方法将在碰撞载荷下的汽车零件的现实优化问题以及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.