Multi-fidelity structural reliability analysis with polymorphic uncertainty - application to fatigue lifetime prediction for structures made of metal foam

非均质材料（如金属泡沫）的代表性体积元可能非常大，以至于尺度分离不成立。因此，不能用有效的材料参数进行结构分析。在这种情况下，只能确定代表表观材料参数边界的随机场;这些边界内的材料参数分布是未知的。因此，对这种非均匀材料结构的可靠性分析必须考虑p-box作为输入参数，用p-box进行可靠性分析的方法计算量很大。与已经非常耗时的可靠性分析方法相比，区间分析中的优化问题或分布函数的参数的变化的解决方案通常增加了另一个迭代循环的计算，从而显着增加了计算的复杂性。因此，为了能够在工程实践中使用这些方法，一个很大的挑战是提高其效率，因此，该项目的目标是开发一个合适的有效的方法，结构的可靠性分析与p盒，并将其应用于寿命预测的金属泡沫材料制成的结构。一个合适的方法进行结构可靠性分析与p盒必须考虑输入参数之间的不确定性的依赖关系。为了获得一个有效的方法，结构可靠性分析的p盒，有效的抽样为基础的方法，必须应用，以进一步提高效率，模型层次必须引入到分析。模型层次结构不仅应该从一个单一的数学模型通过改变离散化参数，但也应该考虑一般的模型类，其信息内容增加的融合和filtering.The效率的结构可靠性分析方法，这是要在这个项目中开发的考虑偶然性以及认知的不确定性，并不局限于由金属泡沫制成的结构。它将用于设计阶段，并可用于早期设计阶段，以研究异质微观结构几何形状对结构寿命的影响，从而优化生产异质材料（如金属泡沫）的工艺参数。在最后的设计阶段，该方法是能够真实地表示的材料参数的不确定性所造成的异质性的微观结构，从而确定的寿命或结构的故障概率的界限。特别是，由于异质微结构的损伤的材料参数的时间依赖性被认为是。

The representative volume element for heterogeneous materials such as metal foams can be so large that scale separation does not hold. Therefore, the structural analysis cannot be performed with effective material parameters. In this case, only random fields can be determined which represent bounds of the apparent material parameters; the distribution of the material parameters within these bounds is unknown. The reliability analysis for structures made of such heterogeneous materials must therefore consider p-boxes as input parameters.Methods for reliability analysis with p-boxes are computationally very intensive. In comparison to the already very time-intensive methods for reliability analysis, the solution of the optimization problems in the interval analysis or the variation of the parameters of the distribution function generally adds another iteration loop to the computations and thus increases significantly the computational complexity. Therefore, in order to be able to use these methods in engineering practice, a great challenge is to increase their efficiency.The objective of the project is therefore to develop a suitable efficient method for structural reliability analysis with p-boxes and to apply it to lifetime prediction for structures made of metal foam. A suitable method for structural reliability analysis with p-boxes must take the uncertain dependencies between the input parameters into account. In order to obtain an efficient method for structural reliability analysis with p-boxes, efficient sampling-based methods must be applied; to further increase efficiency, model hierarchies must be introduced into the analysis. Model hierarchies should not only be generated from a single mathematical model by varying a discretization parameter, but should also consider general model classes, whose information contents increase the efficiency by fusion and filtering.The structural reliability analysis method that is to be developed within this project allows for a consideration of aleatory as well as epistemic uncertainty and is by no means limited to structures made of metal foams. It will be used in the design phase and can be used in the early design phase to investigate the influence of the heterogeneous microstructure geometry on the lifespan of the structure, thereby optimizing process parameters in the production of heterogeneous materials such as metal foams. In the final design phase, the method is able to represent realistically the uncertainties of the material parameters resulting from the heterogeneity of the microstructure and thus to determine bounds for the lifetime or the probability of failure of the structure. In particular, the time dependence of the material parameters due to damage of the heterogeneous microstructure is considered.