All the parameters of interest in engineering design have some degree of uncertainty. It is important to understand the influence of different random parameters on the system or component performance.

In this research project we are computing the probability of failure and constructing a distribution function for a critical response. We have developed innovative BEM methods using sensitivity  formulation coupled with ffirst and second order Reliability Method for predicting the reliability index of structures subjected to fatigue loading.


Multi-Fidelity Analysis:

There are several methods that can be used to evaluate reliability, such as Monte Carlo Simulations (MCS), the First Order Reliability Method (FORM), and the Second Order Reliability Method (SORM).

In this research the reliability of a 2D elastostatic BEM model is evaluated for various levels of uncertainty in design parameters such as the applied stress and the dimensions of the model. To overcome the computational cost of built-up structures with multiple random variables, multi-fidelity (MF) modelling has been developed. By substituting a multi-fidelity model for the high-fidelity model (HFM) used with MCS, similar accuracy to the high-fidelity model could be achieved at a fraction of the cost. Similar improvements could also be seen with FORM and SORM.

The figure below shows the reliability indices and the mean absolute percentage error (MAPE) calculated using SORM with low fidelity and high fidelity models (LFM, HFM) and different multi-fidelity models (MF).

In addition, the higher-order sensitivities of the elastostatic Boundary Element Method (BEM) equations with respect to changes in several geometric variables have been derived for use with the IDM for the purpose of conducting reliability analyses with SORM. Multi-fidelity formulations with the IDM have also been derived, making use of the metamodelling technique Kriging. The use of multi-fidelity modelling enables the creation of a model that has similar accuracy to a high fidelity model, but with a computational cost similar to that of a low-fidelity model, offering significant improvements in efficiency.