The design of complex systems often requires reliability assessments involving a large number of uncertainties and low probability of failure estimations (in the order of 10⁻⁴). Estimating such rare event probabilities with crude Monte Carlo (CMC) is computationally intractable. Specific numerical methods to reduce the computational cost and the variance estimate have been developed such as importance sampling or subset simulation. However, these methods assume that the uncertainties are defined within the probability formalism. Regarding epistemic uncertainties, the interval formalism is particularly adapted when only their definition domain is known. In this paper, a method is derived to assess the reliability of a system with uncertainties described by both probability and interval frameworks. It allows one to determine the bounds of the failure probability and involves a sequential approach using subset simulation, kriging, and an optimization process. To reduce the simulation cost, a refinement strategy of the surrogate model is proposed taking into account the presence of both aleatory and epistemic uncertainties. The method is compared to existing approaches on an analytical example as well as on a launch vehicle fallout zone estimation problem.

The design of complex systems such as launch vehicles involves different fields of expertise that are interconnected. To perform multidisciplinary studies, concurrent engineering aims at providing a collaborative environment which often relies on data set exchange. In order to efficiently achieve system-level analyses (uncertainty propagation, sensitivity analysis, optimization, etc.), it is necessary to go beyond data set exchange which limits the capabilities of performance assessments. Multidisciplinary design optimization methodologies is a collection of engineering methodologies to optimize systems modelled as a set of coupled disciplinary analyses and is a key enabler to extend concurrent engineering capabilities. This article is focused on several examples of recent developments of multidisciplinary design optimization methodologies (e.g. multidisciplinary design optimization with transversal decomposition of the design process, multidisciplinary design optimization under uncertainty) with applications to launch vehicle design to illustrate the benefices of taking into account the coupling effects between the different physics all along the design process. These methods enable to manage the complexity of the involved physical phenomena and their interactions in order to generate innovative concepts such as reusable launch vehicles beyond existing solutions.

The present article proposes an algorithm for the sensitivity analysis of a multidisciplinary problem, in which the derivative-based global sensitivity indices are computed with multifidelity Gaussian process models. Two levels of fidelity are used to estimate the indices, where the low-fidelity samples are obtained by stopping the multidisciplinary analysis solver before convergence. A dedicated refinement strategy for the multifidelity Gaussian process is proposed to ensure the accuracy of the sensitivity index estimation. This algorithm is tested on three multidisciplinary problems of increasing complexity (one analytical and two representative engineering design problems), and proved to be both reliable in detecting the noninfluential variables and computationally efficient, compared to classical Monte Carlo integration and to three other candidate algorithms.