Reliability-Based Multidisciplinary Design Optimization Under Uncertainty for Reusable Flexible Launch Vehicle

Complex systems design problems entail a suitable structure in which all disciplines including their coupled relationships have been considered and modeled at the same time. These types of design problems involve time and computational cost challenges. Multi-Disciplinary Design Optimization (MDO) methods have been developed to address these issues simultaneously. In this research, a Reusable Flexible Launch Vehicle (RFLV) design problem is presented by Reliability-Based Multi-Disciplinary Design Optimization (RBMDO) approach in the primary design phase. Trajectory, structure, aerodynamics, aeroelasticity, and thermal protection system are considered as involved disciplines in the design problem. The study's purpose will be to obtain an optimal trajectory to meet all the control and structure restrictions while estimating optimal body skin and thermal protection thicknesses based on structural design criteria evaluating in re-entry trajectory are in process. The flexible launch vehicle body has been considered as a free-free Bernoulli-Euler beam for bending variation and D’alembert’s principle for inertia force in static model with the aim of assessing structural design standards. The 3DOF longitudinal dynamic equations plus the first bending mode have been considered. By Chebyshev polynomial interpolation, the angle of attack scope has been achievable and then the trajectory optimization problem has been transformed to a discrete nonlinear programming problem (NLP), which leads to numerical integration of state equation and satisfying all path constraints in Bolza optimal control problem. The design problem formulation has been developed by the single-level MDO framework in which optimization has been implemented by Non-Dominated Sorting Genetic Algorithm (NSGA-II). Finally, epistemic and aleatory uncertainties have been applied through Probability Theory to estimate the reliability of constraints those had been affected by uncertainties. The result shows a significant effect of utilizing the evolutionary multi-objective technique against the gradient-based algorithm in design space optimization. The other conclusion is that the sequential reliability analysis structure modeling efficiency is much better compared to the parallel one.