Robust trajectory optimization of space launch vehicle using computational intelligence

Metamodeling techniques using computational intelligence have been used in Uncertainty-based Design Optimization (UDO) to reduce the high computational cost of the uncertainty analysis and improve the performance of stochastic optimization problems with computationally expensive simulation models. Optimal trajectory generation is a major part of Space Launch Vehicle (SLV) design and if it is robust relative to uncertainties can improve vehicle reliability, safety and operational cost. This paper presents a combination of Latin Hypercube Sampling (LHS) and Extreme Learning Machine (ELM) in order to create an appropriate trajectory metamodel for reducing computational time of robust trajectory design optimization of a two-stage-to-orbit SLV. The sampled data of LHS is then used as training data for ELM. Complex and costly uncertainty analyses are replaced by an ELM Neural Network (NN) which is used to instantaneously estimate the mean and standard deviation of objective function and constraints. The evolutionary genetic algorithm is used for global optimization of layers´ connection weights and biases to minimize the learning error during learning phase of NN. A Hybrid Search Algorithm (HSA), which associates Simulated Annealing (SA) as a global optimizer with Simplex as a local optimizer is employed to find robust optimum point of this metamodel. The optimal and robust trajectories are compared. The results show excellent approximation of highly non-linear design space and drastic reduction in overall UDO time, due to greatly reduced number of exact trajectory analyses.