Mission reconstruction for launch vehicles under thrust drop faults based on deep neural networks with asymmetric loss functions

Abstract

Launch failures of launch vehicles due to thrust drop faults have occurred throughout aerospace history, thus studying Mission Reconstruction (MRC) problems is crucial to alleviate the losses resulting from the thrust drop faults. Unlike the traditional trajectory optimization problem with a specified target orbit, the rescue orbit and flight trajectory in the MRC problems need to be optimized simultaneously. To solve the MRC problems rapidly and accurately, a deep neural network-based adaptive collocation method (DNN-based ACM) is proposed. In the offline part, using the datasets generated by convex optimization and adaptive collocation method, deep neural networks (DNN) are trained to map the relationship from the fault states to the optimal rescue orbital elements and terminal control variables. During the DNNs training, an asymmetric loss function is proposed to avoid the positive error of the semi-major axis which renders the trajectory optimization unsolvable. In the online application of the DNNs, the optimal rescue orbit is determined and proper initial guesses are set for the MRC problems. The flight trajectory from the fault position to the optimal rescue orbit can be effectively solved by the ACM with the proper initial guesses. Simulation results validate the effectiveness of the DNN-based ACM, and substantiate the high efficiency performance and optimal performance of the presented MRC method.