Uncertain inverse method by the sequential FOSM and its application on uncertainty reconstruction of vehicle–pedestrian collision accident

Uncertainties widely exist in practical engineering problems. In order to effectively evaluate the unknown parameters under the uncertain measured responses, an efficient uncertain inverse method based on the sequential first order and second moment (FOSM) is proposed. The uncertain inverse problem is firstly transformed as a two-layer optimization problem involved uncertainty propagation and optimization inverse. In the inner layer, the maximum entropy principle is employed to model the probability density functions (PDFs) of the unknown parameters, and the sequential FOSM method is used to estimate the cumulative distribution functions of the calculated responses. In the outer layer, the intergeneration projection genetic algorithm is adapted to achieve the efficient solving of the transformed optimization problem. Two numerical examples are provided to verify the effectiveness of the proposed uncertain inverse method. Further, the proposed uncertain inverse method is applied to the reconstruction of the vehicle–pedestrian collision accident, and the statistical moments and PDFs of the vehicle state parameters before collision are reasonably identified.