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.

实际工程问题中普遍存在不确定性。为了有效地评估不确定测量响应下的未知参数，提出了一种基于顺序一阶和第二矩（FOSM）的有效不确定逆算法。首先将不确定逆问题转化为涉及不确定性传播和优化逆的两层优化问题。在内层，采用最大熵原理对未知参数的概率密度函数（PDF）进行建模，并使用顺序FOSM方法估计所计算响应的累积分布函数。在外层，代间投影遗传算法适用于实现变换优化问题的有效解决。提供了两个数值示例，以验证所提出的不确定逆方法的有效性。此外，将所提出的不确定逆方法应用于车辆与行人碰撞事故的重建，并合理地识别出碰撞前车辆状态参数的统计矩和PDF。