Reliability analysis for structures with multiple temporal and spatial parameters based on the effective first-crossing point

For efficiently estimating the dynamic failure probability of the structure with the multiple temporal and spatial parameters, a transferred limit state function technique is first proposed in this paper. By finding the effective first-crossing point which controls the failure of the structural system, the transferred technique is constructed to transform the dynamic reliability problem into a static one. For determining the effective first-crossing point, the parameter domain is first divided into different dominant domain corresponding to every parameter. Based on the parameter dominant domain, the first-crossing point about each parameter is obtained by comparing the difference value between the point on the failure boundary and the corresponding parameter upper bound. Finally, the effective first-crossing point is determined by finding the point which controls the structure failure. With the transferred technique, two strategies (including the sparse grid integration based on fourth-moment method and the maximum entropy based on dimensional reduction method) are proposed to efficiently estimate the dynamic failure probability. Several examples are employed to illustrate the significance and effectiveness of the transferred technique and the proposed methods for solving the multiple temporal and spatial parameters dynamic reliability. The results show that the proposed methods can estimate the multiple temporal and spatial parameters dynamic failure probability efficiently and accurately.