Analytical formulation of failure probability based on outcrossing rate is proposed for the first time by the research team led by Prof. Lu Zhaohui of FACTE. The results have recently been published on Structural Safety, one of the top journals in the field of reliability engineering with impact factor of 5.712.

The article named “An innovative method for space-time-dependent reliability analysis” focused on variability existing in both spatial and temporal dimension, since the environmental actions and material properties may change both spatially and temporally in a stochastic manner. An innovative space-time-dependent outcrossing rate (STOR) method is proposed for dealing with such reliability problems. The main innovation can be expressed as follow: (1) The space-time-dependent failure probability of a structure is determined based on outcrossing rate which is theoretically derived for the first time, considering the spatiotemporal variability of all basic variables. (2) The spatiotemporal outcrossing is first determined in this study and can be easily distinguished from other outcrossing in fig. 1. (3) An efficient numerical algorithm for computing the failure probability is proposed based on Gauss-Legendre quadrature, in which only 3~5 point is needed in each dimension.

Fig 1. Outcrossing events in spatial, temporal, and spatiotemporal domains

Numerical method to calculate the proposed failure probability is developed with the aid of GL quadrature. Numerical examples are investigated through traditional simulation-based method and the proposed STOR method. It is found that:

(1) Based on the proposed spatiotemporal outcrossing rate, the upper bound of space-time-dependent failure probability can be analytically formulated, which is slightly larger than the exact value of the failure probability. Thus, it is rationale to evaluate space-time-dependent reliability based on the proposed analytical formulation of failure probability.

(2) STOR method is suitable for computationally explicit and strong nonlinear LSFs, with the results being in close agreement with those of MCS. It is indicated that the proposed method has enough accuracy for space-time-dependent reliability analysis.

(3) The space-time-dependent failure probability are always larger than that without considering the spatial variability. It indicates that neglecting spatial variability will underestimate the risk, and thus it is important to conduct space-time-dependent reliability analysis for an appropriate evaluation.

(4) STOR method can efficiently evaluate cumulative failure probability, particularly for problems with small failure probability. The computational time of STOR method is less than 3.2% of existing sample-based methods. Also, the computational time and the total number of LSF calls required is independent from the length of time interval, which enables the efficiency of evaluating long forecast time interval problems.