Multi-failure mode reliability analysis method based on intelligent directional search with constraint feedback

Searching for the most probable point (MPP) by traditional methods cannot avoid the demand for accurate gradients of limit state functions (LSFs) essentially. It is difficult to calculate the accurate gradient of unknown high nonlinear LSFs. In this paper, a multi-failure mode reliability analysis method based on intelligent directional search with constraint feedback (IDS) is proposed, focusing on unknown high nonlinear LSFs. (i): To improve the convergence rate, a point on the feasible domain boundary is settled as a starting point. The starting point is also located in the quadrant containing the MPP. (ii): To further enhance the optimization efficiency, the improved slime mould algorithm (iSMA) is proposed by adding constraint feedback, so that the current optimal point can move towards the LSF during the optimization process. (iii): To overcome the local optimum, iSMA and adaptive Lévy flight are combined which can expand the search area in the exploration phase. Finally, the failure probability of multi-failure mode is obtained by the second-order approximation method (SOAM) based on the MPPs. Three mathematical examples are utilized to demonstrate the excellent accuracy and acceptable efficiency of the proposed method by comparison with other existing methods. The results indicate that when the nonlinearity of LSF is not very high, IDS has the same computational cost as ECC, and the same order of accuracy as an intelligent optimization algorithm. As the nonlinearity of LSF of structural system failure modes increases, the computational cost of IDS will be higher than ECC. However, the accuracy of IDS has always been good enough. When the structural system has a concave LSF, IDS is more efficient than other intelligent optimization algorithms. Results of the engineering example indicate that the proposed method is very suitable for multi-failure mode reliability analysis problems with unknown high nonlinear LSF.