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Weighted Uniform Simulation (WUS) is recently presented as one of the efficient simulation methods to obtain structural failure probability and most probable point (MPP). This method requires initial assumptions of failure probability to obtain results. Besides, it has the problem of variation in results when it conducted with few samples. In the present study three strategies have been presented that efficiently enhanced capabilities of WUS. To this aim, a progressively expanding intervals strategy proposed to eliminate the requirement to initial assumptions in WUS, while low-discrepancy samples simultaneously employed to reduce variations in failure probabilities. Moreover, to improve the accuracy of MPP, a new simple local search method proposed and combined with the simulation that strengthened the method to obtain more accurate MPP. The capabilities of proposed strategies investigated by solving several structural reliability problems and obtained results compared with traditional WUS and common reliability methods. Results show that proposed strategies efficiently improved the capabilities of conventional WUS.

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The real-world applications addressing the nonlinear functions of multiple variables could be implicitly assessed through structural reliability analysis. This study establishes an efficient algorithm for resolving highly nonlinear structural reliability problems. To this end, first a numerical nonlinear optimization algorithm with a new simple filter is defined to locate and estimate the most probable point in the standard normal space and the subsequent reliability index with a fast convergence rate. The problem is solved by using a modified trust-region sequential quadratic programming approach that evaluates step direction and tunes step size through a linearized procedure. Then, the probability expectation method is implemented to eliminate the linearization error. The new applications of the proposed method could overcome high nonlinearity of the limit state function and improve the accuracy of the final result, in good agreement with the Monte Carlo sampling results. The proposed algorithm robustness is comparatively shown in various numerical benchmark examples via well-established classes of the first-order reliability methods. The results demonstrate the successive performance of the proposed method in capturing an accurate reliability index with higher convergence rate and competitive effectiveness compared with the other first-order methods.