A univariate approximation at most probable point for higher-order reliability analysis

This paper presents a new univariate method employing the most probable point as the reference point for predicting failure probability of structural and mechanical systems subject to random loads, material properties, and geometry. The method involves novel decomposition at the most probable point that facilitates a univariate approximation of a general multivariate function, response surface generation of the univariate function, and Monte Carlo simulation. In addition to the effort of identifying the most probable point, the method requires a small number of exact or numerical evaluations of the performance function at selected input. Results of four numerical examples involving elementary mathematical functions and structural/solid-mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of probability of failure. Finally, the fatigue failure of lever arm in a wheel loader has been evaluated, demonstrating the ability of the new method in solving industrial-scale fatigue reliability problems.