Application of first-order reliability method with orthogonal plane sampling for high-dimensional series system reliability analysis

The increasing complexity of modern engineering systems has motivated a shift of research focus from component-level reliability to system reliability with interdependent components. There is a growing demand for efficient reliability methods to analyze high-dimensional systems that involve numerous dependent components and component variables. The first-order reliability method (FORM), which is widely used for component-level reliability analysis, becomes inaccurate for high-dimensional systems composed of numerous components, each with a nonlinear high-dimensional limit state function. By integrating the orthogonal plane sampling, this paper proposes an improved FORM-based method to tackle the curse of dimensionality for series systems. The idea is to construct secant hyperplanes using the orthogonal plane samples so as to reduce the FORM error for high-dimensional nonlinear limit state functions. The design points of secant hyperplanes are projected to high-dimensional system space using an efficient procedure based on the specified correlation matrix of variables. Finally, the series system reliability is computed as high-dimensional multi-normal integral, which is addressed by the equivalent component method. Four numerical examples are investigated to demonstrate the accuracy and efficiency of the proposed method. Results indicate that the proposed method is significantly more efficient than the Monte Carlo simulation and more accurate than the conventional FORM.