Decomposition methods for structural reliability analysis revisited

This paper presents new theoretical results to demonstrate that the referential dimensional decomposition (RDD) and cut-high-dimensional model representation (cut-HDMR), each developed independently and from a distinct perspective, lead to identical function approximations. Therefore, the reliability method stemming from the cut-HDMR approximation is precisely the same as the reliability method rooted in the RDD approximation. However, a second-moment error analysis finds neither the RDD approximation nor the cut-HDMR approximation to be optimal, whereas the approximation derived from the analysis-of-variance dimensional decomposition (ADD) results in minimum error for an arbitrary truncation. The expected errors from the RDD approximations are at least four to eight times larger than the errors from the ADD approximations. Therefore, further enhancements of decomposition-based reliability methods are possible by switching from RDD to ADD approximations. For both approximations, the decomposition can be truncated by an effective superposition dimension linked to respective approximation errors.