On reliability analysis method through rotational sparse grid nodes

Abstract This study aims to develop a rotational sparse grid (R-SPGR) method for statistical moment evaluation and structural reliability analysis with enhanced accuracy and efficiency. The optimal rotational angle in the proposed R-SPGR method is determined by an optimization approach, in which the objective function is constructed in terms of discrepancy between the marginal moments of each input uncertain variables calculated from these rotational sparse grid nodes and their exact values. The R-SPGR nodes allow capturing more information of exact probability distribution for the system response, which is considered critically important to the calculation of statistical moments accurately. Following this, the probability density function (PDF) and failure probability of system response can be efficiently determined by using the saddlepoint approximation technique. To demonstrate the effectiveness of the proposed method, four benchmark examples, one structural analysis example and one practical example of industrial robot are provided here, in which the results obtained from the proposed R-SPGR method are compared with those calculated from the conventional sparse grid (SPGR) method, the maximum entropy problem with fractional moments (ME-FM) method and Monte Carlo simulation (MCS) method. From these illustrative examples involving a wide range of complexity, it is demonstrated that the proposed R-SPGR method has fairly high accuracy and efficiency for structural reliability analysis.