System reliability and sensitivity under statistical dependence by matrix-based system reliability method

Bayesian network modeling of correlated random variables drawn from a Gaussian random field

“…In that context, let nodes in the BN of Figure 18 correspond to ground motion intensities at the locations of the components of a geographically distributed infrastructure system. The ground motion intensity at a location is a function of a median value ̅ (a function of the earthquake magnitude, source-to-site distance, and other geologic characteristics) and inter-and intra-event error terms as shown in (17). Consider that an observation has been made on in Figure 18, e.g., through a ground motion sensor located near component 1 in the infrastructure system.…”

“…The constraint functions are based on (4). The use of nonlinear constrained optimization to determine the terms of an approximate transformation matrix was earlier suggested by Song and Ok [18] and Song and Kang [17]. Hereafter, construction of the approximate transformation matrix by use of the optimization scheme in (13) is referred to as the nodebased optimization approach (NOA).…”

“…Alternatively, the transformation matrix may be determined approximately via numerical optimization [17,18], as described later in this paper. The BN corresponding to the above transformation is shown in Figure 3, where the latent -nodes are introduced as parents of the -nodes.…”

“…We note that the addition of thenodes does not significantly increase the computational complexity of the BN. As suggested by Song and Kang [17] and Song and Ok [18], the transformation in (3) may be regarded as a generalization of the Dunnett-Sobel (DS) class of Gaussian random variables [19]. This class of random variables is defined by * * , 1 … (6) where and are independent standard normal random variables and and are variable-specific coefficients satisfying the conditions 1 / and 1 1.…”

Probability Analysis for the Damage of Gravity Dam

“…Compared with the rigidbody limiting equilibrium method, the FEM used in the calculation of deep anti-sliding measures did not requireliability theories, Enrique Castillo and Carmen Castillo [7] gave the main results that allowed a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. Using a numerical procedure, Junho Song and Won-Hee Kang [8] proposed matrix-based system reliability (MSR) method to compute the probabilities of general system events efficiently by simple matrix operations. KwaiSang Chin and Ying-Ming Wang [9] used failure mode and effects analysis (FMEA) to evaluate a system for possible ways in which failures could occur.…”