Coupling PGD model reduction with importance sampling using adaptive subset simulation for reliability analysis
- The key point of structural reliability analysis is the estimation of the failure probability. This probability is defined as the integral over the failure domain which is given by a limit state function. Usually, this function is only implicit given by an underlying finite element simulation of the structure. It is generally not possible to solve the integral analytically. For that reason, numerical methods based on sampling and surrogates have been developed. Nevertheless, these sampling methods still require a few thousand calculations of the underlying finite element model, making reliability analysis computationally expensive for relevant applications.
Coupling a reduced order model (proper generalized decomposition) with an efficient variance reducing sampling algorithm can reduce the computational cost of reliability analysis drastically. In the proposed method, an importance sampling technique is coupled with a reduced structural model by means of PGD to estimate theThe key point of structural reliability analysis is the estimation of the failure probability. This probability is defined as the integral over the failure domain which is given by a limit state function. Usually, this function is only implicit given by an underlying finite element simulation of the structure. It is generally not possible to solve the integral analytically. For that reason, numerical methods based on sampling and surrogates have been developed. Nevertheless, these sampling methods still require a few thousand calculations of the underlying finite element model, making reliability analysis computationally expensive for relevant applications.
Coupling a reduced order model (proper generalized decomposition) with an efficient variance reducing sampling algorithm can reduce the computational cost of reliability analysis drastically. In the proposed method, an importance sampling technique is coupled with a reduced structural model by means of PGD to estimate the failure probability. Instead of calculating the design point e.g. with optimization algorithms, the design point is adaptively estimated by using the idea of subset simulation. The failure probability is estimated in an iterative scheme based on adaptively computing the design point and refining the PGD model.…