Separable and Standard Monte Carlo Simulation of Linear Dynamic Systems Using Combined Approximations

Reliability analysis of a large-scale system under random dynamic loads can be a very time-consuming task since it requires repeated studies of the system. In many engineering problems, for example, wave loads on an offshore platform, the excitation loads are defined using a power spectral density (PSD) function. For a given PSD function, one needs to generate many time histories to make sure the excitation load is modeled accurately. Global and local approximation methods are available to predict the system response efficiently. Each way has their advantages and shortcomings. The combined approximations (CA) method is an efficient method, which combines the advantages of local and global approximations. This work demonstrates two methodologies that utilize CA to reduce the cost of crude or separable Monte Carlo simulation (MCS) of linear dynamic systems when the excitation loads are defined using PSD functions. The system response is only calculated at a few frequencies within the range of the PSD function, and CA is used to estimate the response for the other frequencies of excitation. This approach significantly reduces the computational time of a crude or separable MCS since it only requires few full analyses of the system depending on the shape of the PSD function. The performances of the proposed methods are demonstrated in two examples.