Norouzi, M., Nikolaidis, E., and Crawford, Z., "Combined Approximation for Efficient Reliability Analysis of Linear Dynamic Systems," SAE Technical Paper 2015-01-0424, 2015, doi:10.4271/2015-01-0424.
The Combined Approximation (CA) method is an efficient reanalysis method that aims at reducing the cost of optimization problems. The CA uses results of a single exact analysis, and it is suitable for different types of structures and design variables. The second author utilized CA to calculate the frequency response function of a system at a frequency of interest by using the results at a frequency in the vicinity of that frequency. He showed that the CA yields accurate results for small frequency perturbations. This work demonstrates a methodology that utilizes CA to reduce the cost of Monte Carlo simulation (MCs) of linear systems under random dynamic loads. The main idea is to divide the power spectral density function (PSD) of the input load into several frequency bins before calculating the load realizations. The system response is only calculated at the central frequency of each bin; for other frequencies the system response is approximated via CA instead of full system analysis. This approach significantly increases the efficiency of the simulation as the approach performs an exact analysis only for the central frequency of each bin. We investigate the performance of the proposed method using a 76 degrees-of-freedom building model.