Probabilistic re-analysis of nonlinear systems when energy of excitation changes

A reliability study of nonlinear mechanical systems under random dynamic loads often requires Monte Carlo simulation in the time domain with hundreds of thousands of replications. The uncertainties involved in design make such analyses necessary for various admissible loads, which can be impractical. The authors have already developed a methodology that reduces the computational cost of Monte Carlo simulation when the load is represented by a Power Spectral Density (PSD) function. This method is based on a probabilistic re-analysis, which uses results from a simulation for a single PSD to estimate the reliability for other admissible PSDs. However, the methodology was limited to PSDs with the same energy content. This paper proposes an approach to extend the applicability of the above method to cases in which the energy content of the PSD functions changes.