Structural reliability analysis using imprecise evolutionary power spectral density functions

Buildings and structures in many regions of the world are exposed to environmental factors that can cause damage or failure, making it essential to model these factors accurately in engineering. Stochastic dynamics are crucial for modelling environmental processes, such as earthquake ground motions and wind loads, which can be characterised by a power spectral density (PSD) function that determines the dominant frequencies and corresponding amplitudes of the process. However, when generating a load model described by a PSD function, uncertainties in the processes must be taken into account, which makes a reliable estimation of the PSD function challenging, especially with only limited data available. This study employs the recently developed imprecise PSD function by using a radial basis function network to optimise data-enclosing bounds that produce an interval-valued PSD function. With this approach, a data set in the frequency domain can be bounded for uncertainty quantification. The method described in this work consists of optimising best-case and worst-case PSD functions within the bounds, which are transformed into a separable evolutionary PSD function. The reliability of structures is determined by an upper and lower failure probability, taking into account the present uncertainties. Advanced interval propagation schemes are linked to the imprecise PSD function to determine the failure probabilities efficiently. The method is illustrated by means of three numerical examples.