Wavelet-based generation of fully non-stationary random processes with application to seismic ground motions

Assessing the performance of earthquake-resistant structural and geotechnical systems is crucial for achieving a desired reliability level and enhancing the resilience of the built environment in seismic-prone regions. Nonlinear dynamic analyses are widely used to quantify structural and geotechnical performance. Still, they require an accurate representation of nonlinear behaviours and proper modelling of the expected seismic events. Stochastic approaches are popular strategies for modelling dynamic actions to account for the uncertain nature of ground shaking. In this framework, joint time-frequency signal representations of seismic records are powerful tools to analyze signals' time-varying amplitude and frequency content. This paper presents a new method for the stochastic generation of artificial accelerograms using the circular harmonic wavelet transform, which possesses joint time-frequency localization capabilities and offers the engineers a clear and transparent interpretation of the results. The proposed approach adopts a new exponential auto-correlation structure for generating the random phases in the "child (generated) signals" starting from the deterministic ones in the "parent record". The effects of the correlation structure and different subdivisions of earthquake records in frequency bands are investigated and discussed, leading to practical considerations for identifying an effective tradeoff between localization in time and frequency domains. The method can be used for seismic assessment and design purposes, and numerical applications illustrate its potency.