Keywords: artificial accelerograms, earthquake engineering, harmonic wavelet transform, signal processing, spectrum-compatible accelerograms.

According to the major international building codes, the accelerograms used for time-history dynamic analyses must be representative of the seismic hazard at the site. Although the direct use of recorded accelerograms is an attractive option, they are often not available in a sufficient number at a given site to produce an acceptable structural assessment, therefore there is an increasing need for artificially-generated time histories of ground shaking. The available methods are mostly stochastic and, with a certain level of abstraction from the underlying physical phenomenon (i.e. the actual seismic genesis is not considered), they handle seismic records as samples of non-stationary random processes. Signal processing comes then helpful to analyse, generate and manipulate such records.

In this context, a common practice is to use the Fourier transform (FT) to look at the signal in the frequency domain, where the distribution of the seismic energy over the frequencies becomes apparent. On the other hand, the non-stationary characteristics of accelerograms can be properly analysed in the time domain. Indeed, the time and frequency domains are in a kind of dualism because they are capable of highlighting some of features of the signal while hiding some others. Joint time-frequency signal representations are therefore deemed as a powerful strategy to deal with the evolutionary frequency content of the accelerograms, and therefore getting the best from the two domains. Among them, the wavelet analysis is a very promising tool, as it exploits localised functions (wavelet) instead of ever-lasting harmonics as a base to decompose a signal. The harmonic wavelet transform (HWT) enjoys the additional advantage of overcoming the limitations of the classical FT without losing a meaningful engineering interpretation in terms frequency content.

In this framework, this paper presents a novel method to generate a set of code-compliant spectrum-compatible accelerograms, which enable the compatibility conditions to be satisfied with a target elastic design spectrum starting from a single record. In a first stage, the parent signal is deterministically modified to become spectrum-compatible. HWT is used to manipulate the record, aiming at preserving most of the original information in both the time and frequency domain. The proposed one-to-one iterative procedure is capable of fitting the record within a prescribed compatibility zone, and the additional energy associated with modification proves to be much less than in the case of a FT-based approach (therefore overcoming one of the main drawbacks of traditional methods of stochastic generation, which often discourages the use of artificial accelerograms). In a second stage, an arbitrary number of accelerograms is randomly generated, reproducing the joint time-frequency properties of the spectrum-compatible accelerogram. The HWT is exploited in this one-to-n procedure to preserve the evolutionary frequency contents throughout the randomisation process.

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