Hilbert transform-based semi-analytic meta-model for maximum response envelopes in dynamics of railway bridges

Abstract

This paper presents an innovative meta-model for fast assessment of dynamic design envelopes of railway bridges. The proposed approach allows the computation of instantaneous amplitudes of dynamic response time series through the integral Hilbert transform (HT). Based upon the semi-analytic solution of the moving load problem of linear bridge structures, which is analytical in the time domain, the HT is obtained in the Cauchy principal value sense in closed-form. Therefore, the proposed HT-based semi-analytic (HTSA) solution provides a direct estimation of the instantaneous response envelopes of railway bridges under high-speed trains. Since the HT demodulates the signals by suppressing the fast-varying oscillating components, the sampling rates needed for tracing the instantaneous amplitudes are considerably lower than those required for sampling the original signals. Thus, the reduction in computational time achieved by the HTSA approach stems from the sub-sampled approximation of instantaneous envelopes. In order to appraise the effectiveness of the proposed HTSA meta-model, four validation case studies are presented, including mono-dimensional and realistic three-dimensional bridge structures. The presented results report substantial reduction in computational cost with limited accuracy loss, and demonstrate the usefulness of the HTSA meta-model for fast comparison of bridge design alternatives during early design stages.