Time–frequency representation of nonlinear structural response through rationally sampled Stockwell analysis

Abstract

The reliable analysis of the non-stationary response of mechanical and structural systems under transient excitations, and in particular the tracking of the time-varying evolution of the dominant modal frequencies during damaging events, remains a long-standing challenge for vibration-based monitoring. A persistent practical limitation is that the time-frequency map on which any subsequent automatic or learning-based identification stage relies is built on a frequency grid that depends on implementation choices. This means that records acquired on different sensors or under different events cannot be compared on a common substrate.The present article addresses the limitation at the representational level by introducing the Stockwell-Ditommaso-Ponzo representation (SDP), obtained by sampling the Stockwell transform on an ordered Farey grid of primitive rational frequencies. Each coefficient is assigned a rational label, an ordered Voronoi frequency cell and an exact logarithmic quadrature weight induced by the Stockwell measure. Subsequent to the declaration of the sampling frequency, the analysed band and the maximum conductor, the support, the cells and the weights are uniquely determined prior to the processing of any record. A time-varying modal frequency, such as that observed when the apparent lateral stiffness of an instrumented building degrades under strong-motion excitation and partially recovers afterwards, is therefore encoded as a deterministic path on a geometry shared across sensors, repeated events and simulations of the same structure.The representation is exercised on the simulated top-floor acceleration of a five-storey reinforced-concrete infilled frame, whose apparent first-mode frequency is observed to drop to approximately 0.8 Hz and partially recovers through the simulated closure of column cracks under gravity. The SDP cell-path captures the four phases of the loss-and-recovery sequence, and engineering-oriented descriptors take values consistent with the physical setup. The proposed representation is intended to function as a reproducible, transform-level front end on which calibrated automatic identification and damage-assessment procedures, including artificial-intelligence-based pipelines, can be built in a controlled manner.