The pulse period, usually written as Tp, governs the dominant timescale of a velocity pulse and wields an outsize influence on how structures respond. Whether a pulse is short and sharp or long and rolling can determine whether a frame sways mildly or lurches into its inelastic range, and the relationship between Tp and a building’s fundamental period can swing structural demands dramatically. Pulse period also feeds directly into ground-motion simulation, pulse-consistent spectral models, and probabilistic seismic hazard analysis, which means that getting Tp wrong can quietly distort downstream estimates of earthquake risk.

Yet despite decades of research, no single method for determining Tp has achieved universal acceptance. Wavelet analysis, peak-point measurements on velocity time histories, analytical pulse-model fitting, and response-spectrum-based techniques all identify the period in different ways. The most popular family of approaches reads Tp directly off a response spectrum, taking the period at the peak of the spectral velocity (the SV method) or at the peak of the product of spectral velocity and spectral displacement (the SV·SD method). These methods are attractively simple, but they hinge on picking one local maximum out of a spectrum that may be jagged, multi-peaked, or contaminated by high-frequency content, and that dependence can produce badly underestimated or overestimated pulse periods for certain records.

The new study takes a fundamentally different route. Instead of hunting for a spectral peak, the researchers define the pulse period using the relative elastic input energy spectrum, EI,r, a quantity from energy-based seismic design that reflects not only the amplitude and frequency content of a ground motion but also its duration and total energy. The rule is elegant: the pulse period is the oscillator period that bisects the area enclosed by the EI,r spectrum and the period axis, leaving exactly half of the spectral energy on each side. Rather than asking where the spectrum peaks, the equal-area criterion asks where the cumulative input energy is balanced, producing a globally representative characteristic period for the record.

To make the integration interval robust, the team devised an adaptive termination criterion. The energy spectrum is computed from 0.01 seconds in steps of 0.01 seconds, and the calculation continues until the spectral tail has decayed sufficiently: the most recent twenty consecutive ordinates must all fall below either one percent of the running spectral peak or an absolute tolerance, with tightly constrained variation between adjacent ordinates. A hard cap of 40 seconds prevents runaway extension for records with persistent long-period content. Sensitivity analyses reported in the paper confirm that the identified pulse periods are essentially insensitive to reasonable variations in these parameters.

Crucially, the authors did not simply assert that their equal-area period is physically meaningful; they tested it. The EI,r-based Tp is prescribed in the analytical pulse model of Mavroeidis and Papageorgiou, while the remaining four pulse parameters, amplitude, phase, number of oscillations, and timing, are optimized with a genetic algorithm that minimizes the squared difference between the extracted pulse and the original velocity time history. Because the pulse period is held fixed during optimization, any agreement between the extracted wavelet and the actual record must flow from the identified period itself. Across the records examined, the optimized pulses reproduced the dominant velocity features and matched the principal range of the 5-percent-damped spectral velocity, supporting the physical reasonableness of the new definition.

The method was then benchmarked against six established techniques: the continuous wavelet transform classification of Baker, a wavelet packet transform approach, variational mode decomposition combined with genetic-algorithm pulse fitting, a signal-only optimization parameterization, and the SV and SV·SD spectrum methods. Across 311 representative pulse-like records, correlation coefficients between the new method and the reference approaches ranged from 0.87 to 0.98, with most above 0.90, indicating strong overall consistency. Detailed case comparisons revealed instructive differences. On some records the SV method seized on a short-period local peak and produced a far too narrow pulse, while the SV·SD method occasionally drifted toward very long periods. The equal-area energy criterion typically landed between the two, capturing the main velocity-pulse scale without the extremes of either peak-chasing approach.

To demonstrate engineering relevance, the researchers classified pulse-like motions into short-, medium-, and long-period groups and assessed the collapse fragility of a four-story, three-bay reinforced concrete frame modeled in OpenSees. The fiber-section model, validated against shake-table test data from the European Laboratory for Structural Assessment, reproduced measured drift profiles, displacement histories, and story shears with satisfactory accuracy. Cloud analyses using the geometric-mean spectral acceleration as intensity measure and the maximum inter-story drift ratio as demand parameter showed that pulse period matters enormously: records with pulses longer than two seconds produced markedly higher collapse fragility, while the short-period group shifted fragility curves toward higher ground-motion intensities and thus more favorable collapse performance. Comparable trends emerged when records were grouped using the CWT and SV·SD methods, reinforcing the conclusion that the observed pulse-period effect is genuine rather than an artifact of one identification technique.

The authors are careful to position the new criterion as a complement rather than a replacement. Different identification methods emphasize different characteristics of complex pulse-like motions, and no single definition suits every record. What the equal-area EI,r approach offers is a measure that is less hostage to a particular local spectral peak, is grounded in the cumulative distribution of input energy that energy-based design frameworks already prize, and carries a clear physical interpretation as an energy-balanced characteristic period. The study also confirms that pulse period is a critical parameter for interpreting the collapse potential of near-fault motions and for building pulse-period-dependent fragility models.

Limitations remain, and the authors flag them candidly. The structural application covered only a four-story bare reinforced concrete frame, so the quantitative fragility results depend on that building’s dynamic properties and its 0.711-second fundamental period. Future work, they write, should extend the framework to structures with different heights, periods, and response mechanisms to probe the interaction between pulse period and structural period more deeply. Even so, the method arrives at a moment when near-fault seismic risk assessment increasingly demands pulse-aware tools, and it provides engineers and hazard analysts with a computationally light, physically grounded way to extract one of the most consequential numbers in earthquake engineering from any velocity record.

Subject of Research: An energy-based method for identifying velocity-pulse periods of near-fault ground motions

Article Title: An efficient energy-based approach for identification of velocity-pulse periods

Article References: Gao, Q., Chang, Z., Monti, G., & Mollaioli, F. (2026). An efficient energy-based approach for identification of velocity-pulse periods. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02677-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02677-5

Keywords: pulse period, near-fault ground motions, input energy spectrum, velocity pulse, seismic fragility, reinforced concrete frame, genetic algorithm, M&P wavelet, probabilistic seismic hazard analysis, earthquake engineering, response spectrum, collapse vulnerability