The research focuses on the Steel Space Truss Roof Structure, or SSTRS, a three-dimensional lattice of steel members whose individual tube sizes collectively determine both the weight of the roof and its capacity to resist gravity and seismic loads. Because each member can, in principle, be drawn from a catalog of available profiles, the design space is enormous, and searching it exhaustively is impossible. This is where metaheuristic algorithms come in: inspired loosely by natural processes such as learning and evolution, they explore the design space intelligently, iteratively refining candidate solutions until an optimal or near-optimal configuration emerges.

Yurdakul’s framework pits four algorithms against one another. Three belong to the relatively recent Rao family, developed by engineer R. Venkata Rao: the standard Rao-1 and Rao-2, and a self-adaptive variant called SapRao. These algorithms are notable for being metaphor-free, meaning they rely on straightforward mathematical comparisons between the best and worst candidate designs in a population rather than elaborate analogies drawn from animal behavior or physical phenomena. They are benchmarked against the well-established Teaching-Learning-Based Optimization algorithm, or TLBO, which simulates a classroom in which learners improve through interaction with teachers and with one another.

The computational engine behind the study is an integrated SAP2000-MATLAB environment. MATLAB scripts drive the finite element software SAP2000 through its Open Application Programming Interface, automating the otherwise laborious cycle of model updating, structural analysis, and constraint checking. Each candidate design is subjected to multiple load scenarios, including dead load, wind, snow, cladding, and seismic actions, with the sizing rules drawn from codes such as the AISC allowable stress design provisions, the Turkish building earthquake code, and Turkish loading standards. The automation means that thousands of design iterations, each requiring a full structural analysis, can be executed without human intervention.

To assess seismic performance, the study goes well beyond simplified equivalent static methods. Both fixed-base and seismically isolated versions of the truss roof were analyzed using nonlinear time-history analyses under scaled bi-directional ground motions, including the often-neglected vertical components of earthquake shaking. The ground motion suites distinguish between near-fault records, which carry the characteristic velocity pulses and directional effects of shaking close to a rupturing fault, and far-fault records, which lack those intense directivity pulses but can still be demanding in their own way. This distinction matters, because the two classes of motion excite structures differently and can expose different vulnerabilities.

The headline computational finding is striking. The standard Rao-1 algorithm achieved exactly the same minimum structural weights as TLBO across the evaluated fixed-base seismic design suites, yet it did so with a 50.68 percent reduction in total execution time. In a field where a single optimization run can consume hours or days of computing, halving the runtime without sacrificing solution quality is a meaningful advance. It suggests that the elegant simplicity of the Rao formulation, far from being a limitation, may actually be an asset when the underlying structural analyses are themselves computationally expensive.

The seismic findings carry equally important implications for practice. Near-fault ground motions induced locally elevated structural demands in the truss, concentrating forces and displacements in ways that designers of long-span roofs cannot afford to ignore. Perhaps more surprising, far-fault records with large displacement pulses could still produce relatively high response ratios even in the seismically isolated configuration. The result is a caution against the assumption that isolation alone guarantees protection: the character of the ground motion, not merely its proximity to the fault, governs how much demand reaches the superstructure.

That said, the isolation system proved remarkably effective at filtering out severe accelerations. Across all optimization algorithms and all ground motion records, the optimized weight of the isolated structure converged to exactly 47.4 percent of the maximum weight obtained for the fixed-base case. In other words, decoupling the roof from the ground through seismic isolation allowed the members to be sized at less than half the weight required for a conventionally fixed design, a difference that translates directly into material savings, lower fabrication costs, and a reduced carbon footprint for large-span construction.

The study situates itself within a rapidly growing body of work on metaheuristic structural optimization, which spans genetic algorithms, particle swarm methods, and hybrid schemes applied to trusses, domes, and bridges. It also connects to an active literature on optimizing seismic isolation systems, including friction pendulum bearings and other sliding devices, whose nonlinear behavior must be captured realistically in analysis. By bringing these two threads together, optimizing the steel superstructure while simultaneously evaluating a nonlinear isolation system under realistic, bi-directional, multi-component earthquake loading, the research offers one of the more complete pictures to date of how long-span roofs can be designed for seismic regions.

For engineers, the practical message is twofold. First, the choice of optimization algorithm matters less for the quality of the final design than for the cost of finding it, and simple, metaphor-free algorithms like Rao-1 deserve a place in the production toolkit. Second, seismic isolation can deliver dramatic weight savings for space truss roofs, but the design must be verified against both near-fault and far-fault suites, because large displacement pulses in distant records can still push response ratios upward. As computational tools become ever more tightly integrated with design codes, studies of this kind point toward a future in which earthquake-resistant long-span structures are not only safer but substantially lighter and cheaper to build.

Subject of Research: Metaheuristic optimization and seismic response of steel space truss roof structures with base isolation

Article Title: Metaheuristic-based optimization of steel space truss roof structures with seismic isolation

Article References: Yurdakul, M. (2026). Metaheuristic-based optimization of steel space truss roof structures with seismic isolation. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02702-7

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02702-7

Keywords: structural optimization, metaheuristic algorithms, Rao algorithms, TLBO, steel space truss, seismic isolation, near-fault ground motions, far-fault ground motions, nonlinear time-history analysis, SAP2000, MATLAB, earthquake engineering

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