Probabilistic seismic hazard analysis (PSHA) has been recognized as a reasonable method for quantifying seismic threats. Traditionally, this method ignores the effect of the focal depth, in which the ground motion prediction equations (GMPEs) are applied to estimate the probability distribution associated with the possible motion levels induced by the site earthquakes, but it is limited by the unclear geological conditions, which makes it difficult to provide a uniform equation, and these equations cannot express the non-linear relationship under geological conditions. Hence, this paper proposed a method to consider the seismic focal depth for the PSHA with the example of California and used a back propagation neural network (BPNN) to predict the peak ground acceleration (PGA) instead of the GMPEs. Firstly, the measured PGA and unknown PGA seismic data applicable to this method were collected separately. Secondly, the unknown PGA data were supplemented by applying the BPNN based on the measured PGA data. Lastly, based on the full-probability equation, PSHA considering the focal depth was completed and compared with the current California seismic zoning results. The results showed that using the BPNN in the PSHA can ensure computational accuracy and universality, making it more suitable for regions with unclear geological structures and providing the possibility of adding other parameters to be considered for the influence of the PSHA.
Originally proposed by the authors, the spring pendulum pounding-tuned mass damper (SPPTMD)—a novel nonlinear damping system comprising a spring pendulum (SP) and motion limiter that dissipates energy through spring resonance amplification and controlled mass-limiter impacts—was theoretically validated for structural vibration control. To experimentally verify its efficacy, a two-story, lightly damped steel frame was subjected to sinusoidal excitation and historical earthquake excitations under both uncontrolled and SPPTMD-controlled conditions. The results demonstrated (1) significant vibration attenuation through SPPTMD implementation and (2) enhanced control effectiveness in soft soil environments compared to stiff soil conditions. Additionally, a numerical model of the SPPTMD–structure system was developed, with computational results showing excellent correlation to experimental data, thereby confirming modeling accuracy.