Wavelet Packet‐Based Diffusion Model for Ground Motion Generation With Multi‐Conditional Energy and Spectral Matching

ABSTRACT Temporal energy distribution strongly affects nonlinear structural response and cumulative damage. We propose a multi‐condition diffusion framework for ground‐motion synthesis that simultaneously matches temporal‐energy evolution and target response spectra. Wavelet packet decomposition is used to represent the ground‐motion signals and enables direct waveform reconstruction via orthogonal filter banks. A Transformer‐based conditional encoder with cross‐attention integrates heterogeneous conditions, including spectral ordinates, Arias intensity, temporal parameters, and Husid curves. The framework adopts the elucidating diffusion model (EDM) with second‐order Heun sampling to improve inference efficiency without sacrificing quality. Tests on the NGA‐West2 database show that explicit temporal‐energy constraints markedly improve control of energy onset and significant duration while preserving response‐spectrum agreement across repeated stochastic samples. The framework yields spectrum‐compatible ground motions with realistic energy evolution and enables conditional sample variability to be quantified through repeated stochastic sampling.