Wavelet Packet-Based Diffusion Model for Ground Motion Generation with Multi-Conditional Energy and Spectral Matching

Temporal energy distribution strongly affects nonlinear structural response and cumulative damage. We propose a multi-conditional diffusion framework for ground motion synthesis that simultaneously matches temporal energy evolution and target response spectra. Wavelet packet decomposition provides the signal representation 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 spectrum matching and maintaining stable diversity sampling. The framework yields spectrum-compatible motions with realistic energy evolution and supports uncertainty quantification via conditional diversity sampling.

💡 Research Summary

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The paper introduces a novel diffusion‑based framework for synthesizing seismic acceleration time histories that simultaneously satisfy target response spectra and prescribed temporal energy evolution. The authors first adopt a Daubechies‑6 wavelet packet decomposition, converting each 16 384‑sample record into a 128 × 128 matrix of coefficients. Because wavelet packet transforms are perfectly invertible, the generated coefficients can be reconstructed into the time domain with numerical errors on the order of 10⁻¹⁴, eliminating the need for iterative phase‑retrieval methods such as Griffin‑Lim. This representation captures non‑stationary amplitude‑frequency characteristics more faithfully than conventional short‑time Fourier transform (STFT) approaches while being computationally efficient.

For conditional generation, the study employs the Elucidating Diffusion Model (EDM), which decouples noise scheduling, loss weighting, and network pre‑conditioning. Gaussian noise is added across a log‑normal distribution of standard deviations (σ ∈