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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Updated: Jun 26, 2025

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
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Spectrum feature extraction method combining Allan variance, VMD, and PSD.

Xu Liu1, Jian Wang2, Fei Liu3

  • 1School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing, 102616, China. liuxucrystal@163.com.

Scientific Reports
|May 14, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new method combining Allan variance, Variational Mode Decomposition (VMD), and power spectral density (PSD) to accurately extract seismic vibration frequencies for structural analysis.

Keywords:
Allan varianceMicro-seismic eventPower spectral density (PSD)Spectrum feature extractionVariational modal decomposition (VMD)

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Area of Science:

  • Geophysics
  • Structural Engineering
  • Signal Processing

Background:

  • Accurate seismic event identification and structural response calculation depend on spectrum feature extraction.
  • Current methods using Variational Mode Decomposition (VMD) lack clear criteria for effective modal component identification, leading to inaccuracies.
  • Existing techniques struggle with precise spectrum feature extraction for seismic analysis.

Purpose of the Study:

  • To develop a novel and accurate spectrum feature extraction method for seismic analysis.
  • To improve the identification of effective modal components in seismic data.
  • To enhance the evaluation of structural responses to seismic loading, particularly for heritage structures.

Main Methods:

  • Utilized Variational Mode Decomposition (VMD) to filter noise and enhance effective signals in triaxial accelerometer data.
  • Employed Power Spectral Density (PSD) to extract seismic frequencies from triaxial accelerometer observations.
  • Applied the Allan method to identify the most reliable accelerometer data for determining seismic excitation vibration frequencies.

Main Results:

  • Successfully filtered noise and extracted relevant seismic signals using VMD.
  • Identified distinct groups of seismic frequencies (26.95 Hz, 12.89 Hz, 12.5 Hz) from triaxial accelerometer data.
  • Validated the method's effectiveness by analyzing a Mw 2.6 micro-seismic event in Beijing, accurately extracting spectrum features.

Conclusions:

  • The proposed combined method (Allan variance, VMD, PSD) offers a reliable approach for spectrum feature extraction in seismic analysis.
  • Accurate extraction of seismic vibration frequencies is crucial for assessing the structural response of heritage sites like the Great Wall.
  • This method has significant implications for the conservation and protection of cultural heritage against seismic hazards.