1.研究の背景

Digital Image Correlation (DIC) modal analysis utilizes DIC technology to non-contact measure structural images during vibration, determining natural frequencies, damping ratios, and other parameters to avoid resonance and enhance structural performance under dynamic loads.

Common DIC modal analysis methods include the Stochastic Subspace Identification (SSI) method and the Bayesian power spectrum method. While SSI accurately identifies modal parameters, its computational speed is slow and time-consuming. The Bayesian power spectrum method quantifies excitation uncertainties but requires excessive computation, limiting its practical engineering applications.

The Revealer research team has developed a cross-power spectrum-based DIC modal analysis method, characterized by simple testing, efficient computation, accurate modal
identification, and precise vibration mode measurement.

2.Method Principle

The cross-power spectrum is a spectral analysis method that describes the correlation between two signals. By calculating the cross-correlation function Pxy(f) of signals x(t), y(t), it is transformed into the frequency domain to obtain the cross-power spectrum P, analyzing phase and amplitude

relationships across frequencies. Key principles include:

• Pxy(f): Cross-power spectrum
• x(t): First signal at time
• Y∗(t−τ): Complex conjugate of the second signal at time t−τ
• τ: Time delay for signal offset in cross-power spectrum calculation
• e−j2πft: Frequency-domain rotation factor for extracting frequency components
• j: Imaginary unit (−1−1)
• t: Time variable
• f: Frequency variable

The cross-power spectrum frequency-domain matrix represents inter-signal relationships among n signals, extracting system natural frequencies and modal matrices.

3.Method Procedure

Step 1: Data Acquisition
Use the Thousand-Eyes Wolf DIC measurement system to capture images of structural components under various excitations (e.g., impact and vibration), recording dynamic responses.

Step 2: Image Processing
Process images to extract displacement fields on the object’s surface. Compute displacement time-series data for all points using DIC algorithms, generating vibration signals

Step 3: Signal Preprocessing
Denoise displacement data and apply high-pass/low-pass filters to remove irrelevant frequency components.

Step 4: Fourier Transform
Convert preprocessed signals to the frequency domain via Fourier transform:

Step 5: Cross-Power Spectrum Calculation
Compute the cross-power spectrum matrix for signal pairs

4.Experimental Analysis

A vibration experiment was conducted on a metal plate (Figure 1). Hammer impact simulated external excitation, and a 3D-DIC high-speed measurement system captured vibration images.

Figure 1: Experimental Setup

A rectangular region was selected to observe composite displacements (Figure 2):

Figure 2: Composite Vibration Displacements

Analysis results using the Revealer DIC modal analysis module are shown below：

Figure 3: Cross-Power Spectrum

Figure 4: Multi-Order Vibration Modes

5.Research Summary

This paper presents a cross-power spectrum-based DIC modal analysis method, integrating Digital Image Correlation (DIC) technology with cross-power spectrum analysis. This method provides high-precision, full-field displacement measurements, identifies modal parameters across multiple observation points, and captures multi-order structural vibration modes.

The proposed method demonstrates significant engineering advantages for health monitoring and dynamic analysis of complex and large-scale structures, such as bridges and high-rise buildings.