Accurately performing modal analysis and identifying modal parameters (frequency, damping ratio, mode shape) using digital image correlation (DIC) technology is a process involving sophisticated experimental design, high-quality data processing, and appropriate parameter identification algorithms. DIC's advantage of providing full-field displacement/strain data makes it highly promising for modal analysis, but it also presents some unique challenges. The following is an introduction to the key algorithms for achieving accurate modal identification:
The displacement data (full-field or reduced data) acquired and processed by DIC technology is input into the modal parameter identification algorithm. The algorithm selection depends on the excitation type and data characteristics.
Frequency domain method (requires input/output or known excitation)
Principle: Calculate the frequency response function matrix between the reference point (force input point) and all response points (DIC measurement points).
step:
Perform Fourier transform on the input (force) and output (displacement) signals.
Calculate the FRF matrix.
Apply mature frequency domain modal parameter identification methods:
Peak picking method: Read the frequency at the peak of the FRF amplitude spectrum, estimate the damping ratio using the half-power bandwidth method, and read the FRF vector at the peak frequency as the mode shape. Simple and fast, but with limited accuracy, especially for dense modes and large damping.
Curve fitting method: Fitting FRF data in the frequency domain using a parametric model (such as the least squares complex frequency domain method). It can simultaneously identify frequency, damping ratio, and mode shape with high accuracy. Suitable for SISO or SIMO data.
Multi-reference point frequency domain method: Utilizing all information from the FRF matrix, it performs better in handling tightly coupled modes. Examples include PolyMAX.
Advantages: The physical meaning is clear and intuitive, and the noise resistance is relatively good (through multiple averaging).
Disadvantages: Requires measurement of excitation force; leakage effect may affect accuracy (windowing is required, but it will reduce resolution); sensitive to nonlinearity.
Time-domain method:
Principle: Modal parameters are identified directly from time-domain displacement response data. This method is particularly suitable for cases involving environmental excitation or where only output data is available (OMA).
Common methods:
Feature system implementation algorithm: Based on a discrete-time state-space model. The system is implemented using the Hankel matrix of the response data. It can identify stability graphs and effectively distinguish between physical and computational modes. It has wide applications.
Random subspace identification: This method is also based on the state-space model. It identifies the system matrix through projection of the response data or QR/SVD decomposition. It is robust and accurate, and is one of the mainstream methods in OMA.
Ibrahim time-domain method: Using free decay response or impulse response function data, modal parameters are solved through eigenvalue decomposition.
Least squares complex exponential method: Using impulse response data, a complex exponential model is established for fitting.
Advantages: No need to measure input force (suitable for OMA); avoids leakage problems; can handle transient and steady-state data.
Disadvantages: More sensitive to noise; requires longer data recording; model order selection is a key challenge (requires stability plot assistance); computational cost may be high (especially for full-field data).
Time-frequency domain method:
Principle: Analyze the joint energy distribution of the signal in time and frequency.
Common methods:
Wavelet transform: decomposes a signal into different scales and times. It can be used to identify modes or damping with frequencies varying over time.
Hilbert-Huang Transform: Decomposes a signal into eigenmode functions through empirical mode decomposition, and then uses the Hilbert transform to find the instantaneous frequency and damping. Suitable for nonlinear and non-stationary signals.
Advantages: It can handle non-stationary signals.
Disadvantages: computationally complex; results interpretation may be subjective; its application in full-field modal analysis is not as mature as the frequency domain/time domain method.
