MATLAB Implementation for Modal Analysis and Processing

Modal analysis is a crucial aspect of structural dynamics, and MATLAB provides powerful tools for implementing various modal processing methods. Time-domain approaches directly handle vibration signals, extracting modal information through integral transformations or direct analysis of time-series characteristics using functions like `integral` and `diff` for signal processing operations. Frequency-domain analysis requires Fourier transformation using `fft` functions first, converting signals to the frequency domain where modal frequencies and damping ratios are identified through peak picking algorithms (e.g., `findpeaks` function) and frequency response function estimation methods. Auto-power spectrum and cross-power spectrum analysis form the foundation of frequency-domain modal analysis, revealing signal energy distribution characteristics through `pwelch` and `cpsd` functions. Coherence functions, implemented via `mscohere`, evaluate linear correlation between input and output signals, commonly used to validate frequency response function reliability. Frequency Response Function (FRF) serves as the core of modal analysis, where structural dynamic characteristics can be estimated through multi-point excitation or response measurements using `tfestimate` functions. Time-frequency analysis techniques like Short-Time Fourier Transform (`spectrogram`) and Wavelet Transform (`cwt`) are suitable for non-stationary signals, effectively capturing instantaneous frequency variations. Hilbert-Huang Transform (HHT) processes nonlinear, non-stationary data through Empirical Mode Decomposition (EMD) algorithms and Hilbert spectral analysis, extracting instantaneous modal characteristics using MATLAB's `emd` and `hilbert` functions. The Random Decrement Technique serves as an efficient data denoising method, particularly suitable for modal parameter identification under ambient excitation through statistical averaging procedures. These methods can be combined in practical engineering applications - for instance, preprocessing data with Random Decrement Technique first, then extracting modal parameters through HHT or frequency response analysis, ultimately achieving high-precision structural dynamics assessment. MATLAB's Signal Processing Toolbox and System Identification Toolbox provide comprehensive function support for efficient implementation of these algorithms, including specialized functions for modal parameter extraction and system identification workflows.