Time Domain Decomposition (TDD) Method for Signal Analysis

Time Domain Decomposition (TDD) is a signal processing technique for modal parameter identification, widely applied in structural health monitoring, vibration analysis, and related fields. This method processes signals directly in the time domain without requiring transformation to the frequency domain, making it particularly suitable for analyzing non-stationary signals.

### Core Concept TDD extracts system modal parameters (such as frequency, damping ratio, and mode shapes) by decomposing measured signals. The fundamental premise is that structural responses can be decomposed into linear combinations of multiple modal responses. Using time-domain signal processing techniques (such as filtering or feature extraction), mixed signals are separated into independent modal components.

### Implementation Process Data Preprocessing: Perform operations like denoising and normalization on raw signals to ensure stability in subsequent analysis. Signal Decomposition: Utilize time-domain methods (e.g., sliding window techniques, matrix decomposition) to break down signals into several components, each corresponding to a specific mode. Modal Parameter Identification: Estimate frequency and damping ratio from the decomposed components and reconstruct mode shapes using spatial information (e.g., multi-channel measurement data).

### Advantages and Limitations Advantages: Avoids reliance on steady-state signals required by frequency-domain methods, making it suitable for transient or nonlinear response analysis. Limitations: Sensitive to noise and requires careful selection of decomposition parameters (e.g., window length, number of components).

When implementing TDD in MATLAB, it is common to combine built-in toolboxes (such as the Signal Processing Toolbox) with custom algorithms (e.g., Singular Value Decomposition) to complete the workflow. In practical applications, attention should be paid to modal aliasing issues, which can be mitigated through cross-validation techniques to enhance reliability.