MATLAB Implementation of Prony Identification for Signal Analysis

Prony identification is a classical method for signal analysis, particularly excelling in power system oscillation mode identification. This technique extracts key parameters such as frequency, damping ratio, and amplitude by fitting exponentially damped sinusoidal functions to the signal. Implementing Prony identification in MATLAB typically involves the following key steps: First, preprocess the raw signal through denoising and normalization procedures. Power system signals often contain noise, and preprocessing significantly improves identification accuracy. In MATLAB, this can be implemented using functions like `smoothdata()` for noise reduction and `normalize()` for amplitude scaling. The core step involves constructing the Hankel matrix. This matrix reorganizes signal samples into a specific structure that forms the foundation for subsequent parameter extraction. The matrix dimension selection directly impacts identification results and is typically determined based on signal characteristics and empirical knowledge. In MATLAB implementation, the `hankel()` function can be used to create this matrix with proper dimension selection through trial and error or automated criteria. Next, solve the eigenvalue problem. Techniques like Singular Value Decomposition (SVD) are employed to extract the main modal components of the signal, which determines the identification capability of the Prony method. Eigenvalue decomposition reveals dominant oscillation modes in the signal. MATLAB's `svd()` function or `eig()` function can be used for this decomposition, with the number of significant singular values indicating the model order. Finally, perform parameter estimation by converting obtained eigenvalues into physical parameters like frequency and damping ratio. This step requires special attention to unit conversions and parameter validation. The conversion involves mathematical operations where eigenvalues are transformed through logarithmic functions and angle calculations to obtain final parameters. The primary advantage of Prony identification over other methods lies in its direct processing capability of time-domain signals and relatively simple implementation process. For power system low-frequency oscillation analysis, the Prony method provides accurate modal parameters that help analyze system stability. In practical applications, selecting appropriate model order is crucial. Overly high orders may lead to spurious modes, while insufficient orders may miss important patterns. Cross-validation serves as an effective means to assess the reliability of identification results, which can be implemented through MATLAB's `crossval()` function or manual data partitioning techniques.