Singular Spectrum Analysis Method for Identification of Non-Stationary Acoustic Signals.

Abstract

The article addresses the topical scientific and applied problem of automated recognition and classification of non-stationary acoustic signals generated by technical equipment or military operations. The main research object is the time series of complex acoustic patterns, the processing of which by classical statistical methods is complicated by their non-stationarity and high noise levels. The aim of the work is to develop a noise-robust method for identifying acoustic emission sources based on time series analysis. To achieve this, the Singular Spectrum Analysis (SSA) method, also known as the “worm” algorithm, was employed. This approach is based on embedding a one-dimensional signal into a multidimensional trajectory matrix followed by singular value decomposition (SVD). The mathematical model describes the process of unfolding the series, calculating principal components, and reconstructing the signal through the procedure of Hankelization. A significant part of the research is devoted to the selection of principal components using an energy criterion, where the set of indices is formed such that the cumulative contribution of eigenvalues exceeds a threshold of 95%. This allows for the automatic separation of informative signal components from the noise subspace. Experimental studies were conducted in two stages: detailed modeling of matrix transformations for a single signal in the Mathcad 15.0 environment and statistical verification on a large sample using a developed software module in Python. Testing the algorithm on signals from a machine drive and model impulses (simulating explosions) confirmed its high adaptability. Based on Monte Carlo statistical simulation (1000 iterations), it was established that the mean absolute percentage error (MAPE) does not exceed 6% at a signal-to-noise ratio (SNR) above 20 dB. The proposed SSA method demonstrated higher accuracy compared to the classical ARIMA(1,1,1) model under intensive noise conditions (5.82% versus 7.45%). It is concluded that the use of SSA for automated acoustic monitoring systems is highly feasible for military and rescue operations.