Accurate identification of building structure frequencies forms the basis for damage detection. The structural dynamic response signal, under ambient excitation, can be transformed into a superposition of multiple single-frequency exponentially damped sinusoids combined with random white noise. However, the peak power spectrum of the response signal tends to exhibit line splitting, compromising the precision of frequency identification. This study examines the accuracy characteristics of the single-frequency free damping vibration signal (SFFDVS) and derives the Cramer–Rao lower bound for the frequency estimator. It thoroughly analyzes the factors influencing the accuracy of SFFDVS frequency identification. The study reveals that the primary cause of spectral line splitting is the random delay inherent in SFFDVS. Based on the maximum likelihood method (MLM), this research introduces the MLM algorithm for SFFDVS and provides a simulation analysis. The findings indicate that the MLM estimation algorithm for frequency parameters effectively addresses spectral line splitting and offers robust noise resistance and recognition accuracy.
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