Natural frequency estimation using complex-frequency excitations

Abstract: Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we investigate the accuracy of natural frequency estimation in mechanical systems under noise using such excitations. The analysis is performed on an underdamped linear time-invariant single-degree-of-freedom spring-mass-damper system. We employ tools from information theory, namely Fisher information, to systematically quantify the sensitivity of complex-frequency excitation to measurement noise. Explicit closed-form expressions are derived relating Fisher information to excitation and system parameters under both Gaussian white and colored noise. The theoretical predictions are verified through Monte Carlo numerical simulations. The results indicate that appropriate selection of excitation parameters can significantly enhance the Fisher information, leading to improved estimation accuracy under complex-frequency excitations compared with conventional harmonic excitations. Experimental results demonstrate the advantages of complex-frequency excitation in terms of both accuracy and robustness of natural-frequency estimation. These findings establish a foundation for the development of high-performance sensors and novel nondestructive evaluation methods.