Natural frequency estimation using complex-frequency excitations

2026-05-12

AI Summary

This work addresses the challenge of accurately estimating the natural frequency of mechanical systems under noisy conditions, where conventional harmonic excitation often yields suboptimal results. The authors propose a complex-frequency excitation with exponentially decaying amplitude and, for the first time, integrate it with Fisher information theory to derive closed-form expressions for Fisher information applicable under both Gaussian white noise and colored noise. Based on a linear time-invariant single-degree-of-freedom system model, Monte Carlo simulations and experimental validation demonstrate that judiciously designed parameters of the proposed excitation significantly enhance Fisher information. Consequently, this approach achieves higher estimation accuracy and greater robustness compared to traditional harmonic excitation under identical noise conditions, offering a promising new methodology for high-performance sensing and non-destructive testing.

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.

Problem

• natural frequency estimation
• complex-frequency excitation
• measurement noise
• Fisher information
• mechanical resonators

Innovation

• complex-frequency excitation
• Fisher information
• natural frequency estimation
• mechanical resonators
• noise robustness