Incipient damage identification through characteristics of the analytical signal response

The analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, while the imaginary part is its Hilbert transform. It has been observed that damage, even at a very low level, yields clearly detectable variations of analytical signal quantities such as phase and instantaneous frequency. This observation can represent a step toward a quick and effective tool to recognize the presence of incipient damage where other frequency-based techniques fail. In this paper a damage identification procedure based on an adimensional functional of the square of the difference between the characteristics of the analytical theoretical and measured signal is proposed. Numerical examples, on a single degree of freedom system and of 3 degrees of freedom building model, prove the efficacy of the proposed method, its robustness in the presence of measuring errors, and show that the use of the signal phase leads to the best damage parameter estimation.