Derivation of a Damage Sensitive Feature Using the Haar Wavelet Transform

In this paper, a damage sensitive feature based on the wavelet transform of the vibration signal is derived. The theoretical aspects of wavelet decomposition of vibration signals are presented. It is shown that the energies of the wavelet coefficients at appropriate scales can be used as damage sensitive features. Expressions for the energies of wavelet coefficients using the Haar wavelet basis function are derived for a single degree and a multidegree of freedom system. It is shown that the energies of the wavelet coefficients extracted at higher scales are functions of the physical parameters of the system and the loading function. Finally, the migration of damage sensitive feature vectors with damage is illustrated for the ASCE Benchmark Structure.