Dyadic wavelet analysis of PDA signals

The dyadic wavelet transform is used to analyze PDA measured signals in order to identify the CASE-damping factor, which may be directly calculated from the dyadic wavelet analysis, not from the correlation study; accordingly, the pile capacity may be more exactly estimated by the CASE method. The dyadic wavelet transform can decompose a PDA measured signal into an incident impact wave and a reflected impulse wave at the certain scale that are clearly shown on the wavelet transform graph. The relation between the incidence and the reflection has been established by a transfer function based on the dyadic wavelet transform and the one-dimensional wave equation, whose phase is the time delay between the incident and the reflected and whose magnitude is a function of the CASE-damping factor. An autocorrelation function analysis method is proposed to determine the time delay and to estimate the magnitude of the transfer function that is determined by the ratio of the maximum of the autocorrelation function to the second peak value represented the reflected wave on the autocorrelation function graph. Thus, the damping factor is finally determined. An analog signal, a PIT signal and five PDA signals demonstrate the proposed methods, by which the time delay, the CASE-damping factor, and pile capacity are determined. The damping factors and pile capacity are good agreement with those by CAPWAP.