Statistical analysis of cavitation erosion impacts in a vibratory apparatus with copulas

A method of analysis of cavitation peaks (impact events) using copulas is developed. Impact events, otherwise known as peaks, are defined as maximum in the pressure amplitude applied to a material surface. These impact events were measured using a high speed pressure sensor in a cavitation apparatus based on the ASTM G32 standard. A total of 46180 impacts were measured over 100 realizations of 4ms long recording. First, the impact duration and amplitude's joint marginals are modeled as gamma distribution (part of the exponential family), determined by a Kolmogorov-Smirnov test (KS test). Then, copulas enable the study of the dependence structure of the measured impacts characteristics. The measured parameters are shown to not be independent but instead have a complex, asymmetric dependence structure. There are almost no impacts that have a combination of a high amplitude (>12MPa) and low duration (<5μs). The Tawn copula best fitted the data, as determined by a maximum likelihood method. An extension of the KS test to two dimensions demonstrated that the copula is a better fit compared with a joint distribution of independent marginals.