CHARACTERIZATION AND SIMULATION OF GUNFIRE WITH WAVELETS

Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The response of a structure to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The methods all used some form of the discrete Fourier transform. The current paper will explore a simpler method to describe the nonstationary random process in terms of a wavelet transform. As was done previously, the gunfiire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. The wavelet transform is performed on each of these records. The mean and standard deviation of the resulting wavelet coefficients describe the composite characteristics of the entire waveform. It is shown that the distribution of the wavelet coefficients is approximately Gaussian with a nonzero mean and that the standard deviation of the coefficients at different times and levels are approximately independent. The gunfire is simulated by generating realizations of records of a single-round firing by computing the inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously discussed gunfire record. The individual realizations are then assembled into a realization of a time history of many rounds firing. A second-order correction of the probability density function (pdf) is accomplished with a zero memory nonlinear (ZMNL) function. The method is straightforward, easy to implement, and produces a simulated record very much like the original measured gunfire record