Study of the Windowing and Overlap-Add Operation for a Super-Gaussian Random Vibration Test

Abstract

Random vibration environmental testing employs the specified statistical properties of the real world vibration to reproduce the desired excitations on the shaker table for fatigue test purposes. Smooth and safe operation is the essential requirement for a long-duration test. Traditionally, the windowing and overlap-add (WOA) method is applied to the acceleration signals of the shaker table, and previous studies have indicated that this operation reduces the kurtoses of the processed signals. To protect the test equipment from abrupt changes in the input voltage, the WOA method is proposed to operate on the input voltage signals in a frame-by-frame form for super-Gaussian environmental testing. To figure out the impacts of the proposed operation on the response kurtoses of a shaker table, we express the system transfer function in the time domain, and the WOA method is analysed considering the transfer function of a dynamic system. Based on the analysis, a further study is made to explain the mechanism of the kurtosis decrease due to the WOA method. Through the study, we find that the kurtosis reduction conclusion is not applicable to all types of super-Gaussian signals, and the kurtoses can be invariable and even increased by allocating the positions of the high-excursion peaks of super-Gaussian signals when the WOA method is applied. A window function is recommended for zero-memory nonlinear (ZMNL) transformation to move the positions of the high-excursion peaks of a super-Gaussian signal, providing a novel way of adjusting kurtosis when WOA method is applied. The proposed WOA method and window function are first verified in a single-input-single-output (SISO) numerical simulation to test their effectiveness under different reference kurtoses. Then, they are evaluated in a two-input-two-output shaker table test. The test results demonstrate that the proposed window function can prevent the kurtosis decrease with the application of the WOA method.