The carrier wave design for the synthesis of non-Gaussian and non-stationary signals using the amplitude modulation method

Abstract

The methods of generating stationary random signals, both Gaussian and non-Gaussian, are quite complete, but the researches on the non-stationary signals are insufficient. Especially, the current methods seldom provide mathematical bases about the kurtoses of the produced signals such that the generations of non-stationary non-Gaussian signals with the desired kurtoses are inefficient, which also decrease the flexibility of the real-time control in shaker table tests. In the article, the amplitude modulation method is employed to realize the signal synthesis. The carrier waves of the method are investigated considering the bursts overlapping situations. At first, the explicit equations between the kurtoses of the synthesized signals and the three crucial parameters (the offset, the distance between a pair of adjacent bursts and the parameter of the Beta-distributed random variables) are deduced for the carrier waves with both overlapped bursts and non-overlapped busts. Meanwhile, to solve the power spectral density variation led by the amplitude modulation method, an explicit expression of a rescaling parameter is also proposed. Furthermore, the impacts of the three parameters are investigated; the focus of the investigation is on how the kurtoses of the synthesized signals are changed by the parameters. Based on the results of the investigation, a test procedure is put forward to apply the proposed equations in a shaker table test. The control process of the test demonstrates that the real-time kurtoses control can be achieved efficiently with the help of the newly proposed equations.