Structural Dynamical Signal Analysis Based On Sparse FFT Algorithm

Sparse Fast Fourier Transformation(SFFT) is a fast Fourier transform(FFT)algorithm, which can restore signal spectrum at a high probability only by using part of signal sample points, based on sparse signal frequency domain feature. For partial sparse signal, SFFT algorithm requires shorter time than FFT does, so SFFT is a sublinear algorithm. SFFT algorithm also shows great theoretical value and potential in structural health monitor area. For example, due to the difficulty of finding the features of structural vibration signals in time domain, it will be much easier to detect the features after FFT, getting the frequency, amplitude and phase from different sine waves. It will save much time to restore signal frequency by using the SFFT algorithm instead of FFT algorithm, with the result meeting requirement.In addition, based on SFFT algorithm, an algorithm which restore sparse signal spectrum at low-frequency sample can be established. Once adopting this algorithm in data acquisition system, the sub-nyquist sampling of high-frequency signal could be conveniently conducted and thus a better restored signal frequency spectrum could be acquired. The most important characteristic of the algorithm theory is the simplicity of hardware implementation. This feature can be distinctive when compared to using the compressed sensing theory to restore the signal frequency spectrum. The paper mainly focus on the following content:The paper introduces the development of sublinear sparse Fourier transform algorithm and mainly focus on the study of SFFT algorithm and presents the error rule of constraint of SFFT algorithm. Meanwhile, the paper elaborates the core technique problem of the algorithm, which includes signal spectrum rearrangement, the design of the window function, frequency domain downsampling, and gives the overall framework of the algorithm.In the paper, the SFFT algorithm is applied to the analysis of structural dynamic signal. The paper mainly studies the capability of restoring sparse signal spectrum and the impact of noise to sparse signals, making comparisons between SFFT and FFT on time complexity of calculating signal spectrums.The paper also conducts a research on an algorithm which restores sparse signal frequency spectrum with low sample rate based on SFFT algorithm, called Big Band algorithm, making comparisons with another compressed sensing algorithm which can also restore sparse signals at a low sampling rate on the hardware implementation, error of signal spectrum restoration and operation time consuming,etc.