Recovery of Under-sampled Signal During Highspeed Machining Condition Monitoring Using Approximate Sparsity in Frequency Domain

Aiming at the problem of under-sampled cutting force signal caused by unreasonable setting of sampling parameters in the high-speed machining condition monitoring system, a method of spectrum sensing based on the principle of approximate sparseness in frequency domain has been proposed. The non-linearity of machining system and sampling process makes the output signal of monitoring system contain higher harmonics, which shows obvious approximate sparsity on the Fourier basis. Using frequency points with large peaks can achieve sparse approximation of the spectrum, and obtain several frequency subsets as the result. The principle of spectrum aliasing is used to calculate the actual frequency range of each frequency subset and correct Fast Fourier Transform (FFT) spectrum of the cutting force measurement. Experiments on high-speed milling of aluminum alloy verify the effectiveness of this method. The results show that the proposed method is effective enough to recover the actual waveform of the cutting force signal, and the relative envelope error between the recovery temporal wave and the test signal is less than 4%. The research results provide some engineering and technical support for applying sparse theory to recover under-sampled signals.