基于STFT时频谱系数收缩的信号降噪方法
Signal Denoising Method Based on STFT Time-Frequency Spectrum Coefficients Shrinkage

针对旋转机械故障振动信号的降噪问题，提出一种基于短时Fourier变换(short time Fourier transform,简称STFT)时频谱系数收缩的信号降噪方法。先将信号进行STFT，得到其时频谱。由于谱系数为复数，故根据模值大小进行谱系数收缩，并利用步长迭代算法在0到谱系数最大模值的区间内估计最优阈值。迭代运算过程中，首先，分别采用基本的硬阈值函数和软阈值函数进行系数收缩；然后，以改进风险函数为阈值评价标准，估计最优阈值；最后，利用最优阈值重新进行谱系数收缩，对得到的新谱进行STFT逆变换，重构降噪后的时域信号。仿真信号与试验数据的处理结果表明，利用所估计的最优阈值，STFT时频谱系数硬、软阈值函数收缩方法均能够实现噪声混合信号的降噪。
A signal denoising method based on short-time Fourier transform (STFT) time-frequency spectrum coefficient shrinkage is presented in light of the denoising of rotating machinery fault vibration signals. The STFT is adopted to transform the target signal into a time-frequency domain, and the spectrum′s complex coefficients are shrunk accordng to their modulus magnitude. A step iterative algorithm is proposed to estimate the optimal threshold at the interval between 0 and the maximum coefficient modulus. First, both the traditional hard and soft threshold functions are used for coefficient shrinkage. The optimal threshold estimation can then be obtained according to the modified risk function. Finally, the inverse STFT is applied to the spectrum coefficients after they are shrunk with the optimal threshold, and the obtained time-domain denoised signals are reconstructed. The results of the emulational signal and experimental data have demonstrated that the STFT time-frequency spectrum coefficient shrinkage method with either the hard or soft threshold function can work well in vibration signal denoising with the estimated optimal threshold.