关键词: 振动与波, 小波变换, 阈值函数, 均方误差, 信噪比, 监测

Abstract: A novel threshold function is constructed based on the wavelet threshold denoising method presented by D.L. Donoho and I.M. Johnstone. This new threshold function has many advantages over the traditional soft/hard threshold functions. It is simple in expression, as continuous as the softthreshold function, and highorder differentiable. Thus, it is convenient for mathematical processing. This new threshold function also overcomes the shortcoming that there is an invariable difference between the estimated wavelet coefficients and the decomposed wavelet coefficients in the soft threshold function. Meanwhile, the new threshold function is more flexible than the soft/hardthreshold function. All these advantages make it possible to construct an adaptive denoising algorithm. Simulation results indicate that the new denoising method adopting the new threshold function can suppress the PseudoGibbs phenomena near the singularities of the signal effectively. And the numerical results also show that the new method gives better MSE performance and SNR gains than the traditional hard/softthreshold methods. This method is applied to the vibration signal denoising of a bridge, and the result shows that it can eliminate the noise effectively.

Key words: vibration and wave, wavelet transform, threshold function, MSE, SNR, health monitoring