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

摘要： 在D.L. Donoho和I. M. Johnstone提出的小波阈值去噪方法的基础上，构造一个新的阈值函数。与传统的软硬阈值函数相比，新阈值函数表达式简单易于计算，克服硬阈值函数不连续的缺点。仿真结果表明，采用新的阈值函数的去噪结果有效抑制在信号奇异点附近产生的PseudoGibbs现象，无论是在视觉效果上，还是在信噪比增益和最小均方误差意义上均优于传统的软硬阈值方法。将该方法应用于桥梁振动信号降噪中，其结果表明该方法可以较有效去除噪声。

关键词: 振动与波, 小波变换, 阈值函数, 均方误差, 信噪比, 监测