中文摘要：

通过研究偏微分方程（Panial differential equation，PDE）在图像去噪中的原理和方法，针对传统滤波去噪方法所存在的问题，提出一种基于PDE的机械振动信号去噪方法。详细分析基于Gauss滤波核函数的PDE去噪模型，并推导模型的离散化过程。与传统去噪方法的对比试验表明，该方法可有效消除振动信号中的噪声干扰，同时保持信号的边缘特性和内部连续性，且去噪之后信号畸变少。因PDE方法本身的平滑特性，该方法的去噪效果受PDE演化的迭代次数和振动信号本身的平滑特性因素的影响，对低频振动信号具有更好的去噪效果。

英文摘要：

By studying on partial differential equation（PDE） with its application in picture denoising, a new kind of method based on PDE is proposed for vibration signal denoising, in view of the shortcomings in the traditional filter denoising method. PDE denoising model based on Gauss core function is analyzed in detail, and its discretization processing of the method is also introduced. Experiments in contrast with the traditional denoising method show that the method can effectively eliminate the noise disturbance, keep the edge property and interior continuity, and also avoid signal distortion after denoising. Because of the smooth property of PDE denoising method, its denoising effect is influenced by PDE iterations series and the smooth property factors of vibration signal, so this method has a better effect for low frequency vibration signal denoising.