二维经验模态分解在工程表面形貌误差评定中的应用

针对目前表面微观形貌面形误差分离方法中存在边界畸变及自适应差等缺点,提出了将具有自适应时频分辨能力的二维经验模态分解算法(bidimensional empirical mode decomposition,BEMD)应用于三维工程表面面型误差分离中,同时用Riesz变换构造单演信号,计算信号整体的频率特征,完成对二维经验模态分解算法的终止准则的改进,使其能严格按照ISO4287所规定的截止波长分离三维表面各频段形貌误差。仿真结果表明,本文新方法相比于国标ISO中高斯滤波以及常用小波滤波,在分离三维工程粗糙表面各面型误差时,所得分离图形效果远优于传统方法所得,且各频段误差对应的三维评定参数误差均小于5%。最后对光学镀膜元件实例进行分析,结果表明该算法能够很好地分离各形貌误差的的空间信息,所得参数评定基准面相对传统方法不存在边界畸变等问题,因此该方法在实际工程表面评定应用中具有可行性。

Application of bidimensional empirical mode decomposition in error evaluation for engineering surface texture

In consideration of the disadvantages such as boundary distortion and poor adaptability in the method for microstructure surface error separation,the bidimensional empirical mode decomposition (BEMD) with adaptive time-frequency resolution capacity was put forward and applied to three-dimensional engineering surface error separation;at the same time,Riesz transform was utilized to construct monogenic signal,calculated overall frequency characteristics of the signal and improved the termination criterion for bidimensional empirical mode decomposition,thus keeping it in strict accordance with the error specified in ISO4287 for each frequency band of the 3D surface with cutoff wavelength and long separation.The simulation results show that compared with Gaussian filter in ISO and commonly-used wavelet filter,this new method can achieve a far better separation effect than traditional methods in error separation for 3D engineering rough surface,and the 3D evaluation parameter errors corresponding to the error in each frequency band are all lower than 5 ％.Finally,an instance analysis was conducted in the optical filming elements,and the results show that the method can well separate the spatial information of each surface error,and the reference surface for parameter evaluation is free from problems such boundary distortion compared with traditional methods.Hence,the application of the method in actual engineering surface error evaluation is of great feasibility.