基于粒子群退火优化BVMD方法的超精密加工表面空间频率分解

Application of Particle Swarm Annealing Optimization BVMD Method in Spatial Frequency Decomposition of Ultra-Precision Machined Surfaces

超精密加工工件表面存在影响其性能的各种空间频率误差,针对工件的不同性能研究,需要采用有效分解手段对含有特定频段空间频率误差的形貌进行提取。传统的空间频率误差分解方法存在严重的模态混叠现象,为了解决这一问题,提出自适应二维变分模态分解(BVMD)算法对三维表面形貌进行分解。首先,由于采集三维形貌数据时会造成截断误差,引入镜像延拓和自卷积Hanning窗方法对数据进行预处理。然后,利用粒子群退火优化算法,对BVMD算法中的惩罚系数和分解层数进行寻优处理。其中,以各模态分量之间的频谱KL散度作为混叠指标,引入最小风险贝叶斯决策理论,综合KL散度与重构误差,构建优化算法适应度函数。最后,对超精密加工实测表面形貌进行分析,并与离散小波分解、二维经验模态分解方法相比较。结果显示,所提方法分解的KL散度值在102量级,远高于其他两种方法,能更好抑制模态混叠,实现超精密加工表面空间频率误差的有效分解。

There exist various kinds of spatial frequency errors on the ultra-precision machined surfaces,which seriously influence their performances.According to different performances of workpieces,it is necessary to use an effective decomposition method to extract the topography containing the spatial frequency errors at specific frequency bands.The traditional spatial frequency error decomposition method has the serious problem of modal aliasing.In order to solve this problem,an adaptive bidimensional variational mode decomposition(BVMD)algorithm is proposed to decompose a three-dimensional surface topography.First,image continuation and self-convolution Hanning window are introduced to preprocess the truncation errors when collecting 3D topographic data.Then,the particle swarm annealing optimization algorithm is used to optimize the penalty coefficient and the number of decomposition layers in the BVMD algorithm.Among them,the fitness function of the optimization algorithm is constructed by taking KL divergence among modal components as aliasing indicators,introducing the minimum risk Bayesian decision theory,and combining KL divergence with reconstruction errors.Finally,the measured topography of the ultra-precision machined surface is analyzed and compared with those by the discrete wavelet decomposition method and the bidimensional empirical mode decomposition methods.The results show that the KL divergence by the proposed method is several hundred,much higher than those by the other two methods.The proposed method has a good inhibition ability for frequency error modal aliasing,and can effectively decompose the spatial frequency errors of an ultra-precision machined surface.