双树复小波稳健滤波在工程表面粗糙度评定中的应用

Application of DT-CWT robust filtering to evaluation of engineering surface roughness

讨论了现有工程表面粗糙度评定基准滤波方法的优缺点。提出双树复小波变换(DT-CWT)具有近似的平移不变性和改进方向选择性等优点适合用于三维表面基准滤波,但其滤波过于理想化易导致滤波基准在野点处畸变。为此,进一步提出将空域双边滤波思想引入DT-CWT来增强双树复小波变换在提取基准面野点处的稳健性。通过低频重构得到基准信号,并对每层重构系数进行双边滤波,最终增强DT-CWT滤波基准的稳健性。仿真结果显示:改进的DT-CWT能很好地抑制异常值干扰引起的滤波基准在野点处产生的畸变,其得到的基准面的精度误差为0.183 2×10-10 m,重构误差为0.016 1×10-10 m,低于传统方法所得。对实测数据进行处理结果表明,双树复小波稳健滤波能很好地克服边界效应并抑制工程表面上深沟对滤波结果的影响。提出的方法为工程表面粗糙度评定提供了一种新方法。

The merits and demerits of existing reference filtering methods for evaluation of the threedimensional engineering surface roughness were discussed.It points out that the Dual-tree Complex Wavelet Transform（DT-CWT）is suitable for the three-dimensional surface reference filter because of its advantages of approximate translation invariance and improved directional selectivity.However,its filtering is too idealistic,which will cause an opposition at the point of distortion of the filtered reference.Therefore,this paper brings the airspace bilateral filtering into the DT-CWT transform to enhance its robustness at the point of distortion of the filtered reference.The low-frequency reference signal was obtained through reconstruction and each reconstructed coefficient was bilaterally filtered,then,the robustness of reference filtering was enhanced by the DT-CWT filtering.The simulation data show that the robustness filtering under the conditions of abnormal interference is enhanced bythe improved DT-CWT,the precision error is 0.183 2×10-10 m and the reconstruction error is 0.016 1×10-10m,which is much lower than that of the traditional methods.The processing results for practical measurement data indicate that the improved method well overcomes the edge effects and suppresses the effects of deep valley in the surface on the filtering results.It provides a new way for evaluation of engineering surface roughness.