The Research Of The Parallel Fast Algorithm Based On Gaussian Filtering In The Characterization Of Engineering Surfaces

With the development of manufacturing industries towards the direction of the micro and nano technology, the importance of parts surface topography become more and more prominent. Gaussian filtering, with its simple structure and zero phase shift characteristics, is accepted by the metrologists and scholars at home and abroad. But there are also many problems, such as the boundary distortion, outliers’ distortion and the problem of computational efficiency should be improved. In this paper, the problem of the boundary distortion and computational efficiency of Gaussian filtering method will be improved.The major measurement methods and measuring instruments of the surface metrology and their respective advantages and disadvantages in the domestic and overseas were introduced in this paper. The surface characterization methods and their respective applicable scopes in the last ten years were summarized, and the basic filtering characteristics of Gaussian filter and its fast algorithm of FFT (fast Fourier transform) and IIR (infinite impulse response filter) cascade approximation method were selective analyzed. Although the reference characterization of FFT is efficient, the boundary distortion (its length is half cut-off wavelength) is its weakness. So this paper selects the latter as the research object and proposed the method based on generalized B-spline approximating Gaussian filtering and the parallel improvement of cascade approximation. The generalized B-spline approximation filtering was achieved by optimizing the parameters t1 and t2, using PSO(Particle Swarm Optimization).To uniform the change of sampling interval and the cut-off wavelength of the filter, this paper discussed the difference between the generalized B-spline filter and Gaussian filter, under the different conditions of the cut-off angular frequency.The transmission characteristics show that when cut-off angular frequency is 1, the deviation between the them is less than 1% and the high precision approximation of the Gaussian filter in the case of operation without any cascaded was achieved. The example shows that the time-consuming of generalized B-spline filtering method is only 1/40 of the Gaussian filtering method.And this paper demonstrated Gaussian filter approximation based on B-spline filter in theory and improved the traditional cascading algorithm. The improved objects are B-spline filtering and Butterworth filtering in this paper. It mainly changed the series form to parallel form in every cascade to save the waiting-time of computer and achieve the high efficiency in computer arithmetics.In theory, the speed of the improved algorithms increased nearly twice as the cascade method. In the simulation 1-D profile, Not only the new method guarantees the approximating accuracy, but also its consuming time is far less than the Gaussian filtering and FFT. Finally, based on the reparability of two-dimensional Gaussian function, the new method was introduced into three-dimensional reference characterization. The simulation and examples show that, there is no boundary distortion in the contrast of an intuitive three-dimensional datum by the use of the improved algorithm,just as the cascade method; in the analysis of roughness parameters, the assessment of accuracy will not be affected, because the results is extremely close to the cascade method and the Gaussian filter; in the contrast of time-consuming, the improved method only takes about 1/2 the cascade method, far less than the Gaussian filtering algorithm.