Surface profiling using sequential sampling and inverse methods. Part I: Mathematical background
Tóm tắt
A novel method is presented for measuring the height profile of the surface of an object, even in the presence of relative motion between the surface and the height sensors. The method involves making height measurements of the surface using several sensors arranged along the scanned surface. The surface profile and the relative motions are mathematically separated by observing that the surface features appear sequentially among the sensor data, while the relative motions appear simultaneously. The proposed linear inverse technique overcomes several limitations of existing profiling methods based on curvature measurements. In contrast with other inverse calculations, the results are quite stable, with noise in the results only about twice the measurement noise. Regularization is introduced as a means of smoothing noise and for achieving solutions for ill-posed cases. This paper focuses on the profile calculation of one-sided objects, and initially uses the assumption that the rigid relative motion between object and sensors is purely translational.
Tài liệu tham khảo
El-Sibaie, M., Jamieson, D., Mee, B., Whitten, B., Kesler, K., Tyrell, D., and Dorsey, J., “Engineering Studies in Support of the Development of High-Speed Track Geometry Specifications,” IEEE/ASME Joint Railroad Conference, Boston, MA, March 18–20 (1997).
Grassie, S., “Measurement of Railhead Longitudinal Profiles: A Comparison of Different Techniques,”Wear,191,245–251 (1996).
Scales, J., Smith, M., and Treitel, S., “Introductory Geophysical Inverse Theory,” Samizdat Press, Center for Wave Phenomena, Department of Geophysics, Colorado School of Mines (2001).
Menke, W., Geophysical Data Analysis: Discrete Inverse Theory, International Geophysics Series Vol. 45.Academic Press, San Diego (1989).
Corbin, J., “Method and Apparatus for Measuring Surface Roughness,”US Patent 4 573 131, US Patent and Trademark Office, Washington, DC (1986).
Aknin, P. and Chollet, H., “A New Approach for the Modeling of Track Geometry Recording Vehicles and the Deconvolution of Versine Measurements,” IAVSD Conference, Pretoria, (1999).
Cooper, J., “Rail Corrugation Measurement,” Proceedings of “Rail Technology,” Nottingham, UK, September 21–29, 207–223 (1981).
Tikhonov, A., Goncharsky, A., Stepanov, V., andYagola, A., Numerical Methods for the Solution of Ill-posed Problems, Kluwer, Dordrecht (1995).
Roberts, R.A. andMullis, C.T., Digital Signal Processing, Addison-Wesley, Reading, MA (1987).
Anderson, E. et al., Lapack User’s Guide, SIAM, Philadelphia, PA (1992).
Dahlquist, G., Björck, Å., andAnderson, N., Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ (1974).
Eisenstat, S.C., Gursky, M.C., Schultz, M.H., andSherman, A.H., “Yale Sparse Matrix Package. I: The Symmetric Codes,”International Journal of Numerical Methods in Engineering,18,1145–1151 (1982).