Application of Regression Spline to Reverse Modeling

[+] Author and Article Information
Giovanni Moroni

Dipartimento di Meccanica,  Politecnico di Milano, via Bonardi n. 9, I-20133 Milano, Italygiovanni.moroni@polimi.it

Marco Rasella

Dipartimento di Meccanica,  Politecnico di Milano, via Bonardi n. 9, I-20133 Milano, Italymarco.rasella@polimi.it

J. Comput. Inf. Sci. Eng 7(1), 95-101 (Oct 26, 2006) (7 pages) doi:10.1115/1.2424245 History: Received September 30, 2005; Revised October 26, 2006

When dealing with inspection or reverse modeling, the problem of free-form curves and surfaces reconstruction has to be faced starting from a set of measured points. Because in point sampling the acquisition error is unavoidable, curves and surfaces fitting should be based on a rigorous diagnostic phase. We consider statistical regression analysis in which, treating error as a variable of the problem, we distinguish between the systematic behavior of measured points and noise in the reconstruction of curves and surfaces. The model we introduce for a regression based free-form reconstruction is the so-called regression spline. It is a well known model in the literature, with a consolidated theory and applications in fields such as chemical, econometric, and biomedical. Our purpose is to discuss the application of this powerful and flexible approach in a reverse modeling environment.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Proposed approach

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Figure 2

Initial shoe sole profile measured points

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Figure 3

Final shoe sole reconstructed profile and knots position

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Figure 4

Initial sets of data

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Figure 5

Residuals histogram

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Figure 6

Fitted curve and knots position

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Figure 7

Fitted aeronautic panel surface



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