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Equilibrium Mechanism Based Linear Curve Fitting Method and Its Application
Technical Paper
2011-01-0785
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
The equilibrium mechanism, which can be considered as the basis of least squares method for linear curve fitting, is investigated in this paper. Both conventional methods, such as vertical offsets method, and total least squares methods, such as perpendicular offsets method, are examined. It is found that both methods have the equilibrium bases. However, the conventional methods may give inaccurate prediction if using vertical offsets method to fit data with variation in horizontal direction or using horizontal offsets method to fit data with variation in vertical direction while the perpendicular method can give best fit solution to data with variation in both vertical and horizontal directions. The application of these methods is also presented in fatigue S-N curve data analysis and two-parameter Weibull distribution in exhaust component fatigue life prediction. Finally, the perpendicular offsets method is recommended in durability analysis for data with variation in both vertical and horizontal directions due to its simplicity and a sound equilibrium basis.
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Wei, Z., Yang, F., and Cheng, H., "Equilibrium Mechanism Based Linear Curve Fitting Method and Its Application," SAE Technical Paper 2011-01-0785, 2011, https://doi.org/10.4271/2011-01-0785.Also In
References
- Guest, P.G. Numerical methods of curve fitting Cambridge University Press Cambridge 1961
- Standard practice for statistical analysis of linear or linearized stress-life ( S - N ) and strain-life ( ε - N ) fatigue data ASTM Designation 2004
- British standard BS7608 Code of practice for fatigue design and assessment of steel structures 1993
- Design and manufacture of wind turbine blades, offshore and onshore wind turbines, DNV-OS-J102 October 2006 Det Norske Veritas
- Wei, Z. The equivalency-based statistical analysis of linear or linearized stress-life ( S-N ) and strain-life ( ε - N ) fatigue data ASTM Committee E08 meeting Atlanta, Georgia, USA November 9 11 2009
- Wei, Z. Forte, T.P. The equivalency-based statistical analysis of linear or linearized stress-life for fatigue data of composite materials Proceedings of ASME 2010 4 th International Conference on Energy Sustainability May 17 22 2010 Phoenix, Arizona, USA
- Wei, Z. Kurth, R.E. Forte, T.P. Probabilistic approach for fatigue life assessment based on S-N curve, PVP2010-25686 Proceedings of the ASME 2010 Pressure Vessels & Piping Division / K-PVP Conference July 18 22 2010 Bellevue, Washington, USA
- Wei, Z. Rice, R.C. Yatomi, M. Nikbin, K.M. The equivalency-based linear regression method for statistical analysis of creep/fatigue data, PVP2010-25691 Proceedings of the ASME 2010 Pressure Vessels & Piping Division / K-PVP Conference July 18 22 2010 Bellevue, Washington, USA
- Weisstein, E.W. Least squares fitting-perpendicular offsets, From MathWorld-A Wolfram web Resource http://mathworld.wolfram.com/LeastSquaresFittingPerpendicularOffsets.html
- Wei, Z. Yang, F. Cheng, H. The equilibrium mechanism of conventional and total least squares and based linear curve fitting methods
- Deming, W.E. Statistical adjustment of data New York J. Wiley & Sons, Inc London Chapman & Hall, Ltd. 1943
- Huffel, S. Vandewalle, J. The total least squares problem: computational aspects and analysis SIAM, Frontiers in Applied Mathematics 1991
- Weibull, W. Fatigue testing and analysis of results Pergamon Press 1961
- Lee, Y.L. Pan, J. Hathaway, R. Barkey, M. Fatigue testing and analysis: Theory and Practice Elsevier Butterworth-Heinemann 2005
- Nelson, W.B. Applied Life Data Analysis John Wiley & Sons, Inc. 2004
- Dong, P. Hong, J. Osage, D. Prager, M. Master S-N curve approach for fatigue evaluation of welded components WRC Bulletin, No.474 2002 Welding Research Council New York
- Awerbuch, J. Hahn, H.T. Off-axis fatigue of graphite/epoxy composites Fatigue of fibrous composite materials, ASTM STP 723 1981 243 273
- Yang, F. Lee, K. Cheng, H. “Effect of Test Data Accuracy on Component Durability Life Prediction in the Weibull Application,” SAE Technical Paper 2010-01-0199 2010 10.4271/2010-01-0199
- Dong, P. Wei, Z. Hong, J. A path-dependent cycle counting method for variable-amplitude multi-axial loading International Journal of Fatigue 2010 32 720 34
- Wei, Z. Dong, P. Multiaxial fatigue life assessment of welded structures Engineering Fracture Mechanics 2010 77 3011 3021