A recently developed equilibrium based curve/surface fitting method is extended to linear function with heteroscedastic data (variable variance). The concept of equilibrium weighted “force” and “moment” is proposed to derive curve fitting formulae, which are exactly the same as that obtained with the traditional weighted least squares (LS) method for a linear function. Furthermore, a system of four equations, i.e., a “force” equilibrium equation, a “moment” equilibrium equation, an “equivalency” equation, and a “moment balance” equation have been established to solve both mean curve and the standard deviation simultaneously. Finally, the application of these methods to data of fatigue and creep lives is presented.
Equilibrium Based Curve Fitting Method for Test Data With Nonuniform Variance
Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 13, 2012; final manuscript received August 18, 2013; published online January 29, 2014. Assoc. Editor: Albert E. Segall.
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Wei, Z., Maleki, S., and Nikbin, K. (January 29, 2014). "Equilibrium Based Curve Fitting Method for Test Data With Nonuniform Variance." ASME. J. Pressure Vessel Technol. April 2014; 136(2): 021203. https://doi.org/10.1115/1.4026020
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