Equilibrium and Equivalency (E2) Linear Surface Fitting Method for Data With Two Independent Variables

Abstract

A recently developed equilibrium and equivalency (E2) mechanisms based curve fitting method is extended to surface fitting for linear function z = f (x, y) = a + bx + cy with two independent variables x and y. The concept of equilibrium of ‘force’ and ‘moment’ is adopted to derive surface fitting formulae, which are exactly the same as that obtained with traditional least squares (LS) method for the linear function. However, E2 method has obvious physical meaning and therefore is more intuitive in quickly and correctly identifying data pattern and subsequent data analysis. Furthermore, the formula based on perpendicular offsets method in terms of data variation along surface normal direction is derived and the results are compared with the traditional methods. Finally, the application of these methods to data of fatigue and creep lives is presented.