Abstract
Sigmoid functions (growth function, logistic function, evolution function, etc.) are used in several fields of science to describe, study and forecast several phenomena of life. Since the sigmoid curves are nonlinear curves, the application of the Fisher- Pry transformation is used for calculating the regression coefficients of the approximated curves. In this paper, the nature of the investigated wear curve makes it necessary to compare the logistic curves and growth function curves. The process of the approximation is based on the principle of least squares: the minimum of the squared sum of differences is searched by the Nelder- Mead unconstrained minimization algorithm. The variables of the optimization are the parameters in the equation of the approximating function. The sigmoid curves can describe mainly the beginning phase and the normal wearing phase of the wear curve, the ending phase of the wear curve is a very quickly increasing function. Therefore on the basis of the results of this study, it could be possible to build a wear- monitoring system, in order to see and follow the differences between the sigmoid curve and the original wear curve, and if these differences are higher than a given limit, this could be the basis of some alert or warning, signaling the possible end of the lifetime.
Published Version
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