PARAMETERIZATIONS OF THE VON BERTALANFFY MODEL FOR DESCRIPTION OF GROWTH CURVES

The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.

An analysis method to determine how changes in dynamic complexity impact on rotor-bearing systems

Condition monitoring performance and diagnosis of rotor-bearing systems depend not only on the methods used, but also on the dynamic complexity of the system itself. Thus, it is important to analyze how changes in parameters under various working conditions impact on dynamic complexity. Most of previous research efforts on this topic have been focused on the analysis of nonlinear dynamics of rotor-bearing systems with different parameters. In this paper, a nonlinearity quantification based analysis method is presented to determine how parameter dynamics impact the complexity of rotor-bearing systems. The dynamic complexity of rotor system is estimated using defined nonlinearity measures. To validate this method, a sliding rotor-bearing system with a loose pedestal is used. The estimates (nonlinearity degrees) and the states of motion are matched with increasing rotational speeds. It is then investigated, how the eccentricities, lubricating oil viscosities, and bearing clearances impacted the dynamic complexity at several critical rotational speeds. These results can guide methodological choices for condition monitoring and diagnosis of rotor systems.