Study and modelling of two apple quality attributes: the soluble solids content and the firmness

Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both random. In this work, a complete study of two apple quality attributes, the soluble solids content and the firmness, is carried out. For each of these characteristics, the system of differential equations is linear and the state variables and the parameters are represented as random variables with their statistical properties (mean values, variances, covariances, joint probability density function) known at the initial time. The dynamic behaviour of these statistical properties is analysed. The variance propagation algorithm is used to obtain an analytical expression of the dynamic behaviour of the mean value, the variance, the covariance and the probability density function. A Monte Carlo method and the Latin hypercube method were developed to obtain a numerical expression of the dynamic behaviour of these statistical quantities and particularly to follow the time evolution of joint probability density function which represents one but the best mean to characterize random phenomena linked with fruit quality attributes.