Hybrid parametric/non-parametric models for lifespan modeling of insulation materials

Abstract

This paper considers the problem of insulation material lifespan modelling. This problem is crucial for aircraft reliability since about 40% of electrical machine failures stem from insulation. According to the material physical properties and to the sightings reported in the literature, the proposed model should relate the logarithm of the insulation lifespan to the logarithm of the electrical stress factors (voltage and frequency) and to the temperature. The possible interactions between these three predominant aging factors must be also considered. Note that, due to a constraint of low experimental cost, the number and configuration of experiments were optimized through a design method. Parametric modelling through multilinear regression requires the estimation of a potentially high number of parameters in view of the reduced data set. The method proposed in this paper thus combines parametric and non-parametric approaches. First, a decision tree automatically classifies the experiments into ranges corresponding to relevant operating modes. Indeed, this method recursively partition the training set by selecting, at each node, the best separating variable and its best splitting value according to prediction performance. However, the predictive model produced by this tree is piecewise constant since a constant value is associated to each leaf of the tree. In this paper we combine this approach with parametric modelling, by associating a multilinear regression model to each region identified by the tree. This approach brings a better understanding of the aging phenomena through the hierarchical organization of the factors and also provides simple, specific and thus effective multilinear models in each lifespan range. The method performance is analysed through real data: training and test sets correspond to experiments on twisted pairs covered by an insulating varnish. The proposed method shows improved performance with respect to multilinear regression on one hand and to regression trees on the second hand.