The Estimation of Accuracy for the Neural Network Approximation in the Case of Sintered Metal Properties

Abstract

The spatial structure of sintered metal powders is described by many qualitative and quantitative micro-geometrical properties. The statistical approach based on univariate and multivariate distributions is very useful for consistent and objective description of such structures. It provides information appropriate for a whole population of sinters, not only particular specimen. Empirical distributions of quantitative properties obtained from the image analysis are very irregular and for this reason inconvenient for further numerical simulations. The smoothing of these distributions is required for data conditioning and preprocessing however, the use of simple regression techniques is limited due to the strict lower and upper bound of cumulative distribution function. Authors propose to use a multilayer perceptron as a non-parametric regression model because of its the well-known smoothing properties. The technical application of such model requires additionally providing of the confidence band or any equivalent measure of uncertainty. The highly non-linear structure of the neural network model makes not possible to use typical linear techniques to estimate variance. Additionally, the simple confidence band estimation leads to non-physical values of the cumulative distribution function: lower than 0 or greater than 1. Authors propose to avoid such difficulties by two methods. Firstly, the lower and upper bound limitation are satisfied by the logit transformation which projects the range [0, 1] into unlimited real range. Secondly, the variance of the neural network model is estimated by jackknife estimator. The article presents such approach with preliminary attempt to an automated data processing by ADCIS Aphelion image analysis software and STATSOFT Statistica data analysis software. The almost full automation of the process is required by materials science engineers due to the lack of the sufficient data processing knowledge and skills. Both software systems provide suitable embedded programming environments: C# for Aphelion and Visual Basic for Statistica. The proposed approach has been tested on the example of pore size distribution in sintered stainless steel AISI 434L.