Determination of scrap/supply probability curves for the mechanical properties of aluminium alloys in hot extrusion using a neural network-like approach

Abstract

In this paper a neural network-like approach that accounts for the different uncertainties in the hot extrusion of AA6082 alloys is given. The results, presented in the form of scrap/supply curves, suggest the use of a probabilistic approach in the process of hot extrusion. The proposed approach considers both the epistemic and aleatory uncertainties and takes into account all the available influential input variables. The use of the CAE neural network, which is a special type of probabilistic neural network, is proposed as a powerful tool in the design and partial optimization of the hot-extrusion processes in real, industrial aluminium production. It was found that mechanical properties and the yield can be additionally optimized by reducing the epistemic uncertainties, which consequently requires more accurate measurements and more reliable control of the production processes.

Introduction

It is well known that the performance of aluminium alloys (e.g., AA6082) during the hot-extrusion process, as well as the mechanical properties of the final product, i.e., yield stress, tensile strength, elongation (Man et al., 2006, Ozerdem and Kolukisa, 2009), are influenced by many different parameters. Of these, the chemical composition, which is well defined by ASTM and internal standards, is widely recognized as being the most influential (Man et al., 2006, Robinson et al., 2009). There are, however, the other process parameters, i.e., casting temperature, casting rate, homogenization, extrusion ratio, ram speed, temperature in different phases of the melt preparation, process engineers (Peruš, Fazarinc, Kugler, & Fajfar, 2010) etc., that also have an important influence. Typically, the influences of process parameters (i.e., the geometry of the extruded profile) on the mechanical properties were investigated using simple statistical methods (Clausen et al., 2001, Hsiang and Lin, 2007). The majority of investigations deal with a comparison of the different parameters in a single process (Hsiang and Lin, 2007, Norasethasopon, 2008, Tryland et al., 2000), but analyses taking into account the entire process path are very rare in the available literature (Jančı´ková, Roubı´ček, & Juchelková, 2009). The latter usually exhibit complex relationships between the parameters and the final properties of the aluminium alloys. Nevertheless, most of the above-mentioned investigations deal with predictive models that tend to be deterministic. As a result, they do not explicitly account for the uncertainties inherent in the models and they typically provide, due to our deliberate choice of simplifications, biased estimates of the performance and the mechanical properties. However, when we realize, that all of the natural and industrial phenomena (i.e., hot extrusion) are influenced by variables that possess random properties, predictive models that are unbiased and explicitly account for all the prevailing uncertainties seem to be the best choice. Therefore, in this paper, analyses of the mutual dependence of several input parameters (i.e., chemical composition, ram speed, extrusion ratio) on the mechanical properties of extruded profiles of AA6082 alloy are reported. For this purpose the CAE method (Grabec and Sachse, 1997, Terčelj et al., 2008), which can be treated as a special type of probabilistic neural network (Specht, 1991), was employed to develop a non-parametric predictive model without a priori assumptions. In order to develop the probability curves for surpassing specified scrap or for exceeding specified mechanical properties by also accounting for the uncertainties in the input variables, in this paper referred to as scrap/supply curves, Latin hypercube sampling was employed (Iman et al., 1981, McKay et al., 1979). It should be noted, however, that both the standard neural networks (e.g., Bhadeshia, 2009, Cevik et al., 2009) and the probabilistic models (e.g., Stepanskiy, 2009, Wang et al., 2010)/probabilistic neural networks (e.g., Übeyli & Übeyli, 2009) are increasingly popular in materials science.

In this paper a scrap/supply probability curve in the hot-extrusion process of an aluminium alloy is defined as the conditional probability of surpassing the specified scrap or attaining/exceeding some specified mechanical properties for a given set of demand variables. More specifically, in aluminium production, the supply probability may be defined as the conditional probability of attaining the specified yield stress, tensile strength or elongation, for given aluminium hot-extrusion production variables, i.e., the chemical composition and technological parameters (extrusion ratio, ram speed, etc.). Similarly, the scrap probability may be defined as the conditional probability of surpassing the specified scrap at the yield stress, tensile strength or elongation for given aluminium hot-extrusion production variables. It should be emphasized that (the application of) neural networks offered a viewpoint that led to a relatively simple solution of a very complex problem. The proposed solution, which is directly applicable in industrial production, combines the use of neural networks and a probabilistic approach, taking into account randomness and different uncertainties.