Indirect measurement of temperature inside a furnace, ARX model identification

Abstract

Thermal processing of ceramic parts at high temperature can be implemented in induction furnaces under vacuum conditions. In production, there is no direct access to these temperatures because of the high temperature level (higher than 1000°C) and also because the load cannot be equipped with temperature sensors. This paper deals with the indirect estimation of load temperatures. The estimation has to be made using transient point temperature measurements in the heating element. Indirect measurement of its temperature requires the calibration of a reference model that relates load temperatures to temperature in the susceptor first. A simplified reference furnace model, based on experimentations and thermal properties of its components, is derived. It is the reference model used to test the capacity of an identified AutoRegressive with eXogeneous variable model (ARX) to reproduce its output. This paper underlines the benefits of using ARX models instead of an analytical model as well as their close connection with convolutive products.