Inverse ARX (IARX) method for boundary specification in heat conduction problems

Heat conduction problems are usually solved either with analytical or numerical simulations, a reduced model using system identification. The use of polynomial models, often used in automation theory, gained the attention thermal community last decades to elaborate these models because their simplicity and performance characterize an invariable system. They allow, for example, estimating local temperature known input heat source. However, (or identified systems) inverse is not straightforward, requiring second inversion step. In this paper, we present novel technique based on ARX (autoregressive exogenous input) that allows estimation unknown (like imposed flux boundary) output (temperature measurement). This new method, named IARX, only requires calibration step as regular and, then, it can estimate by direct calculation parameters. difference between IARX presence future parameters, which were deduced initial discrete form model. We herein example 1D simulation succeeded flux, even high discontinuities measurement noises. Finally, compare proposed method classical Beck’s function specification method. presented advantages like having no restriction number terms performing 45% faster much less memory space consumption than