Insights into the behavior and performance of Linear Structured Filter Coefficients (LSFC) in solving one-dimensional inverse heat conduction problems

Abstract

© 2025 Elsevier Masson SAS.This study investigates the use of an artificial neural network-based method for solving one-dimensional inverse heat conduction problems, providing insights into the behavior of network weights and their performance in estimating heat flux in near real-time, in comparison with classical methods such as the sequential function specification method (SFSM) and Tikhonov regularization based filter solutions. This class of problems involves estimating the unknown boundary heat flux condition from experimental temperature measurements at accessible locations. While neural networks have become increasingly popular in this area, there is limited understanding of how their internal parameters, particularly the weights, behave. This article explores the structure of these neural network weights, showing that they exhibit a well-defined, linear, and approximately antisymmetric pattern for this type of problem. With the aid of the neural network solution, it is possible to identify a model for the filter coefficients, referred to in this study as Linear Structured Filter Coefficients (LSFC). The method was applied to real temperature data obtained from laboratory experiments on an AISI 1040 steel plate, in which the heat flux supplied by a resistive heater was estimated using the LSFC approach. The results were compared with traditional filter-based methods, such as Tikhonov regularization and the Sequential Function Specification Method (SFSM). In this study, the LSFCs provide a more compact solution, requiring fewer temperature data points and resulting in shorter response delays, making them suitable for near real-time heat flux estimation.

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