International Journal of Thermophysics

, Volume 34, Issue 2, pp 284–305 | Cite as

Inverse Identification of Temperature-Dependent Volumetric Heat Capacity by Neural Networks

  • Balázs Czél
  • Keith A. Woodbury
  • Gyula Gróf


An artificial neural network (NN)-based solution of the inverse heat conduction problem of identifying the temperature-dependent volumetric heat capacity function of a solid material is presented in this paper. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. The volumetric heat capacity versus temperature function is to be determined using the measured transient temperature history of a single sensor. In this study, noiseless and noisy artificial measurements were generated by the numerical solution of the corresponding direct heat conduction problem. The inverse problem was solved by back-propagation and radial basis function type neural networks applying the whole history mapping approach. The numerical tests included the comparison of two different data representations of the network inputs (i.e., temperature vs. time and time vs. temperature) and accuracy analysis of the two network types with noiseless and noisy inputs. Based on the results presented, it can be stated that feed-forward NNs are powerful tools in a non-iterative solution of function estimation inverse heat conduction problems and they are likely to be very effective in evaluation of real measured temperature histories to determine the volumetric heat capacity as an arbitrary function of temperature.


Finite difference method Inverse heat conduction problem  Neural network Volumetric heat capacity 



The work was supported by the Hungarian Scholarship Board. This work was connected to the scientific program of the “Development of quality-oriented and harmonized R+D+I strategy and functional model at BME” project. This project was supported by the New Széchenyi Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002). The work was supported by the Grant OTKA 82024.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Balázs Czél
    • 1
    • 2
  • Keith A. Woodbury
    • 1
  • Gyula Gróf
    • 2
  1. 1.Department of Mechanical EngineeringThe University of AlabamaTuscaloosaUSA
  2. 2.Department of Energy EngineeringBudapest University of Technology and EconomicsBudapestHungary

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