A Fractional-Order Dynamical Network Model for Thermoelectric Cooling: Identification and Parameter-Space Structure
- 1University Institute of Intelligent Systems and Numerical Applications in Engineering, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
- 2Department of Process Engineering, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
Abstract
This work presents an experimentally grounded identification and validation framework for a fractional-order three-node thermal network (F3N) describing the dynamic behavior of a thermoelectric cooling system. The framework combines experimental-data-driven parameter-bound estimation, Latin hypercube sampling, and multi-objective evolutionary optimization (NSGA-II) across ten independent seeds, simultaneously minimizing cold- and hot-side temperature prediction errors and their dynamic mismatch. The identified network reproduces the cold- and hot-side transient dynamics on the identification dataset with low RMSE and 95%-calibrated bootstrap prediction bands. Repeatability of the underlying measurements was confirmed by comparing three independent open-loop trials under the identical excitation protocol: cross-trial correlations exceed 0.998 for both channels, with a mean cross-trial standard deviation of 0.20 °C (Tc) and 0.22 °C (Th), and the identification dataset used throughout is the pointwise average of these three trials. A Fisher-information-based identifiability analysis shows that this predictive accuracy coexists with limited practical identifiability at the level of individual physical parameters: 28 of 55 parameter pairs are correlated above |ρ|=0.8, only the transport delay and the Peltier gain are individually well-determined, and a grid-based refit at fixed fractional order indicates that the identified value β^=0.6905 is not distinguishable, in terms of fit quality, from a commensurate integer-order formulation. External validation on three independent closed-loop trials under different operating conditions shows limited transferability of the identified parameters: the cold-side channel retains predictive value, while the hot-side channel does not, a pattern consistent with a non-independent ambient-temperature reference in the validation dataset. The linearized network is shown to be stable under Matignon’s criterion, and a graph-theoretic reformulation distinguishes the physical thermal network from a statistical parameter-compensation network derived from the identifiability analysis. The results characterize both the predictive capability and the parameter-level limitations of a fractional-order network identified from thermal measurements and provide an experimentally grounded basis for analyzing memory-driven thermal dynamics in thermoelectric systems.
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BibTeX
@article{pareja2026fractionalorder,
title = {{A Fractional-Order Dynamical Network Model for Thermoelectric Cooling: Identification and Parameter-Space Structure}},
author = {Miguel F. Ferrer Pareja and Carlos Sánchez Morales and Federico León Zerpa and Alejandro Ramos Martín},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100695},
url = {https://www.mdpi.com/2504-3110/10/10/695},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Fractional-Order Dynamical Network Model for Thermoelectric Cooling: Identification and Parameter-Space Structure
AU - Miguel F. Ferrer Pareja
AU - Carlos Sánchez Morales
AU - Federico León Zerpa
AU - Alejandro Ramos Martín
PY - 2026
DA - 2026/10/03
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100695
UR - https://www.mdpi.com/2504-3110/10/10/695
AB - This work presents an experimentally grounded identification and validation framework for a fractional-order three-node thermal network (F3N) describing the dynamic behavior of a thermoelectric cooling system. The framework combines experimental-data-driven parameter-bound estimation, Latin hypercube sampling, and multi-objective evolutionary optimization (NSGA-II) across ten independent seeds, simultaneously minimizing cold- and hot-side temperature prediction errors and their dynamic mismatch. The identified network reproduces the cold- and hot-side transient dynamics on the identification dataset with low RMSE and 95%-calibrated bootstrap prediction bands. Repeatability of the underlying measurements was confirmed by comparing three independent open-loop trials under the identical excitation protocol: cross-trial correlations exceed 0.998 for both channels, with a mean cross-trial standard deviation of 0.20 °C (Tc) and 0.22 °C (Th), and the identification dataset used throughout is the pointwise average of these three trials. A Fisher-information-based identifiability analysis shows that this predictive accuracy coexists with limited practical identifiability at the level of individual physical parameters: 28 of 55 parameter pairs are correlated above |ρ|=0.8, only the transport delay and the Peltier gain are individually well-determined, and a grid-based refit at fixed fractional order indicates that the identified value β^=0.6905 is not distinguishable, in terms of fit quality, from a commensurate integer-order formulation. External validation on three independent closed-loop trials under different operating conditions shows limited transferability of the identified parameters: the cold-side channel retains predictive value, while the hot-side channel does not, a pattern consistent with a non-independent ambient-temperature reference in the validation dataset. The linearized network is shown to be stable under Matignon’s criterion, and a graph-theoretic reformulation distinguishes the physical thermal network from a statistical parameter-compensation network derived from the identifiability analysis. The results characterize both the predictive capability and the parameter-level limitations of a fractional-order network identified from thermal measurements and provide an experimentally grounded basis for analyzing memory-driven thermal dynamics in thermoelectric systems.
SN - 2504-3110
ER -