Thermal system identification using fractional models for high temperature levels around different operating points

Nonlinear Dynamics

Volumn 70, Issue 2, 2012, Pages 941-950

  Maachou, Asma ^a   Malti, Rachid ^a   Melchior, Pierre ^a   Battaglia, Jean Luc ^b   Hay, Bruno ^c  

^a Ecole Nationale Superieure d'Electronique Informatique et Radiocommunications de Bordeaux   (France)

^b UNIVERSITÉ DE BORDEAUX   (France)

^c LABORATOIRE NATIONAL DE MÉTROLOGIE ET D ESSAIS LNE   (France)

Author keywords

Fractional model; Linear model; System identification fractional calculus; Thermal diffusion

Indexed keywords

ARMCO IRON; CURIE POINTS; FINITE ELEMENT MODELS; FRACTIONAL CALCULUS; FRACTIONAL MODEL; HIGH TEMPERATURE; LARGE TEMPERATURE VARIATIONS; NON-LINEAR MODEL; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; OPERATING POINTS; RATIONAL MODELS; SMALL TEMPERATURE VARIATION; SMALL VARIATIONS; TEMPERATURE VARIATION; THERMAL CHARACTERISTICS; THERMAL MODELING; VALIDATION DATA;

CURIE TEMPERATURE; FERROMAGNETIC MATERIALS; FERROMAGNETISM; FINITE ELEMENT METHOD; IRON; MATERIALS SCIENCE; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARAMAGNETISM; PARTIAL DIFFERENTIAL EQUATIONS; SPECIFIC HEAT; TEMPERATURE DISTRIBUTION; THERMAL DIFFUSION;

THERMAL CONDUCTIVITY;

EID: 84871022355     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0507-y     Document Type: Review

References (32)

1. Adolfsson, K.: Nonlinear fractional order viscoelasticity at large strains. Nonlinear Dyn. 38, 233-246 (2004)
2. Agrawal, O.: Application of fractional derivatives in thermal analysis of disk brakes. Nonlinear Dyn. 38, 191-206 (2004)
3. Aoun, M., Malti, R., Levron, F., Oustaloup, A.: Synthesis of fractional Laguerre basis for system approximation. Automatica 43(9), 1640-1648 (2007)
4. Battaglia, J.L.: Heat Transfer in Materials Forming Processes. Wiley, Chippenham (2008)
5. Battaglia, J.L., Kusiak, A.: Estimation of heat fluxes during high-speed driling. Int. J. Adv. Manuf. Technol. 39, 750- 758 (2005)
6. Battaglia, J.L., Le Lay, L., Batsale, J.C., Oustaloup, A., Cois, O.: Heat flux estimation through inverted non-integer identification models. Int. J. Therm. Sci. 39(3), 374-389 (2000)
7. Benchellal, A., Bachir, S., Poinot, T., Trigeassou, J.C.: Identification of a non-integer model of induction machines. In: 1st IFAC Workshop on Fractional Differentiation and its Applications (FDA), Bordeaux, France (2004)
8. Cois, O., Oustaloup, A., Battaglia, E., Battaglia, J.L.: Noninteger model from modal decomposition for time domain system identification. In: 12th IFAC Symposium on System Identification, SYSID, Santa Barbara, CA (2000)
9. Cois, O., Oustaloup, A., Poinot, T., Battaglia, J.L.: Fractional state variable filter for system identification by fractional model. In: IEEE 6th European Control Conference (ECC'2001), Porto, Portugal (2001)
10. Cugnet, M., Sabatier, J., Laruelle, S., Grugeon, S., Sahut, B., Oustaloup, A., Tarascon, J.M.: On lead-acid battery resistance and cranking capability estimation. IEEE Trans. Ind. Electron. 57(3), 9.9-917 (2010)
11. Dugowson, S.: Les différentielles métaphysiques: histoire et philosophie de la généralisation de l'ordre de dérivation. PhD thesis, Université Paris XIII (1994)
12. Gabano, J., Poinot, T.: Estimation of thermal parameters using fractional modelling. Signal Process. 91(4), 938-948 (2011)
13. Gabano, J.D., Poinot, T.: Fractional modelling and identification of thermal systems. Signal Process. 91(3), 531-541 (2011)
14. Grünwald, A.: Ueber begrenzte Derivationen und deren Anwendung. Z. Angew. Math. Phys. 12, 441-480 (1867)
15. Heymans, N.: Fractional calculus description of non-linear viscoelastic behaviour of polymers. Nonlinear Dyn. 38, 221-231 (2004)
16. Liouville, J.: Mémoire sur quelques questions de géométrie et de mécanique et sur un nouveau genre de calcul pour résoudre ces équations. J. Éc. Polytech. 13, 71-162 (1832)
17. Maachou, A., Malti, R., Melchior, P., Battaglia, J.L., Oustaloup, A., Hay, B.: Thermal identification using fractional linear models in high temperatures. In: The 4th IFAC Workshop on Fractional Differentiation and its Applications (FDA), Badajoz, Spain (2010)
18. Malti, R., Sabatier, J., Akçay, H.: Thermal modeling and identification of an aluminum rod using fractional calculus. In: The 15th IFAC Symposium on System Identification (SYSID), Saint Malo, France (2009)
19. Malti, R., Victor, S., Oustaloup, A., Garnier, H.: An optimal instrumental variable method for continuous-time fractional model identification. In: The 17th IFAC World Congress, Seoul, South Korea (2008)
20. Malti, R., Victor, S., Oustaloup, A.: Advances in system identification using fractional models. J. Comput. Nonlinear Dyn. 3(2), 021401 (2008)
21. Malti, R., Moreau, X., Khemane, F., Oustaloup, A.: Stability and resonance conditions of elementary fractional transfer functions. Automatica 47(11), 2462-2467 (2011)
22. Mathieu, B., Oustaloup, A., Levron, F.: Transfer function parameter estimation by interpolation in the frequency domain. In: EEC'95, Rome, Italy (1995)
23. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley- Interscience, New York (1993)
24. Oldham, K., Spanier, J.: The remplacement of Fick's laws by a formulation involving semi-differentiation. J. Electroanal. Chem. Interfacial Electrochem. 26, 331-341 (1970)
25. Oldham, K., Spanier, J.: A general solution of the diffusive equation for semi-infinite geometries. J. Math. Anal. Appl. 39, 655-669 (1972)
26. Oldham, K., Spanier, J.: Diffusive transport to planar, cylindrical and spherical electrodes. J. Electroanal. Chem. Interfacial Electrochem. 41, 351-358 (1973)
27. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1995)
28. Poinot, T., Trigeassou, J.C.: Identification of fractional systems using an output-error technique. Nonlinear Dyn. 38, 133-154 (2004)
29. Riemann, B.: Versuch einer allgemeinen Auffassung der Integration und Differentiation. In: Gesammelte Mathematische Werke und Wissenschaftlicher, pp. 331-344 (1876)
30. Rodrigues, S., Munichandraiah, N., Shukla, A.K.: A review of state of charge indication of batteries by means of A.C. impedance measurements. J. Power Sources 87, 12- 20 (2000)
31. Sabatier, J., Aoun, M., Oustaloup, A., Grégoire, G., Ragot, F., Roy, P.: Fractional system identification for lead acid battery sate charge estimation. Signal Process. 86(10), 2645-2657 (2006)
32. Sommacal, L., Melchior, P., Cabelguen, J.M., Oustaloup, A., Ijspeert, J.: Fractional multi-models of the gastrocnemius frog muscle. J. Vib. Control 14(9-10), 1415-1430 (2008)