Estimation for inner surface geometry of furnace wall using inverse process combined with grey prediction model. (English) Zbl 1167.80403
Summary: The inner surface geometry of a cylindrical furnace wall is estimated using inverse process method combined with grey prediction model. In estimating process a virtual area extended from the inner surface of furnace wall is used for analysis. The heat conduction equation and the boundary condition are first discretized by finite difference method to form a linear matrix equation; the inverse model is then optimized by linear least-squares error method and the temperatures of virtual boundary are obtained from a few of measured temperatures in furnace wall using the linear inverse model; and finally the temperature distribution of system is got by direct process and the inner surface geometry of furnace wall can be estimated accordingly. The result shows that using inverse process combined with grey prediction model the geometry can be exactly estimated from relatively small number of measured temperatures. Moreover, the effects of measurement error, location, and number of measured points on the estimation for inner surface geometry of furnace wall are discussed in detail.
MSC:
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 80M50 | Optimization problems in thermodynamics and heat transfer |
| 80M20 | Finite difference methods applied to problems in thermodynamics and heat transfer |
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
References:
| [1] | Tikhnov, A. N.; Arsenin, V. Y.: Solution of ill-posed problems, (1977) |
| [2] | Yang, C. Y.: Estimation of the temperature-dependent thermal conductivity in inverse heat conduction problems, Appl. math. Model. 23, No. 6, 469-478 (1999) · Zbl 0934.35209 · doi:10.1016/S0307-904X(98)10093-8 |
| [3] | Lin, J. H.; Chen, C. K.; Yang, Y. T.: Inverse method for estimating thermal conductivity in one-dimensional heat conduction problems, AIAA J. Thermo-phys. Heat transfer 15, No. 1, 34-41 (2001) |
| [4] | Hsu, P. T.; Yang, Y. T.; Chen, C. K.: Simultaneously estimating the initial and boundary conditions in a two-dimensional hollow cylinder, Int. J. Heat mass transfer 41, No. 1, 219-227 (1998) · Zbl 0925.73046 · doi:10.1016/S0017-9310(97)00095-1 |
| [5] | Warrier, G. R.; Witte, L. C.: On the application of the hyperbolic heat equation in transient heat flux estimation during flow film boiling, Numer. heat transfer A 35, No. 4, 343-359 (1999) |
| [6] | Jang, H. Y.; Tuan, P. C.; Chen, T. C.; Chen, T. S.: Input estimation method combined with the finite-element scheme to solve IHCP hollow-cylinder inverse heat conduction problems, Numer. heat transfer A 50, No. 3, 263-280 (2006) |
| [7] | Chiang, C. C.; Chou, S. K.: Inverse geometry design problem in optimizing hull surfaces, J. ship res. 42, No. 2, 79-85 (1998) |
| [8] | Hsieh, C. K.; Kassab, A. J.: A general method for the solution of inverse heat conduction problems with partially unknown system geometries, Int. J. Heat mass transfer 29, No. 1, 47-58 (1986) · Zbl 0585.73196 · doi:10.1016/0017-9310(86)90033-5 |
| [9] | L. Met, X.A. Wang, X.Y. Meng, Finite element method to an inverse problem of three-dimensional heat conduction with partially unknown system geometries, in: Proceedings of the International Conference on Numerical Methods in Thermal Problems, 1991, pp. 1514. |
| [10] | A. N. Alexandrou, An inverse finite element method for directly formulated free and moving boundary problems, in: Proceedings of the First International Conference on Computational Modeling of Free and Moving Boundary Problems, 1991, pp. 149 – 163. |
| [11] | Huang, C. H.; Chao, B. H.: An inverse geometry problem in identifying irregular boundary configurations, Int. J. Heat mass transfer 40, No. 9, 2045-2053 (1997) · Zbl 0933.74500 · doi:10.1016/S0017-9310(96)00280-3 |
| [12] | Huang, C. H.; Chen, H. M.: Inverse geometry problem of identifying growth of boundary shapes in a multiple region domain, Numer. heat transfer A 35, No. 4, 435-450 (1999) |
| [13] | Deng, J. L.: Control problems of grey systems, Syst. control lett. 1, No. 5, 288-294 (1982) · Zbl 0482.93003 · doi:10.1016/S0167-6911(82)80025-X |
| [14] | Deng, J. L.: Essential topics on grey system: theory and applications, (1988) |
| [15] | Chen, C. K.; Tien, T. L.: A new forecasting method of discrete dynamic system, Appl. math. Comput. 86, No. 1, 61-84 (1997) · Zbl 0919.93007 · doi:10.1016/S0096-3003(96)00173-7 |
| [16] | Tien, T. L.; Chen, C. K.: The indirect measurement of fatigue limits of structural steel by the deterministic grey dynamic model \(DGDM(1,1,1)\), Appl. math. Model. 21, No. 10, 611-619 (1997) · Zbl 0925.73004 · doi:10.1016/S0307-904X(97)00077-2 |
| [17] | Box, G. E. P.; Jenkins, G. M.; Reinsel, G. C.: Time series analysis: forecasting and control, (1994) · Zbl 0858.62072 |
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