Reconstruction of characteristics of a fluid flow in the pipe from spectral data using hybrid optimization algorithms

The study tested the natural transverse oscillations of a straight pipe conveying an ideal fluid flow. The purpose of this work was to find fluid mass density and flow velocity from circumstantial measured data. Input data are given by a truncated spectrum of lower natural frequencies of the system. The direct problem for the mathematical model of the system is solved with the help of homotopy perturbation method. Particular criteria of the inverse problem are supposed to be continuous, Lipschitzian, not everywhere differentiable, multiextremal functions. New hybrid optimization algorithms are used in the search for global solutions; the algorithms integrate a stochastic algorithm for scanning a search space with deterministic methods for local search. A numerical example is given.

References

[1] Pandoussis M.P. The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics. Journal of Sound and Vibration, 2008, vol. 310, no. 3, pp. 462-492.

[2] Wang L., Gan J., Ni Q. Natural frequency analysis of fluid-conveying pipes in the ADINA system. Journal of Physics: Conference Series, 2013, vol. 449, p. 012014. DOI: 10.1088/1742-6596/448/1/012014

[3] Dai H.L., Wang L., Qian Q., Gan J. Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method. Applied Mathematics and Computation, 2012, vol. 219, no. 5, pp. 2453-2464.

[4] Li S.-J., Liu G.-M., Kong W.-T. Vibration analysis of pipes conveying fluid by transfer matrix method. Nuclear Engineering and Design, 2014, vol. 266, no. 1, pp. 78-88.

[5] Xu M-R., Xu S.-P., Guo H.-Y. Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method. Computers and Mathematics with Applications, 2010, vol. 60, no. 3, pp. 520-527.

[6] Luczko J., Czerwinski A. Parametric vibrations of pipes induced by pulsating flows in hydraulic systems. Journal ofTheoretical and Applied Mechanics, 2014, vol. 52, no. 3, pp. 719-730.

[7] Mironov M.A., Pyatakov P.A., Andreev A.A. Forced oscillations of a pipe conveying a fluid flow. Akusticheskiy zhurnal [Acoustical Journal], 2010, vol. 56, no. 5, pp. 684-692 (in Russ.).

[8] Dai H.L., Wang L., Ni Q. Dynamics of a fluid-conveying pipe of two different materials. International Journal of Engineering Science, 2013, vol. 73, no. 1, pp. 67-76.

[9] Yuan Y. An iterative method for updating gyroscopic systems based on measured modal data. Applied Mathematics and Computation, 2011, vol. 218, no. 7, pp. 3753-3762.

[10] Kirsch A. An introduction to the mathematical theory of inverse problems. N.Y, Springer, 2011. 308 p.

[11] Chu D., Lin L., Tan R.C.E., Wei Y. Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems. Numerical Linear Algebra with Applications, 2011, vol. 18, no. 1, pp. 87-103.

[12] Renaut R.A., Hnetynkova I., Mead J. Regularization parameter estimation for large scale Tikhonov regularization using a priori information. Computational Statistics & Data Analysis, 2010, vol. 54, no. 12, pp. 3430-3445.

[13] Oberkampf W.L., Barone M.F. Measures of agreement between computation and experiment: Validation metrics. Journal of Computational Physics, 2006, vol. 217, no. 1, pp. 5-36.

[14] Voglis C., Parsopoulos K.E., Papageorgiou D.G., Lagaris I.E., Vrahatis M.N. MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches. Computer Physics Communications, 2012, vol. 183, no. 2, pp. 1139-1154.

[15] Karpenko A.P. Sovremennye algoritmy poiskovoy optimizatsii. Algoritmy, vdokhnovlennye prirodoy [Modern algorithms of searching optimization. Algorithms inspired by Nature]. Moscow, MGTU im. N.E. Baumana Publ., 2014. 446 p.

[16] Luz E.F.P., Becceneri J.C., De Campos Velho H.F. A new multi-particle collision algorithm for optimization in a high performance environment. Journal of Computational Interdisciplinary Sciences, 2008, vol. 1, pp. 3-10.

[17] Bagirov A.M., Al Nuaimat A., Sultanova N. Hyperbolic smoothing function method for minimax problems. Optimization: A Journal ofMathematical Programming and Operations Research, 2013, vol. 62, no. 6, pp. 759-782.

[18] Sulimov V.D., Shkapov P.M. Hybrid algorithms of computational diagnostics of hydromechanical systems. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2014, no. 4, pp. 47-63 (in Russ.).

[19] Lera D., Sergeev Ya.D. Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants. Computations in Nonlinear Science and Numerical Simulations, 2015, vol. 23, no. 1-3, pp. 326-342.

[20] Sulimov V.D., Shkapov P.M. Application of hybrid algorithms to computational diagnostic problems for hydromechanical systems. Journal of Mechanics Engineering and Automation, 2012, vol. 2, no. 12, pp. 734-741.