Hybrid Algorithm of Computational Diagnostics of Hydromechanical Systems
Authors: Sulimov V.D., Shkapov P.M. | Published: 14.09.2014 |
Published in issue: #4(55)/2014 | |
DOI: | |
Category: Mechanics | |
Keywords: inverse problem, criterion function, Lipschitz constant, smoothing approximation, global optimization, Metropolis algorithm, regularization, hybrid algorithm |
Consideration is being given to problems of computational diagnostics of hydromechanical systems. For the mathematical model the inverse problem is formulated and during its solving there is optimization. It is suggested that particular criteria are continuous, Lipschitzian, not everywhere differentiable, multiextremal functions. Search for global solutions carried out with using new hybrid algorithms uniting stochastic scanning algorithm of space variables and the deterministic methods of local search. Numerical examples of the model diagnostics of the coolant phase constitution in the reactor primary circuit were presented.
References
[1] Pulecchi T., Casella F., Lovera M. Object-oriented modelling for spacecraft dynamics: Tools and applications. Simulation Modelling and Theory, 2010, vol. 18, no. 1,pp. 6386. DOI: 10.1016/j.simpat.2009.09.010
[2] Gao C., Zhao Z., Duan G. Robust actuator fault diagnosis scheme for satellite attitude control systems. J. Franklin Inst., 2013, vol. 350, no. 9, pp. 2560-2580.
[3] Ma J., Jiang J. Applications of fault detection and diagnosis methods in nuclear power plants: A review. Progress in Nuclear Energy., 2011, vol. 53, pp. 255-266.
[4] Shang J.S. Simulating plasma microwave diagnostics. J. Sc. Computing, 2006, vol. 28, no. 213, pp. 507-532.
[5] Lavrent’ev M.M., Zharinov S.Yu., Zerkal’ S.M., Soppa M.S. Computational diagnostics of surface characteristics of long cylindrical objects by methods of active location Sib. Zh. Ind. Mat. [J. Appl. Ind. Math.], 2002, vol. V, no. 1 (9), pp. 105-113 (in Russ.).
[6] Goncharsky A.V., Romanov S.Y. Zh. Vychisl. Mat. Mat. Fiz. [Comput. Math. Math. Phys.], 2012, vol. 52, no. 2, pp. 263-269 (in Russ.).
[7] Goncharsky A.V., Romanov S.Y. Supercomputer technologies in inverse problems of ultrasound tomography. Inverse Problems. 2013, vol. 29, no. 7, pp. 1-22.
[8] Wang Y., Yagola A.G., Yang C. Optimization and regularization for computational inverse problems and applications. Berlin, Heidelberg: Springer Verlag, 2010. XVIII. 351 p.
[9] Medeiros J.A.C., Schirm R. Identification of nuclear power plant transients using the Particle Swarm Optimization algorithm. Annals of Nuclear Energy, 2008, vol. 35, no. 4, pp. 576-582.
[10] Lippert R.A. Fixing multiple eigenvalues by a minimal perturbation // Linear Algebra and its Applications, 2010, vol. 432, pp. 1785-1817.
[11] Bai Z.-J., Ching W.-K. A smoothing Newton’s method for the construction of a damped vibrating system from noisy test eigendata. Numerical Linear Algebra with Applications, 2009, vol. 16, no. 2, pp. 109-128.
[12] Poullikkas A. Effects of two-phase liquid-gas flow on the performance of nuclear reactor cooling pumps. Progress in Nuclear Energy, 2003, vol. 42, no. 1, pp. 3-10.
[13] Kinelev V.G., Shkapov P.M., Sulimov V.D. Application of global optimization to VVER-1000 reactor diagnostics. Progress in Nuclear Energy, 2003, vol. 43, no. 1-4, pp. 51-56. DOI: 10.1016/S0149-1970(03)00010-6
[14] Semchenkov Yu.M., Mil’to V.A., Shumskiy B.E. Intercalation of control methodologies of the coolant boiling in reacting core of water-cooled power reactor VVER-1000 into system of reactor internals diagnostics Atomnaya energiya [Nuclear power], 2008, vol. 105, no. 2, pp. 79-82 (in Russ.).
[15] Yang X., Schlegel J.P., Liu Y., Paranjape S., Hibiki T., Ishii M. Experimental study of interfacial area transport in air-water two-phase flow in a scaled 8?8 BWR rod bundle. Int. J. Multiphase Flow, 2013, vol. 50, pp. 16-32.
[16] O’Leary D.P., Rust B.W. Variable projection for nonlinear least squares problems. Computational Optimization and Applications, 2013, vol. 54, no. 3, pp. 579-593.
[17] Karmitsa N., Bagirov A., Maakelaa M.M. Comparing different nonsmooth minimization methods and software. Optimization Methods & Software. 2012, vol. 27, no. 1, pp. 131-153.
[18] Floudas C.A., Gounaris C.E. A review of recent advances in global optimization. J. Glob. Optim., 2009, vol. 45, no. 1, pp. 3-38.
[19] 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. J. Computational Interdisciplinary Sc., 2008, vol. 1, pp. 3-10. DOI: 10.6062/jcis.2008.01.01.0001
[20] 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. DOI: 10.1016/j.cpc.2012.01.010
[21] Yuan G., Wei Z., Li G. A modified Polak-Ribiare-Polyak conjugate gradient algorithm for nonsmooth convex programs. J. Computational and Applied Mathematics, 2014, vol. 255, pp. 86-96.
[22] Bagirov A.M., Al Nuaimat A., Sultanova N. Hyperbolic smoothing function method for minimax problem. Optimization: A Journal of Mathematical Programming and Operations Research. 2013, vol. 62, no. 6, pp. 759-782.
[23] Sulimov V.D. Local smoothing approximation in hybrid algorithm of optimization of hydromechanical systems. Vest. MGTU im. N.E. Baumana. Ser. Estestv. nauki [Herald of the Bauman MSTU. Ser. Natural Sc.], 2010, no. 3, pp. 3-14 (in Russ.).
[24] Izmailov A.F., Solodov M.V. Chislennye metody optimizatsii [Numerical optimization procedure ]. Moscow, Fizmatlit Publ., 2005. 304 p.
[25] McKinnon K.I.M. Convergence of the Nelder-Mead simplex method to a nonstationary point. SIAM J. Contr. Optim., 1999, vol. 9, no. 2, pp. 148-158.
[26] Price C.J., Coope I.D., Byatt D. A convergent variant of the Nelder-Mead algorithm. J. Optim. Theory Appl., 2002, vol. 113, no. 1, pp. 5-19.
[27] Xiao H.F., Duan J.A. Multi-direction-based Nelder - Mead method. Optim.: A J. Math. Progr. Oper. Res., 2012, pp. 1-22.
[28] Lera D., Sergeev Ya.D. Lipschitz and Holder global optimization using space-filling curves App. Num. Math., 2010, vol. 60, no. 1, pp. 115-129.
[29] Sulimov V.D. Hybrid algorithms for optimization of dynamic characteristics of hydromechanical systems Vestn. Lobachevskiy Nizhegorodskogo Un. [Bull. Lobachevskiy Un. of Nizhni Novgorod], 2011, No. 4 (2), pp. 324-326 (in Russ.).
[30] Sulimov V.D., Shkapov P.M. Application of hybrid algorithms to computational diagnostic problems for hydromechanical systems. J. Mech. Engineering and Automation, 2012, vol. 2, no. 12, pp. 734-741. DOI: 10.7463/1113.0604082