Inverse methods and integral-differential model demonstration for optimal mechanical operation of power plants – numerical graphical optimization for second generation of tribology models

Francisco Casesnoves

doi:10.2478/ecce-2018-0005

Inverse methods and integral-differential model demonstration for optimal mechanical operation of power plants – numerical graphical optimization for second generation of tribology models

Authors

Francisco Casesnoves Researcher, Tallinn University of Technology

DOI:

https://doi.org/10.2478/ecce-2018-0005

Keywords:

engineering reliability operational probabilities, functional power plants, inverse problem theory/applications, nonlinear optimization, power engineering

Abstract

Stepping forward from a previous conference contribution, the article focuses on extension of inverse problem algorithms to integral-differential modelling and formal/strict demonstration of graphical-optimization method. It shows evident-mathematical and 3D-imaging proofs of the graphical optimization method with L1 Norm simulations and algorithms. At present, Linear/Nonlinear Optimization mathematical methods constitute the choice of preference in getting improvements for erosion and corrosion simulations- determinations in general tribology, biotribology and tribocorrosion. The method(s) developed are classical numerical optimization settings for objective functions, programming optimization and simulations, and special software for imaging in 3D. Results are diverse and the range of their applications is wide. First, the article provides a definite formal demonstration of the nonlinear graphical optimization both in numerical results and in imaging. Then, the authors propose the development of programming optimization and mathematical proofs-algorithms of the integral-differential model for various models. Subsequently, an overview of stochastic erosion methods based on Markov Chain is presented in the article. Finally, the second generation of tribology models is defined and conceptually explained. To summarise, the article comprises new findings towards modernization of tribology, biotribology and tribocorrosion models, gathering innovative research branches for future extension of the mathematical modelling progress. The results can be applied to both general techniques and mechanical engineering. The analytical and numerical demonstration of the integral-differential model constitutes a key point and essential result of the research. Extension to electromagnetic and electronic models of these methods is also considered feasible and practical

References

M. S. ElTobgy and M. A. Elbestawi, “Finite Element Modeling of Erosive Wear,” International Journal of Machine Tools and Manufacture, vol. 45, no. 11, pp. 1337-1346, Sep. 2005. https://doi.org/10.1016/j.ijmachtools.2005.01.007

F. Casesnoves, M. Antonov, and P. Kulu, “Mathematical Models for Erosion and Corrosion in Power Plants. A Review of Applicable Modelling Optimization Techniques,” in 2016 57th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Oct. 2016. https://doi.org/10.1109/rtucon.2016.7763117 ISBN 978-1-5090-3732-2. USB ISBN 978-1-5090-3730-8. ISBN 978-1-5090-3722-2.

J. Y. Shin, Y. J. Jeon, D. J. Maeng, J. S. Kim, and S. T. Ro, “Analysis of the Dynamic Characteristics of a Combined-Cycle Power Plant,” Energy, vol. 2, pp. 1085-1098, Dec. 2002. https://doi.org/10.1016/s0360-5442(02)00087-7

F. Casesnoves and A. Surzhenkov, “Mathematical Models in Mechanical and Biomedical Tribology With Computational Simulations/Optimization Methods,” International Journal of Scientific Research in Computer Science, Engineering and Information Technology, vol. 2, issue 1, 2017. ISSN 2456-3307.

F. Casesnoves, “Erosion Wear Mathematical Model for WC-Co Reinforcement Hardness Distribution in Fe-Based Alloy Matrix With Evoluted Algorithms,” International Journal of Scientific Research in Science, Engineering and Technology, vol. 3, issue 5, pp. 336-344, 2017. Print ISSN 2395-1990. Online ISSN 2394-4099.

F. Casesnoves, “2D Computational-Numerical Hardness Comparison Between Fe-Based Hardfaces With WC-Co Reinforcements for Integral- Differential Modelling,” in Proc. Materials Science and Applied Chemistry 58th International Conference, 2017, Trans Tech Publications, Switzerland.

F. Casesnoves and A. Surzhenkov, “Inverse Methods for Computational Simulations and Optimization of Erosion Models in Power Plants: A Numerical-Sufactal Nonlinear Optimization of Modelling,” in Proc. 2017 IEEE 58th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Oct. 2017, paper 139. https://doi.org/10.1109/rtucon.2017.8125630

F. Casesnoves, “2D Computational-Numerical Hardness Comparison Between Fe-Based Hardfaces With WC-Co Reinforcements for Integral- Differential Modelling,” Key Engineering Materials, vol. 762, pp 330- 338, Feb. 2018. https://doi.org/10.4028/www.scientific.net/kem.762.330

L. Crocker, A Review of Current Methods for Modeling Erosive Wear. NPL Report, 2011.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Applied Mathematics Series, 55, 1972.

F. Casesnoves, “A Monte-Carlo Optimization Method in Numerical Reuleaux Method for the Movement Analysis of Pseudo-Rigid Bodies,” in Proc. 10th SIAM Conference in Geometric Design and Computing joint to Approximation Theory Conference, Texas, San Antonio, USA, 2007, pp. 4-5.

G. Luenberger, Linear and Nonlinear Programming, 4th ed. Springer, 2008.

A. Ots, Oil Shale Combustion. Tallinn, Estonia: TUT Press, 2004.

K. Holmberg and A. Erdemir, “Influence of Tribology on Global Energy Consumption, Costs, and Emissions,” Friction, vol. 5, issue 3, pp. 263-284, Sept. 2017.

F. Casesnoves, “3D Improved Mathematical Model for Lumbar Intervertebral Ligaments (LILs),” in Proc. SIAM Life Sciences Conference joint to SIAM Annual Conference San Diego, 2012, pp. 25-27.

B. G. Mellor, Surface Coatings for Protection Against Wear. CRC Press. Woodhead Publishing in Materials, 2006.

I. Hutchings, “A Model for the Erosion of Metals With Spherical Particles at Normal Incidence,” Wear, vol. 70, issue 3, pp. 269-281, Aug. 1981. https://doi.org/10.1016/0043-1648(81)90347-1

G. Sheldon, I. Finnie, “The Mechanism of Material Removal in the Erosive Cutting of Brittle Materials,” J. Eng. Ind., vol. 88, issue 4, pp. 393-400. https://doi.org/10.1115/1.3672667

I. Kleis and P. Kulu, Solid Particle Erosion. Springer. 2008. https://doi.org/10.1007/978-1-84800-029-2

F. Casesnoves, “An Optimization Method for Static Wedge-Radiation Filters in Radiation Therapy,” Master Thesis in Physics, Eastern Finland University, 2001.

K. Balamanikandasuthan, K. Arun, and S. Palam, “Design and Fabrication of Erosion Protection Shield for Boiler Tubes and Its Analysis,” International Journal of Mechanical and Materials Engineering, vol. 1, issue 1, pp. 39-52, 2015.

D. Bertsekas, Nonlinear Programming, 2nd ed. Athena Scientific, 2003.

J. Borwein, Convex Analysis and Nonlinear Optimization, 2nd ed. CMS Books in Mathematics. Springer, 2000.

F. Casesnoves, “Large-Scale Multiobjective Matlab Optimization Toolbox (mot) Computing Methods in Radiotherapy Inverse Treatment Planning,” in High Performance Computing Conference, 2007, Nottingham University.

F. Casesnoves, “Geometrical/Computational Dynamics Approximations for Helicopter-Rotor Instantaneous Rotation Center in Turbulence With Numerical Reuleaux Method,” International Journal of Engineering and Innovative Technology, vol. 4, issue 3, pp. 175-184, 2014.

F. Casesnoves, “Geometrical Algorithms for Civil Helicopter (CH) Rotor Blades Instantaneous Rotation Center (IRC) Determination in Deformable/Turbulence Conditions Using the Numerical Reuleaux Method (NRM): A Nonlinear Optimization Method in Aerospace Engineering Dynamics,” in Proc. SIAM Conference on Applied Algebraic Geometry Fort Collins. 2013, pp. 112-114.

F. Hildebrand, Introduction to Numerical Analysis, 2nd ed. Dover Publications, Inc., 1987.

L. Fausett, Applied Numerical Analysis Using Matlab. Pearson International, 2008.

S. Kajda, S. Harvey, and E. Wilusz Eds., Encyclopedia of Tribology. Elsevier, 1990.

H. Liao, B. Normand, and C. Coddet, “Influence of Coating Microstructure on the Abrasive Wear Resistance of WC/Co Cermet Coatings,” Surface and Coatings Technology, vol. 124, issue 2-3, pp. 235-242, 2000. https://doi.org/10.1016/s0257-8972(99)00653-2

S. Basu, Freemat v4.0 Documentation. 2009.

S. Basu, Freemat v4.2 Documentation. 2012.

C. Moler, Numerical Computing With Matlab. SIAM, 2004. https://doi.org/10.1137/1.9780898717952

S. Gherpade, Introduction to Algebraic Geometry. Department of Mathematics Publications. Indian Institute of Technology Bombay, 2014.

W. Cheney and W. Light, A Course in Approximation Theory: Graduate Studies in Mathematics. Am. Math. Soc., vol. 101, 2000.

A. Crowell and J. Slesnicks, Calculus With Analytic Geometry. Version 3.03. GNU Free Documentation License. Free Software Foundation. 2008.

W. Strauss, Partial Differential Equations, 2nd ed. Wiley, 2008.

Q. Chen, D. Li, “Computer Simulation of Solid-Particle Erosion of Composite Materials,” Wear, vol. 255, issue 1-6, pp. 78-84, Aug.-Sept. 2003. https://doi.org/10.1016/s0043-1648(03)00065-6

F. Casesnoves, “Experimental Simulations of the Numerical Reuleaux Method (NRM) for Lumbar Artificial Disk Implants IRC Determination,” in Proc. SIAM Conference in Computational Science and Engineering, 2009, PP1 Section, pp. 1-2.

F. Casesnoves, “Theory and Primary Computational Simulations of the Numerical Reuleaux Method (NRM),” International Journal of Mathematics and Computation, vol. 13, no. D11, pp. 90-110, 2011.

F. Casesnoves, “Applied Inverse Methods for Deformable Solid Dynamics/Kinematics in Numerical Reuleaux Method (NRM),” International Journal of Numerical Methods and Applications, vol. 9, no. 2, pp. 109-131, 2013.

F. Casesnoves, “Applied Inverse Methods for Optimal Geometrical- Mechanical Deformation of Lumbar Artificial Disks/Implants With Numerical Reuleaux Method. 2D Comparative Simulations and Formulation,” Ethan Publishing Computer Science Applications, vol. 2, no. 4, pp. 1-10, 2015.

Casesnoves, F. “Computational simulations of vertebral body for optimal instrumentation design,” Journal of Medical Devices, vol. 6, issue 2, pp. 14-25, 2012. https://doi.org/10.1115/1.4006670

F. Casesnoves, “Computational Simulations of Anterior Vertebral Body for Optimal Surgical Instrumentation Design,” Journal of Medical Devices, vol. 4, issue 2, pp. 25-26, 2010.

V. Camomilla and A. Cereatti, “An Optimized Protocol for Hip Joint Centre Determination Using the Functional Method,” Journal of Biomechanics, vol. 39, issue 6, pp. 1096-1106, 2006. https://doi.org/10.1016/j.jbiomech.2005.02.008

L. Li and D. Li, “Simulation of Corrosion-Erosion of Passive Metals Using a Micro-Scale Dynamical Model,” Wear, vol. 271, pp. 1404-1410, 2011. https://doi.org/10.1016/j.wear.2010.12.056

F. Casesnoves, “Spinal Biomechanics Mathematical Model for Lumbar Intervertebral Ligaments,” in Proc. SIAM Conference on Computational Science and Engineering, 2011, pp. 227-229.

European Commission, European Textbook on Ethics in Research. EUR 24452 EN, 2010.

Notes, References, and Lectures. CEE SIMP Conference. Raw Materials and Circular Economy. Institute of Geology, Tallinn University of Technology, Mektory Technology Innovation Center, 2017.

The European Code of Conduct for Research Integrity. Revised Edition. ALLEA, 2017.