Methodology of non-linear robust estimation for the solutions synthesis of inverse and direct multidisciplinary problems in engineering dimensional chains calculation based on discrete analog data
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2020.4.06Keywords:
inverse boundary value problems in a stochastic formulation, a priori and parametric uncertainties, methods and systems for estimating quantities and processes, decision-making theoryAbstract
This paper analyses the definition of inverse and direct problems in engineering dimensional chains calculation based on discrete analogue data and the methodologies for solving these problems. It is shown that the direct dimensional chains calculation, which belongs to the class of inverse boundary value problems in a stochastic formulation, can be transformed into multi-criteria problems of stochastic optimization with mixed conditions. The new multi-step solutions search methodology for these problems is based on non-linear robust estimation methods. It can be achieved through hierarchical two-level decisions synthesis scheme development. At the first step, this scheme includes identification of surrogate models (in the form of regression equations). At the second step, the effective robust estimates are computed to determine unknown values; estimations of unknown quantities are carried out under a priori and parametric data uncertainties. Results of calculations of inverse and direct problems in engineering dimensional chains for two-stage axial compressors are presented. They were obtained using interactive computer systems for decision-making support “ROD&IDS”.
References
L. Brevault, M. Balesdent, R. Le Riche, and N. Berend, “Multi-level hierarchical MDO formulation with functional coupling satisfaction under uncertainty, application to sounding rocket design”, in Proceedings of the 11th World Congress on Structural and Multidisciplinary Optimisation, 712 June 2015, Sydney, Australia.
A.E. Gelfand and S.K. Ghosh, “Model choice: A minimum posterior predictive loss approach”, Biometrika, 85 (1), pp.1–11, 1998.
T. Gneiting and A.E. Raftery, “Strictly proper scoring rules, prediction, and estimation”, American Statistical Association Journal of the American Statistical Association, 102(477), pp. 359–378, 2007.
S. Lee, D. Rhee, and K. Yee, “Optimal arrangement of the film cooling holes considering the manufacturing tolerance for high pressure turbine nozzle”, in Proceedings of ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, 13–17 June 2006, Seoul, South Korea.
T. Erfani and S.V. Utyuzhnikov, “Control of robust design in multiobjective optimization under uncertainties”, Structural and Multidisciplinary Optimization, 45(2), pp. 247–256, Feb. 2012.
I.N. Egorov and G.V. Kretinin, “Optimization of gas turbine engine elements by probability criteria”, in Proceedings of ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, 24–27 May 1993, Cincinnati, OH.
A.A. Giunta, M.S. Eldred, L.P. Swiler, T.G. Trucano, and S.F. Wojtkiewicz, “Perspectives on optimization under uncertainty: algorithms and applications”, in Proceedings of 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 30 Aug. 1 Sept. 2004, Albany, NY.
K.K. Bodla, J.Y. Murthy, and S.V. Garimella, “Optimization under uncertainty for electronics cooling design applications”, in Proceedings of 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 30 May 1 June 2012, San Diego, CA, pp. 1191–1201.
M. Broggi, M. Faes, E. Patelli, Y. Govers, D. Moens, and M. Beer, “Comparison of Bayesian and interval uncertainty quantification: Application to the AIRMOD test structure”, in Proceedings of 2017 IEEE Symposium Series on Computational Intelligence (SSCI), 27 Nov. 1 Dec. 2017, Honolulu, HI, pp.1–8.
A.-L. Aulich and D. Goerke, “Multidisciplinary automated optimization strategy on a counter rotating fan”, in Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition GT2013, 3–7 June 2013, San Antonio, TX. (ASME paper GT2013-94259)
A.P. Karpenko, Modern algorithms. Algorithms inspired by nature: study guide. Moscow: MSTU Publishing House N.E. Bauman, 2014.
C. Blum, M.J.B. Aguilera, A. Roli, and M. Sampels (Eds.), Hybrid Metaheuristics: An Emerging Approach to Optimization. Berlin: Springer-Verlag, 2008.
K. Deb, Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley, 2001.
X.S. Yang, Nature-inspired Metaheuristic Algorithms. Frome (UK): Luniver Press, 2010.
I. Meniailov, O. Khustochka, K. Ugryumova, S. Chernysh, S. Yepifanov, and M. Ugryumov, “Mathematical models and methods of effective estimation in multi-objective optimization problems under uncertainties”, in Advances in Structural and Multidisciplinary Optimization: Proceedings of WCSMO12, 59 June 2017, Braunschweig, Germany. SpringerLink, 2018.
National priorities. Featured at Sandia. Albuquerque, NM: Sandia, LLC. Accessed on: June 2, 2019. [Online]. Available: www.sandia.gov
High efficiency IOSO design optimization software. Moscow, Russia: Sigma Technology. Accessed on: June 2, 2019. [Online]. Available: www.iosotech.com
Robust Design & Reliability. Trieste, Italy: ESTECO SpA. Accessed on: June 2, 2019. [Online]. Available: http://www.esteco.com/modefrontier/robust-design-reliability/
ISIGHT & The Simulia execution engine. Process automation and design exploration. Trieste, Italy: ESTECO SpA. Accessed on: June 2, 2019. [Online]. Available: https://www.3ds.com/products-services/simulia/products/isight-simulia-execution-engine/
TOSCA Fluid. Design concepts and CFD optimization for fluid flow. Vélizy-Villacoublay, France: Dassault Systèmes. Accessed on: June 2, 2019. [Online]. Available: www.3ds.com/products-services/simulia/products/tosca/fluid/
Optimization and robust design optiSLang. Moscow, Russia: CADFEM-CIS. Accessed on: June 2, 2019. [Online]. Available: www.cadfem-cis.ru/products/ additional/ optislang/
NUMECA International, FineDesign3D. Brussels, Belgium: NUMECA International. Accessed on: June 2, 2019. [Online]. Available: http://www.numeca.com/home
The Complete Software Solution – From Art to Part . White River Junction, VT: Concepts NREC. Accessed on: June 2, 2019. [Online]. Available: http://www. conceptsnrec.com/solutions/software
SoftInWay Inc. "AxSTREAM" Software Platform. Burlington, MA: SoftInWay Inc. Accessed on: June 2, 2019. [Online]. Available: http://www.softinway.com/software/
Intelligent Control and Autonomy Branch. Propulsion Diagnostic Method Evaluation Strategy (ProDiMES). Cleveland, OH: NASA Glenn Research Center. Accessed on: June 2, 2019. [Online]. Available: https://www.grc.nasa.gov/www/cdtb/software/ehmbenchmark.html
M.L. Ugryumov, A.A. Tronchuk, V.E. Afanasjevska, and A.V. Myenyaylov, “Gas turbine engine elements systematic improvement on the base of inverse problem concept by stochastic optimization methods”, in Proceedings of the 20-th ISABE Conference, 1216 Sept. 2011, Gothenburg, Sweden. (ISABE Paper no. 2011–1255).
M.L. Ugryumov, A.A. Tronchuk, V.E. Afanasjevska, and A.V. Myenyaylov, “Stochastic optimization models and method in the turbomachines system improvement problem”, in Proceedings of ASME-JSME-KSME Joint Fluids Engineering Conference, 2429 July 2011, Hamamatsu, Japan. (AJK2011-22057).
S.A. Aivazian, Z.I. Bezhaeva, and O.V. Staroverov, Multivariate observation classification. Moscow: Statistics, 1974.
V.I. Romanovsky, Applications of mathematical statistics in the test case. Moskow-Leningrad: Gostechizdat, 1947.
V.I. Romanovsky, Mathematical statistics. Book 1. Fundamentals of the theory of probability and mathematical statistics. Tashkent: Publishing house of city of Uzbekistan Science Academy, 1961.
V.I. Romanovsky, Mathematical statistics. Book 2. Operational methods of mathematical statistics. Tashkent: Publishing house of city of Uzbekistan Science Academy, 1963.
A.N. Tikhonov and V.Y. Arsenin, Methods for solving ill-posed problems. Moscow: Science, 1986.
V.E. Strilets et. al., Systematic improvement of the elements of complex technical systems based on the concept of inverse problems: monograph. X.: Nat. aerospace. un-t them. N.E. Zhukovsky, Kharkiv Aviation Institute, 2013,148 p.
I.M. Antonyan, V.A. Hot, A.I. Zelensky, and E.M. Ugryumova, “Method for assessing the information content of variables of neural network models of systems and processes with data uncertainty”, News of the Kharkiv National University. Zbirnik naukovyh prac. Seriya: “Mathematical modeling. Information technology. Automation and control systems”, vol. 26, no. 1156, pp. 5–16, 2015.
V. Strilets, N. Bakumenko, S. Chernysh, M. Ugryumov, and V. Donets, “Application of artificial neural networks in the problems of the patient’s condition diagnosis in medical monitoring systems”, Integrated Computer Technologies in Mechanical Engineering – Synergetic Engineering. International Scientific and Technical Conference (ICTM 2019), 28–30 Nov. 2019, Kharkov, Ukraine, Springer Link: 2020, pp. 173–185. Available: https://doi.org/ 10.1007/978-3-030-37618-5_16s
