Madde ömrü tahmininde çok amaçlı programlama tabanlı bir yaklaşım: Weibull dağılımı uygulaması

Weibull dağılımı, hata oranları ve sistem güvenilirliği gibi çeşitli alanlarda yaygın olarak kullanılmaktadır. Geniş uygulaması nedeniyle, Weibull dağılımı için en iyi parametre tahmin yöntemini belirlemek çok önemlidir. En bilinen parametre tahmin yöntemleri en küçük kareler (EKK), ağırlıklı en küçük kareler (AEKK) ve en çok olabilirlik (EÇO) olmasına rağmen, bu yöntemler farklı özelliklere sahiptir ve farklı tahmin sonuçları verebilir. Bu yöntemlerin birlikte değerlendirilerek daha iyi tahmin sonuçları elde edilmesinin amaçlandığı bu çalışmada, çok amaçlı programlama yaklaşımının kullanılması önerilmektedir. Oluşturulan çok amaçlı programlama tahmin modelini çözmek için çok amaçlı bir sezgisel yaklaşım olan baskın sıralı genetik algoritma II yöntemi kullanılmıştır. Önerilen yaklaşımın uygulanabilirliğini göstermek için Kevlar 49 / Epoksi veri seti kullanılmıştır. Elde edilen sonuçlara göre en iyi parametre tahmin sonuçları, EÇO yönteminin tek ve birlikte değerlendirildiği durumlar olan EKK-EÇO ve AEKK-EÇO çok amaçlı tahmin modelleri vermiştir.

Anahtar Kelimeler:

Weibull dağılımı, Pareto optimal çözümler, NSGA-II

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Keshavan, M. K., Sargent, G. A., Conrad, H., Statistical analysis of the Hertzian fracture of pyrex glass using the Weibull distribution function, Journal of Materials Science, 15 (4), 839-844, 1980.
Sheikh, A. K., Boah, J. K., Hansen, D. A., Statistical modeling of pitting corrosion and pipeline reliability, Corrosion, 46 (3), 190-197, 1990.
Qureshi, F. S., Sheikh, A. K., A probabilistic characterization of adhesive wear in metals, IEEE Transactions on Reliability, 46 (1), 38-44, 1997.
Durham, S. D., Padgett, W. J., Cumulative damage models for system failure with application to carbon fibers and composites, Technometrics, 39 (1), 34-44, 1997.
Almeida, J. B., Application of Weilbull statistics to the failure of coatings, Journal of Materials Processing Technology, 92, 257-263, 1999.
Fok, S. L., Mitchell, B. C., Smart, J., Marsden, B. J., A numerical study on the application of the Weibull theory to brittle materials, Engineering Fracture Mechanics, 68 (10), 1171-1179, 2001.
Newell, J. A., Kurzeja, T., Spence, M., Lynch, M., Analysis of recoil compressive failure in high performance polymers using two and four parameter Weibull models, High Performance Polymers, 14 (4), 425-434, 2002.
Dong, M., Nassif, A. B., Combining modified Weibull distribution models for power system reliability forecast, IEEE Transactions on Power Systems, 34 (2), 1610-1619, 2018.
Li, Q. S., Fang, J. Q., Liu, D. K., Tang, J., Failure probability prediction of concrete components, Cement and concrete research, 33 (10), 1631-1636, 2003.
Gunes, D., Tekdemir, I. G., Karaarslan, M. S., Alboyaci, B., Assessment of the impact of electric vehicle charge station loads on reliability indices, Journal of the Faculty of Engineering and Architecture of Gazi University, 33 (3), 1073-1084, 2018.
Daş, M., Balpetek, N., Akpınar, E. K., Akpınar, S., Investigation of wind energy potential of different provinces found in Turkey and establishment of predictive model using support vector machine regression with the obtained results, Journal of the Faculty of Engineering and Architecture of Gazi University, 34 (4), 2019.
Akpınar, E. K., Balpetek, N., Statistical analysis of wind energy potential of Elazig province according to Weibull and Rayleigh distributions, Journal of the Faculty of Engineering and Architecture of Gazi University, 34 (1), 569-580, 2019.
Usta, I., An innovative estimation method regarding Weibull parameters for wind energy applications, Energy, 106, 301-314, 2016.
Usta, I., Arik, I., Yenilmez, I., Kantar, Y. M., A new estimation approach based on moments for estimating Weibull parameters in wind power applications, Energy Conversion and Management, 164, 570-578, 2018.
Abbasi, B., Jahromi, A. H. E., Arkat, J., Hosseinkouchack, M., Estimating the parameters of Weibull distribution using simulated annealing algorithm, Applied Mathematics and Computation, 183 (1), 85-93, 2006.
Örkcü, H. H., Özsoy, V. S., Aksoy, E., Dogan, M. I., Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison, Applied Mathematics and Computation, 268, 201-226, 2015.
Jukić, D., Benšić, M., Scitovski, R., On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution, Computational Statistics and Data Analysis, 52 (9), 4502-4511, 2008.
Marković, D., Jukić, D., Benšić, M., Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journal of Computational and Applied Mathematics, 228 (1), 304-312, 2009.
Pobočíková, I., Sedliačková, Z., Comparison of four methods for estimating the Weibull distribution parameters, Applied mathematical sciences, 8 (83), 4137-4149, 2014.
Datsiou, K. C., Overend, M., Weibull parameter estimation and goodness-of-fit for glass strength data, Structural Safety, 73, 29-41, 2018.
Nassar, M., Afify, A. Z., Dey, S., Kumar, D., A new extension of Weibull distribution: properties and different methods of estimation, Journal of Computational and Applied Mathematics, 336, 439-457, 2018.
Bergman, B., Estimation of Weibull parameters using a weight function, Journal of Materials Science Letters, 5 (6), 611-614, 1986.
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE transactions on evolutionary computation, 6 (2), 182-197, 2002.
Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, John-Wiley and Sons, New York, A.B.D., 2004.
Murugan, P., Kannan, S., Baskar, S., Application of NSGA-II algorithm to single-objective transmission constrained generation expansion planning, IEEE Transactions on Power Systems, 24 (4), 1790-1797, 2009.
Zhao, B., Zhang, X., Chen, J., Wang, C., Guo, L., Operation optimization of standalone microgrids considering lifetime characteristics of battery energy storage system, IEEE transactions on sustainable energy, 4 (4), 934-943, 2013.
Panda, S., Yegireddy, N. K., Automatic generation control of multi-area power system using multi-objective non-dominated sorting genetic algorithm-II, International Journal of Electrical Power and Energy Systems, 53, 54-63, 2013.
Yıldırım Okay, F., Özdemir, S., Improving Coverage in Wireless Sensor Networks Using Multi-Objective Evolutionary Algorithms, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (2), 143-153, 2015.
Wang, M., Wang, J., Zhao, P., Dai, Y., Multi-objective optimization of a combined cooling, heating and power system driven by solar energy, Energy Conversion and Management, 89, 289-297, 2015.
Durmaz, E., Şahin, R., NSGA-II and goal programming approach for the multi-objective single row facility layout problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (3), 941-955, 2017.
Esfe, M. H., Hajmohammad, M. H., Thermal conductivity and viscosity optimization of nanodiamond-Co3O4/EG (40: 60) aqueous nanofluid using NSGA-II coupled with RSM, Journal of Molecular Liquids, 238, 545-552, 2017.
Liu, K., Hu, X., Yang, Z., Xie, Y., Feng, S., Lithium-ion battery charging management considering economic costs of electrical energy loss and battery degradation, Energy conversion and management, 195, 167-179, 2019.
Uçar, U., İşleyen, S., Gökçen, H., Experimental analysis of Meta-Heuristic algorithms for moving customer vehicle routing problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 36 (1), 459-475, 2021.
Andrews, D. F., Herzberg, A. M., Data: a collection of problems from many fields for the student and research worker. Springer Science and Business Media, 2012.
Cooray, K., Ananda, M. M., A generalization of the half-normal distribution with applications to lifetime data, Communications in Statistics-Theory and Methods, 37 (9), 1323-1337, 2008.
Paranaíba, P. F., Ortega, E. M., Cordeiro, G. M., Pascoa, M. A. D., The Kumaraswamy Burr XII distribution: theory and practice, Journal of Statistical Computation and Simulation, 83 (11), 2117-2143, 2013.