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GİRİŞ PARAMETRELERİNİN AĞIRLIKLARINA GÖRE DEĞİŞKEN DİZİ ARALIK SEÇİMİNİN IBI MANTIK ALGORİTMASI İLE OPTİMİZASYON PERFORMANSINA ETKİSİNİN ÇOK BANTLI VİVALDİ ANTEN TASARIMINDA UYGULANMASI

Yıl 2025, Cilt: 13 Sayı: 3, 728 - 744, 30.09.2025
https://doi.org/10.21923/jesd.1577278

Öz

Tasarım parametrelerinin belirlenmesi yanı sıra bu giriş veri seti parametrelerin hangi aralıkta seçileceği optimizasyon problemlerinde hala büyük bir soru olarak en ön planda yer almaktadır. Bu nedenle böyle büyük bir soruya yanıt verebilmek amacıyla burada giriş veri setinin değer genişlik aralığının optimizasyon performansı üzerinde etkisi üzerine detaylı bir çalışma sunulmaktadır. Bu çalışmada, WLAN/WİFİ kablosuz iletişim sistemleri için 2,4 GHz, 3,5 GHz ve 5 GHz için çok bantlı bir Vivaldi anten optimizasyon problemi için giriş parametrelerinin ağırlığına göre değişken giriş veri seti değer aralığı seçilerek optimizasyon performans değişimi takip edilmiştir. Ayrıca yapılan çalışmada giriş parametre sayının fazla olmasının yanı sıra seçilen antenin 3 bantlı olması tasarım problemini oldukça güçleştirmiştir. Bu sorun güncel, mevcut geleneksel algoritmalar karşısında başarısını kanıtlamış ve anten optimizasyon alanında hiç kullanılmamış olan IbI Mantık algoritması kullanılarak aşılmıştır. Tasarım sonuçları MATLAB programı yardımı ile antenin S11 (dB) ve Yönlülük parametrelerinin simülasyonu ile gösterilmiştir. Elde edilen sonuçlar neticesinde optimizasyon maliyet değerinin düştüğü ve böylece daha başarılı sonuçlar elde edildiği görülmüştür. Böylece herhangi bir optimizasyon probleminde değişken giriş veri seti aralığı seçiminin ne kadar önemli olduğu gösterilmiştir. Bu yöntem herhangi başka bir optimizasyon problemine kuşkusuzca uyarlanabilir.

Kaynakça

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  • Chavez-Hurtado, J. L., & Rayas-Sanchez, J. E. (2016). Polynomial-Based Surrogate Modeling of RF and Microwave Circuits in Frequency Domain Exploiting the Multinomial Theorem. IEEE Transactions on Microwave Theory and Techniques, 64(12), 4371-4381. https://doi.org/10.1109/TMTT.2016.2623902
  • Çıldır, A. (2024). THE MICROSTRIP ARRAY ANTENNA WITH REFLECTOR at 1.4 AND 2.4 GHz for RADARS APPLICATIONS. Mühendislik Bilimleri ve Tasarım Dergisi, 12(1), 88-97. https://doi.org/10.21923/jesd.1351302
  • Darmawidjaja, A. R., & Wibowo, E. P. (2021). Design and Simulation of Antipodal Vivaldi Antenna (AVA) AT 2.6 GHz For 5G Communication Optimation. 2021 Sixth International Conference on Informatics and Computing (ICIC), 1-6. https://doi.org/10.1109/ICIC54025.2021.9632925
  • Dhiman, G., Singh, K. K., Soni, M., Nagar, A., Dehghani, M., Slowik, A., Kaur, A., Sharma, A., Houssein, E. H., & Cengiz, K. (2021). MOSOA: A new multi-objective seagull optimization algorithm. Expert Systems with Applications, 167, 114150. https://doi.org/10.1016/j.eswa.2020.114150
  • Dong, J., Qin, W., & Wang, M. (2019). Fast Multi-Objective Optimization of Multi-Parameter Antenna Structures Based on Improved BPNN Surrogate Model. IEEE Access, 7, 77692-77701. https://doi.org/10.1109/ACCESS.2019.2920945
  • Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190. https://doi.org/10.1016/j.knosys.2019.105190
  • Gao, D., Wang, G.-G., & Pedrycz, W. (2020). Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism. IEEE Transactions on Fuzzy Systems, 28(12), 3265-3275. https://doi.org/10.1109/TFUZZ.2020.3003506
  • Gibson, P. J. (1979). The Vivaldi Aerial. 1979 9th European Microwave Conference, 101-105. https://doi.org/10.1109/EUMA.1979.332681
  • Gu, Z.-M., & Wang, G.-G. (2020). Improving NSGA-III algorithms with information feedback models for large-scale many-objective optimization. Future Generation Computer Systems, 107, 49-69. https://doi.org/10.1016/j.future.2020.01.048
  • Hang, D., & Li, X. (2018). Application of Improved Particle Swarm Optimization Algorithm Based on GSO in Optimization Design of FIR Digital Filter. 2018 IEEE International Conference of Safety Produce Informatization (IICSPI), 84-87. https://doi.org/10.1109/IICSPI.2018.8690503
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  • Jain, M., Singh, V., & Rani, A. (2019). A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm and Evolutionary Computation, 44, 148-175. https://doi.org/10.1016/j.swevo.2018.02.013
  • Jia, Y., Luo, J., Ren, X., Shi, G., & Liu, Y. (2024). Design of Low-RCS Vivaldi Antenna Based on Characteristic Mode Analysis. IEEE Antennas and Wireless Propagation Letters, 23(4), 1246-1250. https://doi.org/10.1109/LAWP.2024.3350890
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  • Li, S., Chen, H., Wang, M., Heidari, A. A., & Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems, 111, 300-323. https://doi.org/10.1016/j.future.2020.03.055
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IMPLEMENTATION OF THE EFFECT OF VARIABLE ARRAY RANGE SELECTION DEPENDING ON THE WEIGHTS OF INPUT PARAMETERS ON OPTIMIZATION PERFORMANCE WITH IBI LOGIC ALGORITHM IN MULTI-BAND VIVALDI ANTENNA DESIGN

Yıl 2025, Cilt: 13 Sayı: 3, 728 - 744, 30.09.2025
https://doi.org/10.21923/jesd.1577278

Öz

In addition to determining the design parameters, the range in which the parameters of this input data set will be selected is still a big question in optimization problems. Therefore, in order to answer such a big question, a detailed study is presented here on the effect of the value range of the input data set on the optimization performance. In this study, the optimization performance change was followed by selecting the variable input data set value range according to the weight of the input parameters for a multi-band Vivaldi antenna optimization problem for 2.4 GHz, 3.5 GHz and 5 GHz for WLAN/WIFI wireless communication systems. In addition, in the study, the fact that the number of input parameters was high and the selected antenna had 3 bands made the design problem quite difficult. This problem was overcome by using the IbI Logic algorithm, which has proven its success against current, existing traditional algorithms and has never been used in the field of antenna optimization. The design results were shown by simulating the antenna's S11 (dB) and Directivity parameters with the help of the MATLAB program. As a result of the obtained results, it was seen that the optimization cost value decreased and thus more successful results were obtained. Thus, it has been shown how important the selection of the variable input data set range is in any optimization problem. This method can certainly be adapted to any other optimization problem.

Kaynakça

  • Abderazek, H., Yildiz, A. R., & Mirjalili, S. (2020). Comparison of recent optimization algorithms for design optimization of a cam-follower mechanism. Knowledge-Based Systems, 191, 105237. https://doi.org/10.1016/j.knosys.2019.105237
  • Barmuta, P., Ferranti, F., Gibiino, G. P., Lewandowski, A., & Schreurs, D. M. M.-P. (2015). Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. IEEE Transactions on Microwave Theory and Techniques, 63(1), 56-64. https://doi.org/10.1109/TMTT.2014.2376559
  • BAYER KESKİN, S. E., & GÜLER, C. (2021). DESIGN OF CIRCULAR SLOTTED RECTANGULAR MICROSTRIP PATCH ANTENNA WITH DUAL-RESONANCE FOR WLAN/WIMAX APPLICATIONS. Mühendislik Bilimleri ve Tasarım Dergisi, 9(4), 1296-1301. https://doi.org/10.21923/jesd.676705
  • Belen, M. A. (2024). ÇOK BANDLI UYGULAMALAR İÇİN YÜKSEK PERFORMANSLI MİKROŞERİT ANTEN TASARIMI. Mühendislik Bilimleri ve Tasarım Dergisi, 12(4), 866-875. https://doi.org/10.21923/jesd.1551368
  • Cai, J., King, J., Yu, C., Liu, J., & Sun, L. (2018). Support Vector Regression-Based Behavioral Modeling Technique for RF Power Transistors. IEEE Microwave and Wireless Components Letters, 28(5), 428-430. https://doi.org/10.1109/LMWC.2018.2819427
  • Chavez-Hurtado, J. L., & Rayas-Sanchez, J. E. (2016). Polynomial-Based Surrogate Modeling of RF and Microwave Circuits in Frequency Domain Exploiting the Multinomial Theorem. IEEE Transactions on Microwave Theory and Techniques, 64(12), 4371-4381. https://doi.org/10.1109/TMTT.2016.2623902
  • Çıldır, A. (2024). THE MICROSTRIP ARRAY ANTENNA WITH REFLECTOR at 1.4 AND 2.4 GHz for RADARS APPLICATIONS. Mühendislik Bilimleri ve Tasarım Dergisi, 12(1), 88-97. https://doi.org/10.21923/jesd.1351302
  • Darmawidjaja, A. R., & Wibowo, E. P. (2021). Design and Simulation of Antipodal Vivaldi Antenna (AVA) AT 2.6 GHz For 5G Communication Optimation. 2021 Sixth International Conference on Informatics and Computing (ICIC), 1-6. https://doi.org/10.1109/ICIC54025.2021.9632925
  • Dhiman, G., Singh, K. K., Soni, M., Nagar, A., Dehghani, M., Slowik, A., Kaur, A., Sharma, A., Houssein, E. H., & Cengiz, K. (2021). MOSOA: A new multi-objective seagull optimization algorithm. Expert Systems with Applications, 167, 114150. https://doi.org/10.1016/j.eswa.2020.114150
  • Dong, J., Qin, W., & Wang, M. (2019). Fast Multi-Objective Optimization of Multi-Parameter Antenna Structures Based on Improved BPNN Surrogate Model. IEEE Access, 7, 77692-77701. https://doi.org/10.1109/ACCESS.2019.2920945
  • Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190. https://doi.org/10.1016/j.knosys.2019.105190
  • Gao, D., Wang, G.-G., & Pedrycz, W. (2020). Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism. IEEE Transactions on Fuzzy Systems, 28(12), 3265-3275. https://doi.org/10.1109/TFUZZ.2020.3003506
  • Gibson, P. J. (1979). The Vivaldi Aerial. 1979 9th European Microwave Conference, 101-105. https://doi.org/10.1109/EUMA.1979.332681
  • Gu, Z.-M., & Wang, G.-G. (2020). Improving NSGA-III algorithms with information feedback models for large-scale many-objective optimization. Future Generation Computer Systems, 107, 49-69. https://doi.org/10.1016/j.future.2020.01.048
  • Hang, D., & Li, X. (2018). Application of Improved Particle Swarm Optimization Algorithm Based on GSO in Optimization Design of FIR Digital Filter. 2018 IEEE International Conference of Safety Produce Informatization (IICSPI), 84-87. https://doi.org/10.1109/IICSPI.2018.8690503
  • Hayyolalam, V., & Pourhaji Kazem, A. A. (2020). Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems. Engineering Applications of Artificial Intelligence, 87, 103249. https://doi.org/10.1016/j.engappai.2019.103249
  • Jain, M., Singh, V., & Rani, A. (2019). A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm and Evolutionary Computation, 44, 148-175. https://doi.org/10.1016/j.swevo.2018.02.013
  • Jia, Y., Luo, J., Ren, X., Shi, G., & Liu, Y. (2024). Design of Low-RCS Vivaldi Antenna Based on Characteristic Mode Analysis. IEEE Antennas and Wireless Propagation Letters, 23(4), 1246-1250. https://doi.org/10.1109/LAWP.2024.3350890
  • Karaboga, D., & Basturk, B. (2008). On the performance of artificial bee colony (ABC) algorithm. Applied Soft Computing, 8(1), 687-697. https://doi.org/10.1016/j.asoc.2007.05.007
  • Karimov, A., Nauryzbayev, G., & Hashmi, M. (2024). Ultra-Wide Band Antipodal Vivaldi Antenna with a Metamaterial Structure for 5G Applications. 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI), 2067-2068. https://doi.org/10.1109/AP-S/INC-USNC-URSI52054.2024.10686433
  • Kennedy, J. (t.y.). Swarm Intelligence. Içinde Handbook of Nature-Inspired and Innovative Computing (ss. 187-219). Kluwer Academic Publishers. https://doi.org/10.1007/0-387-27705-6_6
  • Li, J., & Han, Y. (2020). A hybrid multi-objective artificial bee colony algorithm for flexible task scheduling problems in cloud computing system. Cluster Computing, 23(4), 2483-2499. https://doi.org/10.1007/s10586-019-03022-z
  • Li, S., Chen, H., Wang, M., Heidari, A. A., & Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems, 111, 300-323. https://doi.org/10.1016/j.future.2020.03.055
  • Likas, A., Vlassis, N., & J. Verbeek, J. (2003). The global k-means clustering algorithm. Pattern Recognition, 36(2), 451-461. https://doi.org/10.1016/S0031-3203(02)00060-2
  • Liu, S., Zhang, Y., Wang, Y., & Xia, T. (2024). Wideband Vivaldi Antenna and 2 X 8 Antenna Array Design. 2024 International Conference on Microwave and Millimeter Wave Technology (ICMMT), 1-3. https://doi.org/10.1109/ICMMT61774.2024.10672197
  • Liu, S.-B., Zhang, F.-S., Xie, G.-J., Song, L., & Guo, Y.-X. (2025). Miniaturization of Ultrawideband Horizontally Polarized Omnidirectional Vivaldi Antenna Arrays Using Nonuniform Elements. IEEE Transactions on Antennas and Propagation, 73(2), 748-757. https://doi.org/10.1109/TAP.2024.3503775
  • Mahouti, P., Kızılay, A., Tari, O., Belen, A., Belen, M. A., & Çalışkan, A. (2022). Design Optimization of Ultra-Wideband Vivaldi Antenna using Artificial Intelligence. The Applied Computational Electromagnetics Society Journal (ACES). https://doi.org/10.13052/2021.ACES.J.361211
  • Mirrashid, M., & Naderpour, H. (2021). Recent Trends in Prediction of Concrete Elements Behavior Using Soft Computing (2010–2020). Archives of Computational Methods in Engineering, 28(4), 3307-3327. https://doi.org/10.1007/s11831-020-09500-7
  • Mirrashid, M., & Naderpour, H. (2023). Incomprehensible but Intelligible-in-time logics: Theory and optimization algorithm. Knowledge-Based Systems, 264, 110305. https://doi.org/10.1016/j.knosys.2023.110305
  • Naderpour, H., & Mirrashid, M. (2020a). Bio-inspired predictive models for shear strength of reinforced concrete beams having steel stirrups. Soft Computing, 24(16), 12587-12597. https://doi.org/10.1007/s00500-020-04698-x
  • Naderpour, H., & Mirrashid, M. (2020b). Estimating the compressive strength of eco-friendly concrete incorporating recycled coarse aggregate using neuro-fuzzy approach. Journal of Cleaner Production, 265, 121886. https://doi.org/10.1016/j.jclepro.2020.121886
  • Naderpour, H., & Mirrashid, M. (2020c). Proposed soft computing models for moment capacity prediction of reinforced concrete columns. Soft Computing, 24(15), 11715-11729. https://doi.org/10.1007/s00500-019-04634-8
  • Naderpour, H., Mirrashid, M., & Parsa, P. (2021). Failure mode prediction of reinforced concrete columns using machine learning methods. Engineering Structures, 248, 113263. https://doi.org/10.1016/j.engstruct.2021.113263
  • Niu, L., Zhang, H., Zhai, H., Zhu, C., & Wang, N. (2024). An Ultra-wideband Circularly-polarized Vivaldi Antenna with Wide Beam Angel. 2024 International Applied Computational Electromagnetics Society Symposium (ACES-China), 1-3. https://doi.org/10.1109/ACES-China62474.2024.10700002
  • Ochoa, J. S., & Cangellaris, A. C. (2013). Random-Space Dimensionality Reduction for Expedient Yield Estimation of Passive Microwave Structures. IEEE Transactions on Microwave Theory and Techniques, 61(12), 4313-4321. https://doi.org/10.1109/TMTT.2013.2286968
  • Petrocchi, A., Kaintura, A., Avolio, G., Spina, D., Dhaene, T., Raffo, A., & Schreurs, D. M. M.-P. (2017). Measurement Uncertainty Propagation in Transistor Model Parameters via Polynomial Chaos Expansion. IEEE Microwave and Wireless Components Letters, 27(6), 572-574. https://doi.org/10.1109/LMWC.2017.2701334
  • Pierezan, J., dos Santos Coelho, L., Cocco Mariani, V., Hochsteiner de Vasconcelos Segundo, E., & Prayogo, D. (2021). Chaotic coyote algorithm applied to truss optimization problems. Computers & Structures, 242, 106353. https://doi.org/10.1016/j.compstruc.2020.106353
  • Prasad, R. V. H., Vakula, D., & Chakravarthy, M. (2018). A Novel Fractal Slot DGS Microstrip Antenna for Wi-Fi Application. 2018 IEEE Indian Conference on Antennas and Propogation (InCAP), 1-4. https://doi.org/10.1109/INCAP.2018.8770773
  • Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Kevin Tucker, P. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41(1), 1-28. https://doi.org/10.1016/j.paerosci.2005.02.001
  • Rayas-sanchez, J., & Gutierrez-Ayala, V. (2006). EM-Based Statistical Analysis and Yield Estimation Using Linear-Input and Neural-Output Space Mapping. 2006 IEEE MTT-S International Microwave Symposium Digest, 1597-1600. https://doi.org/10.1109/MWSYM.2006.249641
  • Rossi, M., Dierck, A., Rogier, H., & Vande Ginste, D. (2014). A Stochastic Framework for the Variability Analysis of Textile Antennas. IEEE Transactions on Antennas and Propagation, 62(12), 6510-6514. https://doi.org/10.1109/TAP.2014.2360219
  • Sujiansyah, D. A., Syihabuddin, B., Anwar, K., & Adriansyah, N. M. (2018). Antenna Design for Multi-generation 2G-5G for Rural Area Wireless Communications. 2018 International Conference on ICT for Rural Development (IC-ICTRuDev), 7-11. https://doi.org/10.1109/ICICTR.2018.8706865
  • Sun, X.-Y., Wu, B., Zhang, H.-H., Guo, K.-X., Xie, H.-Y., Song, X.-Z., & Su, T. (2024). Ultrawideband Circularly Polarized Halved-Type Vivaldi Antenna With Symmetrical Radiation Pattern. IEEE Antennas and Wireless Propagation Letters, 23(2), 633-637. https://doi.org/10.1109/LAWP.2023.3331383
  • Truong, L. X., Tao, V. Q., Minh Tuan, T., & Vu Bang Giang, T. (2015). Design a microstrip antenna with defected ground structure. 2015 International Conference on Advanced Technologies for Communications (ATC), 160-163. https://doi.org/10.1109/ATC.2015.7388311
  • Uluslu, A. (2023). Fitting nonlinear mathematical models to the cost function of the quadrafilar helix antenna optimization problem. Analog Integrated Circuits and Signal Processing, 115(3), 307-318. https://doi.org/10.1007/s10470-023-02174-8
  • Uluslu, A., & Allaberdiyev, K. (2024). GOOSE ALGORİTMASI KULLANILARAK ÇİFT BANTLI MİKROŞERİT BAĞLANTILI KOMBİNE BANT GEÇİREN FİLTRE TASARIM PROBLEMİNDE DİZİ ARALIK SEÇİMİNİN SONUÇ ÜZERİNDEKİ ETKİSİ. Mühendislik Bilimleri ve Tasarım Dergisi, 12(3), 557-571. https://doi.org/10.21923/jesd.1472691
  • Wang, G.-G., Guo, L., Gandomi, A. H., Hao, G.-S., & Wang, H. (2014). Chaotic Krill Herd algorithm. Information Sciences, 274, 17-34. https://doi.org/10.1016/j.ins.2014.02.123
  • Wang, J., Yang, X., & Wang, B. (2018). Efficient gradient‐based optimisation of pixel antenna with large‐scale connections. IET Microwaves, Antennas & Propagation, 12(3), 385-389. https://doi.org/10.1049/iet-map.2017.0719
  • Xu, R., & WunschII, D. (2005). Survey of Clustering Algorithms. IEEE Transactions on Neural Networks, 16(3), 645-678. https://doi.org/10.1109/TNN.2005.845141
  • Yang, D., Hu, J., & Liu, S. (2018). A Low Profile UWB Antenna for WBAN Applications. IEEE Access, 6, 25214-25219. https://doi.org/10.1109/ACCESS.2018.2819163
  • Yang, X.-S. (2020). Nature-inspired optimization algorithms: Challenges and open problems. Journal of Computational Science, 46, 101104. https://doi.org/10.1016/j.jocs.2020.101104
  • Yi, J.-H., Xing, L.-N., Wang, G.-G., Dong, J., Vasilakos, A. V., Alavi, A. H., & Wang, L. (2020). Behavior of crossover operators in NSGA-III for large-scale optimization problems. Information Sciences, 509, 470-487. https://doi.org/10.1016/j.ins.2018.10.005
  • Zhang, H., & Zhang, F. (2024). A Novel Ultrawideband Miniature Vivaldi Antenna With Sawtooth Outer Edges and Inclined Elliptical Slots. IEEE Antennas and Wireless Propagation Letters, 23(9), 2708-2712. https://doi.org/10.1109/LAWP.2024.3405007
  • Zhang, Y., Wang, G.-G., Li, K., Yeh, W.-C., Jian, M., & Dong, J. (2020). Enhancing MOEA/D with information feedback models for large-scale many-objective optimization. Information Sciences, 522, 1-16. https://doi.org/10.1016/j.ins.2020.02.066
Toplam 54 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik Elektromanyetiği, Antenler ve Yayılma, Kablosuz Haberleşme Sistemleri ve Teknolojileri (Mikro Dalga ve Milimetrik Dalga dahil)
Bölüm Araştırma Makaleleri \ Research Articles
Yazarlar

Ahmet Uluslu 0000-0002-5580-1687

Enes Beyaz Bu kişi benim 0009-0000-9262-7422

Yayımlanma Tarihi 30 Eylül 2025
Gönderilme Tarihi 1 Kasım 2024
Kabul Tarihi 13 Haziran 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 13 Sayı: 3

Kaynak Göster

APA Uluslu, A., & Beyaz, E. (2025). GİRİŞ PARAMETRELERİNİN AĞIRLIKLARINA GÖRE DEĞİŞKEN DİZİ ARALIK SEÇİMİNİN IBI MANTIK ALGORİTMASI İLE OPTİMİZASYON PERFORMANSINA ETKİSİNİN ÇOK BANTLI VİVALDİ ANTEN TASARIMINDA UYGULANMASI. Mühendislik Bilimleri ve Tasarım Dergisi, 13(3), 728-744. https://doi.org/10.21923/jesd.1577278