Research Article
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Crash Performance Optimization of Vehicle Elements Using Arithmetic Optimization Algorithm

Year 2023, Volume: 26 Issue: 3, 1277 - 1283, 01.10.2023

Betul Yildiz

https://doi.org/10.2339/politeknik.1286340

Abstract

In this study, the newly developed arithmetic optimization algorithm is used for the first time in the literature for the optimum design of automobile components exposed to crash. In conjunction with the enhancement of crash and NVH characteristics in the optimization study, the design objective is to minimize vehicle weight. For vehicle performance analysis, a comprehensive automobile structure, faithful to the original, was used. Both multiple crash analysis and vibration analysis of finite element models were performed to examine full, offset and side impact crash scenarios with natural frequencies. The evaluated structural responses are estimated based on the radial basis functions technique. An arithmetic optimization algorithm is used to optimize the vehicle mass under various nonlinear crash and vibration limits. The results revealed the effectiveness of the arithmetic optimization algorithm in the optimum design of vehicle components.

Keywords

Arithmetic optimization algorithm Metaheuristics Crashworthiness Vehicle design Optimum design

References

  • [1] Kiani M., Gandikota I., Parrish A., Motoyama K., and Rais-Rohani M., “Surrogate-based optimisation of automotive structures under multiple crash and vibration design criteria”, International journal of crashworthiness, 18(5): 473-482, (2013).
  • [2] Kiani M., and Yildiz A. R., “A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization”, Archives of Computational Methods in Engineering, 23(4): 723-734, (2016).
  • [3] Sobieszczanski-Sobieski J., Kodiyalam S., and Yang R. Y., “Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash”, Structural and multidisciplinary optimization, 22(4): 295-306, (2001).
  • [4] Simpson T. W., Poplinski J. D., Koch P. N., and Allen J. K. “Metamodels for computer-based engineering design: survey and recommendations”, Engineering with computers, 17(2): 129-150, (2001).
  • [5] Fang H., Rais-Rohani M., Liu Z., and Horstemeyer M. F., “A comparative study of metamodeling methods for multiobjective crashworthiness optimization”, Computers & structures, 83(25-26) : 2121-2136, (2005).
  • [6] Liao X., Li Q., Yang X., Li W., and Zhang W., “A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact”, International Journal of Crashworthiness, 13(3) : 279-288, (2008).
  • [7] Zhu P., Pan F., Chen W., and Zhang S., “Use of support vector regression in structural optimization: application to vehicle crashworthiness design”, Mathematics and Computers in Simulation, 86, 21-31, (2012).
  • [8] Yu L., Gu X., Qian L., Jiang P., Wang W., and Yu M., “Application of tailor rolled blanks in optimum design of pure electric vehicle crashworthiness and lightweight”, Thin-Walled Structures, 161, 107410, (2021).
  • [9] Kirkpatrick S. W., Simons J. W., and Antoun T. H., “Development and validation of high fidelity vehicle crash simulation models”, International journal of crashworthiness, 4(4) : 395-406, (1999).
  • [10] Bayarri M. J., Berger J. O., Kennedy M. C., Kottas A., Paulo R., Sacks J., and Tu J.,”Predicting vehicle crashworthiness: Validation of computer models for functional and hierarchical data”, Journal of the American Statistical Association, 104(487) : 929-943, (2009).
  • [11] Yildiz A. R., and Solanki K. N., “Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach”, The International Journal of Advanced Manufacturing Technology, 59(1-4) : 367-376, (2012).
  • [12] Xiong F., Wang D., Ma Z., Chen S., Lv T., and Lu F., “Structure-material integrated multi-objective lightweight design of the front end structure of automobile body”, Structural and Multidisciplinary Optimization, 57, 829-847, (2018).
  • [13] Xiong F., Zou X., Zhang Z., and Shi X.,”A systematic approach for multi-objective lightweight and stiffness optimization of a car body”, Structural and Multidisciplinary Optimization, 62, 3229-3248, (2020).
  • [14] Zhou G., Ma Z. D., Li G., Cheng A., Duan L., and Zhao W., “Design optimization of a novel NPR crash box based on multi-objective genetic algorithm”, Structural and Multidisciplinary Optimization, 54(3) : 673-684, (2016).
  • [15] Wang D., Jiang R., and Wu, Y., “A hybrid method of modified NSGA-II and TOPSIS for lightweight design of parameterized passenger car sub-frame”, Journal of Mechanical Science and Technology, 30(11) : 4909-4917, (2016).
  • [16] Kohar C. P., Zhumagulov A., Brahme A., Worswick M. J., Mishra R. K., and Inal, K., “Development of high crush efficient, extrudable aluminium front rails for vehicle lightweighting”, International Journal of Impact Engineering, 95, 17-34, (2016).
  • [17] Fang J., Gao Y., Sun G., Xu C., and Li Q., “Multiobjective sequential optimization for a vehicle door using hybrid materials tailor-welded structure”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(17) : 3092-3100, (2016).
  • [18] Pang T., Li Y., Kang H., Sun G., Fang J., and Li Q., “On functionally-graded crashworthy shape of conical structures for multiple load cases”, Journal of Mechanical Science and Technology, 31(6) : 2861-2873, (2017).
  • [19] Yao R., Pang T., He S., Li Q., Zhang B., and Sun G.,” A bio-inspired foam-filled multi-cell structural configuration for energy absorption”, Composites Part B: Engineering, 238, 109801, (2022).
  • [20] Zarei H. R., and Kröger M., “Optimization of the foam-filled aluminum tubes for crush box application”, Thin-Walled Structures, 46(2) : 214-221, (2008).
  • [21] Fan D., Qi‐hua M., Xue‐hui G., and Tianjun Z., “Crashworthiness analysis of perforated metal/composite thin‐walled structures under axial and oblique loading”, Polymer Composites, 42(4) : 2019-2036, (2021).
  • [22] Ren X., Zhang Y., Han C. Z., Han D., Zhang X. Y., Zhang X. G., and Xie Y. M., “Mechanical properties of foam-filled auxetic circular tubes: Experimental and numerical study”, Thin-Walled Structures, 170, 108584, (2022).
  • [23] Marklund P. O., and Nilsson L., “Optimization of a car body component subjected to side impact”, Structural and Multidisciplinary Optimization, 21(5) : 383-392, (2001).
  • [24] Liao X., Li Q., Yang X., Li W., and Zhang W., “A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact”, International Journal of Crashworthiness, 13(3) : 279-288, (2008).
  • [25] Duddeck F., “Multidisciplinary optimization of car bodies”, Structural and Multidisciplinary Optimization, 35(4) : 375-389, (2008). [26] Fang H., Rais-Rohani M., Liu Z., and Horstemeyer M. F., “A comparative study of metamodeling methods for multiobjective crashworthiness optimization” Computers & structures, 83(25-26) : 2121-2136, (2005).
  • [27] Kurtaran, H., Eskandarian A., Marzougui D., and Bedewi N. E., “Crashworthiness design optimization using successive response surface approximations”, Computational mechanics, 29(4-5) : 409-421, (2002).
  • [28] Stander N., Roux W., Giger M., Redhe M., Fedorova N., and Haarhoff J., “A comparison of metamodeling techniques for crashworthiness optimization”, In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (p. 4489), (2004).
  • [29] Kaps A., Czech C., and Duddeck F., “A hierarchical kriging approach for multi-fidelity optimization of automotive crashworthiness problems”, Structural and Multidisciplinary Optimization, 65(4) : 114, (2022).
  • [30] Qian L., Yu L., Huang,Y., Jiang P., and Gu X., “Improved whale optimization algorithm and its application in vehicle structural crashworthiness”, International Journal of Crashworthiness, 28(2) : 202-216, (2023).
  • [31] Yin H., Meng F., Zhu L., and Wen G., “Optimization design of a novel hybrid hierarchical cellular structure for crashworthiness”, Composite Structures, 303, 116335, (2023).
  • [32] Kiani M., Motoyama K., Rais-Rohani M., and Shiozaki H., “Joint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicle”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 228(6):689-700, (2014).
  • [33] Yang Z., Peng Q., and Yang J., “Lightweight design of B-pillar with TRB concept considering crashworthiness”, In 2012 Third International Conference on Digital Manufacturing & Automation (pp. 510-513), IEEE, (2012,).
  • [34] De S., Singh K., Seo J., Kapania R. K., Ostergaard E., Angelini N., and Aguero R., “Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints”, World Electric Vehicle Journal, 12(1) : 3, (2021).
  • [35] Duan L., Sun G., Cui J., Chen T., Cheng A., and Li G., “Crashworthiness design of vehicle structure with tailor rolled blank”, Structural and Multidisciplinary Optimization, 53(2) : 321-338, (2016).
  • [36] Lee K. H., and Kang D. H., “Structural optimization of an automotive door using the kriging interpolation method”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 221(12) : 1525-1534, (2007).
  • [37] Yıldız, B. S., Kumar, S., Pholdee, N., Bureerat, S., Sait, S. M., Yildiz, A. R., ‘’A new chaotic Lévy flight distribution optimization algorithm for solving constrained engineering problems’’, Expert Systems, 39(8) : e12992, (2022).
  • [38] Yıldız B. S., and Yıldız A. R., “Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod”, Materials Testing, 60(3) : 311-315, (2018).
  • [39] Yıldız, B.S., ‘’Robust design of electric vehicle components using a new hybrid salp swarm algorithm and radial basis function-based approach’’, International Journal of Vehicle Design, 83(1) : 38-53,(2020).
  • [40] Yıldız, B. S., ‘’Slime mould algorithm and kriging surrogate model-based approach for enhanced crashworthiness of electric vehicles’’, International Journal of Vehicle Design, 83(1) : 54-68, (2020).
  • [41] Yildirim, A., Demirci, E., Karagöz, S., Özcan, Ş., Yildiz, A. R., ‘’Experimental and numerical investigation of crashworthiness performance for optimal automobile structures using response surface methodology and oppositional based learning differential evolution algorithm’’, Materials Testing, 65(3) : 346-363,(2023).
  • [42] Güler, T., Demirci, E., Yıldız, A. R., Yavuz, U., ‘’Lightweight design of an automobile hinge component using glass fiber polyamide composites’’, Materials Testing, 60(3) : 306-310,(2018).
  • [43] Demirci, E., Yıldız, A. R., ‘’An experimental and numerical investigation of the effects of geometry and spot welds on the crashworthiness of vehicle thin-walled structures’’, Materials Testing, 60(6) : 553-561,(2018).
  • [44] Demirci, E., Yıldız, A. R., ‘’An investigation of the crash performance of magnesium, aluminum and advanced high strength steels and different cross-sections for vehicle thin-walled energy absorbers’’, Materials Testing, 60(7-8) : 661-668,(2018).

Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi

Year 2023, Volume: 26 Issue: 3, 1277 - 1283, 01.10.2023

Betul Yildiz

https://doi.org/10.2339/politeknik.1286340

Abstract

Bu çalışmada çarpışmaya maruz kalan otomobil bileşenlerinin optimum tasarımında yeni geliştirilen aritmetik optimizasyon algoritması litetürde ilk defa kullanılmıştır. Optimizasyon çalışmasında çarpışma ve NVH özelliklerinin güçlendirilmesi ile bağlantılı olarak tasarım amacı araç ağırlığının en aza indirilmesidir. Araç performansı analizi için, aslına uygun, kapsamlı bir otomobil yapısı kullanılmıştır. Doğal frekanslar ile birlikte tam, ofset ve yan etki çarpışma senaryolarını incelemek için sonlu eleman modellerinin hem çoklu çarpma analizi hem de titreşim analizi yapılmıştır. Değerlendirilen yapısal tepkiler, radyal temelli fonksiyonlar tekniğine dayalı olarak tahmin edilir. Çeşitli doğrusal olmayan çarpışma ve titreşim sınırları altında araç kütlesini optimize etmek için aritmetik optimizasyon algoritması kullanılmıştır. Sonuçlar artimetik optimizasyon algoritmasının araç bileşenlerinin optimum tasarımındaki etkinliğini ortaya koymuştur.

Keywords

Aritmetik optimizasyon algoritması Taşıt tasarımı Optimum tasarım Çarpışma Metasezgiseller

References

  • [1] Kiani M., Gandikota I., Parrish A., Motoyama K., and Rais-Rohani M., “Surrogate-based optimisation of automotive structures under multiple crash and vibration design criteria”, International journal of crashworthiness, 18(5): 473-482, (2013).
  • [2] Kiani M., and Yildiz A. R., “A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization”, Archives of Computational Methods in Engineering, 23(4): 723-734, (2016).
  • [3] Sobieszczanski-Sobieski J., Kodiyalam S., and Yang R. Y., “Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash”, Structural and multidisciplinary optimization, 22(4): 295-306, (2001).
  • [4] Simpson T. W., Poplinski J. D., Koch P. N., and Allen J. K. “Metamodels for computer-based engineering design: survey and recommendations”, Engineering with computers, 17(2): 129-150, (2001).
  • [5] Fang H., Rais-Rohani M., Liu Z., and Horstemeyer M. F., “A comparative study of metamodeling methods for multiobjective crashworthiness optimization”, Computers & structures, 83(25-26) : 2121-2136, (2005).
  • [6] Liao X., Li Q., Yang X., Li W., and Zhang W., “A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact”, International Journal of Crashworthiness, 13(3) : 279-288, (2008).
  • [7] Zhu P., Pan F., Chen W., and Zhang S., “Use of support vector regression in structural optimization: application to vehicle crashworthiness design”, Mathematics and Computers in Simulation, 86, 21-31, (2012).
  • [8] Yu L., Gu X., Qian L., Jiang P., Wang W., and Yu M., “Application of tailor rolled blanks in optimum design of pure electric vehicle crashworthiness and lightweight”, Thin-Walled Structures, 161, 107410, (2021).
  • [9] Kirkpatrick S. W., Simons J. W., and Antoun T. H., “Development and validation of high fidelity vehicle crash simulation models”, International journal of crashworthiness, 4(4) : 395-406, (1999).
  • [10] Bayarri M. J., Berger J. O., Kennedy M. C., Kottas A., Paulo R., Sacks J., and Tu J.,”Predicting vehicle crashworthiness: Validation of computer models for functional and hierarchical data”, Journal of the American Statistical Association, 104(487) : 929-943, (2009).
  • [11] Yildiz A. R., and Solanki K. N., “Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach”, The International Journal of Advanced Manufacturing Technology, 59(1-4) : 367-376, (2012).
  • [12] Xiong F., Wang D., Ma Z., Chen S., Lv T., and Lu F., “Structure-material integrated multi-objective lightweight design of the front end structure of automobile body”, Structural and Multidisciplinary Optimization, 57, 829-847, (2018).
  • [13] Xiong F., Zou X., Zhang Z., and Shi X.,”A systematic approach for multi-objective lightweight and stiffness optimization of a car body”, Structural and Multidisciplinary Optimization, 62, 3229-3248, (2020).
  • [14] Zhou G., Ma Z. D., Li G., Cheng A., Duan L., and Zhao W., “Design optimization of a novel NPR crash box based on multi-objective genetic algorithm”, Structural and Multidisciplinary Optimization, 54(3) : 673-684, (2016).
  • [15] Wang D., Jiang R., and Wu, Y., “A hybrid method of modified NSGA-II and TOPSIS for lightweight design of parameterized passenger car sub-frame”, Journal of Mechanical Science and Technology, 30(11) : 4909-4917, (2016).
  • [16] Kohar C. P., Zhumagulov A., Brahme A., Worswick M. J., Mishra R. K., and Inal, K., “Development of high crush efficient, extrudable aluminium front rails for vehicle lightweighting”, International Journal of Impact Engineering, 95, 17-34, (2016).
  • [17] Fang J., Gao Y., Sun G., Xu C., and Li Q., “Multiobjective sequential optimization for a vehicle door using hybrid materials tailor-welded structure”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(17) : 3092-3100, (2016).
  • [18] Pang T., Li Y., Kang H., Sun G., Fang J., and Li Q., “On functionally-graded crashworthy shape of conical structures for multiple load cases”, Journal of Mechanical Science and Technology, 31(6) : 2861-2873, (2017).
  • [19] Yao R., Pang T., He S., Li Q., Zhang B., and Sun G.,” A bio-inspired foam-filled multi-cell structural configuration for energy absorption”, Composites Part B: Engineering, 238, 109801, (2022).
  • [20] Zarei H. R., and Kröger M., “Optimization of the foam-filled aluminum tubes for crush box application”, Thin-Walled Structures, 46(2) : 214-221, (2008).
  • [21] Fan D., Qi‐hua M., Xue‐hui G., and Tianjun Z., “Crashworthiness analysis of perforated metal/composite thin‐walled structures under axial and oblique loading”, Polymer Composites, 42(4) : 2019-2036, (2021).
  • [22] Ren X., Zhang Y., Han C. Z., Han D., Zhang X. Y., Zhang X. G., and Xie Y. M., “Mechanical properties of foam-filled auxetic circular tubes: Experimental and numerical study”, Thin-Walled Structures, 170, 108584, (2022).
  • [23] Marklund P. O., and Nilsson L., “Optimization of a car body component subjected to side impact”, Structural and Multidisciplinary Optimization, 21(5) : 383-392, (2001).
  • [24] Liao X., Li Q., Yang X., Li W., and Zhang W., “A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact”, International Journal of Crashworthiness, 13(3) : 279-288, (2008).
  • [25] Duddeck F., “Multidisciplinary optimization of car bodies”, Structural and Multidisciplinary Optimization, 35(4) : 375-389, (2008). [26] Fang H., Rais-Rohani M., Liu Z., and Horstemeyer M. F., “A comparative study of metamodeling methods for multiobjective crashworthiness optimization” Computers & structures, 83(25-26) : 2121-2136, (2005).
  • [27] Kurtaran, H., Eskandarian A., Marzougui D., and Bedewi N. E., “Crashworthiness design optimization using successive response surface approximations”, Computational mechanics, 29(4-5) : 409-421, (2002).
  • [28] Stander N., Roux W., Giger M., Redhe M., Fedorova N., and Haarhoff J., “A comparison of metamodeling techniques for crashworthiness optimization”, In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (p. 4489), (2004).
  • [29] Kaps A., Czech C., and Duddeck F., “A hierarchical kriging approach for multi-fidelity optimization of automotive crashworthiness problems”, Structural and Multidisciplinary Optimization, 65(4) : 114, (2022).
  • [30] Qian L., Yu L., Huang,Y., Jiang P., and Gu X., “Improved whale optimization algorithm and its application in vehicle structural crashworthiness”, International Journal of Crashworthiness, 28(2) : 202-216, (2023).
  • [31] Yin H., Meng F., Zhu L., and Wen G., “Optimization design of a novel hybrid hierarchical cellular structure for crashworthiness”, Composite Structures, 303, 116335, (2023).
  • [32] Kiani M., Motoyama K., Rais-Rohani M., and Shiozaki H., “Joint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicle”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 228(6):689-700, (2014).
  • [33] Yang Z., Peng Q., and Yang J., “Lightweight design of B-pillar with TRB concept considering crashworthiness”, In 2012 Third International Conference on Digital Manufacturing & Automation (pp. 510-513), IEEE, (2012,).
  • [34] De S., Singh K., Seo J., Kapania R. K., Ostergaard E., Angelini N., and Aguero R., “Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints”, World Electric Vehicle Journal, 12(1) : 3, (2021).
  • [35] Duan L., Sun G., Cui J., Chen T., Cheng A., and Li G., “Crashworthiness design of vehicle structure with tailor rolled blank”, Structural and Multidisciplinary Optimization, 53(2) : 321-338, (2016).
  • [36] Lee K. H., and Kang D. H., “Structural optimization of an automotive door using the kriging interpolation method”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 221(12) : 1525-1534, (2007).
  • [37] Yıldız, B. S., Kumar, S., Pholdee, N., Bureerat, S., Sait, S. M., Yildiz, A. R., ‘’A new chaotic Lévy flight distribution optimization algorithm for solving constrained engineering problems’’, Expert Systems, 39(8) : e12992, (2022).
  • [38] Yıldız B. S., and Yıldız A. R., “Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod”, Materials Testing, 60(3) : 311-315, (2018).
  • [39] Yıldız, B.S., ‘’Robust design of electric vehicle components using a new hybrid salp swarm algorithm and radial basis function-based approach’’, International Journal of Vehicle Design, 83(1) : 38-53,(2020).
  • [40] Yıldız, B. S., ‘’Slime mould algorithm and kriging surrogate model-based approach for enhanced crashworthiness of electric vehicles’’, International Journal of Vehicle Design, 83(1) : 54-68, (2020).
  • [41] Yildirim, A., Demirci, E., Karagöz, S., Özcan, Ş., Yildiz, A. R., ‘’Experimental and numerical investigation of crashworthiness performance for optimal automobile structures using response surface methodology and oppositional based learning differential evolution algorithm’’, Materials Testing, 65(3) : 346-363,(2023).
  • [42] Güler, T., Demirci, E., Yıldız, A. R., Yavuz, U., ‘’Lightweight design of an automobile hinge component using glass fiber polyamide composites’’, Materials Testing, 60(3) : 306-310,(2018).
  • [43] Demirci, E., Yıldız, A. R., ‘’An experimental and numerical investigation of the effects of geometry and spot welds on the crashworthiness of vehicle thin-walled structures’’, Materials Testing, 60(6) : 553-561,(2018).
  • [44] Demirci, E., Yıldız, A. R., ‘’An investigation of the crash performance of magnesium, aluminum and advanced high strength steels and different cross-sections for vehicle thin-walled energy absorbers’’, Materials Testing, 60(7-8) : 661-668,(2018).
There are 43 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Article
Authors

Betul Yildiz 0000-0002-7493-2068

Early Pub Date August 24, 2023
Publication Date October 1, 2023
Submission Date April 20, 2023
Published in Issue Year 2023 Volume: 26 Issue: 3

Cite

APA Yildiz, B. (2023). Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi. Politeknik Dergisi, 26(3), 1277-1283. https://doi.org/10.2339/politeknik.1286340
AMA Yildiz B. Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi. Politeknik Dergisi. October 2023;26(3):1277-1283. doi:10.2339/politeknik.1286340
Chicago Yildiz, Betul. “Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi”. Politeknik Dergisi 26, no. 3 (October 2023): 1277-83. https://doi.org/10.2339/politeknik.1286340.
EndNote Yildiz B (October 1, 2023) Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi. Politeknik Dergisi 26 3 1277–1283.
IEEE B. Yildiz, “Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi”, Politeknik Dergisi, vol. 26, no. 3, pp. 1277–1283, 2023, doi: 10.2339/politeknik.1286340.
ISNAD Yildiz, Betul. “Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi”. Politeknik Dergisi 26/3 (October 2023), 1277-1283. https://doi.org/10.2339/politeknik.1286340.
JAMA Yildiz B. Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi. Politeknik Dergisi. 2023;26:1277–1283.
MLA Yildiz, Betul. “Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi”. Politeknik Dergisi, vol. 26, no. 3, 2023, pp. 1277-83, doi:10.2339/politeknik.1286340.
Vancouver Yildiz B. Aritmetik Optimizasyon Algoritması Kullanarak Taşıt Elemanlarının Çarpışma Performansının Eniyilemesi. Politeknik Dergisi. 2023;26(3):1277-83.

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