İzotropik Plakaların Regressif Topluluk Öğrenmesi Kullanarak Serbest Titreşim Analizi

Öz

Sonlu Elemanlar Yöntemi bir yapının davranışını anlamak ve analiz etmek için kullanılan popüler bir tekniktir. Çeşitli avantajları olmasına rağmen doğru matematiksel modelin geliştirilmesi, kompleks sistemler için hesaplama bakımından maliyetli olabilmesi ve uzmanlık gerektirmesi yönünden bazı dezavantajları bulunmaktadır. Bilgisayar biliminde yakın zamanlarda meydana gelen gelişmeler sayesinde bu tip olumsuzluklar yapay zeka kullanılarak giderilebilmektedir. Bu çalışma, izotropik plakaların temel frekanslarını elde etmek için topluluk öğrenmeli regresör tabanlı bir yöntem sunmaktadır. Bunun için Rastegele Orman Regresörü ele alınmıştır. Ele alınan ince ve kalın izotropik plakalar kare ve dikdörgen geometride olup çeşitli mühendislik uygulamalarında kullanılan Yapı Çeliği, Aernet 100, Al 7108 ve Al 2024 malzemeleri dikkate alınarak tasarlanmıştır. Sonuç olarak önerilen yöntemin 0.9936 korelasyon değeri (R2) ve 0.0019 ortalama karesel hata oranına sahip olduğu görülmüştür. Test seti için ortalama tahmin oranı ise %99.12 olarak elde edilmiştir. Bu sonuçlar göstermektedir ki önerilen yaklaşım sadece bu tip bir problem için uygun olmakla kalmayıp aynı zamanda temel doğal frekansı yüksek doğrulukla tespit edebilmiştir. Önerilen modelin başarısı (%99.12) ve çalışma süresi (0.127 saniye) dikkate alındığında gerçek zamanlı tahmin sistemleri için matematiksel modellere kıyasla avantajlara sahip bir alternatif olduğu sonucuna varılmıştır.

Anahtar Kelimeler

• Titreşim Analizi
• Rastgele Orman Regresörü
• İzotropik Plakalar
• Yapay Zeka
• Doğal Frekans

Free Vibration Analysis of Isotropic Plates Using Regressive Ensemble Learning

Öz

The Finite Element Method (FEM) is a popular technique that is employed to analyze and understand the behavior of a structure. Although it has various advantages, there are some drawbacks such as developing accurate mathematical models, the computational cost for complex systems, and expertise. Thanks to recent advancements in computational science, those drawbacks can be eliminated by integrating artificial intelligence. This study presents an ensemble learning regressor-based technique to evaluate the fundamental natural frequencies of isotropic plate structures. For this purpose, Random Forest Regressor (RFR) has been considered. The isotropic plates have been taken into account as square and rectangular thin and thick plates whose materials have been selected as Structural Steel, Aernet 100, Al 7108, and Al 2024 since they are frequently used in various engineering fields. It has been evaluated that the proposed technique has a 0.9936 correlation score (R2) and 0.0019 mean square error (MSE). The average prediction accuracy has been obtained by 99.12% for the test set. Those indicated that the proposed approach is not only an appropriate model for such a problem but also predicts the fundamental natural frequency accurately. Considering its success (99.12%) and the execution speed (0.127 seconds), it is concluded that the proposed approach is an advantageous alternative technique to the other mathematical models.

Anahtar Kelimeler

• Vibration Analysis
• Random Forest Regressor
• Isotropic Plates
• Artificial Intelligence
• Natural Frequency

Kaynakça

1. Aktaş, G. R., Emül, A., & Orhan, S. (2019). An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration. Uludağ University Journal of The Faculty of Engineering, 24(1), 161–170.
2. Avcar, M., & Saplioglu, K. (2015). An artificial neural network application for estimation of natural frequencies of beams. International Journal of Advanced Computer Science and Applications, 6(6).
3. Belarbi, M. O., Zenkour, A. M., Tati, A., Salami, S. J., Khechai, A., & Houari, M. S. A. (2021). An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates. International Journal for Numerical Methods in Engineering, 122(9), 2360–2387.
4. Breiman, L. (2001). Machine Learning, 45(1), 5–32.
5. Bui, T. Q., & Nguyen, M. N. (2011). A moving Kriging interpolation-based Meshfree method for free vibration analysis of Kirchhoff plates. Computers & Structures, 89(3-4), 380–394.
6. Cheung, Y. K., Tham, L. G., & Li, W. Y. (1988). Free vibration and static analysis of general plate by spline finite strip. Computational Mechanics, 3(3), 187–197.
7. Cuong-Le, T., Nghia-Nguyen, T., Khatir, S., Trong-Nguyen, P., Mirjalili, S., & Nguyen, K. D. (2021). An efficient approach for damage identification based on improved machine learning using PSO-SVM. Engineering with Computers.
8. Hirane, H., Belarbi, M.-O., Houari, M. S., & Tounsi, A. (2021). On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Engineering with Computers.

9. Jung, I. D., Shin, D. S., Kim, D., Lee, J., Lee, M. S., Son, H. J., Reddy, N. S., Kim, M., Moon, S. K., Kim, K. T., Yu, J.-H., Kim, S., Park, S. J., & Sung, H. (2020). Artificial Intelligence for the prediction of tensile properties by using microstructural parameters in high strength steels. Materialia, 11, 100699.
10. Kallannavar, V., Kattimani, S., Soudagar, M. E., Mujtaba, M. A., Alshahrani, S., & Imran, M. (2021). Neural network-based prediction model to investigate the influence of temperature and moisture on vibration characteristics of skew laminated composite sandwich plates. Materials, 14(12), 3170.
11. Le, L. M., Ly, H.-B., Pham, B. T., Le, V. M., Pham, T. A., Nguyen, D.-H., Tran, X.-T., & Le, T.-T. (2019). Hybrid artificial intelligence approaches for predicting buckling damage of steel columns under axial compression. Materials, 12(10), 1670.
12. Lieu, Q. X., Lee, S., Kang, J., & Lee, J. (2018). Bending and free vibration analyses of in-plane bi-directional functionally graded plates with variable thickness using isogeometric analysis. Composite Structures, 192, 434–451.
13. Liu, J., & Yang, X. (2019). Artificial Neural Network for vibration frequency measurement using Kinect V2. Shock and Vibration, 2019, 1–16.
14. Nikoo, M., Hadzima-Nyarko, M., Karlo Nyarko, E., & Nikoo, M. (2018). Determining the natural frequency of cantilever beams using ann and heuristic search. Applied Artificial Intelligence, 32(3), 309–334.
15. Pathirage, C. S., Li, J., Li, L., Hao, H., Liu, W., & Ni, P. (2018). Structural damage identification based on autoencoder neural networks and Deep Learning. Engineering Structures, 172, 13–28.
16. Petyt, M. (2010). Introduction to finite element vibration analysis. Cambridge University Press.
17. Reddy, M. R. S., Reddy, B. S., Reddy, V. N., & Sreenivasulu, S. (2012). Prediction of natural frequency of laminated composite plates using artificial neural networks. Engineering, 04(06), 329–337.
18. Rouzegar, J., & Abdoli Sharifpoor, R. (2016). Finite element formulations for free vibration analysis of isotropic and orthotropic plates using two-variable refined plate theory. Scientia Iranica, 23(4), 1787–1799.
19. Shojaee, S., Izadpanah, E., Valizadeh, N., & Kiendl, J. (2012). Free vibration analysis of thin plates by using a NURBS-based isogeometric approach. Finite Elements in Analysis and Design, 61, 23–34.
20. Zang, Q., Liu, J., Ye, W., Yang, F., Hao, C., & Lin, G. (2022). Static and free vibration analyses of functionally graded plates based on an isogeometric scaled boundary finite element method. Composite Structures, 288, 115398.