Development of Hybrid Machine Learning Models for Predicting the Critical Buckling Load of I-Shaped Cellular Beams

Binh Thai Pham,Vuong Minh Le,Huong-Lan Thi Vu,Van Quan Tran,Tien-Thinh Le,Lu Minh Le,Quang Hung Nguyen,Hai-Bang Ly

doi:10.3390/app9245458

Abstract

The principal purpose of this work is to develop three hybrid machine learning (ML) algorithms, namely ANFIS-RCSA, ANFIS-CA, and ANFIS-SFLA which are a combination of adaptive neuro-fuzzy inference system (ANFIS) with metaheuristic optimization techniques such as real-coded simulated annealing (RCSA), cultural algorithm (CA) and shuffled frog leaping algorithm (SFLA), respectively, to predict the critical buckling load of I-shaped cellular steel beams with circular openings. For this purpose, the existing database of buckling tests on I-shaped steel beams were extracted from the available literature and used to generate the datasets for modeling. Eight inputs, considered as independent variables, including the beam length, beam end-opening distance, opening diameter, inter-opening distance, section height, web thickness, flange width, and flange thickness, as well as one output of the critical buckling load of cellular steel beams considered as a dependent variable, were used in the datasets. Three quality assessment criteria, namely correlation coefficient (R), root mean squared error (RMSE) and mean absolute error (MAE) were employed for assessment of three developed hybrid ML models. The obtained results indicate that all three hybrid ML models have a strong ability to predict the buckling load of steel beams with circular openings, but ANFIS-SFLA (R = 0.960, RMSE = 0.040 and MAE = 0.017) exhibits the best effectiveness as compared with other hybrid models. In addition, sensitivity analysis was investigated and compared with linear statistical correlation between inputs and output to validate the importance of input variables in the models. The sensitivity results show that the most influenced variable affecting beam buckling capacity is the beam length, following by the flange width, the flange thickness, and the web thickness, respectively. This study shows that the hybrid ML techniques could help in establishing a robust numerical tool for beam buckling analysis. The proposed methodology is also promising to predict other types of failure, as well as other types of perforated beams.

Highlights

In the field of structural engineering, the use of steel cellular beams has gained widespread attention thanks to their economic and aesthetic advantages [1,2]
Three hybrid machine learning (ML) models, namely ANFIS-real-coded simulated annealing (RCSA), ANFIS-CA, and ANFIS-SFLA, which are a combination of adaptive neuro-fuzzy inference system (ANFIS) with metaheuristic optimization techniques such as real-coded simulated Annealing (RCSA), cultural algorithm (CA) and shuffled frog leaping algorithm (SFLA), were developed and applied
The performance of the model can be affected by sampling strategy of datasets; the sampling strategy was analyzed by randomly picking data the sampling strategy of datasets; the sampling strategy was analyzed by randomly picking points in the whole dataset to reduce the effect of randomness on the model’s performance

Summary

Introduction

In the field of structural engineering, the use of steel cellular beams has gained widespread attention thanks to their economic and aesthetic advantages [1,2]. Sci. 2019, 9, 5458 design, they are widely used in structural systems subject to bending or funicular structures [3,4,5]. The. I-shaped cellular steel beams are formed from standard I-section beams by cutting regularly circular openings, a specific geometrical feature that results in numerous advantages, for example, the optimum self-weight-depth ratio, improvement of flexural stiffness, or larger section modulus [3]. In combination with the significant compressive strength of concrete slab, the flexural resistance of composite cellular beam is significantly improved [2,6]

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Conclusion