Abstract
This paper presents a data-driven machine learning approach of support vector regression (SVR) with genetic algorithm (GA) optimization approach called SVR-GA for predicting the shear strength capacity of medium- to ultra-high strength concrete beams with longitudinal reinforcement and vertical stirrups. One hundred and forty eight experimental samples collected with different geometric, material and physical factors from literature were utilized for SVR-GA with fivefold cross validation. Shear influence factors such as the stirrup spacing, the beam width, the shear span-to-depth ratio, the effective depth of the beam, the concrete compressive and tensile strength, the longitudinal reinforcement ratio, the product of stirrup ratio and stirrup yield strength were served as input variables. The simulation results show that SVR-GA model can achieve highest accuracy in shear strength prediction based on testing set with a coefficient of determination (R2) of 0.9642, root mean squared error of 1.4685 and mean absolute error of 1.0216 superior to that for traditional SVR model with 0.9379, 2.0375 and 1.4917, which both perform better than multiple linear regression and ACI-318. Furthermore, the sensitivity analysis reveals the most important variables affecting the result of shear strength prediction are shear span-to-depth ratio, concrete compressive strength, reinforcement ratio and the product of stirrup ratio and stirrup yield strength. Three-dimensional input/output maps are employed to reflect the nonlinear variation of the shear strength with the two coupling variables. All in all, the proposed SVR-GA model can achieve excellent accuracy in prediction the shear strength of medium- to ultra-high strength concrete beams with stirrups in comparison with results obtained by traditional SVR, MLP and ACI-318.
Highlights
The shear failure of reinforced concrete beams with stirrups is a common concern of structural engineers (Collins et al 2009; Sagaseta and Vollum 2011; Słowik 2014)
This paper presents a data-driven machine learning approach of support vector regression (SVR) with genetic algorithm (GA) optimization approach called SVR-GA for predicting the shear strength capacity of medium-to ultra-high strength concrete beams with longitudinal reinforcement and vertical stirrups. 148 experimental samples collected with different geometric, material and physical factors from literature were utilized for SVR-GA with 5-fold cross validation
SVR-GA and Support vector machine (SVM) models were both applied to learn the relationship between the normalized ultimate shear strength and eight different input variables (s, b, h0, fc, ft, ρ and ρsvfyv)
Summary
The shear failure of reinforced concrete beams with stirrups is a common concern of structural engineers (Collins et al 2009; Sagaseta and Vollum 2011; Słowik 2014). It is difficult to predict the shear failure accurately due to the influence of a large number of parameters, such as the stirrup spacing, the width and effective depth of the beam, shear span-to-depth ratio, stirrup ratio, longitudinal reinforcement ratio, tensile compressive strength of concrete, and stirrup yield strength. This difficulty is evident in ultra-high strength concrete (UHSC) and ultra-high performance concrete (UHPC) beams (Hossain et al 2017). A machine learning model combining genetic algorithm and support vector regression called hybrid SVR-GA model was proposed to predict the shear strength of ultra-high strength concrete beams with stirrups. It is expected that the shear strength of medium- to ultra-high strength concrete beams with any combination of design parameters can be predicted accurately providing guides for optimal design
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