Back-Propagation Neural Network Optimized by K-Fold Cross-Validation for Prediction of Torsional Strength of Reinforced Concrete Beam

Abstract

Due to the limitation of sample size in predicting the torsional strength of Reinforced Concrete (RC) beams, this paper aims to discuss the feasibility of employing a novel machine learning approach with K-fold cross-validation in a small sample range, which combines the advantages of a Genetic Algorithm (GA) and a Neural Network (NN) to predict the torsional strength of RC beams. This research study not only utilizes the application of a Back Propagation (BP) neural network and the Gene Algorithm-Back Propagation (GA-BP) neural network in the prediction of the torsional strength of the RC beam, but it also investigates neural network parameter optimization, including connection weights and thresholds, using K-fold cross-validation. The root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE) and correlation coefficient (R2) are among the evaluation metrics used to assess the performance of the trained model. To elaborate on the superiority of the proposed network models in predicting the torsional strength of RC beams, a parametric study is conducted by comparing the proposed model to three commonly used empirical formulae from existing design codes. The comparative findings of this research study demonstrate that the performance of the BP neural network is highly similar to that of design codes; however, its accuracy is inadequate. After improving the weights and thresholds by k-fold cross-validation and GA, the prediction of the BP neural network shows higher consistency with the actual measured values. The outcome of this study can be used as a theoretical reference for the optimal design of RC beams in practical applications.

Analysis of RC Beams under Combined Torsion and Shear Using Optimization Techniques Evaluation of NBR 6118 and AASHTO LRFD Standards

“…Equation (41) checks the crushing of the concrete diagonal struts due to combined torsion and shear. Second, regarding the yielding strength of the transverse reinforcement for the case of combined torsion and shear, Clause 5.8.3.6 provides the constraints based on the same concepts stated by Equation (30). According to Clauses 5.8.3.3-4 and 5.8.3.6.2-1, Equations ( 43) and (44) for the shear and torsional strengths resisted by the stirrups, respectively, can be stated as follows [31]:…”

“…Recently, more advanced analytical models for RC members under torsion and combined loading have also been proposed in the literature [26][27][28][29][30]. However, although these models have showed to be very accurate, they are not easy to use for practical design, since they require advanced calculation procedures.…”

“…Substituting the areas of transverse reinforcement per unit length for the shear force, from Equation (22), and for the torque, from Equation ( 27), into Equation (30), gives the following:…”

Power-Efficient Trainable Neural Networks towards Accurate Measurement of Irregular Cavity Volume

“…Forward propagation aims to output the predicted value and the loss value [11]. In contrast, back propagation is based on the gradient descent algorithm and assigns the loss value to each neuron, changing each neuron's corresponding weight, threshold, and loss [12]. However, in the real-world application of irregular volume measurement, the back-propagation techniques in most existing methods are very time-consuming and require a large amount of data.…”

Improved Equations for the Torsional Strength of Reinforced Concrete Beams for Codes of Practice Based on the Space Truss Analogy

“…Since the 1980s, refined versions of models based on the space truss analogy have been proposed that allow one to compute with accuracy the strength of RC beams under pure torsion [ 18 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ], RC beams under torsion combined with other internal forces [ 27 , 28 , 29 , 30 ]. More advanced analytical models have also been proposed in the literature and applied to beams under torsion and combined loadings [ 31 , 32 , 33 , 34 , 35 , 36 ]. Although these models have been shown to be very reliable when compared with experimental results, they are not easy to be used by practitioners as they require advanced calculation procedures to be implemented on the computer.…”