An artificial neural network for predicting the ultimate bending moments in reinforced concrete beams with fiber-reinforced polymer strengthening

A practical artificial neural network tool is proposed for predicting the ultimate bending moments of reinforced concrete beams strengthened by the techniques of externally bonded fiber-reinforced polymer and near-surface mounted fiber-reinforced polymer. Accordingly, the testing database of 131 specimens was gathered for use in developing the artificial neural network model. In this regard, the breadth and height of the beam section, the compression strength of the concrete, the ratio of material reinforcement, and the elastic modulus of fiber reinforced polymer were regarded as input variables, whereas the ultimate bending moment was regarded as an output variable. The performance of the proposed artificial neural network model was compared to the current design model of the American Concrete Institute guide. The comparative analysis demonstrated that the proposed model made more accurate predictions than the current model. Based on the proposed model, a graphical user interface was created to facilitate the prediction of the ultimate bending moments of reinforced concrete beams with fiber-reinforced polymer strengthening.


Introduction
Typically, fiber-reinforced polymer (FRP) composites are used to strengthen reinforced concrete (RC) structures that do not comply with outdated code requirements or that can resist greater static loading, as well as to repair structures that have been damaged by environmental exposures (Aslam el at. 2015;Kadhim et al., 2021;Siddika et al., 2019;Zhang et al., 2017). Over the past several decades, a large number of experimental and theoretical studies have been conducted to fully understand the performance of RC structures strengthened by various techniques, such as externally bonded fiber-reinforced polymer (EB-FRP) and near-surface mounted fiber-reinforced polymer (NSM-FRP). Experimental studies have confirmed the static/dynamic interrelationships between the strength, failure mode, and deflection capacity of such strengthened structures (Bonacci & Maalej 2001;Hosen et al., 2016;Seracino et al., 2007;Lorenzis & Nanni, 2001;Kishi el at. 2017). Theoretical studies for the prediction of the behavior of FRP-strengthened beams have been proposed (ACI 2008;f. -. B. 14 2001;C.-D. 203 2006;JSCE, 1997;C. S806-02 2002). The design guidelines are traditionally computed assuming that the concrete compression zone will be crushed or that the tension reinforcement will fail. Although some of these initial assumptions are required for computational simplicity, they are typically inadequate for reliably predicting the ultimate bending moments of strengthened beams due to the influence of the controlling failure modes. Xue et al., 2010 presented 1 3 theoretical formulas based on the American Concrete Institute (ACI) guide to predict the flexural strength of RC beams strengthened with prestressed carbon FRP plates. As can be seen, the predictions from formulas do not correspond well to the experimental results. The average absolute error (AAE) of the predictions from formulas can reach 14%. In addition, Al-Mahmuod et al., 2009 also calculated the ultimate bending moment of RC beams strengthened by NSM-FRP with an AAE of about 18% when using the existing analytical models. Thus, the research community should improve the accuracy of estimating the flexural strength of RC structures strengthened by different techniques. This study introduces the use of an artificial neural network (ANN) model to predict the moment of strengthened beams based on the input parameters, including geometry of the section and mechanical properties of the materials.
The ANN model is able to produce output data that is more similar to experimental results than other models. ANN has been utilized in numerous areas of civil engineering, including damage detection (Elkordy et al., 1993;Wu et al., 1992), structural analysis and design (Adeli & Park, 1995;Hajela & Berke, 1991;Kaveh & Iranmanesh, 1998;Kaveh & Servati, 2001;Kaveh et al., 2008), and the prediction of shear strength of RC members reinforced with FRP (Perera et al., 2010(Perera et al., , 2014Jumaa & Yousif, 2018;Lee & Lee, 2014;Naderpour 2010). Using a database of experimental results, many ANN models have been developed to predict the shear capacity of the strengthened beams. Unfortunately, no research has been conducted on the use of ANN model to predict the flexural capacity of the strengthened beams. This study employs ANN model to predict the ultimate bending moments of RC beams strengthened by EB-FRP and NSM-FRP techniques. Also, a creative way to make formulation that predict ultimate bending moments that are easy to use is shown.

Proposed ANN model
For the purpose of this study, an extensive survey of the open literature was conducted and a large database containing the test results of a number of 131 RC beams strengthened by EB-FRP and NSM-FRP techniques was assembled. The database of the specimens was collected from 14 different references and is reported in Table 1. All specimens collated in the databases were chosen based on various typical FRP materials, such as glass FRP (GFRP), carbon FRP (CFRP), basalt FRP (BFRP), and they are applied in the techniques of EB laminates, and NSM bars/strips to strengthen RC beams.
The primary objective of network training is to optimize network generalization by minimizing network error. Mean square error (MSE) is the criterion for stopping the training of networks. It is the average squared difference between network outputs and targets. This network involved segmenting the available information into training, testing, and validation sets. After a certain number of iterations, the error on the validation set increases when the network starts to overfit the data. As a result, training was stopped, and the weights and biases that produced the smallest validation error were restored.
The database was randomly divided into training (70%), validation (15%), and test (15%) via the ANN toolbox of Matlab (Matlab 2020a). In the proposed ANN model, the choice of the input parameters has been guided based on the predictions obtained with the flexural capacity equations of different design proposals (ACI 2008;JSCE, 1997). The design equations with the closest predictions to the experimental values were used to define the input variables. In particular, the breadth of the beam (b in mm), the height of the beam section (h in mm), the characteristic compression strength of the concrete (f′ c in MPa), the ratio of the longitudinal steel reinforcement (ρ s in %), the ratio of the FRP longitudinal reinforcement (ρ f in %), and the elastic modulus of FRP (E f in GPa) were considered as the input variables, whereas the ultimate bending moment (M u in kN•m) was considered as the output variable.
Before the training process, it is recommended to scale databases to the interval (− 1, 1) using a normalization procedure to classify the interval of distinct values to the same scale (Golafshani & Ashour, 2016). It is evident that normalization allows orthogonalizing the components of the input vectors to eliminate correlation and achieve a faster convergence during the training process. Normal input and output variable values are expressed as follows: where X is the data sample, X n is the normalized data sample, X min and X max are the minimum and maximum values of the data for the relevant parameter.
Choosing the number of hidden layers and the number of neurons in each hidden layer is the most critical aspect of the ANN model. For both the number of hidden layers and their associated nodes, there is no reliable principle. Some studies (Kaveh & Khalegi, 2000;Naderpour, 2018;Naderpour et al., 2018) showed that a neural network with one hidden layer can be sufficient for achieving good results, so the proposed ANN model also included one hidden layer. In this study, the structure of the proposed ANN model comprises the following parameters: The number of input layer neurons is six, the number of hidden layer neurons is seven, and one neuron from the output layer is used as shown in Fig. 1. Numerous trials with varying numbers of hidden layers and neurons indicate that the proposed model represents the optimal (1)    (Beale et al., 2018). In this study, the LM algorithm (denoted by function Trainlm) with 7 neurons in the hidden layer shows the best performance in the training, testing, and validation processes.

Results and discussion
The performance of the ANN model is illustrated in Fig. 2. The training, testing, and validation processes of the ANN model begin with a high MSE value and then decrease to a smaller value. A minimum MSE value indicates a highquality ANN model, so the best training performance was recorded as 1.8754e-2 at the 48th epoch. The highest general correlation factor (R 2 ) of training, testing, and validation data was found to be 0.99, 0.98, and 0.96, respectively. With an R 2 value close to 1.0, it is highly possible that the proposed model has generated the best outcomes. Definitely, the performance of ANN model for predicting the ultimate bending moments of RC beams strengthened by EB/NSM-FRP techniques is satisfactory. After the ANN model has been successfully trained using the training data sets, it can be saved. The network can then predict the output values corresponding to new input data.
Comparing the ultimate moments of the ANN model to those of another model of the ACI guide (ACI 2008) allowed for evaluating the accuracy of the ultimate moments of the  strengthened beams. As shown in Fig. 3, three statistical measures were employed: AAE, MSE, and standard deviation (SD), which is expressed as Compared to the ACI model, the ANN model reduces the error in estimating the ultimate moments of the strengthened beams by approximately three times. The AAE of the proposed model is approximately 6.42%, whereas the AAE of the existing model is approximately 19.43%. Moreover, the fact that both the mean value and standard deviation are small demonstrates that the ANN network has a strong capacity for generating reliable output data.
In a second comparison, the output of the ANN model is validated against the experimental results of static tests conducted on 131 RC beams strengthened by EB/NSM-FRP techniques. Figure 4a compares the proposed model's prediction to the experimental moments. The best-fit line is nearly parallel to the 45 0 benchmark, demonstrating a strong correlation between the experiment and the predictions. The correlation coefficient between these two variables is 0.98. In constraint, the calculated ultimate moments from the ACI guide are plotted against the database in Fig. 4b. Evidently, the predictions from the ACI guide with R 2 = 0.75 do not correspond well with the experimental results. This comparison shows that the proposed model does a better job than the model that is used now and is described in the ACI guide.
Regarding the limitation of the proposed ANN model, artificial neural networks cannot typically extrapolate, so the training data should extend to the problem domain's boundaries in all dimensions. In other words, future test data should represent between the maximum and minimum of the training database across all dimensions. The proposed ANN models should be retrained and tested using a larger database with a large number of reported specimens to increase their applicability. The ANN can be used with high levels of confidence once it has been correctly trained, validated, and tested using a large experimental database.

ANN model-based user interface development
Concerning ANN-based formulation, the proposed ANN model can predict the ultimate moment of RC beams with EB/ NSM-FRP reinforcement outstandingly well. Due to the complexity of numerical methods, the current ANN model should be used to derive an explicit empirical formulation that is simple to implement in the design. Using the activation functions and parameters (weights, biases, and normalization factors) of the developed ANN model, a specific formula describing the ultimate moment was derived directly. Based on the proposed ANN model, as depicted in Fig. 1, the normalized value of the ultimate moment (M u,N ) was a function of relevant parameters, expressed as where n = 7 is the number of neurons in the hidden layer of the ANN model. Table 2 lists the additional coefficients, h 0 to h n and c i0 to c i6 . The output of the ultimate moment in Eq. (5) was a normalized value between −1 and 1, which needs to be converted into the actual value. Finally, the ultimate moment of strengthened beams with EB/NSM-FRP is expressed as M u = 44.51 × (M u,N + 1) + 12.58, where M u,N and M u are normalized and real moments of strengthened beams with EB/NSM-FRP, respectively.
Regarding graphical user interface (GUI), design teams are currently emphasizing the development of software that is more powerful and user-friendly to predict the various strengths of strengthened structures. For this reason, a substantial effort has been expended to ensure that the GUI developed in this study is practical and useful. In particular, the GUI is a great way to get started with Visual Basic for Applications (Microsoft Office, 2022), as it demonstrates how to transform an Excel spreadsheet into a GUI for the sake of easy predictability. Figure 5 depicts the primary user interface, which is straightforward and incredibly intuitive. As illustrated in this diagram, the GUI encourages the user to request the necessary parameters. Numeric values can be entered by users for the breadth and height of the beam section, compression strength of the concrete, ratio of longitudinal steel reinforcement and FRP reinforcement, and elastic modulus of FRP. By clicking the Predicting button, the ultimate bending moment of strengthened beams is shown right away.

Conclusion
In this study, an ANN model was developed to predict the ultimate bending moment of RC beams strengthened with FRP to resist flexural failure. 131 specimens were derived from experimental data to produce an ANN model for predicting the ultimate bending moment. The performance of the proposed ANN model was compared to the ACI guide. This study yielded the following conclusions.
(1) The proposed ANN model can predict with high accuracy the ultimate bending moment of RC beams that have been strengthened using both EB-FRP and NSM-FRP techniques.
(2) The results of the proposed ANN model showed very low error rates (AAE less than 7%), which is an improvement over the currently used model of the ACI guide. (3) An ANN-based formulation was formed to predict the ultimate bending moment of the strengthened beams. The proposed ANN model and the ANN-based formulation calculated equivalent results. Nevertheless, the ANN-based formulation with the GUI is more straightforward and convenient than the proposed ANN model. It was suggested that the ANN-based formulation with the GUI be used for the practical design phase of the strengthened beams with FRP.

Funding
The authors received no financial support for the research, authorship, and/or publication of this article.

Data availability
On behalf of all authors, the corresponding author states that all data analyzed in this study are available from the corresponding author on reasonable request.

Conflict of interest
The authors declare no competing interests.