An Optimized Neuro-Bee Algorithm Approach to Predict the FRP-Concrete Bond Strength of RC Beams

Over the world, there is growing worry about the corrosion of reinforced concrete structures. Structure repair, rehabilitation, replacement, and new structures all require cost-effective and long-lasting technologies. Fiber Reinforced Polymer (FRP) has been widely employed in both retrofitting existing structures and building new ones. Due to its varied qualities in reinforced concrete and masonry constructions as a repair composite material, FRP have seen a rise in use over the last decade. This material have several advantages such as high stiffness-to-weight and strength-to-weight ratios, light weight, possibly high longevity, and relative ease of usage in the field. Among all the parameters the bond between concrete and FRP composite play an important role in the strengthening of structures. However, the bond behaviour of the FRP-concrete interface is complex, with several failure modes, making the bond strength difficult to forecast, resulting in the FRP strengthened concrete structure. To overcome such kind of issues machine learning models are sufficient to forecast the bond strength of FRP-concrete. In this article Artificial Neural Network (ANN), optimized Artificial Bee Colony (ABC)-ANN and Gaussian Process Regression (GPR) algorithms are deployed to predict the bond strength. The R-value of ABC-ANN and GPR models are 0.9514 and 0.9618 respectively. This research aids researchers in estimating bond strength in less time, at a lower cost, and with less experimental work.


I. INTRODUCTION
Repairing deteriorating, damaged, and deficient civil infrastructure has become a major concern for civil engineers all around the world [1].The rehabilitation of old structures is rapidly expanding, particularly in wealthy countries that finished the majority of their infrastructure in the midnineteenth century [2]. Furthermore, post-World War II constructions gave little consideration to durability concerns, and the United States and Japan lacked understanding of seismic design [3]. Chloride-induced corrosion of steel reinforcements is one of the most prevalent causes of deterioration in reinforced concrete (RC) structures [4]. Reinforcement corrosion reduces the structural performance and service life of RC structures, and affects life-cycle cost of RC structures rises as a result of the maintenance and repair interventions required to address this problem. This issue is particularly serious in some developed countries, where RC infrastructure components have been in use for decades [5,6]. Reinforcing steel corrosion may create cracks in the surrounding concrete owing to the expansion pressure generated during the production of corrosion products, in addition to the loss of effective cross-sectional area of the reinforcing steel [7,8]. The concrete cover may potentially spall as a result of the expansion pressure. In general, such degradation reduces the load carrying capacity of the RC member's or structures and its stiffness [9][10][11]. The escalation of environmental contamination in recent decades has resulted in a substantial increase in corrosion phenomena in RC structures, which has resulted in several collapses, particularly in those structures that have not received appropriate maintenance. [12][13][14][15][16]. The Swiss Federal Laboratory for Materials Testing and Research (EMPA) originally investigated this approach of reinforcing RC beams in the mid-1980s, although much of the research on FRP plate bonding for flexural strengthening has taken place in the last 20 years [17].
The Hyogoken-Nanbu earthquake struck Kobe, Japan, in 1995, causing widespread devastation [18]. As a result, the Japan Building Disaster Prevention Association (JBDPA, 1999) released the Seismic Retrofitting 'Design and Construction Guidelines for Existing RC bridges using Fibre FRP Materials' in September 1999 [19]. As a result, cost-effective and long-lasting solutions are required for concrete structure repair, rehabilitation, replacement, and new construction [20]. Building construction and maintenance might benefit from advanced FRP composite materials [21]. The advanced polymer composite is a hybrid material made up of two major components: fibre and polymer [22]. The fibres have high strength and modulus while matrix material or polymer have low modulus and strength [23]. The fibre uses the matrix's plastic flow to transmit burden/load to the fibre under stress, resulting in a high-modulus and strength composite [24]. The high aspect ratio fibres in the primary phase must be properly distributed and bound with the matrix in the secondary phase. As a result, the fibre, matrix, and interface are the three main components of the composite [25]. To optimize the coupling between the two phases and therefore allow stresses to be dispersed over the matrix and hence transferred to the reinforcement, the interface between the fibre and the matrix must have sufficient chemical and physical bonding stability [26].
FRP has been widely used in civil structure strengthening as a composite material with eminent characteristics [27]. FRP offers several advantages, including corrosion resistance, long durability, and ease of construction, making it one of the finest materials for concrete structure rehabilitation [28]. Bonding is an essential factor in shear and flexural strengthening systems of RC structures. External Bonded FRP (EBF) is the most often used approach for reinforcing existing RC components; nevertheless, despite its simplicity of use, the EBR technique's performance can be significantly harmed by different forms of delamination/debonding of FRP composite from concrete substrate [29].
In concrete sections reinforced with FRP material, the fracture generally begins in the concrete substructure near the FRP strip, and therefore the mechanical properties and failure of the concrete play a major role in retrofitting efficiency. In addition to bond length, FRP strip width, axial stiffness, and its ratio to concrete element width all impact the FRP concrete bond strength [30]. In order to determine the FRP-concrete bond strength, numerous investigational studies have been accompanied to examine the effect of various parameters for both concrete and FRP composite material including adhesive properties [31]. Afterwards on the basis of these investigational and theoretical analysis, several analytical prediction models were developed and implemented in appropriate repair and rehabilitation codes such as fib bulletin [32], Italian National Research Council CNR-DT200/2004 [33], ACI [34], HB305 [35] and CS-TR-55-UK [36].
The majority of these analytical models were developed based on the restricted experiment data, which predict the bond strength in a specific group of data samples, but for other set of data samples the accuracy of the model may be differ depending on the properties of concrete and FRP composite material. Because of the complexities in the offered analytical approaches and the majority of the numerical models given, they are unable to assess the true debonding behaviour. As an alternative and complementary approach, Multiplelinear Regression (MLR) methods are used for predicting bond behaviour: computational methods such as ANN, FL, SVM, FIS, GP, ANFIS, and GEP.
Metaheuristics are well-suited to combinatorial optimization issues because they can frequently discover a satisfactory solution in a reasonable period of time. As a result, they are a viable alternative to exhaustive search, which would require more time. Meta-heuristics are not problem-specific, they may be applied to a wide range of issues. Like, genetic algorithms are used in many possible problems, although they may not always be the best solution to each of these problems. The ABC method is relatively resilient, converges quickly, has a small number of parameters, and is very adaptable.
There are several studies reported in the literature that employed hybrid ANN models in civil engineering applications, and some of them are: Sarir et al. [37] used whale optimization and gene expression programming (GEP) treebased to calculate the bearing capacity of concrete filled steel columns. The GEP tree-based models shows the better performance among all the models (R 2 of Training and testing was 0.928 and 0.939 respectively). The accuracy of PSO-ANN model in terms of coefficient of determination was found as 0.910 and 0.904 for training and testing data respectively. Mansour et al. [38] explored the Neuro-Swarm algorithms to predict the pile settlement. The predicted results reveal that the neuro-swarm model has high accuracy up to a coefficient of determination of 0.892. Apostolopoulou et al. [39] and Sun et al. [40] used ANN and hybrid ABC-ANN to predict and optimized the compressive strength of mortar and concrete samples. Performance of FRP-concrete bond strength by utilizing the ANN and ABC-ANN was evaluated by Jahed et al. [41]. When compared to the ANN model, the anticipated results suggest that ABC-ANN can perform better. The author only employed 150 samples in his dataset, which limits the model's usefulness.
Paji et al. [42] investigated the compressive strength behaviour under fresh and magnetic salty water with machine learning models such as neuro-swarm and neuroimperialism. The training and testing results present the better performance of neuro-swarm optimized algorithm. MLP-GWO (multilayer perceptron -gray wolf optimization) and ANFIS-GWO (adaptive neuro-fuzzy inference system -gray wolf optimization) models were used to calculate the bearing capacity of the piles by Dehghanbanadaki et al. [43]. The results demonstrated that both the MLP and ANFIS approaches were capable of accurately predicting the piles' ultimate bearing capacity. But, MLP-GWO model provided better results in terms of R 2 -value 0.991 for test data. Khari et al. [44] used hybrid neuro-swarm method to forecast the lateral defection of piles. In the lateral deflection prediction process, the suggested PSO-ANN model was proven to be capable of giving high accuracy while also having a low system error. The value of coefficient of determination of training and testing data were 0.953 and 0.944 respectively. Momeni et al. [45] worked on ANN model with two optimizing algorithms, Gravitational Search Algorithm (GSA) and PSO to forecast the deformation of geogrid-reinforced soil structures. The results of both the GSA-ANN and PSO-ANN models were good enough. However, GSA-based ANN prediction model outperforms, with a R-value of 0.981 and a system error of 0.0101 for testing data.
These computational algorithms each have their own structure, as well as various strengths and limitations. It has been demonstrated that their regression abilities are limited [46]. Many researches in the past already done their work in the bond prediction behaviour, but as a consequence, the prediction model established on them is still incomplete and requires additional development.
To accurately design and simulate buildings using FRP composite materials, it is critical to use an accurate and efficient model for forecasting the bond strength of FRPconcrete. Researchers will be able to use the findings of this study, to calculate the FRP-bond strength with greater precision and less experimentation work. The main limitations of this work is that a user can only use the proposed model of this article for an input vector that be within the interval of each input variable.
The work in this paper is divided into seven part. First section deals with the basic information of the degradation of concrete structures, rehabilitation, FRPs and machine learning approaches. In the second section the data related to FRP-concrete bond was collection from the literature and the performance indices used to evaluate the accuracy of this study. In third section, the previously used analytical models were collected and separates into two parts (i) codal models and (ii) models. Codal model are used in the internationally known standards such as Fib, ACI, HB 305 etc. and simple models are directly extracted from the previous articles and used by numerous authors. Section 4 introduces the ANN, ABC-ANN And GPR models. Section 5 deals with the compression of machine learning models with analytical models. In section 6, the proposed formula derived from ABC-ANN is described. The conclusion and future scope are mentioned in the last section.

II. COLLECTION OF DATA
Currently there is no appropriate code for the experimental investigation of FRP-concrete bond strength, and prior studies have only established a few traditional test configurations, such as beams bending tests, single and double shear tests. The bond strength testing setup is depicted in Figure 1. The collected database contains both single and double shear 744 samples results  and parameters which includes f ′ c is the concrete with specified compressive strength (MPa), b f is the width of the FRP laminate/fabric (mm), E f is the modulus of elasticity of FRP material (GPa), t f is the thickness of FRP material (mm), b c is the width of concrete block (mm), f f is the tensile strength of FRP composite (MPa) and L b (mm) is the length FRP bonded material are tabulated in Table 1. Table 2 shows the statistical features of each major component in the database.
where, N is the number of points in the data set, and a and p sets are the actual and projected output sets, respectively.

III. PREDICTION OF BOND STRENGTH USING EXISTING ANALYTICAL FORMULATION
Presently, numerous analytical models for determine the bond strength of FRP-concrete have been established, with varying degrees of success. Some of the most important VOLUME X, 2021 adopted codes in the world recognized association such as ACI, fib bulletin and HB305 were also used to predict the bond strength.

A. CODAL STANDARDS TO PREDICT THE BOND STRENGTH
(a) Codal Model 1 -The first model which is selected in fib Bulletin [32] was given by Neubauer and Rostasy [74] (1997) is expressed below: where, k p is the geometric factor and calculated using below formula. L e is the effective length calculated using equation 8.
(b) Codal Model 2 -To predict the bond strength Chen and Teng [75] (2001) model which was adopted by ACI 440.R-08 [34]. The formula for model prediction is shown below: where, P u = applied load (kN), β p and β L are the geometric parameters, f ′ c is the concrete with specified compressive strength (MPa), L e is the effective length (mm) and b f is the width of the FRP laminate/fabric. The geometric parameter β p , β L and effective length is calculated using below expressions: where, E f is the modulus of elasticity of FRP material (MPa), t f is the thickness of FRP material (mm), b c is the width of concrete block (mm) and L b is the length FRP bonded material.
(c) Codal Model 3 -The fourth FRP bond prediction model is given by Italian National Research Council CNR-DT 200/2004 [33] is expressed as: where, k f is the specific fracture energy and calculated using following formula: where, f c is the mean value of concrete tensile strength. VOLUME X, 2021   [35] standard. The formula given by the authors is expressed as: where, d f = thickness of the failure plane and β a is the range of values as expressed in below equation: where, τ f is the peak interface shear stress and δ f = slip at maximum interface shear stress calculated using below expression: (e) Codal Model 5 -The fifth model is given by the Concrete Society Committee CS-TR-55-UK [36] can be expressed as: where, f c t is the characteristic axial tensile strength of concrete, k b and L e are calculates using equations: where, P u = bond strength (kN), b f = width of FRP laminate/fabric, E f is the modulus of elasticity of FRP material (MPa), t f is the thickness of FRP material (mm), L e is the effective length (mm).
(b) Model 2 - Khalifa et al. (1998) [79] suggested a model to predict the FRP bond strength using equation k and L e is calculated using Equation 29 and Equation 30 respectively.  [80] proposed a model to predict the FRP bond strength using equation k and L e is calculated using Equation 32 and Equation 33 respectively.
where, f f is the tensile strength of FRP material in (MPa) and L e = 100 mm.

IV. ARTIFICIAL INTELLIGENCE TO PREDICT FRP-CONCRETE BOND STRENGTH
To predict the bond strength in this used algorithms are ANN, ANN-ABC and multiple linear regressions.

A. ARTIFICIAL NEURAL NETWORK (ANN)
ANNs are one of the most commonly utilized approaches in the field of artificial intelligence (AI). These techniques are simple, have excellent performance, and have a cheap computational cost [82]. In the literature, there are several varieties of ANNs, including Spiking Neural Networks (SNN), Feedforward Neural Networks (FFNN), Kohonen self-organizing feature map networks (SOM), Recurrent Neural Networks (RNN), and Radial basis function networks (RBF) [83]. The FFNN is the most commonly used and simplest of all ANNs. FFNNs use one-way connections between neurons in various layers to accept information as inputs on one side and produce outputs on another side [84]. FFNNs are classified into two types: Single-Layer Perceptrons (SLP) and Multi-Layer Perceptrons (MLP). There is only one perceptron in SLPs. SLPs, despite their simplicity, are incapable of dealing with non-linear issues. As a result, MLPs with more than one perceptron built in various layers are used [85,86]. In MLP's primary components are the input layer, hidden layer(s), and output layer. The hidden layer contains the activation function, weights, and units (or neurons). Without performing any computational calculation, the input layer takes information from the outer context and transmits it to hidden layers neurons. The majority of a network's internal processing is performed by hidden layers, which are sandwiched in the input and output layers. Finally, the output layer is in charge of delivering network computations to the outside world. The activation function describes how the neurons process the input value to create the output value for the succeeding layer, and the subsequent layers are fully linked by weight.
Data normalization was done before to training the network in order to reduce undesired feature scaling effects and provide higher computational stability. All parameters were converted linearly in accordance with Equation 36 and the Log-sigmoid [87][88][89][90][91][92] activation function detect values in the interval [0, 1]. The normalization process is quantitatively expressed as follows.
where x * = normalizing value, x = original value, x max = upper value in the selected data set, and x min is the lower value in the selected data set.
Artificial neural networks (ANNs) were trained and evaluated using the MATLAB R2021a (MathWorks, 2021) programme [93]. To train the proposed network in MAT-LAB, the feed-forward back propagation method using the VOLUME X, 2021 Levenberg-Marquardt (LM) algorithm was used. The use of a single hidden layer to handle several nonlinear problems has been validated in the literature. Throughout this layer-bylayer training process, the input signals were sent forward, while the error signals were sent back. The weights were continually changed until the output layer gave the desired output. 744 dataset points were divided into three groups on the random basis. For training, validation, and testing, 520 data (70 percent), 112 data (15 percent), and 112 data (15 percent) were acquired, respectively. In the network training process the training and validation sets were employed, while the test and training sets were used to evaluate network performance.
Researchers have used trial and error techniques to identify the optimum number of neurons and the suitable ANN. In this study, 2 to 24 number of neurons were used to define the optimum ANN architecture. To determine the optimum network design, traditional statistical errors and performance metrics, such as MSE and R, were utilized. As a result, the evaluation index (R, MSE) of each pattern is calculated and the outcomes are determined in line with the competence of the responses. Finally, calculate the rank for each of the proposed patterns and the optimum architecture of the network is chosen. The outcomes in the assessment of bond strength in artificial neural network are shown in Table 3.
As indicated in Table 3, the 19 neurons was identified as the best network among all the neurons based on the ranking systems. Figure 3 provides a schematic overview of the selected neural P u estimating networks. The values of the correlation coefficients (R) and MSE in the selected network for training and testing analysis are 0.97094 and 0.9378 and notably small values 0.00105 and 0.00262 respectively. These data demonstrate the optimized artificial neural network's strong capabilities for calculating the bond strength. Although validation of numerical findings is not always included in artificial intelligence-based studies, there have been numerous examples described in the literature where the model dataset is created using numerical modelling without validation [45,94].

B. ARTIFICIAL BEE COLONY -ARTIFICIAL NEURAL NETWORK (ABC-ANN)
For dealing with restricted optimization issues, many deterministic and stochastic methods have been developed. Deterministic methods, such as Feasible Direction [95] and Generalized Gradient Descent [96], involve significant assumptions on the objective function's continuity and differentiability. As a result, their applicability is restricted because these qualities are rarely seen in real-world issues. Stochastic optimization methods, such as Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Evolutionary Programming do not make such assumptions and have been effectively utilized for solving restricted optimization issues in recent years [97]. For numerical optimization challenges, Karaboga developed an Artificial Bee Colony (ABC) method based on honey bee foraging behavior [98]. Karaboga and Basturk evaluated the performance of the ABC method on unconstrained problems to that of other well-known contemporary heuristic algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolution (DE). The ABC method is extended to solve constrained optimization (CO) problems.
One of the most prominent swarm-based heuristic optimization methods is the ABC algorithm. It comprises three sorts of bees: employed bees, onlooker bees, and scout bees. The ABC algorithm makes several assumptions. Among these are: half of the colony is made up of employed bees and other half consists of onlooker bees [93]. The number of employed bees is exactly equal to the number of onlooker bees. The following are the basic steps of the ABC algorithm: The ABC creates a randomly dispersed starting population of SN solutions (food sources), where SN represents the size of the swarm. Let x i = x i1 , x i2 , ..., x in . x i shows the i t h solution in the swarm. Each employed bee x i creates a new applicant solution V i in its near area, as mentioned in Equation 39.
where x i denotes the food supply generated by the employed bees, and n denotes the necessary solution size, random generated number ϕ in the range of 0 and 1, k is a value chosen at random between 0 and the maximum amount of food resources (k̸ =i), between 0 and the maximum number of solutions, j is a random number (weights).
After all employed bees have completed their search, they waggle dance to communicate the food source information with onlooker bees. An onlooker bee evaluates the nectar data of all used bees and picks a food source which is likely to be proportionate to the quantity of its nectar. This probabilistic selection method is a "roulette wheel" selection system, as follows: where, f it i is the fitness value of the i t h swarm solution. It is observed that, the better solution i, the higher probability of the i t h food source will be chosen. The scout bee phase is in charge of determining the maximum number of epochs, which indicates the number of times the solution is permitted to degrade. If a position cannot be enhanced after a certain number of cycles (called a limit), the food supply is thereafter discarded. Assume xi is the discarded source, and the scout bee identifies a new food source to replace it as follows: where, rand(0,1) is a random number within the range [0,1] based on a normal distribution and u b , l b are upper and lower boundaries of the j t h dimension, respectively.  The ABC algorithm's goal is to discover appropriate weights and optimize them in the search environment. To accomplish this goal, several ABC-ANN patterns with varying numbers of bees were created using the suggested 19 neurons in the ANN structure. As a result, the number of bees will be increased until the minimal error is achieved and the test and error research has been completed to identify additional interconnected factors. Table 4, the ABC with 60 bees was recognized as the optimal network established on basis of ranking systems i.e. rank one means optimum number of bees. The test results which obtained from the optimum number of bees in training and testing 0.971409 and 0.956165 are the R values and significantly tiny values 0.00113140 and 0.00187475 are the normalized MSE values.

C. GAUSSIAN PROCESSED REGRESSION (GPR)
GPR is a Bayesian inference method that works with realvalued variables [51]. It is a non-parametric prediction model for a specific dataset function, D = (x i , t i ), i = 1, 2, ..., N VOLUME X, 2021 where x i is an input and t i is a target variable [52]. A distribution function, termed "Gaussian process regression", which may be expressed as, can be used for the Bayesian regression.
In GPR a covariance function called k(x, x') is the primary function. Covariance function can be best performed as: where, σ 2 f = maximum permissible variance and l = length of scale. The output of latent function is given as: Where, f(x) = latent function and ε = Gaussian noise. The latent function is treated as a random variable in GPR. If the difference between x and x' approaches zero for the aforementioned covariance function, this indicates that the f(x) function is near to the real function f(x)'. By adding the noise values, the preceding equation may be rewritten as follows.
where, σ 2 n = variance of n observations and δ(x,x') = Kronecker delta function. The prediction function can be written as: The kernel or covariance function k(x,x') given as:

V. COMPARISON OF PERFORMANCE OF AI MODELS AND EXISTING MODEL
The ANN, mutated ABC-ANN and GPR model, testing and training outcomes are assessed using Equations 1 to 5, used to find out the performance and errors in the predicted values. It should be highlighted that these criteria are evaluated using actual targets created by standardized data in order to offer a clear comparison of model error values. The detailed of each analyzed model is tabulated in Table 5.
The ANN, mutated ABC-ANN, and GPR results are compared to the earlier work, methodologies, and international codes which are mentioned in Equation 6 to Equation 35. Table 6 illustrates the findings of test results obtained from statistical criteria, coefficient of determination R-squared (R 2 ), correlation coefficient (R), as well as error markers of RMSE, MSE, MAE and MAPE. The standard deviation of the original data is 8.7965 which is quite closer to the ABC-ANN model data. Figure 4 and Figure 5 depicts the comparsion study of experimental measured with respect to the predicted data using various AI algorithms and existing models. Figure 6 depicts the scattering of absolute error values (AEV) (kN), so that the error value of the recommended approaches may be compared directly with those of the existing literature models and codal standards. The spreading of values in mutated ANN and GPR models are more focused within the 5 kN range of bond strength. As a consequence, the ABC-ANN and GPR model may be concluded that they are superior than other approaches and have the best precision and robustness. As a result, the AEV of ABC-ANN and GPR are almost (approximately 94.37% of the time) less than 5.98 kN and (approximately 94.33% of the time) less than 5.98 kN respectively.

VI. PROPOSED FORMULATION FROM ABC-ANN
The operation of ANN is only feasible, when the network's input and output weights, as well as bias values, are known at multiple levels. The predicted FRP-concrete bond strength may be calculated using excel spreadsheet application utilizing the findings presented in this Table 7 as a direct form of prediction formulation. Table 7 shows the weight and bias used for predicting the output values. These values are used to find out the X 1 to X 19 constants which were used in the Equation 47.

VII. CONCLUSION AND FUTURE SCOPE
In this article, the FRP-concrete bond strength is evaluated using an ANN, ABC-ANN, and GPR techniques. A hybrid method ABC-ANN is used to optimize the ANN model for better bond strength predictions. In this case, 744 experimental data were gathered from the literature, including concrete compressive strength, FRP laminate/fabric width, FRP material modulus of elasticity, FRP material thickness, concrete block width, FRP composite tensile strength, and FRP bonded material length. All of the data utilized was scaled and standardized between 0 and 1 in order to get the appropriate responses. The ANN, ABC-ANN, and GPR prediction findings were compared with current techniques for evaluating the bond strength of FRP-concrete given by international codal standards and the other four models from the prior literature study. In ANN and ABC-ANN, 70% of the data is utilized for training, 15% for testing, and the remaining 15% for validation. The accuracy of bond strength estimate might be improved by using these two methods, ABC-ANN and GPR. The empirically suggested formulation, which was built utilizing the mutated ABC with ANN's weights and bias, may be easily implemented for bond strength evaluation. The ABC-ANN and GPR prediction results are accurate for more than 90% of experimental data. The main limitations of this work is that a user can only use the proposed model of this article for an input vector that be within the interval of each input variable. Researchers and FRP applicators may benefit from using this model, because it provides good accuracy and consume less time. In future research, the accuracy of this model might be improved by employing a larger number of experimental databases and comparing it to all natural-inspired algorithms in order to improve the prediction of FRP concrete bond strength.