Axial Capacity of FRP-Reinforced Concrete Columns: Computational Intelligence-Based Prognosis for Sustainable Structures

Abstract

Due to the corrosion problem in reinforced concrete structures, the use of fiber-reinforced polymer (FRP) bars may be preferred in place of traditional reinforcing steel. FRP bars are used in concrete constructions to boost the strength of structural elements and retain their longevity. In this study, the axial load carrying capacity (ALCC) of the FRP-reinforced concrete columns has been evaluated using analytical, as well as machine learning, models. A total of fourteen popular analytical models and one proposed machine learning-based model were used to estimate the ALCC of the concrete columns. The proposed machine learning model is based on an artificial neural network (ANN) method. The performance of the ANN, as well as the analytical models, are assessed using six different performance indices. The R-value of the developed ANN model is 0.9758, followed by an NS value of 0.9513. It has been found that the mean absolute percentage error of the best-fitted analytical model is 328.71% higher than the ANN model, and the root-mean-square error value of the best-fitted analytical model is 211.97% higher than the ANN model. The evaluated data demonstrate that the proposed ANN model performs better than the other analytical models. The developed model is quick and easy-to-use to estimate the axial capacity of the FRP-reinforced concrete columns.

1. Introduction

In reinforced concrete (RC) columns, corrosion is an undesired factor that causes the loss of strength and reduces the steel–concrete bond. The presence of corrosion in the RC structure results in the loss of the cross-sectional area of steel and generates excessive pressure, which can cause the cracking of concrete and ultimately leads to the delamination of the covercrete. Axial compressive loads are supported by the columns, which are vertical load-bearing structural elements. The axial load carrying capacity (ALCC) of the structure is responsible for transferring the load from the structure to the foundation. The disintegration of the RC structure is mainly due to the corrosion caused by the reinforcing steel. Steel reinforcement contains a passive oxide layer; once the passive layer is damaged, the corrosion process begins. The covercrete prevents the process of corrosion and protects the steel from rusting. The bond between the steel reinforcements and the concrete fails with the damage in the covercrete, which ultimately leads to the failure of the oxide layer in the steel reinforcing bars. As the stirrups are present outside the longitudinal reinforcement and have a smaller diameter and concrete cover, they tend to corrode faster. Corrosion initiation starts mainly due to two mechanisms: one is carbonation and another is chloride attack. Corrosion caused by chloride attacks is a rising and major problem in RC structures. In coastal areas, the fundamental problem influencing the durability of reinforced concrete (RC) structures is the chloride-induced corrosion of the reinforcing steel. However, in some cases, the construction water also contains chloride ions, which accelerate the corrosion process, and buildings deteriorate at an early stage. In contrast, carbonation is a time-consuming process that happens when the carbon dioxide (CO₂) that is present in the atmosphere attacks the alkalinity of the concrete and ceases its ability to prevent corrosion. The reduction in construction costs, the extension of structures’ lives, and the prevention of the initiation and progression of damage are among the primary aims that may be accomplished by retrofitting techniques. The limitations of the conventional strengthening techniques (concrete jacketing, steel jacketing, etc.) are addressed by the new class of composite strengthening materials (FRP and TRM). Fiber-reinforced polymers, often known as FRP, are a kind of composite material that is becoming an increasingly popular choice for structural retrofitting in a variety of buildings and other types of structures [1,2]. Corrosion resistance, higher strength, low weight, etc., are some of the advantages of these FRP composite materials. Meghdadian et al. [3] retrofitted the core of an RC shear wall system with steel plates and FRP sheets. In another study, Meghdadian et al. [4] studied the nonlinear seismic analysis of composite coupled shear walls strengthened by CFRP sheets. The FRP sheets significantly increase the capacity of the shear wall. A significant amount of research has been done to examine the effectiveness of various FRP reinforcing bars during the past two decades [5,6,7,8,9]. The standard guidelines for the construction and design of structural concrete reinforced with fiber-reinforced polymer bars are ACI 440.1R-15 [10] and CSA S806-12 [11]. However, various studies have also advised not to utilize FRP bars as longitudinal or compression reinforcement in columns. This is because the FRP-reinforced members exhibit unpredictable behavior when subjected to compression. In addition, there is a dearth of information and investigation about the structural performance of FRP-reinforced concrete columns (FRP-RCCs).

Many authors in the literature used FRP composite bars to replace steel reinforcement. The ALCC of the RC columns is mainly affected due to corrosion. Therefore, the partial and full replacement of the reinforcing steel with FRP bars is a good way to tackle corrosion-like problems. However, estimating the ALCC of FRP-RCCs is a tedious process, because it depends on a number of parameters. The analytical models are available in the literature to predict the ALCC of the RC columns but fail due to their assumptions and limited database. The current developments in artificial intelligence (AI) have made it possible to use a different strategy to establish a reliable and robust method for forecasting the ALCC of FRP-RCCs. The application of machine learning (ML) models in civil engineering applications, especially in RC structures, is described [12] in the literature review section.

In this study, a novel and reliable ANN-based ML model has been developed to accurately predict the ALCC of the FRP-reinforced concrete columns. This research paper is categorized into eight parts. The first part covers the basics of corrosion and its effects on RC structures, structural degradation, rehabilitation, and FRP-reinforced rebars. A summarized review of machine learning (ML) applications in concrete structures is presented in Section 2. The significance of this study is summarized in Section 3. In Section 4, the methodology adopted to achieve the objective of this study, as well as the collected database, processing of data, and application of performance indices to find the best-fitted model, are described. Section 5 covers an introduction to AI. The available standard guidelines and an analytical model that can predict the axial capacity of FRP-RCCs are explained in Section 6. The development of the proposed ANN model is also described in Section 6. The results and discussion portion are summarized in Section 7. The findings of the current study and the future scope of work are described in Section 8.

2. Application of ML in Concrete Structures

In the last few years, the applications of ML algorithms in the field of civil engineering have tremendously increased. They cover almost every sector of civil engineering, such as earthquake engineering, concrete technology, foundation engineering, soil mechanics, transportation engineering, the design of steel structures, the design of concrete structures, etc. The highlights of machine learning applications in reinforced concrete columns, beams, and concrete technology, etc., are summarized in the following.

Cakiroglu et al. [13] estimated the axial capacity of FRP-RCCs with a machine learning approach (Kernel Ridge Regression, Support Vector Regression, Lasso Regression, Gradient boosting machine, adaptive boosting, random forest, extreme gradient boosting, and categorical gradient boosting) using 117 datasets, while Murad et al. [14] used only Gene expression programming (GEP). The predicted results show that the extreme gradient boosting algorithm has the greatest precision, with an R-value of 0.9889. The bond strength between Fiber-Reinforced Polymer (FRP) and Fiber-Reinforced Cementitious Mortar (FRCM) with the concrete surface is estimated by Kumar et al. [15,16]. The machine learning algorithms used are Gaussian Process Regression (GPR), Support Vector Machines (SVM), Decision Tree (DT), Ensemble Learning (EL), Linear Regression (LR), ANN, and ABC-ANN, etc. The performance of ANN, GPR, and Artificial Bee Colony (ABC)-ANN models is higher compared to the rest of the models.

Le et al. [17] used ML algorithms to calculate the ALCC of concrete-filled steel tube columns. GPR and ANN algorithms are used to develop the relation between input and output parameters. The effectiveness of the created ANN was evaluated against the current code (ACI [10]) and empirical equations. The performance of the ANN model was better than the rest of the models.

Cakiroglu et al. [18] predicted the ALCC of concrete-filled steel tubular columns with explainable machine learning. It was observed that the LightGBM and CatBoost models outperformed the conventional design codes with accuracy rates of 97.9% and 98.3%, respectively. The compressive strength of lightweight concrete and geopolymer-based sustainable concrete is also determined by Kumar et al. using different machine learning approaches (SVM, LR, EL, GPR, optimized SVM, optimized EL, and optimized GPR). The results show that GPR and optimized GPR have great accuracy compared to other ML models [19,20].

3. Research Significance

In this study, a novel and reliable ANN-based ML model was developed to accurately predict the ALCC of the FRP-reinforced concrete columns. Previous research found that adding FRP rebars to concrete columns significantly improved both their flexural and shear responses. On the other hand, no comprehensive study has produced a solid recommendation for designing FRP-RCCs. Furthermore, previous models in this area relied on a limited set of experimental data and variables for FRP-RCCs. The approaches used to predict the performance of FRP-RCCs are constrained by several factors, including the compressive and tensile strengths of FRP bars. In this study, fourteen analytical models and a machine learning model (ANN) were used to estimate the ALCC of the FRP-RCCs. The established input parameters are used to design the FRP-RCCs using the results of previous investigations. In order to accomplish this objective, a vast variety of input variables, such as the geometric parameters of columns and the mechanical properties of concrete and FRP composites, are taken into consideration. The proposed artificial neural network-based mathematical model was developed to forecast the ALCC of the FRP-RCCs.

4. Dataset and Methodology

This section discusses the collection of the experimental datasets, processing of data, filtration of raw data, and performance indices used to measure the dependability of the analytical and ANN model.

4.1. Collection of Experimental Dataset

A literature review was conducted to collect an experimental dataset of FRP-RCCs (axial capacity) [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]. The ANN model was built using 242 experimental datasets, as shown in

Table 1. Details of the collected database.

Ref.	Input Parameters															Output
	H	Ag	Ctype	f’c	ltype	ρFRP	AFRP	n	dm	EFRP	fFRP	ttype	ds	Cs	Sv	Pu
[21]	3000	372,100	1	43.7	2	1	3721	8	25.4	44.2	608	2	12.7	1	305	15235
[22]	1400	122,500	1	32.6	2	1.9	2327.5	8	60.53	47.6	728	2	39.8	1	120	3929–4006
[23]	1500	73,061.7	1	42.9	2	1.1–3.2	803.68–2337.97	4–12	15.9	55.4	934	2	6.3–12.7	2	35–145	2804–3019
[24]	1500	73,061.7	1	42.9	1	1–2.4	730–1242.05	6–14	12.7	140	1899	1	6.3–9.525	2	35–145	2905–3148
[25]	1400	122,500	1	35	2	0.8–1.9	980–2327.5	8–16	12.7–19.05	46.6–137	728–1902	1–2	9.525–12.7	1	67–120	3900–5159
[26]	1500	73,061.7	1	42.9	1–2	1.7–2.2	1242.04–1607.34	8–10	12.7–15.9	55.4–140	934–1889	1	9.525	1	80	2840–3060
[27]	1000–2000	49,087.4	2	38	2	2.43	1192.8238	6	15.9	62.6	1184	2	9.525	1–2	50–200	1208–2063
[28]	900	14,400	2	34.9	3	1.4	201.6	4	7.9	50	1000	3	6.3	1	100	90--270
[29]	760–3730	73,061.7	1	90	2	1.65	1205.518	6	15.9	43	715	2	9.525	2	76	3830–7126
[30]	800	44,100	1	33.2	2	1.15	507.15	4	12.7	67.9	1641	2	9.525	1	50	615–1285
[31]	800	33,006.4	1	37	2	2.3	759.142	6	12.7	50	1200	2	9.525	2	30–60	479–1309
[32]	800	34,636.1	1	85	2	2.2	761.9942	6	12.7	52	1190	2	9.525	2	30–60	958–1599
[33]	1200	41,600	1	32.75	2	1.83	761.28	6	12.7	46.3	708	2	6.3	1	75–250	787.8–1449.06
[34]	1500	73,061.7	1	70.2	2	2.18–3.27	1592.75–2389.12	8–12	15.9	54.9	1289	2	9.525	2	80	2339–3309
[35]	1500	73,061.7	1	35	1	2.18	1592.745	8	15.9	141	1680	1	9.525	2	80	995–1746
[36]	1500	73,061.7	1	70.2	1	2.18	1592.745	8	15.9	141	1680	1	9.525	2	80	3671
[37]	1500	73,061.7	1	35	2	2.18–3.27	1592.75–2389.12	8–12	15.9	54.9	1289	2	9.525	2	80	852–2134
[38]	1500	73,061.7	1	35	2	2.18	1592.745	8	15.9	54.9	1289	2	9.525	1	80	1511–2060
[39]	1500	73,061.7	1	35.1	2	2.18	1592.745	8	15.9	54.9	1289	2	12.7	2	80	1483–2086
[40]	1500	70,685.8	1	70.2	2	2.18	1540.95	8	15.9	141	1680	2	9.525–12.7	1–2	80	1061–2435
[41]	2000	164,025	1	42.3	2	1	1640.25	6	19.05	48.2–51.3	838–1317	2	9.525	1	152	1943–3200
[42]	2000	164,025	1	42.3	2	1.4–2.5	2296.35–4100.63	8	19.05–25	51.3–54.4	1122–1317	2	9.525	1	152–203	3627–3790
[43]	1800–3600	90,000	1	29.1–55.2	2	1.34–2.55	1206–2295	6–8	50.165	39–44	654–729	3	8	1	150	500–2191
[44]	2000	160,000	1	71.2	2	1	1600	6	19.05	62.7	1236	2	9.525	1	150	3621
[45]	2000	160,000	1	71.2	3	1	1600	6	19.05	62.71646	1646	4	12.7	1	150	3664
[46]	1200	41,600	2	26.8	2	2.22	923.52	6	12.7	59	930	2	7.9	1	75–150	234–1357
[47]	600	40,000	1	25.68	2	0.8–1.5	320–600	4	10–12	43.75–46	574–735	2	8	1–2	30–80	927.7–981.7
[48]	1500	22,500	1	44.7	1	1.4–3.6	315–810	4	10–16	145–151	2000	1	6	1	40–140	113–119
[49]	1500	41,547.6	1	25.6	2	1.63–3.87	677.2259	6–8	12–16	61.4–62.3	1102–1250	2	10	2	50–100	1055–1227
[50]	1150	36,305	1	34	2	0.55–0.92	199.67–334.01	4–5	10	59	930	2	8	2	40–120	342–1286
[51]	2500	73,061.7	1	46.6	2	4.66	3404.675	12	19.05	61.7	1411	2	9.525	2	80	3588
[52]	1750–2500	73,061.7	1	46.6	2	2.19	1600.051	8	15.9	61.8	1449	2	9.525	2	80	1725–1807
[53]	1750–2500	73,061.7	1	46	2	3.28	2396.424	12	15.9	61.8	1449	2	9.525	2	80	1029–1881
[54]	1020–3660	62,730	1	48.4	2	2.87–4.8	1800.35–3011.04	10	19.05	43.4	963	2	9.525	1	300	844–4224
[55]	1750	98,979.8	1	37.4–40.7	2	1.2	1187.758	6	50.165	64	15582	2	32.26	2	50–85	3029–4224
[56]	1100	32,400	1	28.4	3	3.88	1257.12	4	20	45.9	913	4	10	1	60–180	315–1080
[57]	1500	73,061.7	1	52	1–3	1.04–3.3	759.84–2411.03	6–12	12.7–15.9	54.9–144	1289	2	9.525	1–2	80	1775–3620
[58]	1650	122,500	1	38.4–41	2	1.29–2.59	1580.85–3172.75	8–16	50.165	62	1184	2	32.26	1	75–150	133–201
[59]	1200	122,500	1	50	2	3.19–5.13	3907.75–6284.25	8–12	50.17–57.33	45	840	2	8–12	1	38–130	4500–5670
[60]	1600	70,685.84	1	49.3	2	1.6	1130.973	6	15.9	51.2	1372	2	9.5	2	80	2871–3521
[61]	500	22,500	1	37	2	1.63	366.75	6	5.165	41.2	783	3	6	1	90	354.1–774.9
[62]	600–1200	17,671.46	1	40	2	1.63	288.0448	6	50.165	45	800	2	6	1	50	678.62
[63]	1200	14,600	1	26.8	2	2.22	923.52	6	50.165	59	930	2	8	1	75–250	234–1194

. The influencing parameters that affect the ALCC of FRP-RCCs are the height of the specimen (H), gross cross-sectional area (A_g), type of concrete (C_type), compressive strength of concrete (f’_c), type of FRP reinforcement (l_type), percentage of FRP reinforcement ($\rho$_FRP), the cross-sectional area of FRP reinforcing bar (A_FRP), number of FRP bars (n), the diameter of the main FRP bar (d_m), the elastic modulus of FRP bar (E_FRP), the tensile strength of FRP bar (f_FRP), type of tie bar (t_type), the diameter of stirrups (d_s), the configuration of stirrups (C_S), and spacing of stirrups (S_v). The considered output parameter is the axial capacity of the FRP-RCCs (P_u). Normal-weight concrete and geopolymer-based concrete are the types of concrete explored in this paper.

Normal-weight concrete is labeled one, while geopolymer-based concrete is labeled two. The type of FRP reinforcement (l_type) used in the collection database contains three types of FRPs, namely, carbon fiber-reinforced polymer (CFRP), basalt fiber-reinforced polymer (BFRP), and glass fiber-reinforced polymer (GFRP). The BFRP, CFRP, and GFRP labels are one, two, and three, respectively. The considered tie bars (t_type) in the collected database are CFRP, GFRP, BFRP, and steel with labels one, two, three, and four, respectively. The configuration of the stirrups (C_S) includes ties and spirals with labels one and two, respectively. Figure 1 shows the distribution of different input parameters with respect to the output parameter. The statistical parameters, such as minimum, maximum, mean, etc., values, in the selected datasets are shown in

Table 2. Statistical properties of the selected dataset.

S. No.	Parameter	Symbol	Unit	Min.	Max.	(Mean) *	Std.
1.	Height	H	mm	500	3730	(1430.55)	544.81
2.	Cross-sectional gross area	Ag	mm2	14,400	372,100	(64,310.15)	37,405.48
3.	Concrete type	Ctype	-	1	2	(1.07)	0.26
4	Compressive strength of concrete	f’c	MPa	25.60	90	(41.01)	12.31
5.	Type of FRP reinforcement	ltype	-	1	3	(1.99)	0.66
6.	% of FRP reinforcement	$\rho$FRP	%	0.55	5.20	(2.21)	0.98
7.	Area of FRP reinforcement	AFRP	mm2	199.68	6284.25	(1403.13)	963.37
8.	No. of main FRP reinforcement	n	-	3	16	(6.92)	2.45
9.	Diameter of main reinforcement	dm	mm	7.90	60.53	(21.89)	14.77
10.	Elastic modulus of FRP	EFRP	GPa	39	200	(68.69)	36.52
11.	Tensile strength of FRP	fFRP	MPa	450	2000	(1162.74)	393.29
12.	Type of tie bar	ttype	-	1	4	(1.99)	0.61
13.	Diameter of stirrups	ds	mm	6	39.80	(10.21)	5.95
14.	Configuration of stirrups	CS	-	1	2	(1.48)	0.50
15.	Spacing of stirrups	Sv	mm	30	305	(98.19)	52.23
16.	Axial load	Pu	kN	90	15,235	(1867.51)	1574.71

* Mean values are given as statistical parameters.

.

4.2. Data Filtration

A database of 362 experimental results of FRP-RCCs from the literature was collected, and this original database was filtered to improve its reliability model. The data filtration was done on the bases of the kurtosis and skewness of the data. As the dataset has some errors, 120 outliers were removed from the current selection of the dataset. After the removal of outliers, 242 experimental values were used in the development of the ML-based model, and the same dataset was also passed through the analytical models.

4.3. Preparation of Dataset and Performance Criteria

To train machine learning models, the dataset must be pre-processed in a specific order. In this investigation, the dataset was normalized in the range of −1 to +1. Normalization improves computational stability and also helps to reduce feature scaling effects. Equation (1) shows the expression used to normalize the data (−1 to +1).

$$N_{normalized}=2\times \left[\frac{\left(x-x_{min}\right)}{\left(x_{max}-x_{min}\right)}\right]-1$$

(1)

where $N_{normalized}$ is the normalized value, x is the value to be standardized, $x_{min}$ is the minimum value in the selected parameter of the collected database, and $x_{max}$ is the maximum value in the selected parameter of the collected database.

The methodology diagram in Figure 2 illustrates the steps involved in achieving the objective of the current study.

The performance criteria contain different types of performance matrices, such as: correlation coefficient (R), Nash–Sutcliffe efficiency index (NSEI), root-mean-square error (RMSE), a20index, mean absolute error (MAE), and mean absolute percentage error (MAPE). The NSEI and a20-index values, as well as the correlation coefficient, are close to one, indicating the high accuracy of the model. However, the errors such as MAE, MAPE, and RMSE must approach zero to satisfy the precision of the model. The formulations used to calculate these performance indices are expressed in Equations (2)–(7) [64,65,66].

$$R=\frac{{{\displaystyle \sum }}_{i=1}^N\left(Q_i-\overline{Q}\right) \left(U_i-\overline{U}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(Q_i-\overline{Q}\right)}^2 {\left(U_i-\overline{U}\right)}^2}}$$

(2)

$$MAE=\frac{1}{N} {\displaystyle \sum }_{i=1}^N\left|Q_i-U_i\right|$$

(3)

$$MAPE=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left|\frac{Q_i-U_i }{Q_i}\right|\times 100$$

(4)

$$RMSE=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^N{\left(Q_i-U_i\right)}^2}{N}}$$

(5)

$$NS=1-\frac{{{\displaystyle \sum }}_{i=1}^N{\left(Q_i-U_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^N{\left(Q_i-\overline{U_i}\right)}^2}$$

(6)

$$a20-index=\frac{m20}{N}$$

(7)

where N is the total number of collected datasets, $Q_{i }$is the experimental value, $\overline{Q}$ is the mean of the experimental values, $U_i$ is the predicted value, $\overline{U}$ is the mean of predicted values, and m20 is the number of samples obtained from measured values divided by predicted values, and in the range of 0.8 to 1.2.

5. Artificial Intelligence

AI is the imitation of human cognitive processes by technology. Particular uses of AI include expert systems, machine vision, speech recognition, and natural language processing. In general, the functioning of AI systems entails consuming enormous amounts of labeled training data, analyzing these data to look for correlations and patterns, and using those patterns to forecast future states [67,68]. This part of AI algorithms focuses on data acquisition and the creation of rules for transforming data into actionable knowledge. The rules, also known as algorithms, provide computing devices with step-by-step instructions for completing a certain task [69].

A branch of AI known as ML enables software programs to predict future occurrences more accurately without having been explicitly designed to do so. The past is used as input by ML algorithms to predict future output values. Two main categories that can be used to classify ML algorithms are: (a) supervised and (b) unsupervised machine learning. During the training phase of the ML lifecycle, ML algorithms require labeled input and output data. Before being utilized to test and train the model, these training data are frequently labeled by a data scientist during the step known as the preparation phase. In this way, the model may be used to classify new, unseen information and forecast outcomes once the learning process is completed. Unsupervised ML is the training of models on raw and unlabeled training data. It is frequently used to find patterns and trends in unprocessed datasets or to arrange similar data into a predetermined number of categories. It is widely used to better understand the datasets during the initial investigation stage.

6. Description of Analytical Models and Development of ANN Model

6.1. Analytical Models

The ALCC of FRP-RCCs is estimated using fourteen analytical models. The description details of all analytical models with their formulations are shown in

Table 3. Details of analytical models.

S. N.	References	Model	Formulation	Description
1.	Samani and Attard [70]	Model-1	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+0.0025E_{FRP}{A}_{FRP}$	-
2.	Mohammed et al. [26] (A)	Model-2	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\epsilon }_p{E}_{FRP}{A}_{FRP}$	${\epsilon }_p=0.002$
3.	CSA S806-02 [71]	Model-3	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)$	-
4.	AS—3600 [72]	Model-4	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+0.0025E_{FRP}{A}_{FRP}$	-
5.	Mohammed et al. [26] (B)	Model-5	$P_n=0.9{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\epsilon }_{fg}{E}_{FRP}{A}_{FRP}$	εfg = 0.002
6.	Maranan et al. [27]	Model-6	$P_n={\alpha }_1{f}^{\text{’}}{}_c\left(A_g-A_{FRP}\right)+0.002E_{FRPt}{A}_{FRP}$	${\alpha }_1=0.9$
7.	Xue et al. [43]	Model-7	$P_n={\alpha }_1{f}^{\text{’}}{}_c\left(A_g-A_{FRP}\right)+0.002E_{FRPt}{A}_{FRP}$	${\alpha }_1=0.85$
8.	Afifi et al. [23]	Model-8	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\alpha }_g{f}_{FRP}{A}_{FRP}$	${\alpha }_g=0.35$
9.	Hadhood et al. [36]	Model-9	$P_n={\alpha }_1{f^{\prime }}_c\left(A_g-A_{FRP}\right)+0.0035E_{FRP}{A}_{FRP}$	${\alpha }_1=0.85-0.0015{f^{\prime }}_c$
10.	Khan et al. [73]	Model-10	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+\alpha E_{FRP}{A}_{FRP}$	$\alpha =0.61$
11.	CSA S806-12 [11]	Model-11	$P_n={\alpha }_1{f^{\prime }}_c\left(A_g-A_{FRP}\right)$	${\alpha }_1=0.85-0.0015{f^{\prime }}_c\ge 0.67$
12.	Afifi et al. [24]	Model-12	$P_n={\alpha }_1{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\alpha }_{FRP}{f}_{FRPu}{A}_{FRP}$	${\alpha }_1=0.85;{\alpha }_{FRP}=0.25$
13.	Tobbi et al. [22]	Model-13	$P_n={\alpha }_1{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\alpha }_{FRP}{f}_{FRPu}{A}_{FRP}$	${\alpha }_1=0.85;{\alpha }_{FRP}=0.35$
14.	Tobbi et al. [25]	Model-14	$P_n=0.85{f^{\prime }}_c\left(A_g-A_{FRP}\right)+{\epsilon }_{\infty }{E}_{FRP}{A}_{FRP}$	${\epsilon }_{\infty }=0.003$

. For better understanding, the analytical models are assigned different model identities, such in Samani and Attard [70], Mohammed et al. [26] (A), CSA S806-02 [71], AS–3600 [72], Mohammed et al. [26] (B), Maranan et al. [27], Xue et al. [43], Afifi et al. [23], Hadhood et al. [36], Khan et al. [73], CSA S806-12 [11], Afifi et al. [24], Tobbi et al. [22], and Tobbi et al. [25], and are named as Model-1, Model-2, Model-3, Model-4, Model-5, Model-6, Model-7, Model-8, Model-9, Model-10, Model-11, Model-12, Model-13, and Model-14, respectively.

6.2. Artificial Neural Network Backdrop

ANN modeling is an AI-based concept that was established in response to the interest of numerous scientists in the field of computer science. In the same way as the human mind thinks, similarly, AI uses algorithms to create relationships between different variables. The human brain can initiate the learning process by either weakening or strengthening the connections between nerve cells. ANNs are designed to resemble the biological neural networks found in the nervous and brain systems of humans and animals. These networks are employed to analyze tasks based on an important input data parameter, the effects of which are not yet fully understood [36]. The ANN is one of the approaches to artificial intelligence that is regularly used by researchers. The literature describes numerous types of ANNs, such as feed-forward neural networks (FFNNs), spiking neural networks (SNNs), recurrent neural networks (RNNs), Kohonen self-organizing feature map networks (SOMs), and radial basis function networks (RBFNs), etc. One of the most popular and fundamental ANN models is the FFNN, which has been applied in several engineering applications [15]. The FFNNs use one-way connections among neurons in different layers to accept information as inputs and produce outputs. The FFNNs are mainly divided into two parts: single-layer perceptrons (SLPs) and multi-layer perceptrons (MLPs). In ANNs, a variety of software-based models and mathematical models are used to address an extensive range of engineering, scientific, and practical problems in numerous fields. In recent decades, the use of intelligent systems, particularly ANNs, has become so pervasive that these tools can be classified as fundamental and common mathematical operations tools. There are a variety of computational algorithms that have been introduced as ANNs, and each of these models can serve a variety of purposes. ANNs can learn, classify, generalize, and predict variable values due to their ability to retain information introduced during training and adaptability. To improve the model’s general structure and ensure that it operates at a satisfactory level, this training technique is performed.

Each layer consists of a complex network of interconnected “neurons” [74,75,76]. In each of these networks, a mathematical structure with a set of adjustment parameters is considered. The overall structure is modified and optimized using a training procedure to accomplish the desired performance of the model.

The modeling and description of learning in mathematical language involve the assignment of specific parameters called weights and biases. The neuronal values are multiplied by the weights of the connections between each pair of neurons. In the final phase of the process, connections are used to modify the values generated by neurons, which are then added using a bias. The complete formulation to estimate the ALCC of FRP-RCCs is expressed in Equation (8).

$$P_u=f_{HO}\left({{\displaystyle \sum }}_{j=1}^N{W}_{j\left(HO\right)}{Z}_j+K_{HO}\right)$$

(8)

where $f_{HO}$is the activation function in the output layer, $W_{j\left(HO\right)}$ is the weights of the output layer, $Z_j$ is the normalized input values obtained from Equation (9), and K_HO is the output bias.

$$Z_j=f_{IH}\left({{\displaystyle \sum }}_{j=1}^N{W}_{j\left(IH\right)}{N}_{normalized}+K_{IH}\right)$$

(9)

where $f_{IH}$is the activation function in the hidden layer, $W_{j\left(IH\right)}$ is the weights of the hidden layer, and $K_{IH}$ are the hidden layer biases. In Appendix A, an example to estimate the axial capacity of FRP-reinforced concrete columns is given.

The outputs of the activation function produce values for the input process of the neurons of the subsequent layer, as presented in Figure 3. After assigning random beginning weights, the final selected values of the weights are produced by a training procedure using available data [77]. Each ANN layer has a predetermined activation function that impacts its performance [78]. Signals created by neurons travel along the path from top to bottom, as shown in Figure 3.

Development of the ANN Model

The ANN model mainly contains three layers, namely, the input layer (IL), hidden layer (HL), and output layer (OL). According to Section 4, there are fifteen input parameters in the input layer. It is critical to identify the network architecture that provides the best balance of precision and reliability. Since there is no algorithm for estimating the number of hidden layers and the number of neurons located on each layer, the ideal number of hidden layers and neurons was determined by trial and error. In this study, only one HL has been used to develop the ANN model. The neurons in the HL varied from three neurons to twenty-two neurons. The best neuron was chosen based on the performance indices (R and MSE). The correlation value approaching one and the mean squared error approaching zero demonstrate the higher precision of the developed model. The extracted values of the R and MSE (normalized values) of different neurons are shown in

Table 4. Selection of best neuron based on performance criteria.

Neuron	Values								Rank
	R				MSE
	Training	Validation	Testing	All	Training	Validation	Testing	All
3	0.8776	0.9744	0.6363	0.8768	0.006314	0.006466	0.031570	0.010094	15
4	0.9749	0.9260	0.8419	0.9604	0.002522	0.003870	0.007064	0.003398	4
5	0.9377	0.8765	0.7441	0.8336	0.003061	0.009462	0.066793	0.013494	17
6	0.9801	0.9209	0.8791	0.9606	0.001865	0.003829	0.010011	0.003693	5
7	0.9865	0.8160	0.8884	0.9581	0.001290	0.011408	0.006380	0.003523	7
8	0.9842	0.8748	0.8649	0.9599	0.001512	0.007050	0.008649	0.003397	3
9	0.9048	0.4156	0.6146	0.7958	0.009288	0.036732	0.034144	0.017068	19
10	0.9762	0.8238	0.6724	0.9197	0.002299	0.010975	0.023764	0.006782	12
11	0.8510	0.7342	0.7464	0.7769	0.008153	0.015056	0.062307	0.017235	20
12	0.9885	0.9132	0.8479	0.9579	0.001379	0.005058	0.012396	0.003564	8
13	0.9430	0.8376	0.8791	0.8856	0.003440	0.040415	0.007682	0.009571	14
14	0.9706	0.8803	0.8199	0.9355	0.003379	0.006377	0.017911	0.005987	9
15	0.9821	0.8245	0.8734	0.9199	0.001363	0.005888	0.034242	0.006768	11
16	0.9537	0.8930	0.7720	0.9289	0.005970	0.010608	0.015852	0.008130	10
17	0.9648	0.7846	0.7387	0.9128	0.003788	0.015375	0.022055	0.008225	13
18	0.9853	0.9701	0.9689	0.9754	0.001250	0.003510	0.009230	0.002770	1
19	0.9529	0.6910	0.8144	0.8785	0.007226	0.041556	0.017451	0.013854	16
20	0.9809	0.8095	0.0373	0.7944	0.001268	0.009264	0.092013	0.012956	18
21	0.8295	0.1492	0.5001	0.7513	0.017157	0.038012	0.026154	0.021598	21
22	0.9835	0.9242	0.8726	0.9616	0.001627	0.004374	0.010366	0.003335	2
23	0.9843	0.8182	0.6797	0.9283	0.001489	0.009162	0.025395	0.006180	6

. The network design used in this study is referred to as an ANN 15-18-1, where the first character (15) represents the number of ILs, the second character (18) represents the number of neurons in the HL, and the third character (1) represents the number of the output layer. Based on the previous studies, the performance and reliability of the “TanSig” function in the hidden layer are higher compared to other activation functions, such as the “Sigmod”, “Step”, “Sign” and “Linear” activation functions. Similarly, the “purelin” activation function was adopted for the output layer. In this study, the “TanSig” activation function is used between the input and HL of the ANN, while the “purelin” activation function is used between the hidden and OL. The expression of the “TanSig” activation function is shown in Equation (10), and the value of the “purelin” activation function is equal to one.

$$TanSig=\frac{2}{1+e^{-2x}}-1$$

(10)

The correlation coefficient plots of the training, validation, testing, and all datasets with the relevant neurons are shown in Figure 4. It is also evident from Figure 4d, where neuron 18 is designated with a dotted rectangular box and has a greater overall correlation coefficient value.

The plot between the mean squared error and neurons is presented in Figure 5. The plots of the training, validation, testing, and all datasets are shown in Figure 5a, Figure 5b, Figure 5c and Figure 5d, respectively. According to the mean squared values, 18 neurons were chosen as the best neurons, as shown in Figure 5d, and marked with a dotted square box.

7. Results and Discussion

The effectiveness of several analytical models and the ML technique in estimating the axial load carrying capacity of FRP-reinforced concrete columns is covered in this section. A total of six performance indices are used to evaluate the precision and reliability of the existing and ML-based models. A graphical representation of the fitting of the developed model and analytical models is shown by the Taylor diagram. The influence of each individual on the ALCC of FRP-RCCs is depicted by a sensitivity analysis.

7.1. Results of Analytical Models

For simplicity, the analytical models were divided into two groups, and for the easy categorization of the multiple models, this grouping is advantageous. The classification was made on the basis of the R-value. As shown in

Table 5. Performance matrices of analytical models.

Group.	Model	R	MAPE (%)	MAE (kN)	RMSE (kN)	NS	a20-Index
Group-I	Model-1	0.7546	135.82	739.41	1202.40	0.4538	0.4298
	Model-2	0.7546	135.82	739.41	1202.38	0.4538	0.4298
	Model-3	0.7546	135.81	739.40	1202.31	0.4539	0.4298
	Model-4	0.7546	135.82	739.41	1202.40	0.4538	0.4298
	Model-5	0.7546	144.41	759.31	1293.76	0.3976	0.4545
	Model-6	0.7546	144.41	759.31	1293.76	0.3976	0.4545
	Model-7	0.7546	135.82	739.41	1202.38	0.4538	0.4298
Group-II	Model-8	0.7534	181.13	1009.18	1576.13	0.2733	0.4380
	Model-9	0.7609	125.29	711.34	1081.75	0.5365	0.2892
	Model-10	0.7566	139.45	743.11	1225.61	0.4430	0.4545
	Model-11	0.7609	125.27	711.34	1081.68	0.5365	0.2893
	Model-12	0.7551	165.95	879.73	1448.83	0.3305	0.4711
	Model-13	0.7534	181.13	1009.18	1576.13	0.2733	0.4421
	Model-14	0.7546	135.82	739.41	1202.42	0.4538	0.4298

, the R-value of Group-I models is equal to 0.7546, but Group-II has different R-values. Group-I contains the models from Model-1 to Model-7, and Group-II contains the models from Model-8 to Model-14. According to Table 5, the correlation coefficient of Group-1 models is equal to 0.7546. The MAPE value of Model-1, Model-2, Model-3, Model-4, and Model-7 is almost equal to 135.82%. Similarly, the MAPE value of Model-5 and Model-6 is equal to 144.41. The MAE, RMSE, NS, and a20-index of Model-1, Model-2, Model-3, Model-4, and Model-7 are also equal. However, Model-5 and Model-6 have different MAE, RMSE, NS, and a20-index values. The MAPE value of Model-3 is 0.0074%, 0.0074%, 0.0074%, 5.96%, 5.96%, and 0.0074% lower than Model-1, Model-2, Model-4, Model-5, Model-6, and Model-7, respectively. The MAE value of Model-3 is 0.0014%, 0.0014%, 0.0014%, 2.62%, 2.62%, and 0.0014% lower than Model-1, Model-2, Model-4, Model-5, Model-6, and Model-7, respectively. The RMSE, NS and a20-index value of Model-1 are 1202.40 kN, 0.4538 and 0.4298, respectively (also similar to Model-2, Model-3, Model-4, and Model-7). The RMSE, NS, and a20-index of Model-5 and Model-6 are equal to 1293.76K kN, 0.3976, and 0.4545, respectively. The performance of Model-3 is good compared to other Group-1 models, according to all performance indices.

In Group-II, the correlation coefficient of Model-9 and Model-11 is equal to 0.7609. The other performance indices, including a20-index, MAE, MAPE, NS, and RMSE, are also equal. The correlation coefficient of Model-11 is 2.07%, 1.64%, 1.84%, 2.07%, and 1.91% higher than Model-8, Model-10, Model-12, Model-13, and Model-14, respectively. The MAPE value of Model-11 is 30.84%, 0.02%, 10.17%, 24.51%, 30.84%, and 7.77% lower than Model-8, Model-9, Model-10, Model-12, Model-13, and Model-14, respectively.

Similarly, the MAE value of Model-11 is 29.51%, 4.27%, 19.14%, 29.51%, and 3.8% lower than Model-8, Model-10, Model-12, Model-13, and Model-14, respectively. The RMSE value of Model-11 is also lower than other Group-II models. However, the NS value of Model-9 and Model-11 is equal to 0.5365. By considering all the performance indices in Group-II models, the precision of Model-11 is good.

In all the analytical models (Group-I and Group-II), the performance of Model-11 is higher in terms of accuracy and reliability. The scatter plot of all the analytical models is presented in Figure 6. In this figure, some of the experimental values exceed the +30% error range. An almost similar type of plot is observed in all the cases.

7.2. Results of ANN Models

The R-value of the ANN training, validation, testing, and all datasets is 0.9853, 0.9701, 0.9689, and 0.9758, respectively. The MAPE, MAE, RMSE, NS, and a20-index of the ANN training model are 27.47%, 217.91 kN, 324.91 kN, 0.9701, and 0.7222, respectively. Similarly, the performance indices of the ANN validation, ANN testing, and all ANN datasets are shown in

Table 6. Performance matrices of ANN model.

Models (ANN)	R	MAPE (%)	MAE (kN)	RMSE (kN)	NS	a20-Index
Training	0.9853	27.47	217.91	324.91	0.9701	0.7222
Validation	0.9701	29.04	243.47	355.90	0.9385	0.6235
Testing	0.9689	31.84	287.33	427.75	0.9388	0.5833
All	0.9754	29.22	232.04	346.73	0.9513	0.6322

. In an ANN model, the testing dataset performed poorly and reduced the overall precision of the model. The correlation coefficient of the ANN testing dataset is 1.66% and 1.54% lower than the training and validation datasets. The MAPE of the training, validation, and testing dataset is 27.47%, 29.04%, and 31.84%, respectively. The NS of the training dataset is 3.37% and 3.33% higher than the validation and testing datasets, respectively. Similarly, the a20-index of the training dataset is 15.83% and 23.81% greater than the validation and testing datasets.

The scatter plot of the ANN training, validation, testing, and all datasets is shown in Figure 7a, Figure 7b, Figure 7c, and Figure 7d, respectively. Nearly 76% of the training results in Figure 7a fall within the −30% to +30% error range. Similarly, the maximum values in the testing and validation dataset also fall between the −30% and +30% error range.

7.3. Discussion

In this part, the comparison of the best-fit models for Groups I and II using ANN models is described. As mentioned in Section 7.1, the best-fitted models in Group-I and II are Model-3 and Model-11, respectively. The correlation coefficient of Model-3, Model-11, and the ANN model is 0.7546, 0.7609, and 0.9758, sequentially. The other performance metrics of the selected model are shown in

Table 7. Overall results of analytical and ANN model.

Group	Models	R	MAPE (%)	MAE (kN)	RMSE (kN)	NS	a20-Index
Group-I	Model-3	0.7546	135.81	739.40	1202.31	0.4539	0.4298
Group-II	Model-11	0.7609	125.27	711.34	1081.68	0.5365	0.2893
Proposed	ANN-All	0.9758	29.22	232.04	346.73	0.9513	0.6322

. Model-3 and Model-11 both have higher correlation coefficients than the ANN model, which are 29.31% and 28.24% higher, respectively. The MAPE value of the ANN model is 78.48% and 76.67% lower than Model-3 and Model-11, respectively. The MAE and RMSE values of the ANN model are also lower than those of the Group I and II models. Additionally, compared to other models, the NS and a20-index of the ANN model have greater values.

The Taylor plot, shown in Figure 8, shows a graphical representation of the best-fit model. The standard deviation (std.), R, and RMSE values are used to build Taylor diagrams. The green dotted line represents the std. of the original dataset. The plot of the Group-I models is displayed in Figure 8a. Due to identical std. and correlation coefficient values, only three diamond shapes are depicted in Figure 8a. As mentioned earlier, the correlation coefficient of the Group-I models is equal to 0.7546. The standard deviation of Model-1, Model-2, Model-3, Model-4, and Model-7 is approximately equal to 1641.8. However, the standard deviation of Model-5 and Model-6 is equal to 1738.3. Group-I models crossed the standard deviation line of the original dataset. It means that the red diamond shape indicates the positions of Models 1, 2, 3, 4, and 7. Similar to this, the marron diamond shape reveals the locations of Models 5 and 6.

Figure 8b shows the fitting of Group-II models with the ANN model. The RMSE value of the Group-II model lies between 1000 kN to 1500 kN. With lower standard deviation values compared to the original dataset, Models-9 and 11 directly overlap one another. The rest of the models cross the dotted green line. In contrast to the Group-I and II models, Figure 8 clearly shows how the ANN model is fitted. The ANN model is almost above the green dotted line, which also confirms the performance of the ANN model.

7.4. Sensitivity Analysis

To determine the effect of each input parameter on the ALCC of the FRP-RCCs, a sensitivity analysis was also carried out. The influence of different input parameters, including the height of the column, gross cross-sectional area, type of concrete, compressive strength of concrete, type of reinforcement, percentage of FRP reinforcement, the cross-sectional area of FRP reinforcing bar, number of reinforcement bars, the diameter of main FRP bar, the elastic modulus of FRP, the tensile strength of FRP, type of tie bar, the diameter of stirrups, the configuration of stirrups, and spacing of stirrups, are 6.14%, 8.74%, 7.61%, 7.44%, 5.77%, 6.23%, 7.07%, 7.93%, 4.47%, 5.94%, 8.43%, 3.39% 7.84%, 6.82%, and 5.64%, respectively, on the axial capacity of columns. Figure 9 shows the influence of individual parameters on the axial capacity of the column. Among all the parameters, the type of tie bar had the least impact, and the gross area had the highest impact on the axial capacity of the FRP-reinforced concrete column.

7.5. ANN Formulation

As mentioned in Equations (8) and (9), the final formulation to calculate the axial capacity of the FRP-RCCs is expressed as:

$$P_u=-0.2562H_1-0.6818H_2-0.4138H_3+0.3442H_4+0.6794H_5+0.3665H_6-0.2186H_7+0.0162H_8+0.1356H_9-0.1219H_{10}+0.3366H_{11}-0.1624H_{12}-0.0643H_{13}-0.2338H_{14}+0.2614H_{15}+0.6146H_{16}+0.0635H_{17}+0.0597H_{18}+0.5483$$

(11)

The values of H₁, H₂, and H₃ … H₁₈ are given in Equation (12).

$$\left[\begin{array}{l}{H}_1\\ H_2\\ H_3\\ H_4\\ H_5\\ H_6\\ H_7\\ H_8\\ H_9\\ H_{10}\\ H_{11}\\ H_{12}\\ H_{13}\\ H_{14}\\ H_{15}\\ H_{16}\\ H_{17}\\ H_{18}\end{array}\right]=\mathit{tansig}\left[\begin{array}{ccccccccccccccc}-0.5827& -0.8296& -0.6346& -0.9666& 0.2340& -0.8518& -0.5609& -0.8338& -0.4853& 0.0438& -0.1878& -0.2512& 0.5009& -0.4124& 0.2729\\ 0.0723& -2.4522& -0.6674& -1.1529& 0.0858& 0.0041& -0.2373& 0.3052& -0.3725& 0.5354& 1.5488& -0.3435& -1.5813& 0.6435& -0.0808\\ 0.2656& -2.6413& -0.2036& 0.1711& 1.4974& -0.3311& 0.1014& 2.0450& 0.7784& 1.7422& -1.0902& -1.2015& -0.8769& 1.6802& -0.2473\\ -1.6578& -0.0108& -0.9054& 0.0571& -0.5434& -0.3758& -0.3215& 1.7813& 0.6377& -1.1157& 0.7972& 0.0774& 0.5118& 0.0557& 0.6060\\ 0.7488& 0.1225& 0.2548& 0.9867& -0.3134& -0.0721& 0.8007& 0.0979& 0.3640& 0.4308& -1.0478& -0.1737& -0.2355& 0.9088& 0.0347\\ -0.2106& -0.3937& 0.0649& -0.8431& -0.1233& -0.4222& 1.5810& -0.6758& 0.0359& 0.8895& -0.8461& 0.1857& -0.5161& -0.1303& -0.4750\\ -0.5752& -1.1706& 0.6742& -1.7695& 0.4426& 1.2627& 0.4834& -1.3732& -0.6621& 0.8690& -0.2148& 0.9993& -1.3557& -0.2253& 0.6030\\ 0.51816& -1.3115& 0.4526& -0.3394& 0.4739& -0.5386& -0.3947& 1.1873& -0.6302& 0.4543& 1.8916& 0.7649& -0.5212& 1.7632& 1.8756\\ 0.9266& 0.2934& 0.7413& -0.5213& 0.4525& 0.5973& 0.7670& -0.9736& 0.3712& -0.3068& 0.2666& -0.0564& -2.2281& 0.1960& -1.4175\\ 0.1671& -0.1265& -1.1971& 0.1704& 2.2187& -1.6753& 0.9613& 0.2695& -0.5158& 0.2201& 1.2846& 0.4319& 0.7907& -0.9225& -1.0057\\ -0.6508& -2.0762& -0.0101& 0.9812& 0.0077& 1.4384& -0.4446& 1.1282& -0.5702& -0.5056& -0.3634& 0.3736& -1.4670& -0.3122& 0.0531\\ 0.6298& -1.9662& -0.5534& -1.7093& -1.8111& 1.0477& -0.4170& 0.2893& 0.2868& 1.1817& -0.3762& 0.7513& -0.4544& 0.5351& 0.4046\\ 0.9438& 2.0091& -0.5981& 0.6681& -0.7847& 0.8802& -0.2860& -0.5782& 0.6144& 0.9868& 3.2694& 0.4274& -0.9088& -0.0206& -2.0350\\ 0.0097& -0.5401& 1.3089& 0.6558& 0.0631& 0.9111& -2.2218& 1.1285& 0.6963& 0.8654& -1.1089& 0.1233& -0.3251& -0.1323& 0.4052\\ 0.9245& 1.3715& 1.1279& -0.3295& 0.3555& -0.2090& 1.0134& -0.9055& -0.7213& -0.1859& 0.4658& -0.4284& 0.6993& 2.1124& 0.4976\\ 0.7552& 0.0314& 0.8807& -1.7313& 1.2137& -1.0657& -0.6440& 0.5445& -0.3663& 1.2025& 0.7568& -0.8837& 1.2440& 0.3712& -0.1608\\ 1.1201& 0.4953& -1.8330& -0.6915& -0.1528& 0.3137& 0.9074& 1.2418& -0.5146& 0.1960& 0.9462& 0.0098& -1.0206& 1.5247& 1.7170\\ -0.6267& -0.2465& 2.0139& -0.1213& -0.9209& 0.2843& -0.3688& 0.2684& 0.1735& 0.0859& -0.3341& -0.5276& -0.1479& -1.1879& -0.0141\end{array}\right]\times \left[\begin{array}{c}H\\ Ag\\ C_{type}\\ f^{\prime }{}_c\\ l_{type}\\ {\rho }_{FRP}\\ A_{FRP}\\ n\\ d_m\\ E_{FRP}\\ f_{FRP}\\ t_{type}\\ d_s\\ C_s\\ S_v\end{array}\right]+\left[\begin{array}{c}1.9368\\ 1.6644\\ -1.2967\\ 1.1727\\ -0.8391\\ 1.1182\\ -1.2847\\ 0.0742\\ -2.0109\\ 0.1978\\ -0.7532\\ -0.2741\\ 1.2286\\ -0.6611\\ 1.9754\\ -1.6154\\ 1.4589\\ -2.5560\end{array}\right]$$

(12)

8. Conclusions and Future Scope of Work

For estimating the axial capacity of FRP-RCCs, the study described in this paper suggests a reliable numerical method. The procedures involved in developing an ANN model and the data utilized in the phases of training, validation, and testing are explained in detail. The constructed ANN model is compared to a broad range of accessible design codes and approaches from the literature. The devised approach and the outcomes acquired and given in the study are summarized in the following findings:

• The development of computational predictive models requires the collection of an experimental dataset from the literature, which for each sample includes three categories of input variables: geometric dimensions, mechanical properties of concrete and FRP composite materials.
• In Group-I models, the best-fitted model is Model-3, with a correlation coefficient value of 0.7546. The values of other performance matrices such as MAPE, MAE, RMSE, NS, and a20-index are 135.81%, 739.40 kN, 1202.31 kN, 0.4539, and 0.4298, respectively.
• Similarly, in Group-II models, the best-fitted model is Model-11, with performance indices such as R, MAPE, MAE, RMSE, NS, and a20-index being 0.7609, 125.27%, 711.34 kN, 1081.68 kN, 0.5365, and 0.2893, respectively.
• The correlation coefficient of the ANN model is 0.9758, which is 29.31% and 28.24% higher than Model-3 and Model-11, respectively. The general precision of the ANN model is higher compared to the analytical models.
• Researchers, engineers, and other interested users may quickly estimate the ALCC of the FRP-RCCs using the established formulation.

A limitation in the constructed ANN model is that it is only applicable to values that fall within the input and output ranges. As the presented model is developed using only 242 experimental datasets, more experimental data may be added, and the quality of the model can be improved to increase its precision and the permissible range of input and output parameters. To further increase the model’s reliability, some of the less crucial input parameters may be removed from the database.