Compressive strength prediction of admixed HPC concrete by hybrid deep learning approaches

Abstract

The estimation of compressive strength includes time-consuming, finance-wasting, and laboring approaches to undertaking High-performance concrete (HPC) production. On the other side, a vast volume of concrete consumption in industrial construction requires an optimal mix design with different percentages to reach the highest compressive strength. The present study considered two deep learning approaches to handle compressive strength prediction. The robustness of the deep model was put high through two novel optimization algorithms as a novelty in the research world that played their precise roles in charge of model structure optimization. Also, a dataset containing cement, silica fume, fly ash, the total aggregate amount, the coarse aggregate amount, superplasticizer, water, curing time, and high-performance concrete compressive strength was used to develop models. The results indicate that the AMLP-I and GMLP-I models served the highest prediction accuracy. R² and RMSE of AMLP-I stood at 0.9895 and 1.7341, respectively, which declared that the AMLP-I model could be presented as the robust model for estimating compressive strength. Generally, using optimization algorithms to boost the capabilities of prediction models by tuning the internal characteristics has increased the reliability of artificial intelligent approaches to substitute the more experimental practices.

Keywords

HPC concrete compressive strength deep learning arithmetic optimization algorithm grasshopper optimization algorithm

1 Introduction

The massive demand for concrete in every industrial construction caused a vast consumption of materials in concrete production. These issues aimed researchers to look for an optimal concrete that maintains the primary properties of normal concrete and improves the concrete’s mechanical properties. Recently, admixtures like silica fume, fly ash, metakaolin, ground granulated blast furnace slag and rice husk ash are at the top of the admixture list used in concrete mixture designs [1 –6]. Most of the admixtures are applied to substitute the concrete’s cohesive material, mainly the different types of cement [7, 8].

The similarity of fly ash to the normal Portland cement in terms of particle size and shape and water usage reduction percentage paved the way to consider it a partial replacement of cement in the concrete design. The best form of fly ash substitution is achievable with a superplasticizer, which can help improve concrete’s mechanical and applicable properties like strength, workability, durability, eco-saving, and cost-saving properties [9]. Fly ash is partially replaced with cohesive concrete material to reach the optimal concrete design with an alternative enhancement of properties. Reduction of CO₂ emission in using fly ash in a concrete mix design and the reported increment of compressive strength of admixed concrete are mostly feasible [10 –12]. As it is reported, the optimal percentage of fly ash substitution with the cohesive material of the concrete is located between 20% to 50%, where the upper percentage range can be increased up to 10% if the compressive strength in the early days of concrete is unimportant [13, 14].

A concrete’s aggregates can be divided into coarse aggregate, fine aggregate, and filler. The main task of filler is to fill the missed atmosphere between the coarse and fine aggregates. The size of silica fume particles helps this admixture handle the roles of filler and pozzolanic action [15, 16]. Also, the pozzolanic reaction of silica fume and its particle size presents a remarkable increment in concrete properties [17 –22]. Although the rise of silica fume usage in the concrete mix design leads to a decrement in its workability, adding silica fume has a remarkable impact on the short-term compressive strength rising [23, 24]. As the porosity of the concrete decreases, the compressive strength of the concrete tends to increase more. This engagement of compressive strength is rooted in the proper usage of silica fume coupled with superplasticizer (filler properties of silica fume) [25 –27]. A self-consolidating concrete in the sulfuric acid medium admixed with silica fume was implemented in a study. This study replaced about 9% of concrete cohesive material with silica fume. The results demonstrated a considerable increase in the concrete’s CS of with silica fume [28]. Another study also considered the effects of micro-silica on the compressive and flexural strength of cement mortar. This study also declared cement mortar’s compressive and flexural strength enhancement due to micro-silica addition [29].

The compressive strength of concrete is the main indicator of concrete which is the foundation of other properties of concrete. Estimating compressive strength producing samples of concrete with various mix designs is a time-wasting and finance-wasting method normally implemented in different sites and labs. The recent development of artificial intelligence models facilitated the difficulty of compressive strength estimation. [30 –32]. Dao et al. developed ANN and ANFIS-based prediction models to estimate the prediction of compressive strength. They employed 210 samples to put forward the precise estimation of geopolymer concrete compressive strength [33]. In another study, Liker and Mustafa provided a prediction model for compressive strength. They used 52 different concrete mixtures with fly ash for this aim, which ended in 180 samples[34]. Ali et al., in their study, computed the mechanical features of concrete containing tensile strength, compressive strength, and flexural strength for roller compacted concrete pavement. They applied classification-based regression models such as random forest and M5 prime models to implement the prediction of mentioned properties [35]. Saridemir also used a multi-layer neural network to predict concrete’s compressive strength, including micro-silica. He employed 195 samples with 33 various mixture designs. This feedforward multi-layer network provided a robust prediction of compressive strength [30]. Moodi et al. (2022) employed machine learning techniques of Radial Basis Function Neural Networks (RBFNN), ANN, and Support vector regression (SVR) frameworks for estimating the compressive strength of constructional samples without using any adjusting tool to optimize the working procedure of main prediction models and the correlation coefficient values could be computed at 0.971, 0.973, and 0.901, respectively [36]. In another research, Chen et al. (2022), with using 324 concrete samples in a dataset including 5 inputs as independent constituents, namely cement, water, coarse aggregates, fine aggregates, and superplasticizers, modeled the mechanical feature of compressive strength with the conventional support vector regression (SVR) model and without any complementing certain approach. The results operated that the estimation reliability and accuracy of SVR were R² = 0.973, RMSE = 1.595, MAE = 0.312, MAPE = 2.469 [37]. Pazuki et al. utilized an RBF neural network to define the CS. They provided 327 SCC samples including CFFA to generate the estimation model [38]. Behnood et al. [39] developed a hybrid model, coupling ANN, and Grey wolf optimization algorithm to predict the compressive strength of concrete admixed with silica fume. A multi-objective optimization was considered in their study to reach the ANN model with the lowest error. Siddique et al. [40] also used the ANN model to predict the CS of self-compacting concrete, including bottom ash. They studied the effects of input on the compressive strength of various concrete ages. The developed ANN-I and ANN-II models delivered a good prediction of compressive strength.

Based on previous research, most studies have employed the prediction models without using any successor tool to enhance the ability of the main anticipating model. Using the machine learning technique has solely led to setting the arbitrary parameters of models with inefficient desired numbers based on previous research. Alternatively, using optimization algorithms and prediction models separately can enter more errors in the modeling process. Therefore, in the present study, the prediction of CS of an HPC admixed with silica fume and fly ash is goaled utilizing Artificial neural networks (ANN). For this purpose, as the novelty of this paper and in the scientific world, ANN was optimized with an arithmetic optimization algorithm, and a grasshopper optimization algorithm was developed that has not been proposed in any research. Many researchers are using ANN for predictions of specific features of construction materials successfully such as: (Lin and Wu, 2021, Dao et al., 2020, Moradi et al., 2021, Singh et al., 2021, Wu, 2021); however, for GOA and AOA optimization algorithms (Qin et al., 2021, Lv & Peng, 2021, Kandiri et al., 2021, Kaveh & Hamedani, 2022, Agushaka & Ezugwu, 2021, Abualigah et al., 2022, Gürses et al., 2021) with acceptable results [41 –51].

Also, a dataset containing cement, coarse aggregate, total aggregate, fly ash, silica fume, superplasticizer, water, curing time, and compressive strength was applied as input and target values. Three ANN models were optimized with an arithmetic algorithm named AMLP-I, AMLP-II, and AMLP-III, and three optimized with grasshopper algorithms named GMLP-I, GMLP-II, and GMLP-III trained and tested by the abovementioned intakes to achieve a precise prediction model of compressive strength. The evaluation of six proposed hybrid models considered several statistical metrics: R², RMSE, MDAPE, MAPE, and VAF.

2 Materials and methodology

A dataset containing the amount of cement (C), silica fume, fly ash, total aggregates, coarse aggregates, water, superplasticizer, curing time, and compressive strength are collected from the literature [14, 52]. Different mix designs of concrete for the ages of 28 days to 180 days are considered to estimate the long-term and short-term compressive strength of HPC concrete. The dataset is divided into three parts based on the water to cement ratio of 0.3, 0.4, and 0.5. also, the cement applied in this collection is classified as Portland cement of ASTM Ttype1. Moreover, the fly ash is of low calcium, the same as the type of ASTM class F. the frequency of dataset members’ usage in different mix designs is depicted in Fig. 1. In Table 1, the data set’s main statistical properties are also listed. A preferred data set can be categorized into two types: I- independent parameters, as the constituents composed to produce the concrete HPC samples; II-dependent parameters of concrete compressive strength that are altered by the inputs presented as data type I. Thus, all data will be fed to a hybrid model. To this end, the training phase is done to model get learned with input and output (target) values. In this phase, 30 percent of data is used with the sigmoid function. In the next stage, data will be validated in which the model will be asked to produce output values by entering 15 percent of inputs. Then the target values are enrolled in the model to remodify the weights and biases using input (I) and target (II) data based on the Mean Squared Error (MSE). Therefore, in the final testing phase, the remaining 15 percent of inputs will be entered to model the compressive strength values. However, during the modeling process, the number of neurons in hidden layers is optimized to generate the best conditions for working the developed model at a desirable level to have low cost and network complexity [53, 54]. Figure 2 has shown the process of current research stages and coupling ANN with optimizers.

Fig. 1

The histogram of input and target variables: a) C b) CT (day) c) CA/C ratio d) CA/TA ratio e) FA/C ratio f) SF/C ratio g) SP/C ratio (%) h) W/C ratio i) CS value (MPa).

Table 1

Statistical properties’ explanation for data applied in train and test steps

Variables	Abbr	Statistical Properties
		Train Step				Test Step
		Min	Max	Ave	St.dev	Min	Max	Ave	St.dev
Cement (kg/m³)	C	394	500	419.7	41.147	394	500	415.1	37.850
Fly ash (kg/m³)	FA	0	275	98.9	70.87	0	225	106.1	53.062
Micro-Silica (kg/m³)	MS	0	43.3	22.05	17.78	0	43.3	21.3	18.27
Superplasticizer (%)	SP	0	13	4.56	3.26	0	10.5	4.25	2.67
Coarse Aggregates (kg/m³)	CA	1082	1157	1132.6	24.86	1086	1157	1135.8	23.37
Total Aggregates (kg/m³)	TA	1668	1867	1804.9	64.16	1681	1867	1807.7	61.63
Water ((kg/m³)	W	118.2	205	165.05	28.22	118.2	205	167.02	30.51
Curing time (days)	CT	28	180	69.64	49.35	28	180	66.04	51.86
Compressive Strength (MPa)	CS	24	06.3	64.49	4.65	35.6	107.8	62.9	17

Fig. 2

Schematic view of current research stages.

2.1 Artificial neural network (ANN)

Artificial neural network structures are inspired by the biological networks shown in the human brain and are classified as computational black-box processes [55, 56]. A biological neural network consists of a large number of neurons that are connected to influence each other in order to provide optimized results and be highly accurate. An ANN structure mostly contains several layers with different numbers of neurons in the layers. Layer one, called the input layer, is not the operational layer and has tasks that receive data. The several neurons in the input layer rely on the dataset’s number. The hidden and output layers are the operational layers of the ANN structure, each neuron in these layers obtains a signal from the previous neuron and sends an output signal to the succeeding neuron after the process is complete. This strategy includes linear and nonlinear mathematical relationships such as: $N_{j} = \sum_{i = 1}^{n} I N_{i} w_{i, j} + B_{j}$ (1) $OU T_{J} = f (N_{j})$ (2)

In Equations (1) and (2), B_j is the bias of jth neuron, IN_i is the ith input signal. w_i,j is the ith input of jth neuron’s weight. In addition, f is the activation function. The best-known activation function is the hyperbolic tangent-sigmoid function, which is utilized in this work as the hidden layer activation function and is constructed in the following [57 –59]. $f (N_{j}) = \frac{2}{1 + 2 \times e^{- 2 \times N_{j}}} - 1$ (3)

The output layer structure has one neuron and is organized as an operation layer. The activation function for this layer is primarily a pure line.

In addition, a training method is run on the ANN model, and biases and weights are set so that the precision of the model output matches a satisfactory level. This training function in this study is the Levenberg-Marquardt algorithm because of its high performance in compressive strength prediction models [60].

2.2 Arithmetic optimization algorithm (AOA)

The Arithmetic Optimization Algorithm is a candidate-based algorithm with an algebraic concept that uses arithmetic operators to update and find new positions of a set without calculating their results [61]. Arithmetic is one of the fundamental algorithmic procedures of number theory that begins with the initialization of randomly generated candidate solutions and is a major feature of current mathematics. $C = [\begin{matrix} c_{1, 1} & \dots & c_{1, j} \\ ⋮ & ⋱ & ⋮ \\ c_{N, 1} & \dots & c_{N, j} \end{matrix}]$ (4)

The algorithm contains two main sections: exploitation and search. Then developing the initial candidates, need to define and implement the exploration or development search space utilizing the Mathematical Optimizer Accelerator Facility (MOA). $MOA = Min + iter \times (\frac{Max - Min}{Ma x_{iter}})$ (5)

Where Max and Min determine the maximum and minimum values of MOA. The iter is the current iteration and Max_iter is the number of maximum iterations.

The exploratory search function is performed by highly distributed values applying arithmetic multiplication (M) and division (D) operators to the exploratory search function. Operators M and D produce high variability and do not help to achieve goals, but applying subtraction (S) and addition (A) arithmetic operators in the utilization stage leads to the best goals.

If r₁ > MOA the search step of the algorithm is in progress. Using the M and D operators, he position of the search step is updated utilizing Equation 6.

$c {(iter + 1)}_{i, j} = {\begin{matrix} best (c_{j}) \div (MOP + ɛ) \times ((ub - lb) \times μ + lb) r_{2} > 0.5 \\ best (c_{j}) \div (MOP) \times ((ub - lb) \times μ + lb) otherwise \end{matrix}$ (6)

Where best (c_j) is the global best position, lb and ub are the lower and upper the explore area’s bound. ɛ shows a little value, and μ sets the control parameter to explore the method and is set to 0.499 in this study. MOP is determined as math optimization probability and is computed in the following. $MOP (iter) = 1 - \frac{ite r^{1 / - α}}{Ma {x_{iter}}^{1 / - α}}$ (7)

In Equation 7, α denotes the precision sensitivity parameter used during the iteration and is equal to 5.

In addition, if r₁ < MOA the exploit step occurs. In this step, arithmetic operators S and A are applied for the deep dense domain search. This depth-first exploration is modeled in the following:

$c {(iter + 1)}_{i, j} = {\begin{matrix} best (c_{j}) - (MOP) \times ((ub - lb) \times μ + lb) r_{3} > 0.5 \\ best (c_{j}) + (MOP) \times ((ub - lb) \times μ + lb) otherwise \end{matrix}$ (8)

The schematic flowchart of the hybrid arithmetic base neural network is shown in Fig. 3.

Fig. 3

Hybrid AMLP predictive model’s schematic flowchart.

2.3 Grasshopper optimization algorithm (GOA)

GOA is a swarm-based algorithm that models the behavior of the grasshopper insect to converge on the best solution [62]. The life cycle of a grasshopper includes egg, nymph, and adulthood [63]. In adulthood, a grasshopper exhibit a swarm-based demeanor covering long distances, with two characteristics: long range and rapid movements. The behavior of this grasshopper can be represented by a formula in the following: $x_{i} = S_{i} + G_{i} + A_{i}$ (9)

Hence, x_i determines the position of ith grasshopper, and S_i is the parameter that shows the social interaction of grasshoppers.

$\begin{matrix} S_{i} = \sum_{\begin{matrix} j = 1 \\ i \neq j \end{matrix}}^{N} s (d_{ij}) {\hat{d}}_{ij}, d_{ij} = | x_{i} - x_{j} |, \\ {\hat{d}}_{ij} = \frac{x_{i} - x_{j}}{d_{ij}} \end{matrix}$ (10)

d_ij donates the space between ith and jth grasshopper and ${\hat{d}}_{ij}$ shows the unit vector between ith and jth grasshopper. s shows the social force’s strength. $s (x) = f e^{\frac{- x}{l}} - e^{- x}$ (11)

In Equation 11, f and l show the strength or length of the force of attraction. Since locusts are wingless, wind direction is the main criterion for movement. $A_{i} = u {\hat{e}}_{w}, G_{i} = - g {\hat{e}}_{g}$ (12)

Where G_i and A_i are the gravity force and wind advection of ith grasshopper. ${\hat{e}}_{w}$ and ${\hat{e}}_{g}$ are the unit vector that defines the direction of wind advection and the direction of gravity force to the center of the earth. Furthermore, g and u are the gravity constant and the wind drift constant, respectively. Considering Equations (10)–(12), Equation (9) can be rewritten as follows. $X_{j}^{d} = c [\sum_{\begin{matrix} j = 1 \\ i \neq j \end{matrix}}^{N} c \frac{u b_{d} - l b_{d}}{2} s (| x_{i}^{d} - x_{j}^{d} |) \frac{x_{i} - x_{j}}{d_{ij}}] + {\hat{D}}_{d}$ (13)

ub_d and lb_d are the upper and lower boundary, ${\hat{D}}_{d}$ is the dth dimension value, and N is the population number. c is a reducing coefficient. c is reducing with the Increase iterations to balance exploitation and search. This parameter improves utilization as the number of iterations increases. $c = c_{max} - Iter \times \frac{c_{max} - c_{min}}{M . Iter}$ (14)

In the present study, the values of c_min and c_max are equal to 0.0001 and 1, respectively. In Fig. 4, the flowchart of optimizing the ANN model by the Grasshopper algorithm.

Fig. 4

Hybrid GMLP predictive model’s schematic flowchart.

2.4 Evaluation of hybrid models

Some statistical measures are believed to assess the robustness of the two new hybrid models (GRBFN and ERBFN).

∘ Coefficient of determination (R²): $R^{2} = {(\frac{\sum_{n = 1}^{N} (t_{n} - \bar{t}) (p_{n} - \bar{p})}{\sqrt{[\sum_{n = 1}^{N} {(t_{n} - \bar{p})}^{2}] [\sum_{n = 1}^{N} {(p_{n} - \bar{p})}^{2}]}})}^{2}$ (15)

∘ Root mean squared error (RMSE): $RMSE = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} {(t_{n} - p_{n})}^{2}}$ (16)

∘ Mean absolute percentage error (MAPE): $MAPE = \frac{1}{N} \sum_{n = 1}^{N} (\frac{t_{n} - p_{n}}{t_{n}} \times 100 %)$ (17)

∘ Median of absolute percentage error: $MDAPE = median (\frac{t_{n} - p_{n}}{t_{n}} \times 100 %)$ (18)

∘ Variance account factor $VAF = (1 - \frac{var (t_{n} - p_{n})}{var (t_{n})}) * 100$ (19)

Where t_n and p_n are measured and predicted values, respectively. N shows the samples’ total number. $\bar{p}$ and $\bar{t}$ determine the average values of predicted and measured parameters, respectively.

3 Results and discussion

Compressive strength (CS) estimation is the main issue considered in evaluating concrete properties. The experimental process of CS prediction is done by making a sample for each concrete mixture design. Also, highlighting the effect of admixtures on the CS with the experimental form requires an extended range of time, budget, and laboring. Moreover, the huge volume of concrete consumption needed material, and CO₂ emission forced researchers and constructors to apply by-product admixtures in the concrete mix design. The present study employs the concrete mix design of two admixtures, fly ash and silica fume. These admixtures are replaced with the cohesive material of HPC concrete with the presence of a superplasticizer. A different mix of concrete containing fly ash, silica fume, and superplasticizer is tested, and the compressive strength is recorded.

Two hybrid feedforward multi-layer perceptron neural networks (MLP) optimized by arithmetic optimization algorithm and grasshopper optimization algorithm employed to perform the compressive strength prediction of the concrete. In the process of modeling, six predictive models one hidden layer AOA base MLP (AMLP-I), two hidden layers AOA base MLP (AMLP-II), three hidden layers AOA based MLP (AMLP-III), one hidden layer GOA based MLP (GMLP-I), two hidden layers GOA based MLP (GMLP-II), and three hidden layers GOA based MLP (GMLP-III) developed to serve the best prediction of compressive strength. Also, in these models, the number of neurons in each hidden layer structure is optimized by the optimization algorithms, and Levenberg-Marquardt was in charge of training the weights and biases. The activation function of the hidden layers is assumed to be the sigmoid activation function, and the output layer utilizes the pure line as an activation function.

The intake set of data to run the hybrid proposed models included cement, fly ash/cement ratio, silica fume/ cement ratio, superplasticizer/cement ratio, coarse aggregate/cement ratio, total aggregate/cement ratio, water/cement ratio, curing time as input and the compressive strength as target values. The data set is normally rand-permed to have all ages of concrete and all percentage of admixture in both the training and testing step, then the data set is divided into the training and testing phase with the proportion of 70% and 30%, respectively. Table 1 shows that the maximum and minimum data in the training and testing step represent the fair use of all materials ranges in both phases.

Introduced statistical indicators to assess the accuracy of models. Based on these metrics, the workability and performance of the models are evaluated, and the best model that outperforms an acceptable prediction can be selected accurately. The statistical metrics used in this study are R², RMSE, MAPE, MDAPE, and VAF.

The robustness of the models is validated considering the RMSE values of proposed hybrid models with the model developed by Yin et al. [52], which applied the same data set in their study. The best value of RMSE obtained from the Yin et al. work stood at 4.876, and the RMSE’s value for this paper is 1.7341, which declared the precise accuracy of the proposed hybrid models.

Table 2 shows AMLP and GMLP with one, two, and three hidden layers considering the R² and RMSE. As it is clear from Table 2, in both models, the best amount of R² and RMSE is for a model with a hidden layer, namely AMLP-1 and GMLP-I. in both hybrid models, the layered model shows a good convergence in the training phase and testing phase as well. It is noticeable that the AMLP and GMLOP model, the AMLP-II, and GMLP-II present the weakest results compared to other delivered models. Also, for both AMLP-I and GMLP-I, R² and RMSE are better than the training phase.

Table 2
Statistical properties of the training and the testing phases of all hybrid models

Models Number of Hidden Layers Training step Testing step

RMSE R² RMSE R²

AMLP-I 1 2.2271 0.977 1.7341 0.9895

AMLP-II 2 2.6432 0.9677 2.2392 0.9849

AMLP-III 3 2.4516 0.9739 1.9555 0.9874

GMLP-I 1 2.4995 0.9708 2.5828 0.9779

GMLP-II 2 2.7149 0.9664 2.6567 0.9754

GMLP-III 3 2.609 0.9684 2.5793 0.9778

Models	Number of Hidden Layers	Training step	Testing step
AMLP-I	1	2.2271	0.977	1.7341	0.9895
AMLP-II	2	2.6432	0.9677	2.2392	0.9849
AMLP-III	3	2.4516	0.9739	1.9555	0.9874
GMLP-I	1	2.4995	0.9708	2.5828	0.9779
GMLP-II	2	2.7149	0.9664	2.6567	0.9754
GMLP-III	3	2.609	0.9684	2.5793	0.9778

Figure 5 represents the k-fold cross-validation of the AMLP model and GMLP model in the training and the testing step.it is obvious from Fig. 5(a–d) that each model’s best results are for the models with one hidden layer. Also, the figure demonstrates that the worst results are for models with two hidden layers in both models.

Fig. 5

The k-fold cross-validation of hybrid AMLP and GMLP models in the train and the test phases: a) AMLP-Train b) AMLP-Test c) GMLP-Train d) GMLP-Test.

As demonstrated in Table 2, the AMLP-I and GMLP-I model performs best in their group. As it is clear from Table 3, the best R² values are obtained from AMLP-I in the test phase, and the next model with a higher R² value is the GMLP-I in the testing phase. AMLP-I model could get 0.9770 in the training phase while GMLP-I could obtain 0.9708 with 0.6% lower than the earlier model. However, in the testing phase, AMLP-I was 0.8% more than GMLP-I with the correlation index of R² with 98.95% and 98.17% for the AMLP-I and GMLP-I alternatively. However, Ayubi rad, in a study, employed the model LSSVR -least square support vector regression- according to the couple simulated annealing (CSA) for finding the non-linear relation between the mechanical compressive strength feature of concrete and eight ingredients as inputs containing cement, the water, the fine aggregates, fly ashes, the superplasticizer, the blast furnace slags, the coarse aggregates, Ages of the sample). According to the R² index of 92% and RMSE error indicator of 6.17 MPa, train and test results have indicated that the ANN model and CSA-LSSVR have great potential to predict the compressive strength rates [64]. In another study, Gholampour et al. investigated the application of machine learning to estimating concrete constituents. In another study, Dao et al. (2020) utilized ANN to estimate the compressive strength rates of constructional materials. That maximum R² value was calculated as 0.976 in the training phase, and an R² in the test phase was computed as 0.972 [44]. The best RMSE values are the least that belong to the AMLP-I model again in the testing phase, and the highest RMSE value is for the GMLP-I model in the training phase. AMLP-I model could be assessed by RMSE at a level of 2.23 MPa in the training phase, while GMLP-I could obtain 2.50, which is 12.1% higher than the earlier model. However, in the testing phase, AMLP-I was 33% more than GMLP-I, with the correlation index of RMSE with 1.73 and 2.30 MPa for the AMLP-I and GMLP-I, respectively.

Table 3

The output results of the best models in the training and testing steps considering statistical metrics

Best Models	Structure	Step	Statistical Metrics
			R²	Rank	RMSE	Rank	MAPE	Rank	MDAPE	Rank	VAF	Rank	Total Rank
AMLP-I	9-13-1	Train	0.9770	2	2.2271	3	2.2818	2	1.4099	2	97.6454	2	11
		Test	0.9895	4	1.7341	4	1.9750	4	1.5208	1	98.9055	4	17
GMLP-I	9-30-1	Train	0.9708	1	2.4995	1	2.2850	1	0.9526	3	97.0298	1	7
		Test	0.9817	3	2.2956	2	2.2139	3	0.7948	4	98.0724	3	15

In contrast with R², the second stage considering RMSE value is for the training step of the AMLP-I model. The MAPE values caught from the models showed the same trend as R2. Also, from the MAPE index point of view, the AMLP-I model was assessed by MAPE at a level of 2.2818 MPa in the training phase, while GMLP-I could obtain 2.2850 MPa. However, in the testing phase, AMLP-I was 13% more than GMLP-I with the correlation index of R² with 1.97 and 2.21 MPa for the AMLP-I and GMLP-I, respectively. In the case of MDAPE, GMLP-I achieved the best values in both the training and the testing. The VAF values also went by the R² value with the same ranking. The best model among four models with delivered results in Table 3 is evaluated through a ranking system. The ranking system showed that the AMLP-I and GMLP-I models caught the first and second stages in the test phase. Moreover, the third and fourth stages are for the AMLP-I and GMLP-I in the training phase.

A comprehensive understanding of models’ behavior is obtainable from the scatter plot drawn for the AMLP models and GMLP models in Fig. 6. The scatter plot proves that the test phase performed better in all models than in the training phase. The GMLP-I and AMLP-I have the best behavior compared with other models. Also, the fitted line for AMLP-I in the test phase depicted the best matches with the Y = X line. GMLP-I with R² of 0.9708 in the training phase was improved in the testing phase by as much as one percent with the rate of 0.9817. But relative to GMLP-II correlation rate was reduced to 0.9664 with a 0.45% reduction percentage. By increasing the number of hidden layers to three, the R² index was calculated at 0.9684.

Fig. 6

Scatter plot of hybrid AMLP and GMLP models: a) AMLP-I b) AMLP-II c) AMLP-III d) GMLP-I e) GMLP-II f) GMLP-III.

4 Conclusion

The HPC compressive strength estimation is studied in this work. A data set is including fly ash and silica fume considered to develop the prediction model. Two multi-layer perceptron-based prediction models were optimized by arithmetic, and grasshopper optimization algorithms were applied to perform the compressive strength prediction. The outset of results can be summarized as follow.

A dataset containing fly ash and silica fume integrated with a superplasticizer was employed to run the proposed prediction models

An arithmetic optimization algorithm optimized two multi-layer perceptron models, and grasshopper optimization algorithms were applied to implement the prediction.

The AMLP-I model showed its precise capability to predict the HPC compressive strength.

The GMLP-I model also generated a robust prediction with acceptable accuracy in the prediction of compressive strength.

The best prediction accuracy was obtained from AMLP-I in the test phase, and the lowest prediction accuracy was obtained from GMLP-I in the training phase.

The output of both models showed a robust prediction potential of compressive strength. However, the AMLP-I showed the best results and was better qualified to model the prediction of compressive strength.

References

Xie

, Fang

, Lu

, Li

and Li

, Effects of the addition of silica fume and rubber particles on the compressive behaviour of recycled aggregate concrete with steel fibres, J. Clean. Prod. 197 (2018), 656–667. doi: 10.1016/j.jclepro.2018.06.237.

Ahmed

, Al-Dawood

, Abed

, Mannan

M.A.

and Al-Samarai

, Impact of using different materials, curing regimes, and mixing procedures on compressive strength of reactive powder concrete - A review, J. Build. Eng. 44 (2021), 103238. doi: 10.1016/j.jobe.2021.103238.

Ahmed

, Mahaini

, Abed

, Mannan

M.A.

and Al-Samarai

, Microstructure and Mechanical Property Evaluation of Dune Sand Reactive Powder Concrete Subjected to Hot Air Curing, Materials (Basel) 15(1) (2021), 41. doi: 10.3390/ma15010041.

L.G.

, Huang

Z.H.

, Zhu

, Kwan

A.K.H.

and Chen

H.Y.

, Synergistic effects of micro-silica and nano-silica on strength and microstructure of mortar, Constr. Build. Mater. 140 (2017), 229–238. doi: 10.1016/j.conbuildmat.2017.02.115.

Eskandari-Naddaf

and Kazemi

, ANN prediction of cement mortar compressive strength, influence of cement strength class, Constr. Build. Mater. 138 (2017), 1–11. doi: 10.1016/j.conbuildmat.2017.01.132.

Duran Atiş

, Strength properties of high-volume fly ash rollercompacted and workable concrete, and influence of curing condition, Cem. Concr. Res. 35(6) (2005), 1112–1121. doi: 10.1016/j.cemconres.2004.07.037.

Cho

Y.K.

, Jung

S.H.

and Choi

Y.C.

, Effects of chemical composition of fly ash on compressive strength of fly ash cement mortar, Constr. Build. Mater. 204 (2019), 255–264. doi: 10.1016/j.conbuildmat.2019.01.208.

Lezgy-Nazargah

, Emamian

S.A.

, Aghasizadeh

and KhaniPredicting

, the mechanical properties of ordinary concrete andnano-silica concrete using micromechanical methods, Sādhanā 43(12) (2018), 196. doi: 10.1007/s12046-018-0965-0.

Zhang

, Afzal

Prediction of the elastic modulus of recycled aggregate concrete applying hybrid artificial intelligence and machine learning algorithms, Struct. Concr., 2021.

10.

Hansen

T.C.

, Long-term strength of high fly ash concretes, Cem. Concr. Res. 20(2) (1990), 193–196. doi: 10.1016/0008-8846(90)90071-5.

11.

, Chen

and Zheng

, Artificial Intelligence in Civil Engineering, Math. Probl. Eng. 2012 (2012), 1–22. doi: 10.1155/2012/145974.

12.

Ganesh Babu

and Siva Nageswara Rao

, Efficiency of fly ash in concrete with age, Cem. Concr. Res. 26(3) (1996), 465–474. doi: 10.1016/S0008-8846(96)85034-4.

13.

Ganesh Babu

and Siva Nageswara Rao

, Early strength behaviour of fly ash concretes, Cem. Concr. Res. 24(2) (1994), 277–284. doi: 10.1016/0008-8846(94)90053-1.

14.

Lam

, Wong

and Poon

, Effect of Fly Ash and Silica Fume on Compressive and Fracture Behaviors of Concrete, Cem. Concr. Res. 28(2) (1998), 271–283. doi: 10.1016/S0008-8846(97)00269-X.

15.

Huang

, Jiang

, Wang

, Zhu

and Afzal

, Prediction of long-term compressive strength of concrete with admixtures using hybrid swarm-based algorithms, Smart Struct. Syst. 29(3) (2022), 433–444.

16.

Sabir

B.B.

, Mechanical properties and frost resistance of silica fume concrete, Cem. Concr. Compos. 19(4) (1997), 285–294. doi: 10.1016/S0958-9465(97)00020-6.

17.

Bajja

, Dridi

, Darquennes

, Bennacer

, Le Bescop

and Rahim

, Influence of slurried silica fume on microstructure and tritiated water diffusivity of cement pastes, Constr. Build. Mater. 132 (2017), 85–93. doi: 10.1016/j.conbuildmat.2016.11.097.

18.

Rostami

and Behfarnia

, The effect of silica fume on durability of alkali activated slag concrete, Constr. Build. Mater. 134 (2017), 262–268. doi: 10.1016/j.conbuildmat.2016.12.072.

19.

, Xiao

, Yuan

and Ou

, Microstructure of cement mortar with nano-particles, Compos. Part B Eng. 35(2) (2004), 185–189. doi: 10.1016/S1359-8368(03)00052-0.

20.

Singh

L.P.

, Karade

S.R.

, Bhattacharyya

S.K.

, Yousuf

M.M.

and Ahalawat

, Beneficial role of nanosilica in cement based materials - A review, Constr. Build. Mater. 47 (2013), 1069–1077. doi: 10.1016/j.conbuildmat.2013.05.052.

21.

Mukhopadhyay

A.K.

Next-Generation Nano-based Concrete Construction Products: A Review, in Nanotechnology in Civil Infrastructure, Berlin, Heidelberg: Springer Berlin Heidelberg (2011), 207–223. doi: 10.1007/978-3-642-16657-0_7.

22.

L.G.

, Zheng

J.Y.

, Zhu

and Kwan

A.K.H.

, Combined usage of micro-silica and nano-silica in concrete: SP demand, cementing efficiencies and synergistic effect, Constr. Build. Mater. 168 (2018), 622–632. doi: 10.1016/j.conbuildmat.2018.02.181.

23.

Cherian

, Determining the amount of earthquake displacement using differential synthetic aperture radar interferometry (D-InSAR) and satellite images of Sentinel-1 A: A case study of Sarpol-e Zahab city, Adv. Eng. Intell. Syst. 1(01) (2022).

24.

Mazloom

, Ramezanianpour

A.A.

and Brooks

J.J.

, Effect of silica fume on mechanical properties of high-strength concrete, Cem. Concr. Compos. 26(4) (2004), 347–357. doi: 10.1016/S0958-9465(03)00017-9.

25.

Norhasri

M.S.M.

, Hamidah

M.S.

and Fadzil

A.M.

, Applications of using nano material in concrete: A review, Constr. Build. Mater. 133 (2017), 91–97. doi: 10.1016/j.conbuildmat.2016.12.005.

26.

Rashad

A.M.

, A comprehensive overview about the effect of nano-SiO2 on some properties of traditional cementitious materials and alkali-activated fly ash, Constr. Build. Mater. 52 (2014), 437–464. doi: 10.1016/j.conbuildmat.2013.10.101.

27.

Shaikh

F.U.A.

, Shafaei

and Sarker

P.K.

, Effect of nano and micro-silica on bond behaviour of steel and polypropylene fibres in high volume fly ash mortar, Constr. Build. Mater. 115 (2016), 690–698. doi: 10.1016/j.conbuildmat.2016.04.090.

28.

Jalal

, Pouladkhan

, Harandi

O.F.

and Jafari

, Comparative study on effects of Class F fly ash, nano silica and silica fume on properties of high performance self compacting concrete, Constr. Build. Mater. 94(90) (2015), 104.

29.

Azimi-Pour

and Eskandari-Naddaf

, ANN and GEP prediction for simultaneous effect of nano and micro silica on the compressive and flexural strength of cement mortar, Constr. Build. Mater. 189 (2018), 978–992. doi: 10.1016/j.conbuildmat.2018.09.031.

30.

Sarıdemir

, Effect of specimen size and shape on compressivestrength of concrete containing fly ash: Application of geneticprogramming for design, Mater. Des. 56 (2014), 297–304. doi: 10.1016/j.matdes.2013.10.073.

31.

Özcan

, Gene expression programming based formulations forsplitting tensile strength of concrete, Constr. Build. Mater. 26(1) (2012), 404–410 doi: 10.1016/j.conbuildmat.2011.06.039.

32.

Masoumi

, Najjar-Ghabel

, Safarzadeh

and Sadaghat

, Automatic calibration of the groundwater simulation model with high parameter dimensionality using sequential uncertainty fitting approach, Water Supply 20(8) (2020), 3487–3501. doi: 10.2166/ws.2020.241.

33.

Topİu

.B.

and Sarıdemir

, Prediction of compressivestrength of concrete containing fly ash using artificial neuralnetworks and fuzzy logic, Comput. Mater. Sci. 41(3) (2008), 305–311. doi: 10.1016/j.commatsci.2007.04.009.

34.

Dao

, Trinh

, Ly

H.-B.

and Pham

, Prediction of Compressive Strength of Geopolymer Concrete Using Entirely Steel Slag Aggregates: Novel Hybrid Artificial Intelligence Approaches, Appl. Sci. 9(6) (2019), 1113. doi: 10.3390/app9061113.

35.

Ashrafian

et al., Classification-Based Regression Models for Prediction of the Mechanical Properties of Roller-Compacted Concrete Pavement, Appl. Sci. 10(11) (2020), 3707, doi: 10.3390/app10113707.

36.

Moodi

, Ghasemi

and Mousavi

S.R.

, Estimating the compressive strength of rectangular fiber reinforced polymer-confined columns using multilayer perceptron, radial basis function, and support vector regression methods, J. Reinf. Plast. Compos. 41(3-4) (2022), 130–146.

37.

Chen

, Li

, Wu

, Zuo

, Lu

and Zhou

, Compressive strength prediction of high-strength concrete using long short-term memory and machine learning algorithms, Buildings 12(3) (2022), 302.

38.

Pazouki

, Golafshani

E.M.

and Behnood

, Predicting the compressive strength of self-compacting concrete containing Class F fly ash using metaheuristic radial basis function neural network, Struct. Concr. (2021)–10.1002/suco.202000047.

39.

Behnood

and Golafshani

E.M.

, Predicting the compressive strength of silica fume concrete using hybrid artificial neural network with multi-objective grey wolves, J. Clean. Prod. 202 (2018), 54–64. doi: 10.1016/j.jclepro.2018.08.065.

40.

Siddique

, Aggarwal

and Aggarwal

, Prediction of compressive strength of self-compacting concrete containing bottom ash using artificial neural networks, Adv. Eng. Softw. 42(10) (2011), 780–786. doi: 10.1016/j.advengsoft.2011.05.016.

41.

Lin

C.-J.

and Wu

N.-J.

, An ANN model for predicting the compressive strength of concrete, Appl. Sci. 11(9) (2021), 3798.

42.

Moradi

M.J.

, Khaleghi

, Salimi

, Farhangi

and Ramezanianpour

A.M.

, Predicting the compressive strength of concrete containing metakaolin with different properties using ANN, Measurement 183 (2021), 109790.

43.

Gürses

, Bureerat

, Sait

S.M.

and Yıldız

A.R.

, Comparison of the arithmetic optimization algorithm, the slime moldoptimization algorithm, the marine predators algorithm, the salpswarm algorithm for real-world engineering applications, Mater.Test. 63(5) (2021), 448–452.

44.

Van Dao

, Ly

H.-B.

, Vu

H.-L.T

, Le

T.-T.

and Pham

B.T.

, Investigation and optimization of the C-ANN structure in predicting the compressive strength of foamed concrete, Materials (Basel). 13(5) (2020), 1072.

45.

N.-J.

, Predicting the compressive strength of concrete using an RBF-ANN model, Appl. Sci. 11(14) (2021), 6382.

46.

Qin

, Hu

and Yang

, The improved grasshopper optimization algorithm and its applications, Sci. Rep. 11(1) (2021), 1–14.

47.

and Peng

, A novel periodic learning ontology matching model based on interactive grasshopper optimization algorithm, Knowledge-Based Syst. 228 (2021), 107239.

48.

Kandiri

, Sartipi

and Kioumarsi

, Predicting compressive strength of concrete containing recycled aggregate using modified ANN with different optimization algorithms, Appl. Sci. 11(2) (2021), 485.

49.

Abualigah

, Almotairi

K.H.

and Abd

, Elaziz, M. Shehab and M. Altalhi, Enhanced Flow Direction Arithmetic Optimization Algorithm for mathematical optimization problems with applications of data clustering, Eng. Anal. Bound. Elem. 138 (2022), 13–29.

50.

Agushaka

J.O.

and Ezugwu

A.E.

, Advanced arithmetic optimization algorithm for solving mechanical engineering design problems,e, PLoS One 16(8) (2021), 0255703. doi: 10.1371/journal.pone.0255703.

51.

Kaveh

and Hamedani

K.B.

, Improved arithmetic optimization algorithm and its application to discrete structural optimization, in, Structures 35 (2022), 748–764.

52.

Yin

, Liu

, Lu

, Nie

and Jia

, Prediction of the compressive and tensile strength of HPC concrete with fly ash and micro-silica using hybrid algorithms, Adv. Concr. Constr. 12(4) (2021), 339–354.

53.

Nurlan

, A novel hybrid radial basis function method for predicting the fresh and hardened properties of self-compacting concrete, Adv. Eng. Intell. Syst. 1(01) (2022).

54.

Cheng

, Kitchen

and Daniels

, Novel hybrid radial based neural network model on predicting the compressive strength of long-term HPC concrete, Adv. Eng. Intell. Syst. 1(02) (2022).

55.

Erdal

H.I.

, Karakurt

and Namli

, High performance concrete compressive strength forecasting using ensemble models based on discrete wavelet transform, Eng. Appl. Artif. Intell. 26(4) (2013), 1246–1254. doi: 10.1016/j.engappai.2012.10.014.

56.

Lima

R.N.

, de Almeida

G.M.

, Braga

A.P.

and Cardoso

, Trend modelling with artificial neural networks. Case study: Operating zones identification for higher SO 3 incorporation in cement clinker, Eng. Appl. Artif. Intell. 54 (2016), 17–25. doi: 10.1016/j.engappai.2016.05.002.

57.

Topcu

İ.B.

, Karakurt

and Sarıdemir

, Predicting thestrength development of cements produced with different pozzolans byneural network and fuzzy logic, Mater. Des. 29(10) (2008), 1986–1991. doi: 10.1016/j.matdes.2008.04.005.

58.

Chen

, Kou

C.-H.

and Ma

S.-W.

, Prediction of slump flow of high-performance concrete via parallel hyper-cubic gene-expression programming, Eng. Appl. Artif. Intell. 34 (2014), 66–74. doi: 10.1016/j.engappai.2014.05.005.

59.

Topcu

İ.B.

and Sarıdemir

, Prediction of properties ofwaste AAC aggregate concrete using artificial neural network,117-125, Comput. Mater. Sci. 41(1) (2007), doi: 10.1016/j.commatsci.2007.03.010.

60.

Golafshani

E.M.

and Behnood

, Automatic regression methods for formulation of elastic modulus of recycled aggregate concrete, Appl. Soft Comput. 64 (2018), 377–400. doi: 10.1016/j.asoc.2017.12.030.

61.

Abualigah

, Diabat

, Mirjalili

, Abd Elaziz

and Gandomi

A.H.

, The arithmetic optimization algorithm, Comput. Methods Appl. Mech. Eng. 376 (2021), 113609.

62.

Saremi

, Mirjalili

and Lewis

, Grasshopper Optimisation Algorithm: Theory and application, Adv. Eng. Softw. 105 (2017), 30–47. doi: 10.1016/j.advengsoft.2017.01.004.

63.

Rogers

S.M.

, Matheson

, Despland

, Dodgson

, Burrows

and Simpson

S.J.

, Mechanosensory-induced behavioural gregarization in the desert locust Schistocerca gregaria, J. Exp. Biol. 206(22) (2003), 3991–4002. doi: 10.1242/jeb.00648.

64.

Ayubi Rad

and sadegh Ayubirad

, Comparison of artificial neural network and coupled simulated annealing based least square support vector regression models for prediction of compressive strength of high-performance concrete, Sci. Iran. 24(2) (2017), 487–496. doi: 10.24200/sci.2017.2412.