Development of articial intelligence based model for prediction of the compressive strebgth of self compacting concrete

Development of artificial intelligence-based model for prediction of the compressive strength of self-compacting concrete Hai-Bang Ly1, *, Binh Thai Pham1, Thuy-Anh Nguyen1, May Huu Ngu

Development of artificial intelligence-based model for prediction

of the compressive strength of self-compacting concrete

Hai-Bang Ly1, *, Binh Thai Pham1, Thuy-Anh Nguyen1, May Huu Nguyen 1,2,*

1 Civil Engineering Department, University of Transport Technology, 54 Trieu Khuc, Thanh Xuan, Hanoi 100000, Vietnam

2 Civil and Environmental Engineering Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan

* Corresponding authors

Email addresses: banglh@utt.edu.vn (H.-B Ly), binhpt@utt.edu.vn (B P Pham),

anhnt@utt.edu.vn (T.-A Nguyen), and nguyenhuumay@hiroshima-u.ac.jp (M H Nguyen)

Abstract:

This study investigated the usability of an artificial neural network model (ANN) and the Grey Wolf Optimizer (GWO) method for predicting the compressive strength of self-compacting concrete (SCC) The ANN-GWO model was developed using an experimental database of 115 samples obtained from various sources considering nine key factors of SCC The validation of the proposed model was evaluated via six indices including correlation coefficient, mean squared error, mean absolute error, IA, Slope, and mean

absolute percentage error In addition, the importance of each parameter affecting the compressive strength of SCC was investigated utilizing partial dependence plots The findings demonstrated that the proposed ANN-GWO model is a reliable predictor of SCC compressive strength Following that, an examination of the parameters impacting the compressive strength of SCC was provided

Keywords: Artificial Neural Network (ANN); Grey Wolf Optimizer (GWO) algorithm;

compressive strength; self-compacting concrete;

The construction industry in Japan has quickly adopted the use of self-compacting concrete (SCC), a concrete type that can approach and fill the corners of formwork without the requirement for a compaction phase [6,7] Since then, various studies have been focused on developing the applications of this kind of concrete [8,9] On the one hand, SCC is listed as

a kid of high-performance concrete, flexible deformability, good segregation resistance, and less blocking surrounding the reinforcement The exclusion of the compaction step

brings several advantages of SCC, including economic efficiency (e.g., accelerated casting speed, saving labor, energy, and cost), enhances the working environment, and proposes a novel approach to automating the concrete construction [6,10–13]

On the other hand, to achieve its desired flowable behaviors and proper mechanical properties, SCC requires a complex manipulation of several mixture variables [10,11] For instance, the water-to-binder (w/b) ratio of SCC is lower than conventional concrete, which

is usually supported by special additives and superplasticizers to obtain the desired workability [14–17] Also, the grading of the aggregates, including aggregate shapes, texture, mineralogy, and strength, are always carefully considered to ensure workability and concrete strengths [18,19] These features lead to a significant challenge to establishing a universal correlation between the SCC properties and its constituent parameters [8,9,20] In other words, they bring out the need for predicting the properties of SCC in both the fresh and hardened stages The traditional applications of analytical models to represent the influence of each of these parameters on the properties of SCC, and then optimizing this model utilizing regression analysis However, so far, no explicit equations have been established due to these methods being less productive for nonlinearly separable data and complicated [21,22]

In this regard, over the past few decades, various modeling methods utilizing artificial intelligence (AI) techniques have been adopted, such as artificial neural networks (ANNs), genetic algorithm (GA), and expert system (ES) for modeling a variety of current problems

in the field of civil engineering [23–25] Among these, ANN is a more prevalent and efficient approach since its ability to classify to capture interrelationships among input-

output data pairs Numerous researchers have proposed their own ANN models for predicting the concrete strength [26–28] Regarding SCC, several models have also been presented for predicting the compressive strength [29–31] Yeh has soon demonstrated the opportunities of adapting ANN to predict high-performance concrete's compressive strength [29] The viability of utilizing ANNs to forecast the characteristics of SCC that uses fly ash as a cementitious substitute was examined by Douma et al [30] In these models, numerous experimental results were collected from the previous studies and employed for training and evaluating the proposed model Siddique et al presented the useability of neural network for predicting the compressive strength of SCC based on some input properties [31] Their proposed model could be easily extended to different input parameters of the experimental results, containing bottom ash as a replacement of sand Despite this, there has not been a detailed investigation into an improved ANN model for predicting the compressive strength of SCC The need for a novel, appropriate artificial neural network model to forecast the strength of SCC is developing on a continuous basis,

in step with the advancement of scientific knowledge

Therefore, in the present research, the artificial neural network (ANN) approach coupled with the Grey Wolf Optimizer (GWO) algorithm for forecasting the compressive strength

of SCC is examined For this target, a variety of databases from different independent sources was gathered and employed to train and assess the proposed model The ANN model is established on the basis of two groups of input parameters, including concrete mixture components (i.e., the contents of binder, fine and coarse aggregates, superplasticizer and water-to-binder ratio), and the fresh properties SCC such as slump

flow, V-funnel and L-box tests The output predicted parameter is the compressive strength

of SCC The influence of the used parameters on the compressive strength of SCC was then discussed

2 Materials and methods

2.1 Machine learning methods

2.1.1 Artificial Neural Network (ANN)

Artificial Neural Network (ANN) is being widely used to solve prediction problems by drawing on biology's understanding of how the nervous system functions [32–35] ANN contains many simple processing elements, the so-called neurons An ANN is made up of nodes and linked parts that are divided into three layers: the input layer, hidden layer, and output layer Because of this training process, the neural network produces a model that can predict a target parameter from an input value that has been provided [36]

In general, an ANN includes the minimum number of neurons that can simulate the training progress A linking between nodes carries a weighted representative of some earlier learning stage On the basis of the changes in weights, the input-output correlation could be established The system has to be educated to recreate the input-output correlation, which is called optimal weights [37,38] In an ANN model, the correlation between the input and output variables is determined by the collected data points Because they are very independent of one another, it is feasible to execute a large number of processes at the same time

In order to take advantage of these benefits, most suggested models determine the number

of hidden layers and the number of nodes by using a rule of thumb or by looking for random designs that meet specific criteria Furthermore, several appropriate numbers of parameters similar to learning speed and momentum are needed for chosen hidden layers and nodes [29–31,39] As a final point, all of the research stated that ANN is a reliable method for estimating the compressive strength of concrete

2.1.2 Grey Wolf Optimizer (GWO) algorithm

Over two past decades, metaheuristic optimization algorithms have commonly been applied

in most engineering fields For example, the Grey Wolf Optimizer (GWO) algorithm, one

of the models developed by Mirjalili et al., was invented based on the leadership and hunting skills of the grey wolf pack's communal life [40] In order to simulate the order of management, each wolf pack comprises of four main forms of grey wolves, including alpha (α), beta (β), delta (δ), and omega (ω) In this structure, grey wolves follow strict rules which clearly divide their responsibilities Accordingly, α wolves work as the most responsible wolves, whereas ω wolves have the least responsibility (Fig 1) The following orders in the pack are β and δ wolves, respectively

Each location of a grey wolf in the GWO algorithm might result in a viable solution to the optimization problem From a mathematical standpoint, the optimal option is chosen among

α, β, and δ wolves with the closest proximity to the prey Every iteration follows the same method for the second and third-best answers The locations of all other wolves (i.e., ω ones) are meant to be determined by the positions of α, β and δ wolves On the basis of this

technique, several works [41–43] focused on the reliability of the GWO model for estimating compressive strength

Fig 1 The categorized leadership structure of grey wolves.

B range between 0.26 -0.45, 590 - 935 kg, 0 and 60%, 656 - 1038, 480 - 880 mm, and 370 -

733 kg, respectively The V-funnel test value ranges from 1.95 to 19.2, the superplasticizer dose is between 0.74 and 21.84, and the L-box test value is between 1.95 and 19.2 Besides, the compressive strength values are in the range of 10.2 to 86.8 MPa Specifically, statistical analysis of input and output variables is detailed in Table 1

Table 1

Statistical analysis of the inputs and output

Herein, the proposed ANN model is trained using 70 percent of the 115 experiments, while

30 percent of the data are utilized to evaluate the model Thus, there are 81 samples for the training data set and 34 samples used to determine the projected performance of the ANN network All data are scaled within the range of [0,1] to reduce the numerical errors while conducting simulations, as recommended in Witten et al [56], using Equation (1):

2.3 Quality assessment criteria

In this study, six statistical indicators were employed to assess the accuracy of the proposed model, which are the correlation coefficient (R), root mean square error (RMSE), index of agreement (IA), mean absolute error (MAE), slope, and mean absolute percentage error (MAPE) To measure the correlation between the actual and predicted values in regression problems, the R criterion, which is generally in the range [-1; 1], is extensively employed in the literature [57] The average degree of inaccuracy between actual and predicted outputs

is measured by the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) [58] In terms of quantitative accuracy, the smaller the values of RMSE, MAE, and MAPE are, as well as the closer the absolute value of the

correlation coefficient is to one, the more accurate the machine learning model is These values are represented by:

where: N is the number of databases; Q AV and Q AV are the actual values and the average

real values; Q PV and Q PV are predicted values and average predicted values are calculated according to the forecasting model

2.4 Partial Dependence Plot

The partial dependency plot (PDP) is introduced by Friedman [59] for the purpose of interpreting complex Machine Learning algorithms Some algorithms are predictive, but they do not show whether a variable has a positive or negative effect on the model Hence, the partial dependency plot helped depict the functional relationship between the inputs and the targets At the same time, PDP can show whether the relationship between the target and a feature is linear, monotonic or more complex

Let X = X X1, 2, ,X n being the inputs for a model with the predictive function Y(X) X

is subdivided into two subsets XM and its complement X N  X \ XM

For the output Y (X) of a machine learning algorithm, the partial dependence of y on a subset of variables XM is defined as:

To simplify the construction of PDP (3), set XM = X1 as the predictor variable of interest with unique values PDP (3) then follows the following steps:

Step 1: For i {1, 2, k}; Copy the training database and replace the original value of X1

with X1i is the constant From a modified copy of training data, compute the vectors of the predicted values

- Calculate the mean predicted value to obtain Y X1 1i

Step 2: From pairs X Y X1i, (1 1i)(a, b) with i = 1,2, k, draw graphs representing PDP

3 Results and discussions

3.1 Analysis of Optimal ANN-GWO Parameters

It is discussed in this part how to optimize the structure of the proposed ANN-GWO model, including how to determine population size in the GWO algorithm and the neurons associated with the hidden layers In machine learning algorithms, the structure of the ANN model plays a crucial role As previously mentioned, the ANN structure includes three layers, with the number of hidden layers consisting of one or more layers In various research, it has been proved that the ANN structure with one hidden layer is capable of solving complicated nonlinear problems, including finding a correlation between input and output variables [60–62] Therefore, in this study, the structure of ANN-GWO with one hidden layer is proposed The next problem is to determine the number of neurons in the

hidden layer as well as the optimal population size of the GWO optimization algorithm For this purpose, the GWO optimization algorithm was run with the population changing from

30 to 300 with a step of 30, the hidden layer's neuron changed from 3 to 30 by 3 To determine optimal parameters, a grid search technique was utilized The effects of the different values of the two parameters on the performance of the proposed were evaluated according to the 6 statistical criteria mentioned above Here, a maximum number of iterations of 1000 is used to define the parameters

Fig 2 presents 3D models of the mesh search As observed, when the number of neurons is low, the population size changes in the increasing direction, the model efficiency is still low That is reflected by the low values of R, IA, while RMSE, MAE, and MAPE are high

In the case of low population size, the increase in the number of nerve cells does not allow

an increase in performance The case where the number of neurons increases while increasing the number of population sizes allows the model's performance to increase The results of the mesh search technique show the best performance of the ANN-GWO model obtained when the number of neurons is 21, and the population size is 240 Then, all the performance evaluation criteria of the model are satisfied

30 27 24 0.94

21 300

21 300

21 300

21 300

21 300

21 300

Fig 2 Calibration of the optimal number of neurons and GWO's population size based on

(a) R, (b) IA, (c) Slope, (d) RMSE, (e) MAE, and (f) MAPE The optimal zone is also highlighted

3.2 Analysis of Convergence of Monte Carlo simulations

The preceding part used 1000 Monte Carlo simulations to optimize the number of neurons

in the hidden layer and the population size in the GWO optimization technique In this section, convergence estimation of all the quality assessment criteria was performed based

on 1000 Monte-Carlo simulations The line representing the normalized convergence of the six statistical criteria is shown in Fig 3 For the R, IA, and Slope indices, only roughly 200 simulations with the test set and 100 with the training set are required to obtain convergence results (less than 0.1 percent) After 200 iterations, the RMSE index seems to

be the harshest since only 1% of normalized convergence is reached There is a distinct difference between MAE and MAPE compared with RMSE, when their convergence is identical to those of R, IA, and Slope The obtained results indicated that all 6 criteria achieve static convergence per 1000 Monte Carlo simulations That means that such runs were enough to assess the effectiveness of the proposed model

0 200 400 600 800 1000

Nr of Monte Carlo runs

99.4 99.6 99.8 100 100.2 100.4

0 200 400 600 800 1000

Nr of Monte Carlo runs

96 98 100 102 104

0 200 400 600 800 1000

Nr of Monte Carlo runs

96 98 100 102 104 106 108

Fig 3 Statistical convergence over 1000 random samplings for (a) R, (b) IA, (c) Slope, (d)

RMSE, (e) MAE and (f) MAPE

3.3 Analysis of Distribution of Performance Criteria

The statistical assessment of the ANN-GWO model's performance is reported in this section Fig 4 shows the probability distribution over 1000 simulations of the criteria, namely, R (Fig 4a), IA (Fig 4b), slope (Fig 4c), RMSE (Fig 4d), MAE (Fig 4e), and MAPE (Fig 4f) The probability distribution function for the training set, test set were presented by solid, and dashed lines, respectively In addition, the summary statistical information including quantiles Q25, Q50, Q75, mean, StD, the max and min values of the

R, IA, slope, RMSE, MAE, and MAPE distributions for the training and testing databases are highlighted in Table 3

0.92 0.94 0.96 0.98 1

IA

0 20 40 60 80 100 120

0 0.2 0.4 0.6 0.8 1

Fig 4 Probability distribution over 1000 random samplings for (a) R, (b) IA, (c) Slope, (d)

RMSE, (e) MAE and (f) MAPE

Table 3

Statistical analysis over 1000 random samplings quality assessment criteria

database The slope criterion values were 0.917 and 0.012 with the training database; 0.951 and 0.012 with the testing database The mean and standard deviation of RMSE for the training database were 5.099 and 0.390, while for the testing database were 6,594 and 0.445 For MAE, these values were 4.150 and 0.343 respectively for the training database and 5.238 and 0.354 for the testing database Finally, for MAPE criterion, the mean and standard deviation were 9,519 and 0.742 for the training database, while for the testing database, these values were 12,214 and 0.834, respectively The obtained results indicated that the ANN-GWO model could be employed as a good predictor of the compressive strength of SCC with high accuracy.

3.4 Analysis of ANN Optimization by GWO

The weight and bias values of ANN's neurons were optimized using the GWO algorithm in this section based on three statistical criteria, namely, R, RMSE, and MAE, over the process Fig 5 presents a cost function that evaluates the convergence of criteria in the network training process It can be seen that an increase in the number of repetitions can decrease the RMSE and MAE value, while the R value tends to increase The findings of five hundred iterations have likewise been shown to be trustworthy The R, RMSE, and MAE measures are essentially identical from iteration 200 onwards, as can be shown As a result, the maximum number of iterations for ANN-GWO was chosen as 500, which ensures the relative error between two iterations is less than 0.1%