International Journal of Engineering Advanced Research eISSN: 2710-7167 | Vol. 4 No. 3 [September 2022]
Journal website: http://myjms.mohe.gov.my/index.php/ijear
CONCRETE MIX DESIGN BY USING THE ARTIFICIAL NEURAL NETWORK APPROACH WITH LIMITED
DATASETS
S.F. Senin1*, R. Rohim2 and A. Yusuff3
1 2 3 School of Civil Engineering, College of Engineering, Universiti Teknologi MARA, Cawangan Pulau Pinang,
Kampus Permatang Pauh, Pulau Pinang, MALAYSIA
*Corresponding author: [email protected]
Article Information:
Article history:
Received date : 14 July 2022 Revised date : 26 July 2022 Accepted date : 25 August 2022 Published date : 9 September 2022
To cite this document:
Senin, S.F., Rohim, R., & Yusuff, A.
(2022). CONCRETE MIX DESIGN BY USING THE ARTIFICIAL NEURAL
NETWORK APPROACH WITH LIMITED DATASETS.
International Journal of Engineering Advanced Research, 4(3), 35-46.
Abstract: In this article, a model for an artificial neural network (ANN) is develop to predict the concrete's compressive strength at three different days; 7, 14 and 28 days for civil engineering structures. The concrete compressive strength dataset for the ANN model was compiled utilizing limited number of datasets from a laboratory work in accordance with the American Concrete Institution (ACI) standards. The developed optimal model ANN can be used to predict the compressive strength of concrete after 7, 14, and 28 days with high accuracy because the MSE value is very insignificantly small. Regarding the prediction of 28-day compressive strength with the optimal model ANN, it is found that this optimal model is reliable as it was compared with the equation of Abram and Lyse. The prediction error of the model ANN and the empirical equation ranged from 0.5 to 11.7%, which proves the predictive ability and reliability of the model ANN of the present work, even by employing limited datasets.
Keywords: Artificial Neural Network, Compression Strength, Concrete Mix Design.
1. Introduction
Concrete mix design is the science of choosing appropriate proportion for concrete in order to produce a concrete proportion that satisfies the pavement construction requirements. Many factors found to affect the selection of the concrete mix proportions, such as the specific gravity of materials, type and strength of cement, minimum and maximum content of cement, water-to- cement ratio, mixing water requirements, aggregate-to-cement ratio, types, shape and maximum size of aggregates, grading of aggregates, entrapped air content, concrete exposure conditions, properties of concrete in green and hardened concrete. The right amount of those factors is determined in order to fulfill the need of minimum compressive strength (CS) to withstand the applied construction loads, acceptable workability property, and durability depending on the environmental exposure conditions. In addition to these requirements, the mix's cement proportion should be as low as practical to minimize the cost of construction. Due to these issues, the formulation of the proper concrete mix proportion is a crucial task to ensure the properties of the green and hardened concrete is achieved for the specific construction requirements.
2. Literature Review
In the civil engineering construction, concrete is the most often utilised material due to its versatility to be casted to any required shapes. Cement, aggregates, and water are combined with certain proportion to fulfil certain mechanical desired properties. The CS of a concrete is an example of concrete mechanical properties that is important to be achieved especially at its 28-day after the concrete mix has been casted and cured (Hameed, Abed, Al-Ansari, & Alomar, 2022).
The main issue with concrete mix design among the engineers is that this practice is subjected to several trial-and-error concrete mixes exercise during the mix design phase (Kharazi, Lye, &
Hussein, 2013). These trial mix with varying water to cement ratio induce engineers to increase their spending time on-site and had to invest certain cost in order to achieve certain minimum CS, yet with large variation of CS estimation errors once testing the hardened concrete after 28-days.
These errors will be made more significant if the concrete mix calculation is computed by manual approach; as these process will deal with the estimation of certain parameters using graphs (Abdul Qader et al., 2022). A study conducted by (Tanmay Kalola, 2021) mentioned that the maximum percentage error between desired and the actual CS at 28-days for grade concrete of 30 N/mm2 is ranging from 4.14 percent to 40 percent based on the several trial concrete mixes prepared by their Indian Code. This large range of the error percentage due to the laboratory trial mix works and manual computation can be possibly reduced, if another new numerical approach that able to estimate this compressive strength reliably by taking account the variation of the mix from a laboratory dataset.
One of the existing approach, the traditional statistical method, was found to produce an unsatisfactory results when applied to model complex task such as pattern recognition of problem in the CS estimation from a concrete mix ingredients (Abiodun et al., 2019). Pattern recognition of the CS values and the component of concrete mix is considered to be a complex task as the there is a strong nonlinear relation between them (Tran, Mai, Nguyen, & Ly, 2021). Therefore, a more
Over the last decade, the artificial neural networks (ANN) have grown in popularity to model complex tasks and are now employed by many researchers and engineers to solve the civil engineering problems such as the CS prediction. The advantage of ANN is that there is no need to employ a specific modelling equation to fit the normality requirements in any statistical study (Senin et al. 2022). ANN automatically manages to learn these huge datasets containing the CS and concrete mix ingredient by adapting its weights and bias values on minimizing the errors (Alzubaidi et al., 2021). As a result, an optimal ANN model can be developed by employing appropriate CS datasets taken from a limited number of measurements.
2.1 Problem Statement
The ANN model is utilized to predict the concrete CS in this study by using a limited number of datasets, which is the commonly faced by the on-site engineers. One of the most significant factors impacting the model’s performance is the ANN architecture development. As a result, the major objective of this article is to examine and improve the ANN architecture for predicting the concrete CS. The optimal ANN architecture is decided by the model’s performance, which is assessed using well-known statistical metrics, mean squared error (MSE). In our best knowledge, a very limited study using a limited number of datasets on-site to estimate the CS of concrete. Therefore, in this study, the concrete mix design will be modelled by using 3 different CS experimental datasets (7, 14 and 28 days) from a limited number of datasets by varying the number of hidden layers and the neuron numbers to obtain the most optimal network.
3. Method
3.1 General overview
We want to develop an optimal artificial neural network (ANN) for the concrete mix design in our study. We attempt to develop an ANN that able to predict the compressive strength of the concrete mix using a small number of tested concrete mix compositions from a published research work of (Garg, 2003). The four primary components of a concrete mix, specifically, cement, 10 mm and 20 mm coarse aggregate, and water are modelled by the ANN approach to predict the CS of the concrete. The 7, 14 and 28 days of CS of trial concrete mix was defined as a function of the four parameters (the water content, the cement content, 10 mm coarse aggregate content, 20 mm coarse aggregate content) after the generated ANN was translated into the source code and condensed into a single equation. Figure 1 presented the flow chart of the study to give some overview of the overall work done in this paper.
3.2 Database of the Concrete Mix Ingredients
The properties of all ingredients of the concrete mix used in this study were tested in accordance to the provision of ACI design code (Chaubey, 2020) and compiled with limited number of database consisting of 55 samples. As shown in Table 1, a few samples dataset from a research work were presented for the reader’s view. To ensure a robust ANN model, we performed an attempt on testing a wide-ranging input database consisting of variety of concrete mix proportion according to the cylinder compressive strength as shown in Table 2. According to (Chaubey,
2020), the samples tested under each compressive strength test were casted from a cylindrical steel mould with a diameter of 150 mm and 300 mm height.
Figure 1: The Flow Chart of the Study Needed input
and output variables
Development of ANN model
to output prediction
Estimate the compressive strength of the unseen mix
composition
Validation of the ANN model output
with testing and empirical
equations Database of a
laboratory test
• 55 samples of trial concrete mix of extracted from a
published research work
• Cylinder concrete samples
• ACI standard
• Free water content (input)
• Cement content (input)
• 10 mm coarse aggregates (input)
• 20 mm coarse aggregates (input)
• 28-day compressive strength (output)
• Input & output data
transformation analysis
• Perform trial hyperparametric analysis to obtain the optimal ANN model
Table 2: Ranges of Input Variables of the Concrete Mix Design
Input variables Minimum Value Maximum Value
Water 185 190
Cement 266 429.2
Aggregates (10mm) 204.3 366.3
Aggregates (20mm) 136.2 274.8
3.3 ANN Model Development
In this work, an attempt is made to establish a working ANN model for predicting the compressive strength of normal concrete. All ANN models were developed, trained, and tested with the MATLAB Neural Fitting Tool (Mathworks, 2022). The procedure for determining the optimal performance of the ANN models is described below. The workflow follows the typical scheme of extracting and collecting data from the literature, pre-processing, and finally using the data set as input to ANN and is described in detail below.
3.3.1 Transformation and the Splitting of the Datasets
Both the input and output variables in the datasets need to be transformed or normalised range, which is often done within the range of 0 to 1 as shown in Equation 1. Dataset normalization can also expedite the training time by starting the training process for each feature within the same scale (Nayak, Misra, & Behera, 2014). It is especially useful for modelling application where the inputs are generally on widely different scales, such as in our case in this paper.
The lower bound (LB) and the upper bound (UB) of this transformation were decided to be 0 and 1, respectively.
𝑉′= ( 𝑉−𝑀𝑖𝑛𝐴
𝑀𝑎𝑥𝐴−𝑀𝑖𝑛𝐴) (𝑈𝐵 − 𝐿𝐵) + 𝐿𝐵 Eqn. 1
It is worth to note that V is the original input and output variables, V’ is the transformed variable values in the range between the LB and the UB. MaxA and MinA is the most maximum values and the least value of the original input/output variables in the datasets, respectively. The transformed datasets were split into two main subgroups; the training and testing datasets when the data transformation is complete. The training datasets typically comprises between 70 to 80 percent of the total number of datasets (Joseph, 2022). The remainder datasets are then used for testing or split between validation subsets. However, in this study, 70 percent of the total datasets were used as the training datasets, while the remaining 30 percent were selected as the tested datasets as suggested by (Senin et al., 2022) in their study.
3.3.2 Training the Transformed Training Datasets for the Optimal ANN Model
The ANN models in this study employ from a shallow to deep network architecture; which means that the models were trained by using one to multilayers feed-forward neural network. The number of input and output variables and training patterns have been associated in numerous studies to the number of hidden neurons; nevertheless, these relationships cannot be universally accepted.
Therefore, to deal with this complex scenario and to avoid overfitting issues, various number of hidden layers were tested ranging from 1 to 5 numbers by the trial-and-error approach as shown
in Table 3 (Blum, 1992). Additional hyperparameters such as by varying number of neurons numbers in each hidden layers were investigated at to determine whether they have any significant impact on the performance of the model, in addition to the literature's suggested relationship between the number of input and hidden neurons. The optimal performance of the proposed ANN model was quantified by the mean square error (MSE) during the training of the back-propagation process for each variation on the hidden layer and the neuron numbers. Equation 2 present the MSE formula used in this paper.
𝑀𝑆𝐸 = 1
𝑁∑𝑁𝑖=1(𝑉′− 𝑉𝑝𝑟𝑒𝑑)2 Eqn. 2 where;
N is the number of the training datasets used to model the network V’ is the transformed training output (compressive strength) 𝑉𝑝𝑟𝑒𝑑 is the predicted transformed training output
The activation function employed in the hidden and the output layer was the logsig and pureline function with the maximum epoch number set to 1000 to avoid the risk of overfitting during the training of the ANN model process. The full architecture of the proposed ANN model to predict the compressive strength of three duration is shown in Figure 2.
Table 3: Selection of Each Hyperparameters Settings of the ANN Model
Network type Feed-Forward Backpropagation
Training function TRAINCGB
Adaptation learning function TRAINGD
Performance function MSE
Number of trial hidden layers 1 to 5
Numbers of trial neurons in each hidden layer 1 to 5 Maximum epoch value
The activation function
10000
LOGSIG and PURELINE
4. Results and Discussion
4.1 Optimal ANN Model Development
In this study, a total of 25 possible configurations based on the proposed architecture networks shown in Figure 2 were trained in order to find the optimal ANN model. The comparison of MSE results of those possible 25 architectures of ANN model with different neuron number is depicted by Figure 3,4 and 5 for each 7, 14 and 28-days CS, respectively. The explanation on these figures is presented in the following sections.
Figure 2: The Proposed Architecture of the ANN Model (n =1 until 5)
F
Figure 3: MSE (vertical axis) vs. Neuron Number (Horizontal Axis) of 7-Days Compressive Strength Hidden
Layer Hidden
Layer 1
Hidden Layer 2
…Hidden Layer n
Compressive strength at 7, 14 & 28 days Water
Cement
Aggregate (10 mm)
Aggregate (20 mm)
Output Layer Input
Layer
0.010 0.020.03 0.040.05 0.060.07 0.080.090.1 0.11
1 2 3 4 5
1 Hidden Layer 2 Hidden Layer 3 Hidden Layer 4 Hidden Layer 5 Hidden Layer
Figure 4: MSE (Vertical Axis) vs. Neuron Number (Horizontal Axis) of 14-Days Compressive Strength
Figure 5: MSE (Vertical Axis) vs. Neuron Number (Horizontal Axis) of 28-Days Compressive Strength 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
1 2 3 4 5
1 Hidden Layer 2 Hidden Layer 3 Hidden Layer 4 Hidden Layer 5 Hidden Layer
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1 2 3 4 5
1 Hidden Layer 2 Hidden Layer 3 Hidden Layer 4 Hidden Layer 5 Hidden Layer
4.1.1 The Optimal ANN Model for 7-Days Compressive Strength
Based on Figure 3, it can observe that ANN model simulated by single hidden layer (HL) with 2 neurons is the optimal network that had successfully learned the 70 percent dataset to predict the 7 days compressive strength of the concrete mix. The rest of the ANN model that simulated with more than one hidden layer showed a significant higher MSE values than the former network when the neuron number is two. The MSE value of this optimal network is 0.0209, which found to be the most minimum values among the other proposed ANN architecture as shown in Table 4.
Table 4: MSE values for 7-Day Compressive Strength for Various Neuron Number and Hidden Layer Neuron Number 1 HL 2 HL 3 HL 4 HL 5 HL
1 0.0371 0.0342 0.0493 0.0270 0.0522 2 0.0209 0.0483 0.0731 0.0503 0.0761 3 0.0930 0.0631 0.0459 0.0441 0.0541 4 0.0277 0.0257 0.0629 0.0844 0.1032 5 0.0492 0.0343 0.0515 0.0412 0.0252
When the neuron number is at set to be 3, this optimal network MSE value was observed to be suddenly increased by more than 300 percent to 0.0930. This is due to that fact as the number of neurons is forced to increase unnecessarily from its optimal value, chances to experience overfitting of the ANN model will occur as mentioned by (Khaki & Wang, 2019).
4.1.2 The Optimal ANN model for 14-days Compressive Strength
It can be concluded that the model ANN, simulated by a single hidden layer (HL) with 5 neurons, is the optimal network that successfully learned the training datasets to predict the 14-day compressive strength of the concrete mix as shown in Figure 4. The optimal ANN model showed a significantly higher MSE value (0.0562) than the rest of the proposed network.
4.1.3 The Optimal ANN model for 28-days Compressive Strength
As can be shown in Figure 5, the model ANN with a four hidden layer (HL) and 2 neurons is the most appropriate network that learnt the training datasets to accurately forecast the concrete mix's compressive strength after 28 days. The MSE value for the optimal model ANN was 0.0299, which is the most minimum MSE value than the other ANN model with similar neuron number. The summary of the performance in terms of MSE of this proposed model is shown in Table 5 below.
Compressive strength of a concrete evaluated at 28-days is the most important mechanical strength in civil engineering practice as it is referred as the standard property of a concrete material to be used in the infrastructure. Therefore, in the next section, the optimal ANN model for 28-days will be accessed its reliability.
Table 5: MSE Values for 28-Day Compressive Strength for Various Neuron Number and Hidden Layer Neuron Number 1 HL 2 HL 3 HL 4 HL 5 HL
1 0.0350 0.0340 0.0592 0.0506 0.0587 2 0.0346 0.0374 0.0582 0.0299 0.0558 3 0.0487 0.0426 0.0359 0.0810 0.0408 4 0.0163 0.0561 0.0224 0.0631 0.0481 5 0.0212 0.0438 0.0323 0.0241 0.0419
4.2 Evaluation of the 28-day Compressive Strength ANN Prediction Model Reliability with other Empirical Equations
In order to evaluate the reliability of the optimal 28-days compressive strength ANN model, an empirical model formulated by Abram’s and Lyse model and cited by (Namyong, Sangchun, &
Hongbum, 2004) were employed. Their empirical equation to estimate the 28-day CS, 𝑓𝑝, can be written as the following Equation 3;
𝑓𝑝 = 𝑒2.98−1.588(𝑤
𝑐)−0.00642𝑐+7.6888( 𝑐 𝑠+𝑔)
Eqn. 3
Where:
w is the water content (kg/m3) c is the cement content (kg/m3)
s and g are the aggregate content (kg/m3)
Certain proportion of the concrete proportion of the concrete mix was submitted to the optimal ANN model and its 28-days compressive strength were estimated and compared with the Equation 3. The comparison of both results was shown in Figure 6.
Figure 6: Comparison of the Optimal ANN Compressive Strength and the Empirical Equation at 28-Days 0
5 10 15 20 25 30 35
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Predicted Compressive Strength at 28-Days Abram's & Lyse Model
According to Figure 6 and the computation done by the Equation 3 cited from (Namyong et al., 2004) is fairly excellent at forecasting the 28-days concrete compressive strength because only minor variations found between the ANN-based model and the empirical equation. The highest percentage error between the ANN and the empirical equation is 11.7 percent meanwhile the lowest percentage error is 0.5 percent, which recommend that the developed optimal ANN model for 28-days compressive strength is reliable and relatively accurate.
5. Conclusions
The study had successfully developed the optimal ANN concrete mix design model based on limited number of training dataset. The following summarizes the findings of the study: -
a) The optimal ANN model used to predict the compressive strength at 7, 14 and 28-days were developed by unique number of neuron number and hidden layer numbers. This is highly influenced by the pattern of the datasets, since all other hyperparameters such as activation function, training function etc. were set to be fixed.
b) The developed optimal ANN model may be utilised to forecast the compressive strength of concrete after 7, 14, and 28 days with accurate as the MSE value is very insignificantly small.
c) As regard to 28-days compressive strength prediction using the optimal ANN model, it is observed that this optimal model is reliable as the has been compared with the Abram’s and Lyse equation. The error of the prediction of both ANN model and the empirical equation were range from 0.5 to 11.7 percent, which prove the prediction capability and ANN model reliability of the current work.
6. Acknowledgement
The authors acknowledged Center of Civil Engineering Studies, Universiti Teknologi MARA Cawangan Pulau Pinang, Permatang Pauh Campus for the support of the provision of MATLAB software for this study.
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