Prediction of Compressive Strength of Rice Husk Ash Concrete through Different Machine Learning Processes

: Cement is among the major contributors to the global carbon dioxide emissions. Thus, sustainable alternatives to the conventional cement are essential for producing greener concrete structures. Rice husk ash has shown promising characteristics to be a sustainable option for further research and investigation. Since the experimental work required for assessing its properties is both time consuming and complex, machine learning can be used to successfully predict the properties of concrete containing rice husk ash. A total of 192 data points are used in this study to assess the compressive strength of rice husk ash blended concrete. Input parameters include age, amount of cement, rice husk ash, super plasticizer, water, and aggregates. Four soft computing and machine learning methods, i.e., artiﬁcial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS), multiple nonlinear regression (NLR), and linear regression are employed in this research. Sensitivity analysis, parametric analysis, and correlation factor (R 2 ) are used to evaluate the obtained results. The ANN and ANFIS outperformed other methods. methodology for study.


Introduction
The world is making progress by leaps and bounds. New technologies and innovations are being introduced every day in every field. These advancements have altered the course of human history. One of the main aspects that has played a crucial role in shaping modern human civilization is infrastructure. From caves, mankind has started to live in strong and pleasing dwellings made by their own creative and innovative minds. Still, today infrastructure is considered to be the main element for progress in any country. The construction material that is used in abundance throughout the world for the construction of infrastructure is cement. However, along with the advantages of cement there are also certain adverse effects. Cement is said to be responsible for seven percent of the total carbon dioxide emissions worldwide [1]. It produces carbon dioxide while reacting when water is added to it. Secondly, a high temperature is required during the production of cement [2]. This high temperature is achieved by burning fossil fuels which increase the carbon footprint of cement. Our planet earth is suffering from problems of grave danger. Environmental deterioration and global warming are some of these alarming issues. If not Table 1. Environmental impact of rice husk ash (RHA).

Material in Which RHA Is Used Results Reference
Concrete Utilization of RHA results in reduction of global warming potential (GWP) [17] Mortar Use of RHA results in reduction of harmful environmental impacts [18] Concrete RHA aids in reducing carbon footprint of concrete [19] Concrete blocks Utilization of RHA shows positive environmental results [20] Hence, RHA can be utilized successfully as a cementitious material. RHA does not produce excessive amount of carbon dioxide. It can be used as a structural concrete. Not only does it contribute towards the strength of the concrete but also towards the long term durability properties of concrete [21]. The rate of environmental deterioration does not allow one to spend an amount of time on research and development of RHA blended concrete (RBC quently, extensive lab works cannot be carried out on RBC. Along with that th ways an uncertainty regarding the mix design of RBC. This is due to the hyg nature of RHA. Therefore, to predict the properties of different SCMs, artifici gence (AI) is being used throughout the globe. AI is used by different research sess and predict the strength of concrete mixes. Table 2 lists the different previou conducted on SCMs to predict different properties. Different techniques such as neural networks (ANN), LR, adaptive neuro-fuzzy inference system (ANFIS), an are used to successfully model and predict different properties of materials [22, As AI research depends on mathematical modelling and parameters , it is a programming work and needs great optimization and care. Therefore, four p ming techniques are being used to predict the compressive strength of RHA-ba crete in this research. These techniques are ANFIS, ANN, MNLR, and LR. To ac targeted accuracy and to cater the complexity of programming these four techni be compared with each other. A vast database of peer reviewed literature is model the prediction of compressive strength.  The rate of environmental deterioration does not allow one to spend an extensive amount of time on research and development of RHA blended concrete (RBC). Consequently, extensive lab works cannot be carried out on RBC. Along with that there is always an uncertainty regarding the mix design of RBC. This is due to the hygroscopic nature of RHA. Therefore, to predict the properties of different SCMs, artificial intelligence (AI) is being used throughout the globe. AI is used by different researchers to assess and predict the strength of concrete mixes. Table 2 lists the different previous studies conducted on SCMs to predict different properties. Different techniques such as artificial neural networks (ANN), LR, adaptive neuro-fuzzy inference system (ANFIS), and MNLR are used to successfully model and predict different properties of materials [22,23].
As AI research depends on mathematical modelling and parameters, it is a complex programming work and needs great optimization and care. Therefore, four programming techniques are being used to predict the compressive strength of RHA-based concrete in this research. These techniques are ANFIS, ANN, MNLR, and LR. To achieve the targeted accuracy and to cater the complexity of programming these four techniques will be compared with each other. A vast database of peer reviewed literature is used to model the prediction of compressive strength.

Data Collection
To predict the compressive strength (CS) of RHA, mathematical models are developed using a dataset of 192 data points from the vast literature review and existing studies on machine learning [12,13,[35][36][37][38][39]. These data were collected through google Scopus. The constituents of concrete include RHA, OPC, aggregates, super plasticizer (SP), and water. The type of cement and curing methodology used in all the mixes is same. The CS of cubic specimens is converted into CS of cylinders by using 0.8 as a factor (as per BS 1881: Part 120:1983). The only output parameter in this study is compressive strength. The input parameters consist of main variables such as percentage of SP, curing age (CA), quantity of water used (W), amount of OPC (OPCP), quantity of aggregates (AGG), and amount of RHA (RHAP). Moreover, the description of collected data and its statistics are given in Table 3.

Methodology
The methodology section provides a brief detail about the approaches being made to determine the CS of concrete mathematically as shown in Figure 2. First, the AI processes used in this research are explained. The results obtained from AI data processing techniques are assessed for validity by different statistical parameters.

Modeling Techniques
Machine learning-based modeling has been used in the past to predict the different mechanical properties of materials [40][41][42]. These types of modeling techniques can be utilized to develop models for prediction of a property of material. They do not need any knowledge of the rudimentary experimental processes. This section of paper provides a brief introduction of the predictive models used in this study. These models are as follow: ANN is an artificial data analyzing technique. It is inspired by the learning capability of human brain. The most widely used type of ANN is feedforward back propagation (FFBP). As evident from Figure 3, an FFBP consists of at least three layers , namely, the input layer, hidden layer, and output layer. The nodes of these layers are connected in a proper sequence along with some weights. The input layer nodes do not perform any function on input data. Their function is to just receive the data from outside. It is a hidden layer where data are biased, weighted, and summed up. These processed data are then sent out to the output layers [43,44].
There are basically two types of FFBP, namely, single layer perceptron (SLP) and multiple layers perceptron (MLP). Both types of FFBP have their own advantages and disadvantages. Alhough the SLP is simple and easy to use, it cannot handle nonlinear relations. On the other hand, MLP are complex, but they can be applied to nonlinear relations.
Comparison of predicted compressive strength with experimental compressive strength

Computer based modelling
Data collected from peerreviewed literature

Modeling Techniques
Machine learning-based modeling has been used in the past to predict the different mechanical properties of materials [40][41][42]. These types of modeling techniques can be utilized to develop models for prediction of a property of material. They do not need any knowledge of the rudimentary experimental processes. This section of paper provides a brief introduction of the predictive models used in this study. These models are as follow: ANN is an artificial data analyzing technique. It is inspired by the learning capability of human brain. The most widely used type of ANN is feedforward back propagation (FFBP). As evident from Figure 3, an FFBP consists of at least three layers, namely, the input layer, hidden layer, and output layer. The nodes of these layers are connected in a proper sequence along with some weights. The input layer nodes do not perform any function on input data. Their function is to just receive the data from outside. It is a hidden layer where data are biased, weighted, and summed up. These processed data are then sent out to the output layers [43,44].
There are basically two types of FFBP, namely, single layer perceptron (SLP) and multiple layers perceptron (MLP). Both types of FFBP have their own advantages and disadvantages. Alhough the SLP is simple and easy to use, it cannot handle nonlinear relations. On the other hand, MLP are complex, but they can be applied to nonlinear relations.  Mathematically, an MLP operates in following way: Step 1: The inputs are summed and weighted as where = number of total inputs, = current input number, = weight between the previous layer, and the jth neuron and b are used to define the termination of process.
Step 2: This step includes an activation function. There are various types of activation functions such as sigmoid, ramp, and Gaussian functions. However, this research utilizes sigmoid function which is defined as Step 3: This represents the final outputs. The final outputs depend on the outputs calculated by hidden nodes. The final outcome can be expressed as In above equation, = weighted connection between kth output node to jth hidden node. Similarly, ′ = bias output of kth output node.
In this research, 70 percent of the data points are selected randomly for the training of data, and 30 percent for validation.

ANFIS
ANFIS is a technique that utilizes the combined effect of artificial neural networks and fuzzy logic [45]. Figure 4 shows a brief illustration of the ANFIS technique. An artificial neural network is used to minimize the chances of error in the output data. Thus , the fuzzy logic is implied to demonstrate the expert knowledge [42]. Fuzzy logic rules are applied as if-then while mathematically programming for the desired input and output datasets. An ANFIS model consists of five layers normally. These are (1) fuzzification, (2) set of rules, (3) normalization, (4) defuzzification, (5) aggregation.

Input variables
Concealed layers/ Blackbox Outputs Figure 3. Illustration of ANN.
Mathematically, an MLP operates in following way: Step 1: The inputs are summed and weighted as where n = number of total inputs, I i = current input number, ω ij = weight between the previous layer, and the jth neuron and b are used to define the termination of process.
Step 2: This step includes an activation function. There are various types of activation functions such as sigmoid, ramp, and Gaussian functions. However, this research utilizes sigmoid function which is defined as Step 3: This represents the final outputs. The final outputs depend on the outputs calculated by hidden nodes. The final outcome can be expressed as In above equation, ω jk = weighted connection between kth output node to jth hidden node. Similarly, b k = bias output of kth output node.
In this research, 70 percent of the data points are selected randomly for the training of data, and 30 percent for validation.

ANFIS
ANFIS is a technique that utilizes the combined effect of artificial neural networks and fuzzy logic [45]. Figure 4 shows a brief illustration of the ANFIS technique. An artificial neural network is used to minimize the chances of error in the output data. Thus, the fuzzy logic is implied to demonstrate the expert knowledge [42]. Fuzzy logic rules are applied as if-then while mathematically programming for the desired input and output datasets. An ANFIS model consists of five layers normally. These are (1) fuzzification, (2) set of rules, (3) normalization, (4) defuzzification, (5) aggregation.  Layer 1 is the fuzzification layer. It contains all the function members of the input variables. A Gaussian function is used in this layer to predict the outcome. Mathematically, it can be expressed as where ai and εi are parameters of a function membership. Layer 2 contains nodes which send the output by multiplying the input by certain weightages. This layer utilizes the fuzzy AND logic by using the equation listed below: Layer 3 has an aim to normalize the data. It normalizes the functions of membership. It calculates the ratios between different firing strength using the following expression: Layer 4 is known as the defuzzification layer. It contains nodes that conclude the fuzzy logic rules. This layer contains square nodes, which can be expressed by following function: where mi, ni, and ri are linear parameters. Layer 5 has a function of aggregation. It sums up the previous layers and presents the final output mathematically as follows: All the data points are used for the training of data.
Off the shelf functionality of MATLAB is used for ANN and ANFIS techniques in this research.

MNLR
MNLR is a technique which is used to model a random nonlinear relationship between the dependent and independent variables. The following equation represents the MNLR [41]: where a = intercept, β = slope or coefficient, K = number of observations. The above equation can make an estimate for the value of Y for each value of X. Layer 1 is the fuzzification layer. It contains all the function members of the input variables. A Gaussian function is used in this layer to predict the outcome. Mathematically, it can be expressed as where a i and ε i are parameters of a function membership. Layer 2 contains nodes which send the output by multiplying the input by certain weightages. This layer utilizes the fuzzy AND logic by using the equation listed below: Layer 3 has an aim to normalize the data. It normalizes the functions of membership. It calculates the ratios between different firing strength using the following expression: Layer 4 is known as the defuzzification layer. It contains nodes that conclude the fuzzy logic rules. This layer contains square nodes, which can be expressed by following function: where m i , n i , and r i are linear parameters. Layer 5 has a function of aggregation. It sums up the previous layers and presents the final output mathematically as follows: All the data points are used for the training of data.
Off the shelf functionality of MATLAB is used for ANN and ANFIS techniques in this research.

MNLR
MNLR is a technique which is used to model a random nonlinear relationship between the dependent and independent variables. The following equation represents the MNLR [41]: where a = intercept, β = slope or coefficient, K = number of observations. The above equation can make an estimate for the value of Y for each value of X.

LR
LR is a technique in which there is linear relationship between the dependent and independent variables. It can be represented mathematically as follows: Crystals 2021, 11, 352 8 of 23 The above equation can be utilized to find values of Y for each input value X.
In above equations of MNLR and LR, "Y" stands for compressive strength of RHA. Similarly, the values of "X" represents inputs which are age, water content, RHA content, SP content, and the percentage of aggregates.
The models are developed in Microsoft Excel by authors for MNLR and LR techniques using the above equations.

Results
A total of 192 data points are used for all the models and techniques. A total of 134 data points are used for training, and 58 data points for validation. The results of machine learning techniques and regression models are given in Appendix A.

ANN
Parametric adjustments are made before running the proposed ANN model. These parameters include number of hidden layers, total number of neurons per hidden layer, training function for neural networks, epochs, and maximum number of iterations. These parameters are determined through the hit and trial method in this research. The details of the parametric adjustment are given in Table 4. It is noteworthy that the correlation factor for ANN predicted CS (R 2 = 0.98) is quite high. The prediction result for ANN is plotted in Figure 5. The above equation can be utilized to find values of Y for each input value X.
In above equations of MNLR and LR, "Y" stands for compressive strength of RH Similarly, the values of "X" represents inputs which are age, water content, RHA conte SP content, and the percentage of aggregates.
The models are developed in Microsoft Excel by authors for MNLR and LR tec niques using the above equations.

Results
A total of 192 data points are used for all the models and techniques. A total of 1 data points are used for training, and 58 data points for validation. The results of machi learning techniques and regression models are given in Appendix A.

ANN
Parametric adjustments are made before running the proposed ANN model. The parameters include number of hidden layers, total number of neurons per hidden lay training function for neural networks, epochs, and maximum number of iterations. Th parameters are determined through the hit and trial method in this research. The deta of the parametric adjustment are given in Table 4. It is noteworthy that the correlation factor for ANN predicted CS (R 2 = 0.98) is qu high. The prediction result for ANN is plotted in Figure 5.

ANFIS
Similarly, before training the data on ANFIS, parametric adjustments were made. These included total number of epochs and function used for the activation of ANFIS. The parametric adjustments for ANFIS are given in Table 5. MATLAB is used for ANFIS. The correlation factor for ANFIS predicted CS (R 2 = 0.89) is also quite high. Figure 6 shows that the predicted results are quite close to the experimental values. Figure 7 shows the rules assigned to ANFIS for the optimum outcome.

ANFIS
Similarly, before training the data on ANFIS, parametric adjustments were made. These included total number of epochs and function used for the activation of ANFIS. The parametric adjustments for ANFIS are given in Table 5. Table 5. Parametric adjustments for ANFIS.

Parameters Description
Training function trimf Epochs 6 Training completed at epoch 2 MATLAB is used for ANFIS. The correlation factor for ANFIS predicted CS (R 2 = 0.89) is also quite high. Figure 6 shows that the predicted results are quite close to the experimental values.

ANFIS
Similarly, before training the data on ANFIS, parametric adjustments were These included total number of epochs and function used for the activation of A The parametric adjustments for ANFIS are given in Table 5. MATLAB is used for ANFIS. The correlation factor for ANFIS predicted C 0.89) is also quite high. Figure 6 shows that the predicted results are quite close experimental values. Figure 7 shows the rules assigned to ANFIS for the optimum outcome.

MNLR
The results predicted by MNLR were not close to the experimental results. The correlation factor for MNLR predicted CS (R 2 = 0.70) confirms the same. The correlation factor for training and validation is 0.75 and 0.69, respectively. The same can be confirmed by the dispersion of points in Figure 8 below.

MNLR
The results predicted by MNLR were not close to the experimental results. The correlation factor for MNLR predicted CS (R 2 = 0.70) confirms the same. The correlation factor for training and validation is 0.75 and 0.69, respectively. The same can be confirmed by the dispersion of points in Figure 8 below.

LR 40
LR gave the results which were far away from the experimental results. A weak correlation (R 2 = 0.63) existed between the experimental and predicted results. The correlation factor for LR training and LR validation is 0.64 and 0.62, respectively. It can be seen in Figure 9 below that points are dispersed.

Sensitivity and Parametric Analysis
Different variables are used to find the CS of RBC. Sensitivity analysis (SA) is used to determine the relative contribution of these variables to the result. SA is carried out mathematically by using the following Equations: where f max (x i ) is the maximum, and f min (x i ) is the minimum output of the predictive models, respectively. Thus, i represents the input domain and other input variables that are kept constant. It is obvious from the graphical representation (shown in Figure 10) that the contribution of different input variables on the CS of RBC is same as that in real life.

MNLR
The results predicted by MNLR were not close to the experimental results. The correlation factor for MNLR predicted CS (R 2 = 0.70) confirms the same. The correlation factor for training and validation is 0.75 and 0.69, respectively. The same can be confirmed by the dispersion of points in Figure 8 below.

LR 40
LR gave the results which were far away from the experimental results. A weak correlation (R 2 = 0.63) existed between the experimental and predicted results. The correlation factor for LR training and LR validation is 0.64 and 0.62 , respectively. It can be seen in Figure 9 below that points are dispersed.

LR 40
LR gave the results which were far away from the experimental results. A weak correlation (R 2 = 0.63) existed between the experimental and predicted results. The correlation factor for LR training and LR validation is 0.64 and 0.62 , respectively. It can be seen in Figure 9 below that points are dispersed.

Sensitivity and Parametric Analysis
Different variables are used to find the CS of RBC. Sensitivity analysis (SA) is used to determine the relative contribution of these variables to the result. SA is carried out mathematically by using the following Equations: where max ( ) is the maximum, and min ( ) is the minimum output of the predictive models, respectively. Thus, i represents the input domain and other input variables that are kept constant. It is obvious from the graphical representation (shown in Figure 10) that the contribution of different input variables on the CS of RBC is same as that in real life.

Sensitivity and Parametric Analysis
Different variables are used to find the CS of RBC. Sensitivity analysis (SA) is used to determine the relative contribution of these variables to the result. SA is carried out mathematically by using the following Equations: where max ( ) is the maximum, and min ( ) is the minimum output of the predictive models, respectively. Thus, i represents the input domain and other input variables that are kept constant. It is obvious from the graphical representation (shown in Figure 10) that the contribution of different input variables on the CS of RBC is same as that in real life. Along with sensitivity analysis, a parametric analysis (PA) is also carried out. This helps in determining the influence of the input parameters on the output parameter. This shows the trend of CS when all the input variables are kept constant at their mean value except one input. The change in CS is recorded when one input variable is varied from its minimum value to its maximum value. All the results of PA are shown in Figure 11 below.
The sublots in front of each graph in Figure 11 represent the constant parameters of parametric analysis for each input. The literature used for obtaining experimental values includes [12,[35][36][37][38][39]. It can be observed from the results that when water is increased from a certain limit, a reduction in CS occurs. This is also obvious from previous studies. De Sensale [39] conducted research in which a water to cement ratio (w/c) of 0.4 gave more CS than w/c of 0.5. RHAP contributes towards the enhancement of strength, but when RHAP is increased by 30 percent, it results in decrease of compressive strength. This is due to the fact that, as discussed in Section 1, RHA contains 90 percent silica. By increasing the RHA percentage, the amount of silica is also increased. This silica remains unreacted by increment of RHA and results in reduced CS of RBC [37].
It can be seen from the above results that the regression models did not show satisfactory results as compared to the machine learning processes. This is due to certain limitations in regression models, such as pre-defined equations that cannot learn the relationship between input variables and the function properly. Whereas, machine learning has efficiently predicted the relationship between input and output variables. The machine learning techniques gave results closer to the experimental values. Along with sensitivity analysis, a parametric analysis (PA) is also carried out. This helps in determining the influence of the input parameters on the output parameter. This shows the trend of CS when all the input variables are kept constant at their mean value except one input. The change in CS is recorded when one input variable is varied from its minimum value to its maximum value. All the results of PA are shown in Figure 11 below. The sublots in front of each graph in Figure 11 represent the constant parameters of parametric analysis for each input. The literature used for obtaining experimental values includes [12,[35][36][37][38][39]. It can be observed from the results that when water is increased from a certain limit, a reduction in CS occurs. This is also obvious from previous studies. De Sensale [39] conducted research in which a water to cement ratio (w/c) of 0.4 gave more CS than w/c of 0.5. RHAP contributes towards the enhancement of strength, but when RHAP is increased by 30 percent, it results in decrease of compressive strength. This is due to the fact that, as discussed in Section 1, RHA contains 90 percent silica. By increasing the RHA percentage, the amount of silica is also increased. This silica remains unreacted by increment of RHA and results in reduced CS of RBC [37].

Cement
It can be seen from the above results that the regression models did not show satisfactory results as compared to the machine learning processes. This is due to certain limitations in regression models, such as pre-defined equations that cannot learn the relationship between input variables and the function properly. Whereas, machine learning has efficiently predicted the relationship between input and output variables. The machine learning techniques gave results closer to the experimental values.

Conclusions
Different models for prediction of CS of RBC are developed in this study. The models developed in this study are based on wide range of data which consist of different parameters demonstrated by experimental studies that are available in the literature. The models considered the most influential parameters on CS as inputs. The results obtained in this research are closer to the experimental research. The following conclusions can be drawn from the obtained results: 1. The PA has shown that the input parameters used in this research are effectively utilized by the model to predict the CS. Moreover, the statistical parameter R 2 shows the accuracy of the data used for the training and validation of different models.

Conclusions
Different models for prediction of CS of RBC are developed in this study. The models developed in this study are based on wide range of data which consist of different parameters demonstrated by experimental studies that are available in the literature. The models considered the most influential parameters on CS as inputs. The results obtained in this research are closer to the experimental research. The following conclusions can be drawn from the obtained results:

1.
The PA has shown that the input parameters used in this research are effectively utilized by the model to predict the CS. Moreover, the statistical parameter R 2 shows the accuracy of the data used for the training and validation of different models.

3.
It is evident by the comparison of ANN and ANFIS with the regression models that both ANN and ANFIS have a high command on prediction of CS of RBC. Therefore, they are suitable for the predesign of RBC. 4.
The proposed models can provide the basis for using RBC in different structures rather than discarding it.
Concrete containing RHA has a great potential to replace OPC concrete. It is recommended that extensive research be carried out by including more parameters. These parameters should include temperature, corrosion, and resistance to chlorine and acid attacks. Other advanced programming techniques such as an M5P tree and gene expression programming can be used to make further predictions.