Predicting the compressive strength of cellulose nanofibers reinforced concrete using regression machine learning models

Abstract

Cellulose nanofibers (CNFs) are the newly introduced plant-based materials in the construction industry to ensure sustainable development. The use of artificial intelligence (AI) techniques especially machine learning (ML) models has assisted to economized civil engineering. This research aims to determine the compressive strength of cellulose nanofibers reinforced concrete by using supervised regression machine learning techniques for analysis before adopting to utilize. To achieve this task, the machine learning models: Random Forest (RF), Linear Regression (LR), Support Vector Regressor (SVR), Gradient Boosting Regressor (GBR), Ada Boosting Regressor (ABR), K-Neighbor Regressor (KNN), Bagging Regressor (BR), XG Boost Regressor (XGBR), Decision Tree (DT), and Pruned Decision Tree (PDT) were implemented. An experimental-based dataset containing 695 data points was prepared and split into two categories (Training dataset = 70%, Testing dataset = 30%) for the evolution of ML models. There were seven independent variables: cement (kg/m³), water (kg/m³), CNFs (kg/m³), superplasticizer (kg/m³), fine aggregate (kg/m³), coarse aggregate (kg/m³), and age (Day) variables as an input and one dependent variable: compressive strength fc of CNFs reinforced concrete (MPa) as an output. The following metrics were employed to gauge the ability of the model: R², MAPE, MAE, MSE, and RMSE. The findings specified that seven out of ten models (RF, BR, XGBR, DT, GBR, ABR, and KNN) to predict the compressive strength of CNFs concrete had a firm capability (R² >0.72, MAPE ≤ 0.1, and MAE ≤ 5) confirming to the standard of R² value greater than 0.60 and metrics values very less, close to one. According to the sensitivity analysis of Random Forest model, water and cement were the factors with the biggest effects on the prediction of CNFs reinforced concrete, while the smallest effecting variable was coarse aggregate. It was concluded that the RF, BR, and DT were the premier predicting models.

Keywords:

• Artificial intelligence
• machine learning
• Cnfs concrete
• compressive strength
• prediction
• sensitivity analysis

1. Introduction

The world’s second-most consuming substance is concrete, right after water. Cement manufacturing sector is the second-biggest industrial emitter of carbon dioxide (CO₂), accounting for around 7% of worldwide emissions and the third-largest industrial energy user in the world (Amiri & Hatami, 2022; Kolour, 2019). A promising novel path to sustainable development will be the introduction of a new green material in construction industry (Balea et al., 2019; Hilal et al., 2022 ; Li et al., 2021). Some potential answers come from plant-based materials (Taheri et al., 2022). The usage of nanomaterial additives is a related development (Barnat-Hunek et al., 2019; Kamasamudram, 2019). The short- and long-term characteristics of cement-based composites have appeared and continue to reveal considerable assurance for improvement through nanotechnology [9]. Nanotechnology is an interdisciplinary area of science and engineering that focuses on recognizing and operating with materials at proportions between 1–100 nanometers (Yang et al., 2015). The extraction and use of nanomaterials from environmentally friendly, inexpensive, abundant, renewable, and biodegradable natural resources is one of the most encouraging approaches for sustainable development incorporating nanotechnology (Falinski et al., 2018). The most prevalent biopolymer on earth, cellulose, which is found in a variety of renewable biomass sources like trees, plants, tunicates, and bacteria, is one such appealing bioresource (Jiang et al., 2018). The CNFs are fibers that have undergone mechanical fibrillation and acid hydrolyses to produce nanosized, super durable, and highly surface-area nanofibers (Onuaguluchi & Banthia, 2016). The wood, rice straw, bagasse, banana, pine apple leaf, cotton, etc. are all sources of CNFs (Moon et al., 2011). Constructionally, cellulose is a linear, high-molecular-weight polysaccharide with repeated glucose units connected by 1–4 glycosidic linkages. These linear chains of glucose units, which contain hydroxyl groups, join together by intermolecular hydrogen bonds and Van Der Waals forces to create elementary fibrils (Da Silva et al., 2021).

Concrete, reinforced with cellulose nanofibers is made by using nanoparticles that enhance the hydration of the cement and the microstructure of the hardened matrix (Paul et al., 2018). In this way, it makes use of capacity of concrete to improve performance when building civil works around the globe (Hisseine et al., 2019). The emergence of the most expressive works in this field began in 2010, which exemplifies how recent this field of study is (Santos et al., 2021). Around 4.4 billion tons of concrete are produced annually around the globe. By 2050, the figure is anticipated to rise to more than 5.5 billion tons (Lehne & Preston, 2018). The concrete industry is unsustainable because of the large production and consumption of Portland cement, which has negative environmental effects (García et al., 2016; Jonoobi et al., 2015; Metaxa et al., 2021; Nechyporchuk et al., 2016; Sun et al., 2016; Takasi, 2019; Trache et al., 2017; Yu et al., 2020). Nanofibrillar cellulose is one of the modifying additives whose application in cement composites is now actively under study (Barabanshchikov et al., 2021). Some researchers have investigated the effects of cellulose nanofibers and nanocrystals on concrete (Collet et al., 2013; Machado et al., 2016, 2017; Peters et al., 2010); nanofibrillated cellulose cement mortar as potential reinforcement (Ardanuy Raso et al., 2012; Ardanuy et al., 2012; Claramunt et al., 2015; Ferrara et al., 2015; Goncalves et al., 2019); addition of micro/nanofibrils in extruded cement mortar (da Costa Correia et al., 2018; Fonseca et al., 2019); mechanical behavior of micro/nanomaterials in cement based composites (Claramunt et al., 2019; da Costa Correia et al., 2019; Dai et al., 2015; El Bakkari et al., 2019; Hoyos et al., 2019; Jiao et al., 2016; Kamasamudram et al., 2021; Mejdoub et al., 2017; Onuaguluchi et al., 2014; Reixach et al., 2019; Zhang & Scherer, 2020); and the influence of cellulose nanoparticles on oil well cement paste (Correia et al., 2015; Tang et al., 2019).

Compressive strength is one of the key mechanical properties of concrete (Mohr et al., 2005; Supit & Nishiwaki, 2019). The quality of a concrete mixture that allows it to sustain compression is known as compressive strength (Jha et al., 2020; Pham et al., 2021; Sobhani et al., 2010). The compressive strength of concrete must meet set requirements in order for construction to produce the intended results and extend the useful life of infrastructure (de Larrard & Belloc, 1997; Poon et al., 2004; Öztaş et al., 2006). The compressive strength (fc) which is measured in megapascals (MPa) can be prescribed as the maximum applied force (F) in newton dividing it by the cross-sectional area (A) in meter square (Ahmad, Farooq, et al., 2021; de Prado-Gil et al., 2022; Marani & Nehdi, 2020; Nafees et al., 2021). It can be simplified into the following formula in Equation 1:

(1) $\mathit{fc}=\frac{F}{A}$(1)

The compressive strength of CNFs concrete is typically used to determine its quality because it directly relates to the composition of the hardened mixture and serves as a standard benchmark (Hisseine et al., 2019). Physical experiments are frequently used to assess the compressive strength of CNFs concrete; however, these investigations are costly and time-wasting to conduct. As a result, the working efficiency is quite low (Metaxa et al., 2021). Therefore, technology advancements enable the employment of alternative methodologies, such as artificial intelligence (AI), deep learning (DL), and machine learning (ML) methods, to solve engineering problems at a cheaper cost (Feng et al., 2020). Considering the desired ratio of mixing various ingredients (cement, water, CNFs, superplasticizers, fine aggregate, coarse aggregate, and time), these methods enable predicting the compressive strength of CNFs concrete (Silva et al., 2020). In this context, artificial intelligence techniques and machine learning methods are increasingly being utilized to predict the compressive strength of concrete. Machine learning (ML) has two main perspectives named supervised and unsupervised ML which are used to accomplish regression, classification, and clustering tasks (Shahmansouri et al., 2021). Because of this, it is now simple to estimate the compressive strength as well as other mechanical properties by the development of ML techniques (Chopra et al., 2015). In particular, by the application of specific techniques such as ML regression algorithms that learn from the input dataset and deliver incredibly accurate results to determine the compressive strength of CNFs reinforced concrete. The compressive strength of CNFs concrete is currently predicted using a number of machine learning techniques, including Artificial Neural Network (ANN), ensemble approaches, and generalized additive models (GAM) (de Prado-Gil et al., 2022).

Machine learning is one of the main techniques for artificial intelligence. Instead of directly coding a system, machine learning trains it using algorithms to learn from data (Jha et al., 2020). This leads to rapid and more precise outcomes, which lowers error rates to almost nonexistent levels. The two main categories of machine learning approaches are supervised and unsupervised. Supervised machine learning develops a model using known independent and dependent data in order to determine output, while unsupervised machine learning identifies hidden patterns or intrinsic structures in raw data. The flowchart of the machine learning methods and regression models used in the study is shown in Figure 1.

Figure 1. Flowchart of machine learning techniques and regression models.

The aim of supervised machine learning is to design a model that generates predictions based on evidences when there is uncertainty. Using a defined set of independent data and defined responses to the dependent data, supervised learning builds an algorithm to produce precise predictions for the response to incoming data. To design predictive algorithms, supervised machine learning possesses classification and regression methods (Chopra et al., 2015). Classification techniques predict discrete responses and classify input dataset into groups. Continuous responses are predicted via regression algorithms. The supervised machine learning regression models implemented in this work are Random Forest (RF), Linear Regression (LR), Support Vector Regressor (SVR), Gradient Boosting Regressor (GBR), Ada Boosting Regressor (ABR), K-Neighbor Regressor (KNN), Bagging Regressor (BR), XG Boost Regressor (XGBR), Decision Tree (DT), and Pruned Decision Tree (PDT). On the other hand, unsupervised learning recognizes fundamental data structures or hidden patterns. Table 1 displays the comparisons among various methods for predicting the mechanical properties of concrete and shows a significant improvement by the ML models.

Table 1. Comparative analysis among various methods with the ML models

Methods/Models	Definition	Advantage	Drawback	ML Models
Experimental Methods	A trial examination used as a means of measuring either a physical or a chemical characteristic of a material.	High level of control; good prediction accuracy; results can be duplicated.	Possibility of human error; costly; time-consuming.	Time saving; cheaper; no possibility of human error.
Statistical Models (SM)	Modeling the relationship between the decision variables and a concrete mixture objective.	Precise; it is possible to build statistical models using equations with interactive terms.	Costly and time consuming; cannot capture complex relationships between data.	Better predictions; time saving; cheaper; more empirical high predictive accuracy.
Analytical Models (AM)	Models are been proposed based on the conceptual postulation of how the hydrated cement interacts with other particles.	Accounts the most important factors that affect the strength of concrete; to design concrete mixtures.	Limited to conventional concrete or normal concrete.	Applicable at large scale of civil engineering and gives precise results.
Numerical Models (NM)	Numerical modeling uses mathematical models to describe the physical conditions of geological scenarios using numbers and equations.	The result of numerical model is nearly the same as what the mathematical model predicts when the element size is nearly zero.	Difference between the actual and the predicted results; need a high level of knowledge.	Performances of machine learning models on simulating historical data is superior to those of numerical model; numerous executions.
Conventional Models (CM)	Models developed from statistical analysis of experimental data predicting the compressive strength of conventional concrete.	Convenient in providing explicit mathematical formulas; prediction accuracy satisfactorily.	Perform poorly in dealing with complex materials; unreliable for estimating properties of several types of concrete.	Applicable to various type of concrete; precise prediction; strong deal with complex data.
Empirical Models (EM)	Generic term for activities that create models by observation and experiment.	Computer-based; operates on a simple semantic principle; close correspondence.	Applicability is limited; leading to higher error when forecasting ‘‘unseen” data; experimental data are always needed.	Accurately predicting the properties of complex concrete materials.
Traditional methods	Classical experimental methods and regression methods based on mathematical statistics.	More accurate in predicting the compressive strength of concrete in simpler situations.	Accurate prediction of will become very difficult at more factors; test data are non-repeatable.	Generate reliable prediction models through training, output highly accurate results.
Traditional Statistics (TS)	Analyzing and summarizing data; Mainly focused on traditional data analysis.	Promotes data reduction before modeling.	Preferable to use less number of input features; limited in techniques and approaches.	Read data of all sorts; solving more complex problems; reasoning.

There are different machine learning algorithms and techniques used by the researchers to different prediction targets at various dataset points. Some of them are listed in Table 2.

Table 2. Prediction properties using different approaches (Ahmad, Ostrowski, et al., 2021)

No	Models	Abbreviations	Datapoints	Prediction Target	Fiber
1	Intelligent rule-based enhanced multiclass support vector machine and fuzzy rules	IREMSVM-FR with RSM	114	Compressive strength	Fly Ash
2	Random forest	RF	131	Compressive strength	Fly Ash GGBFS
3	Multivariate adaptive regression spline	M5, MARS	114	Compressive strength Slump test L-box test V-funnel test	Fly Ash
4	Random kitchen sink algorithm	RKSA	40	V-funnel test J-ring test Slump test Compressive strength	Fly Ash
5	Adaptive neuro fuzzy inference system	ANFIS	55	Compressive strength	_
6	Artificial neuron network	ANN	114	Compressive strength	Fly Ash
7	Artificial neuron network	ANN	69	Compressive strength	Fly Ash
8	Individual and ensemble algorithm	GEP, DT, and bagging ANN	270	Compressive strength	Fly Ash
9	Individual with ensemble modeling	Bagging and boosting	1030	Compressive strength	Fly Ash
10	Multivariate	MV	21	Compressive strength	Crumb rubber with SF
11	Gene expression programming	GEP	277	Axial capacity	_
12	Adaptive neuro fuzzy inference system	ANFIS with ANN	7	Compressive strength	POFA
13	Response surface method, gene expression programming	RSM, GEP	108	Compressive strength	Steel
14	Ensemble machine learning models	RF, KNN, GB, XGB	515	Compressive strength	Self-compacting concrete
15	Artificial neuron network	ANN	1030	Compressive strength	Highperformance concrete

The study focuses on predicting the compressive strength of cellulose nanofibers reinforced concrete by the implementation of machine learning models. Dataset was prepared including samples of cellulose nanofibers concrete, mortar, and cement paste. Ten regression machine learning models were developed for determining the compressive strength because it is the key mechanical property. The number of dataset points under this research were kept higher to develop a strong predicting model. Engineering features were studied to examine the arrangement, ability and capacity of dataset variables. Finally, model performance evaluation was conducted to get decisions on the predicting performance of each model and sensitivity analysis was performed to calculate the compressive strength of CNFs concrete.

2. Materials and methods

The ability of RF, LR, SVR, ABR, KNN, BR, XGBR, DT, PDT, and GBR models to predict the compression strength of CNFs reinforced concrete for training and testing dataset was comprehensively analyzed by the metrics: Coefficient of Determination (R²), Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). K-fold cross validation value was also determined to compare the R² values of testing dataset. Nevertheless, the coefficient of determination value which is denoted by R² is perceived as the best of metrics for algorithm judgment. Additionally, the result of R² is evaluated as acceptable and applicable if value range is in between 0.60 and 0.75, good and desired model if value range is from 0.75 to 0.90, and indicates excellent projection if the result of R² is greater than 0.95. Whereas, the R² values below 0.60 indicate bad performance and unacceptable. In the end, sensitivity analysis was performed to study and explore the contribution of each independent variable.

2.1. Experimental dataset

The outcomes of 695 samples of CNFs-reinforced concrete were included in the dataset compiled during the investigation. The dataset was summarized in Table 3 along with the quantity of data “Number of datapoints”, “Reference”, where each datapoint was located “Sr. No. in Excel file”, and its proportion “Percentage”. The dataset contained three types of datapoints: concrete, mortar, and cement paste. Figure 2 illustrated the percentage of each data type available in dataset. There are basically five steps to follow in machine learning to reach at the target, it is explained in Figure 3.

Figure 2. Quantities of data type in percentage.

Figure 3. Flowchart of working steps on regression machine learning model.

Table 3. Experimental dataset

Sr. No.	Reference	No. of datapoints	Sr. No. in excel file	Percentage
1	Takasi [24]	216	159–374	31.10
2	Chopra et al (Chopra et al., 2015).	147	375–521	21.15
3	Kolour (Kolour, 2019)	142	2–143	20.43
4	Kamasamudram (Kamasamudram, 2019)	80	611–690	11.51
5	Oh JA et al (Oh et al., 2022).	30	581–610	4.32
6	Mejdoub et al (Jiao et al., 2016).	21	560–580	3.02
7	Jiao et al (Onuaguluchi et al., 2014).	18	537–554	2.59
8	Hisseine et al (Hisseine et al., 2019).	15	522–536	2.16
9	Da Silva et al (Da Silva et al., 2021).	12	147–158	1.73
10	Kamasamudram et al (da Costa Correia et al., 2019).	6	691–696	0.86
11	Barnat-Hunek et al (Barnat-Hunek et al., 2019).	5	555–559	0.72
12	Alzoubi et al (Alzoubi et al., 2020).	3	144–146	0.43
Total		695		100.00

The dataset designed, which is described in Table 3, was used for the supervised regression machine learning models. Dataset, in collection, discuss how cellulose nanofibers can be used to strengthen concrete and cement composites (CNFs). The dataset explains the reinforcement of concrete and cement composites with cellulose nanofibers (CNFs). Seven parameters were taken as input, cement, water, CNFs, superplasticizer, fine aggregates, coarse aggregates, and age, and one parameter as output compressive strength fc. These parameters were employed in the Jupyter Notebook (anaconda) python software in order to indicate the graphical representation as well as to check the dataset variable relationships and prediction power of the model. It was evident that the independent parameters had a major impact on the model’s performance (Hameed et al., 2021).

2.2. Training and testing division of dataset

It is essential for supervised regression machine learning algorithms to benchmark the dataset by separating it into subdivision of training dataset and testing dataset. The model is created using the training set of the dataset, and its performance is evaluated using the testing set of data. The training subset of the data is specified to build the model while testing dataset demonstrates the perfection of the algorithm in the prediction of compressive strength of CNFs reinforced concrete. Therefore, in this study 70% of the dataset was set out for training the model and the remaining 30% was for testing the compressive strength of CNFs concrete. Equation 2 describes the dataset splitting command:

(2) $\mathrm{x\_train},\mathrm{x\_test},\mathrm{Y\_train},\mathrm{Y\_test}=\mathrm{train\_test\_split}\left(\mathrm{xscaled},\mathrm{Y},\mathrm{test\_size}=0.3,\mathrm{random\_state}=1\right)$(2)

2.3. Model development

In this study, ten machine learning models (RF, LR, SVR, ABR, KNN, BR, XGBR, DT, PDT, and GBR) were arranged to determine the compressive strength of CNFs reinforced concrete and cement composites. After data preparation, the dataset file was loaded into the model and input variables and output variable were commenced into the regression learning algorithms. The prediction model was generated using the training dataset which contained 70% of the data, while remaining 30% was utilized for testing the data. The parameters developed for each algorithms were listed in Table 4.

Table 4. Parameters specification to develop model

Model	Parameters
RF	n_estimators=100; criterion=‘squared_error’; max_depth=None; min_samples_split=2; min_samples_leaf=1; min_weight_fraction_leaf=0.0; max_features=1.0; and random_state=None
LR	fit_intercept=True; copy_X=True; n_jobs=None; and positive=False. SVR: kernel=‘rbf’; degree=3; gamma=‘scale’; coef0=0.0; tol=0.001; and cache_size=200
GBR	loss=‘squared_error’; learning_rate=0.1; n_estimators=100; criterion=‘friedman_mse’; min_samples_split=2; max_depth=3; init=None; random_state=None; and validation_fraction=0.1
ABR	n_estimators=50; learning_rate=1.0; loss=‘linear’; random_state=None KNN: n_neighbors=i where i was in range (1,45) n_neighbors=2 got the best result; weights=‘uniform’; and leaf_size=30
BR	n_estimators=10; max_samples=1.0; max_features=1.0; random_state=None; and base_estimator=‘deprecated’
XGBR	base_score=0.5; booster=‘gbtree’; learning_rate=0.3; max_depth=6; n_estimators=100; and random_state=0
DT	criterion=‘squared_error’; splitter=‘best’; max_depth=None; min_samples_split=2; min_samples_leaf=1; and random_state=None
PDT	criterion=‘squared_error’; splitter=‘best’; max_depth=None; min_samples_split=2; min_samples_leaf=1; and random_state=None

2.4. Metrics analysis of model’s performance

To evaluate the effectiveness and precision of supervised regression machine learning models designed to predict the compressive strength fc (MPa) of CNFs concrete, five statistical performance criteria: Coefficient of Determination (R²), Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) were used. Equations 3, 4, 5, 6, and 7 can be used to calculate R², MSE, RMSE, MAE, and MAPE, respectively (Ahmad, Farooq, et al., 2021; de Prado-Gil et al., 2022; Marani & Nehdi, 2020; Nafees et al., 2021).

(3) $R^2=1-\frac{\sum {\left(y_i-{\hat{y}}_{\mathit{i}}\right)}^2}{\sum {\left(y_i-{\bar{y}}_{\mathit{i}}\right)}^2}$(3)

(4) $\mathit{MSE}=\frac{1}{n}\sum {\left(y_i-{\hat{y}}_{\mathit{i}}\right)}^2$(4)

(5) $\mathit{RMSE}=\sqrt[2]{\frac{1}{n}\sum {\left(y_i-{\hat{y}}_{\mathit{i}}\right)}^2}$(5)

(6) $\mathit{MAE}=\frac{1}{n}\sum \left|\left(y_i-{\hat{y}}_{\mathit{i}}\right)\right|$(6)

$\mathit{MAPE}=\frac{100}{n}{{\displaystyle \sum }}^{\mathit{ }}\frac{(y_i-{\widehat{y}}_{\mathit{i}})}{y_i}|,$

where $y_i$ = fc (output variable), ${\hat{y}}_{\mathit{i}}$= CS fc estimated, ${\bar{y}}_{\mathit{i}}$ = mean of fc actual, and n = total number of points in dataset. The units of R² and MAPE were considered in percentage while MAE, MSE, and RMSE were expressed in megapascal as the compressive strength of CNFs concrete. The projection outcome of the compressive strength of CNFs reinforced concrete using ML models can be enunciated in such a way that the values of MSE, MAPE, MAE, RMSE metrics are inversely proportional to the prediction accuracy, smaller the values of MSE, MAPE, MAE, and RMSE higher will be the accuracy rate. On another hand, if R² value which was the dominant metrics of this study and directly proportional to the accuracy level, the bigger (closer to 1), the potential and performance of model to prediction will be bigger and vice versa (de Prado-Gil et al., 2022).

3. Results and discussion

3.1. Correlation coefficient analysis

The exploratory data analysis (r) between the independent variables (x): cement, water, CNFs, superplasticizers, fine aggregates, coarse aggregates, and age and the dependent variable (Y) compressive strength fc was conducted to assess the interdependence of variables. The obtained value of r showed the correlation ratio between the variables, the higher the value the stronger will be the correlation. In this research each variable would be investigated by the coding in Jupyter Notebook. While computing correlation coefficient value, the peculiar command was given into the model to analyze the correlation heatmap, Equation 8(8) $\mathrm{plt}.\mathrm{figure}\left(\mathrm{figsize}=\left(10,7.5\right)\right)$(8) ,9(9) $\mathrm{ax}=\mathrm{sns}.\mathrm{heatmap}(\mathrm{dataset}.\mathrm{corr}(),\mathrm{cmap}=\mathrm{coolwarm},\mathrm{annot}=\mathrm{True},\mathrm{linewidth}=2)$(9) specifies the command run in the Jupyter Notebook Python software to print heatmap while Figure 4 shows the heatmap graph of r. The correlation coefficient can also be calculated through Equation 10(10) $\mathit{r}=\frac{{{\displaystyle \sum }}^{\mathit{\hspace{0.17em}}}[(x_i-\bar{x})(y_i-\bar{y})]}{\frac{}{}}\sqrt{{(x_i-\bar{x})}^2\ast {(y_i-\bar{y})}^2},$(10) .

Figure 4. Correlation heatmap between the independent and dependent parameters.

(8) $\mathrm{plt}.\mathrm{figure}\left(\mathrm{figsize}=\left(10,7.5\right)\right)$(8)

(9) $\mathrm{ax}=\mathrm{sns}.\mathrm{heatmap}(\mathrm{dataset}.\mathrm{corr}(),\mathrm{cmap}=\mathrm{coolwarm},\mathrm{annot}=\mathrm{True},\mathrm{linewidth}=2)$(9)

(10) $\mathit{r}=\frac{{{\displaystyle \sum }}^{\mathit{\hspace{0.17em}}}[(x_i-\bar{x})(y_i-\bar{y})]}{\frac{}{}}\sqrt{{(x_i-\bar{x})}^2\ast {(y_i-\bar{y})}^2},$(10)

where, r = Correlation coefficient, x_i = Independent variable, $\bar{X}$= Mean of independent variable, y_i = fc (dependent variable), $\bar{Y}$= Mean of actual fc, i = 1, … , n, and n = Total number of points in dataset (Sobhani et al., 2010). It can be observed that correlation coefficient value of not even a single variable is bigger than 0.85 which proves that there is no serious mutual correspondence between the independent variables, this shows that the independent variables are not multicollinear and participate individually to develop each model.

Tables 5 and 6 recorded the outlier values, descriptive analysis, and the mathematical demonstration of the variable implied to run the model. Table 5 displayed the mean, median (50%), quarter (75%), mode, standard deviation, minimum, maximum, sample variance, skewness and sum of input variables: cement (Kg/m³), water (Kg/m³), CNFs (Kg/m³), superplasticizers (Kg/m³), fine aggregates (Kg/m³), coarse aggregates (Kg/m³), and age (day) and the output variable: compressive strength fc (MPa) were utilized to design the compression strength of CNFs reinforced concrete by implementing supervised regression machine learning models. Figure 5 showed the graph of the number of outliers in each variable. It can be observed that outlier percentage of four variables: cement, water, coarse aggregate, and age is zero, and two variables: fine aggregates and compressive strength was merely 1 and 2 percent, respectively, which is the representation of a good dataset. Only two variables: cellulose nanofibers and superplasticizers had an outlier percentage nearly equals to 11, which is also very low, it can be ignored because six out of eight (75%) variables does not have outlier so this small percentage did not affect the impact of dataset to predict the output.

Figure 5. Box plot of the number of outliers in each independent variable.

Table 5. Descriptive analysis of the input and output variables

Variables		Abbreviation	Count	Mean	Median	Quarter	Mode	St. D	Min	Max	Sample Variance	Skewness	Sum
Input	Cement (Kg/m^3)	C	695.00	381.26	411.00	510.74	500.00	145.51	126.17	580.00	21173.64	−0.35	264972.96
	Water (Kg/m^3)	W	695.00	157.88	180.00	205.85	175.00	60.40	12.29	290.00	3648.17	−0.24	109727.00
	Cellulose Nanofiber (Kg/m^3)	CNFs	695.00	0.46	0.16	0.42	0.00	1.67	0.00	40.00	2.78	19.53	320.68
	Superplasticizer (Kg/m^3)	SP	695.00	0.40	0.00	0.00	0.00	1.77	0.00	27.50	3.14	8.25	280.71
	Fine Aggregate (Kg/m^3)	FA	695.00	288.13	219.98	481.50	0.00	331.26	0.00	1699.32	109736.00	1.74	200250.00
	Coarse Aggregate (Kg/m^3)	CA	695.00	265.38	0.00	579.40	0.00	443.04	0.00	1253.75	196284.00	1.21	184441.00
	Age (Day)	A	695.00	35.31	28.00	56.00	28.00	25.45	1.00	91.00	647.74	–	24538.00
Output	Compressive Strength fc (MPa)	CS	695.00	47.10	47.40	55.60	55.00	13.68	7.50	97.90	187.12	0.11	32734.87

Table 6. Outlier analysis of variables

	C (Kg/m^3)	W (Kg/m^3)	CNFs (Kg/m^3)	SP (Kg/m^3)	FA (Kg/m^3)	CA (Kg/m^3)	A (Day)	CS (MPa)
*Q1	218.53	98.8	0.0	0.0	0.0	0.0	14.0	37.93
*Q3	510.74	205.85	0.42	0.0	481.5	579.4	56.0	55.6
*IQR	292.21	107.05	0.42	0.0	481.5	579.4	42.0	17.67
Lower outlier limit	−219.785	−61.775	−0.63	0.0	−722.25	−869.1	−49.0	11.43
Upper outlier limit	949.055	366.425	1.05	0.0	1203.75	1448.5	119.0	82.105
Numbers of outlier upper	0	0	76	74	12	0	0	8
Numbers of outlier lower	0	0	0	0	0	0	0	3
% of outlier upper	0	0	11	11	2	0	0	1
% of outlier lower	0	0	0	0	0	0	0	0

*Q1= 1st quartile (q=0.25), Q3= 3rd quantile (q=0.75), IQR= Interquartile Range

In addition, to execute and analyze the outliers of dataset, following mathematical steps of Equation 11(11) $\mathrm{IQR}=\mathrm{Q}3---\mathrm{Q}1$(11) –13(13) $\mathrm{Lower}\mathrm{limit}=\left(\mathrm{Q}1–1.5\right)\ast \mathrm{IQR}$(13) were used:

Interquartile range is given by,

(11) $\mathrm{IQR}=\mathrm{Q}3---\mathrm{Q}1$(11)

(12) $\mathrm{Upper}\mathrm{limit}=\left(\mathrm{Q}3+1.5\right)\ast \mathrm{IQR}$(12)

(13) $\mathrm{Lower}\mathrm{limit}=\left(\mathrm{Q}1–1.5\right)\ast \mathrm{IQR}$(13)

Anything below the lower limit and above the upper limit is considered an outlier.

The multivariate analysis of independent and dependent variables exhibiting the density and frequency of each variable in the building is displayed in the histogram and density curve of Figures 6 ,7, respectively. This can be seen that the density curve showed a smooth flow and satisfactory result.

Figure 6. Multivariate analysis of all input and output variable.

Figure 7. (a). The density curves of variables at X and Y axis: Cement, water, CNFs, and superplasticizers.

Figure 7. (b). The density curves of variables at X axis: Cement, Water, CNFs, and Superplasticizers; and Y axis: Fine aggregate, coarse aggregate, age and compressive strength fc.

Figure 7. (c). The density curves of variables at X axis: Fine aggregate, coarse aggregate, age and compressive strength fc; and Y axis: Cement, water, CNFs, and superplasticizers.

Figure 7. (d). The density curves of variables at X and Y axis: Fine aggregate, coarse aggregate, age and compressive strength fc.

3.2. Predicting capability of supervised regression machine learning models

Table 7 displays the consequence of R², MSE, RMSE, MAE, and MAPE for the training and testing dataset values of the supervised regression models: RF, LR, SVR, GBR, ABR, KNN, BR, XGBR, DT, and PDT, for the prediction of compressive strength fc of CNFs reinforced concrete. Normally, the error in training dataset allocates the acceptability of the flourished model, while the error in the test dataset presents the abstraction capability of the designed model. Figure 8 (a,b) presents the metrcis values for RF, GBR, ABR, KNN, BR, XGBR, and DT models.

Figure 8. (a) R² and (b) MAPE, RMSE, and MAE values of RF, GBR, ABR, KNN, BR, XGBR, and DT models.

Table 7. Capability metrics of the supervised regression ML models

Sr. No.	Model	Training R^2	Testing R^2	K Fold	MSE	RMSE	MAPE	MAE
1	RF	0.97	0.81	0.82	34.20	5.84	0.09	4.10
2	LR	0.40	0.43	0.34	102.00	10.09	0.21	7.15
3	SVR	0.37	0.33	0.38	118.93	10.09	0.24	7.9
4	GBR	0.91	0.76	0.78	43.5	10.09	0.10	4.6
5	ABR	0.72	0.75	0.63	43.5	10.09	0.12	4.68
6	KNN	0.91	0.72	0.79	49.43	10.09	0.11	4.80
7	BR	0.95	0.80	0.79	49.44	10.09	0.11	4.80
8	XGBR	0.99	0.79	0.78	37.96	10.1	0.10	4.19
9	DT	0.99	0.79	0.77	37.96	10.09	0.10	4.17
10	PDT	0.69	0.59	0.59	73.04	5.84	0.16	6.72

3.2.1. Coefficient of determination R² >95%

In Table 7, it is elaborated that regression models: RF, BR, XGBR, and DT exhibit the coefficient of determination R² values of the training dataset are greater than 95% which is excellent harmony with the training data, this indicate that models can execute excellent determination of the compressive strength of CNFs reinforced concrete. While analyzing the predicting capability of the RF, BR, XGBR, and DT models, the testing dataset provides a more objective foundation for estimating the compressive strength of CNFs concrete. Table 7 reveals that the RF, BR, XGBR, and DT models are acceptable for prediction because the testing dataset R² values of these models are 0.81, 0.80, 0.79, and 0.79, respectively, which is much higher than 0.60, which proves that these algorithms can determine accurately the compressive strength fc satisfactorily. Nafees et al. have discussed that the value of R² is evaluated as acceptable and applicable if value range of a model is in between 0.60 and 0.75, good and desired model if value range is from 0.75 to 0.90, and indicates excellent projection if the result of R² is greater than 0.95. Whereas, the R² values below 0.60 indicate bad performance and unacceptable (Nafees et al., 2021). This is also observed that MSE, RMSE, MAPE, and MAE values of these models are very low.

Figure 9. Scatter plot of R² between the actual fc and predicted fc by (a) RF, (b) BR, (c) XGBR, and (d) DT models..

It can be seen in Figure 9(a,b,c) that the testing dataset prediction values of RF, BR, XGBR, and DT models are closer to the prediction line and similar to the actual fc dataset values. Also, the dispersion of data points is very less.

3.2.2. Coefficient of determination R² >90%

It can be seen that the training dataset R² values for the models GBR and KNN were greater than 90% which illustrate good accordance with the training dataset and can find out the compressive strength of CNFs close to actual values. Table 7 expresses that by comparison of metrics of the GBR and KNN models with test dataset, these models are considerable for prediction because the testing dataset R² values of these models are 0.76 and 0.72 greater than 0.60 (de Prado-Gil et al., 2022; Nafees et al., 2021). R² values greater than 0.60 can safely predict compressive strength fc satisfactorily. It can be observed that MSE, RMSE, MAPE, and MAE values of these models are also good.

Figure 10. Scatter plot of R² between the actual fc and predicted fc by (a) GBR and (b) KNN models..

It can be identified in Figure 10(a,b) that the testing dataset prediction values of GBR and KNN models as compared to RF model are not closer to prediction line and also not much similar to actual fc dataset values. And the scattering of data points is more than RF model.

3.2.3. Coefficient of determination R² >65%

It can be appreciated that the training dataset of models ABR and PDT shows R² values greater than 65% which is also acceptable. Although, R² value of testing dataset of PDT model is not acceptable due to less than 0.60, but the testing dataset R² value of ABR model is 0.75 which is great achievement as compared to PDT and MSE, RMSE, MAPE, and MAE values of ABR cannot be ignored. It can be seen in Figure 11 that the testing dataset prediction values of ABR model as compared to RF model is a little bit far to prediction line and also different to actual fc dataset values. And the distribution or diffusion of data points is more than RF model.

Figure 11. Scatter plot of R² between the actual fc and predicted fc by ABR model..

3.2.4. Coefficient of determination R² <65%

It can be seen in Table 5 that the training dataset R² values for the models LR and SVR were R² = 0.40 and R² = 0.37, respectively, and testing dataset R² values were 0.43 and 0.33, respectively. The R² values of LR, SVR indicate bad performance and unacceptable to determine the compressive strength of CNFs concrete, because these regression models hold R² values smaller than 0.60 (de Prado-Gil et al., 2022; Nafees et al., 2021). The MSE values of these models are higher than other models. Therefore, the models LR and SVR have weak predicting capability for the compressive strength of CNFs reinforced concrete.

3.2.5. Predicting capability of the best supervised regression models

After analyzing each of the ten models profoundly, it was acquired as outcome that the best algorithm to determine the compressive strength of CNFs reinforced concrete precisely and perfectly are RF, BR, and DT. Table 7 displays the metrics of the RF, BR, and DT models, where it can be noticed that not only training dataset R² value of these models is greater than 0.95 indicating a good predictor of compressive strength but also the testing dataset demonstrate R² values 0.81 (K-fold cross validation = 0.82), 0.80, and 0.79, respectively, which are highly acceptable and applicable for predicting the compressive strength of CNFs reinforced concrete. Figure 12 is presented to separately display the R², RMSE, MAPE, and MAE of the best machine learning models of the research.

Figure 12. R², RMSE, MAPE, and MAE of the best machine learning models RF, BR, and DT.

It can be summarized by declaring that the RF, BR, and DT models expressed a preferable predicting capability compressive strength of CNFs concrete, consequently these can be evaluated as the best supervised regression machine learning models.

3.3. Sensitivity analysis of the CNFs reinforced concrete

One of the most crucial problems that concrete mixture developers may face is to identify the ingredients with most significant influence on the compressive strength of cellulose nanofibers reinforced concrete (Hameed et al., 2021). In this study, the sensitivity analysis method was only executed on Random Forest model to discover if any of the seven input variables have productive impact on the compressive strength of CNFs reinforced concrete because it has the highest value of coefficient of determination. Sensitivity analysis is a method for determining how each independent variable (x) affects the dependent (Y) variable. The dependent variable is influenced more by the independent variables of high sensitivity and vice versa. Jesus et al. analyzed that water and cement are the variables with the highest contribution affecting percentage 28.39% and 23.47%, respectively, as compared to other variables to the compressive strength of self-compacting concrete (da Costa Correia et al., 2019). It was also estimated by Ayaz et al. that cement had 32% influence on predicting the compressive strength of concrete (Supit & Nishiwaki, 2019).

The sensitivity analysis results, analyzed on RF model indicate that there is a significant and considerable impact of all independent parameters, cement, water, CNFs, superplasticizers, fine aggregates, coarse aggregates, and age on the perdition of dependent parameter the compressive strength of cellulose nanofibers reinforced concrete.

Figure 13. Contribution of independent parameters to output variable in Random Forest model.

Figure 13 displays the outcomes of sensitivity analysis, it can be observed that cement 34.14%, water 36.87% are the most prominent independent parameters in the determination of compressive strength of CNFs concrete. Besides, it can be obliged that independent parameters: CNFs 6.05%, superplasticizers 3.05%, fine aggregates 6.67%, coarse aggregates 1.33%, and age 11.88% have also good contribution. The amount of independent variables and datapoints utilized to run the model affect the sensitivity analysis’s findings. Also, the results of these analysis change due to the various percentage of concrete design and by adding fresh independent variables (Supit & Nishiwaki, 2019).

4. Conclusions

Now a days, cellulose nanofibers which are the smallest plant-based particles are used to strengthen the concrete, cement paste, and cement mortar. But the experimental strength analysis is time taking, expensive and complex. To counter these factors machine learning models are used to predict the strength. However, prediction value of the model is also affected by the number of dataset points. Therefore, this work focused on predicting the compressive strength of concrete reinforced with CNFs using ten regression supervised machine learning models, dataset developed contains 695 datapoints which is a high extent and covers three types of the samples: concrete, cement mortar and cement paste. To predict the compressive strength of CNFs reinforced concrete, seven input variables were considered as independent parameters: cement (kg/m³), water (kg/m³), CNFs (kg/m³), superplasticizer (kg/m³), fine aggregate (kg/m³), coarse aggregate (kg/m³), age (Day) and compressive strength fc (MPa) as dependent variable. The predictive capability of each model was analyzed by the five metrics: R², MSE, RMSE, MAPE, and MAE. This study has narrated the application of ten models: RF, LR, SVR, GBR, ABR, KNN, BR, XGBR, DT, and PDT for the projection of the compressive strength of CNFs reinforced concrete, cement paste and mortar. A dataset of 695 samples from numerous experimental studies was acquired and divided into two groups: training (70%) and testing (30%).

The results of the test dataset showed that the RF (R² = 0.81, MSE = 34.20, RMSE = 5.84, MAPE = 0.09, and MAE = 4.10), Bagging Regressor (BR) (R² = 0.80, MSE = 49.44, RMSE = 10.09, MAPE = 0.11, and MAE = 4.80) and Decision Tree (DT) (R² = 0.79, MSE = 37.96, RMSE = 10.09, MAPE = 0.10, and MAE = 4.18) models presented the highest performance accuracy. However, it was also manifested that the LR (R² = 0.43, MSE = 102.00, RMSE = 10.09, MAPE = 0.21, and MAE = 7.15) and SVR (R² = 0.33, MSE = 118.39, RMSE = 10.09, MAPE = 0.24, and MAE = 7.9) models are not good models for predicting the compressive strength, this was demonstrated by the presented values of coefficient of determination are smaller than 0.60. Therefore, RF, BR, and DT are the best models. The sensitivity analysis of the RF model reports that cement and water with the contribution percentage of 34.24% and 36.87%, respectively, are foremost and important variables influencing and prediction of compressive strength of CNFs reinforced concrete. While, the coarse aggregate contribution percentage (1.33%) was the lowest worth. It can be concluded that cement and water enhance the compressive strength of CNFs reinforced concrete but coarse aggregate diminish it. In addition, CNFs, superplasticizers, fine aggregate, coarse aggregate, and age participate moderately to the designing and building of RF model. Hence, the extent of each independent parameters is recognized by the RF, BR, and DT algorithms.

In future, to promote the application of nanomaterials and artificial intelligence in construction industry, this research further can be enhanced by: (1) increasing datapoints, (2) varying number of input variables, (3) changing number of output variables, (4) developing new models for example classified supervised machine learning models, and (5) research on other mechanical properties.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data used to support the findings of this study are included in this published article.

Additional information

Funding

This work was supported by the Key R & D Projects in Yunnan Province under Grant 202203AC100004.