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

Figures & data

Figure 1. Flowchart of machine learning techniques and regression 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.

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

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

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

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

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

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.

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

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

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

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

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

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

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Data availability statement

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