Prediction of concrete compressive strength using deep neural networks based on hyperparameter optimization

Figures & data

Table 1. Descriptive statistics.

Notation	Parameter	Maximum	Minimum	Mean	Standard deviation
CM	Cement (kg/m^3)	540.0	102	281.16	104.50
SL	Slag (kg/m^3)	359.4	0.00	73.89	86.27
FL	Fly ash (kg/m^3)	200.1	0.00	54.18	63.99
WT	Water (kg/m^3)	247.0	121.75	181.56	21.35
SP	Superplasticizer (kg/m^3)	32.2	0.00	6.20	5.97
CA	Coarse aggregates (kg/m^3)	1145.0	801.00	972.91	77.75
FA	Fine aggregates (kg/m^3)	992.6	594.00	773.57	80.17
AG	Age (days)	365.0	1.0	45.66	63.16
CS	Compressive strength (N/mm^2)	82.6	2.33	35.81	16.70

Figure 1. Coefficients of cross correlation between different variables.

Figure 2. Methodology.

Figure 3. A typical DNN.

Figure 4. Working of a neuron in a DNN.

Table 2. Statistical performance of DNN and regression models.

Model	Number of hidden layers	Number of neurons in each layer	Learning rate	Epochs	Training data		Testing Data
					MSE	R^2	MSE	R^2
DNN1	3	8	0.001	489, early stopping	33.01	0.87	42.57	0.84
DNN2	3	8	0.001	353, early stopping	29.72	0.91	35.13	0.87
DNN 3	11	16, 18,36, 26, 36, 26, 22, 18, 38, 10, 24	0.001	131, early stopping	15.67	0.94	32.22	0.87
DNN 4	5	12, 16, 16,40, 26	0.001	181, early stopping	14.77	0.96	28.76	0.89
MLR	–	–	–	–	71.35	0.72	109.7	0.59

Note: The values in bold are optimal values.

Figure 5. Progression of loss curve with epochs—DNN2.

Figure 6. Scatterplot of actual and predicted values of compressive strength—DNN2.

Figure 7. Progression of loss curve with epochs—DNN4.

Figure 8. Scatterplot of actual and predicted values of compressive strength—DNN4.

Figure 9. Scatterplot of actual and predicted values of CS from the multiple linear regression equation using test data.