Concrete Compressive Strength Data Set
Task: regression
Number of instances: 1030
Number of attributes: 7 (numerical)
Type of attribute to be predicted: numerical
Download the data: DataConcrete
Concrete is a construction material with a nonlinear mechanical behaviour difficult to predict. The objective is here to analyze a dataset of 1030 distinct formulations of concretes in order to model the compression strength according to the formulation. The potentially influential variables are the contents (in kg/m3) of 7 different components (the cement, the blast furnace slags, the fly ashes, the water, the superplasticizers,
the coarse aggregates, the fine aggregates) and the age of the material.
Sources: Prof. ICheng Yeh, Department of Information Management, ChungHua University, Hsin Chu, Taiwan. Data found in the UCI Machine Learning Repository.
Model with 1 variable
* If (Age is lower than 50) then (Compression strength decreases)
Mean Error: 10,7 MPa

Mean Square Error: 13,8 MPa

Maximal Error: 47,3 MPa

Maximum : 45,6 MPa (Age is higher than 60 days)

Minimum : 16,5 MPa (Age is minimal)

This model suggests that it is necessary to wait 60 days before the concrete stabilizes and reaches its maximum compression strength. The following graph represents the model (in red) and the experimental values (points in green):
Model with 2 variables
* If (Age is lower than 50) then (Compression strength decreases)
* If (Cement
increases) then (Compressive strength increases)
Mean Error: 8,4 MPa

Mean Square Error: 10,6 MPa

Maximal Error: 41,9 MPa

Maximum : 73,6 MPa (Age is higher than 60 days, Cement is maximal)

Minimum : 1,8 MPa (Age is minimal, Cement is minimal)

In addition to the influence of the age, this model is linked to the content of cement that clearly increases the compression strength (in a quasi linear way). The following graph represents the model for an age lower than 5 days (in red) and an age of 100 ± 20 days (in green):
Model with 3 variables
* If (Age is lower than 50) then (Compression strength decreases)
* If (Cement
increases) and (Superplasticizer
increases) then (Compressive strength increases)
Mean Error: 8,9 MPa

Mean Square Error: 9 MPa

Maximal Error: 40 MPa

Maximum : 81,9 MPa (Age is higher than 60 days, Cement is maximal, Superplasticizer is higher than 20 kg/m3)

Minimum : 0 MPa (Age is minimal, Cement is minimal, Superplasticizer is minimal)

This model includes the content of superplasticizer which increases the compression strength. However, there is a threshold (20 kg/m3): above it the superplasticizer does not have effect any more as the following graph shows (obtained with age = 100 ± 40 days):
Model with 4 variables
* If (Cement
decreases) and (Age decreases) then (Compressive strength decreases)
* If (Cement
increases) and (Blast Furnace Slagincreases) and (Superplasticizer
increases) then (Compressive strength increases)
Mean Error: 5,9 MPa

Mean Square Error: 7,8 MPa

Maximal Error: 35,8 MPa

Maximum : 101 MPa (Age is maximal, Cement is maximal, Superplasticizer is higher than 12 kg/m3, Blast Furnace Slag is maximal)

Minimum : 0 MPa (Age is minimal, Cement is minimal, Superplasticizer is minimal, Blast Furnace Slag is minimal)

This model adds the influence of the content of Blast Furnace Slag which increases the compression strength. The next graph is obtained with age = 100 ± 40 days and Superplasticizer = 15 ± 4 kg/m3:
Model with 5 variables
* If (Cement
increases) and (Blast Furnace Slag increases) and (Superplasticizer
increases) and (Age increases) then (Compressive strength increases)
* If (Cement
decreases) and (Water is higher than 120) then (Compressive
strength decreases)
Mean Error: 5,4 MPa

Mean Square Error: 7,2 MPa

Maximal Error: 29,9 MPa

Maximum : 92,4 MPa (Age is maximal, Cement is maximal, Superplasticizer is maximal, Blast Furnace Slag is higher than 305 kg/m3, water is lower than 110 kg/m3)

Minimum : 0 MPa (Age is minimal, Cement is minimal, Superplasticizer is minimal, Blast Furnace Slag is minimal, water is higher than 190 kg/m3)

This model reveals the negative influence of water on the compression strength of concrete. The following graph is obtained with age = 100 ± 20 days and cement = 200 ± 30 kg/m3:

