Predicting Performance of Lightweight Concrete with Granulated Expanded Glass and Ash Aggregate by Means of Using Artificial Neural Networks
Abstract
:1. Introduction
2. Materials and Methods
3. Results
4. Application of ANN
- Characteristics of the problem: regressive; this description of dependencies is used to build models showing the actual relationships between the input data (explanatory ones) and the output variable (explained one). Then, the steps are executed in the following sequence: values of the explanatory variables, AN, then value of the explained variable;
- Number of input data: 15;
- Network type: feedforward ANN with two hidden layers, two input neurons corresponding to the share of GEGA 2 mm and GEGA 4 mm in a specimen, one output neuron corresponding to the predicted value (strength, density or porosity), connections between neurons of “each other” type (full connection);
- Learning algorithm backward error propagation algorithm;
- Number of neurons in the first hidden layer: from 2 to 12, in the second hidden layer from 2 to 17, depending on the forecasted variable;
- Function of error: mean square error of ANN;
- Function of neuron activation–sigmoid function.
5. Discussion of Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Shortcuts
LWC | lightweight concrete |
LWA | lightweight aggregate |
GEGA | granulated expanded glass aggregate |
GAA | granulated ash aggregate |
ANN | artificial neural networks |
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Setting Start Time [min] | Setting End Time [min] | Compressive Strength [MPa] | Blaine Fineness [cm2/g] | Loss of Roasting [%] | Water Demand [%] | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
2d | 28d | |||||||||||
155 | 195 | 30.2 | 57.3 | 3504 | 3.4 | 27.5 | ||||||
Content [%] | ||||||||||||
SiO2 | Al2O3 | Fe2O3 | CaO | MgO | SO3 | Na2O | K2O | TiO2 | Cl | |||
21.7 | 6.2 | 3.1 | 63.4 | 1.0 | 3.9 | 0.16 | 0.64 | 0.25 | 0.06 | |||
Mineralogical composition, content [%] | ||||||||||||
Na2Oeq | C3S | C2S | C3A | C4AF | ||||||||
0.7 | 63.1 | 7.6 | 6.1 | 8.9 |
Aggregate Type | Content [%] | ||||||||
---|---|---|---|---|---|---|---|---|---|
SiO2 | Al2O3 | Fe2O3 | CaO | MgO | SO3 | Na2O | K2O | Loss of Roasting | |
GEGA | 63.33 | 0.74 | - | 14.19 | 2.98 | 0.32 | 13.35 | 0.57 | 4.53 |
GAA | 52.82 | 24.28 | 7.5 | 4.5 | 3.19 | 0.43 | - | 0.2 | 7.1 |
Property | GEGA 2 mm | GEGA 4 mm | GAA 8 mm | |
---|---|---|---|---|
Water absorption WA24 | [%] | 15.2 | 17.8 | 16.5 |
Volume density ρa | [kg/m3] | 380 | 350 | 1350 |
Density of dried grain ρrd | [kg/m3] | 340 | 310 | 1250 |
Density of saturated grain ρssd | [kg/m3] | 360 | 330 | 1290 |
Porosity P | [%] | 37 | 42 | 37 |
Crumble indicator Xr | [%] | 22.3 | 25.9 | 17.8 |
pH after 24 h | - | 11.9 | 11.9 | 11.1 |
Bulk density in a loose state ρb | [kg/m3] | 200 | 180 | 680 |
Thermal conductivity of 40 cm layer of aggregate | W/m·K | 0.71 | 0.69 | 0.85 |
Specimens Designation [%] | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
LWC | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
GEGA 2 mm | 0 | 25 | 50 | 75 | 0 | 0 | 25 | 25 | 25 | 50 | 50 | 0 | 0 | 75 | 100 |
GEGA 4 mm | 0 | 0 | 0 | 0 | 100 | 75 | 50 | 25 | 75 | 50 | 25 | 50 | 25 | 25 | 0 |
GAA 8 mm | 100 | 75 | 50 | 25 | 0 | 25 | 25 | 50 | 0 | 0 | 25 | 50 | 75 | 0 | 0 |
Specimens Designation LWC | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
Apparent density [kg/m3] | 1560 | 1378 | 1177 | 877 | 1078 | 1028 | 1058 | 1117 | 929 | 903 | 1041 | 1059 | 1304 | 1060 | 1002 |
Porosity po [%] | 20.8 | 17.7 | 16.0 | 22.1 | 67 | 45.0 | 27.4 | 24.0 | 65.9 | 26.4 | 20.1 | 36.6 | 25.6 | 19.3 | 15.2 |
Compressive strength [MPa] | 18.65 | 21.35 | 13.43 | 3.72 | 12.49 | 4.59 | 4.29 | 10.1 | 4.21 | 5.44 | 6.99 | 5.38 | 8.92 | 6.37 | 6.86 |
Lab, Test LWC | Share of GEGA 2 mm | Share of GEGA 4 mm | Concrete Density [kg/m3] | Concrete Porosity [%] | Concrete Strength [MPa] |
---|---|---|---|---|---|
1 | 0 | 0 | 1560 | 20.8 | 18.65 |
2 | 0.25 | 0 | 1378 | 17.7 | 21.35 |
3 | 0.5 | 0 | 1177 | 16.0 | 13.43 |
4 | 0.75 | 0 | 877 | 22.1 | 3.72 |
5 | 0 | 1.0 | 1078 | 67.0 | 12.49 |
6 | 0 | 0.75 | 1028 | 45.0 | 4.59 |
7 | 0.25 | 0.50 | 1058 | 27.4 | 4.29 |
8 | 0.25 | 0.25 | 1117 | 24.0 | 10.1 |
9 | 0.25 | 0.75 | 929 | 65.9 | 4.21 |
10 | 0.5 | 0.5 | 903 | 26.4 | 5.44 |
11 | 0.5 | 0.25 | 1041 | 20.1 | 6.99 |
12 | 0 | 0.5 | 1059 | 36.6 | 5.38 |
13 | 0 | 0.25 | 1304 | 25.6 | 8.92 |
14 | 0.75 | 0.25 | 1060 | 19.3 | 6.37 |
15 | 1.0 | 0 | 1002 | 15.2 | 6.86 |
Testing Dataset | Network 2-11-15-1 for Density | Network 2-11-15-1 for Porosity | Network 2-11-15-1 for Strength | ||||||
---|---|---|---|---|---|---|---|---|---|
Lab. Test | ANN | Relative Error [%] | Lab. Test | ANN | Relative Error [%] | Lab. Test | ANN | Relative Error [%] | |
1 dataset (Lab. test LWC 14,15) | 1060 | 1005.31 | −5.16 | 19.03 | 18.773 | −2.73 | 6.37 | 5.476 | −14.04 |
1002 | 976.03 | −2.59 | 15.2 | 17.397 | −14.45 | 6.86 | 5.933 | −13.52 | |
2 dataset (Lab. test LWC 3,7) | 1177 | 1132.83 | −3.75 | 16.0 | 18.126 | 13.28 | 13.43 | 15.091 | 12.37 |
1058 | 977.27 | −7.63 | 27.4 | 30.276 | 10.49 | 4.29 | 4.799 | 11.86 | |
3 dataset (Lab. test LWC 9,11) | 929 | 948.78 | 2.13 | 65.9 | 59.937 | −9.05 | 4.21 | 4.778 | 13.49 |
1041 | 1020.21 | −1.99 | 20.1 | 21.086 | 4.91 | 6.99 | 7.689 | 10.01 | |
4 dataset (Lab. test LWC 1,5) | 1560 | 1339.91 | −14.11 | 20.8 | 19.959 | −4.04 | 18.65 | 21.601 | 15.82 |
1078 | 987.66 | −8.38 | 67.0 | 57.772 | −13.77 | 12.49 | 13.627 | 9.11 | |
5 dataset (Lab. test LWC 6,12) | 1028 | 1062.04 | 3.31 | 45.0 | 50.97 | 13.27 | 4.59 | 4.126 | −10.11 |
1059 | 1073.93 | 1.41 | 36.6 | 33.278 | −9.08 | 5.38 | 4.743 | −11.84 | |
6 dataset (Lab. test LWC 5,11) | 1078 | 1044.83 | −3.08 | 67.0 | 75.317 | 12.41 | 12.49 | 11.322 | −9.36 |
1041 | 923.08 | −11.33 | 20.1 | 22.982 | 14.34 | 6.99 | 6.169 | −11.75 | |
7 dataset (Lab. test LWC 2,13) | 1378 | 1477.18 | 7.19 | 17.7 | 18.512 | 4.59 | 21.35 | 18.351 | −14.05 |
1304 | 1429.97 | 9.66 | 25.6 | 29.21 | 14.1 | 8.92 | 10.125 | 13.51 | |
8 dataset (Lab. test LWC 6,10) | 1028 | 1008.79 | −1.87 | 45.0 | 52.077 | 15.73 | 4.59 | 4.099 | −10.71 |
903 | 990.43 | 9.68 | 26.4 | 22.641 | −14.24 | 5.44 | 4.654 | −14.46 | |
9 dataset (Lab. test LWC 1,2) | 1560 | 1307.31 | −16.19 | 20.8 | 17.937 | −13.76 | 18.65 | 18.026 | −3.35 |
1378 | 1305.18 | −5.13 | 17.7 | 17.829 | 0.73 | 21.35 | 22.068 | 3.36 | |
10 dataset (Lab. test LWC 5,9) | 1078 | 1003.46 | −6.91 | 67.0 | 64.153 | −4.25 | 12.49 | 10.658 | −14.67 |
929 | 983.25 | 5.84 | 65.9 | 65.008 | −1.35 | 4.21 | 4.633 | 10.05 |
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Kurpinska, M.; Kułak, L. Predicting Performance of Lightweight Concrete with Granulated Expanded Glass and Ash Aggregate by Means of Using Artificial Neural Networks. Materials 2019, 12, 2002. https://doi.org/10.3390/ma12122002
Kurpinska M, Kułak L. Predicting Performance of Lightweight Concrete with Granulated Expanded Glass and Ash Aggregate by Means of Using Artificial Neural Networks. Materials. 2019; 12(12):2002. https://doi.org/10.3390/ma12122002
Chicago/Turabian StyleKurpinska, Marzena, and Leszek Kułak. 2019. "Predicting Performance of Lightweight Concrete with Granulated Expanded Glass and Ash Aggregate by Means of Using Artificial Neural Networks" Materials 12, no. 12: 2002. https://doi.org/10.3390/ma12122002