Multi-Objective Optimization of Sustainable Concrete Containing Fly Ash Based on Environmental and Mechanical Considerations
Abstract
:1. Introduction
1.1. Fly Ash
1.2. Optimization Method
1.3. Environmental Evaluation
1.4. Research Significance
2. Research Methodology
2.1. Data Collection
2.2. Collected Database and Statistical Analysis
2.3. Research Program and Modelling Plan
2.3.1. Genetic Algorithm (GA)
2.3.2. Genetic Programming (GP)
2.3.3. Evolutionary Polynomial Regression (EPR)
2.3.4. Artificial Neural Network (ANN)
ANN Using “Back Propagation (ANN-BP)”
ANN Using “Gradually Reduced Gradient (ANN-GRG)”
ANN Using “Genetic Algorithm (ANN-GA)”
2.3.5. Model Performance Assessment
3. Results and Discussion
3.1. Behavior of the Concrete Mixes and Environmental Impact (EI)
3.2. Prediction of Compressive Strength (Fc) and Environmental Impact (P)
3.2.1. Model (1)—Using the GP Technique
3.2.2. Models (2, 3, and 4)—Using ANN Techniques
3.2.3. Model (5)—Using the EPR Technique
4. Conclusions
- Regarding Fc28, the GP model was the simplest and the least accurate one (80.9%). Then, EPR had an accuracy of 89.9%, and finally the three ANN models had almost the same accuracy of ≈94.0%;
- Regarding P, all five models had almost the same accuracy (99.0%);
- The prediction accuracy of the EPR model was lower than the ANN models, but their outputs were closed-form equations that could be used manually or as software, unlike the ANN output, which cannot be used manually;
- The results indicate that the accuracy of the ANN model was slightly affected by the training algorithm. The back propagation (BP) showed the best level of accuracy (94.9% and 97.8%), gradually reduced gradient (GRG) came in the second with accuracies of 94.2% and 99.2%, and the genetic algorithm (GA) showed the lowest level of accuracy with 93.0% and 99.0% for Fc28 and P, respectively;
- The summation of the absolute weights of each neuron in the input layer of the developed ANN model indicated that for both Fc28 and P, cement content (C) was the most important factor, and then aggregate content (FAg and CAg). Fly ash and water content came last in the importance ranking;
- Both the GP and EPR models indicated that the environmental impact factor (P) depended only on the cementitious materials (C and FA);
- The GA technique successfully reduced the 56 and 6 terms of conventional polynomial regression quadrilateral formula to only 28 and 3 terms for Fc28 and P, respectively, without a significant impact on accuracy;
- Similar to any other regression technique, the generated formulas were valid within the considered range of parameter values; beyond this range, the prediction accuracy should be verified.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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W | C | FA | Fag | Cag | Fc28 | P |
---|---|---|---|---|---|---|
kg/m3 | kg/m3 | kg/m3 | kg/m3 | kg/m3 | MPa | - |
Training dataset | ||||||
171.58 | 199.19 | 85.79 | 388.65 | 835.47 | 34.5 | 5.3 |
202.16 | 459.46 | 68.92 | 326.13 | 713.03 | 42.5 | 9.5 |
220.48 | 237.29 | 34.60 | 770.12 | 352.57 | 27.1 | 4.9 |
252.37 | 283.79 | 167.24 | 667.68 | 305.88 | 33.6 | 8.3 |
233.76 | 477.06 | 71.56 | 383.18 | 585.98 | 36.9 | 9.8 |
150.14 | 101.71 | 101.71 | 542.80 | 754.80 | 8.5 | 4.0 |
196.07 | 435.71 | 65.36 | 295.71 | 771.13 | 41.1 | 9.0 |
155.22 | 168.32 | 147.16 | 357.72 | 879.94 | 25.4 | 6.0 |
161.46 | 322.92 | 107.64 | 376.63 | 785.04 | 41.7 | 7.9 |
172.12 | 278.58 | 119.39 | 335.14 | 828.50 | 53.0 | 7.4 |
160.62 | 160.62 | 160.62 | 364.24 | 860.37 | 33.0 | 6.1 |
258.82 | 324.80 | 187.77 | 637.66 | 292.24 | 39.5 | 9.4 |
154.59 | 107.41 | 146.56 | 386.88 | 884.30 | 13.4 | 5.0 |
162.20 | 226.28 | 226.28 | 320.43 | 831.12 | 48.0 | 8.5 |
223.88 | 238.81 | 59.70 | 756.47 | 346.29 | 29.2 | 5.5 |
146.40 | 385.27 | 96.32 | 216.44 | 952.93 | 27.7 | 8.8 |
242.48 | 538.85 | 80.83 | 365.71 | 549.76 | 42.0 | 11.0 |
154.46 | 94.28 | 146.44 | 395.32 | 882.93 | 10.5 | 4.7 |
220.25 | 199.32 | 64.78 | 773.17 | 354.07 | 22.9 | 4.9 |
171.55 | 239.98 | 103.13 | 372.31 | 820.54 | 45.5 | 6.4 |
161.67 | 425.45 | 47.27 | 212.46 | 935.37 | 38.2 | 8.5 |
257.16 | 234.58 | 234.58 | 390.51 | 581.41 | 20.9 | 8.8 |
171.55 | 239.98 | 103.13 | 372.31 | 820.54 | 47.0 | 6.4 |
150.94 | 131.47 | 68.17 | 545.71 | 752.41 | 11.9 | 3.8 |
171.58 | 199.19 | 85.79 | 388.65 | 835.47 | 33.5 | 5.3 |
173.01 | 286.71 | 88.98 | 518.31 | 645.04 | 43.7 | 6.9 |
213.26 | 197.47 | 29.62 | 794.88 | 363.82 | 21.3 | 4.2 |
290.79 | 379.62 | 67.32 | 372.02 | 554.49 | 19.9 | 8.0 |
178.50 | 311.39 | 54.54 | 348.25 | 821.22 | 50.0 | 6.7 |
200.55 | 435.97 | 65.40 | 333.89 | 722.64 | 40.7 | 9.0 |
198.28 | 450.64 | 67.60 | 319.87 | 732.08 | 43.6 | 9.3 |
150.99 | 116.89 | 87.67 | 545.87 | 749.42 | 7.4 | 4.0 |
150.70 | 102.09 | 102.09 | 544.84 | 751.22 | 5.8 | 4.0 |
244.25 | 321.65 | 105.54 | 685.94 | 313.97 | 42.5 | 7.8 |
125.31 | 250.63 | 205.06 | 379.92 | 830.85 | 35.6 | 8.6 |
252.27 | 390.92 | 69.33 | 383.09 | 602.78 | 32.0 | 8.3 |
199.96 | 425.45 | 63.82 | 339.08 | 724.87 | 38.9 | 8.8 |
154.76 | 125.62 | 146.72 | 377.93 | 883.29 | 17.1 | 5.3 |
225.86 | 513.31 | 77.00 | 338.79 | 623.73 | 43.9 | 10.5 |
237.33 | 241.35 | 120.68 | 717.57 | 328.73 | 28.5 | 6.7 |
232.81 | 200.70 | 115.40 | 739.77 | 338.63 | 20.0 | 5.9 |
151.80 | 132.21 | 68.55 | 545.76 | 750.22 | 8.8 | 3.9 |
231.42 | 279.30 | 69.82 | 729.15 | 333.97 | 35.6 | 6.3 |
105.59 | 211.17 | 258.10 | 381.99 | 855.63 | 24.0 | 8.9 |
203.96 | 485.63 | 72.84 | 317.49 | 702.32 | 48.4 | 10.0 |
216.33 | 240.48 | 240.48 | 400.33 | 635.89 | 38.8 | 9.0 |
230.38 | 548.51 | 82.28 | 324.45 | 608.54 | 47.9 | 11.2 |
232.71 | 484.81 | 72.72 | 380.34 | 585.88 | 37.7 | 9.9 |
202.29 | 430.41 | 64.56 | 334.99 | 721.96 | 40.3 | 8.9 |
249.55 | 323.31 | 136.39 | 668.08 | 305.58 | 42.7 | 8.4 |
130.56 | 343.57 | 147.24 | 220.58 | 971.16 | 22.5 | 9.0 |
253.69 | 347.61 | 115.22 | 385.24 | 596.58 | 30.3 | 8.4 |
241.52 | 281.77 | 120.76 | 698.01 | 319.65 | 36.5 | 7.4 |
297.03 | 228.26 | 228.26 | 379.99 | 529.80 | 16.6 | 8.6 |
196.93 | 468.88 | 70.33 | 286.11 | 758.61 | 46.1 | 9.7 |
138.68 | 118.87 | 178.30 | 496.49 | 771.89 | 10.1 | 5.8 |
234.12 | 508.97 | 76.35 | 370.78 | 578.11 | 40.3 | 10.4 |
149.86 | 116.02 | 87.01 | 544.79 | 753.39 | 10.4 | 3.9 |
154.36 | 83.19 | 146.34 | 401.91 | 882.33 | 8.4 | 4.5 |
254.63 | 324.62 | 162.31 | 651.85 | 298.78 | 41.2 | 8.9 |
247.22 | 282.53 | 141.27 | 683.56 | 313.19 | 35.5 | 7.8 |
217.32 | 198.47 | 49.62 | 782.23 | 358.46 | 22.4 | 4.6 |
161.60 | 195.52 | 195.52 | 358.39 | 826.09 | 41.5 | 7.4 |
196.93 | 468.88 | 70.33 | 286.11 | 758.61 | 47.3 | 9.7 |
229.22 | 200.20 | 100.10 | 749.77 | 343.07 | 21.4 | 5.6 |
242.07 | 242.07 | 141.21 | 704.62 | 322.38 | 26.9 | 7.1 |
198.88 | 405.87 | 60.88 | 346.21 | 731.71 | 37.2 | 8.4 |
214.66 | 310.50 | 166.73 | 397.23 | 644.16 | 45.0 | 8.8 |
172.12 | 278.58 | 119.39 | 335.14 | 828.50 | 50.5 | 7.4 |
225.59 | 479.99 | 72.00 | 349.67 | 633.94 | 39.9 | 9.9 |
202.16 | 459.46 | 68.92 | 326.13 | 713.03 | 43.1 | 9.5 |
235.58 | 318.08 | 49.70 | 717.32 | 328.87 | 39.3 | 6.6 |
294.42 | 294.42 | 158.10 | 376.65 | 540.14 | 19.9 | 8.3 |
138.68 | 118.87 | 178.30 | 496.49 | 771.89 | 9.6 | 5.8 |
227.80 | 277.32 | 39.62 | 744.96 | 341.42 | 33.0 | 5.7 |
231.63 | 454.17 | 68.13 | 393.07 | 593.85 | 35.2 | 9.3 |
223.69 | 199.72 | 84.88 | 761.67 | 348.85 | 22.7 | 5.3 |
178.19 | 222.50 | 39.38 | 400.28 | 824.38 | 33.0 | 4.8 |
231.14 | 240.15 | 100.06 | 732.67 | 335.68 | 29.8 | 6.3 |
227.94 | 239.94 | 79.98 | 743.87 | 340.67 | 29.6 | 5.9 |
155.62 | 131.30 | 68.08 | 542.01 | 748.28 | 9.6 | 3.8 |
203.96 | 485.63 | 72.84 | 317.49 | 702.32 | 47.3 | 10.0 |
212.44 | 401.17 | 71.14 | 393.13 | 655.13 | 47.4 | 8.5 |
172.12 | 278.58 | 119.39 | 335.14 | 828.50 | 50.5 | 7.4 |
150.70 | 102.09 | 102.09 | 544.84 | 751.22 | 6.1 | 4.0 |
195.08 | 433.52 | 65.03 | 296.92 | 772.97 | 39.0 | 8.9 |
151.27 | 117.11 | 87.84 | 543.86 | 750.84 | 7.9 | 4.0 |
292.59 | 337.75 | 111.96 | 374.32 | 547.36 | 21.0 | 8.2 |
199.96 | 425.45 | 63.82 | 339.08 | 724.87 | 38.4 | 8.8 |
240.49 | 320.65 | 80.16 | 700.02 | 320.27 | 41.4 | 7.3 |
Validation dataset | ||||||
171.55 | 239.98 | 103.13 | 372.31 | 820.54 | 49.5 | 6.4 |
150.94 | 131.47 | 68.17 | 545.71 | 752.41 | 12.5 | 3.8 |
224.52 | 510.27 | 76.54 | 339.96 | 626.77 | 43.2 | 10.5 |
171.58 | 199.19 | 85.79 | 388.65 | 835.47 | 33.5 | 5.3 |
122.64 | 126.87 | 296.02 | 394.96 | 837.80 | 30.6 | 8.2 |
178.12 | 356.23 | 62.86 | 374.87 | 764.13 | 48.9 | 7.6 |
236.72 | 280.86 | 95.29 | 713.23 | 326.56 | 36.2 | 6.9 |
146.87 | 132.18 | 137.08 | 506.00 | 762.97 | 13.1 | 5.2 |
255.12 | 302.83 | 162.61 | 387.42 | 590.31 | 32.7 | 8.6 |
146.87 | 132.18 | 137.08 | 506.00 | 762.97 | 11.2 | 5.2 |
196.98 | 198.87 | 56.82 | 574.90 | 609.75 | 23.2 | 4.7 |
202.29 | 430.41 | 64.56 | 334.99 | 721.96 | 39.6 | 8.9 |
196.57 | 446.75 | 67.01 | 331.02 | 725.75 | 44.0 | 9.2 |
145.75 | 116.60 | 87.45 | 547.51 | 757.15 | 9.0 | 4.0 |
126.32 | 210.53 | 210.53 | 393.26 | 834.18 | 66.5 | 8.0 |
196.57 | 468.03 | 70.20 | 285.59 | 760.33 | 45.1 | 9.6 |
223.52 | 475.57 | 71.34 | 352.37 | 637.53 | 38.9 | 9.8 |
170.60 | 293.59 | 142.83 | 450.21 | 687.75 | 54.3 | 8.1 |
150.14 | 101.71 | 101.71 | 542.80 | 754.80 | 7.3 | 4.0 |
213.58 | 356.64 | 118.22 | 395.25 | 649.47 | 43.2 | 8.6 |
114.09 | 300.23 | 200.15 | 224.89 | 990.10 | 21.6 | 9.3 |
177.96 | 267.93 | 47.46 | 390.90 | 805.02 | 44.5 | 5.8 |
W | C | FA | FAg | CAg | Fc28 | P | |
---|---|---|---|---|---|---|---|
kg/m3 | kg/m3 | kg/m3 | kg/m3 | kg/m3 | MPa | - | |
Training set | |||||||
Min. | 105.6 | 83.2 | 29.6 | 212.5 | 292.2 | 5.8 | 3.8 |
Max. | 297.0 | 548.5 | 258.1 | 794.9 | 971.2 | 53.0 | 11.2 |
Avg. | 201.1 | 292.7 | 105.2 | 469.7 | 635.1 | 31.7 | 7.3 |
SD | 42.2 | 125.5 | 50.8 | 165.3 | 202.0 | 13.0 | 2.0 |
VAR | 0.2 | 0.4 | 0.5 | 0.4 | 0.3 | 0.4 | 0.3 |
Validation set | |||||||
Min. | 114.1 | 101.7 | 47.5 | 224.9 | 326.6 | 7.3 | 3.8 |
Max. | 255.1 | 510.3 | 296.0 | 713.2 | 990.1 | 66.5 | 10.5 |
Avg. | 178.1 | 276.3 | 111.9 | 425.1 | 727.9 | 34.0 | 7.2 |
SD | 37.5 | 127.4 | 59.7 | 109.5 | 125.3 | 15.9 | 2.1 |
VAR | 0.2 | 0.5 | 0.5 | 0.3 | 0.2 | 0.5 | 0.3 |
W | C | FA | FAg | CAg | Fc28 | P | |
---|---|---|---|---|---|---|---|
W | 1.00 | ||||||
C | 0.47 | 1.00 | |||||
FA | −0.19 | −0.36 | 1.00 | ||||
FAg | 0.29 | −0.44 | −0.11 | 1.00 | |||
CAg | −0.78 | −0.11 | 0.15 | −0.80 | 1.00 | ||
Fc28 | 0.23 | 0.68 | −0.10 | −0.34 | −0.03 | 1.00 | |
P | 0.40 | 0.88 | 0.12 | −0.54 | −0.03 | 0.68 | 1.00 |
Hidden Layer | |||||||||
---|---|---|---|---|---|---|---|---|---|
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | |||
Input Layer | (Bias) | −0.20 | 1.95 | 1.47 | 1.09 | 0.14 | 1.86 | −0.11 | |
W | 0.22 | 1.09 | 1.48 | 0.44 | −0.05 | 0.63 | 0.05 | ||
C | 0.15 | −3.86 | −1.37 | 0.45 | 0.38 | −3.43 | −0.20 | ||
FA | −0.16 | -0.80 | 1.58 | 0.18 | 0.10 | -0.68 | −0.32 | ||
FAg | −0.12 | 1.79 | 3.03 | 0.07 | 0.24 | 1.15 | −0.31 | ||
CAg | 0.30 | −0.59 | −2.40 | −0.14 | 0.27 | −1.01 | 0.02 | ||
Hidden Layer | |||||||||
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | (Bias) | ||
Output Layer | Fc28 | −0.83 | −2.73 | −0.37 | 1.67 | 3.25 | 3.56 | 1.04 | −2.04 |
P | 2.15 | 0.01 | −0.11 | 0.13 | 1.05 | 0.15 | -2.47 | −0.25 |
Hidden Layer | |||||||||
---|---|---|---|---|---|---|---|---|---|
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | |||
Input Layer | (Bias) | 0.96 | 0.88 | 1.05 | 2.79 | −0.95 | 0.74 | −2.50 | |
W | 2.00 | −0.89 | 0.17 | −0.28 | −1.25 | 0.15 | 1.32 | ||
C | −6.73 | 0.18 | −0.76 | 1.52 | 6.05 | 0.44 | −0.97 | ||
FA | −2.04 | −0.44 | −0.49 | 1.09 | 1.81 | 0.09 | 1.41 | ||
FAg | 3.24 | −0.08 | 0.29 | −0.84 | −2.77 | −0.56 | 2.17 | ||
CAg | −0.95 | 0.93 | 0.34 | −0.88 | 1.17 | −0.47 | −2.07 | ||
Hidden Layer | |||||||||
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | (Bias) | ||
Output Layer | Fc28 | −3.70 | 2.16 | −0.60 | −0.43 | −4.52 | 4.12 | 0.89 | −2.63 |
P | −0.08 | -0.03 | −3.29 | 3.18 | -0.08 | -0.02 | −0.02 | −0.33 |
Hidden Layer | |||||||||
---|---|---|---|---|---|---|---|---|---|
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | |||
Input Layer | (Bias) | 1.77 | 0.32 | 0.61 | −0.57 | 0.61 | −1.43 | 1.87 | |
W | 0.89 | −0.18 | 2.78 | −2.57 | 1.11 | −4.93 | 4.45 | ||
C | −2.52 | 2.07 | −2.30 | 3.37 | 6.53 | 6.68 | −7.43 | ||
FA | −1.62 | 1.38 | −1.34 | 1.46 | 1.08 | 0.61 | −0.87 | ||
FAg | 1.42 | −0.14 | −1.13 | 0.80 | −1.50 | -3.41 | 4.18 | ||
CAg | 1.67 | −0.20 | 1.19 | −1.25 | −0.27 | 1.31 | −1.03 | ||
Hidden Layer | |||||||||
(1–1) | (1–2) | (1–3) | (1–4) | (1–5) | (1–6) | (1–7) | (Bias) | ||
Output Layer | Fc28 | −0.07 | −1.84 | 2.73 | 2.55 | 2.63 | 3.93 | 4.33 | −2.41 |
P | −3.10 | 3.27 | −0.08 | −0.11 | 0.30 | −0.07 | −0.09 | −0.18 |
Item | Technique | Model | SSE | Avg. Error % | R2 |
---|---|---|---|---|---|
Fc28 | GP | Equation (1) | 4238 | 19.1 | 0.788 |
ANN-BP | Figure 3, Table 3 | 306 | 5.1 | 0.986 | |
ANN-GRG | Figure 3, Table 4 | 392 | 5.8 | 0.983 | |
ANN-GA | Figure 3, Table 5 | 568 | 7.0 | 0.974 | |
EPR | Equation (3) | 1195 | 10.1 | 0.957 | |
P | GP | Equation (2) | 0 | 0.8 | 0.999 |
ANN-BP | Figure 3, Table 3 | 3 | 2.2 | 0.994 | |
ANN-GRG | Figure 3, Table 4 | 0 | 0.8 | 0.999 | |
ANN-GA | Figure 3, Table 5 | 1 | 1.0 | 0.999 | |
EPR | Equation (4) | 0 | 0.4 | 1.000 |
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Onyelowe, K.C.; Kontoni, D.-P.N.; Ebid, A.M.; Dabbaghi, F.; Soleymani, A.; Jahangir, H.; Nehdi, M.L. Multi-Objective Optimization of Sustainable Concrete Containing Fly Ash Based on Environmental and Mechanical Considerations. Buildings 2022, 12, 948. https://doi.org/10.3390/buildings12070948
Onyelowe KC, Kontoni D-PN, Ebid AM, Dabbaghi F, Soleymani A, Jahangir H, Nehdi ML. Multi-Objective Optimization of Sustainable Concrete Containing Fly Ash Based on Environmental and Mechanical Considerations. Buildings. 2022; 12(7):948. https://doi.org/10.3390/buildings12070948
Chicago/Turabian StyleOnyelowe, Kennedy C., Denise-Penelope N. Kontoni, Ahmed M. Ebid, Farshad Dabbaghi, Atefeh Soleymani, Hashem Jahangir, and Moncef L. Nehdi. 2022. "Multi-Objective Optimization of Sustainable Concrete Containing Fly Ash Based on Environmental and Mechanical Considerations" Buildings 12, no. 7: 948. https://doi.org/10.3390/buildings12070948