# Prediction of Concrete Compressive Strength Using a Back-Propagation Neural Network Optimized by a Genetic Algorithm and Response Surface Analysis Considering the Appearance of Aggregates and Curing Conditions

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Experimental Data

- The number of small angles (less than 90 degrees) in concrete. As the size of the aggregate increases, the number of these angles decreases, which can greatly help increase the compressive strength of the concrete as the stress concentration points in the mortar are reduced. On the other hand, if the mechanical properties of the aggregates are suitable, the failure mode will be based on the formation of cracks in the mortar, which according to the cases mentioned above, these cracks will occur in different places, and the concrete sample will collapse at once. In other words, it can be said that the concrete sample is hollow from the inside and cannot withstand the load. Although many scientists have suggested the use of nanoparticles, fibers and the manufacture of composite concrete with the aim of strengthening the mortar and sometimes increasing the adhesion between the mortar and the aggregate, which leads to obtaining acceptable results.
- The size of a small angle (between zero and 90 degrees) in concrete. Quadrilateral aggregates with angles close to 90 degrees should be used as much as possible to create the smallest stress concentration in the mortar. In other words, the closer the aggregate angle is to zero, the higher the concentration intensity in the mortar and the lower the compressive strength of the concrete sample.

## 4. Response Surface Analysis

## 5. Neural Network and Genetic Algorithm

## 6. Results and Discussion

- The results obtained from the response surface analysis for both aggregate geometries (rounded and angular) show that when the curing temperature increases, the compressive strength of the concrete decreases. Additionally, increasing the size of aggregate leads to the compressive strength of the concrete increasing. As a result, the appearance of the aggregate has no effect on this overall trend. This is fully consistent with the analysis of the data in Figure 6 and the justifications stated at the end of Section 3, which also demonstrates the accuracy of the response surface analysis.
- According to the contours presented in the response surface analysis, it is clear that in order to have the maximum compressive strength of the concrete, the largest size of aggregate should be selected. Although it is clear that the color spectra of angular aggregates are greater than the color spectra of rounded aggregates (dark violet is not present in Figure 8a). This means that the ranges of compressive strength changes are more sensitive to the angular aggregate geometry. On the other hand, it is clear that the boundary lines separating the color spectrum are curved, which can be considered a segment of the elliptical geometric shape, which is necessary to obtain the optimal states. It is necessary to calculate and consider the minimum in the local coordinates of the curvature lines representing the best state.
- If the maximum aggregate size is used, the results for both aggregate geometry (rounded and angular) show that in order to have the maximum compressive strength, the curing temperature should be in the range of 5–15 °C (dark blue and dark purple in Figure 8a,b, respectively). This issue is exactly in line with the interpretation provided in the last paragraph of Section 3 of this article.
- From the compressive strength intervals presented in the results of the response surface analysis, it can be clearly seen that in the best conditions, the maximum compressive strengths for rounded and angular aggregates are equal to 101 and 130 MPa, respectively. In other words, using rounded aggregates with maximum aggregate size and considering the best curing conditions (5 < T < 15) leads to a 30% increase in compressive strength of concrete with similar conditions and the use of angular aggregates.

## 7. Conclusions

- Concrete specimens with rounded aggregates possess much higher compressive strength compared to concrete specimens with angular aggregates;
- With increasing the aggregate size, the compressive strength of concrete increases;
- An increase in the curing temperature leads to a decrease in the compressive strength of the concrete;
- An increase in aggregate size increases the effects of the curing temperature on the compressive strength of the concrete;
- The observed nonuniformity trend between the results is related to the heterogeneity in the arrangement or location of aggregates in concrete;
- The presence of an angle plays a key role as the stress concentration and the formation of cracks in the mortar, which greatly depends on the number and the size of small angles (less than 90 degrees) in the concrete. The closer the aggregate angle is to zero, the higher the concentration intensity in the mortar and the lower the compressive strength of the concrete sample;
- The ranges of compressive strength changes are more sensitive to the angular aggregate geometry;
- The highest compressive strength in concrete specimens for both aggregate shapes is achieved with a 10 °C curing temperature;
- Neural network optimized by algorithm genetic provides more accurate results, i.e., the laboratory data fitted better on the prediction line.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Results of the uniaxial mechanical test under compression load and the details of data used in each stage of the neural network structure.

Experiment No. | Specimen No. | Repeat No. | Strength (N) | Mean Results (N) | Training (ANN) | Testing (ANN) | Validation (ANN) |
---|---|---|---|---|---|---|---|

1 | 10S-R-5T | 1 | 71,327.1 | 71,664.8 | |||

2 | 2 | 70,251.4 | |||||

3 | 3 | 73,415.9 | |||||

4 | 10S-R-10T | 1 | 68,492.3 | 68,967.4 | |||

5 | 2 | 68,587.2 | |||||

6 | 3 | 69,822.7 | |||||

7 | 10S-R-15T | 1 | 66,861 | 67,674.9 | |||

8 | 2 | 66,286.7 | |||||

9 | 3 | 69,877 | |||||

10 | 10S-R-20T | 1 | 59,114.7 | 60,510.3 | |||

11 | 2 | 58,673.5 | |||||

12 | 3 | 63,742.7 | |||||

13 | 10S-R-25T | 1 | 49,395.2 | 51,235.9 | |||

14 | 2 | 49,842.1 | |||||

15 | 3 | 54,470.4 | |||||

16 | 10S-R-30T | 1 | 46,067.5 | 43,761 | |||

17 | 2 | 45,249.1 | |||||

18 | 3 | 39,966.4 | |||||

19 | 20S-R-5T | 1 | 98,550 | 98,928.2 | |||

20 | 2 | 98,285.3 | |||||

21 | 3 | 99,949.3 | |||||

22 | 20S-R-10T | 1 | 99,417.8 | 98,894.7 | |||

23 | 2 | 99,813.5 | |||||

24 | 3 | 97,452.8 | |||||

25 | 20S-R-15T | 1 | 94,039.16 | 94,939.3 | |||

26 | 2 | 94,668.3 | |||||

27 | 3 | 96,110.44 | |||||

28 | 20S-R-20T | 1 | 92,579.9 | 91,000.5 | |||

29 | 2 | 93,036.8 | |||||

30 | 3 | 87,384.8 | |||||

31 | 20S-R-25T | 1 | 76,488.8 | 78,499.3 | |||

32 | 2 | 77,212.5 | |||||

33 | 3 | 81,796.6 | |||||

34 | 20S-R-30T | 1 | 69,372 | 66,372 | |||

35 | 2 | 68,044.9 | |||||

36 | 3 | 61,699.1 | |||||

37 | 30S-R-5T | 1 | 110,808.3 | 110,295.6 | |||

38 | 2 | 112,549.1 | |||||

39 | 3 | 107,529.4 | |||||

40 | 30S-R-10T | 1 | 116,790.2 | 115,963.1 | |||

41 | 2 | 113,983.4 | |||||

42 | 3 | 117,115.7 | |||||

43 | 30S-R-15T | 1 | 105,251.8 | 106,306.7 | |||

44 | 2 | 108,002 | |||||

45 | 3 | 105,666.3 | |||||

46 | 30S-R-20T | 1 | 103,123.3 | 101,249.1 | |||

47 | 2 | 99,897.5 | |||||

48 | 3 | 100,726.5 | |||||

49 | 30S-R-25T | 1 | 92,283.1 | 89,866.6 | |||

50 | 2 | 95,732 | |||||

51 | 3 | 81,584.7 | |||||

52 | 30S-R-30T | 1 | 69,846 | 73,665.8 | |||

53 | 2 | 72,198.2 | |||||

54 | 3 | 78,953.2 | |||||

55 | 10S-A-5T | 1 | 65,210.49 | 65,561.7 | |||

56 | 2 | 64,937.1 | |||||

57 | 3 | 66,537.51 | |||||

58 | 10S-A-10T | 1 | 63,802.5 | 63,308.4 | |||

59 | 2 | 63,489.4 | |||||

60 | 3 | 62,633.3 | |||||

61 | 10S-A-15T | 1 | 61,651.54 | 62,498 | |||

62 | 2 | 61,073.1 | |||||

63 | 3 | 64,769.36 | |||||

64 | 10S-A-20T | 1 | 54,939.68 | 56,391.1 | |||

65 | 2 | 55,791.3 | |||||

66 | 3 | 58,442.32 | |||||

67 | 10S-A-25T | 1 | 46,586.07 | 48,500.4 | |||

68 | 2 | 45,985.7 | |||||

69 | 3 | 52,929.43 | |||||

70 | 10S-A-30T | 1 | 43,243.46 | 40,844.7 | |||

71 | 2 | 40,013.68 | |||||

72 | 3 | 39,276.96 | |||||

73 | 20S-A-5T | 1 | 71,668.45 | 72,082.2 | |||

74 | 2 | 70,882.4 | |||||

75 | 3 | 73,695.75 | |||||

76 | 20S-A-10T | 1 | 70,673.23 | 71,245.5 | |||

77 | 2 | 71,964.9 | |||||

78 | 3 | 71,098.37 | |||||

79 | 20S-A-15T | 1 | 68,035.75 | 69,020.5 | |||

80 | 2 | 67,145 | |||||

81 | 3 | 71,880.75 | |||||

82 | 20S-A-20T | 1 | 61,283.04 | 63,010.9 | |||

83 | 2 | 62,435.6 | |||||

84 | 3 | 65,314.06 | |||||

85 | 20S-A-25T | 1 | 57,222.39 | 55,022.9 | |||

86 | 2 | 55,998.2 | |||||

87 | 3 | 51,848.11 | |||||

88 | 20S-A-30T | 1 | 49,231 | 45,949 | |||

89 | 2 | 40,379.6 | |||||

90 | 3 | 48,236.4 | |||||

91 | 30S-A-5T | 1 | 102,781.5 | 103,360.9 | |||

92 | 2 | 101,729.5 | |||||

93 | 3 | 105,571.7 | |||||

94 | 30S-A-10T | 1 | 106,382.9 | 107,317.5 | |||

95 | 2 | 105,097.8 | |||||

96 | 3 | 110,471.8 | |||||

97 | 30S-A-15T | 1 | 101,490.2 | 100,298.2 | |||

98 | 2 | 103,727.6 | |||||

99 | 3 | 95,676.76 | |||||

100 | 30S-A-20T | 1 | 94,583.05 | 96,700.9 | |||

101 | 2 | 90,389.1 | |||||

102 | 3 | 105,130.5 | |||||

103 | 30S-A-25T | 1 | 89,030.25 | 86,299.6 | |||

104 | 2 | 84,037.54 | |||||

105 | 3 | 85,831.02 | |||||

106 | 30S-A-30T | 1 | 66,212.73 | 70,529.1 | |||

107 | 2 | 62,824.3 | |||||

108 | 3 | 82,550.27 |

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**Figure 1.**Different geometries of aggregates: (

**a**) general classification [25]; (

**b**) rounded aggregates used in the present research; (

**c**) angular aggregates used in the present research.

**Figure 2.**Various sizes of aggregates used in the present research based on the BS EN 13043 standard.

**Figure 5.**Bar chart of concrete compressive strength in terms of different curing conditions considering various geometries of aggregate, including (

**a**) rounded aggregates and (

**b**) angular aggregates.

**Figure 8.**Contour plot of compression load vs. simulations effects of aggregate size and curing temperature as a result of response surface analysis for different specimen batches, including (

**a**) concrete specimen made of rounded aggregates and (

**b**) concrete specimen made of angular aggregates.

Parameters | Title 2 |
---|---|

Number of hidden layers | 1 |

Number of neurons in hidden layer | 6 |

Transition function of hidden layer | Tansig |

Transition function output layer | Tansig |

Input Data form | [−1,1] |

Goal error | MSE |

Training algorithm | LM |

Testing performance | R, MSE, RMSE, MAE |

Parameters | Value |
---|---|

Population | 100 |

Crossover factor | 0.7 |

Mutation factor | 0.2 |

Criteria | BPNN | BPNN-GA | ||||
---|---|---|---|---|---|---|

Training Data | Test Data | All Data | Training Data | Test Data | All Data | |

MSE | 0.006 | 0.059 | 0.0162 | 0.0014 | 0.0021 | 0.0017 |

R | 0.976 | 0.972 | 0.977 | 0.998 | 0.996 | 0.997 |

RMSE | 0.076 | 0.243 | 0.127 | 0.037 | 0.046 | 0.041 |

MAE | 0.054 | 0.189 | 0.086 | 0.026 | 0.036 | 0.028 |

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## Share and Cite

**MDPI and ACS Style**

Reza Kashyzadeh, K.; Amiri, N.; Ghorbani, S.; Souri, K.
Prediction of Concrete Compressive Strength Using a Back-Propagation Neural Network Optimized by a Genetic Algorithm and Response Surface Analysis Considering the Appearance of Aggregates and Curing Conditions. *Buildings* **2022**, *12*, 438.
https://doi.org/10.3390/buildings12040438

**AMA Style**

Reza Kashyzadeh K, Amiri N, Ghorbani S, Souri K.
Prediction of Concrete Compressive Strength Using a Back-Propagation Neural Network Optimized by a Genetic Algorithm and Response Surface Analysis Considering the Appearance of Aggregates and Curing Conditions. *Buildings*. 2022; 12(4):438.
https://doi.org/10.3390/buildings12040438

**Chicago/Turabian Style**

Reza Kashyzadeh, Kazem, Nima Amiri, Siamak Ghorbani, and Kambiz Souri.
2022. "Prediction of Concrete Compressive Strength Using a Back-Propagation Neural Network Optimized by a Genetic Algorithm and Response Surface Analysis Considering the Appearance of Aggregates and Curing Conditions" *Buildings* 12, no. 4: 438.
https://doi.org/10.3390/buildings12040438