# Compressive Strength Prediction of Rice Husk Ash Concrete Using a Hybrid Artificial Neural Network Model

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## Abstract

**:**

^{2}(0.9709), VAF (97.0911%), RMSE (3.4489), and MAE (2.6451). The proposed model also had better predictive accuracy than that of previously developed models on the same data. The sensitivity results show that age is the most important parameter for predicting the compressive strength of RHA concrete.

## 1. Introduction

_{2}) produced in the forging process is a heavy burden (approximately 7%) on the atmosphere. Considering the harm of CO

_{2}to the environment and human beings, energy conservation and emission reduction have become normal goals in concrete application. Searching for ovel materials to replace parts of cement, namely, supplementary cementitious materials (SCMs), is one of the most effective ways to solve this problem.

^{2}) equal to 0.9932. Zhang et al. [42] improved the random forest (RF) model to predict the compressive strength of lightweight concrete (LWC). The extreme learning machine (ELM) model was applied for the compressive strength prediction of lightweight foamed concrete [43]. Compared with these models, an artificial neural network (ANN) model with a simple structure, and good capabilities for processing high-dimensional data and complex parameter relationships is more favored in predicting the concrete strength of RHA [44,45,46,47]. Getahun et al. [48] developed an ANN model to forecast the 28-day compressive strength of a composite concrete mixture with RHA and reclaimed asphalt pavement (RAP). The prediction results illustrated that the ANN model could accurately fit the relationship between the considered components and the strength, as evidenced by excellent performance indices: R was 0.9811 and the root mean square error (RMSE) was 0.648. To optimize the selection scheme of the ANN model on weight and bias values, and further improve model performance, many scholars modified this model using numerous optimization algorithms for predicting concrete strength, e.g., grey wolf optimization (GWO) [49,50], particle swarm optimization (PSO) [51,52], the genetic algorithm (GA) [53], the whale optimization algorithm (WOA) [54], and simulated annealing (SA) with PSO [55]. For the strength prediction of RHA concrete, Andalib et al. [56] utilized the bat algorithm (BA), PSO, and teaching–learning-based optimization (TLBO) algorithm to optimize the ANN model for predicting compressive strength. The performance results showed that all optimized ANN models achieved satisfactory prediction accuracy, especially the BA–ANN model (RMSE = 5.898); Hamidian et al. [33] proposed four hybrid ANN models to estimate the compressive strength of RHA concrete. On the basis of the results of the performance analysis of all models, the PSO-with-two differential-mutations (PSOTD)-based ANN model achieved superior performance than that of other models, indicated by the higher R

^{2}values (0.9697). There are still many newly developed and excellent optimization-algorithm-based populations that have not been applied to the strength prediction of RHA concrete. Population initialization also needs attention to maximize the predictive potential of ANN models.

## 2. Data and Methods

#### 2.1. Rice Husk Ash Concrete

^{3}), RHA (kg/m

^{3}), a superplasticizer (kg/m

^{3}), an aggregate (kg/m

^{3}), and water (kg/m

^{3}) to produce a series of concrete samples. Freshly poured concrete needs to be cured, and its strength must be measured after a certain time. Therefore, age (days) is also an important variable in predicting concrete strength. In this paper, 192 compressive-strength data from Iftikhar et al. [57] were utilized to evaluate RHA concrete. The statistical information of these variables and the compressive strength of the target concrete samples is listed in Table 1.

#### 2.2. Reptile Search Algorithm

## 3. Development of the Novel CMRSA–ANN Model

^{2}, RMSE, variance accounted for (VAF), and mean absolute error (MAE). The definition of these indices can be found in the literature [69,70], and their formulars are expressed as follows:

_{t}and c

_{t}are the values of the t-th measured and predicted, respectively; $\overline{C}$ is the average of the measured values.

## 4. Prediction Model Development

#### 4.1. ANN Model

^{2}and RMSE, as shown in Table 3. The ANN model with two hidden layers (four neurons in the first hidden layer and three neurons in the second hidden layer) had the best performance, with a higher R

^{2}(0.8772) and lower RMSE (5.8632) than those of other models.

#### 4.2. CMRSA–ANN Model

#### 4.3. SOA–SVM Model

#### 4.4. SOA–RF Model

#### 4.5. ELM Model

^{2}is equal to 0.8932 and RMSE is equal to 5.4682.

#### 4.6. Empirical Model

## 5. Results and Discussion

^{2}and VAF (0.9679 and 96.7884%), and the lowest values of RMSE and MAE (2.9991 and 2.3169). Following this model, two other hybrid models (SOA–SVM and SOA–RF) also had superior predictive accuracy than that of the unoptimized ML (ANN and ELM) and empirical models. On the other hand, the proposed CMRSA–ANN model still achieved better predictive performance than that of other models, indicated by the higher values of R

^{2}and VAF (0.9709 and 97.0911%), and the lower values of RMSE and MAE (3.4489 and 2.6451). Although the performance of the SOA–SVM and SOA–RF models in the testing phase was worse than that using the training set, they still achieved higher predictive accuracy than that of the unoptimized ML models. The ANN model achieved better performance than that of the ELM model in the testing phase, proving that the prediction accuracy of the ELM model is unstable for solving regression problems.

^{2}value. These results also indicate that the CMRSA–ANN model could better explain the relationship between the input parameters and the compressive strength of RHA concrete.

## 6. Conclusions

^{2}(0.9679 and 0.9709), VAF (96.7884% and 97.0911%), RMSE (2.9991 and 3.4489), and MAE (2.3169 and 2.6451) among all models in the both the training and the testing phases. The performance comparison between the proposed and optimized ANN models also indicated that the CMRSA could effectively improve the prediction ability of the ANN model.

^{2}(0.9491 and 0.8941) and VAF (95.0044% and 89.5048%), and lower RMSE (4.5436 and 6.5743) and MAE (3.0904 and 4.8037) in the testing phase. It is effective and necessary to use an optimization (such as population-based) algorithm to improve the performance of ML models.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Illustration of hunting behavior for RSA proposed by Abualigah et al. [61]: (

**a**) exploration; (

**b**) exploitation.

**Figure 2.**Flowchart of generating CMRSA–ANN model to predict the compressive strength of RHA concrete.

Variables | Statistical Indices | ||||
---|---|---|---|---|---|

Min | Max | Mean | Median | St. D | |

Cement | 249.0 | 783.0 | 409.02 | 400.00 | 105.47 |

RHA | 0.0 | 171.0 | 62.33 | 57.00 | 41.55 |

Superplasticizer | 0.0 | 11.3 | 3.34 | 1.85 | 3.52 |

Aggregate | 1040.0 | 1970.0 | 1621.51 | 1725.00 | 267.77 |

Water | 120.0 | 238.0 | 193.54 | 203.00 | 31.93 |

Age | 1.0 | 90.0 | 34.57 | 28.00 | 33.52 |

Compressive strength | 16.0 | 104.1 | 48.14 | 45.95 | 17.54 |

Variables | Cement | RHA | Superplasticizer | Aggregate | Water | Age | Compressive Strength |
---|---|---|---|---|---|---|---|

Cement | 1 | −0.219 | 0.253 | −0.238 | 0.083 | −0.106 | 0.370 |

RHA | 1 | −0.021 | −0.139 | 0.136 | −0.033 | −0.023 | |

Superplasticizer | 1 | −0.205 | 0.268 | −0.000 | 0.301 | ||

Aggregate | 1 | −0.549 | −0.063 | 0.147 | |||

Water | 1 | 0.011 | −0.244 | ||||

Age | 1 | 0.495 | |||||

Compressive strength | 1 |

Tests | Structure | Performance | ||
---|---|---|---|---|

HL-1 | HL-2 | R^{2} | RMSE | |

1 | 2 | / | 0.8322 | 6.8525 |

2 | 4 | / | 0.7839 | 7.7690 |

3 | 6 | / | 0.8100 | 7.2921 |

4 | 8 | / | 0.8225 | 7.0476 |

5 | 10 | / | 0.8554 | 6.3611 |

6 | 4 | 3 | 0.8772 | 5.8632 |

7 | 4 | 6 | 0.8312 | 6.8726 |

8 | 6 | 8 | 0.8025 | 7.4350 |

9 | 8 | 10 | 0.8143 | 7.2101 |

10 | 10 | 12 | 0.8338 | 6.8193 |

Tests | Neuron Numbers | Performance | |
---|---|---|---|

R^{2} | RMSE | ||

1 | 20 | 0.5268 | 11.5078 |

2 | 30 | 0.6460 | 9.9534 |

3 | 40 | 0.7327 | 8.6492 |

4 | 50 | 0.7595 | 8.2046 |

5 | 60 | 0.7851 | 7.7555 |

6 | 70 | 0.7997 | 7.4873 |

7 | 80 | 0.8589 | 6.2835 |

8 | 90 | 0.8373 | 6.7479 |

9 | 100 | 0.8932 | 5.4682 |

10 | 110 | 0.8788 | 5.8235 |

Model | Performance (Training Set) | Model | Performance (Test Set) | ||||||
---|---|---|---|---|---|---|---|---|---|

R^{2} | VAF % | RMSE | MAE | R^{2} | VAF % | RMSE | MAE | ||

ANN | 0.8772 | 87.7619 | 5.8632 | 4.1423 | ANN | 0.8572 | 86.0686 | 7.6353 | 5.2808 |

CMRSA–ANN | 0.9679 | 96.7884 | 2.9991 | 2.3169 | CMRSA–ANN | 0.9709 | 97.0911 | 3.4489 | 2.6451 |

SOA–SVM | 0.9595 | 96.0957 | 3.3651 | 1.2528 | SOA–SVM | 0.9494 | 95.0044 | 4.5436 | 3.0904 |

SOA–RF | 0.9224 | 92.2384 | 4.6610 | 3.2359 | SOA–RF | 0.8941 | 89.5048 | 6.5743 | 4.8037 |

ELM | 0.8932 | 89.3163 | 5.4682 | 4.0644 | ELM | 0.7020 | 70.6826 | 11.0294 | 8.5905 |

Empirical | 0.2023 | 50.0783 | 14.9418 | 12.0202 | Empirical | 0.3716 | 57.3263 | 16.0169 | 13.1709 |

No. | Measured | Predicted | |||||
---|---|---|---|---|---|---|---|

ANN | CMRSA–ANN | SOA–SVM | SOA–RF | ELM | Empirical | ||

1 | 82.20 | 100.09 | 87.90 | 83.20 | 78.36 | 95.91 | 64.96 |

2 | 72.80 | 72.04 | 74.38 | 75.93 | 69.61 | 83.15 | 55.26 |

3 | 43.50 | 44.85 | 43.59 | 42.07 | 42.81 | 37.48 | 31.36 |

4 | 48.70 | 41.82 | 47.91 | 43.25 | 54.26 | 32.36 | 39.11 |

5 | 16.00 | 27.32 | 16.50 | 22.53 | 28.28 | 30.40 | 20.62 |

6 | 85.70 | 75.39 | 85.31 | 84.08 | 73.81 | 94.46 | 62.58 |

7 | 43.00 | 39.93 | 44.88 | 38.92 | 35.43 | 38.80 | 17.57 |

8 | 33.60 | 30.16 | 33.05 | 31.06 | 33.00 | 23.74 | 23.33 |

9 | 94.00 | 92.21 | 92.18 | 80.18 | 78.79 | 81.86 | 81.00 |

10 | 31.10 | 34.15 | 31.28 | 31.15 | 33.57 | 31.17 | 10.31 |

11 | 57.30 | 55.35 | 58.61 | 59.18 | 52.92 | 61.25 | 57.31 |

12 | 41.30 | 40.49 | 38.96 | 39.98 | 40.03 | 46.12 | 28.98 |

13 | 20.80 | 24.08 | 24.19 | 20.48 | 26.86 | 20.58 | 11.78 |

14 | 22.70 | 38.28 | 19.66 | 33.55 | 35.84 | 32.02 | 47.24 |

15 | 38.80 | 38.68 | 36.91 | 40.64 | 39.48 | 42.21 | 20.21 |

16 | 60.00 | 60.42 | 63.35 | 54.54 | 59.20 | 49.98 | 54.46 |

17 | 55.50 | 53.28 | 61.66 | 59.50 | 51.22 | 70.86 | 49.78 |

18 | 61.00 | 63.75 | 62.30 | 62.09 | 54.07 | 63.77 | 57.04 |

19 | 63.00 | 59.20 | 58.12 | 61.35 | 55.48 | 57.46 | 60.53 |

20 | 66.00 | 70.44 | 69.78 | 63.07 | 63.24 | 74.16 | 56.84 |

21 | 52.00 | 50.39 | 54.58 | 55.85 | 53.52 | 48.25 | 26.83 |

22 | 43.30 | 50.25 | 48.77 | 43.25 | 43.49 | 50.56 | 50.28 |

23 | 26.00 | 35.75 | 24.35 | 34.61 | 34.82 | 24.83 | 22.97 |

24 | 64.50 | 67.10 | 63.77 | 66.99 | 64.85 | 34.38 | 56.76 |

25 | 35.30 | 36.41 | 36.21 | 35.36 | 35.36 | 32.85 | 24.82 |

26 | 83.20 | 88.88 | 76.67 | 86.11 | 80.21 | 69.73 | 73.68 |

27 | 50.00 | 50.77 | 51.73 | 48.15 | 44.58 | 60.87 | 39.90 |

28 | 56.50 | 57.93 | 56.92 | 57.31 | 53.43 | 44.06 | 62.27 |

29 | 35.50 | 20.85 | 30.46 | 33.68 | 39.28 | 35.10 | 34.13 |

30 | 36.10 | 34.92 | 34.59 | 36.03 | 35.78 | 32.35 | 16.05 |

31 | 20.90 | 42.96 | 15.75 | 33.59 | 35.93 | 44.32 | 53.03 |

32 | 51.00 | 60.39 | 61.63 | 54.00 | 54.33 | 50.00 | 54.81 |

33 | 95.20 | 79.24 | 92.32 | 97.05 | 80.43 | 71.92 | 56.78 |

34 | 28.00 | 30.20 | 29.90 | 27.95 | 29.14 | 26.68 | 22.74 |

35 | 60.00 | 56.15 | 57.96 | 60.36 | 57.60 | 53.10 | 30.99 |

36 | 46.80 | 45.49 | 45.32 | 44.13 | 45.88 | 34.48 | 35.04 |

37 | 39.30 | 35.34 | 35.41 | 37.21 | 37.24 | 38.70 | 18.93 |

38 | 38.00 | 38.96 | 36.98 | 39.21 | 43.23 | 25.48 | 23.56 |

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## Share and Cite

**MDPI and ACS Style**

Li, C.; Mei, X.; Dias, D.; Cui, Z.; Zhou, J.
Compressive Strength Prediction of Rice Husk Ash Concrete Using a Hybrid Artificial Neural Network Model. *Materials* **2023**, *16*, 3135.
https://doi.org/10.3390/ma16083135

**AMA Style**

Li C, Mei X, Dias D, Cui Z, Zhou J.
Compressive Strength Prediction of Rice Husk Ash Concrete Using a Hybrid Artificial Neural Network Model. *Materials*. 2023; 16(8):3135.
https://doi.org/10.3390/ma16083135

**Chicago/Turabian Style**

Li, Chuanqi, Xiancheng Mei, Daniel Dias, Zhen Cui, and Jian Zhou.
2023. "Compressive Strength Prediction of Rice Husk Ash Concrete Using a Hybrid Artificial Neural Network Model" *Materials* 16, no. 8: 3135.
https://doi.org/10.3390/ma16083135