# Multigene Expression Programming Based Forecasting the Hardened Properties of Sustainable Bagasse Ash Concrete

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## Abstract

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## 1. Introduction

_{2}per ton of concrete produced [2,3,4]. The idea of green concrete is gaining popularity as a way to diminish the harmful impacts of concrete while still addressing the underlying problem. Green concrete is made by substituting industrial waste with traditional cementitious materials. Commonly used wastes that can be used as cement replacement are electric arc furnace slag, rubber ash, fly ash, volcanic ash, rice husk ash, metakaolin, and sugarcane bagasse ash [5,6]. The use of these materials is seen as a low-carbon alternative to traditional building materials and a way to reduce energy use and carbon emissions effects. Sugarcane bagasse is the primary fuel used in the sugarcane industry around the world [7]. It is one of the agricultural wastes that remain after processing and extraction in the same industry. Bagasse and residue ash make up about 26% and 0.62% of each ton of sugarcane, respectively [8]. The ash is disposed of in landfills, raising significant environmental problems [9]. As a result, environmentally friendly applications for bagasse ash (BA) are being explored in the construction sector. Several experimental studies have indicated that BA can be used as a cement substitute in concrete with a substantial improvement in mechanical properties. Chusilp et al. (2009) [10] observed that concrete including 20% BA by mass of binder had greater compressive strength (${\mathrm{f}}_{\mathrm{c}}^{\prime}$) and better stability. Sobuz et al. (2014) [11] stated that maximum strength of BA concrete (BAC) could be obtained by replacing 10% of the cement. According to Jagadesh et al. (2018) [12], the ${\mathrm{f}}_{\mathrm{c}}^{\prime}$ of the concrete with 30% raw BA was reduced by nearly 50%. The reduction in ${\mathrm{f}}_{\mathrm{c}}^{\prime}$ was attributable to the larger size of particles, which expands the pore size. Almost a 27% increase in ${\mathrm{f}}_{\mathrm{c}}^{\prime}$ was observed when 10% binder was replaced with BA. The increase in ${\mathrm{f}}_{\mathrm{c}}^{\prime}$ is caused by the presence of finer silica and the finer BA particles acts as a filler, which in turn improves the density and strength of concrete. Similar observations are reported by Bahurudeen et al. (2015) [13] where the authors noted that at 25% replacement, the compressive strength of BAC decreases due to dilution effect. In addition, the durability properties of BAC are reported to be much better than normal concrete [10,14,15].

## 2. Modeling Techniques and Database

#### 2.1. Multigene Expression Programming

#### 2.2. Modeling Database

#### 2.3. Cross-Validation with k-Fold Algorithm

#### 2.4. Models Evaluation by Statistical Measures

## 3. Mix Proportions for Bagasse Ash Concrete (BAC)

## 4. Results and Discussion

#### 4.1. Mechanical Properties of BAC

_{2}.

#### 4.2. Formulation of BAC Mechanical Properties

#### 4.3. Models Validation by Experimental Data

#### 4.4. Statistical Analysis and Generalizability of the Models

_{m}is higher than 0.5, then the requirements for external validation of models are satisfied [80]. Table 5 shows that external validation requirements are met for all the three proposed MEP models for ${\mathrm{f}}_{\mathrm{c}}^{\prime}$, ${\mathrm{f}}_{\mathrm{STS}}$ and ${\mathrm{f}}_{\mathrm{FS}}$.

#### 4.5. 10-Fold Cross-Validation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Experimentally tested results of (

**a**) compressive strength, (

**b**) tensile strength, (

**c**) flexural strength of bagasse ash concrete (BAC).

**Figure 3.**Comparison of actual and model predicted compressive strength (

**a**) variation in data (

**b**) scattered plot.

**Figure 4.**Comparison of actual and model predicted splitting tensile strength (

**a**) variation in data (

**b**) scattered plot.

**Figure 5.**Comparison of actual and model predicted flexural strength (

**a**) variation in data (

**b**) scattered plot.

**Figure 6.**Compressive strength (${\mathrm{f}}_{\mathrm{c}}^{\prime}$) model validation by experimental results (

**a**) variation in data (

**b**) scattered plot.

**Figure 7.**Splitting tensile strength (${\mathrm{f}}_{\mathrm{STS}}$) model validation by experimental results (

**a**) variation in data (

**b**) scattered plot.

**Figure 8.**Flexural strength (${\mathrm{f}}_{\mathrm{FS}}$) model validation by experimental results (

**a**) variation in data (

**b**) scattered plot.

**Figure 9.**Deviation of the error between the actual and predicted results of MEP models developed for (

**a**) ${\mathrm{f}}_{\mathrm{c}}^{\prime}$ (

**b**) ${\mathrm{f}}_{\mathrm{STS}}$ (

**c**) ${\mathrm{f}}_{\mathrm{FS}}$.

Setting Parameters | Optimum Value |
---|---|

Subpopulation | 50 |

length of code | 40 |

Subpopulation size | 250 |

Number of generations | 1000 |

Mutation probability | 0.01 |

Crossover probability | 0.9 |

Mathematical operators | +, −, ×, ÷ |

Variables | 0.5 |

Tournament size | 4 |

Operators | 0.5 |

Parameter | Unit | Range | Min | Max | Mean | SD |
---|---|---|---|---|---|---|

W/C | - | 0.3 | 0.3 | 0.6 | 0.47 | 0.074 |

CC | Kg/m^{3} | 444 | 112 | 555 | 336.5 | 98.5 |

BA% | % | 50 | 0 | 50 | 13.41 | 10.46 |

FA | Kg/m^{3} | 614 | 239 | 853 | 603.5 | 232.1 |

CA | Kg/m^{3} | 772 | 477 | 1249 | 884.6 | 392.3 |

Mix | Cement Kg/m3 | CA Kg/m3 | BA Kg/m3 | W/C | FA Kg/m3 | Water Kg/m3 | Density (Kg/m3) | |||
---|---|---|---|---|---|---|---|---|---|---|

Cement | CA | FA | BA | |||||||

NC | 366 | 1013.5 | 0 | 0.5 | 742.3 | 183 | 3150 | 2510 | 1680 | 2450 |

10BA | 329.4 | 1013.5 | 36.6 | 0.5 | 742.3 | 183 | ||||

20BA | 292.8 | 1013.5 | 73.2 | 0.5 | 742.3 | 183 | ||||

30BA | 256.2 | 1013.5 | 109.8 | 0.5 | 742.3 | 183 | ||||

40BA | 219.6 | 1013.5 | 146.4 | 0.5 | 742.3 | 183 |

Models | Data | R | RMSE | RSE | NSE | MAE | RRMSE | ρ | OF |
---|---|---|---|---|---|---|---|---|---|

${\mathrm{f}}_{\mathrm{c}}^{\prime}$ | Training | 0.91 | 3.47 | 0.16 | 0.87 | 2.96 | 0.04 | 0.020 | |

Testing | 0.94 | 2.98 | 0.12 | 0.89 | 2.98 | 0.09 | 0.046 | 0.036 | |

Validation | 0.93 | 2.87 | 0.15 | 0.89 | 1.67 | 0.04 | 0.020 | ||

${\mathrm{f}}_{\mathrm{STS}}$ | Training | 0.90 | 2.43 | 0.23 | 0.85 | 3.67 | 0.09 | 0.047 | |

Testing | 0.92 | 2.65 | 0.26 | 0.91 | 3.69 | 0.12 | 0.062 | 0.031 | |

Validation | 0.92 | 3.25 | 0.31 | 0.90 | 3.98 | 0.10 | 0.052 | ||

${\mathrm{f}}_{\mathrm{FS}}$ | Training | 0.91 | 3.92 | 0.29 | 0.86 | 1.87 | 0.13 | 0.068 | 0.052 |

Testing | 0.91 | 3.34 | 0.28 | 0.87 | 1.45 | 0.15 | 0.078 | ||

Validation | 0.93 | 3.67 | 0.19 | 0.86 | 2.87 | 0.16 | 0.079 |

S.No. | Mathematical Expression | Requirement | ${f}_{c}^{\text{'}}$ | ${f}_{STS}$ | ${f}_{FS}$ | Reference |

1. | $R=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({M}_{i}-{\overline{M}}_{i}\right)({P}_{i}-{\overline{P}}_{i})}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{({M}_{i}-{\overline{M}}_{i})}^{2}{{\displaystyle \sum}}_{i=1}^{n}{({P}_{i}-{\overline{P}}_{i})}^{2}}}$ | R > 0.8 | 0.92 | 0.92 | 0.91 | [78] |

2. | $k=\frac{{{\displaystyle \sum}}_{i=1}^{n}({M}_{i}-{P}_{i})}{{M}_{i}{}^{2}}$ | 0.85 < k < 1.15 | 1.00 | 0.99 | 1.01 | [79] |

3. | ${k}^{\prime}=\frac{{{\displaystyle \sum}}_{i=1}^{n}({M}_{i}-{P}_{i})}{{P}_{i}{}^{2}}$ | 0.85 < k’ < 1.15 | 0.98 | 0.98 | 1.05 | [79] |

4. | ${R}_{m}={R}^{2}\times (1-\sqrt{\left|{R}^{2}-{R}_{0}{}^{2}\right|}$ | R_{m} > 0.5 | 0.67 | 0.71 | 0.64 | [80] |

${R}_{0}{}^{2}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({P}_{i}-{M}_{i}{}^{0}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{({P}_{i}-\overline{{P}_{i}{}^{0}})}^{2}},{M}_{i}{}^{0}=k\times {P}_{i}$ | ${R}_{0}{}^{2}\cong 1$ | 0.98 | 0.98 | 0.97 | ||

$\stackrel{\xb4}{{R}_{0}{}^{2}}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({M}_{i}-{P}_{i}{}^{0}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{({M}_{i}-\overline{{M}_{i}{}^{0}})}^{2}},{P}_{i}{}^{0}={k}^{\prime}\times {M}_{i}$ | $\stackrel{\xb4}{{R}_{0}{}^{2}}\cong 1$ | 0.98 | 0.99 | 0.98 |

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**MDPI and ACS Style**

Amin, M.N.; Khan, K.; Aslam, F.; Shah, M.I.; Javed, M.F.; Musarat, M.A.; Usanova, K.
Multigene Expression Programming Based Forecasting the Hardened Properties of Sustainable Bagasse Ash Concrete. *Materials* **2021**, *14*, 5659.
https://doi.org/10.3390/ma14195659

**AMA Style**

Amin MN, Khan K, Aslam F, Shah MI, Javed MF, Musarat MA, Usanova K.
Multigene Expression Programming Based Forecasting the Hardened Properties of Sustainable Bagasse Ash Concrete. *Materials*. 2021; 14(19):5659.
https://doi.org/10.3390/ma14195659

**Chicago/Turabian Style**

Amin, Muhammad Nasir, Kaffayatullah Khan, Fahid Aslam, Muhammad Izhar Shah, Muhammad Faisal Javed, Muhammad Ali Musarat, and Kseniia Usanova.
2021. "Multigene Expression Programming Based Forecasting the Hardened Properties of Sustainable Bagasse Ash Concrete" *Materials* 14, no. 19: 5659.
https://doi.org/10.3390/ma14195659