# Predicting Maximum Work Duration for Construction Workers

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}of the test set were 0.1378, 0.1123, and 0.8182, respectively, showing that the prediction performance was generally accurate. This study can help construction practitioners and governments to rationally design the work–rest schedules of transportation infrastructure construction workers and thus protect them from the risks brought about by heat stress.

## 1. Introduction

## 2. Literature Review

## 3. Problem Statement

**Property**

**1.**

**Property**

**2.**

## 4. Development of a Prediction Model for MWD

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

Algorithm 1 Trial-and-error method to find $({x}_{1}^{*},{f}^{*})$ |

Initialize a sufficiently small ${f}_{0}$ (i.e., smaller than ${f}^{*}$). Define ${\widehat{f}}_{0}={f}_{0}$ and ${\widehat{f}}_{-1}={f}_{0}$; |

Set the tolerance gap $t=0.01$ and the current gap $g=\mathrm{inf}$; |

$k=0$; |

while $g>t$: |

$k=k+1$; |

${f}_{k}=f(\overline{x}({\widehat{f}}_{k-1}))$; // predict the initial value of $f$ using the final predicted value in the last round |

if ${f}_{k-1}\ge {\widehat{f}}_{k-1}$: |

${f}_{k}=\mathrm{max}({f}_{k},{\widehat{f}}_{k-2})$; |

else: |

${f}_{k}=\mathrm{min}({f}_{k},{\widehat{f}}_{k-2})$; |

${\widehat{f}}_{k}=\frac{{\widehat{f}}_{k-1}+{f}_{k}}{2}$; |

$g=\left|{\widehat{f}}_{k}-{\widehat{f}}_{k-1}\right|$; Return ${f}^{*}={\widehat{f}}_{k}$. |

## 5. Case Study

^{2}of the test set were 0.1378, 0.1123, and 0.8182, respectively, showing that the prediction performance was generally accurate.

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The relationship between ${x}_{1}^{\#}\mathrm{and}{x}_{1}^{\&}$ given ${f}^{\#}<{f}^{\&}$.

Feature | Way of Generation | Min Value | Mean Value | Max Value | Standard Deviation |
---|---|---|---|---|---|

Age | Assumption: a random integer between 28 to 65 | 28 | 48.24 | 65 | 10.58 |

Height (cm) | Assumption: a random integer between 155 to 185 | 155 | 170.03 | 185 | 9.06 |

Weight (kg) | Assumption: a random integer between 55 to 85 | 55 | 69.99 | 85 | 8.20 |

Average temperature | Calculated from Hong Kong Observatory considering the daily highest and lowest temperatures in August 2022 | 25.84 | 27.80 | 29.95 | 0.94 |

MWD | Calculated by Equation (2) | 1.68 | 5.50 | 3.18 | 0.97 |

Feature | Way of Generation | Distribution |
---|---|---|

Alcohol drinking habits * | Assumption: a random integer in set {0,1,2} | 0: 104, 1: 96, 2: 110 |

Smoking habits ** | Assumption: a random integer in set {0,1,2} | 0: 94, 1: 112, 2: 104 |

Job nature *** | Assumption: a random variable with any of the following binary features to be 1 and the other three to be 0: is_bar_bender_and_fixer, is_carpenter, is_concretor, and is_plumber | is_bar_bender_and_fixer = 1: 74, is_carpenter = 1: 88, is_concretor = 1: 79, is_plumber = 1: 69 |

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**MDPI and ACS Style**

Yan, R.; Yi, W.; Wang, S.
Predicting Maximum Work Duration for Construction Workers. *Sustainability* **2022**, *14*, 11096.
https://doi.org/10.3390/su141711096

**AMA Style**

Yan R, Yi W, Wang S.
Predicting Maximum Work Duration for Construction Workers. *Sustainability*. 2022; 14(17):11096.
https://doi.org/10.3390/su141711096

**Chicago/Turabian Style**

Yan, Ran, Wen Yi, and Shuaian Wang.
2022. "Predicting Maximum Work Duration for Construction Workers" *Sustainability* 14, no. 17: 11096.
https://doi.org/10.3390/su141711096