# Application of Temperature and Process Duration as a Method for Predicting the Mechanical Properties of Thermally Modified Timber

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{3}) and compared with the results obtained by genetic algorithm (GA) (T = 208 °C, t = 122 min, and $\rho $ = 0.728 g/cm

^{3}). It is possible to obtain models that describe experimental results well with stochastic modeling and evolutionary algorithms.

## 1. Introduction

^{3}of TM wood is placed on the market annually [3].

## 2. Materials and Methods

#### 2.1. Description of the Resources Needed for the Experiment

^{3}, 0.472 g/cm

^{3}, and 0.366 g/cm

^{3}, respectively. For modified samples, the average density for Beech was 0.655 g/cm

^{3}, for Linden 0.455 g/cm

^{3}, and 0.353 g/cm

^{3}for Fir. The test samples had a minimum length of 19 times the depth of the section. Ten samples without visible defects, full cross-section, free from knots and resin pockets, with the dimensions of 380 mm × 50 mm × 20 mm, were prepared for bending strength test. Before the TM process, all samples were dried to a constant weight, over 24 h in a drying chamber from the “Kambič” manufacturer, at a temperature of 103 °C. Drying was carried out to determine the oven-dry mass for further mass-loss calculations. After drying, the samples were cooled in a desiccator and weighed in an unmodified state. They were then transferred to a vacuum reactor, where the thermal modification process was performed according to a commercial process (Silvapro

^{®}, Silvaprodukt, Ljubljana, Slovenia) [48]. After the specimens were placed in a vacuum-pressure reactor, about 95% vacuum was achieved in the chamber, while the absolute pressure was about 5 kPa. The parameters of the heat treatment process for testing the mechanical and physical properties of European beech (Fagus sylvatica), Linden (Tilia sp.), and silver fir (Abies alba) are following the parameters used in commercial processes [48]. The heating of the samples goes through five phases in which the samples were heated to maximum temperatures (170 °C, 180 °C, 195 °C, 210 °C, 220 °C) and treated with different maximum durations of the process (78, 120, 180, 240, 276 min). In the next 12 h, the samples were cooled and weighed.

#### 2.2. Experimental Procedure and Setup

#### 2.3. Polynomial Form of Bending Strength Function

#### 2.4. Modelling by Genetic Programming

- -
- Set of functions F = {+, −, *, /}
- -
- Input variable vectors X
_{1}, X_{2}, X_{3}, Set T= {T, t, ρ}—set of terminals, temperature (T), time (s), and density (ρ). - -
- R-makes a set of randomly generated constants that can be found in the expression (r
_{1}= 0.517009973526; r_{2}= 0.930670022964478) - -
- Size of population G = 500,
- -
- Initial depth of binary wood 5,
- -
- Depth of wood at mutation and crossing 8,
- -
- Probability of crossing 90%,
- -
- Probability of mutation 5%,
- -
- Probability of reproduction 20%,
- -
- Selection method, Elite selection,
- -
- Method of initialization of mixed population ‘’ramped half and half’’
- -
- Number of iterations (evolutions).
- -
- The criterion function of chromosome goodness-of-fit testing (computer programs) is defined by multiple regressions, as follows:

#### 2.5. Optimization of Bending Strength of Thermally Modified Wood by Classical Mathematical Analysis Method

_{1}, ∆

_{2,}and ∆

_{3}, as follows:

_{B}= F

_{B max}. The maximum bending strength was obtained for the values of thermal modification parameters T = 187 °C, t = 126 min and ρ = 0.780 g/cm

^{3}. Figure 3 shows the maximum bending force that depends on the input parameters. In contrast, the whole diagram represents the behavior of the maximum bending force and the relationship between the two input variables. The extreme point Fs max (T, t, $\rho $) shows the intensity of the change of the bending force depending on the individual change of each of the analyzed bending process parameters. Mathematical models of the maximum force are obtained and determined with two variables through the optimal point, with an orthogonal cross-section:

#### 2.6. Optimization of Bending Strength of Thermally Modified Wood by Genetic Algorithm

- -
- population size 500,
- -
- number of iterations 272,
- -
- probability of mutation 5%,
- -
- crossing probability 90%,
- -
- probability of reproduction 20%,
- -
- rank selection method.

^{3}, where the maximum bending force of the thermally modified wood was F = 5950 N. The comparison of this result with the maximum value obtained by the regression analysis, where the maximum force is F = 6438 N, indicates that the forces are approximately equal.

## 3. Results and Discussion

#### 3.1. Comparative Results of Bending Strength Experiment and Modelling

#### 3.2. The Comparison of the Optimal Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Bending test: (

**a**) 4-point bending procedure, (

**b**) rectangular cross-sectional sample dimensions [49].

**Figure 3.**Graphic representation of the function: (

**a**) (YT, $\rho $ maximum bending force depending on the duration of the process (t) and wood density ($\rho $), (

**b**) (YT, $\rho $) maximum bending force depending on the process temperature (T) and wood density ($\rho $), (

**c**) (YT, t) maximum bending force depending on the process temperature (T) and the duration of the process (t).

**Figure 4.**Graphic representation of the function of: (

**a**) Y

_{T}thermal modification parameters on bending strength depending on the temperature of the thermal modification process (T), (

**b**) Y

_{t}thermal modification parameters on bending strength depending on the duration of the thermal modification process (t), (

**c**) $\mathrm{Y}\rho $ thermal modification parameters on bending strength depending on the wood density ($\rho $).

**Figure 5.**Comparative results of experiments (blue curve), stochastic model (black curve), and GP model (red curve) in bending.

Parameters/Levels | Lowest | Low | Centre | High | Highest |
---|---|---|---|---|---|

Coding–classical experimental design | −1.682 | −1 | 0 | 1 | 1.682 |

Temperature (°C) X_{1} = T | 170 | 180 | 195 | 210 | 220 |

Process duration (min) X_{2} = t | 78 | 120 | 180 | 240 | 276 |

Density (g/cm^{3})X _{3} = ρ | 0.330 | 0.430 | 0.580 | 0.730 | 0.830 |

Coding-orthogonal array (X_{i}) | −1.682 | −1 | 0 | 1 | 1.682 |

N Species * | T °C | t min | $\mathsf{\rho}$ g/cm ^{3} | X_{0} | X_{1} | X_{2} | X_{3} | X_{1}X_{2} | X_{1}X_{3} | X_{2}X_{3} | X_{1}X_{2}X_{3} | X_{1}^{2} | X_{2}^{2} | X_{3}^{2} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 Fir | 180 | 120 | 0.43 | 1 | −1 | −1 | −1 | 1 | 1 | 1 | −1 | 1 | 1 | 1 |

2 Fir | 210 | 120 | 0.43 | 1 | 1 | −1 | −1 | −1 | −1 | 1 | 1 | 1 | 1 | 1 |

3 Fir | 180 | 240 | 0.43 | 1 | −1 | 1 | −1 | −1 | 1 | −1 | 1 | 1 | 1 | 1 |

4 Fir | 210 | 240 | 0.43 | 1 | 1 | 1 | −1 | 1 | −1 | −1 | −1 | 1 | 1 | 1 |

5 Beech | 180 | 120 | 0.73 | 1 | −1 | −1 | 1 | 1 | −1 | −1 | 1 | 1 | 1 | 1 |

6 Beech | 210 | 120 | 0.73 | 1 | 1 | −1 | 1 | −1 | 1 | −1 | −1 | 1 | 1 | 1 |

7 Beech | 180 | 240 | 0.73 | 1 | −1 | 1 | 1 | −1 | −1 | 1 | −1 | 1 | 1 | 1 |

8 Beech | 210 | 240 | 0.73 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

9–14 Linden | 195 | 180 | 0.58 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

15 Linden | 170 | 180 | 0.58 | 1 | −α | 0 | 0 | 0 | 0 | 0 | 0 | (−α)^{2} | 0 | 0 |

16 Linden | 220 | 180 | 0.58 | 1 | α | 0 | 0 | 0 | 0 | 0 | 0 | α^{2} | 0 | 0 |

17 Linden | 195 | 78 | 0.58 | 1 | 0 | −α | 0 | 0 | 0 | 0 | 0 | 0 | (−α)^{2} | 0 |

18 Linden | 195 | 276 | 0.58 | 1 | 0 | α | 0 | 0 | 0 | 0 | 0 | 0 | α^{2} | 0 |

19 Fir | 195 | 180 | 0.33 | 1 | 0 | 0 | −α | 0 | 0 | 0 | 0 | 0 | 0 | (−α)^{2} |

20 Beech | 195 | 180 | 0.83 | 1 | 0 | 0 | α | 0 | 0 | 0 | 0 | 0 | 0 | α^{2} |

N * | Experimental Results Y [N] | Standard Deviations | Results Per Models | |
---|---|---|---|---|

Stochastic Model(Y _{R}) [N] | Genetic Model(GP) [N] | |||

1 | 2665 | 2.05 | 2522 | 2569 |

2 | 3081 | 4.21 | 2830 | 3146 |

3 | 2873 | 3.40 | 2887 | 2928 |

4 | 2164 | 4.02 | 2359 | 1889 |

5 | 6150 | 6.10 | 5183 | 6438 |

6 | 5299 | 4.00 | 4165 | 5053 |

7 | 5110 | 7.06 | 4394 | 4880 |

8 | 2653 | 6.47 | 2210 | 2977 |

9 | 4403 | 5.32 | 4459 | 4283 |

10 | 4201 | 4.11 | 4237 | 4461 |

11 | 4856 | 5.15 | 4396 | 4621 |

12 | 4438 | 4.06 | 4559 | 4161 |

13 | 4606 | 3.27 | 4379 | 4282 |

14 | 4394 | 5.84 | 4959 | 4299 |

15 | 4015 | 3.11 | 3695 | 4054 |

16 | 2200 | 5.04 | 2283 | 2602 |

17 | 4123 | 3.75 | 4220 | 4628 |

18 | 2976 | 4.10 | 2774 | 2905 |

19 | 2761 | 5.06 | 2293 | 2897 |

20 | 3933 | 6.24 | 4519 | 4502 |

Method | Optimal TM Parameters | ||
---|---|---|---|

T (°C) | t (min) | ρ (g/cm^{3}) | |

Classic mathematical analysis | 193 | 126 | 0.780 |

Genetic algorithm (GA) | 197 | 121 | 0.728 |

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**MDPI and ACS Style**

Chu, D.; Hasanagić, R.; Hodžić, A.; Kržišnik, D.; Hodžić, D.; Bahmani, M.; Petrič, M.; Humar, M.
Application of Temperature and Process Duration as a Method for Predicting the Mechanical Properties of Thermally Modified Timber. *Forests* **2022**, *13*, 217.
https://doi.org/10.3390/f13020217

**AMA Style**

Chu D, Hasanagić R, Hodžić A, Kržišnik D, Hodžić D, Bahmani M, Petrič M, Humar M.
Application of Temperature and Process Duration as a Method for Predicting the Mechanical Properties of Thermally Modified Timber. *Forests*. 2022; 13(2):217.
https://doi.org/10.3390/f13020217

**Chicago/Turabian Style**

Chu, Demiao, Redžo Hasanagić, Atif Hodžić, Davor Kržišnik, Damir Hodžić, Mohsen Bahmani, Marko Petrič, and Miha Humar.
2022. "Application of Temperature and Process Duration as a Method for Predicting the Mechanical Properties of Thermally Modified Timber" *Forests* 13, no. 2: 217.
https://doi.org/10.3390/f13020217