Non-destructive test method of wood moisture content based on multiple varying bounds integral numerical method

Cui Guo; Yixue Wang; Haibin Wang; Xiongbo Zheng; Bin Zhao; Cui Guo; Yixue Wang; Haibin Wang; Xiongbo Zheng; Bin Zhao

doi:10.3934/era.2025098

Electronic Research Archive

2025, Volume 33, Issue 4: 2246-2274. doi: 10.3934/era.2025098

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Non-destructive test method of wood moisture content based on multiple varying bounds integral numerical method

1.
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
2.
College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
3.
College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China

Received: 18 January 2025 Revised: 11 March 2025 Accepted: 25 March 2025 Published: 16 April 2025

For the wood moisture content (MC) detection engineering problem by planar capacitive sensors, a high accuracy is required. To meet this demand, we constructed a mathematical model in this paper, as this is an inverse problem in the multi-physics fields. Furthermore, we proposed a new numerical method with high accuracy, which is called the multiple varying bounds integral method. We applied this numerical method to establish a high accuracy and compact numerical scheme for solving this model. Because the unknown function is continuous in some physical fields and discontinuous in others, we needed to use different numerical methods to construct numerical schemes in these fields. For example, we used the multiple varying bounds integral (MVBI) method and interpolation methods. Next, based on the results of the numerical experiments, a regression model was established between capacitance and the dielectric constant of wood. The results indicated that the larger the value of dielectric constant, the larger the value of capacitance. This is consistent with the physical principle. Moreover, the determination coefficient $ R^{2} $ of the regression model was greater than 0.91. Additionally, the confidence degree exceeded 0.99, which implies that the reliability of the regression model is strong. This indicates that the regression model shows a high goodness of fit and high confidence degree.
- wood moisture content,
- multiple varying bounds integral numerical method,
- dielectric constant,
- regression analysis,
- mathematical model
Citation: Cui Guo, Yixue Wang, Haibin Wang, Xiongbo Zheng, Bin Zhao. Non-destructive test method of wood moisture content based on multiple varying bounds integral numerical method[J]. Electronic Research Archive, 2025, 33(4): 2246-2274. doi: 10.3934/era.2025098

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Abstract

For the wood moisture content (MC) detection engineering problem by planar capacitive sensors, a high accuracy is required. To meet this demand, we constructed a mathematical model in this paper, as this is an inverse problem in the multi-physics fields. Furthermore, we proposed a new numerical method with high accuracy, which is called the multiple varying bounds integral method. We applied this numerical method to establish a high accuracy and compact numerical scheme for solving this model. Because the unknown function is continuous in some physical fields and discontinuous in others, we needed to use different numerical methods to construct numerical schemes in these fields. For example, we used the multiple varying bounds integral (MVBI) method and interpolation methods. Next, based on the results of the numerical experiments, a regression model was established between capacitance and the dielectric constant of wood. The results indicated that the larger the value of dielectric constant, the larger the value of capacitance. This is consistent with the physical principle. Moreover, the determination coefficient $ R^{2} $ of the regression model was greater than 0.91. Additionally, the confidence degree exceeded 0.99, which implies that the reliability of the regression model is strong. This indicates that the regression model shows a high goodness of fit and high confidence degree.

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