木材导热系数的分形与神经网络模型
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摘要
本论文通过多种手段对木材的导热系数进行了理论和实验研究。提出了一个计算横纹导热系数的分形模型和一个预测导热系数的人工神经网络模型，并利用瞬态测量法的实验数据对模型进行了验证。
首先对传统的瞬态平面热源法进行了改进。通过拉普拉斯变换方法求解了一维有限厚度平板的非稳态导热微分方程，得到了平板木材试样的温度随时间和平板厚度变化的短时间公式，并由此建立了恒定热流加热的木材导热系数瞬态测量实验台。利用此实验台测量了不同含水率落叶松和红松试样的径向导热系数并与文献中的数据进行了比较。该实验台还可以同时测量出木材的热扩散系数和比热等热物性参数。
其次，提出了一个对木材的横纹导热系数进行理论估算的分形模型。通过扫描电镜图片对木材试样横纹剖面的多孔结构特征进行了观察，并利用分形理论对其进行了分析。采用盒维数法计算得到了4种木材纤维多孔结构的分形维数分别为1.38、1.49、1.38和1.44。然后研究了单个木材细胞的导热过程，通过热阻网络模拟的方法分别推导出了其弦向和径向导热系数的表达式，并由木材孔隙率与分形维数的关系式得到了其导热系数随分形维数变化的表达式。根据此分形模型对木材的径向导热系数进行了计算并将其结果与实验测量结果和文献中的数据进行了比较。
最后，建立了预测木材导热系数随各种物性参数变化的人工神经网络模型。网络类型为单隐层BP神经网络，以木材的温度和孔隙率为输入量，并以其导热系数为输出量。设隐层的神经元数分别为3～8个构建了6个神经网络，并利用桦木的导热系数对它们分别进行了训练。通过对训练误差的比较分析，得到了具有最优性能的网络型式为隐层具有6个神经元的网络，其训练结果的平均相对误差为0.21％，平均绝对误差为0.000433W／mK。利用该最优网络对不同温度和孔隙率情况下桦木的导热系数进行了预测，并将预测结果与实验和文献中的数据进行了对比。
研究结果表明，利用改进后的瞬态平面热源法能快速地对不同含水率的木材
The thermal conductivity of wood was studied in this thesis using several theoretical and experimental methods. A fractal model and an artificial neural network (ANN) model were proposed to predict the thermal conductivity of wood, and the experimental data was used to validate them.
First, the traditional transient plane source (TPS) method was improved. The transient heat conduction differential equation of one-dimensional slab with limited thickness was solved using Laplace transform. Moreover, the short time formula that describes the temperature of the flat wood as a function of time and thickness was obtained. The experimental equipment for measuring the thermal conductivity of wood at constant heat flux was also built. Subsequently, the thermal conductivity of the samples of larch and Korean pine with different moisture contents were measured using the improved transient measurement method, and the measured results were compared with the available literature data. In addition, the other thermal properties such as thermal diffusivity and specific heat can be measured simultaneously.
Secondly, a fractal model was proposed to predict the transverse thermal conductivity of wood. The porous structure of wood samples on their cross sections was observed using the scanning electron microscope (SEM) images and analyzed via the fractal theory. The box-counting dimensions of four kinds of wood samples were calculated, which are equal to 1.38, 1.49, 1.38 and 1.44, respectively. Moreover, the heat conduction process of a single cell was studied and the tangential and radial thermal conductivity of wood were obtained by the thermal resistance network method. The relationship between the thermal conductivity and the porosity was achieved, and the formula that describes the thermal conductivity changing with fractal dimension was also gained. According to the proposed fractal model, the radial thermal conductivity of wood was calculated and compared with the experimental and the available literature data.
Finally, to predict the variance of the thermal conductivity versus the physical properties of wood, a model based on artificial neural network was proposed. The
首先对传统的瞬态平面热源法进行了改进。通过拉普拉斯变换方法求解了一维有限厚度平板的非稳态导热微分方程，得到了平板木材试样的温度随时间和平板厚度变化的短时间公式，并由此建立了恒定热流加热的木材导热系数瞬态测量实验台。利用此实验台测量了不同含水率落叶松和红松试样的径向导热系数并与文献中的数据进行了比较。该实验台还可以同时测量出木材的热扩散系数和比热等热物性参数。
其次，提出了一个对木材的横纹导热系数进行理论估算的分形模型。通过扫描电镜图片对木材试样横纹剖面的多孔结构特征进行了观察，并利用分形理论对其进行了分析。采用盒维数法计算得到了4种木材纤维多孔结构的分形维数分别为1.38、1.49、1.38和1.44。然后研究了单个木材细胞的导热过程，通过热阻网络模拟的方法分别推导出了其弦向和径向导热系数的表达式，并由木材孔隙率与分形维数的关系式得到了其导热系数随分形维数变化的表达式。根据此分形模型对木材的径向导热系数进行了计算并将其结果与实验测量结果和文献中的数据进行了比较。
最后，建立了预测木材导热系数随各种物性参数变化的人工神经网络模型。网络类型为单隐层BP神经网络，以木材的温度和孔隙率为输入量，并以其导热系数为输出量。设隐层的神经元数分别为3～8个构建了6个神经网络，并利用桦木的导热系数对它们分别进行了训练。通过对训练误差的比较分析，得到了具有最优性能的网络型式为隐层具有6个神经元的网络，其训练结果的平均相对误差为0.21％，平均绝对误差为0.000433W／mK。利用该最优网络对不同温度和孔隙率情况下桦木的导热系数进行了预测，并将预测结果与实验和文献中的数据进行了对比。
研究结果表明，利用改进后的瞬态平面热源法能快速地对不同含水率的木材
The thermal conductivity of wood was studied in this thesis using several theoretical and experimental methods. A fractal model and an artificial neural network (ANN) model were proposed to predict the thermal conductivity of wood, and the experimental data was used to validate them.
First, the traditional transient plane source (TPS) method was improved. The transient heat conduction differential equation of one-dimensional slab with limited thickness was solved using Laplace transform. Moreover, the short time formula that describes the temperature of the flat wood as a function of time and thickness was obtained. The experimental equipment for measuring the thermal conductivity of wood at constant heat flux was also built. Subsequently, the thermal conductivity of the samples of larch and Korean pine with different moisture contents were measured using the improved transient measurement method, and the measured results were compared with the available literature data. In addition, the other thermal properties such as thermal diffusivity and specific heat can be measured simultaneously.
Secondly, a fractal model was proposed to predict the transverse thermal conductivity of wood. The porous structure of wood samples on their cross sections was observed using the scanning electron microscope (SEM) images and analyzed via the fractal theory. The box-counting dimensions of four kinds of wood samples were calculated, which are equal to 1.38, 1.49, 1.38 and 1.44, respectively. Moreover, the heat conduction process of a single cell was studied and the tangential and radial thermal conductivity of wood were obtained by the thermal resistance network method. The relationship between the thermal conductivity and the porosity was achieved, and the formula that describes the thermal conductivity changing with fractal dimension was also gained. According to the proposed fractal model, the radial thermal conductivity of wood was calculated and compared with the experimental and the available literature data.
Finally, to predict the variance of the thermal conductivity versus the physical properties of wood, a model based on artificial neural network was proposed. The
引文
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