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林业科学 ›› 2021, Vol. 57 ›› Issue (11): 142-151.doi: 10.11707/j.1001-7488.20211114

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基于模糊最小绝对非线性回归的木材热物性参数预测模型

曹书博1,李嘉豪1,周世玉2,刘晓平1,周玉成1,*   

  1. 1. 山东建筑大学信息与电气工程学院 济南 250101
    2. 山东建筑大学热能工程学院 济南 250101
  • 收稿日期:2020-10-19 出版日期:2021-11-25 发布日期:2022-01-12
  • 通讯作者: 周玉成
  • 基金资助:
    泰山学者优势特色学科人才团队(2015162)

Prediction of Wood Thermophysical Parameters Based on the Fuzzy Least Absolute Nonlinear Regression

Shubo Cao1,Jiahao Li1,Shiyu Zhou2,Xiaoping Liu1,Yucheng Zhou1,*   

  1. 1. School of Information and Electrical Engineering, Shandong Jianzhu University Jinan 250101
    2. School of Thermal Engineering, Shandong Jianzhu University Jinan 250101
  • Received:2020-10-19 Online:2021-11-25 Published:2022-01-12
  • Contact: Yucheng Zhou

摘要:

目的: 利用试验测量获得的木材体积比热、径向及弦向导热系数和热扩散系数,建立基于模糊最小绝对非线性回归的木材体积比热模型和各向异性导热模型,分析木材热物性参数规律,为木材导热规律研究、木材热物性评价标准制定提供理论基础和数据支撑。方法: 试验样品由130种常见木材切割得到,其中用于测量木材体积比热的试验样品为直径18 mm、厚度2 mm的圆片形状样品,每种材种随机选择20种;用于测量木材导热系数和热扩散系数的试验样品为2块50 mm×50 mm×20 mm的长方体样品,每种材种随机选择20种。首先,利用Hot Disk热常数分析仪测试样品热物性参数,获得木材体积比热、径向及弦向导热系数和热扩散系数,经滤波降噪和归一化处理后,将试验数据分成训练集和验证集;然后,提出适用于小样本数据集回归分析的模糊最小绝对非线性回归方法,建立木材体积比热模型和各向异性导热模型。该方法将最小绝对回归准则与模糊逻辑理论相结合,首先构建高斯隶属度函数,对数据进行模糊化;然后构建单值模糊器,生成模糊规则库,采用乘积推理机对输入空间元素进行模糊推理,得到推理结果;最后采用最小绝对回归准则优化结果,建立一类具有非线性属性的木材径向、弦向导热系数和热扩散系数模型,并对各向异性木材的导热和热扩散过程进行实时分析和预测。结果: 模糊最小绝对非线性回归(FLANR)对木材体积比热预测结果的拟合度为0.997 6,平均相对误差、最大相对误差和均方误差分别为0.026 0%、0.049 1%和0.035 2%;与之相比,自适应模糊神经网络(ANFIS)预测结果的拟合度为0.963 1,平均相对误差、最大相对误差和均方误差分别为0.189 3%、2.176 2%和0.799 3%。对于木材各向异性导热模型,单独比较模型中的一个输出变量(木材径向导热系数)可知,FLANR预测结果的拟合度为0.958 1,平均相对误差、最大相对误差和均方误差分别为0.190 2%、0.348 1%和0.085 3%;与之相比,模糊最小二乘法(FLS)预测结果的拟合度为0.604 5,平均相对误差、最大相对误差和均方误差分别为2.169 4%、5.260 9%和2.910 6%。FLANR预测结果的拟合误差明显小于ANFIS和FLS,所建立模型具有较好的拟合效果和泛化性。结论: 采用模糊最小绝对非线性回归对木材体积比热和各向异性导热建模是可行的,该方法计算时间短且泛化性较好,所建立木材热物性参数模型可为木材导热规律研究、木材热物性评价标准制定提供理论基础和数据支撑。

关键词: 木材, 热物性参数, 模糊回归, 平面热源法

Abstract:

Objective: In this paper, the volume specific heat, radial and tangential thermal conductivity and thermal diffusion coefficient of wood obtained from experimental measurement were used to establish the wood volume specific heat model and wood anisotropic thermal conductivity model based on fuzzy least absolute nonlinear regression method, analyze the law of wood thermophysical parameters, and provide a basis for the study of wood thermal conductivity law. It was expected to provide a theoretical basis and data support for the formulation of wood thermophysical property evaluation standards. Method: The experimental samples were obtained by cutting 130 kinds of common woods. Among them, the experimental samples used to measure the volume specific heat of wood were 18 mm in diameter and 2 mm in thickness; the experimental samples for measuring the thermal conductivity and thermal diffusion coefficient of wood were two rectangular samples of 50 mm×50 mm×20 mm. Firstly, the Hot Disk thermal constants analyser was used to test the thermal physical parameters of the experimental samples, and the volume specific heat, radial heat conduction rate, radial thermal diffusion coefficient, axial thermal diffusivity and axial thermal diffusion coefficient of wood samples were obtained. The experimental data were divided into two parts: training set and validation set. Furthermore, a fuzzy least absolute nonlinear regression method suitable for regression analysis of small sample data sets was proposed, and the wood volume specific heat model and anisotropic heat conduction model of wood were established. Firstly, Gaussian membership function was constructed to blur the data. Then a singleton fuzzier was constructed to generate the fuzzy rule base. The product inference engine was used to carry out fuzzy reasoning on the input space elements, and the reasoning results were obtained. Finally, the least absolute regression criterion was used to optimize the obtained results, and a class of nonlinear wood radial and axial thermal diffusivity and thermal conductivity models were established. The model was used to analyze and predict the thermal diffusion and thermal conductivity processes of anisotropic wood in real time. Result: The results showed that the fitting degree of the fuzzy least absolute nonlinear regression (FLANR) was 0.997 6, and the mean velative error(MRE), maximum relative error(MARE) and mean square error(MSE) were 0.026 0%, 0.049 1% and 0.035 2%, respectively. In comparison, the fitting degree of ANFIS prediction was 0.963 1, and the MRE, MARE and MSE were 0.189 3%, 2.176 2% and 0.799 3%, respectively. For the wood anisotropic heat conduction model, a single comparison one of the output variables (the wood axial heat conduction rate) in the wood anisotropic thermal conductivity model showed that the fitting degree of the predicted results of FLANR was 0.958 1, and the MRE, MARE and MSE were 0.190 2%, 0.348 1% and 0.085 3%, respectively. In comparison, the fitting degree of FLS prediction was 0.604 5, and the MRE, MARE and MSE were 2.169 4%, 5.260 9% and 2.910 6%, respectively. The fitting error of FLANR prediction was obviously less than those of ANFIS and FLS, and the model had a good fitting effect and generalization. Conclusion: It might be feasible to use the fuzzy least absolute nonlinear regression to model the specific heat of wood volume and anisotropic thermal conductivity of wood. The calculation time of this method was short and the generalization was good. The established wood thermal physical property parameter model would provide guidance for the follow-up research on wood thermal conductivity.

Key words: wood, thermal property parameters, fuzzy regression, plane source method

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