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首先把路面温度场简化为非周期一维温度场,用分离变量法得到齐次边界条件下与温度场基本方程相容的傅里叶级数;然后用格林公式在边界展开热传导方程,得到傅里叶级数系数的常微分方程组,并用拉普拉斯变换求解;最后用实测数据标定的材料参数预测路面温度场。分析结果表明:傅里叶级数第4项仅在-0.1℃～0.1℃范围内波动;初始温度扰动对温度场有短时影响,如果扰动深度增大则影响时间变长;用实测数据标定模型后,模型可以较准确地预测路面温度场,标准差为1.88℃。
Firstly, the pavement temperature field is simplified to a non-periodic one-dimensional temperature field. The Fourier series is obtained by using the method of separate variables and is compatible with the basic equations of the temperature field under the homogeneous boundary conditions. Then the Green’s formula is used to develop the heat conduction equation at the boundary, In this paper, we use the Laplace transform to solve the ordinary differential equations of the coefficient series in the inner surface of the pavement. Finally, the pavement temperature field is predicted by the material parameters calibrated by the measured data. The analysis results show that the fourth term of Fourier series only fluctuates within the range of -0.1 ℃ ~ 0.1 ℃. The initial temperature disturbance has a short-term effect on the temperature field. If the disturbance depth increases, the influence time will be longer. After the model, the model can predict the pavement temperature field more accurately, with a standard deviation of 1.88 ℃.