Estimation method for area distribution of water film thickness on airport runway modified by measured data in real time
Article Text (Baidu Translation)
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摘要: 为精准预估不同跑道状况与降雨条件下跑道水膜厚度的面域分布，基于二维浅水方程建立了水膜厚度面域分布数值模型，开发了基于格心型有限体积法和HLL(Harten, Lax and van Leer)格式近似Riemann解的数值求解算法；在此基础上，引入水膜厚度的实测数据，通过构造伴随方程，采用梯度下降法获取了实际降雨条件下的最优曼宁系数，从而动态修正了二维浅水方程的计算结果，精准预估了跑道水膜厚度面域分布；采用北京首都国际机场安全预警平台的水膜厚度实测数据和车载式LiDAR系统获取的路面高程数据，计算分析了曼宁系数更新间隔和高程空间采样间隔对模型求解效率和精度的影响，并采用实测数据验证了算法的准确性。研究结果表明：为满足水膜厚度实时监测需求，在综合考虑计算耗时与求解精度的条件下，曼宁系数的最优更新间隔为30~300 s，对于表面平整的道面，高程的最优空间采样间隔为0.1~0.5 m，对于存在车辙等病害的道面，高程的最优空间采样间隔为0.10~0.25 m；在真实降雨条件下，水膜厚度计算值与实测值的平均误差为0.13 mm，最大误差为0.76 mm，满足机场对水膜厚度的监测需求。由此可见，建立的跑道水膜厚度面域分布预估方法能够准确计算出给定高程道面的水膜厚度分布及其时间演化，可为湿滑跑道的抗滑性能评价与风险预警提供可靠的数据支撑。Abstract: To accurately predict the area distributions of water film thickness on the runway under different runway and rainfall conditions, a numerical model of area distribution of water film thickness was built according to the two-dimensional shallow water equations. A numerical algorithm was developed on the basis of the lattice finite volume method and the approximate Riemann solution in Harten, Lax and van Leer (HLL) format. On this basis, the measured data of the water film thickness were incorporated, and the optimal Manning coefficient under the actual rainfall conditions was obtained by the construction of the adjoint equation and the use of the gradient descent method. In this way, results of the two-dimensional shallow water equations were dynamically modified, and the area distribution of water film thickness on the runway was accurately estimated. The influences of the update interval of Manning coefficient and the spatial sampling interval of elevation on the calculation efficiency and accuracy of the model were analyzed by calculation. In the calculation, the measured data of the water film thickness from the security early-warning platform of the Beijing Capital International Airport and the pavement elevation data collected by a vehicle-mounted LiDAR system were employed. The accuracy of the algorithm was verified by the measured data. Research results show that under the real time monitoring requirements of water film thickness and the comprehensive consideration of time consumption and calculation accuracy, the optimal update interval of Manning coefficient is 30-300 s. The optimal spatial sampling interval of elevation is 0.1-0.5 m for the runway with an even surface and 0.10-0.25 m for the runway with diseases such as ruts. Under the actual rainfall conditions, the average error between the calculated water film thickness and the measured value is 0.13 mm, and the maximum error is 0.76 mm. This can meet the monitoring requirement of the airport for the water film thickness. It can be seen that the proposed estimation method for the area distribution of water film thickness on the runway can accurately obtain the distribution and time evolution of water film thickness on a runway with a given elevation. By this method, reliable data support can be provided for the skid resistance evaluation and risk early-warning for wet runways.
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图 2 不同更新间隔下水膜厚度的计算值与实测值对比
Figure 2. Comparison of water film thicknesses between calculated and measured values under different update intervals
图 3 不同更新间隔下的时间占用率与误差
Figure 3. Time occupancies and calculation errors under different update intervals
图 4 不同高程空间采样间隔下正常路面的水膜厚度分布
Figure 4. Water film thickness distributions of normal pavement under different elevation spatial sample intervals
图 5 不同高程空间采样间隔下车辙路面的水膜厚度分布
Figure 5. Water film thickness distributions of rutting pavement under different elevation spatial sample intervals
图 6 不同空间采样间隔下纵断面x=5 m处水膜厚度对比
Figure 6. Comparison of water film thicknesses at vertical section of x=5 m under different spatial sample intervals
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