基于磁场梯度张量的拉索断丝监测方法

针对目前兴起的拉索损伤磁记忆检测方法易受环境干扰磁场影响的问题，该研究基于磁场梯度张量和磁荷面积分理论研究温室拉索断丝监测方法，推导拉索钢丝的磁场梯度计算公式，提出拉索断丝位置和断丝数量的判定方法，并采用磁场试验进行对比验证。为了验证试验的可重复性，对于每一种测试工况均设定了2组试验。理论计算表明，3个方向的磁感应强度沿拉索长度方向的磁场梯度（Bxz,Byz和Bzz）曲线均在断丝位置（500 mm）出现突变，一束拉索中断丝2根与断丝1根时3个磁场梯度曲线突变处包围的面积的比值的平均值约为2。磁场试验结果表明，断丝位置为496 mm，与实际断丝位置（500mm）的误差为0.8%，通过2次测量，一束拉索中断丝2根与断丝1根时3个磁场梯度曲线突变处包围的面积的比值的平均值约为2。2次测量结果的差别极小，验证了试验的可重复性和可靠性。实际工程中，取3个磁场梯度判断的断丝数量的平均值，可以有效减小三轴磁传感器探头位置带来的误差。该研究为拉索断丝监测提供了理论依据，且有效排除了环境磁场干扰。

Cable wire breakage monitoring method using magnetic gradient tensor

Abstract: A safety risk has often posed a great threat to large-span greenhouse structures with the cables in extreme weather, such as snow and wind. It is very necessary to detect the broken wires in the cables of large-span greenhouse structures. However, the environmental magnetic field can dominate the magnetic memory detection for cable damage. In this study, an effective detection was presented for the broken wires using magnetic gradient tensor and magnetic charge surface integral theory, in order to remove the influence of the environmental magnetic field. The magnetic gradient tensor was then combined with the magnetic charge surface integral to derive the calculation formula for the magnetic gradient of cable wires. The characteristic information of cable wires was given before and after the wires broke. The judgment was also proposed for the wire breakage position and number of broken wires. The magnetic test was carried out to verify the evaluation. Theoretical calculation results show that there was a sudden change in the magnetic gradient curve at the wire breakage position when a broken wire occurred in a cable. As such, the baseline was established for the position of wire breakage using the bottom of the trough and the inflection point between the peak and trough of the magnetic gradient curve. Once there were two broken wires in a cable, the areas enclosed by the abrupt changes of magnetic gradient curves were 2.07, 2.89, and 2.13 times those in one broken wire, with an average value of 2.37 with integer of 2, according to theoretical calculation. There was no effect of the cable length on the amplitude of mutation in the magnetic gradient curve. The average values of the environmental magnetic gradient''s absolute values account for 0.17%, 0.92% and 0.21% of the total magnetic gradient respectively. The influence of the environmental magnetic gradient can be ignored and it can be considered that the measured total magnetic gradient is equal to the cable''s own magnetic gradient. The experimental results show that the theoretical and actual wire breakage positions were 496, and 500 mm, respectively, with an error of 0.8%, in terms of the average value of abrupt changes in the magnetic gradient curves. There was a great increase in the areas and peaks/troughs depths that were surrounded by the abrupt changes of magnetic gradient curves, as the number of broken wires increased, according to the superposition effect. In order to verify the repeatability of the experiment, measurement was conducted twice for each wire-breaking condition. As for the first test results, the areas surrounded by the abrupt changes of magnetic gradient curves in the two broken wires were 1.47, 1.78, and 1.34 times those in the one broken, with an average value of 1.53 with integer of 2. As for the second test results, the area ratios were 1.48, 1.84, and 1.31, with an average value of 1.54 with integer of 2. The very small deviation between the results of the two measurements verified the repeatability and reliability of the monitoring. Anyway, the number of broken wires should be judged by three magnetic gradients in the practical engineering application. This finding can provide a theoretical basis for cable wire breakage monitoring, and effectively eliminate the interference of the environmental magnetic field.