Abstract: In this paper, the problem of sensor array around ferromagnetic equipment is studied. The mathematical model about optimization of positions and number of sensor is established, and the model is solved by genetic algorithm. First of all, we choose the rotational ellipsoid with less requirements for the number and distance of sensors as the model of far-field calculation of magnetic field. In the rotational ellipsoid model, improper sensor distribution will cause the condition number of the magnetic field calculation coefficient matrix to be too large, and the model will be ill-conditioned. So the calculated far-field magnetic results are not reliable. Therefore, in this paper, we take the condition number of coefficient matrix in the rotating ellipsoid model as the optimization objective, and then establish a mathematical model to optimize the number and position distribution of sensors above a single device. Secondly, we verifie through experiments that the model is effective for optimizing the position and number of sensors in a single piece of equipment. The number of sensors used is small, and results of the model are reliable. Finally, we generalize the optimization model to multiple pieces of equipment. Taking two pieces of equipment as the representative, the sensor positions are calculated by two methods of simultaneous optimization and separate optimization. According to the experiment and calculation, the two methods have high accuracy of far-field magnetic field calculation, but the method of separate optimization is more simple and easy to operate in the actual calculation.

Key words: ferromagnetic equipment, sensor array, rotational ellipsoid, optimization model

摘要： 本文研究了铁磁性设备周围空间传感器布阵的问题。我们建立了关于传感器位置和数量优化的数学模型,并通过遗传算法对模型进行求解。首先,本文选用对传感器数量和距离要求较少的旋转椭球体作为磁场远场换算的模型。在旋转椭球体模型中,传感器分布位置不当会导致磁场计算系数矩阵的条件数过大,模型将出现病态,因而计算得到的远场磁场结果不可靠。所以,本文以旋转椭球体模型中的系数矩阵条件数为优化目标,建立数学模型优化单个设备上方传感器的数量与位置分布,并利用遗传算法对模型求解。其次,通过实验验证了本模型对于单个设备的传感器位置和数量优化是有效的,且所用传感器数量少,计算结果可靠。最后,将单个设备传感器位置和数量的优化模型推广到多个设备,以两个设备为代表用同时优化和分别优化两种方法计算传感器位置,根据实验计算这两种方法都具有较高的远场磁场计算精度,但分开优化的方法在实际计算更加简便、容易操作。

关键词: 铁磁性设备, 传感器布阵, 旋转椭球体, 优化模型