基于磁偶极子的磁场梯度张量缩并的试验验证及相关参数确定

Experimental verification and related parameter's determination for magnetic gradient tensor contraction using magnetic dipole

近十年发展起来的基于磁偶极子的磁场梯度张量缩并理论虽然可较好地描述磁源,不受测量系统的朝向的影响,但其理论尚不够完善,磁场梯度张量的模量的空间分布规律及相关参数的取值尚不明确。为解决此问题,对基于磁偶极子的磁场梯度张量的模量及参数k的三维空间分布特性进行理论分析,结果表明其空间分布均为椭球状。对参数k与角度θ的关系提出显式的近似计算公式,假设检验表明,提出的拟合公式与理论值高度吻合。采用基于电流脉冲的步进电机角度控制系统和三维磁传感器设计试验系统,对磁场梯度张量的模量的空间分布特性和参数k的拟合公式进行验证,试验结果表明,理论值与试验值基本一致,可为磁场梯度张量缩并理论的应用提供依据和参考。

The magnetic gradient tensor contraction theory, developed during the past 10 years, can effectively describe a magnetic source without being influenced by the orientation of magnetic measuring instrument. However, this theory is imperfect for the spatial distribution of magnetic gradient tensor's modulus and the related parameter values are unclear. In order to solve this problem, three-dimensional distribution of magnetic gradient tensor's modulus and the related parameter k is analyzed, and it is shown that the spatial distribution is ellipsoid geometrically. An explicit and approximate formula is put forward for the relation between the parameter k and angle θ, and the result of K-S hypothesis-test shows that the values from the fitted formula are in accordance with the theoretical values. An experimental system is designed by using four three-axis magnetic sensors and an angle control system of current-pulsed stepper motor to verify the spatial distribution of magnetic gradient tensor's modulus and the parameter k. Experiment results show that the experiment values are in accordance with the theoretical values. These can provide reference for the application of the magnetic gradient tensor contraction theory.