Department of Energy, Systems, Territory and Construction Engineering (DESTEC), University of Pisa, 56122 Pisa, Italy.
Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy.
Sensors (Basel). 2023 Apr 8;23(8):3832. doi: 10.3390/s23083832.
Direct measurement of electric currents can be prevented by poor accessibility or prohibitive technical conditions. In such cases, magnetic sensors can be used to measure the field in regions adjacent to the sources, and the measured data then can be used to estimate source currents. Unfortunately, this is classified as an Electromagnetic Inverse Problem (EIP), and data from sensors must be cautiously treated to obtain meaningful current measurements. The usual approach requires using suited regularization schemes. On the other hand, behavioral approaches are recently spreading for this class of problems. The reconstructed model is not obliged to follow the physics equations, and this implies approximations which must be accurately controlled, especially if aiming to reconstruct an inverse model from examples. In this paper, a systematic study of the role of different learning parameters (or rules) on the (re-)construction of an EIP model is proposed, in comparison with more assessed regularization techniques. Attention is particularly devoted to linear EIPs, and in this class, a benchmark problem is used to illustrate in practice the results. It is shown that, by applying classical regularization methods and analogous correcting actions in behavioral models, similar results can be obtained. Both classical methodologies and neural approaches are described and compared in the paper.
电流的直接测量可能会因为难以接近或技术条件苛刻而受到阻碍。在这种情况下，可以使用磁传感器测量源附近区域的磁场，然后可以使用测量数据来估计源电流。不幸的是，这被归类为电磁逆问题（EIP），并且必须谨慎处理传感器的数据以获得有意义的电流测量值。通常的方法需要使用合适的正则化方案。另一方面，行为方法最近在这类问题中得到了广泛应用。重建的模型不必遵循物理方程，这意味着必须准确控制近似值，特别是如果旨在从示例中重建逆模型。在本文中，提出了一种系统的研究方法，用于比较不同学习参数（或规则）在 EIP 模型的（重新）构建中的作用，与更评估的正则化技术相比。特别关注线性 EIP，并在此类中，使用基准问题来实际说明结果。结果表明，通过应用经典正则化方法和行为模型中的类似校正操作，可以获得类似的结果。本文中描述并比较了经典方法和神经方法。
