Individual information

While additional sensors improve the accuracy of estimated physical quantities, they also increase costs and are often subject to industrial and technical constraints. Optimizing sensor placement is therefore a critical challenge in electromagnetic applications, particularly for electrical machines, where accurate condition monitoring and fault diagnostics are essential to ensuring reliability and preventing failures. This paper investigates sensor placement within the framework of the Parameterized Background Data-Weak (PBDW) method, explicitly incorporating positional constraints. The method is examined in both constrained and unconstrained settings and systematically compared with two alternatives: the Discrete Empirical Interpolation Method (DEIM) and the Maximal Volume (Maxvol) algorithm. Numerical results indicate that PBDW achieves stable performance across diverse scenarios and offers clear advantages for complex sensor placement problems, particularly those arising in practical electromagnetic applications.

The need for electrical machines is growing in a wide range of applications nowadays, such as for energy production, automotive, marine, and medical equipment, etc. The reliability, efficiency, performance and operational safety are always critical issues, which implies that the monitoring and analysis during the operation of the equipment need to be strengthened. In general, more sensors can give higher accuracy of the estimated physical quantity, but bring a more expensive cost. To address this issue, an algorithm principally based on the parameterized background data-weak (PBDW) method is proposed and adopted in this work to optimize both the number and the location of sensors. Besides, to further investigate the performance of the proposed algorithm, a prototype concerning an anisotropic magnetostatic problem is studied as an example for the placement of magnetic sensors. The numerical experiments shows that the proposed method can achieve very satisfactory results in different aspects.