Optimal sensor placement for electromagnetic problems: A PBDW-based approach with position constraints

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.