Toroidal massive ferromagnetic cores are used in a wide range of electromagnetic applications, such as current sensors, inductances, static converters and filters. Growing interest exists in the industrial field with regards simulation tools to reduce experimental campaigns and improve product knowledge and performance. Accurate simulation results require a consideration of precise electromagnetic laws, such as the exact non-linear magnetic behavior of toroidal magnetic cores. Under the influence of an external surface magnetic field that was created by a surrounding coil, the local magnetic state through a ferromagnetic core cross-section was ruled by a combination of magnetic domain kinetics and external magnetic field diffusion. Conventional methods to simulate magnetic behavior are based on a separation of magnetic contributions, where microscopic Eddy currents from domain wall motions and macroscopic currents from external magnetic field variations are considered separately. This separation is artificial, because both loss mechanisms occur simultaneously and interact. In this study, an alternative solution was proposed through the resolution of a two-dimensional anomalous fractional magnetic field diffusion. The fractional order constitutes an additional degree of freedom in the simulation scheme, which can be identified by comparison with the experimental results. By adjusting this order, accurate local and global simulation results can be obtained on a broad frequency bandwidth and allow for the precise prediction of the dynamic magnetic behavior of a toroidal massive magnetic core.

An alternative sensing solution is described to measure local magnetic hysteresis cycles through a laminated magnetic core. Due to the reduced space gap separating two successive laminations, it is impossible to interpose the usual oversize magnetic sensors (wound coil, Halleffect sensor). In this study, the space issue has been solved by printing the needle probe method for the magnetic state monitoring and by using a micrometric Giant Magneto Resistance (GMR) for the magnetic excitation measurement. An instrumented magnetic lamination including the non-invasive monitoring solution has been built and moved successively to every lamination position of the whole laminated ferromagnetic core. A precise cartography of the hysteresis losses has been reconstructed from all these local measurements and the average values compared to the classic measurement methods obtained with a wound coil. The relative agreement between the experimental results observed opened doors to large improvement in the estimation of magnetic losses and in the design of magnetic circuits.

Wireless Sensor Network (WSN) applications that favor more local computations and less communication can contribute to solving the problem of high power consumption and performance issues plaguing most centralized WSN applications. In this study, we present a fully distributed solution, where leaks are detected in a water distribution network via only local collaborations between a sensor node and its close neighbors, without the need for long-distance transmissions via several hops to a centralized fusion center. A complete approach that includes the design, simulation, and physical measurements, showing how distributed computing implemented via a distributed Kalman filter improves the accuracy of leak detection and the power consumption is presented. The results from the physical implementation show that distributed data fusion increases the accuracy of leak detection while preserving WSN lifetime.

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This paper reviews the use of the fractional derivative operators for the dynamic magnetization of ferromagnetic specimens. Magnetic behaviors in ferromagnetic specimens are strongly nonlinear and frequency dependent. Magnetism has an atomic origin but the magnetic behavior as observed at the human scale is highly affected by phenomena occurring at larger scales. Under the influence of an external magnetic field, the homogeneity of a ferromagnetic sample magnetization is linked to the excitation dynamics. Models and simulations in this domain are strongly needed, as they provide theoretical explanations and allow us to anticipate complex phenomena, difficult to observe in a practical way. On the one hand, such multi-scale dynamical behaviors can hardly be taken into account with the usual mathematical operators. On the other hand, correct simulation results on large frequency bandwidths can be obtained using fractional derivative operators. The use of fractional derivatives can be envisaged through different approaches: Lump models based on time fractional differential equations is one option, and fractional anomalous diffusion equations is another. In this manuscript, these two methods are detailed and compared. Theoretical results are compared to experimental ones, and conclusions and perspectives are drawn such as possible improvements.