## 4 The Proposed Magnetic Characterization Method  
Taking into account the aforementioned pros and cons of the already existing magnetic characterization techniques, the simple and differential arrangements of the fluxgate magnetometer are the most advantageous for a portable and low-cost catalyst characterization system. For this reason, the authors propose the following simple, economical, and novel magnetic measurement setup based on dual fluxgate magnetometers, as Figure 5 depicts. A catalyst deactivation, the nanoparticle event this method is mainly developed to sense, reduces the production and results in extra cost in the industrial processes, so it is vital to have proper techniques to detect the aforementioned important information concerning catalytic materials. The proposed method of the dual arrangement aims to detect with accuracy the magnetization of the sample, as well as its position, albeit with different implementations. The experimental setup is depicted in Figure 9, where the two magnetometers and the sample in STP conditions (1 atm pressure, 20 \({}^{\circ}\)C, and 0% humidity) can be seen. It should be noted that all magnetometers were calibrated before their use in a Bartington open-ended triple-layer magnetic shield (Figure 9). Magnetic field offset is then identified and subtracted from the measured data to form the actual data fed to the inverse algorithm. The sample under study is a cobalt-based material, embedded in carbon, with a hexagonal close pack (hcp) crystal structure, weight of 0.076 gr, content of cobalt 20% wt., and saturation  
Figure 8: Schematic diagram of the proposed setup consists of two fluxgate magnetometers, two compensation coils, and three drive coils [127]. magnetization 150 emu/g. Magnetometer 1 is placed at x = 0.05 m, y = 0.05 m, and z = 0.015 m, while magnetometer 2 is positioned at x = 0.1 m, y = \(-\)0.05 m, and z = 0.015 m, in the system's coordinate system. The positions the sample can be placed at are discretized in a grid of cells 2 cm long along the x-axis, starting at 0 cm as depicted in Figure 9. The sample is placed at the fourth cell of the constructed grid, which extends from 0.06 to 0.08 m.  
Two experiments are conducted. First, the magnetization of the sample is calculated via the magnetic field measurements, considering the sample placement (cell '4') known. Next, the magnetization and the position of the sample are both calculated from the measurements of the magnetometers. Concerning the first experiment, the magnetization of the sample, under the effect of the earth's magnetic field, is calculated. For this reason, two sets of measurements (Figure 9a) are conducted sequentially and in very fast succession: one with the sample present and a second without the sample present. The values of the magnetic field in the three axes for the two measurement sets are illustrated in Figures 10 and 11, respectively. The values derived from magnetometer 1 are depicted in blue and the values derived from magnetometer 2 in red. The magnetic field of the sample is calculated by subtracting the values of the fields depicted in Figure 11 (sample absent) from the values of the field depicted in Figure 10 (sample present) for each of the axes for both the magnetometers. This way the background field (sample absent) is minimally varied between the two measurements; it can be considered static in amplitude so the subtraction yields the magnetic field values due to the sample. Then, the differential evolution (DE) algorithm is applied to the sample magnetic field for the magnetization of the sample to be calculated, employing the values of both magnetometers.