## 2 Theoretical Investigation of Monitoring Models
### Analysis of the Main Component Characteristics and System Performance of the Sensor Structure
#### 2.4.4 The Impact of Current-Carrying Wires on System Performance  
[PERSON]'s circuital law establishes that current-carrying conductors generate concentric magnetic flux loops, which can perturb both the static field distribution of permanent magnets and the operational accuracy of Hall effect sensors through magnetic superposition effects. The static magnetic field generated by permanent magnets through domain alignment undergoes vector superposition when it is proximate to the current-induced dynamic fields. This interaction modifies the spatial flux density gradient, which is particularly critical in sensor fusion applications. In particular, if the direction of the current in the wire is opposite to the direction of the magnetic field of the permanent magnet, it may cause some cancellation or amplification, depending on the relative orientation. The NdFeB permanent magnets employed here had a coercivity of H\(\epsilon\approx\) 836 kA/m. Even with a current of I = 1000 A passing through the wire, the magnetic field strength generated at r = 1 cm would be H = 1/2\(\pi\)r \(\approx\) 16 kA/m, which is far below Hc. Therefore, the risk of demagnetization under typical currents is extremely low, and it does not have a significant impact on the magnetic field strength of the permanent magnet. If the Hall sensor's accessories have current-carrying wires, the magnetic field generated by the current will superimpose onto the target magnetic field, leading to measurement deviations. The level of interference depends on factors such as current magnitude, distance, and direction. The following methods can be used to reduce this interference: (1) Physical isolation, increasing the distance between the wire and the sensor. (2) Magnetic shielding, using high-permeability materials to wrap the wire, which can attenuate the interference magnetic field. (3) Orthogonal layout, adjusting the sensor's sensitive axis to be perpendicular to the direction of the interfering magnetic field, effectively minimizing the impact of the unwanted magnetic field. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Operating** & **Tensile** & **Compressive** & **Flexural** & **Flexural** & **Fluidity** \\
**Temperature Range** & **Strength** & **Strength** & **Strength** & **(MPa)** & **(mm)** \\ (\({}^{\circ}\)**C**) & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(mm)** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Key performance parameters of epoxy resin. 2.4.5. The Influence of the Environment on System Performance  
Hall elements are able to work stably over a wide temperature range and are resistant to humidity and corrosion. However, strong electromagnetic interference may lead to inaccurate outputs or an increase in signal noise in a Hall sensor. The NdFeB permanent magnets in the sensor have excellent magnetic stability at room temperature, with a maximum magnetic energy product of 287 kJ/m\({}^{3}\), and their magnetization strength is largely unaffected by external electromagnetic influences. As a result, this type of magnet is widely applied in devices that require long-term magnetic field stability, such as hard disk drives, MRI machines, and more. However, there are some drawbacks, including poor corrosion and oxidation resistance, requiring protective measures for long-term use. Moreover, NdFeB permanent magnets have a low operating temperature, with a maximum working temperature of only 80 \({}^{\circ}\)C, so they are unsuitable for high temperatures and possess poor thermal stability. While there are high-temperature grades of neodymium-iron-boron permanent magnets available, they come at a high production cost. Given that both permanent magnets and Hall elements are brittle materials, they are susceptible to damage if not properly protected during use. Furthermore, in anchor cable applications, grouting of tendon body holes or deformation of the surrounding geotechnical material can impact the sensors installed within the tendon. Hence, protective designs for the sensor structure are essential.