## 2 Theoretical Investigation of Monitoring Models
### Analysis of the Main Component Characteristics and System Performance of the Sensor Structure  
#### 2.4.1 Hall Effect Sensor  
The Hall probe is a semiconductor magnetoelectric device based on the Hall effect used to detect variations in the magnetic field. The Hall effect refers to the phenomenon where, under the influence of a magnetic field, current flowing through a conductor of a certain width and thickness causes electrons to move along the conductor. The magnetic field exerts the Lorentz force on the electrons, making them deflect transversely in the conductor. The deflection of the electrons leads to their accumulation, with charge buildup on both sides of the conductor, which generates a potential difference known as the Hall voltage. The Hall probe detects the strength and direction of the magnetic field by measuring this Hall voltage [30].  
There are various types of magnetic field sensors available, such as AMR, GMR, TMR, fluxgate, and micro-search-coil magnetometers. Magnetoresistive (MR) sensors exhibit superior performance compared with Hall effect devices, featuring compact dimensions, nT-level sensitivity, and enhanced magnetic stability. Nevertheless, anisotropic magnetoresistance (AMR) sensors demonstrate limited operational bandwidth and intrinsic Barkhausen noise interference. Giant magnetoresistance (GMR) devices face constraints, including reduced resolution/linearity, bulkier form factors, intricate manufacturing procedures, and interlayer coupling effects that restrict practical implementations. Tunnel magnetoresistance (TMR) sensors achieve exceptional magnetic sensitivity, broad dynamic range, micron-scale resolution, and low-power compact designs; however, their complex material and fabrication processes result in prohibitive costs, rendering them impractical for large-scale deployment and sustained monitoring in civil infrastructure applications [30].  
While fluxgate magnetometers and search-coil sensors achieve high-precision measurements in dedicated frequency bands for geomagnetic and navigational applications, their inherent limitations render them impractical for sustained structural health monitoring in civil infrastructure. Search-coil sensors demonstrate heightened sensitivity to dynamic magnetic fields (dB/dt) but negligible response to static fields due to the absence of the time-varying flux required for induced electromotive force (EMF) generation [31].  
Additionally, the simplified signal processing requirements of Hall effect sensors--characterized by linear outputs and minimal conditioning circuitry--provide critical advantages for field instrumentation's integration and operational sustainability. In contrast, alternative sensor technologies often necessitate auxiliary electronics, escalating the system intricacy and lifecycle expenses.  
In summary, Hall effect sensors offer optimal suitability for infrastructure monitoring applications through five key attributes: (1) cost-effectiveness, facilitating scalable deployment; (2) ultralow-power operation, enabling years-long autonomy; (3) dual-mode static/dynamic field detection versatility; (4) harsh-environment durability; and (5) Simplified integration through native digital interfacing capabilities. Although alternative technologies may surpass Hall sensors in niche high-precision or specialized spectral applications, the latter's cost-benefit ratio and operational pragmatism establish clear superiority for mainstream structural monitoring implementations.