# A Low-Cost IoT-Based Bidirectional Torque Measurement System with Strain Gauge Technology
## 2 Related Work
The experimental results demonstrated that, after calibration and neural network-based compensation, the system achieved a measurement accuracy of 0.1% of full scale, highlighting the effectiveness of advanced hybrid calibration and compensation methods in demanding industrial applications. [PERSON] et al. demonstrated that wireless strain gauge systems can reliably monitor pavement deformation under hydraulic loading, achieving measurement accuracy comparable to traditional wired sensors [18]. These systems offer the added benefits of simplified installation and robust data transmission, even when exposed to temperature fluctuations and dynamic loading scenarios. The findings highlight the practical viability of wireless strain gauge technology for large-scale infrastructure monitoring, supporting the transition toward more efficient and scalable sensing networks in civil engineering applications. In the field of robotic actuation, integrated torque sensors have been used to investigate intrinsic friction and torque ripple, particularly in applications requiring bidirectional torque measurement [19]. After the implementation of compensation strategies, the root mean square error of the torque measured by the joint sensor was reduced to 11% relative to an external reference, demonstrating the effectiveness of calibration and compensation protocols [19]. This work underscores the necessity of bidirectional calibration for robotic and automotive systems that experience frequent load reversals and dynamic operational conditions. Advancements in sensor calibration have led to the development of universal, on-site calibration models for six-axis force-torque (FT) sensors, enabling compensation for environmental and installation effects using only the sensor's own data. Experimental results show that these models can address parameters such as center of mass, crosstalk, and inclination, thereby improving measurement reliability in field deployments without the need for laboratory recalibration [20]. Such approaches facilitate broader and more flexible application of FT sensors in diverse and unpredictable environments. Other researchers have explored alternative approaches to torque measurement and calibration. [PERSON] et al. [21] proposed a virtual torque sensing approach for wind turbine gearboxes using fiber-optic strain sensors mounted on ring gears. Their method leveraged operational deflection shape analysis to isolate torque-related deformations, achieving an average normalized root mean square error of 0.7%. This technique provided a robust, cost-effective alternative to traditional shaft-mounted sensors, suitable for dynamic, harsh operational environments. [PERSON] et al. [22] proposed a practical calibration method for mechanical torque measurement on wind turbine drive trains using electrical power measurements instead of direct mechanical calibration, thereby reducing calibration costs while maintaining traceability to international standards. Uncertainty analysis and robust calibration protocols are also critical. [PERSON] et al. [23] conducted a comprehensive uncertainty analysis of a 5 MN-m torque transducer using Monte Carlo simulations and fuzzy set theory, revealing a relative expanded uncertainty below 0.06% in the upper torque range. [PERSON] et al. [24] developed a strain-gauge-based telemetry system for real-time torque monitoring on rolling mill spindles, achieving a measurement error of 0.2% after calibration and demonstrating significant benefits in reducing downtime and extending equipment lifespan. The use of advanced signal processing and sensor fusion techniques for fault detection and quantitative diagnosis in rotating machinery is also gaining traction. [PERSON] and [PERSON] [25] proposed a method for diagnosing shaft misalignment based on speed signal analysis and neural network modeling, demonstrating the growing role of data-driven approaches in enhancing the reliability and diagnostic capabilities of sensor systems.