Abstract: This paper proposes a method to improve the accuracy of an electromagnetic force equilibrium sensor by combining a BP network with a sensor, utilizing the strong nonlinear mapping capability of the BP network. Keywords: Electromagnetic force equilibrium sensor, accuracy, BP network 1 Introduction A sensor is a device that converts non-electrical input information into electrical signal output, playing a crucial role in process detection and control. Accuracy is an evaluation index reflecting the combined influence of sensor system errors and random errors, indicating how close the measurement result is to its theoretical value, directly affecting the performance of the entire control and detection application system. Accuracy can usually be improved and nonlinear errors minimized by using the theoretical straight line method, endpoint line method, optimal straight line method, least squares method, or hardware compensation. However, these methods have limited capabilities, and they are ineffective when the accuracy decreases due to changes in the surrounding environment or variations in the sensor's own parameters. This paper proposes combining the BP algorithm from neural networks with the sensor, which can greatly improve the accuracy of the sensor's output signal. Simulation results show that the BP algorithm has unique advantages in suppressing sensor temperature drift and time drift. 2 Working Principle of Electromagnetic Force Balance Sensor Electromagnetic force balance sensors are mainly used in electronic balances. An important feature of electronic balances is that when measuring the mass of the object being measured, the weight of the weight is not measured; instead, the electromagnetic force is used to balance the weight of the object. The weighing pan is connected to the coil via a support rod. Within the weighing range, when the weight mg of the object being measured acts on the coil through the support rod in the upward direction, if a current flows through the magnetic field, the coil will generate an electromagnetic force F, which can be expressed by the following formula: F = KBLI where K is a constant (related to the unit of measurement), B is the magnetic induction intensity, L is the length of the coil wire, and I is the current intensity through the coil wire. The electromagnetic force F and the weight mg of the object being measured on the weighing pan are equal in magnitude and opposite in direction, thus achieving balance. Simultaneously, the elastic spring causes the weighing pan support to return to its original position. That is, F = KBLI = mg. From the above equation, it can be seen that the current I flowing through the energized coil in the magnetic field is proportional to the mass of the object being measured. Measuring the current I allows us to determine the mass m of the object. To further improve the accuracy of any balance control system, a closed-loop control system is needed, as shown in Figure 1. If the weight of the object being weighed is increased, the balance will become unbalanced. A photodetector detects the transient displacement of the coil in the magnet. This displacement is then processed by a preamplifier and a PID controller to generate a change output. This change is compared with a fixed sawtooth wave, widening the pulse width modulation (PWM). This PWM then controls the current switch, reducing the current. Since the constant current source remains constant, the current flowing through the coil increases, thus increasing the electromagnetic force and canceling it out, achieving a new balance. However, during use, the electronic balance is affected by temperature, changes in sensor parameters over time, and environmental factors such as airflow, vibration, and electromagnetic interference, all of which cause drift and measurement errors. The influence of ambient temperature, airflow, vibration, and electromagnetic interference can be minimized by restricting the operating conditions of the electronic balance. Temperature drift, however, mainly stems from the influence of ambient temperature and the balance's internal mechanisms; its causes are complex, and the resulting drift is significant, requiring suppression. 3. Neural Networks for Sensor Nonlinear Correction A temperature-affected sensor system can be represented as: y = f(x,t). Here, y represents the sensor output, x represents the sensor input, and t represents the ambient temperature. Due to the nonlinear errors generated by the sensor and temperature errors, f(x,t) exhibits nonlinearity. Neural networks offer a novel approach to eliminating and compensating for the nonlinear characteristics of sensor systems, as shown in Figure 2: [align=center] Figure 2 Sensor Nonlinear Error Correction[/align] 3.1 BP Network Model The BP network is a hierarchical feedforward neural network based on the principle of stochastic approximation, typically consisting of three layers: an input layer, intermediate layers (hidden layers), and an output layer. A multi-layer feedforward neural network with n-dimensional input and m-dimensional output using the BP algorithm performs a continuous mapping from n-dimensional Euclidean space to a finite field in m-dimensional Euclidean space; this mapping is highly nonlinear. Since signal processing capabilities originate from the multiple composites of simple nonlinear functions, the network possesses extremely strong function reproduction capabilities. White H has proven that a three-layer BP network can solve any nonlinear mathematical problem. The BP algorithm consists of forward propagation of information and backward propagation of error. The input pattern is processed layer by layer from the input layer through hidden units and propagated to the output layer. The state of each neuron only affects the state of the next neuron. If the desired output value is not obtained at the output layer, the error signal is returned along the original connection path, modifying the weights of each neuron to minimize the error and achieve the desired goal. The learning rule of the BP network is to use gradient descent, where the weights change along the negative gradient of the error function, gradually reducing the root mean square error and approximating the nonlinear function. 3.2 Algorithm Implementation In this system, the number of neurons in the input layer, intermediate layer, and output layer are 2, 5, and 1, respectively. The input variables are the target parameter—the mass value to be corrected—and the non-target parameter—temperature, respectively. The output variable is the corrected mass value. The network structure is shown in Figure 3. [align=center] Figure 3 BP Network Structure Diagram[/align] The activation functions for the intermediate and output layers of the BP network are logsig and purelin, respectively, with a recognition accuracy of 1e-5. This experiment involved 485,221 training iterations (on a PIII computer, approximately 8 hours). After training, the network's learning rate was 0.7943. The relative errors (full-scale relative errors) of each sampling point before and after training are shown in Figure 4: [align=center] Figure 4 Comparison of absolute errors of each mass sampling point at different temperatures[/align] It is clear from the figure that after adopting the BP algorithm, the system has a strong ability to suppress the influence of temperature. Connecting the learned neural network in series with the original sensor system can form a sensor system with temperature correction function. 4 Conclusion Utilizing the nonlinear mapping relationship of neural networks, function approximation of arbitrary data can be achieved. This paper uses a BP network to implement data fitting for an electromagnetic force balance sensor. Simulation results show that this method is feasible and effective, and the fitting accuracy is significantly better than commonly used methods. However, the inherent defects of the BP algorithm, such as slow convergence speed and susceptibility to local minima, should be fully considered during programming. References: 1. Wang Xu. Principles and Applications of Artificial Neural Networks [M], Shenyang: Northeastern University Press, 2000, 51-68. 2. Si Duanfeng. Research on a New Algorithm for Sensor Characteristic Compensation Based on BP Neural Network [J], Sensor Technology, 2000, 9: 11-14. 3. Teng Zhaosheng. Temperature Influence and Compensation of Electromagnetic Force Balance Sensors [J], Sensor Technology, 1998, 17(2): 28-30.