# Weigh-in-Motion Method Based on Modular Sensor System and Axle Recognition with Neural Networks
## 1 Introduction  
Overloading is a key issue and difficult point in the management of highway freight vehicles, while the traditional truck scale requires vehicles to wait in line, stop, and weigh, which often leads to congestion at the toll stations [1, 2]. With the increasing demand for highway freight transportation in China, weigh-in-motion (WIM) technology, which enables accurate weight measurement while vehicles are in motion, is becoming increasingly important and has been developed rapidly. This technology holds notable research significance and engineering application value. The goal of WIM systems is to obtain the number of axles and gross vehicle weight after the vehicle travels through WIM sensors at a constant speed. The advantage lies in the high traffic efficiency, whereas the challenge is to ensure weighing accuracy [3, 4]. Currently, WIM systems are primarily divided into axle-load measurement and whole-vehicle-load measurement. Axle-load measurement weighs the individual axle loads to obtain the gross vehicle weight [5]. The accuracy is generally improved by changing the sensor type [6], optimizing the sensor layout [7], and improving the weighing algorithm [8]. For example, in 2011, [PERSON] et al. proposed a WIM system based on a multi-sensor and Radial Basis Function (RBF) neural network. The proposed system shortened the testing time andimproved the accuracy [9]. When a vehicle is in motion, the axle loads change constantly as the center of mass moves. Therefore, the method of calculating the gross vehicle weight by weighing the axle loads at different times has defects in the weighing principle, which limits the improvement in the weighing accuracy of axle-load measurement and leads to untraceable weighing results. Compared with axle-load measurement, whole-vehicle-load measurement has a significant improvement in weighing accuracy. For example, in 2017, [PERSON] et al. [10] proposed a whole-vehicle-load measurement algorithm based on a Back Propagation (BP) neural network. This algorithm corrected the weighing signal by combining the axle type, speed, and acceleration, resulting in a weighing error of less than 0.5%. However, it does not support weighing multiple vehicles traveling through platforms simultaneously, and the traffic efficiency is low. At present, most whole-vehicle-load measurement systems using a large-platform scale still face the challenge of calculating the number of axles and the load of the individual axle [11]. To identify the number of axles, most whole-vehicle-load measurement systems are equipped with axle recognition devices [12], which increases the cost and reduces the system's reliability due to the high failure rate of these devices. In 2015, [PERSON] et al. [13] used an expert algorithm to segment the entire weighing process of the vehicle, calculated the number of axles, and realized whole-vehicle-load measurement, but did not perform a quantitative analysis of axle recognition and weighing results. In summary, whole-vehicle-load measurement has a higher accuracy. Furthermore, the axle load change caused by vehicle acceleration and deceleration will not affect the gross vehicle weight in whole-vehicle-load measurement. Then, whole-vehicle-load measurement has better robustness for vehicles traveling at variable speeds. Consequently, this paper proposes a new modular WIM system that enables accurate axle recognition and weighing while multiple vehicles travel through platforms simultaneously. First, a new sensor module structure is designed, in which multiple scales are cascaded to create a combined scale, and each scale can be used independently or in combination. Second, instead of relying on specialized axle recognition devices, axle recognition is performed directly using the weighing signal from the WIM sensors. Therefore, an axle recognition algorithm based on a Transformer-Gated Recurrent Unit (GRU) is designed to classify the weighing signal at each time point and output the recognition results.