applied sciences Article Identification of Vehicle Loads on an Orthotropic Deck Steel Box Beam Bridge Based on Optimal Combined Strain Influence Lines  
[PERSON], [PERSON]\({}^{\star}\), [PERSON] and [PERSON] School of Civil, Architecture and Environment, Hubei University of Technology, Wuhan 430068, China  
\({}^{\star}\) Correspondence: [EMAIL_ADDRESS]  
[PERSON], [PERSON]; [PERSON]; [PERSON]; [PERSON], [PERSON] Identification of Vehicle Loads on an Orthotropic Deck Steel Box Beam Bridge Based on Optimal Combined Strain Influence Lines. _Appl. Sci._**2022**, 12, 9848. [[https://doi.org/10.3390/app1299848](https://doi.org/10.3390/app1299848)]([https://doi.org/10.3390/app1299848](https://doi.org/10.3390/app1299848))  
Received: 12 September 2022  
Accepted: 27 September 2022  
Submitted: 30 September 2022  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Accepted: 27 September 2022  
Submitted: 30 September 2022  
Kalman filter for moving vehicle identifications and used experiment tests to validate the accuracy of the method. [PERSON] et al. [10] developed an inverse analysis technique based on the finite element method and mode superposition method for impact force identification. The Bridge Weigh-in-motion (B-WIM) system is a technique for monitoring and identifying vehicle loads by placing sensors (e.g., strain gauges) on the underside of bridges, which is cheap, nondestructive to the roadway, and without effects of traffic [11; 12; 13]. B-WIM is mainly based on the [PERSON] [14] algorithm. It constructs an error function between the measured and theoretical strain and solves the vehicle's axle weight and gross weight using the least square method. The precision of the actual influence line extraction affects the accuracy of the vehicle's load identification. The practical simple support bridge is between simple support and consolidation constraints at both ends. For the usual B-WIM system, the recognition of axle information, such as speed, the number of axles, and wheelbase, is a prerequisite for axle weight identification. [PERSON] [15] proposed a wavelet-based method for detecting information on the axle. [PERSON] [16] proposed an equivalent shear method for the identification of axle information by only using the strain response collected by weighing sensors. It does require special axle information detection devices. [PERSON] et al. [17] proposed a method for detecting axle information based on shear strains. [PERSON] et al. [18] used accelerometers to capture vehicle axle information by using a peak filter, and magnetometers were utilized to evaluate vehicle speeds by detecting changes in the magnetic field. After axle information has been identified, the axle's weight was predicted by minimizing the difference between measured and predicted bridge responses based on the influence theory. [PERSON] [19] promoted the identification accuracy of the influence line by adjusting constraint conditions on the support and smoothing the peak of the response to match the actual bridge engineering situation. [PERSON] et al. [20] proposed an iterative dynamic weighing algorithm between the Morse algorithm and the measured influence line to correct the ill-condition problem of the equation. [PERSON] [21] followed the method proposed by [PERSON] [22] and used influence lines calibrated by field tests to calculate axle weights. Moreover, he researches the influence of the choice of influence lines, the shape of the influence line, and the sampling frequency during the axle's weight identification. [PERSON] [23] proposed a maximum likelihood estimation method for obtaining the influence line of a bridge structure. The algorithm used different girder types for calibration and identification of the influence line, and it was found that the algorithm was highly noise resistant. [PERSON] [24] applied Tikhonov regularization to the traditional B-WIM algorithm to improve vehicle load identification accuracy.