Current methods for estimating heavy-duty tire loads rely on indirect approaches such as cameras, radar, and accelerometers to obtain tire deformation information. Empirical formulas are then used to fit and estimate tire loads. However, these methods have low estimation accuracy, poor real-time performance, and high susceptibility to environmental conditions. When a tire is under load, it deforms, causing the distances between internal surface points to change predictably. Therefore, we propose the estimation of tire vertical loads by analyzing the distances between characteristic internal surface points.

We designed a monitoring system consisting of flexible strain sensors, data acquisition and transmission equipment, and upper-computer control software to monitor the deformation patterns of internal surface points under load. We then installed axial, circumferential, and lateral distance sensors in the tire. Using vertical load, tire pressure, and speed as variables, we conducted experiments on a drum test bench to measure the changes in internal surface characteristic point distances under load. We analyzed the periodic deformation patterns of different internal points during tire movement and identified the peak circumferential contact stretch at the tire crown and the noncontact stretch at the tire sidewall as characteristic points for estimating vertical load. We also used correlation analysis to examine the effects of speed and pressure on these points. Based on these two characteristic points, we developed empirical, semiempirical, and machine-learning models for estimating the vertical load of heavy-duty tires.

The machine-learning models demonstrated excellent performance. Among them, the XGBoost model performed the best, with a coefficient of determination (R²) of 0.9856, a root mean square error (RMSE) of only 181 kgf, and a mean absolute error (MAE) of 128 kgf, displaying high accuracy and stability. The Random Forest model achieved an R² of 0.9705, an RMSE of 382 kgf, and an MAE of 294 kgf, also exhibiting strong regression performance. The neural network model showed moderate error metrics. In comparison, traditional models performed less reliably. The semiempirical model had an R² of 0.9288 and moderate error metrics. The empirical model for the crown circumferential region significantly outperformed that for the sidewall region, highlighting the differences in mechanical properties and deformation patterns between these areas. The sidewall region is more challenging to monitor and estimate.

The verification results demonstrate that the proposed method for estimating the vertical load of heavy-duty tires based on internal surface feature point distance monitoring achieves high accuracy. This approach not only provides a new method for tire load estimation but also offers a technical solution for predictive maintenance of heavy-duty tires. Additionally, the proposed detection method and load estimation model have important reference value for load monitoring of tires in heavy machinery and can be applied to a broad range of tire-based transportation equipment.

During winter in high-altitude regions, coal transported via railways can freeze onto the walls of train carriages, making it difficult to unload completely. Detecting the residual frozen coal and formulating effective removal plans is essential in such cases. At present, video detection is mainly used for this purpose but often suffers from issues such as inaccurate estimation of residual frozen coal volume and high sensitivity to light conditions. To address these challenges, this article introduces a measurement method for detecting residual frozen coal in train compartments using spin type LiDAR.

The method first determines the head and tail of a single open-top carriage using periodic changes in the point cloud data. The system then extracts all point cloud data for the specific carriage. Preprocessing of point cloud data is then performed, which includes extracting point cloud data within the carriage based on the relative position of the radar and the vehicle compartment, correcting for contour tilt and removing motion distortions in the point cloud, performing coordinate system transformation on point cloud data and using a motion displacement fusion algorithm to stitch single-frame point clouds, applying statistical filtering and voxel grid methods to simplify the extracted point cloud data, smoothing the point cloud using the moving least squares method to eliminate ghosting artifacts. To slice point cloud data, the carriages are segmented into equal spaces; these segmented point clouds are then projected and filtered. For point cloud contour extraction, the ray 360-degree algorithm and the alpha algorithm are applied. By employing the Shoelace theorem, the cross-sectional area of the point cloud contour is calculated. Multiplying this area by the segmentation spacing determines the volume size of the point cloud in the compartment.

Experiments demonstrated the relationship between voxel grid size and sampling quality. With the increase of voxel grid size, the number of point clouds decreases rapidly; however, the average distance between point clouds increases linearly, and the variance of point cloud distance rises exponentially. Experiments were also conducted to analyze the relationship between slice spacing and estimation accuracy in our proposed fusion volume estimation method. Results showed that, for a fixed detection volume, the calculation accuracy decreased with increased slice spacing. Conversely, at a set slice width, larger detection volumes resulted in a linear increase in the relative error range while reducing the absolute error range. We compared and analyzed the detection accuracy of our proposed fusion algorithm with other algorithms through experiments. The relative error of our proposed fusion algorithm was significantly smaller than that of the other two algorithms, and it decreased as the volume increased. The 360-degree scanning algorithm fluctuated greatly, around 10%, while the alpha algorithm demonstrated more stable results with relative error rates maintained at around 8%. The proposed fusion algorithm demonstrated superior accuracy and stability compared with the other two algorithms.

The winter frozen coal residue measurement method proposed in this research achieved high detection accuracy. This method can be widely applied not only for detecting frozen coal residues in railway transportation but also for evaluating residual goods in open transportation vehicles used on highways or waterways. Furthermore, the detection hardware can be equipped on mobile carriers for identifying concave surfaces, such as ground depressions, slopes, or even cave-like structures.