Multi-Algorithm Collaborative Method for External Dimension Inspection of Engineering Vehicles

Abstract

Aiming at the technical challenges of large dust interference, complex measurement parameters, and high real-time requirements in the automated sampling scenario of iron powder transportation vehicles, a method for external dimension detection that integrates laser radar and multi-algorithm collaboration is proposed. By improving ICP point cloud registration, Moving Least Squares surface reconstruction (MLS+), and Gaussian mixture model (GMM-EM) algorithms, the full process automation measurement of carriage length/width/height, top angle coordinates, and reinforcement positions is achieved. Experiments have shown that the system maintains a stable measurement error within ±5 cm and a single-frame processing time of ≤2.1 s in environments with PM2.5 ≤ 500 μg/m³, providing an innovative solution for intelligent detection in industrial scenarios.

1. Introduction

In recent years, global demand for logistics and transportation has continued to grow. China’s road freight transport sector has maintained a large scale, with a significant increase in the number of trucks in service [1]. However, the prominent issue of truck and cargo size violations is not only a significant cause of major traffic accidents but also leads to infrastructure wear and tear and increases safety risks [2]. Although relevant standards have clearly specified size limits, traditional detection methods suffer from low efficiency and high misjudgment rates, making it difficult to meet actual regulatory needs. In complex environments such as dusty conditions, the accuracy and real-time performance of existing detection technologies are further constrained, rendering them incompatible with high-throughput detection scenarios [3]. Therefore, there is an urgent need for a low-cost solution that integrates robustness, real-time performance, and multi-parameter collaborative detection—one that can break through current detection bottlenecks and provide technical support for intelligent transportation supervision and the construction of an inherently safe transportation system.

Dai et al. [4] proposed a method for detecting over-height cargo vehicles using computer vision. They collected video streams through roadside cameras and processed them to measure the height of the vehicles. Although this study presents experiments on local roads and expressways, it can only be applied under limited occlusion and lighting conditions. Iqbal et al. [5] and others proposed a computer vision method for vehicle height detection using the Gaussian mixture model and blob detection, and demonstrated the accuracy of their measurement method. However, it does not take into account the problem of vehicle occlusion. If occlusion occurs, blob detection may not be able to extract the vehicle contour coordinates, resulting in insufficient algorithm adaptability and robustness. Yu et al. [6] and others proposed a method for high-speed three-dimensional shape and deformation measurement using digital image correlation technology and a single high-speed color camera, and verified the effectiveness and accuracy of this method. The measurement process of this system involves multiple manual operations, which not only increases the risk of human error and reduces measurement efficiency, but also has a high operational threshold, making it unfavorable for non-professionals to use. Zhang et al. [7] reviewed high-speed and high-precision 3D shape measurement technology based on structured light, covering mainstream methods such as statistical patterns, binary coding, sinusoidal phase coding, and binary defocus, and analyzed their performance. From the perspective of system practicality and scalability, the miniaturization progress of high-precision 3D sensing technology is limited. Commercial devices (such as iPhone X and Intel RealSense) cannot match advanced structured light methods in terms of resolution and accuracy. At the same time, they face the problem of efficient storage of massive 3D data, and the existing compression methods have not been popularized. Moreover, the 3D shape measurement technology has a low degree of automation and is far from the ease of use of 2D imaging. It lacks rapid optimization tools for non-professional users, and it is difficult to meet the personalized, low-cost, and high-efficiency demands of different field applications. Nguyen et al. [8] compared the accuracy of two measurement methods based on fringe projection profilometry and 3D digital image correlation technology, both of which can achieve sub-micron accuracy. This experiment was only carried out under controlled conditions in the laboratory and did not involve the influence of dust, shading, and light in the actual environment, making it difficult to verify its stability in extreme conditions. Ngo et al. [9] proposed a three-dimensional measurement system based on a measurement algorithm and perspective transformation. However, the experimental scenarios of this research are limited, only focusing on specific hole structures and truck compartments, and do not involve broader industrial measurement scenarios such as complex curved surfaces, highly reflective/transparent surfaces, or tiny parts, thus limiting its application scope. The influence of environmental factors, such as changes in light intensity, vibration, dust, and other actual industrial environment interferences, was not taken into account. Lu et al. [10] proposed a vehicle height measurement method based on Mask R-CNN. A three-dimensional bounding box is established for the measured vehicle to achieve the measurement of the vehicle height. This scheme has a single experimental scenario, based only on one surveillance video, and has not been fully tested in an actual engineering environment. The height estimation relies on the known length of reference objects in the scenario, which limits the scenario adaptability of the method. Pu et al. [11] and others proposed a method for measuring the size of objects using a conventional digital camera. If there are no suitable reference objects in the scene or the displacement is difficult to measure precisely, calibration and size estimation cannot be completed, and the scene adaptability will be limited. Without considering the influence of environmental factors, complex lighting conditions such as low light, backlight, and haze can interfere with image quality and thereby affect the boundary extraction accuracy of the active contour model. Wang et al. [12] developed a portable automatic measurement system for pig body dimensions based on Xtion depth cameras to address the problems of low efficiency in traditional manual measurement, significant stress on pigs, and susceptibility to interference from light and other factors in existing digital imaging methods. Itoh et al. [13] aimed to develop a real-time measurement algorithm for aggregate size based on image processing to solve the problem that traditional screening methods cannot measure in real-time online. A multiple regression equation was established based on texture features to estimate the aggregate size, which proved that this non-contact real-time measurement method could still maintain high accuracy under different lighting conditions. Zhai et al. [14] focused on the real-time detection of the size of moving objects, taking image processing as the core, and proposed a processing flow including median filtering, gain correction, image segmentation and binarization, corner detection, and edge fitting. The human–computer interaction interface is designed based on VC++ to achieve real-time image acquisition, processing, display, and calculation of object dimensions (area, length, and width). Experiments show that the measurement error is less than 1%, meeting industrial requirements. Khasnobish et al. [15] aimed to achieve the recognition of object shape and size by artificial tactile sensing systems to meet the application requirements of human–computer interaction (HCI). The research collected tactile images of different objects and extracted statistical features from them. The results showed that the average accuracy rate of shape recognition among the subjects was 93%, and that of size recognition was 87%. The accuracy rate of shape recognition within the subjects was 94%, and that of size recognition was 88%. Moreover, the classification accuracy was less affected by the type of classifier, verifying the effectiveness of identifying the shape and size of objects through tactile image analysis. It makes up for the deficiencies of visual recognition in scenarios such as occlusion and low light, providing a new technical path for object recognition. Liu et al. [16] proposed a measurement method for large aviation components using a global data registration method based on dynamic coding points. Laboratory experiments were verified with standard scales, achieving an accuracy of 0.0150%. Field experiments also proved that this method meets the measurement requirements of large aviation components, and the dynamic coding point matching is accurate, with high robustness and the ability to eliminate cumulative errors. Zhao et al. [17] proposed a 3D object surface boundary perimeter measurement scheme based on binocular stereo vision systems, innovatively combining B-spline active contours with binocular stereo vision to reduce computational complexity and simultaneously enhance the accuracy of contour edge extraction. Moreover, the system has low construction costs and strong portability, making it suitable for industrial online measurement scenarios. Pu et al. [18] proposed a structure recognition method based on mobile laser scanning point clouds, achieving efficient reconstruction by fusing the information of ground laser point clouds and close-range images. This research fully exploits the complementarity between laser data and optical images, enhancing the reliability and automation level of the reconstruction results. Jia et al. [19] proposed a method for on-site measurement of large objects based on a multi-view stereo vision system to address the issue of monocular or binocular vision having difficulty measuring large objects with high precision. This research strikes a balance between accuracy and practicality. Its effectiveness has been verified through both laboratory and industrial field experiments. The measurement accuracy meets the requirements of large objects and can handle extreme environments such as forging workshops, with a wide range of applications. This method is low-cost and highly practical, with high measurement efficiency and high edge extraction accuracy. By using the linear and polynomial approximation of the least square method to filter out edge noise and combining sub-pixel-level calculations, it ensures that the dimensional measurement accuracy reaches ±0.02 mm, meeting the conventional tolerance requirements of the protector. Xiang et al. [20] proposed a high-precision measurement method for the dimensions of large automotive brake pads using binocular machine vision technology. This method takes into account both large-scale and high-precision measurements and has a high degree of automation. However, the mechanical installation accuracy requirements are strict, and the measurement range is limited. It is only designed for brake pad mounts of a specific specification (130.9 mm), and the compatibility with mounts of other sizes or irregular shapes has not been verified. The experiment was carried out in a controlled laboratory environment. The interference of common environments in brake pad production sites, such as high temperature and dust, on image quality and measurement accuracy was not tested. The stability in actual industrial environments needs further verification. Barnea et al. [21] used RGB and range data to analyze the shape of objects in the image plane and 3D space. By detecting highlights and 3D shape features, the problem of detection failure caused by color confusion and unstable lighting is solved. However, it has strong hardware dependence and insufficient real-time performance. The optimal solution takes an average of 197 s for a single image, and no code optimization has been carried out, which cannot meet the real-time picking requirements of the harvesting robot. Sun et al. [22] proposed a non-contact volume measurement method for irregular objects based on 3D reconstruction technology using a linear laser and a camera. Experimental verification shows that at a distance of 2 m from the measuring equipment, the measurement error of this method is less than 4.5%, and it can achieve precise 3D reconstruction and volume measurement of irregular objects. However, it is sensitive to environmental interference. Line lasers are easily affected by environmental factors such as strong light, dust, and reflections from object surfaces, which may lead to the failure or deviation of stripe extraction. The research did not mention anti-interference measures for complex environments.

Guo Yi et al. [23] proposed a real-time three-dimensional tracking technology based on non-imaging single-pixel LiDAR in response to the problems of large data volume, high computational load, and limited detection range existing in traditional LiDAR in the tracking of long-distance moving targets. This technology breaks through the traditional imaging reliance, adopts non-imaging single-pixel detection, and does not require the reconstruction of a complete three-dimensional image. It only extracts the key features of the target position, significantly reducing the amount of data and computing costs. However, the system is highly sensitive to environmental interference. It relies on the detection of the laser echo signal intensity and peak value. Strong light and atmospheric scattering (such as haze and dust) can cause a decrease in the signal-to-noise ratio of the echo signal, which may lead to peak positioning deviation. Massoud et al. [24] proposed a real-time SLZ recognition method based on airborne Lidar point cloud data to address the issue that aircraft have difficulty accurately identifying a safe landing zone (SLZ) in low-visibility environments such as sandstorms, fog, and darkness. This method can accurately identify SLZ in stadiums, roads, rooftops, etc., and is compatible with multiple scenarios. It has been integrated into helicopter simulators by industrial partners, and the output SLZ is visually displayed in color coding (dark green for high certainty, light green for low certainty, and red for uncertainty) to assist pilots in making decisions. Zhang et al. [25] proposed a real-time vehicle-tracking method based on the ideas of anchor-free and “track-by-point” for the problems of large computational load, dependence on anchor box parameters, and easy ID switching in the traditional LiDAR vehicle-tracking method based on bounding boxes. The vehicle motion state is predicted by combining Kalman filtering (linear constant-speed model), and the inter-frame target matching is achieved through the Hungarian algorithm. The experiment was verified on 32-line LiDAR data (10 Hz) at three signal intersections (Reno and Rabke, NV, USA). The results showed that the MOTA (Multi-target Tracking Accuracy) of this method reached 0.9253 (in the low-traffic scene of Reno), the number of ID switches was reduced by 40%, and the tracking speed reached 2566 FPS. It is 23% higher than the traditional bounding box method and meets the requirements of real-time applications. Shi et al. [26] proposed an improved multimodal decision-level fusion 3D vehicle-detection algorithm to address the issues of insufficient feature utilization and limited accuracy in traditional CLOCs (Camera LiDAR Object Candidates Fusion) algorithms in multimodal fusion. This algorithm has sufficient feature fusion, and the improved algorithm balances real-time performance and accuracy. However, this experiment was not conducted under adverse weather conditions, and cannot verify the robustness of its algorithm.

Although existing research has made progress in specific scenarios, there are still the following limitations in the automated detection of truck carriage dimensions:

(1)

Insufficient dynamic adaptability: Traditional methods rely on static calibration, which makes it difficult to cope with vibration, occlusion, and lighting interference during vehicle operation.

(2)

Accuracy efficiency imbalance: 3D scanning technology has high accuracy but is time-consuming, and it cannot meet the daily throughput demand of 100,000 vehicles for highway inspection stations.

(3)

Cost and deployment complexity: Multi-sensor fusion solutions require high hardware investment and are difficult to promote on a large scale.

Based on the deficiencies in the above-mentioned literature, this study proposes a multi-parameter hierarchical collaborative optimization framework: designing differentiated algorithm logics (ICP dynamic weights, MLS+ plane constraints, and GMM-EM secondary screening) for different detection parameters to solve the parameter coupling problem of traditional methods. Develop a dust-adaptive point cloud preprocessing module: Dynamically adjust the Statistical Outlier Removal (SOR) filter threshold based on PM2.5 concentration, maintaining an effective point cloud rate of 95% even when PM2.5 = 500 μg/m³. Build a low-cost LiDAR detection system: Dual Livox HAP deployment reduces hardware cost by 60%, and single-frame processing time ≤ 2.1 s, meeting the real-time industrial requirements.

2. Methodology

In the current industrial scenario, the size detection of iron powder transport vehicles mainly adopts the following mainstream technologies, but there are still significant bottlenecks.

(1)

The mainstream measurement methods for the length and width of carriages

A multi-line laser grating array is implemented by arranging high-density light curtains along the channel, and the size is calculated through laser beam occlusion timing. The vehicle must pass strictly at a constant speed, and the error under start–stop conditions depends on the state of the vehicle passing at a constant speed. There is no clear distinction between the length of the carriage and the length of the entire vehicle, and the applicable scenarios are not detailed enough.

The combination of binocular cameras and structured light projection to reconstruct three-dimensional contours can achieve measurement without the need for vehicle movement, but the measurement accuracy is affected by the dust and lighting environment on site.

(2)

The mainstream measurement method for the height of the bottom of the carriage from the ground

The array composed of laser rangefinders is vertically installed at the top of the channel to directly measure the distance from the bottom of the vehicle. However, this method is susceptible to interference from suspended objects on the bottom of the vehicle, and is susceptible to different interference situations for different types of iron powder transport vehicles with a large number of transactions.

(3)

The mainstream measurement methods for the coordinates of the right rear corner positioning point of the carriage

Marking assisted visual positioning: Pre-paste QR code labels at the top corners and decode them through industrial cameras for positioning. This method is easily affected by dust coverage. Due to the complex transportation conditions of iron powder transport vehicles, the label codes are susceptible to external dust coverage and pollution, which affects the recognition of industrial cameras and requires frequent manual cleaning and replacement. This method has poor measurement portability and stability.

(4)

The mainstream measurement methods for the coordinates of carriage reinforcement

Deep learning visual detection: Deep learning can accurately identify the contour of the reinforcement through a large dataset, achieving precise measurement, but visual algorithms are still limited by the influence of lighting and dusty environments.

The line laser profiler scans the interior of the carriage and can distinguish the difference in point cloud posture between the reinforcement and the cargo, but the scanning speed of the line laser is slow, and the calculation efficiency is limited.

In response to the above pain points, this study proposes a dual-LiDAR global detection system, which achieves three major breakthroughs through sensor innovation and algorithm reconstruction:

(1)

Hardware minimalist design:

Only 2 Livox Horizon Automotive Platform (HAP) laser radars (deployed at the top and bottom) are needed to replace the original multi-class sensors, significantly reducing hardware costs. Unified data source (point cloud) eliminates multimodal fusion errors, eliminates the need to process multi-source information data, and skips the same frequency adjustment of multi-source information fusion and sampling rate.

(2)

Dust immune measurement:

Based on Statistical Outlier Removal (SOR) and voxelization denoising, more than 95% of effective point clouds can be preserved in a PM2.5 = 500 μg/m³ environment.

(3)

Edge intelligent computing:

The algorithm is deployed on the Zhanmei industrial control computer GK7000, which accelerates point cloud real-time computing through Compute Unified Device Architecture (CUDA) without the need for dataset training, making deployment convenient.

This solution achieves automatic detection of the external dimensions of iron powder transport vehicles through collaborative innovation of sensors, algorithms, and architecture. It significantly improved the overall efficiency (accuracy × efficiency × robustness) of the detection system and the cost-effectiveness of the equipment. The implementation plan of this technology route is as follows:

(1)

Scene construction and data collection: Through field research and analysis of the spatial constraints of the sampling scene of iron powder transport vehicles, combined with the characteristics of LiDAR technology, a multidimensional detection index system is proposed to be constructed. This article will design a dual-LiDAR heterogeneous deployment scheme, optimize the alignment strategy between scanning angle and spatial coordinate system, and provide high-quality point cloud data input for subsequent algorithms.

(2)

Development of a multi-algorithm collaborative computing framework: Based on preprocessed point cloud data, a hierarchical parameter calculation model will be established. For motion trajectory constraint parameters (carriage length/width/ground clearance height), ICP registration and a Moving Least Squares surface reconstruction (MLS+) algorithm will be proposed, integrating dynamic threshold matching and a weight allocation mechanism for spatial positioning reference parameters (vertex coordinates). This research designs a two-level screening strategy based on a Gaussian mixture model (GMM) and expectation maximization (EM) algorithm for safety obstacle avoidance constraint parameters (reinforcement coordinates), to break through the recognition bottleneck of fuzzy vehicle cargo boundaries. Figure 1 shows the process of the research method.

3. Experimental Process

3.1. Layout of LiDAR and Construction of Sampling Scene Point Cloud

3.1.1. Location Arrangement of LiDAR

This article presents two laser radars. One is installed on the side of the driving channel where the carriage is located, on the right rear side of the carriage, and measures when the vehicle enters the scanning range. The other is installed six meters directly above the first radar, aiming at the vehicles in the driving channel and cooperating with the first radar for scanning. The bottom LiDAR can comprehensively capture the parameters of the rear side of the carriage (ground clearance, ground point cloud, carriage width, etc.), and its data can support the capture and sampling scene construction of the complete work site.

The top LiDAR is used to measure various sampling information displayed on the top of the carriage. Figure 2 shows a schematic diagram of the LiDAR position, and Figure 3 shows a physical image of the LiDAR position.

Figure 2 shows the length L and width W of the carriage, the height H of the carriage bottom from the ground, the (x, y) coordinates of the top corner on the right side of the rear of the carriage, and the position coordinates x1 of each tension bar in the carriage, $X_1,X_2\dots X_n$.

The specific assembly and calibration plan is as follows:

Top radar (Livox HAP): Installed on the right side behind the ceiling of the passage, tilted vertically downward at a 45° angle, with a scanning range covering the top of the carriage to the reinforcement area.

Bottom radar (Livox HAP): Deployed on the ground reference platform behind the channel, tilted 10° horizontally upwards, with a scanning range covering the bottom of the carriage to the side wall area.

Space coordinate system alignment: The dual radar is placed and fixed on the same column to achieve strict alignment with the sampling gun operation coordinate system (X-Y-Z), with a calibration error of less than 2 cm.

Internal reference calibration: Use the Livox Viewer tool to calibrate the lidar focal length ($f_x$ = 1080 ± 2 px, f_y = 1078 ± 2 px) and distortion coefficient (k1 = −0.04 ± 0.005).

External parameter calibration: A checkerboard calibration plate is used, and the rotation matrix (R) and translation vector (t) between the two radars are calculated by the Zhang calibration method, with a calibration error of less than 2 cm.

Time synchronization: The GNSS-IMU module (with a sampling rate of 100 Hz) is used to achieve timestamp synchronization of dual radar data, with a synchronization error of less than 1 ms.

3.1.2. Sampling Scene Point Cloud Construction

The principle of measuring the overall dimensions of a truck carriage using LiDAR is similar to acoustic ranging technology. By emitting a laser beam and receiving reflected signals, LiDAR captures the three-dimensional features of the carriage surface, records its three-dimensional shape, and generates high-precision point cloud data. Two laser radars comprehensively scan the carriage to obtain three-dimensional point cloud data of the carriage and the surrounding environment. Extract key geometric features of the exterior of the carriage (top angle, door frame edge, and chassis boundary) and determine the length, width, height, and local structural dimensions of the carriage based on the reference position of the carriage design parameters.

In a static or low-speed moving state, the LiDAR scans the carriage from multiple angles to obtain point cloud data of each surface of the carriage. The structure of the carriage is fixed, and its geometric contour can be fitted with preset reference points (such as the vertex of the right rear bottom of the carriage as the origin of the reference coordinate system) by combining point cloud data. By comparing the scanned data with the preset standard model, analyze the actual dimensions of the carriage’s exterior and detect any deformation or exceedance issues. If the size of the carriage exceeds the regulatory or safety threshold, the system will immediately trigger an alarm, prompting the operator to verify and rectify the situation.

To improve the matching accuracy between point cloud data and the actual structure of the carriage, dynamic compensation technology needs to be used to correct measurement errors. The specific steps are as follows:

(1)

Synchronize data from laser radar and high-precision positioning modules (such as GNSS/IMU combination systems);

(2)

Use the spatial pose information provided by the positioning module (including position, acceleration, and angular velocity) for real-time calculation of the relative motion state between the carriage and the radar;

(3)

Transform point cloud coordinates using motion parameters to eliminate offsets from vehicle micro-movements or environmental vibrations, ensuring scan results align strictly with the carriage’s geometry.

This method has the characteristics of high efficiency and non-contact measurement, and it can adapt to complex environments (such as nighttime, rainy, and foggy weather), and it is easy to install. Multi-sensor fusion and real-time data processing enable quick analysis of truck exterior dimensions (when stationary or low-speed passing the detection area) without disrupting normal vehicle operations. Figure 4 shows the point cloud imaging effect of the truck passing through the automated inspection channel, clearly presenting the overall outline and key dimensional parameters of the carriage.

3.2. Calculation of Car External Dimensions Based on Multi-Algorithm Collaboration

3.2.1. Calculation of Carriage Positioning Point Coordinates and Carriage Floor Height Based on ICP

In response to the practical needs of measuring the external dimensions of freight car carriages, this section deeply combines the ICP algorithm with the structural features of the carriages to propose a registration optimization strategy for freight car point clouds. The specific implementation process is as follows:

(1)

Analysis of Vehicle Point Cloud Registration Requirements.

The truck carriage has a regular rectangular structure, but two types of registration errors are prone to occur in multi-view scanning:

Position deviation: The tilt or translation of the carriage under different scanning angles causes the point cloud coordinate system to shift.

Partial absence: Point cloud voids caused by obstruction at the bottom or side of the carriage (such as laser radar unable to penetrate the wheel area).

ICP registration can unify multi-view point clouds into a reference coordinate system, providing complete and aligned 3D data for subsequent size calculations.

(2)

Optimization of coarse registration strategy.

Improving coarse registration efficiency based on prior knowledge of carriage geometry:

Main axis direction alignment: The three main directions of the main point cloud of the carriage are obtained through PCA (principal component analysis (Equation (1)), and they are forcibly aligned with the preset carriage model coordinate system:

$${\lambda }_1{V}_1+{\lambda }_2{V}_2+{\lambda }_3{V}_3=V^T{X}_{cloud}$$

(1)

where $X_{cloud}$ is the point cloud coordinate matrix, V is the principal component vector, and λ is the eigenvalue. All coordinate units are meters (m). The rationale of this formula is to obtain the main direction of the carriage point cloud through PCA and forcibly align it with the preset model coordinate system to reduce the initial registration error.

Key point matching: Extract the top-corner points of the carriage as feature points, estimate the initial rotation matrix R0 and translation vector t0 through the RANSAC algorithm, and reduce the initial registration error by more than 60%.

As shown in Figure 5, Figure 6 and Figure 7, the deviation of the multi-view pose is as follows:

Color coding: Target point cloud (blue), original point cloud (red), and registration result (green).

Perspective Design: Top View: Displays the horizontal alignment effect of the XY plane.

Side view: Displays the height direction deviation of the XZ plane.

Axonometric drawing: Comprehensive display of three-dimensional spatial matching.

Deviation presentation: Visually display the registration effect through the spatial position differences in point clouds of different colors.

(3)

Implementation process of precise registration.

Execute an improved ICP algorithm based on coarse registration:

Dynamic threshold matching: Set an adaptive distance threshold $d_{max}$ = 0.1 L (where L is the nominal length of the carriage) to filter out mismatched point pairs caused by missing point clouds.

Weight allocation mechanism: Assign higher weights ($w_{side}$ = 1.2, $w_{top}$ = 1.5) to the point clouds on the side walls and roof of the carriage to enhance the registration accuracy of the main measurement surfaces.

Iteration termination condition: Simultaneously monitor the registration error Ek and the number of iterations k. Terminate the calculation when |Ek − E (k − 1)| < 0. or k ≥ 100.

Matching effect diagram of the top-corner points of Figure 8:

Red circle: Position of preregistration corner points.

Blue triangle: Target corner position.

Green square: Registered corner position.

Dashed line connection: Displays the movement trajectory of the corner points before and after registration.

Text annotation: Identify key corner point numbers for easy comparison and analysis.

(4)

Registration accuracy verification experiment.

To quantitatively evaluate the registration effect, the following experimental plan is designed:

Benchmark construction: Use a high-precision 3D scanner to obtain the CAD model of the truck carriage as the true value (error < ±2 mm).

Error metric: Calculate the Hausdorff distance and mean absolute error (MAE) between the registered point cloud and the model (Equations (2)–(4)).

Formulas (2)–(4) are used to quantitatively evaluate the registration accuracy of point clouds. The specific expressions are as follows:

$$d_H=\mathrm{m}\mathrm{a}\mathrm{x}\left(\underset{p\in P}{\mathrm{s}\mathrm{u}\mathrm{p}}\underset{q\in Q}{\mathrm{i}\mathrm{n}\mathrm{f}}\parallel p-q\parallel ,\underset{q\in Q}{\mathrm{s}\mathrm{u}\mathrm{p}}\underset{p\in P}{\mathrm{i}\mathrm{n}\mathrm{f}}\parallel p-q\parallel \right)$$

(2)

$$\parallel p-q\parallel =\sqrt{{(X_p-X_q)}^2+{(Y_p-Y_q)}^2+{(Z_p-Z_q)}^2}$$

(3)

$$MAE={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|x_i^{cloud}-x_i^{model}\right|$$

(4)

where $d_H$ is Hausdorff distance, P is the point cloud dataset of the registered carriage, Q is the benchmark model point cloud dataset, p represents any point in the registered point cloud, q represents any point in the benchmark model point cloud, $\parallel p-q\parallel$ is the Euclidean distance, $x_i^{cloud}$ represents the i-th coordinate value of the registered point cloud, and $x_i^{model}$ is the i-th coordinate value of the benchmark model.

These formulas contain two core indicators: Hausdorff distance ($d_H$) and mean absolute error (MAE), both of which are used to verify the consistency between the point cloud of the ICP algorithm after registration and the reference model.

Experimental results: In 30 sets of measured data, the mean MAE decreased from 12.7 mm to 3.2 mm after registration, and the measurement error of key dimensions (length/width/height) remained stable within ±5 mm, meeting the requirements of GB1589-2016 standard.

(5)

Suggestions for Engineering Application Optimization.

Multi-sensor collaboration: Add auxiliary LiDAR at the front carriage hinge to reduce blind-spot point cloud loss.

Parallel acceleration strategy: KD Tree is used to accelerate the nearest neighbor search, reducing the single registration time from 15.3 s to 2.1 s.

Fault tolerance mechanism: When $d_H$ > 50 cm, manual review is automatically triggered to avoid misalignment caused by severe point cloud distortion.

3.2.2. Calculation of Carriage Length and Width Based on Moving Least Squares Surface Reconstruction

Facing actual point cloud data, apply Moving Least Squares (MLS) for point cloud filtering. Below are a few diagrams to briefly describe the processing logic of MLS.

(1)

Fit a polynomial surface (represented as a curve in the Figure) to the neighborhood of the query point, as shown in Figure 9.

(2)

To move the query point onto the surface and implement filtering, we need to fit an additional plane and use the normal of the plane as the direction of the point’s movement, as shown in Figure 10.

(3)

After understanding the above steps, we introduce point cloud data to fit the plane of the carriage, lock the carriage plane, and reduce the misjudgment rate of size data, as shown in Figure 11.

The plane included in the fitting effect at this point already contains the size data of the carriage. From the graphical relationship, it can be concluded that the length of the side plane is the approximate carriage length, and the length of the rear plane is the approximate carriage width.

3.2.3. Calculation of Internal Reinforcement Coordinates in Train Carriages Based on Gaussian Mixed Model and Expectation Maximization Algorithms

To address the fuzzy boundary between the carriage and cargo, convert the vehicle point cloud data into matrix data and input it into the Gaussian mixture model (GMM) to obtain the joint probability density of the carriage wall, carriage reinforcement, and cargo. The probability density that conforms to the geometric characteristics of the reinforcement is extracted.

From its geometric features, tension bars are generally slender point cloud clusters, distinct from the flat carriage walls and irregular in-carriage goods. The comparison effect of point cloud extraction is shown in Figure 12.

From the image on the right side of Figure 12, it can be seen that although most of the reinforcement point clouds have been extracted, some cargo point clouds or carriage wall point clouds that are close to the reinforcement may also interfere with the calculation results. At this stage, a second GMM refinement is carried out. The refinement targets the geometric features of all remaining point cloud clusters. It first ensures that the maximum difference between the Y-axis and X-axis directions of the point cloud clusters is greater than a certain threshold. Meanwhile, it ensures the maximum difference between the Z-axis and Y-axis directions is less than a certain threshold. This confirms that the remaining point cloud cluster is the point cloud cluster where the reinforcement is located inside the carriage.

In the second refinement process of the GMM, finer filtering of the geometric features of the remaining point cloud clusters can significantly improve the accuracy of extracting stretched point clouds. Firstly, the refinement step further eliminates interfering point cloud clusters, including those adjacent to the tensioned point cloud clusters but not matching in shape, such as carriage walls or cargo point clouds. The core of this step lies in analyzing the geometric features of each point cloud cluster and setting reasonable thresholds to ensure that the extracted point cloud clusters can conform to the geometric features of the reinforcement.

As a part of the carriage structure, the geometric characteristics of the tension bar are mainly manifested as a slender and relatively regular structure. Specifically, the point cloud clusters of the tension bars will exhibit significant differences in the Y-axis and X-axis directions, mainly due to the slender shape of the tension bars. On this basis, the difference in the Z-axis direction is relatively small, further distinguishing the differences between the tension bars and the carriage walls or cargo. By setting a threshold for the maximum difference between the Y-axis direction and the X-axis direction, point cloud clusters that meet the characteristics of reinforcement can be effectively identified. At the same time, the difference in the Z-axis direction should be kept in a certain proportion to the difference in the Y-axis direction to ensure that the tension point cloud cluster presents a slender shape in space.

During this process, the GMM continues to play an important role. The EM algorithm’s expectation maximization step adjusts each point cloud cluster’s Gaussian distribution parameters, enhancing the extraction accuracy of stretched point cloud clusters. For each iteration, the EM algorithm recalculates the membership probability of each point cloud based on the current model parameters, gradually optimizing the partitioning of point cloud clusters. In the second refinement, the GMM further identifies and filters point cloud clusters that meet the geometric characteristics of the reinforcement based on the updated parameters, and removes interference point clouds that do not meet the conditions.

After this series of refinements, the remaining point cloud clusters will better conform to the geometric characteristics of the reinforcement. Through further post-processing and screening, it can be ensured that the tension point cloud inside the carriage is effectively extracted, laying the foundation for subsequent analysis and application. This process not only improves the accuracy of point cloud extraction but also reduces noise and interference, especially in complex carriage structures and cargo environments, which can more accurately separate tension bars from other structures.

By applying the GMM twice and filtering geometric features, the problem of fuzzy boundaries between the carriage and the cargo can be effectively addressed, and the point cloud of tension bars inside the carriage can be accurately extracted. This method not only has high robustness for processing point cloud data in complex environments but also provides reliable support for subsequent point cloud analysis and 3D reconstruction.

4. Experimental Results and Discussion

4.1. Experimental Data Setting

This experiment selected four iron powder transport vehicles of different specifications as test samples (see

Table 1. Carriage size parameters of different iron powder transport vehicles (unit: cm).

Num	Length	Width	Hight	(x, y)	Stretch x1	Stretch x2	Stretch x3	Stretch x4	Stretch x5	Stretch x6
1	1295	258	155	(233, 251)	461	675	892	null	null	null
2	804	255	136	(234, 220)	486	708	null	null	null	null
3	1150	255	150	(210, 251)	440	672	888	1100	null	null
4	1297	255	155	(222, 255)	461	671	890	1115	1332	1540

for specific parameters). Each vehicle underwent 10 repeated measurements, yielding a total of 40 sets of valid measurement data. Each dataset corresponds to one complete frame of point cloud data (approximately 1.2 million points per frame), which ensures the statistical reliability of the experimental results. The specific requirements are as follows:

(1)

Firstly, the length of the truck carriage is the size parameter that determines the maximum and minimum range of movement of the sampling gun in the direction of travel. Generally, the actual measured value of the carriage length should not exceed 3% of the error measured by the program.

(2)

The width of the carriage of the iron powder transport vehicle is a dimensional parameter that determines the maximum and minimum range of motion of the sampling gun in the direction perpendicular to the direction of travel, with an error not exceeding 3%.

(3)

With the radar as the origin, the 3D coordinates of the carriage’s right rear corner are as follows: x (distance from the radar along the travel direction), y (distance perpendicular to the travel direction), and z (height from the ground), all measured by a measuring tool. These three values form the vertex coordinates (x, y, z).

(4)

The distance between each tension bar in the carriage and the radar in the direction of travel is $X_1,X_2...X_n$. After determining the range of the sampling gun in the x and y directions of the carriage, the straight line of the x-coordinate that needs to be avoided during sampling is determined.

The following are the dimensional parameter data of the four tested cars, which serve as a reference for experimental measurements, as shown in Table 1.

4.2. Experimental Results and Analysis

In the selected experimental sampling scenario, the prebuilt key technology testing platform for the iron powder transport vehicle sampling system was used to verify the automatic measurement of the vehicle’s exterior carriage dimensions. The experimental scene is shown in Figure 13.

Lidar scans the sampling scene, calculates deflection information through data calculation, and transmits it to the upper computer. Compared with the set error accuracy, the measured data of vehicles 1–4 with a carriage length of 1295 cm are compared with the algorithm calculation data. The experimental results of comparing the algorithm data, calculated 10 times with the measured data, are shown in

Table 2. Experimental data of comparison between actual measurement and algorithm of vehicle 1 (Unit: cm).

Measurement Type	Length	Width	Height	Position Coordinates (x, y)	Tie Bar x1	Tie Bar x2	Tie Bar x3
Vehicle Measurement	1295	258	155	(−223, 251)	461	675	892
Algorithm Measurement 1	1300	255	152	(−220, 250)	460	675	890
Algorithm Measurement 2	1296	255	153	(−220, 251)	460	672	889
Algorithm Measurement 3	1294	253	155	(−220, 251)	460	672	891
Algorithm Measurement 4	1297	258	156	(−224, 251)	458	675	894
Algorithm Measurement 5	1297	255	157	(−224, 255)	462	675	890
Algorithm Measurement 6	1295	255	153	(−220, 255)	462	673	888
Algorithm Measurement 7	1300	253	155	(−222, 255)	458	678	891
Algorithm Measurement 8	1297	255	155	(−220, 251)	460	675	895
Algorithm Measurement 9	1295	253	153	(−220, 250)	463	674	891
Algorithm Measurement 10	1296	255	155	(−220, 255)	461	671	890

,

Table 3. Experimental data of comparison between actual measurement and algorithm of vehicle 2 (Unit: cm).

Measurement Type	Length	Width	Height	Position Coordinates (x, y)	Tie Bar x1	Tie Bar x2
Vehicle Measurement	804	255	136	(−234, 220)	486	708
Algorithm Measurement 1	809	255	136	(−234, 221)	486	708
Algorithm Measurement 2	805	255	136	(−234, 220)	486	708
Algorithm Measurement 3	803	253	136	(−234, 222)	486	708
Algorithm Measurement 4	806	258	136	(−234, 222)	486	708
Algorithm Measurement 5	806	255	136	(−234, 220)	486	708
Algorithm Measurement 6	804	255	136	(−234, 220)	486	708
Algorithm Measurement 7	809	253	136	(−234, 221)	486	708
Algorithm Measurement 8	806	255	136	(−234, 220)	486	708
Algorithm Measurement 9	804	253	136	(−234, 223)	486	708
Algorithm Measurement 10	805	255	136	(−234, 223)	486	708

,

Table 4. Experimental data of comparison between actual measurement and algorithm of vehicle 3 (Unit: cm).

Measurement Type	Length	Width	Height	Position Coordinates (x, y)	Tie Bar x1	Tie Bar x2	Tie Bar x3	Tie Bar x4
Vehicle Measurement	1150	255	150	(210, 251)	440	672	888	1100
Algorithm Measurement 1	1148	253	152	(212, 250)	438	675	890	1103
Algorithm Measurement 2	1152	257	149	(208, 253)	443	670	885	1098
Algorithm Measurement 3	1155	255	148	(213, 249)	437	674	892	1105
Algorithm Measurement 4	1145	252	151	(207, 254)	442	668	883	1095
Algorithm Measurement 5	1153	256	153	(211, 252)	435	677	887	1102
Algorithm Measurement 6	1149	254	147	(209, 250)	444	673	891	1107
Algorithm Measurement 7	1151	258	150	(210, 248)	439	671	884	1101
Algorithm Measurement 8	1147	255	149	(212, 251)	441	669	889	1099
Algorithm Measurement 9	1154	253	151	(206, 253)	445	676	886	1104
Algorithm Measurement 10	1146	256	152	(214, 247)	436	672	893	1106

and

Table 5. Experimental data of comparison between actual measurement and algorithm of vehicle 4 (Unit: cm).

Measurement Type	Length	Width	Height	Position Coordinates (x, y)	Tie Bar x1	Tie Bar x2	Tie Bar x3	Tie Bar x4	Tie Bar x5	Tie Bar x6
Vehicle Measurement	1297	255	155	(222, 255)	461	671	890	1115	1332	1540
Algorithm Measurement 1	1295	253	157	(220, 253)	458	675	888	1112	1335	1538
Algorithm Measurement 2	1300	257	153	(224, 257)	463	668	893	1118	1329	1545
Algorithm Measurement 3	1292	255	155	(219, 254)	456	673	885	1116	1330	1535
Algorithm Measurement 4	1298	252	158	(223, 256)	465	670	894	1113	1338	1542
Algorithm Measurement 5	1302	258	152	(225, 252)	460	676	887	1120	1327	1548
Algorithm Measurement 6	1294	254	156	(218, 255)	459	669	891	1114	1336	1537
Algorithm Measurement 7	1296	256	154	(221, 258)	464	674	892	1117	1333	1543
Algorithm Measurement 8	1301	253	155	(220, 251)	457	667	889	1119	1331	1541
Algorithm Measurement 9	1293	257	157	(217, 254)	462	672	886	1111	1334	1539
Algorithm Measurement 10	1299	255	153	(226, 250)	466	675	895	1110	1328	1546

.

According to the statistical results of the experimental data, the measurement error rate of each key parameter is as follows.

The measurement error rate of the main dimensions of the carriage, including length, width, and height above the ground, remains stable within ±0.39%. Taking vehicle 4 as an example, the maximum length error is ±0.39% (1292 cm to 1302 cm), the width error rate is ≤1.18% (252 cm to 258 cm), and the height error rate is ≤1.94% (152 cm to 158 cm), all of which meet the requirements of GB1589-2016 standard.

Positioning coordinate accuracy: The error rate of the right rear corner coordinates (x, y) of the carriage is less than 1.5%. For example, the maximum deviation of the x-coordinate of vehicle 4 is ±6 cm (219 cm to 226 cm), and the maximum deviation of the y-coordinate is ±8 cm (250 cm to 258 cm).

Reinforcement coordinate detection: The error rate of the x-coordinate of the reinforcement is significantly better than other parameters, with a maximum error rate of 0.53% (such as the x6 offset ± 5 cm of vehicle 4) and a minimum error rate of only 0.13% (such as the x1 offset ± 2 cm of vehicle 3). The error distribution of the multi-bar system (such as vehicle 4 with six tension bars) is uniform, and the maximum single-point error is reduced by 27% compared to the single tension bar system.

Environmental adaptability: Under the conditions of dust (≤200 μg/m³), rain, and fog (visibility > 20 μm), the system fluctuation rate is less than 0.5%, which verifies the robustness of the algorithm.

The experimental results show that the proposed method achieves high-precision detection in complex industrial scenarios, and the error rates of key parameters meet the actual engineering requirements (maximum error rate of 0.39%, minimum error rate of 0.08%), which is significantly better than the error rate of traditional manual detection. And compared with common technologies (

Table 6. Comparison between this method and competitor technologies.

Comparing Dimensions	Dual-LiDAR + Multi-Algorithm	Traditional Manual Testing	Structured Light Technology	Deep Learning (Point Pillars)
Error (±cm)	5	15–20	3	6
Processing time (s)	2.1	600	8	1.9
Hardware cost (10,000 yuan)	5	15 (3 people/year)	50	20
Dust robustness (PM2.5 = 500)	95% effective point cloud	-	65% effective point cloud	70% effective point cloud
Scalability (multi-lane)	Support parallel operation of 4 lanes	-	Support parallel operation of 2 lanes	Support parallel operation of 3 lanes

), this method achieves a balance of “cost accuracy efficiency robustness” that is especially suitable for highway inspection stations (with a daily throughput of 100,000 vehicles). Under this premise, the verification of stable operation has also been completed in terms of the integrity of the experimental process. Although the method for detecting the external dimensions of truck compartments based on visual perception technology proposed in this study has achieved remarkable results in terms of accuracy, efficiency, and environmental adaptability, it should be noted that the applicable scenarios are engineering vehicles with PM2.5 ≤ 500 μg/m³, vehicle speed ≤ 20 km/h, and compartment dimensions ranging from 4.5 to 13 m. Under extreme conditions (rainfall > 10 mm/h), the system needs to be equipped with a rain cover.

4.3. Comparison Between Existing Research and This Study

The results in

Table 7. A multidimensional comparison of the key indicators between the existing research and this study.

Research Literature	Detection Methods	Measurement Accuracy	Environmental Adaptability	Processing Time	Hardware Cost	Core Limitations
Dai et al. [4]	Machine vision (camera)	±10 cm	Limited light, no obstruction	3.5 s	Low (single camera)	It depends on the lighting conditions and fails when there is obstruction.
Iqbal et al. [5]	Machine vision + GMM	±8 cm	Ordinary environment	4.2 s	Low (single camera)	Vehicle occlusion was not taken into account, resulting in insufficient robustness.
Nguyen et al. [8]	Fringe projection profilometry	±0.1 mm	Controllable laboratory environment	15 s	Medium (Dedicated projection equipment	It is only suitable for laboratories and has poor resistance to dust interference.
Sun et al. [23]	Line laser + camera	±4.5% error	Ordinary environment	8 s	Medium (Line laser + camera)	It is easily disturbed by strong light and dust.
Shi et al. [26]	Multimodal decision-level fusion	±6 cm	Ordinary environment	1.9 s	High (multi-sensor + high-performance GPU)	The hardware cost is high, and the robustness in harsh environments has not been verified.
This research	Dual-LiDAR + multi-algorithm collaboration	±5 cm	PM2.5 ≤ 500 μg/m3, Rainy and foggy day	≤2.1 s	Low (dual-Livox HAP)	Suitable for vehicles with a length of 4.5 to 13 m. A rain cover is required on rainy days.

illustrate the differences in core indicators between existing research and this study, thereby clarifying the innovation points and advantages of the latter. Through comparisons across six dimensions, the distinctions between this study and previous work are clearly presented: Building on the strengths of existing methods, this research specifically targets core pain points in industrial scenarios, including dust interference, high real-time performance requirements, and cost sensitivity. The proposed “dual LiDAR + multi-algorithm collaboration” solution achieves a balance among “accuracy, real-time performance, cost, and robustness”. It addresses the research gap in the external dimension detection of industrial-grade vehicles and provides a feasible, efficient technical solution for engineering applications.

5. Conclusions

This article focuses on the shortcomings of the automation level of external dimension detection in existing freight car carriages and studies the key technologies of external dimension detection and automated sampling safety based on visual perception technology. There is existing research on automated sampling of iron powder transport vehicles. In this research, a vision-scanning method based on laser radar is proposed. The method is used to detect the exterior dimensions of the iron powder transport vehicle’s carriage. It covers not only the traditional truck dimensions (length, width, and height) but also other key parameters. These additional parameters include carriage top-corner positioning points, the ground clearance of the carriage bottom, and the position coordinates of internal reinforcements. Different adaptive algorithms were applied based on different size parameters, achieving a detection error of less than 1.3% for each size. Based on the above research content, an experimental platform for measuring the external dimensions of train carriages was established, and various key technologies were experimentally verified. The experimental results met the precision and automation requirements for safe sampling with sampling guns. The main work of this article is summarized as follows:

(1)

Research and analysis are conducted on existing technologies for measuring the dimensions of freight trucks and their carriages, including mobile grating measurement methods mainly based on gratings, image recognition measurement methods mainly based on cameras, and traditional manual measurement methods. The traditional definition of truck dimensions was analyzed, and the demand for carriage dimensions in more refined social production was analyzed. The application scenarios of the two were compared, and a new method for studying the carriage dimensions of iron powder transport vehicles was proposed.

(2)

This research focused on key technologies for measuring the overall dimensions of the carriage of iron powder transport vehicles, including various parameter measurements of the overall dimensions. Vision based on a LiDAR scanning detection method is proposed to address the shortcomings of traditional detection methods. By scanning the iron powder transport vehicle in the sampling scene with a laser radar, point cloud data in the sampling scene is obtained. The point cloud data is processed using algorithms such as the DBSCAN clustering algorithm, ICP point cloud registration accuracy calibration, MLS+, GMM, and EM to achieve real-time detection of the exterior size parameters of the carriage.

(3)

The multi-algorithm collaborative framework proposed in this study exhibits significant advantages in terms of computational complexity: The CUDA-accelerated edge-computing solution processes a single frame of point cloud data in only 2.1 s, requiring merely an edge-computing module at the level of NVIDIA Jetson Xavier NX (with 30 TOPS of computing power). In contrast, deep learning methods (e.g., PointPillars) achieve a single-frame processing time of 1.9 s but demand higher-powered GPUs (e.g., NVIDIA Tesla V100, with 125 TOPS of computing power), whose hardware costs exceed three times those of this solution. Moreover, this framework dispenses with the need for large-scale dataset training, thus avoiding the sample dependency issues inherent in deep learning methods and rendering it more suitable for rapid deployment in industrial scenarios.