Fault diagnosis of driving gear in battery swapping system using heterospectral-symmetrized-derived point cloud feature tree

Abstract

The rack-and-pinion drive mechanism (RPD) is a critical transmission component in the battery swap system (BSS) of electric heavy trucks (EHTs). The transmission mechanism in the RPD typically operates under conditions of low speed, speed fluctuations, and short-term sampling, posing challenges for accurate fault diagnosis. To address these issues, this study proposes a fault diagnosis method based on the Heterospectral-Symmetric-Derived Point Cloud Feature Tree (HS-PCFT): First, multiple SDP (symmetric point pattern) variants are generated using Hybrid-dimensional vibration signals to construct multi-perspective symmetric patterns. Based on this, these images are converted into coordinate points and a structured point cloud feature tree is constructed to capture geometric differences across different fault modes. Subsequently, the point cloud is voxelized and input into a lightweight 3D convolutional neural network (3D CNN) for classification. The fault diagnosis algorithm was validated on the BSS platform, achieving an accuracy rate of 97.83%. Comparative studies indicate that the proposed method outperforms traditional 2D/3D networks and conventional machine learning methods. This research proposes an effective representation path from signals to structured geometry, providing an effective solution for fault diagnosis in low-speed and complex industrial environments.

Keywords

Battery swapping system fault diagnosis symmetrized dot pattern point cloud 3D CNN

Introduction

In recent years, electric heavy trucks (EHTs) have been widely used in high-frequency and high-intensity transportation scenarios, and their core advantage lies in their green energy drive and efficient operation capability. Compared with the traditional charging mode, the Battery Swapping System (BSS) plays a key role as a quick replenishment solution to ensure the continuous operation and operational efficiency of the vehicle. Among them, the drive mechanism widely adopts Rack and Pinion Drive (RPD) to complete the precise movement and positioning of the battery box, in which the drive gear is the core of the transmission, and its operation status directly affects the execution efficiency of the switching task and the stability of the system.

However, the RPD structure in the BSS operates for a long time under complex working conditions such as high-frequency reciprocating loads and electrical coupling disturbances, and is prone to mechanical wear under long-term loads, especially the active drive gear components are more prone to typical failures in the form of tooth-face abrasion, crack extension, and tooth breakage. These failures usually originate from the micro-discharge phenomenon induced by short-term potential fluctuations in the system,¹ as well as the accumulation of fatigue under long-term loading, resulting in tooth damage gradually evolving into functional failure.² Statistical data show that gear damage has become an important causative factor for the frequent occurrence of BSS failures, and if early and accurate identification cannot be realized, it will seriously affect the battery replacement efficiency and vehicle operation safety. Beyond reliability and safety, early identification of drivetrain degradation is also relevant to industrial noise and vibration management in swapping stations, as incipient defects may elevate vibration levels, promote structural transmission to surrounding assemblies, and potentially increase radiated noise and on-site vibration exposure during operation and maintenance.

Frequent gear failures not only affect the stability of system operation, but also put forward higher requirements for fault diagnosis. Driving gears face a series of diagnostic challenges in the typical working conditions of BSS: low rotational speed makes the effective fault characteristics weak, which is difficult to be effectively separated from the noise; control lag and load perturbation cause speed fluctuations, which leads to the characteristic frequency aliasing and characteristic drift; in addition, due to the limitations of the structure and actual working conditions of the battery exchange device, the collected vibration signals often have short-term sampling and local information loss problems, which makes it difficult to fully reflect the fault characteristics in the raw data. At the same time, some of the traditional feature extraction methods and single-scale model training strategy, in the low-speed, weak signal or speed perturbation of the complex conditions, feature differentiation ability and generalization performance still needs to be improved. For this reason, in recent years, researchers have explored multiple paths around the time-frequency modelling of vibration signals, map conversion and deep learning classification.

For the identification of low rotational speed signals, commonly used methods include acoustic emission techniques,³ local mean decomposition (LMD)⁴ and variational modal decomposition (VMD),⁵ which are used to enhance the local divisibility of weak signals; however, these methods are sensitive to ambient noise and parameter configurations, and have large computational overheads, which limit their real-time application capabilities. In the problem of discontinuous and short-time sampling, migration learning,⁶ sample expansion⁷ and sliding window strategy⁸ have been introduced to improve the diagnostic performance under small-sample conditions, but they are still susceptible to boundary effects and velocity perturbations, and there is a risk of pseudo-frequency interference. In terms of noise suppression, although decomposition and reconstruction methods (e.g., EEMD^{9
,} wavelet transform¹⁰) and adaptive deep networks (e.g., residual attention model¹¹) have certain denoising ability, they are more dependent on the size of the training samples and the design of the model, and it is difficult to cope with the interference of multi-source coupling.

For the problem of disordered spectral distribution under speed perturbations, order analysis¹² and time-frequency transformation¹³ provide possible solutions; however, their effectiveness at low speeds is constrained by limited frequency resolution and strong dependence on accurate speed-synchronization signals, which compromises practicality. To address these limitations, optimization-driven adaptivity has been increasingly explored to reduce parameter sensitivity and improve robustness under noisy and speed-perturbed conditions. Specifically, adaptive feature mode decomposition can be achieved via metaheuristic optimization guided by a health indicator,¹⁴ adaptive CNN performance can be improved through automatic hyperparameter tuning using amended gorilla troop optimization with quantum-gate mutation,¹⁵ and early weak-fault signatures can be enhanced by flow-direction-optimized spectral-kurtosis-based filtering.¹⁶ However, these studies mainly enhance adaptivity at the preprocessing or network-configuration stage and are still predominantly based on 1D/2D representations, leaving room for a more structured representation pathway to improve geometric separability under complex conditions. From this representation perspective, visual mapping methods such as Symmetrized Dot Pattern (SDP) have been introduced into fault mapping construction, which transforms one-dimensional vibration signals into two-dimensional structural images via polar-coordinate mapping and strengthens inter-class differences while preserving key temporal characteristics.

However, conventional SDP is still typically confined to single-channel, single-scale maps, which limits the diversity and robustness of feature representations across multiple operating conditions. For this reason, some studies have attempted to introduce modal decomposition (e.g., VMD¹⁷) or statistical fusion mechanisms (e.g., Chebyshev distance combined with EMD¹⁸) for multi-graph optimization, but the overall stability is still insufficient due to the accuracy of parameter selection and consistency of fusion strategies; in addition, parallel SDP,¹⁹ multi-channel fusion,^20,21 and holographic spectrum construction²² are other methods that enhance the ability of multi-source information expression, they are prone to local information loss or overfitting risk under high-dimensional structure.

Meanwhile, with the development of 3D structural modelling technology in the field of target recognition, 3D deep learning methods based on point cloud, view and voxel modelling have been gradually introduced into the intelligent diagnosis task of mechanical structures. PointNet²³ directly processes unstructured 3D point sets with efficient geometric modelling capability; MVCNN²⁴ improves the model’s adaptability to attitude changes through multi-view image fusion; and VoxNet²⁵ uses the 3D convolutional grid structure combined with 3D convolutional operations to achieve local feature modelling of spatial structures. Although the above methods perform well in the target classification task, there are still some bottlenecks in their feature characterization ability in scenarios oriented to complex working conditions in mechanical failures.

For the problem of weak signal features of rack and pinion structure under low-speed working conditions, this paper integrates multiple SDP images to construct point cloud structure, and enhances the feature expression with the difference of petal density; in order to cope with the feature instability caused by the fluctuation of rotational speed, this paper design multiple SDP image layers with different parameters to express different feature dimensions, so as to improve the stability and robustness of the features; In the face of short sampling and noise interference problems, the combination of difference map construction and 3D convolutional extraction strategy is used to realize the effective extraction of structural features and interference suppression. In summary, this paper proposes a fault identification method based on point cloud feature tree and 3D convolutional network, which shows good adaptive ability and classification performance in terms of saliency enhancement of weak features, feature stability preservation under speed perturbation, and robustness suppression of noise interference.

The contributions and innovations of this paper are as follows:

(1) Aiming at the problem of weak fault signals of the rack and pinion structure of the battery switching system under low-speed conditions, this paper fuses multiple SDP images to construct a three-dimensional point cloud structure, preserves the diversity of petal densities, and realizes the diversified expression and reinforcement of fault features, which improves the recognition ability of fault modes under low-speed conditions.

(2) Aiming at the problem of feature stability degradation caused by rotational speed fluctuation in the battery exchange process, this paper constructs a three-dimensional point cloud structure for the joint expression of multi-scale SDP maps, which fuses the geometric distribution information at different scales and enhances the stability and robustness of the feature expression under the speed fluctuation.

(3) For the weakening of effective features caused by complex noise interference and short sampling, this paper realizes the fusion expression of multi-map information on the unified point cloud structure through differentiated multiple representations and 3D convolution module, which improves the anti-interference ability of the model.

The structure of the remaining part of this article is as follows: The Fault diagnosis scheme elaborates on the fault diagnosis methods in detail, including the point cloud feature tree method constructed based on SDP variants, point cloud voxelization preprocessing, and 3D CNN structure design. The Case study is based on the vibration data of the driving gears of the rack and pinion transmission devices in the battery swap system of four modes, presents the training and diagnosis results, and verifies the effectiveness of the proposed method. Through Comparative case studies analysis, the performance advantages of the proposed method under complex working conditions were verified. The Conclusion of this study is presented at the end.

Fault diagnosis scheme

In this study, a 3D point cloud feature tree fault diagnosis scheme based on multi-source mapping structure is constructed for the typical operating states and fault modes of driving gears in BSS, as shown in Figure 1. The overall process consists of three parts: signal atlas construction, spatial structure modelling and 3D feature recognition. Among them, the signal atlas construction is based on a variety of SDP improvement methods to encode the gear vibration signals with symmetric graphs, aiming to reinforce the differences in geometric distribution under different fault states. In the map construction, single-channel and multi-channel hybrid strategies are used: for the method based on unidirectional response modelling, the vertical (V-direction) vibration signals are uniformly used as inputs to ensure the consistency of the signal source and the sensitivity to the fault features; while for the SDP variants with multi-channel fusion mechanisms, such as the Parallel-SDP, M-SDP and multi-source map fusion strategies, vertical is introduced, Horizontal and Axial (V+H+A) three-channel signals are jointly constructed to enhance the expressive integrity of spatial features and structural discrimination. This hybrid strategy is based on the intrinsic differences in the compositional mechanisms of each method, and aims to extract discriminative features that coexist with structural significance and pattern diversity. Subsequently, all the generated images are uniformly converted to polar coordinate point sets and stacked along the Z-axis in the order of methods to construct a hierarchical point cloud feature tree structure. On this basis, the point cloud is mapped into a 3D raster by voxelization, and then a lightweight 3D convolutional neural network (3D CNN) carries out multi-layer convolution and feature extraction to achieve highly robust classification and identification of the gear operating state. This method effectively improves the diagnosis accuracy and stability under low-speed disturbance and complex background.

Figure 1.

Flowchart of fault diagnosis method.

Point cloud feature tree construction based on SDP variants

In order to realize high-precision fault diagnosis of gears under low-speed and non-stationary interference conditions, this paper proposes a 3D point cloud feature tree method that integrates multiple Symmetrized Dot Pattern (SDP) variants. The method takes the original vibration signal as input, uses single-channel (vertical V-direction) or multi-channel (A/H/V) strategy to construct multiple SDP maps, obtains the structural coordinate points through polar coordinate mapping, and stacks them along the Z-axis according to a unified hierarchical strategy to form a 3D spatial point cloud $P$ , which is ultimately used as the input for the depth model.

The input signal consists of a single-channel vibration signal $s (t)$ and a three-channel vibration signal $s_{c} (t)$ , where $c \in {A, H, V}$ represents the vertical, horizontal, and axial channels, respectively. Each SDP variant is mapped in polar coordinates to produce a 2D point $(x_{i}^{(j)}, y_{i}^{(j)})$ . The subscript $j$ indicates that the point is from the $j$ -th SDP map variant. After mapping, the three-dimensional point cloud structure is constructed in a uniform manner as follows:

z_{j} = j \cdot z_{gap}, j = 0, 1, \dots, 6

(1)

where

z_{g a p}

is the inter-layer vertical distance parameter used for hierarchical stacking of different SDP maps in space to ensure that the output of the feature method can be uniformly encoded into a uniform space.

1. Original SDP graph (single channel). This approach provides the mapping basis for all SDP variants, generating rotationally symmetric 2D polar coordinate maps from single-channel signals using the following mapping equation²⁶:

r_{i}^{(0)} = \frac{s (i) - s_{\min}}{s_{\max} - s_{\min}}

(2)

θ_{i}^{(0)} = θ_{0} + s (i + l) \cdot \frac{g}{s_{\max} - s_{\min}}

(3)

x_{i}^{(0)} = r_{i}^{(0)} \cos (θ_{i}^{(0)}), y_{i}^{(0)} = r_{i}^{(0)} \sin (θ_{i}^{(0)})

(4)

Where:

s (i)

is the

i

-th sampling point of the original signal;

l

is the delay factor;

g

is the angular amplification coefficient;

θ_{0}

is the starting angle of the mirror symmetry axis;

s_{\max}, s_{\min}

is the upper and lower normalization limit.

2. VMD-SDP graph (single channel). The method first performs a variational modal decomposition (VMD) on a single-channel signal $s (t)$ to extract a number of dominant modal components $I M F_{k} (t)$ . The optimization objective is to minimize the sum of the bandwidths of all modal signals²⁷:

\min_{{I M F_{k}}, {ω_{k}}} \sum_{k} {‖ \partial_{t} [(δ (t) + \frac{j}{π t}) * I M F_{k} (t) e^{- j ω_{k} t}] ‖}_{2}^{2}

(5)

To ensure a principled determination of the modal number

K

, an adaptive stopping strategy is adopted prior to SDP mapping. Starting from a small initial value,

K

is progressively increased. For each candidate

K

, the reconstructed signal is

\hat{s} (t) = \sum_{k = 1}^{K} I M F_{k} (t)

(6)

The normalized reconstruction residual is then defined as

ε (K) = \frac{∥ s (t) - \sum_{k = 1}^{K} I M F_{k} (t) ∥_{2}}{∥ s (t) ∥_{2}} .

(7)

In this study, the residual threshold is set to

ε_{0} = 0.03

, and the frequency-separation tolerance is defined as

δ = 0.10 ω_{\max}

, where

ω_{\max}

denotes the maximum absolute center frequency. The decomposition is terminated when either

ε (K) \leq ε_{0}

or the minimum adjacent frequency separation satisfies

| ω_{k} - ω_{k - 1} | \leq δ

Applying this criterion to the dataset yields a concentrated distribution of selected modes (median $K$ = 6, mean $K$ = 6.06, with $K \in [4, 8]$ ). Therefore, $K$ = 6 is adopted as a representative value for the VMD-SDP construction to maintain consistent feature representation across samples.

Each modal component is then treated separately using the original SDP mapping:

r_{i, k}^{(1)} = \frac{I M F_{k} (i) - \min I M F_{k}}{\max I M F_{k} - \min I M F_{k}}

(8)

θ_{i, k}^{(1)} = θ_{0} + I M F_{k} (i + l) \cdot \frac{g}{\max I M F_{k} - \min I M F_{k}}

(9)

x_{i, k}^{(1)} = r_{i, k}^{(1)} \cos (θ_{i, k}^{(1)}), y_{i, k}^{(1)} = r_{i, k}^{(1)} \sin (θ_{i, k}^{(1)})

(10)

All IMF modal points are plotted together in a single SDP diagram, forming multiple “petals”.

3. VMD-MultiSDP graph (single channel). With the help of each modal point set $(x_{i, k}^{(1)}, y_{i, k}^{(1)})$ generated by VMD-SDP, this paper further employs Gaussian smoothing to enhance each modal scale expression:

\begin{array}{l} x_{i, k}^{(2)} = x_{i, k}^{(1)} * G_{σ_{k}}, y_{i, k}^{(2)} = y_{i, k}^{(1)} * G_{σ_{k}} \\ σ_{k} = α \cdot std ({IMF}_{k}) \end{array}

(11)

where

G_{σ_{k}}

denotes the Gaussian smoothing corresponding to the standard deviation

σ_{k}

applied to the point cloud after IMF mapping to enhance the robustness of the scale features. Finally, the multiscale 2D point set is constructed as:

P^{(2)} = \cup_{k = 1}^{M} {(x_{i, k}^{(2)}, y_{i, k}^{(2)})}

(12)

A separate SDP map is generated for each IMF modality, which corresponds to multiple images in total for multi-scale feature separation.

4. Parallel-SDP graph (multi-channel). Apply the base SDP mapping to each of the three channel signals $s_{c} (t) (c = V, H, A)$ and set different initial angles $θ_{0}^{(c)}$ , e.g. $0 °, 120 °, 240 °$ , to form a three-channel unified map:

r_{i, c}^{(3)} = \frac{s_{c} (i) - s_{\min}^{(c)}}{s_{\max}^{(c)} - s_{\min}^{(c)}}

(13)

θ_{i, c}^{(3)} = θ_{0}^{(c)} + s_{c} (i + l) \cdot \frac{g}{s_{\max}^{(c)} - s_{\min}^{(c)}}

(14)

x_{i, c}^{(3)} = r_{i, c}^{(3)} \cos (θ_{i, c}^{(3)}), y_{i, c}^{(3)} = r_{i, c}^{(3)} \sin (θ_{i, c}^{(3)})

(15)

5. MVMD-SDP graph (multi-channel). The MVMD decomposition is performed for each channel $s_{c} (t)$ to produce the modal component $I M F_{c, k} (t)$ , which is then mapped in the same way as VMD-SDP:

r_{i, c, k}^{(4)} = \frac{I M F_{c, k} (i) - \min I M F_{c, k}}{\max I M F_{c, k} - \min I M F_{c, k}}

(16)

θ_{i, c, k}^{(4)} = θ_{0} + I M F_{c, k} (i + l) \cdot \frac{g}{\max I M F_{c, k} - \min I M F_{c, k}}

(17)

x_{i, c, k}^{(4)} = r_{i, c, k}^{(4)} \cos (θ_{i, c, k}^{(4)}), y_{i, c, k}^{(4)} = r_{i, c, k}^{(4)} \sin (θ_{i, c, k}^{(4)})

(18)

6. MCSDP graph (multi-channel). The three-channel SDP mapping point sets $(x_{i, c}^{(3)}, y_{i, c}^{(3)})$ are first generated separately, and then the discrete image response is constructed:

I_{c} (x, y) = \sum_{i} α_{i, c} δ (x - x_{i, c}^{(3)}, y - y_{i, c}^{(3)})

(19)

Fusion of channel mapping by:

I_{fusion} (x, y) = \max_{c \in {V, H, A}} I_{c} (x, y)

(20)

Finally, the fused non-zero pixel locations are mapped to a 2D point set:

P^{(5)} = {\begin{cases} (x, y) & I_{fusion} (x, y) > 0 \end{cases}}

(21)

In addition to the max-based fusion in equation (20), alternative averaging-based strategies were also evaluated in the experimental section for completeness.

7. Holographic SDP map (multi-channel). For each channel $s_{c} (t)$ , the time-domain signal $s_{c, 1} (t)$ and the frequency-domain signal $s_{c, 2} (t)$ are extracted and polar mapping is applied separately:

r_{i, c, m}^{(6)} = \frac{s_{c, m} (i) - \min s_{c, m}}{\max s_{c, m} - \min s_{c, m}}

(22)

θ_{i, c, m}^{(6)} = θ_{0}^{(c, m)} + s_{c, m} (i + l) \cdot \frac{g}{\max s_{c, m} - \min s_{c, m}}

(23)

x_{i, c, m}^{(6)} = r_{i, c, m}^{(6)} \cos (θ_{i, c, m}^{(6)}), y_{i, c, m}^{(6)} = r_{i, c, m}^{(6)} \sin (θ_{i, c, m}^{(6)})

(24)

Hierarchical determination of SDP variants

In order to avoid arbitrary stacking of different SDP variants along the Z-axis, a data-driven hierarchical determination strategy is adopted.

For the $j$ -th SDP variant, the mapped two-dimensional point set of the $i$ -th sample is denoted as $(x_{i}^{(j)}, y_{i}^{(j)})$ .

The spatial expansion of this variant on that sample is quantified as:

Δ x_{i}^{(j)} = \max (x_{i}^{(j)}) - \min (x_{i}^{(j)})

(25)

Δ y_{i}^{(j)} = \max (y_{i}^{(j)}) - \min (y_{i}^{(j)})

(26)

and the corresponding expansion radius is defined as

R_{i}^{(j)} = \sqrt{{(Δ x_{i}^{(j)})}^{2} + {(Δ y_{i}^{(j)})}^{2}}

(27)

To ensure robustness against sample-specific fluctuations and outliers, the final expansion score of the $j$ -th SDP variant is calculated using the median value over all samples:

R^{(j)} = {median}_{i} (R_{i}^{(j)})

(28)

All SDP variants are sorted in ascending order of $R^{(j)}$ , and the stacking index $j$ in the constructed 3D point cloud is assigned according to this order. Variants with more compact spatial distributions are placed at lower layers, while those with more diffuse structures are stacked at higher layers.

Integrate the 2D point sets generated by all variants and uniformly assign spatial hierarchies, and finally construct the 3D point cloud feature tree $P$ :

P = \cup_{j = 0}^{6} {(x_{i}^{(j)}, y_{i}^{(j)}, z_{j}) ∣ i = 1, \dots, N_{j}}, z_{j} = j \cdot z_{gap}

(29)

This construction ensures that all variant mapping outputs are fused and form a continuous, unified spatial structure that provides a reliable basis for subsequent voxelized coding with 3D convolutional network inputs.

Voxel-based feature encoding and 3D CNN classification

In order to further extract the spatial structure information in the point cloud feature tree and realize the recognition of gear multi-category patterns, this paper adopts the voxelization method to transform the point cloud feature tree into a regular tensor structure, and constructs a three-dimensional convolutional neural network (3D CNN) model to carry out the in-depth feature extraction and classification discrimination on the voxel data. The overall process mainly includes the following two steps:

Voxelization preprocessing method for point clouds

Since point cloud data is essentially an unstructured representation, if the original dense point set is directly used as the input to the 3D convolutional neural network, it will lead to high data dimensionality and serious structural redundancy, which is not conducive to the training and inference of the deep model. The voxel structure, on the other hand, can effectively portray the distribution pattern of 3D objects in space, with the advantages of strong regularity and easy to analyse and store. Therefore, the point cloud data need to be converted into regularized voxel grid representation before feeding into the 3D CNN network.

In this paper, we adopt a binary voxel occupancy grid to discretize the point cloud into a sparse regular tensor. The voxel state is defined in binary form: if a voxel cell contains at least one point, it is considered as a “non-empty voxel” with a value of 1; otherwise, it is considered as an “empty voxel” with a value of 0. This encoding facilitates the mapping of the original point cloud structure into a sparse regular tensor. To further examine the influence of voxel filling strategies on feature representation, alternative density-based and intensity-based voxel encodings are also implemented and evaluated in the experimental section, while keeping the voxel resolution and network configuration unchanged.

After the construction of the 3D point cloud feature tree $P$ (where the points are shaped like $(x_{i}^{(j)}, y_{i}^{(j)}, z_{j})$ ), the next step is to map these discrete coordinates to the 3D raster space. To this end, a voxel coordinate system²⁸ is constructed before voxel subdivision: let $(x_{\min}, y_{\min}, z_{\min}) = \min_{(x, y, z) \in P} (x, y, z)$ be the smallest boundary point of the entire point cloud, and let the voxel edge length be $L$ . Then, for any point $(x_{i}^{(j)}, y_{i}^{(j)}, z_{j}) \in P$ , its corresponding voxel index $(I, J, K)$ can be calculated by the following formula:

{\begin{cases} I = INT (\frac{x_{i}^{(j)} - x_{\min}}{l}) \\ J = INT (\frac{y_{i}^{(j)} - y_{\min}}{l}) \\ K = INT (\frac{z_{j} - z_{\min}}{l}) \end{cases}

(30)

where

INT

denotes downward rounding. With the above formula, each 3D feature point can be correctly quantized to voxel coordinates and organized into 3D indexed form for subsequent voxelized input to the 3D convolutional neural network.

3DCNN structural design

Aiming at the 3D tensor input after point cloud feature tree voxelization, this paper designs a 3D CNN based on the improved structure of VoxNet for accomplishing deep feature extraction and classification discrimination in different modes. As shown in Figure 2, the overall structure of the model consists of three sets of convolutional pooling modules, a global average pooling layer, and two layers of fully connected networks, forming an end-to-end discriminative process from feature extraction to classification output.

Figure 2.

3D CNN network architecture.

The three-layer convolution module in the front-end of the network is used to extract local structure, regional features and global semantic information, respectively. Among them, the first convolutional module captures the local edges and symmetric distributions in the point cloud, the second module further refines the structural correlations between spatial regions, and the third module focuses on the higher-order features after multi-scale fusion. Each convolutional layer adopts a 3×3×3 kernel size, and is coupled with batch normalization and ReLU nonlinear activation function to enhance the expressive capability. The pooling operation adopts the maximum pooling strategy to gradually compress the spatial dimension and improve the discriminative and anti-interference properties of the feature map.

After convolutional extraction, each channel is compressed into a single statistic using global average pooling (GAP) to reduce the number of parameters and enhance feature stability. This process outputs fixed-length vectors as inputs to the classification subnetwork. The fully connected module consists of two linear layers, where the output dimension of the first layer is set to 128 and a Dropout mechanism is introduced to alleviate the overfitting problem under small sample conditions. The final classification layer uses a Softmax activation function and outputs four-dimensional vectors corresponding to the four states of the rack and pinion structure: normal, unilateral tooth wear, bilateral tooth wear and tooth broken. The overall network has strong spatial feature modelling capability while maintaining a lightweight structure, providing a stable deep representation base for subsequent classification training.

In the model training phase, the loss function is used to guide the gradual update of network parameters. In this paper, the cross-entropy loss function $L$ is used to measure the difference between the predicted distribution and the true label, which is defined as follows:

L = - \frac{1}{m} [\sum_{a = 1}^{m} {\hat{y}}_{a} \ln \frac{\exp (v_{a})}{\sum_{b = 1}^{n} \exp (v_{b})}]

(31)

where

m

denotes the number of training samples,

n

is the total number of categorized categories,

{\hat{y}}_{a}

is the true label of the

a

-th sample,

v_{a}

is the predicted log-odds value of the corresponding category, and

v_{b}

denotes the network output of all categories on the current sample.

In order to achieve an efficient gradient update process, this paper adopts the Adam optimization algorithm to iteratively optimize the network parameters. The algorithm is able to adaptively adjust the learning rate of different parameters and performs stably when dealing with non-smooth targets and sparse gradients, which helps to improve the convergence speed and overall performance of network training.

Case study

Experiment and sample description

In order to verify the effectiveness of the proposed fault diagnosis method and simulate the actual operating conditions of the rack and pinion structure (Rack and Pinion Drive, RPD) in the battery switching system of the electric heavy trucks (EHTs), a dedicated experimental platform was built in this study as shown in Figure 3. The platform is driven by a servomotor with a rotational speed of 3000 RPM, which is combined with a 16:1 ratio reducer to drive the main gear (24 teeth) to drive the pinion gear (20 teeth), realizing the reciprocating linear operation of the platform along a 2100 mm track. The complete travel cycle is about 6.3s, including acceleration, quasi-uniform speed and deceleration phases, of which the quasi-uniform speed phase lasts about 1s, and the speed of the active gear is stabilized at 170-190 RPM.

Figure 3.

Structure of the test bench.

The condition monitoring system consists of triaxial vibration accelerometers mounted in the vertical, horizontal and axial channels of the support structure and Hall effect velocity sensors, which are located above the active gears for simultaneous acquisition of velocity disturbances and vibration characteristics. The sampling frequency is set to 20 kHz and the signals are intercepted at a quasi-uniform phase, with a single sample length of 20,000 points, for a total of four channels of data, including vibration signals and velocity signals in all three directions.

The platform introduces three typical gear failure modes: unilateral tooth wear, bilateral tooth wear and tooth broken, and uses the normal condition as a control. All failures are prepared by high-precision machining to ensure controllable defects. To exclude assembly errors, non-fault variables (e.g., critical phase and tightening torque) were kept consistent. A total of 151 sets of samples were collected in the experiment, covering four operating states, and for each mode, the samples were divided into training samples and test samples, and the specific distribution of the samples is shown in Table 1.

Table 1.

Description of training and test samples.

Pattern (Abbreviation)	Labeled sample set	Testing data sample
Normal (NM)	1∼17	1∼8
Unilateral tooth wear (UTW)	18∼38	9∼17
Bilateral tooth wear (BTW)	39∼71	18∼30
Tooth broken (TB)	72∼106	31∼45

Geometric feature representation and point cloud tree construction

On the basis of clarifying the construction mechanism of the point cloud feature tree, this paper further verifies the geometric performance differences of the structure under different failure modes with experimental data to support the feasibility and interpretability of its classification and identification. In order to characterize the geometric distribution of signals under different gear states, this paper fuses 11 layers of image features generated by different SDP mapping methods, and performs unified coordinate extraction and spatial fusion processing for each sample, and finally constructs a 3D point cloud feature tree with a hierarchical structure.

Multi-SDP feature mapping and visualization

To comprehensively capture the geometric differences of vibration signals under different failure modes, this paper constructs a collection of graph methods composed of 11 layers of SDP methods, and performs multi-view mapping and unified coordinate extraction operations on each sample. Specifically, based on the method framework defined by the Fault diagnosis scheme, salient point extraction is performed on the symmetrical images generated for each SDP variant respectively, and they are uniformly converted into normalized two-dimensional Cartesian coordinates. This processing procedure ensures that the coordinate points from different graph sources have geometric consistency and center alignment characteristics, providing a foundation for the subsequent construction of multi-level point cloud structures.

In order to further enhance the interpretability of the intermediate process and to visualize the differences in the mapping structure of each SDP method among different modes, five representative SDP methods (including SDP, VMD-SDP, VMD-MultiSDP, MVMD-SDP, and Holographic-SDP) are selected in this paper and the mapping morphology is comparatively visualized under four types of typical modes (NM, UTW, BTW, TB) under four typical modes are visualized for comparison. The morphology of the map contains geometrical features such as the number of petals, density distribution, symmetry structure and edge contour, and its morphological changes clearly reveal the effects of different categories of modes on the structural perturbations triggered by the original vibration signals with respect to the distribution characteristics of the modes.

Table 2 shows the spectral visualization matrix of the 5×4 structure, with each row corresponding to an SDP spectral generation strategy and each column representing a pattern category. It can be observed that under normal conditions (NM), all types of SDP maps exhibit high symmetry and petal balance. However, as the severity of the fault increases (e.g., tooth broken TB), the symmetry of the image is significantly disrupted, the number of petals decreases, their density becomes concentrated, or obvious structural distortions occur. This trend validates the good distinguishability of the multi-source SDP perspective at the image level and provides a solid geometric foundation for the subsequent construction of a three-dimensional point cloud feature tree.

Table 2.

Comparison of SDP feature-based visualization for different failure modes.

Pattern/SDP method	NM	UTW	BTW	TB
SDP
VMD-SDP
VMD-MultiSDP/(IMF3)
MVMD-SDP
Holographic-SDP

Layered fusion and point cloud tree formation

In order to achieve the unified fusion of multi-view mapping, based on the construction logic of the Fault diagnosis scheme in this paper, hierarchical mapping operations are performed on all samples: the 2D point set $(x_{i}, y_{i})$ extracted by method $j$ is added with height markers $z_{j} = j \cdot z_{gap}$ to form the final 3D point cloud $(x_{i}, y_{i}, z_{j})$ . This approach realizes the orderly fusion of multiple viewpoint features structurally and preserves the geometric distribution characteristics of each type of method at the spatial level.

To validate the expression differences of the constructed point cloud feature tree under different modes, Figure 4 shows the point cloud structure visualization results of four typical operating conditions. It can be observed that there are significant differences among the modes in terms of point cloud density distribution, spatial hierarchical structure, and symmetry morphology: the normal mode exhibits a symmetrical and balanced morphology overall, with compact and clear petal layers; the unilateral tooth wear mode exhibits non-uniform density changes in the upper region, showing slight shifts and interlayer fractures; bilateral tooth wear further exacerbates these differences, with the point cloud exhibiting a bimodal distribution trend; and the tooth broken mode exhibits significant asymmetry and high-density concentrated distribution, particularly in the middle and upper layers, where numerous dense cluster structures are evident.

Figure 4.

Comparison of point cloud feature tree structures under different modes.

These structural differences reveal that different patterns exhibit distinct spectral response characteristics under a multi-source SDP perspective, validating the effectiveness of point cloud feature trees in structurally expressing geometric information. This provides a stable and interpretable geometric foundation for subsequent voxelization and 3D convolution processing.

Voxelization mapping

To feed the constructed point cloud feature tree into the deep convolutional model, it is necessary to convert its unstructured point set representation into a regular 3D tensor. In this paper, we directly adopt the voxelization process defined in the Fault diagnosis scheme: converting the normalized point set into a sparse binary (0-1) voxel tensor to provide structured input suitable for three-dimensional convolutional neural networks. In the subsequent experiments, this paper selected two commonly used voxel resolutions, 32³ and 64³, as input configurations; The sensitivity of these parameters will be analyzed in detail in the subsequent parameter selection and sensitivity analysis.

Training and diagnostic results

Training settings

In order to verify the performance of the designed three-dimensional convolutional neural network (3D CNN) model in the fault identification task, this paper conducts systematic training and verification of the network. The model structure has been described in detail in 3D CNN structural design. This section mainly describes the specific parameter Settings and implementation process in the training stage.

The Adam optimizer was used during training, with an initial learning rate set to 1×10⁻⁴, a maximum number of iterations set to 50, and a batch size set to 16. In terms of sample division, each category of pattern samples was randomly divided into a training set and a validation set at a ratio of 7:3, and category weights were introduced to mitigate the bias caused by imbalance. To enhance training stability and avoid overfitting, the Dropout mechanism is introduced during training. Unless otherwise specified, results are reported from a single run under the fixed split; the robustness to stochastic training effects is further examined in the subsequent ablation and robustness analyses.

Evaluation indicators

In order to comprehensively measure the classification performance of the model, this paper introduces four commonly used metrics: Accuracy, Precision, Recall and F1-score. The definitions are as follows:

A = \frac{T_{P} + T_{N}}{T_{P} + F_{P} + T_{N} + F_{N}}

(32)

P = \frac{T_{P}}{T_{P} + F_{P}}

(33)

R = \frac{T_{P}}{T_{P} + F_{N}}

(34)

F_{1} = 2 \times \frac{P \times R}{P + R}

(35)

Among them, $T_{P}$ , $T_{N}$ , $F_{P}$ , and $F_{N}$ denote the true, true negative, false positive, and false negative categories, respectively. The classification accuracy $A$ reflects the overall prediction accuracy, while the accuracy $P$ and the completeness $R$ assess the prediction accuracy and coverage of the model for the positive categories, respectively, and the $F_{1}$ -score, as the reconciled mean of the two, provides a more robust evaluation basis under the scenario of slightly unbalanced samples.

Ablation study on multi-channel fusion

To evaluate the effectiveness of the fusion strategy in equation (20), we compared the original pixel-wise max fusion with channel-wise mean fusion and energy-based weighted average fusion. All experiments were conducted under the same fixed data split, identical HS-PCFT construction, and identical 3D CNN training configuration. Since the differences among fusion operators primarily manifest at the response magnitude level prior to discretization, the comparison was performed using the intensity-based voxel representation to preserve amplitude variations introduced by different fusion mechanisms. As verified in the voxelization analysis, binary and intensity representations yield comparable classification performance; therefore, this setting does not alter the overall methodological conclusion.

As summarized in Table 3, the max fusion achieves 97.17 ± 1.79 accuracy (Macro-F1: 0.9703 ± 0.0159), outperforming mean (89.35% ± 3.47%) and weighted fusion (87.61% ± 2.06%). Averaging-based strategies tend to smooth localized high-response geometric structures, whereas the max operation preserves the most salient channel responses, leading to more discriminative 3D feature representations. These observations support the effectiveness of the max-based fusion mechanism in the proposed MCSDP graph.

Table 3.

Comparison of different multi-channel fusion strategies.

Fusion strategy	Accuracy/%	Macro-F1
Max	97.17 ± 1.79	0.9703 ± 0.0159
Mean	89.35 ± 3.47	0.8472 ± 0.0700
Weighted	87.61 ± 2.06	0.8392 ± 0.0392

Stacking-order sensitivity analysis

In addition to voxel size and inter-layer distance $z_{gap}$ , the HS-PCFT framework involves the stacking order of SDP variants along the Z-axis, which determines the assignment of the stacking index $j$ in equation (29). To evaluate whether the stacking order significantly influences the 3D CNN feature learning process, a controlled sensitivity experiment was conducted. Under fixed conditions (32³ voxel resolution, $z_{gap}$ = 0.2, identical network architecture, hyperparameters, and training/validation split), only the mapping between SDP variants and the stacking index $j$ was altered. Three strategies were compared: the proposed data-driven order, the reverse order, and 10 random permutations.

Table 4 shows that the proposed data-driven stacking order achieved the highest validation accuracy and Macro-F1. Reversing the hierarchy resulted in a performance decrease of 2.18% in accuracy, indicating that spatial organization along the Z-axis is not arbitrary. Across 10 random permutations, the average accuracy was 96.74% with a standard deviation of 1.15%. These results suggest that while the 3D CNN exhibits a certain degree of robustness to stacking variations, the proposed hierarchical strategy provides consistently strong and stable performance.

Table 4.

Stacking-order sensitivity analysis under fixed 32³ voxelization and $z_{gap}$ = 0.2

Stacking strategy	Accuracy/%	Macro-F1
Proposed (current)	97.83	0.9767
Reverse	95.65	0.9533
Random (mean ± std,n = 10)	96.74 ±1.15	0.9645 ±0.0129

Effect of voxel filling strategies

To investigate whether richer voxel encoding can improve the discriminative capability of the proposed HS-PCFT representation, we compare three voxel filling strategies, including the binary occupancy grid adopted in this study, a density-based encoding, and an intensity-based encoding. The voxel resolution, inter-layer spacing, fixed train/validation split, network architecture, and training hyperparameters are kept identical for a fair comparison. To account for stochastic effects, each configuration is trained for $R$ = 10 independent runs, and mean ± standard deviation are reported.

The comparison in Table 5 shows that the density-based representation consistently degrades performance, whereas the intensity-based representation achieves an accuracy comparable to the binary occupancy grid but does not provide a clear improvement in either mean performance or stability. A possible explanation is that density values are more sensitive to local point accumulation and perturbations, which may amplify noise-induced variations and increase sparsity-related instability in high-dimensional voxel space. In contrast, the binary occupancy grid emphasizes structural topology and provides a parsimonious and robust representation. Therefore, the binary occupancy grid is retained as the default voxelization scheme in this work, and the density/intensity variants are reported as an ablation study to demonstrate robustness to voxel filling choices.

Table 5.

Comparison of voxel filling strategies (grid size 32³, $z_{gap}$ = 0.2, fixed split $R$ = 10 repeated trainings).

Voxel filling strategy	Accuracy/%	Macro-F1
Binary occupancy (0/1)	97.17 ±1.79	0.9703 ±0.0159
Density-based (normalized point count)	89.13 ±2.05	0.8878 ±0.0195
Intensity-based (avg. Normalized radial magnitude)	96.52 ±2.10	0.9614 ±0.0223

Effect of order-tracking preprocessing

To further examine whether low-speed conditions may cause spectral smearing, we introduce a conventional order-tracking (OT) preprocessing stage as a front-end ablation. Specifically, the tachometer-measured instantaneous speed $v (t)$ (RPM) is converted into angular position via numerical integration, and the vibration signals are resampled onto a uniform angular grid with a fixed length. The OT-preprocessed signals are then fed into the same HS-PCFT construction (including the same SDP-variant set and data-driven stacking rule), voxelization setting (binary occupancy, 32³, $z_{gap}$ = 0.2), and 3D CNN classifier. To ensure fairness, we keep the train/validation split and all training hyper-parameters unchanged and report mean ± std results over $R$ = 10 repeated trainings.

As shown in Table 6, OT preprocessing does not improve performance; instead, it leads to a consistent decrease in both accuracy and Macro-F1. This suggests that the discriminative cues captured by HS-PCFT are not merely due to speed-fluctuation-induced frequency smearing that OT aims to compensate. OT relies on angular resampling and tends to emphasize quasi-stationary order components, which may distort or attenuate short-duration transient signatures and the geometric distribution patterns preserved across SDP variants. Therefore, HS-PCFT differentiates fault-related transients from inherent speed non-stationarity primarily through its multi-variant geometric encoding and 3D spatial fusion, rather than depending on conventional order-tracking compensation.

Table 6.

Influence of OT preprocessing (fixed split, $R$ = 10).

Pipeline	Accuracy/%	Macro-F1
HS-PCFT (raw signals)	97.17 ± 1.79	0.9703 ± 0.0159
OT → HS-PCFT	93.91 ± 1.37	0.9286 ± 0.0158

Influence of network depth

To verify whether the relatively shallow 3D CNN architecture with global average pooling is sufficient to capture high-level semantic features, we conduct a depth ablation study. Three variants are evaluated under identical settings (same HS-PCFT representation, voxelization configuration, fixed train/validation split, and $R$ = 10 repeated trainings): (i) a shallow model (original architecture with three convolutional blocks), (ii) a medium model with one additional convolutional block, and (iii) a deeper model with two additional convolutional blocks. All other hyper-parameters remain unchanged to ensure a fair comparison.

The results in Table 7 indicate that increasing network depth yields a moderate performance improvement (approximately 1–1.3% in accuracy from shallow to deep). However, the shallow model already achieves strong performance (above 97% accuracy), suggesting that the proposed HS-PCFT representation effectively encodes discriminative geometric information even with a lightweight backbone. The relatively small performance gap among the three variants further implies that the diagnostic capability primarily stems from the feature representation rather than excessive network depth. Considering the limited dataset scale (151 samples), the shallow architecture strikes a favorable balance between model capacity and generalization. When larger-scale datasets are available, the HS-PCFT voxel representation can be seamlessly integrated with more expressive backbones such as 3D-ResNet or sparse 3D CNNs, indicating good scalability of the proposed representation framework.

Table 7.

Depth ablation of the 3D CNN backbone ( $R$ = 10, fixed split).

Model	Accuracy/%	Macro-F1
Shallow (3 conv)	97.17 ± 1.47	0.9703 ± 0.0159
Medium (+1 conv)	98.04 ± 0.69	0.9798 ± 0.0071
Deep (+2 conv)	98.48 ± 1.47	0.9835 ± 0.0157

Parameter selection and sensitivity analysis

In the process of constructing point cloud feature trees and encoding 3D voxels, the selection of key parameters has a significant impact on the model performance. To further validate the robustness and sensitivity of the proposed diagnostic model to different feature expression parameters, this paper focuses on analysing the influence of two key parameters on the model classification effect: one is the different voxel mesh sizes; and the other is the interlayer spacing parameter $z_{gap}$ when constructing the point cloud feature tree.

The voxel grid resolution affects how finely the point-cloud structure is represented in the 3D tensor. A finer grid (e.g., 64³) can preserve more geometric details, but it also increases computational overhead and may aggravate overfitting under limited data. Therefore, two commonly used resolutions, 32³ and 64³, are selected for comparison in this study. On the other hand,

z_{gap}

reflects the inter-layer spacing of different SDP variants in constructing the point cloud feature tree. Too small a spacing may lead to too much overlap between image layers and interfere with the spatial structure expression; while too large a spacing may weaken the coupling relationship between SDP layers and lead to the separation of upper and lower layer features. Therefore, three settings of

z_{gap}

= 0.01, 0.2 and 0.4 are selected in this paper, and combined with the voxel size variation for comprehensive comparison. The classification accuracy of the model under each parameter combination is shown in Table 8.

Table 8.

Comparison of model classification accuracy for different combinations of voxel size and interlayer spacing.

Voxel size	z__gap	Non-zero voxel ratio/%	Accuracy/%
64×64×64	0.01	5.69	92.24
32×32×32	0.2	15.34	97.83
64×64×64	0.2	5.69	95.65
32×32×32	0.4	15.34	93.76

As can be seen from Table 8, taking accuracy and computational efficiency into account, the model performs optimally under the combination of $z_{gap}$ = 0.2 and voxel size of 32³, and the classification accuracy reaches 97.83%. Under other combinations of conditions, whether increasing the voxel resolution or adjusting the interlayer spacing, the model accuracy decreased to different degrees, indicating that the selected parameter combination achieved an optimal balance between feature expression and structural retention.

It is worth noting that although a finer resolution such as 64³ can theoretically preserve more geometric details, it also substantially increases the input dimensionality (from 32,768 to 262,144 voxels). For each sample, the non-zero voxel ratio is defined as $ρ = N_{nz} / N_{all}$ , where $N_{nz}$ is the number of non-empty voxels and $N_{all} = G^{3}$ ; the reported value is the dataset mean $\bar{ρ}$ averaged over all samples. As additionally reported in Table 8, the dataset-level mean non-zero voxel ratio $\bar{ρ}$ decreases from 15.34% for the 32³ grid to 5.69% for the 64³ grid, indicating a substantially sparser representation at higher resolution. With a limited number of training samples (151 samples in this study), such high-dimensional sparse representations increase the difficulty of reliable parameter estimation and may weaken generalization capability. This observation is consistent with the curse of dimensionality in sparse voxel spaces, where increased dimensionality and reduced effective density can degrade generalization under limited data.

Model training results and visualization analysis

Figure 5 shows the accuracy curve of the model on the training set and validation set during training. It can be seen that as the number of training iterations increases, the model accuracy steadily improves and eventually converges, with the validation set accuracy reaching 97.83%, indicating that the model has good generalization ability.

Figure 5.

Training progress.

In addition, Figure 6 shows the confusion matrix of the samples of each category in the validation set. Most of the four modes are successfully distinguished, and there is only one misclassification between the normal mode and the tooth broken mode, which may be due to the presence of local sudden disturbances or short-term shock components in some of the normal samples, resulting in features being confused with the tooth broken class in terms of spatial structure.

Figure 6.

Confusion matrix obtained by 3D CNN.

To further verify the feature discrimination ability of the proposed model in the embedding space, this paper performs principal component analysis (PCA) on the deep features extracted by 3D CNN and maps them to the 3D space for visualization. As shown in Figure 7, the four fault modes show an overall good clustering and separation trend in the 3D principal component space, reflecting the effectiveness of deep features in significant fault identification. However, it is also observed that there are a small number of normal samples close to the edge of the tooth broken cluster, suggesting that there still exists a certain feature ambiguity near the boundary of the abnormality, which needs to be further improved in the follow-up study to further enhance the model’s discriminative robustness to the distribution of the features under the critical state.

Figure 7.

Three-dimensional visualization of 3D CNN features.

Comparative case studies

To comprehensively validate the classification performance of the method proposed in this paper for fault identification in gear rack structures, multiple comparative experiments were designed, selecting representative methods from three perspectives: structural differences, network depth, and academic tradition. In terms of structure, considering that this paper constructs 3D voxel inputs based on point cloud feature trees, three models with distinct structural differences were selected for comparison: a 3D CNN network based on voxel tensors, a PointNet network based on raw point cloud inputs, and a 2D CNN network based on three-view projections, each representing different information representation strategies; In terms of network depth, the performance differences between the 3D CNN in this paper and the lightweight VoxNet network were compared. Additionally, considering the widely adopted baseline approach of feature engineering + classifier in traditional fault diagnosis research, this paper also introduced manually extracted features such as time-domain, frequency-domain, and wavelet packet energy entropy, and combined them with an SVM classifier to form a classic comparison method. All methods utilize a unified original data source, sample division method (four fault categories randomly divided into training and validation sets at a 7:3 ratio), and consistent evaluation metrics (classification accuracy, F1-score, and training time), ensuring the comparability and scientific rigor of the results. Unless otherwise specified, Table 9 reports the results from a single run under the fixed split, while the robustness to stochastic training effects is further examined in the subsequent ablation and robustness analyses.

Table 9.

Comparison of classification accuracy, F1 score and training time of different methods on rack and pinion structure dataset (single run, fixed 7:3 split).

Diagnostic method	Accuracy/%	F1-score	Training time/s
3D CNN /(This paper)	97.83	0.978	19.85
Voxnet	91.30	0.913	21.74
PointNet	73.91	0.741	17.53
MVCNN	88.89	0.889	21.67
Time domain features + SVM	90.67	0.875	6.79
Frequency domain features + RBF	89.33	0.891	6.88
Wavelet packet energy entropy + RBF	92.00	0.920	6.91

In terms of specific configurations, the VoxNet method constructs a shallow network structure with two layers of 3D convolution and two layers of full connectivity, using 32³ voxel input, with the number of training rounds set to 20; the PointNet method samples 1024 points for each point cloud sample, generates a 1024-dimensional feature vector through the PointNet encoder, and then performs classification using two layers of FC layers; The multi-view CNN method projects the point cloud onto three planes (XY, XZ, and YZ), constructs a 64 × 64 three-channel grayscale image input, and uses a 2D CNN composed of three layers of convolutional and pooling structures for classification; In traditional shallow methods, temporal domain features include mean, skewness, kurtosis, and variance; frequency domain features include spectral skewness and total energy; and wavelet packet features extract the energy distribution and entropy values of four decomposition layer nodes. These features are uniformly standardized using Z-score before being input into an SVM linear kernel or RBF kernel classifier for recognition.

The experimental results are shown in Table 9. Under the fixed split, the proposed 3D CNN achieves 97.83% accuracy and 0.978 F1-score on the validation set, with the training time controlled to be less than 20 seconds, indicating strong classification capability with practical computational cost. Although VoxNet is a lightweight model, it still achieves an accuracy of 91.30%, with training time controlled at around 22 seconds, making it suitable for embedded deployment; PointNet method directly deals with the global point cloud, and its structure is simple but sensitive to small samples and local changes, with a final accuracy of 73.91%, which is obviously lagging behind in terms of performance; Although the 2D CNN method based on three-view data does not directly process 3D data, it still achieves 88.89% accuracy after integrating multi-view information, and the F1-score reaches 0.889, which is better than the traditional method with single-channel feature input; the feature engineering and SVM method synthesizes three types of features in the time domain, frequency domain, and wavelet packet, in which the highest accuracy is 92.00% and the F1-score reaches 0.920, which indicates that the traditional method still has strong competitiveness under the premise of sufficiently extracting the effective features, but it relies on the feature selection more highly. In summary, the 3D CNN method proposed in this paper fully exploits the spatial features of point cloud graphs under a multi-angle modelling strategy, achieving high classification accuracy while maintaining reasonable computational costs, demonstrating greater practicality and engineering adaptability.

Discussion

Discussion on robustness and deployment

The proposed HS-PCFT framework was validated on a laboratory-scale test bench; the platform was constructed to follow a 1:1 structural configuration of practical battery swapping systems in terms of transmission structure, sensor placement, and operating conditions, thereby improving representativeness for real-world scenarios.

To further examine robustness under environmental disturbances, an input-perturbation evaluation was performed by injecting additive white Gaussian noise (AWGN) into the voxelized validation samples under the same fixed split and trained model. As shown in Table 10, the performance drop is gradual and controlled as SNR decreases, indicating stable behavior under moderate AWGN perturbations.

Table 10.

Robustness evaluation under AWGN perturbations at different SNR levels.

SNR (dB)	Accuracy/%	Macro-F1
No noise	97.83	0.9747
30	95.65	0.9529
25	93.48	0.9252
20	91.30	0.9008

In practical deployment, station-specific adaptation can be achieved via transfer learning or fine-tuning using historical operational data, allowing compensation for installation variations, sensor gain differences, and speed distribution shifts. These strategies support reliable model migration from laboratory conditions to field environments.

Implications for industrial noise and vibration management in battery swapping stations

Battery swapping stations operate under high-throughput, repetitive duty cycles, where rack-and-pinion drivetrains can gradually develop wear and meshing defects. Under low rotational speed, speed fluctuations, and short-duration measurements, early fault signatures are weak and easily masked by background noise. If undetected, such defects can increase vibration levels, promote structural transmission to surrounding assemblies, and potentially elevate radiated noise and on-site vibration exposure during operation and maintenance—issues aligned with the journal’s emphasis on industrial noise/vibration consequences and occupational exposure concerns.

From a practical maintenance viewpoint, HS-PCFT provides a representation-oriented route to improve weak-feature separability: multi-variant SDP mappings are organized into a structured 3D point-cloud hierarchy and learned by a lightweight voxel-based 3D model. This complements optimization-driven studies on adaptive preprocessing and model tuning by focusing on preserving discriminative geometric cues in mapped structures, enabling earlier identification of incipient gear defects and supporting condition-based interventions before vibration/noise escalation.

For deployment, the pipeline can be integrated into existing vibration monitoring chains (segment → SDP variants → HS-PCFT → voxelization → 3D inference) to output fault states and confidence. Key considerations include latency under station cycle-time constraints, sensor placement repeatability, and domain shift across stations; these can be mitigated via periodic re-calibration and additional multi-site field data.

Conclusion

This paper addresses the fault diagnosis requirements for drive gears in electric heavy truck battery exchange systems operating under low-speed, speed-fluctuating, and weak-feature conditions. It proposes a point cloud feature tree construction method based on multi-spectrum fusion symmetric patterns, mapping one-dimensional vibration signals to three-dimensional structured spectral expressions. The method begins with spectral transformation, generates multi-source symmetric images using various SDP variants, converts them into polar coordinate points, and constructs a hierarchical three-dimensional point cloud feature tree, enhancing geometric feature distinguishability across fault modes.

The main advantages of this method are as follows: First, multiple SDP spectrum construction mechanisms capture detailed features of signals at different structural levels from the perspectives of modal decomposition, channel fusion, and scale perturbation, effectively enhancing feature significance under low-speed fault conditions; Second, the point cloud feature tree structure forms a clear spatial hierarchical representation through the normalized stacking of spectrum polar coordinates, maintaining structural consistency in the fusion of multi-source spectra; Third, mapping point clouds to 3D voxel tensors facilitates unified modelling, providing a standardized input framework for subsequent spatial analysis networks of any type. The lightweight 3D CNN adopted in this paper serves as an example to validate the usability and high-precision performance of this structure.

This study introduces new modelling concepts—spatial mapping of signal features, structural fusion of mapping data, and unified representation of point-cloud morphology—creating a novel graph-to-structure approach for diagnosing mechanical faults under complex conditions. Future work will examine its adaptability and real-time deployable capability across multi-device, multi-state industrial sensing scenarios.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

This work was supported by Henan Provincial Science and Technology Research Project (Grant No. 262102221057), Henan Provincial Technology Deputy Directors Program (Enterprise Appointment Program), and Innovation Funds Plan of Henan University of Technology (Grant No. 2021ZKCJ07).

ORCID iD

Menglong Zhang

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