It is an important assumption in machine learning that the training data and test data are independent and identically distributed. However, the distribution of data will shift in the process of neural network training process, causing the subsequent layers of the network to learn new distribution changes, and the training speed becomes slower and more difficult to converge than independent and identical distribution. Batch normalization (Ioffe and Szegedy, 2015; Santurkar et al., 2018) can be used to solve this problem.

For the input vector x 1 , x 2 , x 3 , … x N of dimension (N, C, H, W), batch normalization is performed on the dimension C of the batch size. The calculation process is as follows:

1) First the mean value of the input vector μ B is calculated in the entire batch:

Convolutional layers are always used to extract features. Among the various types of convolutional layers, 2D convolutional layer is often used in image-related tasks, such as image classification and detection. 1D convolutional layer is often used in natural language process–related tasks. Due to the high computing efficiency of convolutional operators, in many recent works, it is a trend that fully connected layers are replaced by several convolutional layers.

In the case of insufficient training data, there are several methods to improve accuracy during the training stage, such as data argumentation, meta learning, and transfer learning. Data argumentation can expand the data set by applying different transforms on the original data while meta learning focuses on learning the method to learn.

Transfer learning depends on the similarity between the source data and target data. When the target data are insufficient, the model on a similar data set with enough data is trained first, then the target data set is fine-tuned. This method always performs better than when only training the model on the target data set owing to the knowledge learned in the big data set. It is a common method in image tasks when data are limited and can also be applied to other domains.

Suppose the input data dimension is (N, C, H, W), then batch normalization is performed on the channel of N. However, due to the capacity of the graphics cards, N is generally not very large to keep fast inference speed, which may result in poor batch normalization. On the other hand, group normalization is performed on the channel of C. Generally, C may reach a value of 128 or 256, or even greater within the network, so it will not adversely affect the result of normalization. Group normalization is performed on the channel dimension, and therefore group normalization can solve the problem of poor performance when batch normalization is used with small batches. This is the reason why this article uses group normalization in PointNet++ to replace the original batch normalization to improve its accuracy.

The calculation process of group normalization is as follows:

1) Different from batch normalization, group normalization first groups different channels and normalizes each group:

The meaning of ⌊ k C / ( C / G ) ⌋ = ⌊ i C / ( C / G ) ⌋ is to round the quotient of the number of channels and the number of groups of elements with indices k and i. If they are the same, then they are in the same group. The group size is a hyper-parameter and is generally set to 32.

2) After the grouping, the process of group normalization is similar to batch normalization, assuming that the input vector in the same group is:

The proposed model uses PointNet++ as the basic model to improve. Group normalization is used to replace batch normalization, and the fully connected layer is replaced with several 1D convolutional layers. The network structure is shown in Figure 1, which contains two cascaded sampling modules with a feature extraction module, then the feature is fed to three cascaded 1D convolutional layers to get the final classification.

Suppose the i n p u t s ∈ x = { x 1 , x 2 , … x N } , where x i is a d dimension vector, and the feature extracted by the PointNet layer has a dimension of C. The input point cloud should be sampled first, and a subset of N1 points is sampled from the initial N points. The sampling method adopts the farthest point sampling method that the farthest point is selected each time to maximize the mutual distance between the points in the sampling subset. The sampling result obtained by this sampling method is easier to converge than the result obtained by random sampling. Then, for each point in the subset, K points are selected with the closest distance, and ( N 1 , K , d + C ) neighboring points are extracted in total, and these points are sent to the PointNet layer to extract the resulting ( N 1 , d + C 1 ) features. After this, through a sampling and feature extraction module of the same structure, ( N 2 , d + C 2 ) features are extracted. Then, the extracted ( N 2 , d + C 2 ) features by the two cascading sampling and PointNet modules are sent to the final PointNet layer to extract the ( 1 , C 4 ) features. The PointNet layer is the same as in PointNet++, which includes multilayer perceptron and max pooling layers. Then, three cascading 1D convolution layers are used to get the final classification and the numbers of the features decreased after each 1D convolution layer. Assuming the final classification category as cls , then cls =  conv 1 d ( ∏ i = 1 2 pointnet sample ( x ) )

The deep learning model is a data-driven model. Because of the small amount of power equipment data, it is necessary to pretrain on a large public data set first, and then fine-tune on the collected power equipment data set. The public data set ModelNet40 is used to pretrain the model. ModelNet40 was released in 2015, containing 3D models of 40 categories (including computers, bottles, airplanes, etc.). Figure 2 shows some examples of ModelNet40. This data set is collected by the Princeton Vision and Robotics Laboratory. It is often used to evaluate point cloud deep learning models for semantic segmentation, instance segmentation, and classification.

ModelNet40 contains a total of 12,311 point cloud models, each of which includes three models which have 512, 1024, or 2048 points. Among them, there are 9843 point cloud models in the training set, and the remaining 2468 point cloud models are divided into test sets. The improved PointNet++ model is pretrained using point clouds with a single model point cloud number of 1024.

The pretraining is based on the Ubuntu 18.04 platform, the graphics card model is 16 GB Telsa T4, and the PyTorch (Paszke et al., 2019) version is 1.6.

The training parameters are configured as follows. The training epochs are set to 200, the batch size is 24, and the initial learning rate is 0.001. After every 20 rounds, the learning rate decays to 0.7 times. The optimizer is the Adam optimizer (Kingma and Ba, 2014), and the momentum parameter is set to 0.9, and the L2 decay is set to 0.0001.

After 200 epochs of training, the accuracy of the model on ModelNet40 reaches 92.9% at the instance level, and the average accuracy on the class is 90.7%. Subsequent experiments are fine-tuned on this pretrained model. The comparison of the results between our model and previous networks is shown in Table 1.

The RS-Ruby laser radar of Sagitar can be used to collect the point cloud data of the transmission line. Using CloudCompare point cloud processing software, cloud points of the transmission line are collected by the laser radar and can be segmented and marked as different types. Figure 3 shows the point cloud distribution of the transmission line data set.

In this article, four commonly used categories of transmission lines: transmission lines, transmission towers, ground, and vegetation are segmented and labelled, and a labelled data set with 343 instances was obtained. Figure 4 shows some examples of the transmission line data set. The number of labelled instances of each type of equipment is shown in Table 2.

The transmission line point cloud data set is divided by random selection, 80% of which is used for training on the basis of the pretrained PointNet++, and the rest is used for testing.

First, the proposed model with batch normalization is trained. The training parameter configuration is as follows: the training epochs are set to 100, the batch size is 24, the initial learning rate is 0.001, the initial 10 rounds learning rate linearly rises from 0 to 0.001, and after this, the learning rate decays to 0.99 times in each round. The optimizer uses the SGD optimizer, the momentum is set to 0.9, and the L2 decay is set to 0.0001. After 100 epochs of training, the accuracy of the model on the transmission line point cloud data set reached 94.9%.

In the case of limited computing power, the proposed model with group normalization was also trained to compare between two normalization methods. The training parameters are the same as before except the batch size is set to 2. After 100 rounds of training, the accuracy of the model on the transmission line point cloud data set reached 92.4%.

It can be seen from the results shown in Table 3 that the recognition accuracy is also affected due to the limited computing power. Analyzing the model structure, it can be found that when the batch size is reduced, the number of participants in the batch normalization at the same time is decreased, which leads to the loss of training accuracy. Through group normalization, only in the normalization process, the advantage of being affected by the number of channels, not related to the batch size, improves the normalization effect of the model, thereby improving the performance of the model.

To show the effectiveness of the proposed model, we also tried PointNet and PointNet++ in our transmission lines data set when the batch size was 24, and the results are shown in Table 4. The results show that the proposed model can achieve a similar accuracy with PointNet++ while having a faster inference speed and smaller model size.

Using the same training parameters as the previous training, the training batch size was only changed and the experiments were performed when the batch sizes were 2, 4, and 8; the experimental results are shown in Table 5. It can be seen from the table that when the batch size becomes smaller, the model accuracy of the batch normalization method decreases. As the batch size increases, the model accuracy also increases; while the accuracy with group normalization method is stable, leading to more suitable scenarios where the computing power of the device is limited. And even when the batch size is 2, the accuracy achieved can be 94.6, which is not much smaller than 95.4 that PointNet++ achieves when the batch size is 24.

Figure 5 shows the visualized results of the part of our transmission lines data sets. It can be seen that the transmission lines and pylons are classified well. And if more data are collected, the vegetation and grounds can also be classified better.