Research on power equipment troubleshooting based on improved AlexNet neural network

3.1. AlexNet

AlexNet is a deep convolutional neural network model proposed by Alex Krizhevsky et al. in [25], which made a remarkable breakthrough in the ImageNet image classification challenge. AlexNet uses a deep convolutional neural network structure, which consists of five convolutional layers, three fully connected layers, and a final output layer. The structure is shown in Fig. 1.

Fig. 1AlexNet structure

The main features of AlexNet are as follows:

(1) Alternating stacks of convolutional and pooling layers: the first 5 layers of AlexNet are alternating stacks of convolutional and pooling layers. The first convolutional layer uses 96 filters of size 11×11 with a step size of 4. Subsequent convolutional layers use smaller filters (size 5×5 or 3×3) but with more channels. The pooling layer uses the maximum pooling for downsampling to reduce the size of the feature map.

(2) ReLU nonlinear activation function: AlexNet uses a modified linear unit (ReLU) as an activation function to increase the nonlinear expressiveness of the network. The ReLU function perfectly handles the gradient vanishing problem and speeds up the computation.

(3) Local Response Normalization (LRN): after each convolutional layer, AlexNet introduces a local response normalization layer. This layer operation allows neurons with larger responses to get larger response values, thus improving the generalization ability of the network.

(4) Dropout regularization: AlexNet introduces the Dropout regularization technique to reduce overfitting between the fully connected layers. By randomly setting the output of some neurons to 0, Dropout can force the network to learn features that are more robust and have better generalization performance.

(5) Multi-GPU parallel training: AlexNet is the first deep learning model to fully utilize multiple GPUs for parallel training. By assigning different parts of the neural network to different GPUs and communicating and synchronizing between GPUs, AlexNet is able to accelerate the training process of the network and improve the performance.

AlexNet is a deep convolutional neural network model that successfully achieves the classification task on large-scale image datasets by using advanced techniques such as deep convolutional and pooling layers, ReLU activation function, LRN, Dropout, etc., which lays the foundation for the development of subsequent deep neural network models.

3.2. Whale optimization algorithm

Mirjalili S and Lewis A invented an intelligent optimization algorithm - Whale Optimization Algorithm based on the habits of whales, a large group of predators living in the oceans [26]. The algorithm carries out three main activities for prey, which are encircling predation, bubble attack and searching for prey. The size of the whole whale population is set as $N$ provided that the search algorithm space is $d$-dimensional, and the position of the $i$th whale in the $d$-dimensional space is denoted as $X_i=(X_i^1,X_i^2,\cdots X_i^D)$, $i=\mathrm{1,2},\cdots N$, and the position where the whale captures the prey is the global optimal solution of the algorithm.

4.1. Multi-scale image processing

Traditional image recognition mainly extracts target features through layer-by-layer abstraction, in which the size of the sensory field of view is the key to obtaining target features. If the field of view is too small, only local features can be observed, and there is a possibility of losing the key information of the power equipment image; on the contrary, a lot of invalid information of the surrounding scene may be detected, which obstructs the correct infrared image feature extraction. The use of multi-scale image input enables the network to perceive the volume, texture, structure, etc. of power equipment at different scales, along with the impact of extreme weather, street buildings, light and other complex conditions which increase the difficulty of image extraction. The use of multi-scale image processing can accomplish better recognition results for power equipment targets at different distances. In this paper, the PAN model is applied [30] (Fig. 2) to obtain the image feature information, and utilize the bottom-up path technique of this model to increase the whole feature hierarchy, so as to obtain the image size features of different scales and improve the robustness of the model.

Fig. 2PAN model

4.2. Improved AlexNet model

Aiming at the shortcomings of AlexNet algorithm in image recognition, which is slow and prone to overfitting, the authors improve the model performance by reducing the number of convolutional layers, increasing the number of pooling layers, modifying the activation function, using the BN instead of LRU, and optimizing the weights and bias of AlexNet by using the whale optimization algorithm.

(1) Convolutional layers number reduction. The number of convolutional layers in the current AlexNet structure is 5 layers, which can effectively extract the deep features of infrared images of power equipment, but the deeper number of network layers leads to a long training time prone to overfitting. In this paper, a 3-layer convolutional neural network is used with 32 5×5 convolutional kernels in layer 1, 32 3×3 convolutional kernels in layer 2 and 64 5×5 convolutional kernels in layer 3, respectively. This setup can effectively maintain the number of convolutional layers, while reducing the problem of too deep layers, using a large number of convolutional kernels to complete the in-depth identification of image features, but still be able to maintain the ability to extract image features, and reduce the complexity of the model caused by the overfitting problem.

(2) Pooling layers number increase. Pooling layer is mainly used to reduce the size of the parameter matrix along with the reduction of other network parameters. Only one pooling layer is added after the second convolutional layer and the third convolutional layer of the AlexNet model, because the number of pooling layers is relatively small to avoid the loss of information and features, as well as to reduce the complexity of the model, improve the model invariance to spatial transformations, and reduce the sensory wildness of the network, which can reduce the risk of overfitting relatively.

(3) Activation function modification. The current AlexNet algorithm uses the ReLU activation function to solve the gradient disappearance and improve the convergence speed, but the neuron’s “death phenomenon” is easy to occur during the training process. As a result the neuron may no longer be activated by any data, so the network will not be able to perform the backpropagation and learning, then the ReLU function does not do amplitude compression of the data, resulting in the number of layers of the algorithm. As the ReLU function does not compress the data, the algorithm expands as the number of layers increases. In order to solve this problem, this paper chooses Leaky ReLU as the activation function, which can complete the backpropagation and solve the problem of gradient disappearance with the expression shown below:

where $a$ is a fixed slope, when $x<=$0, Leaky ReLU function can be back-propagated to solve the ReLU function neuron “death phenomenon”, and can solve the problem of gradient disappearance. However, because the value domain of Leaky ReLU activation function has no fixed interval, it is necessary to normalize the result of Leaky ReLU function with the expression as follows:

where $b_{x,y}^i$ is the normalized activation function value, $a_{x,y}^i$ denotes the output of the neuron at the $i$th kernel location $(x,y)$ after its processing by the Leaky ReLU function, $n$ is the number of feature images, $N$ is the total number of feature image output channels, $\alpha$ is the scaling factor, and $\beta$ is the exponential term.

(4) Exchange of LRN with BN layer. The parameter update of each layer in the inverse training process leads to changes in the input data distribution of the upper layer, which makes the deeper layer constantly re-adapt to the parameter update of the bottom layer, and the deeper the layer is, the more drastic the change in the parameter input distribution will be. Usually, in order to achieve better training results, a lower learning rate is often set, and saturation nonlinearity has to be avoided. In order to solve this problem, this study introduces the regularization layer of Batch Normalization (BN) [31] instead of LRN. The BN data normalization algorithm is shown in Eq. (9):

where $x^{\left(k\right)}$ denotes the input neurons, $E\left[x^{\left(k\right)}\right]$ denotes the neuronal mean value of the training data elements, and $\sqrt{Var\left(x^{\left(k\right)}\right)}$ denotes one standard deviation of the activation of the training data neuron $\sqrt{Var\left(x^{\left(k\right)}\right)}$. If only this normalization formula is used for a certain layer, it will reduce its expressive power, which in turn will affect the network’s ability to learn features. For this reason learnable parameters $\alpha$ and $\beta$ are introduced for each neuron. The expression is as follows:

4.3. Improved whale optimization algorithm to optimize model parameters

Considering that the whale algorithm has low convergence accuracy and is easy to fall into the local optimum, this study further optimizes the performance of the algorithm from the population initialization and the dynamic division of the adaptive convergence factor.

4.3.2. Adaptive factor optimization

In order to further improve the local search and global optimal ability of the traditional whale optimization algorithm, this paper optimizes the factor $a$. The optimization expression is as follows:

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$a=a_{max}-\left(2-e^{\frac{t}{t_{max}}}\right)\times \left(a_{max}-a_{min}\right),$

where $a_{max}$ and $a_{min}$ denote the factor maximum and minimum values, respectively. In the early stage of the algorithm, due to a small value of $t$, the whale individual approaches the global optimal individual slowly, which is favorable to the global search. In the middle and late stage of the algorithm, the value of $t$ gradually increases, the whale individual and the global optimal whale individual are located in the region close to each other, which is favorable to the local search, and maintains the diversity of the population. So the dynamics balances the algorithm's ability of the local search and the global optimal ability to avoid effectively the premature convergence phenomenon.

In order to better improve the recognition effect of AlexNet model in images, weights and bias being important components of the model performance, the parameter optimization is applied for the network model based on the whale optimization algorithm with the following steps:

Step 1: Define the objective function. Set the classification accuracy of AlexNet model as the objective function of whale optimization algorithm.

Step 2: Initialize whale individuals. Represent each whale individual as a set of neural network parameters.

Step 3: Calculate the fitness function. According to each whale individual, calculate the performance metric (classification accuracy) of the neural network as the fitness function of the individual.

Step 4: Update the global optimal solution. Select an individual whale with the highest fitness as the global optimal solution.

Step 5: Update whale position and velocity. For each whale individual, update the position and velocity of the whale based on the global optimal solution and the current optimal solution.

Step 6: Adjust the parameters. Update the weights and biases of the neural network by adjusting the parameter values of the individual whales.

Step 7: Iterative update: Repeat steps 3 to 6 until a preset stopping condition is reached, i.e. till the maximum number of iterations or the target accuracy rate.

Step 8: Output the optimal solution. Output the neural network parameter settings corresponding to the global optimal solution, i.e. as the best parameters of the optimized AlexNet neural network.

Therefore, the modified Alexnet power device is applied for infrared image detection process as shown in Fig. 3.

Fig. 3Flowchart of infrared image detection process

5.1. Performance comparison of whale optimization algorithm

In order to illustrate the performance of the improved whale optimization algorithm in this paper, the ACO algorithm, PSO algorithm, WOA algorithm and the algorithm of this paper-IWOA are selected for comparison. Table 1 shows six commonly used benchmark functions. Tables 2-7 show the comparison of the performance results of the four algorithms with the six benchmark functions. The maximum value, minimum value, variance and standard value are chosen as the measure of the performance comparison of the four algorithms.

Based on the data provided in Tables 2-7, the IWOA clearly outperforms the other algorithms in terms of minimum, maximum, mean, and standard value results for the six functions studied. The superiority of IWOA compared to ACO and PSO is clearly demonstrated in these tables. In addition, the IWOA exhibits a clear performance advantage over the WOA, especially on functions F3, F5 and F6.

It is noteworthy that IWOA has a minimum value of 0 when the dimensions are between 2 and 5, while the IWOA consistently provides favorable results on all six functions when the dimensions are between 10 and 30. This suggests that the overall performance of IWOA is greatly improved by strategies such as population initialization, call behavior optimization, and individual filtering. The consistently superior results obtained by IWOA on various statistical metrics, as well as its significant advantages over competing algorithms, validate the superiority of the population initialization, adaptive convergence factors, and dynamic partitioning employed in optimizing its overall performance.

5.2. Experimental comparison subjects

In order to verify that the algorithm (IAlexNet) in this paper has the effect, the AlexNet model, the YOLO v3 model from [13], and the Faster R-CNN model from [8] are selected for comparison. The Alexnet model is mainly composed of 5 convolutional layers, 3 maximum pooling layers, 3 FC layers using leaky ReLU activation function. YOLO v3 mainly uses DarkNet53 as the backbone network, 2 DBL units, 2 residual units and leaky ReLU activation function. Faster R-CNN uses VGG16 as the base model. Faster R-CNN uses VGG16 as the base model and leaky ReLU activation function. This study applies Tensorflow1.10.0 as an open source framework, Windows 10 as the operating system. The required hardware performance is: CPU of Core I7-6700, RAM of 16GB, and hard disk capacity of 1T. Fig. 4 shows the infrared images of some of the commonly used electric power devices.

Fig. 4Some commonly used electrical equipment

a) Surge arrester

b) Circuit breakers

c) Transformers

d) Insulators

5.3. Comparison of algorithm accuracy

In order to verify the performance of the algorithms in this paper, the accuracy values of the four algorithms we compared, and the results are shown in Fig. 5. The figure demonstrates that with the gradual increase in the number of training times, all the four algorithms show different degrees of upward trend in training accuracy values. When the number of training times reaches 400, the algorithm in this paper takes the lead in approaching stability and always maintains a flat state. While the AlexNet accuracy curve had an upward trend throughout the training process, the accuracy curves of YOLO v3 and Faster R-CNN algorithms also moved upward. Therefore, throughout the training process, the accuracy of this paper’s algorithm is better than the other three algorithms, indicating that this paper's algorithm has a more obvious improvement effect in AlexNet.

5.4. Comparison of algorithm effectiveness

This paper takes and considers 100 images of the above four power devices for verifying the algorithms performance. Table 8 shows the recognition results of the four algorithms for the four types of power equipment. From the results shown in the table, it is found that these algorithms have different results for the recognition rate of power equipment, but the advantage of this paper’s algorithm is more obvious. The color of the surrounding scene has a certain impact on the infrared image of the device, and the multi-scale image input of this paper’s algorithm reduces the impact of these invalid elements, thus making the device feature extraction more accurate. In a lightning arrester, the recognition rate of AlexNet, YOLO v3, Faster-RCNN increased by 6.54 %, 5.68 % and 3.95 %, respectively, in a circuit breaker, the recognition rate of AlexNet, YOLO v3, and Faster-RCNN is improved by 3.54 %, 3.47 % and 1.57 %, respectively. And finally, in mutual inductors, the recognition rate of AlexNet, YOLO v3, and Faster-RCNN is improved by 5.97 %, 4.94 % and 4.14 %, respectively, and in insulators, the recognition rate of AlexNet, YOLO v3, and Faster-RCNN is improved by 5.83 %, 4.67 %, and 4.38 %, respectively.

Fig. 5Comparison of training accuracy of four algorithms

Table 9 contains the recognition time comparison results for the four algorithms and four types of power equipment, and demonstrates that the IAlexNet algorithm applied in this paper has a clear advantage over AlexNet, and for YOLO v3, Faster -RCNN the advantage is even more dramatic. That substantiates such an optimization of the original AlexNet structure to improve the time complexity, decrease the recognition time.

Recall Rate (R) and Precision Rate (P) are the most important methods to measure the model recognition, in which Recall Rate (R) and Precision Rate (P) equations are as follows:

where, $T_p$ and $F_p$ denote the number of positive samples and negative samples being recognized correctly, respectively, $F_n$ denotes the number of positive samples being misclassified as negative samples, and $n$ denotes the number of all samples labeled as positive samples. In order to further verify the recognition effect of this paper’s algorithm before and after the improvement, the algorithm is optimized with or without SPP, with or without Leaky ReLU activation function, and with or without WOA in eight different conditions as shown in Table 10. Fig. 6 shows the PR results of this paper's algorithm with or without SPP, with or without Leaky ReLU activation function, and with or without WOA algorithm optimization for different algorithms in four kinds of power devices. From the results of the four devices, although the four algorithms show a downward trend, but the PR results of this paper’s algorithm has a more obvious advantage, which indicates at the increase of SPP, Leaky ReLU function and that the use of the WOA algorithm for the optimization of this paper’s algorithm is effective.

Fig. 6PR values of four kinds of power devices which are the main improvement elements of this paper’s algorithm

a) Surge arrester

b) Circuit breakers

c) Transformers

d) Insulators

Fig. 7 shows the PR results of the four algorithms feature recognition, that explain that with the gradual increase in the R value, the four algorithms of the P value are in a gradual decline, and this paper algorithm R value in the range of [0, 0.6] is more gentle, compared to the other algorithms R value being equal to [0, 0.5], that demonstrates a more stable effect.

Fig. 7PRs of four power devices for four algorithms

a) Surge arrester

b) Circuit breakers

c) Transformers

d) Insulators

As per test diagnostic results of the four algorithms shown in Fig. 7, the mixed fault detection brings some detection difficulty to the model, compared to Fig. 6 having the categorized faults, where the fault identification samples during the detection process are more concentrated due to the troubleshooting in one device, and therefore the results can be obtained more accurately. The results of fault diagnosis shown in Fig. 7 (performed in the AlexNet model), three number 1 fault diagnosis results are wrong, two number 2 fault diagnosis results are wrong, number 3 fault diagnosis results are correct, three number 4 fault diagnosis results contain errors, two number 5 fault diagnosis also contain errors, and the comprehensive fault diagnosis success rate is 80 %. In the fault diagnosis using YOLO v3 model, two number 1 fault diagnosis results contain errors, two number 2 fault diagnosis results contain errors, number 3 faults all diagnosed correctly, one number 4 fault diagnosis contains an error, one number 5 fault diagnosis contains an error, the comprehensive fault diagnosis success rate is 88 %. In the Faster R-CNN model for fault diagnosis, one number 1 fault diagnosis result contains an error, two number 2 fault diagnosis results contain errors, 1 number 3 fault diagnosis, 1 number 4 fault diagnosis and 1 number 5 fault diagnosis results contain an error each, so the comprehensive fault diagnosis success rate is 88 %. And finally using the model in this paper for fault diagnosis, 1 number 1 fault diagnosis result contains an error, 2 number 2 fault diagnosis result contain errors, number 3 fault diagnosis and number 4 fault diagnosis results are all correct, 1 number 5 fault diagnosis contains an error, so the comprehensive fault diagnosis success rate is 92 %. From the above results, the four algorithms fault detection accuracy has been reduced, but the detection effect of the algorithm in this paper still has a certain advantage, and can better find the faults occurring in the power equipment.

To further illustrate the generality and robustness of the algorithms analyzed in this paper, the infrared images of power devices under different scenarios (Rainy day scenario, Hazy scenario, Cloudy scenario, and Sunny day scenario) we chosen for recognition. A mutual inductor was chosen as the research object, and its detection results from the four algorithms are shown in Fig. 8. From the detection results shown in Fig. 8, under four different scenarios, this paper’s algorithm still has a good PR value, and has better application results compared to the other three algorithms. Especially in the hazy day scenario, the PR values of the other three algorithms are significantly lower than those of this paper's algorithm. So the feature acquisition ability of the proposed model for images is significantly enhanced, and the performance of the model is improved by the optimization of the WOA algorithm.

Fig. 8PRs of four algorithms in different scenarios

a) Rainy day scenario

b) Hazy day scenario

c) Cloudy day scenario

d) Sunny day scenario

5.5. Power equipment fault diagnosis

This subsection consists of the fault diagnosis of transformers, which are most frequently used in power equipment, as the object of study. At present, the faults of this type of equipment generally happen due to high-temperature overheating (for the sake of subsequent expression, the number is set to 1 and so on), low-temperature overheating (the number is set to 2), high-energy discharge (the number is set to 3), low-energy discharge (the number is set to 4), partial discharge (the number is set to 5), and normal state (the number is set to 6). Usually when a power transformer failure occurs, the device inside the transformer will dissolve hydrogen, methane, ethylene, acetylene and other gases, and the release of these gases captured by the infrared instrumentation gives the important information to determine the power transformer condition. A collection of 300 sets of power fault data from [32] is applied here. These 300 sets of data are distributed into the corresponding six categories of data based on the type of equipment failure. Among them, those numbered 1-50 belong to the number 1 faults, those numbered 61-100 belong to the number 2 faults, those numbered 101-150 belong to the number 3 faults, those numbered 151-200 belong to the number 4 faults, those numbered 201-250 belong to the number 5 faults, and those numbered 251-300 belong to the normal state of number 6. These data are also divided into a training set and a test set where 240 sets of sample data belong to the training set and 60 sets belong to the test set (the allocation results are shown in Table 11).

Table 12 shows the test results of the four algorithms in six equipment states, and these results explain that the recognition effect of this paper’s algorithm is obvious. For these six states of equipment faults, this paper’s algorithm improves the recognition rate by an average of 7 % compared to traditional AlexNet, and improves the recognition rate by an average of 4 % compared to YOLO v3 and Faster R-CNN, especially in the low-energy discharge faults, the algorithm of this paper has achieved 100 % recognition effect. These results demonstrate that the PAN-based model can effectively remove the interference influence around the device in image recognition. However, the AlexNet model has the advantages of increasing the pooling layer, modifying the activation function, using the BN layer instead of the LRN, and optimizing the model parameters using the WOA algorithm and other measures to improve the recognition performance of the model.

In order to further illustrate the effectiveness of the algorithmic aspects of this paper, this research authors selected 50 mixed test samples of different device faults (where 10 are selected for each non-normal state) and tested the four algorithms in comparison. The test results are shown in Fig. 9.

Fig. 9Fault diagnosis results for four algorithms

a) Alexnet troubleshooting results

b) YOLO v3 troubleshooting results

c) Fast R-CNN troubleshooting results

d) IAlexnet troubleshooting results

Fig. 10Fault diagnosis of two power substations

a) Paitou substation

b) Lizhu substation

In order to further illustrate the identification effect that the model in this paper has, the authors take the power equipment of Paitou Substation and Lizhu Substation under the jurisdiction of Shaoxing Branch of the State Electric Power Company, the author’s organization, as the practice object. Sample data of equipment records from January 2023 to May 2023 are collected. The authors selected a mixed test sample set of 30 transformer faults from each substation and compared them using four algorithms, and the results are shown in Fig. 10.

As per Fig. 10(a), the authors found that in the Pai Tau substation, the IAlexNet model has 4 errors, the traditional AlexNet model has 6 errors, YOLO v3 and Faster R-CNN have 7 errors, and as per Fig. 10(b), the IAlexNet model has 3 faults, the traditional AlexNet model has 5 errors, the YOLO v3 model has 6 errors, and the Faster R-CNN has 7 error faults. As per these results, the proposed algorithm has good results in the actual equipment detection process, and the detection success rate is close to 90 %.