Diagnosis of Loose Core Fault in Saturable Reactor of Thyristor Valve Based on Vibration Signal Time-Frequency Analysis and CNN

The saturable reactor is one of the core components of the thyristor valve, which plays a role in suppressing current changes and balancing voltage distribution. Due to long-term operation under complex working conditions, the vibration of the reactor can cause the core to loosen. To detect faults in time, a fault diagnosis method is proposed for loose cores in saturable reactors of thyristor valves based on time-frequency analysis of vibration signals and convolutional neural networks. The two-dimensional time-frequency spectrum of the vibration signal is obtained using the short-time Fourier transform method. A convolutional neural network model structure is designed to extract time-frequency spectrum features and diagnose different levels of core looseness faults through learning and training. An experiment was carried out to collect core fault information under variable working conditions. The effectiveness of the method proposed in this paper was verified based on experimental data validation. Through comparative experiments, it was found that the proposed method is superior to existing fault diagnosis methods.


Introduction
The ultrahigh voltage thyristor valve is an important piece of equipment for high-voltage direct current transmission engineering [1].The saturable reactor is also the key equipment of the valve, which can protect the thyristor in variant operating conditions [2].Long-term stress causes plastic deformation of the tension strip of the saturated reactor core, which can lead to a decrease in tension force and even rupture of the tension belt.Finally, it causes changes in the core structure and increases iron loss.Alternatively, the insulation damage of the iron core caused by vibration may cause overheating under eddy current effects.In severe cases, this will lead to unplanned shutdowns of DC transmission projects and serious economic losses.Therefore, it has theoretical significance and engineering value to conduct fault diagnosis research on the problem of core looseness in saturable reactors.
In current engineering, conventional power outage appearance inspection and inductance measurement techniques cannot effectively distinguish the internal core status of reactors.When the saturable reactor operates, the core vibrates because of magnetostriction.Core structure affects its vibration characteristics.Therefore, vibration signals can be used to analyze the core looseness fault.
At present, there is little research on the fault diagnosis of saturable reactors.However, there are abundant research achievements in fault diagnosis based on vibration signals [3][4][5][6][7].In practical engineering, thyristor valves operate under different conditions, which can affect the vibration characteristics of saturable reactors.Due to the lack of a bridge arm current measurement device, the operating conditions of the thyristor valve cannot be measured.Therefore, the fault vibration characteristics of the saturable reactor are in an unknown and variable state, which poses difficulties in analyzing vibration signals to diagnose the core's loose state.Under unknown operating conditions, it is difficult to achieve an accurate diagnosis of core looseness using traditional time-domain and frequency-domain statistical features combined with general machine learning algorithms.Due to the similar characteristics of vibration fault signals under different working conditions, a large number of misjudgments occur.In recent years, convolutional neural networks (CNNs) are usually applied in the fault diagnosis of electrical equipment such as AC transformers and reactors [8][9][10][11].They can construct deeper network structures, possess stronger learning abilities for high-dimensional input features, and effectively mine the hidden features of input data.Therefore, based on the deep mining ability of CNN, it is easy to learn the vibration characteristics of saturable reactors under different operating conditions, which effectively overcomes the problem of misjudgment under variable operating conditions.
In terms of fault features, existing studies usually convert raw vibration data into image features as input to CNNs.Time-frequency spectrum analysis can transform one-dimensional vibration time series into two-dimensional spectral features, which is a commonly used method for sequence data visualization processing [12][13][14].However, there is currently no research on using a certain timefrequency spectrum feature to identify the core looseness fault of saturable reactors.
A fault diagnosis method is proposed for the core looseness.The short-time Fourier transform is used to process the vibration signal of the reactor to obtain a two-dimensional time-frequency spectrum image.A CNN model is designed.This model combines multilayer convolution and pooling layers to extract spectral image features and learns the vibration characteristics of different core loosenesses of saturated reactors under multiple operating conditions.Finally, two fully connected layers are used to achieve pattern classification.

Structure and vibration feature of the saturable reactor
The saturable reactor is described in Figure 1(a).It contains windings, cores, cover plates, and screws.The outer side of the winding is poured with epoxy resin.The core is installed on the outer side of the epoxy resin.The saturable reactor is connected as a whole by a cover plate and screw.The partial detailed diagram of the core is shown in Figure 1  The main source of vibration for saturable reactors is core magnetostriction.The magnetic leakage between the joints of silicon steel sheets and the laminations generates electromagnetic force, which causes the vibration of the core.When the saturable reactor operates normally, there are components in the vibration frequency of the core at odd and even multiples of 50 Hz.In addition, the nonlinear and resonant characteristics of equipment can also exacerbate the complexity of core vibration [15].

Short-time Fourier transformer
The vibration signal has nonstationary characteristics.Traditional Fourier transform cannot effectively mine its features.By adding windows, the vibration signal of the entire time-domain process is divided into several small segments with equal lengths, and each segment can be approximated as a stationary signal.By applying a Fourier transform on these small segments, the frequency characteristics of the signal in different time dimensions can be obtained, which is the short-time Fourier transform method (STFT) [16].It is defined as: where   is the window function, and  is the time corresponding to the center coordinate of the window.The frequency obtained through the STFT can be regarded as the instantaneous frequency of the point.

Convolutional neural networks
A deep convolutional neural network model structure is designed in this paper, with the model structure shown in Figure 2. The model converts the original time-frequency spectrum features of size 500×500×3 into feature pictures of size 4×4×16 through 7 consecutive 2D convolutional pooling layers.The parameters of the 2D convolutional pooling layer group are shown in Table 1.The convolutional pooling layer contains a convolutional layer, a batch normalization layer, a maximum pooling layer, and a ReLU activation layer arranged in sequence.Convolutional layers do not change the size of feature images.However, the maximum pooling layer will reduce the length and width of the 2D feature image by half.Original features are sequentially stacked through multiple convolutional pooling layers to achieve data dimensionality reduction and key fault feature extraction.The feature picture obtained from the input data through multilayer convolutional pooling layer group operation is expanded into a one-dimensional sequence.It is input into the first fully connected layer.The ReLU activation function is set between two fully connected layers.There are 5 neurons in the second fully connected layer, which represent fault types.Finally, the softmax layer is built to calculate sample classification results.

Fault diagnosis process
The diagnosis process for core looseness fault based on STFT-CNN is shown in Figure 3, and the specific steps are as follows: 1) Vibration signals of variable operating conditions under different levels of core looseness fault conditions are collected, and the signals are preprocessed.
2) The appropriate window function is selected.The window length and adjacent window overlap parameters are configured.The vibration signal is converted into a 2D time-frequency picture using STFT and is divided into training, validation, and testing sets.
3) A deep CNN network is built.The 2D time-frequency pictures of saturable reactors under different fault levels are used as inputs, and the fault level category matrix is constructed as outputs.Network parameters are configured for training.
4) The trained model is tested using validation sets.If the diagnostic performance is not met, we proceed to step 3 and reconfigure the network parameters until the model is validated.
5) The STFT-CNN diagnostic model is applied to detect faults in the test set.

Test parameters
During the experiment, different degrees of core looseness faults are simulated, including five modes: screw bolt-off (SO), total looseness (TL), severe looseness (EL), slight looseness (SL), and normal state (NS).In each mode, the saturable reactor is in a mixed operating state of multiple operating conditions.Table 2 describes the experimental parameters.9 current peaks represent 9 different operating conditions.During the experiment, under each operating condition, 5 fault modes will be simulated, and data will be collected.From the picture, it can be seen that there are some differences in fault data of different levels under the same working condition, but it is difficult to detect visually.In particular, the two adjacent fault modes are almost identical and difficult to distinguish with the naked eye.In addition, under the same fault mode, there are significant differences in the vibration signals of different working conditions.In practical engineering, saturable reactors operate under complex variable operating conditions for a long time, and their fault modes and load conditions have an impact on the vibration signal.

Fault diagnosis results and analysis
The vibration data collected in the experiment are divided into 5 groups according to the fault mode, with each group containing various working conditions.Each group of data is segmented and resampled to obtain a dataset.The dataset is divided into a half training set, a quarter validation set, and a quarter testing set.All datasets use the STFT method to construct time-frequency spectrum pictures.The data from Figure 5 is selected to construct 2D time-frequency spectrum pictures, as shown in Figure 6.Comparing Figure 5 and Figure 6, there are significant differences in different fault degrees with the same working conditions.The difference in the same type of fault mode is greater under different working conditions.The STFT algorithm converts the vibration signal into a timefrequency spectrum, which can display the difficult-to-detect feature change information.7.As the number of iterations increases, the training accuracy of the model increases, and the corresponding losses gradually decrease.At the 763rd iteration, the validation set accuracy of the model reaches a peak of 99.73%, and the model at this time is selected as the final diagnostic model.The testing set is input into the model, and Figure 8 shows the confusion chart of the diagnosis result.Its vertical axis is the real category.The prediction category is in the horizontal axis, and a~e correspond to five core looseness fault states.The greater the diagnostic results of the confusion chart are concentrated on the diagonal, the better the performance of the algorithm is.In the figure, among all the test samples, only slight misjudgments are observed for total looseness and slight looseness, which verifies the effectiveness of the proposed method.To compare the diagnostic effects of different combination models on the core looseness fault of a saturable reactor, this method is compared with classic deep learning methods such as AlexNet [17], VGGNet-16 [18], ResNet-50 [19], and typical machine learning algorithms such as DT (Decision Tree), SVM (Support Vector Machine) and FCNN (Fully Connected Neural Network).They use the same training, validation, and testing set, whereas machine learning algorithms use the time domain and frequency domain statistical features (TFSF) of the dataset as input [20].The results are shown in Table 3.In Table 3, the F1 value is a comprehensive indicator of recall and precision, which is used to characterize the performance of the algorithm model.The higher the F1 value is, the better the algorithm's performance.The average F1 value is the average indicator value obtained after multiple test sets.The minimum F1 value is the smallest indicator value in multiple tests.They are the results of 30 experiments for every method.From the table, it can be seen that after multiple testing experiments, whether in the least ideal situation or overall situation, the F1 values of the proposed algorithm are better than those of the comparison method, and the parameter size is the smallest.This indicates that our method achieves better results with fewer resources.In addition, compared to the difference between the average F1 value and the minimum F1 value, our method is the smallest.This indicates that the diagnostic performance is less affected by operating conditions and the degree of faults.It can ensure high accuracy in different testing scenarios.Six methods with the largest average F1 value are selected to construct the confusion matrix, as shown in Figure 9. Except for the methods in this article, there are a large number of misjudgments in other methods.Among them, SVM, AlexNet, and VGGNet-16 have the most severe misclassification cases, with almost every mode experiencing diagnostic errors.In addition, among all 5 types of modes, the three progressive failure modes of total looseness, severe looseness, and slight looseness have the most cases of misjudgment.This is because these three fault modes are progressive and have similar characteristics.Especially in the case of variable operating conditions, the faults of the three modes will be similar under different operating conditions.However, a poor condition in our method is very rare, which proves that our method has better performance in feature extraction and classification of vibration signals.It can effectively explore the differences between progressive faults and improve diagnostic accuracy.
The above comparative results indicate that the method proposed in this paper consumes fewer resources.The diagnostic effect is good and stable.It is less affected by changes in operating conditions and will not experience significant performance differences in different application scenarios.

Conclusion
Saturable reactors are prone to core looseness during long-term operation under variable operating conditions.The feature similarity of core vibration signals under multiple operating conditions poses a significant challenge to the accuracy of fault diagnosis.In response to this issue, this paper proposes a fault diagnosis method based on vibration signal time-frequency analysis, which effectively solves the problem of misjudgment of core looseness faults under different operating conditions.1) A new method for diagnosing core looseness faults has been proposed.This method uses a short-time Fourier transform to convert the vibration signal into a two-dimensional time-frequency spectrum image, which highlights different fault characteristics under variable operating conditions.A deep convolutional neural network model is constructed to mine the fault information contained in the frequency spectrum.The effectiveness of the proposed method has been demonstrated through experiments.
2) Compared to commonly used algorithms, it has better performance.Compared with classical deep learning methods, this method has better diagnostic and stable performance, with a smaller parameter size.Compared with traditional machine learning algorithms, the diagnostic accuracy of the method is far ahead. (b).
(a) Saturable reactor (b) Core cross section Figure 1.Structure of a certain model of a saturable reactor

Figure 3 .
Figure 3. Diagnosis process for core looseness fault based on STFT-CNN 4. Core looseness test4.1.Test platformFigure4describes the core looseness fault test platform.It contains three parts: a power circuit, a saturable reactor, and vibration acquisition equipment.The power circuit is composed of the charging part and the H-bridge cabinet.The charging part provides power for the platform and controls the switching of the experiment.The H-bridge cabinet rectifies the incoming voltage and provides voltage excitation for the saturable reactor.The voltage peak on the saturable reactor can be adjusted by changing the equivalent stray capacitor, which can simulate the reactor's operating conditions.The vibration collection equipment is arranged around the saturable reactor.The data is collected and uploaded to the computer.

Figure 5 .Figure 5
Figure 5. Vibration signals of the core looseness fault experiment

Figure 6 .
Figure 6.Time-frequency spectrum diagrams of the core looseness fault experiment The divided training and validation sets are input into the CNN for training, and the training process of the model is shown in Figure 7.As the number of iterations increases, the training accuracy of the model increases, and the corresponding losses gradually decrease.At the 763rd iteration, the validation set accuracy of the model reaches a peak of 99.73%, and the model at this time is selected as the final diagnostic model.The testing set is input into the model, and Figure 8 shows the confusion chart of the diagnosis result.Its vertical axis is the real category.The prediction category is in the horizontal axis, and a~e correspond to five core looseness fault states.The greater the diagnostic

Table 1 .
Convolutional pooling layer group parameters

Table 3 .
Comparison of algorithm diagnosis results Figure 9. Confusion matrix of the comparison algorithm diagnosis results