AC Series Arc Fault Diagnosis Method Based on AO-VMD Multidimensional Feature Extraction

In view of the difficulty in determining the number of mode components K and penalty factor α in VMD, which leads to poor signal decomposition effect and low diagnosis and recognition rate due to insufficient feature extraction in AC arc fault, an arc fault diagnosis method based on the Aquila algorithm was proposed to optimize the multivariate feature extraction of variational mode decomposition. First of all, the arc fault test platform was set up to consider the resistive, inductive, capacitive, and other household loads were considered to obtain the normal and fault current data. Second, the optimal K and α parameters were obtained by AO-VMD optimization and then decomposed into intrinsic mode functions (IMFs) by substituting them into VMD. Then, the time domain characteristics of the IMF2 component, the Energy Entropy of IMFs, and the Fuzzy Entropy of the kurtosis maximum IMFk component were extracted respectively, and the multidimensional fault characteristic matrix was constructed. Finally, the random forest (RF) model was used to accurately identify arc faults. The experiment shows that the average fault recognition rate of each type of load is above 99%, which has an excellent diagnostic effect.


Introduction
In an AC system, AC arc faults may be caused by aging insulation of the low-voltage power supply line, ground failure, and loose wiring terminal slip [1].At present, the arc fault problem mainly focuses on three aspects, among which parallel arc and ground arc faults are easy to be detected by traditional protection devices.When a series of arc faults occur, the arc fault is equivalent to the resistance in series in the line, resulting in a great reduction in line current, so that circuit breakers, fuses, and other protection devices can not normally trip to protect the line [2].Therefore, in order to reduce the various losses caused by arc faults in the low-voltage AC distribution network, how to effectively solve the accurate identification and diagnosis of low-voltage AC series arc faults has become a difficult point.
Fault arc detection methods are mainly divided into those based on arc mathematical models, physical characteristics, and pattern recognition.The widely used fault identification method is pattern recognition now.Yu et al. [3] adopted wavelet transform for resistive, inductive, and group inductive loads, and identified fault arcs through the improved AlexNet model, which has high diagnostic accuracy.Miao et al. [4] improved EMD to improve the accuracy of arc fault feature extraction and established an arc fault diagnosis model combined with a machine learning algorithm.However, the analysis was only conducted from the perspective of the time domain, resulting in incomplete arc fault information analysis.Yang et al. [5] combined wavelet decomposition and EMD, extracted arc fault features from multiple angles by using the window division method, and then set threshold values for arc diagnosis.However, wavelet analysis has some problems in fault detection of mixed uncertain signals.EMD is not ideal in dealing with overlapping frequency bands, which is prone to the problem of spectrum aliasing.
Compared with wavelet transform and EMD technology, the VMD method can effectively overcome the mode aliasing problem of these two methods, but the premise of effective and accurate decomposition of VMD is to select appropriate decomposition parameters.If the parameters are not selected properly, it will take too much execution time and the decomposition effect is not good.Low voltage AC system is complex and varied, with many loads, weak arc fault features, and many influencing factors, and inaccurate signal decomposition will greatly affect the feature extraction and diagnosis results of fault arc.
To sum up the above defects, this paper proposes an arc fault diagnosis method based on the AO to optimize VMD to extract multidimensional fault features and RF.Firstly, the Aquila algorithm is used to optimize VMD parameters, so that it has a good decomposition effect and can accurately reflect fault information.Secondly, arc fault features are extracted from the IMFs components after the optimal parameter VMD decomposition from the perspectives of time domain, energy, and entropy, and multidimensional fault feature vectors are constructed to avoid incomplete fault information extracted by a single feature.Finally, it is input into RF for arc fault diagnosis.

VMD Principle
The decomposition process of the VMD method is essentially a process of constructing and solving variational problems [6].It decomposes the original signal into several IMF components and minimizes the bandwidth and sum of all IMF components.
When penalty factors Į and Lagrange multipliers t O are introduced into Formula (1), the variational problem is transformed into a non-binding variational solution. ^`^` The solution of the saddle point in Formula (2) is to solve the optimal value of Formula (1), initialize the parameter ^1 ˆk u , ^1 ˆk Z , Ô , n , and iteratively update ˆk u , k Z through Formula (3) and Formula (4).
Then, the new ˆk u , k Z is updated with Formula (5).
When the condition of Formula ( 6) is satisfied, the iteration is stopped.As can be seen from the above formula, when VMD decomposes signals, the basic parameters K and Į determine the decomposition effect of VMD, and they are usually set artificially based on experience [7].In the practical application of arc fault signal, if the selected K value is too large, it will be decomposed into too many modal components, which will interfere with the extraction of effective information.The small value of K will cause insufficient signal decomposition, and then generate a mode aliasing phenomenon.Į represents the initial central constraint strength of each mode.Therefore, selecting the appropriate K and Į values can help us to extract features more effectively and accurately.So, the Aquila algorithm (AO) is introduced in this paper to optimize them.

AO-VMD optimization process
AO is a new intelligent optimization algorithm proposed in 2021 [8], featuring strong optimization ability and fast convergence.The optimal parameters K and Į were obtained and then substituted into VMD for the decomposition of arc fault signals.The AO-VMD optimization process is shown in Figure 1

Current signal acquisition
The experiment uses a 220 V/50 Hz AC power supply.We switch S1 and S2 on when collecting normal state data and switch S1 and S2 on when collecting fault state data.The current waveform is collected by the current sensor through the data acquisition device, transmitted and stored in the SD card of the intelligent gateway, and finally checked and saved in the notebook.The experimental circuit diagram and the experimental platform are shown in Figure 2 below, and Table 1 shows the various load parameters adopted in this paper.

Current waveform analysis
Experiments were conducted on resistive, capacitive, and inductive loads respectively and data were collected.In order to eliminate the dimensional influence of indicators on the judgment of final detection results, each set of data was normalized and the load waveforms were obtained, as shown in Figure 3 below.The comparison of time-domain waveforms before and after arc fault can be seen that the proportion of flat shoulder increases and obvious fault features such as a large number of impact signals are present.However, if fault features are extracted only from time domain features such as "flat shoulder" and impact signals, there are a lot of interference noises in the actual line, which will lead to incorrect identification due to environmental interference factors and too few extracted features.Therefore, this paper adopts the VMD method to decompose arc signals, so as to further extract fault features for arc fault diagnosis.

Time domain feature extraction
The low and medium-frequency component IMF2 can well reflect arc fault information in Figure 4, and has better stability and anti-noise interference ability than the original signal.Therefore, in this paper, five indexes including variance, kurtosis, peak factor, pulse factor, and waveform index are used to extract time-domain features of the IMF2 component.Their formulas are shown in Table 3 below.
Table 3.Time Domain Characteristic Index Definition Feature Index Formula of Definition Variance 2 1

Fuzzy entropy feature extraction
For the rest of the middle and high-frequency IMFs components, the larger the kurtosis is, the more shock features will be, and the more fault information will be contained.Therefore, the IMFk component with the largest kurtosis value is selected for analysis.Entropy is a feature extraction method.Generally, the larger the entropy is, the larger the signal complexity will be.In this paper, Fuzzy Entropy (FE) is selected as the characteristic quantity [9].Compared with sample entropy, it adopts the fuzzy membership function as the hard threshold criterion in entropy, which is more suitable for nonlinear and non-stationary fault signals.

Energy entropy feature extraction
Certain energy is bound to be generated after an arc fault occurs in the line, so the energy entropy of decomposed IMFs components is selected as one of the characteristic quantities [10].

Random forest fault diagnosis model
Firstly, the AO is used to optimize the VMD to obtain the optimal parameters, so as to ensure that the decomposed VMD contains more accurate fault information.Secondly, the time domain features, energy entropy, and fuzzy entropy fault features are extracted respectively from the decomposed IMFs component, and the multidimensional fault feature matrix is constructed.Finally, a random forest

Experimental verification
In this paper, four groups of load data obtained from the established AC arc fault experiment platform were selected for experimental verification.160 groups of experiments were conducted for each of the four loads as diagnostic samples.The feature quantity of RF model is n=7, the number of decision trees is set to 300, and the depth of the decision tree is set to 10.For the convenience of viewing the results, this article sets the normal status to "0" and the fault status to "1", and sorts them.Figure 6 shows the troubleshooting results for the final four household loads.According to the comparison between the predicted results of each load and the actual diagnosis results, the average diagnostic accuracy of LED lamp, electric kettle, and notebook load is as high as 99.375%, while the diagnostic accuracy of hair dryer is slightly lower as 98.125%, which is analyzed to be due to the IMF2 component of the current waveform of a hair dryer after VMD decomposition.The calculated accuracy of the four loads is above 99%, which proves the superiority and accuracy of the proposed method.

Contrastive analysis
The comparison I: Comparative analysis on the necessity of VMD parameter optimization.When no VMD parameter optimization is carried out, the default value of VMD decomposition is set as [K, Į]= [4,2000] according to the study in article [11].When the AO-VMD parameters proposed in this paper are optimized, the results are shown in Table 4.By comparison, the signals with default VMD decomposition have mode aliasing and signal overdecomposition, which will interfere with the subsequent correct diagnosis of the AC arc fault state.After the AO-VMD optimization, each mode component was clearly distinguished, which could well reflect the signal characteristics of each frequency band.This paper proves the superiority of the AO-VMD method for signal decomposition and the necessity of parameter optimization for VMD.
Comparison II: A comparative analysis of single-feature extraction and multidimensional fusion feature extraction was carried out.Time domain features, energy entropy, fuzzy entropy, and constructed multidimensional fault features of each load were extracted respectively for random forest diagnosis, and the judgment results of each load were obtained as shown in Table 5 below.Table 5 shows that the judgment accuracy of multi-dimensional feature extraction for each load is higher than that of single feature extraction, and the total average judgment accuracy exceeds about 2%, which proves the necessity and superiority of the multidimensional feature extraction method proposed in the article.

Conclusion
Arc fault feature extraction of low-voltage AC lines is deeply affected by environmental interference noise and insufficient feature extraction.In order to reduce the influence of these factors, this paper proposes a joint fault diagnosis model based on AO-VMD and RF, and draws the following conclusions: x In view of the difficulty in determining the [K, Į] value, which leads to poor signal decomposition effect, AO is used to optimize VMD parameters, proving that the proposed AO-VMD has a better decomposition effect than the VMD set with given artificial parameters, effectively avoiding mode alipping and over-decomposition phenomena, and extracting more abundant fault features.And the final fault diagnosis accuracy is higher.
x Multidimensional feature extraction is carried out for IMF components of VMD decomposition respectively.VMD can not only realize effective signal decomposition but also reduce the interference of environmental noise to a certain extent.Fault features extracted after VMD decomposition are more accurate, effectively enhance the ability to detect fault arcs, and have higher recognition accuracy than a single feature. x The diagnostic results of the random forest model show that this method can effectively detect and accurately diagnose low-voltage AC arc faults, greatly reduce the interference noise and improve the shortcomings of inadequate response of a single characteristic quantity, and the average recognition rate reaches more than 99%, which proves the effectiveness, accuracy, and universality of the proposed method under resistance, capacitance and inductive loads.

Figure 2 .
Figure 2. Experimental circuit and platform diagram

Figure 3 .
Figure 3.The current waveform of each load

4 .
Ac arc fault diagnosis flow based on multi-dimensional feature extraction AO-VMD decomposition was carried out for the collected waveforms of each load current, and the optimization range of VMD parameters was set to K=[4,10], Į=[500,4000].The minimum envelope entropy of each component was taken as the fitness function to calculate the [K, Į] value of each load, as shown in Table 2.The decomposed image was shown in Figure 4 below.

Figure 4 .
Figure 4. Decomposition waveform of each load current As shown in Figure 4, the original signal of different loads is decomposed into K variational mode components IMF by VMD, and the frequency of each mode increases in turn.The waveform image after VMD decomposition can be more intuitive to see the difference.Compared with the normal state, the fault arc signal fluctuates sharply, the impact component increases greatly, the signal becomes more complex, and the fault characteristics are obvious and easy to analyze and extract.

Figure 5 .
Figure 5. Flowchart for AC series arc fault diagnosis

Figure 6 .
Figure 6.Random forest diagnosis results of each load function; f t is the original signal to be decomposed; H is the convergence precision, " , and K is the maximum decomposition number;t G is the impact 0 H ! . below.

Table 1 .
Information for Each Load Parameter

Table 4 .
IAO-VMD and VMD Diagnosis Results

Table 5 .
Comparison of Diagnosis Results Between Single-feature and Multidimensional Feature