PSO–SOM Neural Network Algorithm for Series Arc Fault Detection

. Self-organizing feature map (SOM) neural network is a kind of competitive neural network with unsupervised learning. It has the strong abilities of self-organization and self-learning. However, the classiﬁcation accuracy of SOM neural network may decrease when the features of tested object are not obvious. In this paper, the particle swarm optimization (PSO) algorithm is used to optimize the weight values of SOM network. Three indexes, i.e., intra-class density, standard deviation and sample diﬀerence, are used to judge the weight value, which can improve the classiﬁcation accuracy of the SOM network. PSO–SOM network is applied to the detection of series arc fault in electrical circuits and compared with conventional SOM network and learning vector quantization (LVQ) network. The detection accuracy of the PSO–SOM network is 95%, which is higher than conventional SOM network and LVQ network.


Introduction
In the low voltage supply environment, the insulation ability of electrical wires or appliances will decline because of the aged or damaged insulation layer.When the voltage reaches a certain value, an arc fault may occur.When a series arc fault occurs, the current value is o en less than the threshold of the circuit breaker.But its temperature can reach to thousands of degrees and it is not easily extinguished.While maintaining voltage is 20 V, the arc can still maintain a continuous and stable combustion.It is easy to cause the electrical fire.Statistical analysis shows that the proportion of electric fires caused by arc faults is up to 50%.erefore, the detection of series arc fault is meaningful to ensure electrical safety.
e research of arc fault detection mainly focuses on arc simulation model, current feature extraction and detection algorithm.Cassie and Mayr models are proposed early [1,2].
e Cassie arc model is mainly used for large current periods before current crosses zero.e Mayr arc model is mainly used for small current periods when the current crosses zero.On the basis of Cassie model and Mayr model, Habedank model [3], modified Mayr model [4], Schwamaker model [5], segmented arc model [6][7][8][9] and so on, have been proposed.Current feature extraction mainly includes time domain feature extraction and frequency domain feature extraction.
e detection algorithms mainly include neural network [17,18], support vector machine (SVM) [19,20], Chirp-zeta transform [21], matrix coefficients [22], quantum probability mode [23] etc. Neural network, SVM, and Chirp-zeta transform are o en used in indoor power distribution system.Matrix coefficients method are suitable for circuit with few load types, mainly used for aircra arc fault detection.Quantum probability model is mainly applied to arc fault detection of photovoltaic power generation system.
In this paper, the particle swarm optimization (PSO) algorithm is used to optimize self-organizing feature map (SOM) neural network.ree indexes, i.e., intra-class density, standard deviation and sample difference, are used to judge the weight value, which can improve the classification accuracy of the SOM network.PSO-SOM algorithm is applied to the detection of series arc fault in electrical circuits and compared with conventional SOM network and learning vector quantization (LVQ) network.e block diagram of complete description is shown as Figure 1.

Current Features Extraction
e current is selected as the detection signal and the current data are collected by arc fault experiment platform.e experimental platform is mainly composed of power supply, arc generator, loads, and acquisition device.e power supply is 220 V and 50 Hz AC.Arc generator is mainly composed of fixing carbon electrode and moving copper electrode.TDS1001C-SC of Tektronix oscilloscope and TPP0101 10X of voltage probe are selected to collect data.e current data are obtained by the sampling resistance method.e sampling resistance method is to connect a resistor in series in the circuit and measure the voltage across the resistor, then use Ohm's law to get the current.e sample data come from five types of load circuits, as shown in Table 1.e current features are extracted from both time domain and frequency domain.

Features Extraction in Frequency Domain.
e fast Fourier transform (FFT) is used to obtain the current amplitude spectrum.
e amplitudes of 0~2000 Hz are selected for features extraction.e frequency range is divided into ten intervals on average.e mean current amplitude of each interval is calculated as one feature value in the frequency domain, and there are ten feature values in total.
A set of feature values under the conditions of lamp and inductor in series load, lamp load, induction cooker load, computer load, and hand drill load are shown in Tables 2-6.
It can be seen from Tables 2-6 that the amplitudes of fault current are higher than those of normal current when the loads are lamp and inductor in series, lamp and computer.e amplitudes of fault current are lower than those of normal current in low frequency band and higher than those of normal current in high frequency band when the load is induction cooker.
e amplitude difference between fault current and normal current is not obvious when the load is hand drill.e experimental data of five types of load circuit current are measured and the induction cooker load circuit current is taken as an example to illustrate features extraction, as shown in Figure 2. ere are obvious differences between fault current and normal current.

PSO-SOM Algorithm for Arc Fault Detection
In order to improve the classification accuracy, the PSO is used to optimize the weight values of SOM [24][25][26].PSO-SOM is applied to the detection of series arc fault in different load circuits.ree indexes, i.e., intra-class density, standard deviation and sample difference, are used to judge the weight value.where represents the 푡ℎ input vector, w represents the weight vector between the 푡ℎ neuron of competitive layer and the 푡ℎ neuron of input layer, represents the number of input layer neurons.(c) e neuron with the minimum Euclidean distance in the competitive layer is the winning neuron.Update neuron weight vectors within a certain distance around the winning neuron, as (2).
where new and old represent the weight vectors of updated and before update, respectively.Here, 휂(푖) represents learning rate varying with training frequency and is determined by (3).
where max is the maximum of learning rate, min is minimum of learning rate, and is the maximum of training steps.
e radius of the weight update range is determined by (4).
where min is the minimum of dynamic radius, max is the maximum of dynamic radius.(d) A er the training of the network, the test sample is input into the network.e winning neuron is the category of detection result.

PSO Algorithm.
PSO is a swarm intelligence optimization algorithm and the purpose is to solve the optimal value by imitating the movement rule of birds in the process of (1) where is the speed of the particle in the last iteration, 푘+1 is the speed a er this update.is the individual extreme value of the particle and is population extreme value of the particle.1 and 2 are nonnegative constants and take 1.5 here.1 and 2 are random numbers between 0 and 1. is the position of particle before updated, 푘+1 is the position of particle a er updated.(c) Repeat the calculation process of the second step until all particles converge to a certain point which is the optimal value.

PSO-SOM Algorithm Design.
e PSO algorithm is used to optimize the weight values of SOM network.ree predation.e main training process of the PSO algorithm is as follows.
(a) Determine the fitness function and generate a certain number of particles in the feasible domain.Each particle is a potential optimal solution.(b) Calculate the each particle value according to the fitness function, and select the individual and group extreme value.en update the position and speed of all particles according to ( 5) and ( 6).
(5) In addition, other parameters of PSO-SOM model are set [31,32].In the SOM network, the number of competing neurons is 6 × 6 = 36, the maximum of the network learning rate is 0.2, the minimum is 0.05, the maximum and minimum of the weight update radius is 1.5 and 0.8, the training steps are 200.In the PSO algorithm, the swarm size is 10, the maximum of individual speed is 0.5, the individual position coordinate range is ±2, the maximum of training steps is 100.indexes, i.e., intra-class density, standard deviation and sample difference, are used to judge the weight value, which can improve the classification accuracy of the SOM network.
(a) Intra-Class Density.Intra-class density is used to measure the aggregation degree of the same category of data, as shown in (7).
where is the window width parameter and takes 0.1 here, is the Euclidean distance between the weight vector and input vector, is the step function and takes 1 when the independent variables is greater than or equal to 0, or takes 0. (b) Standard Deviation.e standard deviation is used to measure the dispersion degree of data, as shown in (8).
where is the weight vector of the 푡ℎ neuron, v is the average vector value, is the number of competing neurons.(c) Sample Difference.Sample difference is used to measure the similarity degree among the same category of neurons, as shown in (9).
where min 푑푖푠푡 푣 , 푣 is the minimum of the Euclidean distance of the 푡ℎ neuron weight vector.
e fitness function of PSO algorithm is obtained by using the above three indexes, as shown in (10).e PSO-SOM algorithm flow chart is shown in Figure 3.

Arc Fault Detection.
e PSO-SOM algorithm is used to establish the arc fault detection model [27][28][29][30].e model inputs are forty-nine in total, including thirty-nine feature values in the time domain and ten feature values in the frequency domain.e outputs are ten kinds of states, i.e., fault or normal state of lamp and inductor in series load, fault or normal state of lamp load, fault or normal state of induction cooker load, fault or normal state of computer load, fault or normal state of hand drill load, as shown in Table 7.Ten kinds of work states are numbered.e binary encoding method is adopted, and the encoding length is 4 bits.e first three bits represent the type of load and the last bit represents normal state or fault state.
e PSO-SOM model needs to cluster ten categories of samples.Each category takes 100 groups of samples.Among (1) Initialize the connection weight vectors and other parameters.
(2) Calculate the Euclidean distance between the weight vectors and the input vectors, as (11).
where represents the 푡ℎ input vector, represents the weight vector between the 푡ℎ neuron of hidden layer and the 푡ℎ neuron of input layer, represents the number of input layer neurons.(3) If the category of output layer neuron according to the nearest neuron is the same as actual category of data, the weight vectors between hidden layer and input layer are modified according to (12).
Otherwise, the weight vectors are modified according to (13).
where new and old respectively represent the corrected weight and the weight before correction, represents the learning rate.
Twenty groups of detection results of LVQ network are selected for demonstration, as shown in Figure 6.Twenty groups of detection results of conventional SOM network are selected for demonstration, as shown in Figure 7.
Four hundred groups of testing samples are input into PSO-SOM network, conventional SOM network, and LVQ network, respectively.e detection results are counted in Table 8. e detection accuracy of the PSO-SOM network is 95%, while those of the conventional SOM network and LVQ network are 56% and 53.25%.It shows the effectiveness of the LVQ network algorithm.
Here, twenty groups of detection results are selected for demonstration, as shown in Figure 4. e horizontal axis represents the sample number, and the number 1-2 represents the fault state sample of lamp and inductor in series load, the number 3-4 represents the normal state sample of lamp and inductor in series load, the number 5-6 represents the fault state sample of lamp load, the number 7-8 represents the normal state sample of lamp load, the number 9-10 represents the fault state sample of hand drill load, the number 11-12 represents the normal state sample of hand drill load, the number 13-14 represents the fault state sample of computer load, the number 15-16 represents the normal state sample of computer load, the number 17-18 represents the fault state sample of induction cooker load, the number 19-20 represents the normal state sample of induction cooker load.e vertical axis represents the category.
e blue circle indicates the correct category and the red asterisk indicates the detection result.If the two symbols coincide in the same category, the detection result is right.Otherwise, the detection result is wrong.It can be seen that there are nineteen results are correct, and only one result is wrong when the work state is normal state of lamp and inductor in series load.
e optimization process of the PSO algorithm is shown in Figure 5. e horizontal axis represents the training times and the vertical axis represents the particle fitness.It can be seen that all particles converge to the optimum fitness value of 0.0092 a er 25 times of training.

Comparison with the Conventional SOM Network and LVQ Network Algorithms
Arc fault detection of PSO-SOM network is compared with conventional SOM network and LVQ network.e LVQ is a kind of competitive neural network with supervised learning.
e LVQ network consists of input layer, hidden layer, and output layer.e main steps of LVQ network are as follows.5: e optimization process of PSO algorithm.Advances in Mathematical Physics to judge the weight value.PSO-SOM network is applied to the detection of series arc fault in electrical circuits.e current is selected as the detection signal of arc fault.e current features are extracted from both time domain and frequency domain.Forty-nine feature values are taken as inputs of PSO-SOM model.Ten kinds of work states are taken as outputs of PSO-SOM model.e detection accuracy of the PSO-SOM network model is about 95%, which is higher than that of conventional SOM network model and LVQ network model.

Conclusions
In this paper, PSO algorithm is used to optimize the weight values of SOM network and three indexes, i.e., intra-class density, standard deviation and sample difference, are used

3. 1 .
SOM Neural Network.SOM neural network is a kind of competitive neural network with unsupervised learning.It has the strong ability of self-organization and wide applications in classification problem.e network structure consists of input layer and competition layer.e input layer corresponds to a group of high-dimensional input vectors.e competition layer consists of ordered nodes in two-dimensional grid.e input vectors and output nodes are connected by weight vectors.e learning steps of SOM neural network are as follows: (a) Initialize the network structure, the neuron numbers each layer, and the weight values.(b) Input the training samples and use Equation (1) to calculate the Euclidean Distances between the weight vector and the input vector.

F 2 :
e time domain features extraction of induction cooker load circuit.Current difference average Advances in Mathematical Physics them, 60 groups of samples are selected as training data randomly, and the remaining 40 groups of samples as testing data.en, there are 400 groups of samples as testing data in total.

F 4 :
Detection results of PSO-SOM mode.