# PSO–SOM Neural Network Algorithm for Series Arc Fault Detection

Authors: Na Qu; Jiatong Chen; Jiankai Zuo; Jinhai Liu
Journal: Advances in Mathematical Physics
 (2020)

---

## Abstract

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.


---

## Body

## 1. 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 often 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%. Therefore, the detection of series arc fault is meaningful to ensure electrical safety.The 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]. The Cassie arc model is mainly used for large current periods before current crosses zero. The 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 [6–9] and so on, have been proposed. Current feature extraction mainly includes time domain feature extraction and frequency domain feature extraction. The time domain feature is mainly based on the zero-rest phenomenon of arc fault current [10]. The frequency domain feature extraction is mainly based on Fourier transform [11–13] and wavelet transform [14–16]. The 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 often used in indoor power distribution system. Matrix coefficients method are suitable for circuit with few load types, mainly used for aircraft 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. 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 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. The block diagram of complete description is shown as Figure 1.Figure 1
The block diagram of complete description.


## 2. Current Features Extraction

The current is selected as the detection signal and the current data are collected by arc fault experiment platform. The experimental platform is mainly composed of power supply, arc generator, loads, and acquisition device. The 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. The current data are obtained by the sampling resistance method. The 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. The sample data come from five types of load circuits, as shown in Table1. The current features are extracted from both time domain and frequency domain.Table 1
Load type and sampling resistance.
Load type
Load name
Sampling resistance
Resistive and inductive load
Lamp and inductor in series
100 Ω
Resistive load
Lamp
100 Ω
Eddy current load
Induction cooker
1 Ω
Switching power supply load
Computer
50 Ω
Series motor load
Hand drill
50 Ω


### 2.1. Features Extraction in Frequency Domain

The fast Fourier transform (FFT) is used to obtain the current amplitude spectrum. The amplitudes of 0~2000 Hz are selected for features extraction. The frequency range is divided into ten intervals on average. The 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 Tables2–6.Table 2
Frequency domain feature values of lamp and inductor in series load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Lamp and inductor in series
0.0318
0.0194
0–200
0.0124
0.0005
200–400
0.0129
0.0007
400–600
0.0120
0.0015
600–800
0.0115
0.0007
800–1000
0.0108
0.0014
1000–1200
0.0106
0.0010
1200–1400
0.0078
0.0016
1400–1600
0.0082
0.0011
1600–1800
0.0064
0.0009
1800–2000Table 3
Frequency domain feature values of lamp load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Lamp
3.7304
2.9273
0–200
0.9459
0.0210
200–400
0.5663
0.0911
400–600
0.4564
0.0758
600–800
0.2605
0.0204
800–1000
0.2916
0.0973
1000–1200
0.2300
0.0542
1200–1400
0.1797
0.0569
1400–1600
0.2215
0.0611
1600–1800
0.1782
0.0290
1800–2000Table 4
Frequency domain feature values of induction cooker load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Induction cooker
0.1383
1.7710
0–200
0.0500
0.2482
200–400
0.1131
1.4436
400–600
0.0774
0.2819
600–800
0.0480
0.0533
800–1000
0.1119
0.1298
1000–1200
0.0723
0.0539
1200–1400
0.0664
0.0306
1400–1600
0.0748
0.0353
1600–1800
0.0660
0.0349
1800–2000Table 5
Frequency domain feature values of computer load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Computer
0.6353
0.0197
0–200
0.7551
0.0033
200–400
0.6838
0.0026
400–600
0.6898
0.0019
600–800
0.7297
0.0012
800–1000
0.7902
0.0006
1000–1200
0.5011
0.0016
1200–1400
0.6562
0.0011
1400–1600
0.6743
0.0016
1600–1800
0.6181
0.0006
1800–2000Table 6
Frequency domain feature values of hand drill load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Hand drill
15.4219
16.3304
0–200
0.2571
0.3504
200–400
0.3232
0.3253
400–600
0.1677
0.1674
600–800
0.0714
0.0574
800–1000
0.0894
0.1255
1000–1200
0.0704
0.0567
1200–1400
0.0569
0.0773
1400–1600
0.1135
0.0937
1600–1800
0.0552
0.0640
1800–2000It can be seen from Tables2–6 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. The 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. The amplitude difference between fault current and normal current is not obvious when the load is hand drill.


### 2.2. Features Extraction in Time Domain

In the time domain, one cycle of current is divided into ten segments on average. Four features of current,i.e., current average, current pole difference, current variance and current difference average, are calculated. The current average, current pole difference, and current variance respectively correspond to one number in each segment and ten numbers in one cycle. The difference average contains nine numbers in one cycle, because it is obtained by calculating the current difference between two adjacent segments. Thirty-nine numbers are obtained as current features in time domain.The 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 Figure2. There are obvious differences between fault current and normal current.Figure 2
The time domain features extraction of induction cooker load circuit. (a) Current average, (b) current pole difference, (c) current variance, and (d) current difference average.
(a)
(b)
(c)
(d)


## 2.1. Features Extraction in Frequency Domain

The fast Fourier transform (FFT) is used to obtain the current amplitude spectrum. The amplitudes of 0~2000 Hz are selected for features extraction. The frequency range is divided into ten intervals on average. The 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 Tables2–6.Table 2
Frequency domain feature values of lamp and inductor in series load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Lamp and inductor in series
0.0318
0.0194
0–200
0.0124
0.0005
200–400
0.0129
0.0007
400–600
0.0120
0.0015
600–800
0.0115
0.0007
800–1000
0.0108
0.0014
1000–1200
0.0106
0.0010
1200–1400
0.0078
0.0016
1400–1600
0.0082
0.0011
1600–1800
0.0064
0.0009
1800–2000Table 3
Frequency domain feature values of lamp load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Lamp
3.7304
2.9273
0–200
0.9459
0.0210
200–400
0.5663
0.0911
400–600
0.4564
0.0758
600–800
0.2605
0.0204
800–1000
0.2916
0.0973
1000–1200
0.2300
0.0542
1200–1400
0.1797
0.0569
1400–1600
0.2215
0.0611
1600–1800
0.1782
0.0290
1800–2000Table 4
Frequency domain feature values of induction cooker load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Induction cooker
0.1383
1.7710
0–200
0.0500
0.2482
200–400
0.1131
1.4436
400–600
0.0774
0.2819
600–800
0.0480
0.0533
800–1000
0.1119
0.1298
1000–1200
0.0723
0.0539
1200–1400
0.0664
0.0306
1400–1600
0.0748
0.0353
1600–1800
0.0660
0.0349
1800–2000Table 5
Frequency domain feature values of computer load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Computer
0.6353
0.0197
0–200
0.7551
0.0033
200–400
0.6838
0.0026
400–600
0.6898
0.0019
600–800
0.7297
0.0012
800–1000
0.7902
0.0006
1000–1200
0.5011
0.0016
1200–1400
0.6562
0.0011
1400–1600
0.6743
0.0016
1600–1800
0.6181
0.0006
1800–2000Table 6
Frequency domain feature values of hand drill load circuit.
Load name
Mean amplitude of fault current (%)
Mean amplitude of normal current (%)
Frequency range/Hz
Hand drill
15.4219
16.3304
0–200
0.2571
0.3504
200–400
0.3232
0.3253
400–600
0.1677
0.1674
600–800
0.0714
0.0574
800–1000
0.0894
0.1255
1000–1200
0.0704
0.0567
1200–1400
0.0569
0.0773
1400–1600
0.1135
0.0937
1600–1800
0.0552
0.0640
1800–2000It can be seen from Tables2–6 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. The 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. The amplitude difference between fault current and normal current is not obvious when the load is hand drill.


## 2.2. Features Extraction in Time Domain

In the time domain, one cycle of current is divided into ten segments on average. Four features of current,i.e., current average, current pole difference, current variance and current difference average, are calculated. The current average, current pole difference, and current variance respectively correspond to one number in each segment and ten numbers in one cycle. The difference average contains nine numbers in one cycle, because it is obtained by calculating the current difference between two adjacent segments. Thirty-nine numbers are obtained as current features in time domain.The 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 Figure2. There are obvious differences between fault current and normal current.Figure 2
The time domain features extraction of induction cooker load circuit. (a) Current average, (b) current pole difference, (c) current variance, and (d) current difference average.
(a)
(b)
(c)
(d)


## 3. 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 [24–26]. PSO–SOM is applied to the detection of series arc fault in different load circuits. Three indexes, i.e., intra-class density, standard deviation and sample difference, are used to judge the weight value.


### 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. The network structure consists of input layer and competition layer. The input layer corresponds to a group of high-dimensional input vectors. The competition layer consists of ordered nodes in two-dimensional grid. The input vectors and output nodes are connected by weight vectors.The 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.(1)
d
j
=
∑
i
=
1
m
x
i
−
w
i
j
2
,
wherex
i represents the i
t
h input vector, w
i
j represents the weight vector between the j
t
h neuron of competitive layer and the i
t
h neuron of input layer, m represents the number of input layer neurons.
(c)
The 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).(2)
w
new
=
w
old
+
η
i
x
i
−
w
i
j
,
wherew
new and w
odd represent the weight vectors of updated and before update, respectively. Here, η
i represents learning rate varying with training frequency and is determined by (3).(3)
η
i
=
r
max
−
i
m
a
x
g
e
n
r
max
−
r
min
,
Wherer
max is the maximum of learning rate, r
min is minimum of learning rate, and m
a
x
g
e
n is the maximum of training steps.
The radius of the weight update range is determined by (4).(4)
l
=
l
max
−
i
m
a
x
g
e
n
l
max
−
l
min
,
wherel
min is the minimum of dynamic radius, l
max is the maximum of dynamic radius.
(d)
After the training of the network, the test sample is input into the network. The winning neuron is the category of detection result.


### 3.2. 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 predation. The 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. Then update the position and speed of all particles according to (5) and (6).(5)
V
k
+
1
=
ω
V
k
+
c
1
a
1
P
i
−
X
+
c
2
a
2
P
g
−
X
,
(6)
X
k
+
1
=
X
k
+
V
k
+
1
,
whereV
k is the speed of the particle in the last iteration, V
k
+
1 is the speed after this update. P
i is the individual extreme value of the particle and P
g is population extreme value of the particle. c
1 and c
2 are nonnegative constants and take 1.5 here. r
1 and r
2 are random numbers between 0 and 1. X
k is the position of particle before updated, X
k
+
1 is the position of particle after updated.
(c)
Repeat the calculation process of the second step until all particles converge to a certain point which is the optimal value.


### 3.3. PSO–SOM Algorithm Design

The 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.(a)
Intra-class density. Intra-class density is used to measure the aggregation degree of the same category of data, as shown in (7).(7)
D
=
∑
j
=
1
p
∑
i
=
1
n
R
−
α
i
j
f
R
−
α
i
j
,
whereR is the window width parameter and takes 0.1 here, α
i
j is the Euclidean distance between the weight vector and input vector, f is the step function and takes 1 when the independent variables is greater than or equal to 0, or takes 0.
(b)
Standard deviation. The standard deviation is used to measure the dispersion degree of data, as shown in (8).(8)
S
=
∑
i
=
1
n
v
i
−
v
a
v
e
2
n
−
1
,
wherev
i is the weight vector of the i
t
h neuron, v
a
v
e is the average vector value, n 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).(9)
L
=
∑
i
=
1
n
min
d
i
s
t
v
i
,
v
d
a
t
a
,
Wheremin
d
i
s
t
v
i
,
v
d
a
t
a is the minimum of the Euclidean distance of the i
t
h neuron weight vector.
The fitness function of PSO algorithm is obtained by using the above three indexes, as shown in (10).(10)
y
=
S
D
L
.
The PSO–SOM algorithm flow chart is shown in Figure3.Figure 3
The flow chart of PSO–SOM algorithm.


### 3.4. Arc Fault Detection

The PSO–SOM algorithm is used to establish the arc fault detection model [27–30]. The model inputs are forty-nine in total, including thirty-nine feature values in the time domain and ten feature values in the frequency domain. The 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. The binary encoding method is adopted, and the encoding length is 4 bits. The first three bits represent the type of load and the last bit represents normal state or fault state.Table 7
Load corresponding number in different working conditions.
Load type
Work state
Corresponding number
Lamp and inductor in series
Fault
0010
Normal
0011
Lamp
Fault
0100
Normal
0101
Induction cooker
Fault
0110
Normal
0111
Computer
Fault
1000
Normal
1001
Hand drill
Fault
1010
Normal
1011The PSO–SOM model needs to cluster ten categories of samples. Each category takes 100 groups of samples. Among them, 60 groups of samples are selected as training data randomly, and the remaining 40 groups of samples as testing data. Then, there are 400 groups of samples as testing data in total.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.Here, twenty groups of detection results are selected for demonstration, as shown in Figure4. The 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. The vertical axis represents the category. The 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.Figure 4
Detection results of PSO–SOM mode.The optimization process of the PSO algorithm is shown in Figure5. The 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 after 25 times of training.Figure 5
The optimization process of PSO algorithm.


## 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. The network structure consists of input layer and competition layer. The input layer corresponds to a group of high-dimensional input vectors. The competition layer consists of ordered nodes in two-dimensional grid. The input vectors and output nodes are connected by weight vectors.The 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.(1)
d
j
=
∑
i
=
1
m
x
i
−
w
i
j
2
,
wherex
i represents the i
t
h input vector, w
i
j represents the weight vector between the j
t
h neuron of competitive layer and the i
t
h neuron of input layer, m represents the number of input layer neurons.
(c)
The 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).(2)
w
new
=
w
old
+
η
i
x
i
−
w
i
j
,
wherew
new and w
odd represent the weight vectors of updated and before update, respectively. Here, η
i represents learning rate varying with training frequency and is determined by (3).(3)
η
i
=
r
max
−
i
m
a
x
g
e
n
r
max
−
r
min
,
Wherer
max is the maximum of learning rate, r
min is minimum of learning rate, and m
a
x
g
e
n is the maximum of training steps.
The radius of the weight update range is determined by (4).(4)
l
=
l
max
−
i
m
a
x
g
e
n
l
max
−
l
min
,
wherel
min is the minimum of dynamic radius, l
max is the maximum of dynamic radius.
(d)
After the training of the network, the test sample is input into the network. The winning neuron is the category of detection result.


## 3.2. 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 predation. The 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. Then update the position and speed of all particles according to (5) and (6).(5)
V
k
+
1
=
ω
V
k
+
c
1
a
1
P
i
−
X
+
c
2
a
2
P
g
−
X
,
(6)
X
k
+
1
=
X
k
+
V
k
+
1
,
whereV
k is the speed of the particle in the last iteration, V
k
+
1 is the speed after this update. P
i is the individual extreme value of the particle and P
g is population extreme value of the particle. c
1 and c
2 are nonnegative constants and take 1.5 here. r
1 and r
2 are random numbers between 0 and 1. X
k is the position of particle before updated, X
k
+
1 is the position of particle after updated.
(c)
Repeat the calculation process of the second step until all particles converge to a certain point which is the optimal value.


## 3.3. PSO–SOM Algorithm Design

The 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.(a)
Intra-class density. Intra-class density is used to measure the aggregation degree of the same category of data, as shown in (7).(7)
D
=
∑
j
=
1
p
∑
i
=
1
n
R
−
α
i
j
f
R
−
α
i
j
,
whereR is the window width parameter and takes 0.1 here, α
i
j is the Euclidean distance between the weight vector and input vector, f is the step function and takes 1 when the independent variables is greater than or equal to 0, or takes 0.
(b)
Standard deviation. The standard deviation is used to measure the dispersion degree of data, as shown in (8).(8)
S
=
∑
i
=
1
n
v
i
−
v
a
v
e
2
n
−
1
,
wherev
i is the weight vector of the i
t
h neuron, v
a
v
e is the average vector value, n 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).(9)
L
=
∑
i
=
1
n
min
d
i
s
t
v
i
,
v
d
a
t
a
,
Wheremin
d
i
s
t
v
i
,
v
d
a
t
a is the minimum of the Euclidean distance of the i
t
h neuron weight vector.
The fitness function of PSO algorithm is obtained by using the above three indexes, as shown in (10).(10)
y
=
S
D
L
.
The PSO–SOM algorithm flow chart is shown in Figure3.Figure 3
The flow chart of PSO–SOM algorithm.


## 3.4. Arc Fault Detection

The PSO–SOM algorithm is used to establish the arc fault detection model [27–30]. The model inputs are forty-nine in total, including thirty-nine feature values in the time domain and ten feature values in the frequency domain. The 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. The binary encoding method is adopted, and the encoding length is 4 bits. The first three bits represent the type of load and the last bit represents normal state or fault state.Table 7
Load corresponding number in different working conditions.
Load type
Work state
Corresponding number
Lamp and inductor in series
Fault
0010
Normal
0011
Lamp
Fault
0100
Normal
0101
Induction cooker
Fault
0110
Normal
0111
Computer
Fault
1000
Normal
1001
Hand drill
Fault
1010
Normal
1011The PSO–SOM model needs to cluster ten categories of samples. Each category takes 100 groups of samples. Among them, 60 groups of samples are selected as training data randomly, and the remaining 40 groups of samples as testing data. Then, there are 400 groups of samples as testing data in total.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.Here, twenty groups of detection results are selected for demonstration, as shown in Figure4. The 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. The vertical axis represents the category. The 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.Figure 4
Detection results of PSO–SOM mode.The optimization process of the PSO algorithm is shown in Figure5. The 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 after 25 times of training.Figure 5
The optimization process of PSO algorithm.


## 4. 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. The LVQ is a kind of competitive neural network with supervised learning. The LVQ network consists of input layer, hidden layer, and output layer. The main steps of LVQ network are as follows.(1)
Initialize the connection weight vectors and other parameters.
(2)
Calculate the Euclidean distance between the weight vectors and the input vectors, as (11).(11)
L
=
∑
i
=
1
m
x
i
−
w
i
j
2
,
wherex
i represents the i
t
h input vector, w
i
j represents the weight vector between the j
t
h neuron of hidden layer and the i
t
h neuron of input layer, m 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).(12)
w
new
=
w
old
+
η
x
−
w
old
.Otherwise, the weight vectors are modified according to (13).(13)
w
new
=
w
old
−
η
x
−
w
old
,wherew
new and w
odd respectively represent the corrected weight and the weight before correction, η represents the learning rate.Twenty groups of detection results of LVQ network are selected for demonstration, as shown in Figure6. Twenty groups of detection results of conventional SOM network are selected for demonstration, as shown in Figure 7.Figure 6
Detection results of LVQ network.Figure 7
Detection results of conventional SOM network.Four hundred groups of testing samples are input into PSO–SOM network, conventional SOM network, and LVQ network, respectively. The detection results are counted in Table8. The 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.Table 8
Detection result comparison.
Algorithm
Number of test samples
Number of correct results
Detection accuracy (%)
LVQ network
400
213
53.25
SOM network
400
224
56
PSO–SOM network
400
380
95


## 5. 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 to judge the weight value. PSO–SOM network is applied to the detection of series arc fault in electrical circuits. The current is selected as the detection signal of arc fault. The 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. The 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.



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*Source: 6721909-2020-01-25.xml*