Machine Learning Based Prediction for the Response of Gas Discharge Tube to Damped Sinusoid Signal

Abstract

In order to predict the circuit response of a Gas Discharge Tube (GDT) to an electromagnetic pulse, a “black box” model for a GDT based on a machine learning method is proposed and validated in this paper.Firstly, the machine learning model of the Elman neural network is established by taking advantage of the existing measurement data to dampen the sinusoid signal, and then the established model is adopted to predict the response waveform of an unknown injection current grade and frequency.Without considering the complex physical parameters and dynamic behavior of GDTs, the Elman neural network modeling method is simpler than the existing physical or Pspice model.Validation experiments show a good agreement between the predicted and the measured waveforms.

1. Introduction

A Gas Discharge Tube (GDT) is filled with a kind of inert gas, which can reduce the overvoltage to the normal voltage. It is widely used to protect electrical or electronic devices against electromagnetic conducted interference [1,2,3,4]. The simulation of GDT behavior is an efficient way to design a protective circuit. In some complex circuits, reliable measurement is difficult [5]. Protective devices are mixed with other circuit devices in complex circuits, so it is practically impossible to test the performance of protective devices independently.Simulation can provide a way to obtain the current and voltage waveforms.

In recent years, mathematical models and Pspice models have been developed. The model of mathematics uses physical and mathematical parameters [6]. The parameters are related to the operation of GDT. This model not only includes electrical variables, but also the thermodynamic variables of state. There are still some problems to be researched, as the physical mechanism of GDTsare complex. The Pspice model uses circuit components to characterize the operation process of GDTs based on a mathematical model [7]. To ensure simulation convergence at the same time, the model is simplified appropriately. Both the mathematical model and thePspice model are based on some physical parameters of GDTs, which are often not readily available to ordinary users [8]. These physical parameters include the air gap spacing and air pressure of a GDT and the materials used for the cathode and anode of a GDT. The GDT manufacturer will not provide these.

Therefore, a “black box” model based on the machine learning method is proposed in this paper for predicting the electromagnetic pulsed response of GDT.Based on several sets of test data, this method can predict the response of GDT under different pulse excitation characteristics. Machine learning can obtain useful information directly from the raw data [9,10,11]. Firstly, it usually determines the eigenvalues and target values by analyzing the problem. Data areusually divided into training data and test data. Second, the prediction model of machine learning is trained by an algorithm based on training data. Finally, the model is used to predict the test data, and the ERR function is used to evaluate the prediction results.

Common machine learning methods includesupport vector machines, Bayes algorithms, decision trees, neural networks and so on [12,13,14,15,16,17,18,19,20]. Machine learning is a branch of artificial intelligence. It usually obtains useful information through some data mining methods. The neural network method has strong nonlinear processing ability, which can be used for multi classification, fitting and prediction. The support vector machine method has a strong generalization ability, but it is difficult to solve multi classification problems using it. A Bayes algorithm is an algorithm based on a priori probability. Adecision tree is a multi-classification algorithm similar to the tree model. The Bayes and decision tree methods are mostly used in classification problems. The problem studied in this paper relates to predicting the response of a GDT. These methods are not very suitable. So far, few people have used machine learning methods to model GDTs. One study used a neural network to predict the response of surge protective devices in [21]. In the experiment, IEC 61000-4-24 was used to establish the test system. The injected current waveform was square wave. A Narx neural network was used to predict the response waveform on different grades at the same half width. Unlike that article, more attention is paid to the precision of the rising time and half width in this paper. Because the response data of the electromagnetic interference of a GDT is continuous and has strong non-linearity, the Elman neural network method is chosen in this paper. It is suitable to deal with the time series problem and is often used in signal prediction [22,23,24].

In this paper, a neural network model is built to predict the circuit response of a GDT to adamped sinusoid signal. The damped sinusoid signal is one of the most common conduction interferences in electric systems. The measured data are the responses of a GDT to a damping sinusoidal signal of three frequencies. Two neural network models are established in this paper. One method is for predicting the residual current of GDT with different current levels at the same frequency. The other model is based on the response data of two frequencies to predict the residual current of a GDT at the third frequency. The third frequency is between the two frequencies. Results show that this method can effectively predict the circuit responses of a GDT. The error between measured data and predicted data is small.

2. Research Settings and Basic Data

The current injection method is used to research the circuit response of GDTs. The injection signal is a damping sinusoidal signal. The experimental methods are based on IEC61000-4-24.

The damped sinusoidal signal is produced by the damped signal generator. The frequency of injection signals is 1 MHz, 3 MHz and 5.6 MHz, which were chosen. These are several test frequency points specified in the MIL-STD-461E and CS116 standards. The damped sinusoidal generator thatwas used is also a device developed according to this standard.In the measurement, the voltage level of the signal source ranges from 50% to 100%. The corresponding voltage peak ranges from 400 V to 12.6 kV. The voltages of the signals are shown in

Table 1. The voltages of signals.

Grade (%)	1 MHz (V)	3 MHz (V)	5.6 MHz (V)
50%	821	6300	6300
55%	905	6900	6900
60%	987	7600	7600
65%	1071	8200	8200
70%	1154	8800	8800
75%	1237	9400	9400
80%	1300	10,100	10,100
85%	1400	10,700	10,700
90%	1492	11,300	11,300
95%	1580	11,900	11,900
100%	1675	12,600	12,600

. The grade column in Table 1 is the level of the injected current.This is the characteristic of the damped signal generator.Different pressure grades correspond to different voltages at different frequencies.

The measuring circuit is shown in Figure 1. The dampedsinusoidal transient generator’s type is POG-CS116. The generator complies with MIL-STD 461 D, E, F and G, paragraph CS 116. It can deliver waves from 10 kHz to 100 MHz at 6, 9 or 17 discrete frequencies. The current probe’s model is CIP-100. It is a high-performance broadband device. The bandwidth (3 dB points) is 20 kHz to 200 MHz. The transfer impedance is 1 Ω. The Sampling rate of the oscilloscope is 5GB/s, and the analog bandwidth is 1GHz. The model of the GDT is Epcos ec90. Taking 1 MHz as an example, the typical waveforms of injected current and residual voltage are shown in Figure 2.

3. Establishment of Machine Learning Model

The response data of a GDT is mainly residual voltage. In this paper, two neural network prediction models are established: (1) A neural network is built to predict the circuit response of different injection currents at the same frequency. (2) The neural network model is trained with the response data of two frequencies to predict the response in these two frequency ranges. By comparing the applicability of several neural networks, an Elman neural network is finally selected. The response of the GDT is a time domain waveform response. This neural network method is related to time series and is suitable for signal prediction.

An Elman feedback network has feedback connections between layers, so it retains past information. The Elman neural model theory believes that the information of the past will affect the future. The past information is related to future information. It has the input layer, the output layer, the connection layer and the hidden layer. The connection relationship is shown in Figure 3. The input layer contains data information, and the connection layer contains time domain information. It is more consistent with the information contained in the GDT circuit response data in the modeling process. As a result, anElman neural network can predict the circuit response of a GDT well. AnElman network uses an error function to correct weights. It is defined in Equation (1):

$$E=\frac{1}{2}{\displaystyle \sum }_{k=1}^m{\left({\mathit{m}}_{\mathit{k}}-{\mathit{y}}_{\mathit{k}}\right)}^2$$

(1)

where y_k is the predicted output vector of the network and m(k) is real output vector. Elman’s expression is defined below:

$$h\left(k\right)=f\left({\mathit{W}}_{\mathbf{2}}c\left(k\right)+{\mathit{W}}_{\mathbf{1}}x\left(k\right)\right)$$

(2)

x(k) is the input data, W₁ is the weight of input layer to hidden layer, W₂ is the weight of hidden layer to connection layer, W₃ is the weight between hidden to output layer, c(k) is the connection layer’s output and h(k) is the hidden layer’s output,

$$c\left(k\right)=h\left(k-1\right)$$

(3)

the output is y(k),

$$y\left(k\right)=g\left({\mathit{W}}_{3}h\left(k\right)\right)$$

(4)

W₁, W₂ and W₃ can be calculated through the derivation of E. f(x) usually uses the sigmoid function defined in Equation (5): h(x) and f(x) are linear.

$$f\left(x\right)=\frac{1}{1+e^{-x}}$$

(5)

This paper uses the training data to train the model, and then uses the model to predict the response of the test data. In the first neural network model, the network is trained on the GDT’s response data on different voltages at the same frequency. Then the data on other voltages thatare not used in training data are tested on the model. In the circuit response of the GDT, the measured data include injection current and residual voltage. Part of the data is used as training data and part as test data. The training data are the measured data at some injected current level. The test data are the other measured data. The input data’s attributes are the peak of the voltage that the pulse source generated and the peak of residual voltage. The output is a residual voltage waveform. The peak of the residual voltage in the training data is known, but the peak of the residual voltage in the test data is unknown.In order to calculate the peak of the residual voltage on the test data, a neural network was trained to predict the peak value first. Then, the neural network was trained on input data. After training, the model was used to predict the residual voltage waveforms on test data. This dual modeling method makes pattern-building more accurate.

In the second neural network model, a neural network is trained on the GDT’s response data on different voltages at two frequencies. The network is used to predict the response of the GDT at the third frequency. The circuit response data of the GDT under 1 MHz and 5.6 MHz are used to train the model, and the response data of the GDT under 3 MHz to test the model. The attributes of the input data in the training data are the peak of the voltage that the pulse source generated and the voltage level. The output data is the residual voltage waveform.

4. The Prediction of GDT’s Response

The current pulse injected is a damped sinusoidal signal. The frequencies of the damped sinusoidal signals are 1 MHz, 3 MHz and 5.6 MHz. The established method of the neural network is described in Section 3.

4.1. The Prediction of GDT’s Response with Different Pulse Current Injection Grades at the Same Frequency

One part of 1 MHz data is training data and one part is test data. The training data arethe grade of 50%, 60%, 70%, 80%, 90% and 100% of the injection current. The testing data arethe other data from 50% to 100% of the injection current grade. First, the residual voltage waveforms of the GDT were aligned before training the neural network. Alignment refers to the preprocessing of data. The residual waveform is aligned according to the front time of the waveform. Due to the strong nonlinearity of the GDT’s response, modeling is difficult. Alignment is equivalent to temporarily ignoring the time factor, which is conducive to improving the prediction accuracy of the model. The network was trained on the training data. After training, the model was tested on test data and restored response time by aligning time. During data preprocessing, the alignment position of the data is recorded. After modeling, the reverse process of alignment is used to restore the data to the original data, which is conducive to comparative analysis.

The peak value and half width of the residual waveform are related to the damage to the protected devices. The ERR equation is shown in Equation (6): where m is a value indicating the peak value or half width of the measured residual waveform, p represents the peak value or half width of the predicted residual waveform.

$$\mathrm{ERR}=\frac{\left|m-p\right|}{m}\times 100\%$$

(6)

The partial test waveforms are shown in Figure 4. The prediction of the GDT’s response at 85% current injection grade of 1 MHz is shown in Figure 4a. The trainging data and testing data’s division of 5.6MHz is same as 1MHz. Figure 4b shows the prediction of the GDT’s response at 85% of the current injection grade of 5.6 MHz.

The ERR between measured waveform and predicted waveform was calculated with Equation (6). The results of the peak ERR areshown in

Table 2. The peak ERR between measurement and prediction of 1 MHz and 5.6 MHz.

Frequency (MHz)	Grade (%)	Measured Peak (V)	Predicted Peak (V)	Peak ERR (%)
1	85	990.0	1007.9	1.8
5.6	85	970.0	961.9	0.8

. The frequency column represents the frequency of the injection current. The grade column is the level of the injected current. Its corresponding current amplitude can be found in Table 1. The peak ERR of 1 MHz is 1.8%. The peak ERR of 5.6 MHz is 0.8%. The results of the pulse width ERR is shown in

Table 3. The ERR of half width between measurement and prediction of 1 MHz and 5.6 MHz.

Frequency (MHz)	Grade (%)	Measured Pulse Width (ns)	Predicted Pulse Width (ns)	Pulse Width ERR (%)
1	85	13.6	12.2	10.3
5.6	85	19.6	20.6	5.1

. The pulse width ERR of 1 MHz is 10.3%. The half width ERR of 5.6 MHz is 5.1%.

It can be seen from Figure 4 that the predicted waveform is basically consistent with the measured waveform. However, from the ERR values of peak and half width, it is obvious that the ERR value of Peak is small. The reason for this is that in the modeling process, there are more peak modeling parameters and less parameters related to half width. This makes the learning of the network insufficient. However, the ERR of half width is less than 15%, which is acceptable in engineering applications. The extraction of input parameters will continue to be studied in the future.

4.2. The Prediction of the Response of GDT Circuits with Different Pulse Current Injection Peak at Different Frequency

The training data arethe response data of the GDT at a frequency of 1 MHz and 5.6 MHz. The testing data rethe response data of GDT at a frequency of 3 MHz. The neural network was trained on training data. Then, the trained network was used to predict the response of the GDT on the test data. Figure 5 shows the prediction of the GDT’s responses with the current injection level of 90% at 3 MHz.

Table 4. The peak ERR between measurement and prediction of 1 MHz and 3 MHz.

Grade (%)	Measured Peak (V)	Predicted Peak (V)	Peak ERR (%)
90	930	923.0	0.7

and

Table 5. The ERR of half width between measurement and prediction of 3 MHz.

Grade (%)	Measured Pulse Width (ns)	Predicted Pulse Width (ns)	Pulse Width ERR (%)
90	22.2	20.2	9

are comparisons between the measured waveform and the predicted. The representation of each column is the same as in Table 1 and Table 2. The peak ERR of 3 MHz is 0.7%. The half width ERR of 3 MHz is 9%.

It can be seen from Figure 5 that the predicted waveform is basically consistent with the measured waveform. The neural network model established basically describes the protective characteristics of the GDT. The ERR value of Peak is smaller than half width, which is similar to the above reasons. Because of the stronger nonlinearity, it is more difficult to predict the response of different grades of GDT at different frequencies. More modeling parameters need to be extracted. In the follow-up, multi method combination modelling will be studied to increase modeling parameters.

In the future, we will use the subsection modeling method to model the just on conduction state to the complete conduction state. The subsection modeling method will have a stronger modeling ability. After subsection modeling, the accuracy of the model may be improved by introducing a wider range of frequencies.

5. Conclusions

In this paper, the machine learning method is used to predict the response of a GDT’s responses to a damped sinusoid signal. The measurement system is set up according to IEC61000-4-24. The frequencies of 1 MHz, 3 MHz and 5.6 MHz are chosen as test frequency points, as specified in the MIL-STD-461E and CS116 standards to test the responses of the GDT.The Elman neural network method is used to establish the predicted model. In order to study the prediction of the GDT’s response, two kinds of models are established. One model is used to predict the GDT’s responses at different grades. The other is used to predict the GDT’s response at different grades and frequencies.Through modeling and analysis, the prediction results are basically consistent with the experimental results.It is proven that this research method is feasible. It performs well in the nonlinear response prediction of the GDT. More research can be carried out based on this approach.

In the following work, the following studies will be carried out: (1) More frequencies will be tested to establish the model with higher accuracy. (2) The data of the GDT from just conduction to complete conduction will be added into the data. (3) Comparison between different types of GDT will be researched. A more extensible machine learning model will be built.