Research on imbalanced data fault diagnosis of on-load tap changers based on IGWO-WELM

Yan Yan; Yong Qian; Hongzhong Ma; Changwu Hu; Yan Yan; Yong Qian; Hongzhong Ma; Changwu Hu

doi:10.3934/mbe.2023226

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4877-4895. doi: 10.3934/mbe.2023226

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Research article

Research on imbalanced data fault diagnosis of on-load tap changers based on IGWO-WELM

1.
State Grid Ningxia Electric Power Research Institute, Yinchuan 750002, China
2.
College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China
3.
Zhongwei Power Supply Company of State Grid Ningxia Electric Power Co. Ltd, Zhongwei 755000, China

Academic Editor: Yang Kuang

Received: 21 October 2022 Revised: 11 December 2022 Accepted: 16 December 2022 Published: 04 January 2023

Aiming at the problem of on-load tap changer (OLTC) fault diagnosis under imbalanced data conditions (the number of fault states is far less than that of normal data), this paper proposes an OLTC fault diagnosis method based on an Improved Grey Wolf algorithm (IGWO) and Weighted Extreme Learning Machine (WELM) optimization. Firstly, the proposed method assigns different weights to each sample ac-cording to WELM, and measures the classification ability of WELM based on G-mean, so as to realize the modeling of imbalanced data. Secondly, the method uses IGWO to optimize the input weight and hidden layer offset of WELM, avoiding the problems of low search speed and local optimization, and achieving high search efficiency. The results show that IGWO-WLEM can effectively diagnose OLTC faults under imbalanced data conditions, with an improvement of at least 5% compared with existing methods.

Keywords:

imbalanced data,
OLTC,
IGWO,
WELM,
IGWO-WELM

Citation: Yan Yan, Yong Qian, Hongzhong Ma, Changwu Hu. Research on imbalanced data fault diagnosis of on-load tap changers based on IGWO-WELM[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4877-4895. doi: 10.3934/mbe.2023226

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Abstract

1. Introduction

The brain function of people will be impaired after an extended period of drug abuse across a diverse variety. The classification accuracy of the eight encephalic regions (ERs) in the left and right hemispheres of the prefrontal lobe was analyzed on the basis of the fNIRS data acquired to identify the differences, if any. Statistical analysis was then performed on the eight ERs to find out which of them stand out in drug abusers. The study Innovations: 1) Drug abusers were classified; 2) The differences in classification accuracy were identified by classifying the drug abusers in conjunction with the ERs via CNN; 3) ERs with discernible distinctions in the drug abusers were identified through statistical analysis on the eight ERs in the left and right hemispheres of the prefrontal lobe.

In recent years, near-infrared research is still a new field, and its advantages are gradually recognized by researchers ^[1]. NIRS in optical brain imaging is a spectral measurement method based on scalp detection, which measures the hemodynamic function of brain tissue using optical injection and detection points, and can record blood-oxygen level ^[2,3]. Compared with electroencephalography (EEG), a novel mode of brain functional imaging, it has the advantages of convenient wearing, high anti-interference ability and portability ^[4]. In human body, oxyhemoglobin (HbO2) and deoxyhemoglobin (Hbb) have specific absorption for near-infrared light at 700–900 nm. However, other biological tissues in the brain are relatively transparent in this wavelength range. Therefore, the changes in near-infrared light intensity at 760 and 850 nm emitted into the brain were measured, and the indirect changes in brain functional activity were based on the hemodynamic data transformed according to the Beer-Lambert law ^[5].

Song et al, using fNIRS to extract oxy-Hb signals from schizophrenia patients and healthy people to construct a prefrontal brain network, and extract features from it to classify schizophrenia patients and healthy people, with a total accuracy rate of 85.5% ^[6]. Hu et al. propose a hybrid, multi-dimensional fusion structure of spatial and temporal segmentation model for the automated detection of thermography defects. In the model, creatively designed attention blocks the resources for local interaction along neighboring pixels, allowing for an adaptive recalibration of the feature maps. The performance of the two classifications is improved ^[7]. Kim et al. used NIRS technology to study the relationship between walking speed and blood oxygen activation in brain regions ^[8]. The proposed network of Koh et al. addresses the need in deep learning to match the data function of a time series with an appropriate network structure. This improves the classification accuracy of EEG and human activity signals ^[9]. Holtzer researched that changes in walking step length lead to activation of the prefrontal cortex, while Caliandro found that when the walking step length increases, the blood oxygen concentration of the lateral frontal cortex also shows an increasing trend ^[10,11]. Rodriguez-Rodriguez et al., in the process of monitoring type 1 diabetes mellitus (DM1), creatively used machine learning technology, developed six-feature selection techniques and four predictive algorithms, obtaining the best average performance and the best algorithm classification accuracy ^[12]. Li et al. calculated the normal people and schizophrenia patients in the 60 s task state ^[13]. Hennrich et al. collected human near-infrared signals and compared the classification performance of deep neural networks (DNN) for three mental tasks ^[14]. Abibullaev et al. used DNN to classify four mental tasks with an accuracy rate of 94% ^[15].

fNIRS is used in the rehabilitation of stroke patients with motor imaging therapy, which can better monitor the changes in the treatment process ^[16]. Akiyama et al., using fNIRS to study the bilateral frontal cortex of depression patients ^[17]. fNIRS monitors the neonatal brain development stage, and its cerebral oxygen metabolism and hemodynamic characteristics are significantly different from those of adults ^[18].

fNIRS is mainly aimed at evaluating and imaging the degree of brain damage in drug addicts, and detecting differences in the activation of the forehead brain area of people with different degree of addiction and Long-term methamphetamine users mid-near infrared detection showed abnormal activation of the prefrontal cortex, orbital frontal cortex, and the anterior cingulate gyrus ^[19,20]. Now fNIRS has been applied in many fields, such as the research of brain development, the research of perception and cognition, the research of motor control, the research of mental illness, the research of stroke and brain injury ^{[21,22,23,24]}.

According to the demographic scale, oral statement and medical examination, 30 drug addicts were selected. According to the experimental paradigm containing resting state and drug addiction induction, the near-infrared hemoglobin concentration data was collected. There are 30 subjects in total, classified into three classify. and Based on the CNN model, classification is performed.

2. Materials and methods

2.1. Participates

Study participant criteria: 1) Meet the diagnostic criteria for disorders caused by DSM-5 psychoactive substances; 2) Patients within six months of a withdrawal period; 3) Junior high school education and above; 4) Age 18–41 years; 5) Voluntary study participation and willingness to sign the informed consent form. Exclusion criteria: 1) Severe cognitive dysfunction, inability to cooperate and complete project-related assessment and testing; 2) Patients with severe physical diseases; 3) Patients with severe psychotic symptoms; 4) Current participation in other psychological interventions and treatments; 5) Current abuse of other substances that affect mental activities (except nicotine). The study was following with the declaration of Helsinki and was approved by the Ethics Committee of Shanghai University (Approval No. ECSHU2020-071).

2.2. Subject description

According to the demographic scale prepared in the early stage, data of 30 subjects (all men), such as drug use type, drug history, average drug dosage, and drug use frequency, were collected and recorded. Moreover, combining these data with personal health information collected from hospital records and experts' discussion and suggestions, three types of drugs were finally screened out, including methamphetamine, heroin, and mixed drugs, where ten subjects each were taking methamphetamine, heroin, and mixed drugs. Table 1 non-sensitive information of participants. METH: means Methamphetamine.

Table 1. Non-sensitive information of participants.

N	30
Sex (M/F)	Male
Age range (Year)	19–41
Years of education	10 ± 2.72
Years of drug abuse	8.2 ± 4.74
Drug abuse per week:	Most people 3–5 times a week.
withdrawals	1.4 ± 0.98
Reasons for taking drugs	decompression needs; sex; emotion; curiosity; emotional frustration
Subject No.	1	2	3	4	5	6	7	8	9	10
Age: Year	41	28	25	35	35	39	29	35	33	32
Type of drug	METH	METH	METH	METH	METH	METH	METH	METH	METH	METH
Drug history	12	9	8	9	17	12	11	7	7	12
Subject No.	11	12	13	14	15	16	17	18	19	20
Age: Year	37	31	38	26	32	29	37	26	38	32
Type of drug	Heroin	Heroin	Heroin	Heroin	Heroin	Heroin	Heroin	Heroin	Heroin	Heroin
Drug history	14	6	13	8	4	5	12	13	17	17
Subject No.	21	22	23	24	25	26	27	28	29	30
Age: Year	37	31	31	24	40	34	35	40	39	36
Type of drug	Heroin, Cannabis, LSD, MDMA, Molly, Magu	Pethidine hydrochloride, heroin, MDMA, ketamine, METH	Cocaine, MDMA, Molly, ketamine, LSD, cannabis,	Cannabis, Cocaine, LSD, trimethoprim, MDMA, Molly	Heroin, Meth, MDMA	METH, heroin, ketamine, MDMA	METH, heroin, pethidine hydrochloride	Heroin, METH, ketamine, MDMA, cannabis	Heroin, METH, MDMA, ketamine, pethidine hydrochloride	Heroin, METH, MDMA, ketamine, cannabis
Drug history	16	11	7	6	19	13	11	20	20	19

| Show Table

DownLoad: CSV

2.3. Near-infrared spectroscopy technology equipment introduction

NIRSIT (OBELAB, Seoul, Korea) and a light source with dual wavelength vertical-cavity surface-emitting laser were used with the following technical spectrum: continuous wave, 780 nm and 850 nm; spatial resolution, 4 × 4 mm²; time resolution, 8.13 Hz; number of light points, 24; number of detection points, 32; and detection depth, 0.2–1.8 cm. The NIRS system used in the experiment allowed measurement of signals from four Source-Detector separations (15, 21.2, 30 and 33.5 mm) and hemodynamic reaction changes at different depths ^[25,26]. It is a functional NIRS device with 204 channels. Figure 1 NIRSIT wearing method in the experiment.

Figure 1. NIRSIT wearing method in the experiment.

DownLoad: Full-Size Img PowerPoint

2.4. NIRSIT channel and functional area division

The NIRSIT channel and functional area are shown in Figure 3. The four advanced functional areas detected through the forehead near-infrared device are as follows: the dorsolateral prefrontal cortex (DLPFC), ventrolateral prefrontal cortex (VLPFC), frontopolar prefrontal cortex, and orbital frontal cortex (OFC). Regarding specific channel distribution, the right DLPFC has 1, 2, 3, 5, 6, 11, 17 and 18 channels. The left dorsolateral prefrontal lobe has 19, 20, 33, 34, 35, 38, 39 and 43 channels. The VLPFC of the left and right hemispheres have 4, 9, 10, 40, 44 and 45 channels. The left and right OFC have 14, 15, 16, 29, 30, 31, 32, 46, 47 and 48 channels. The frontopolar prefrontal cortex electrode arrangement has 7, 8, 12, 13, 21, 22, 23, 24, 25, 26, 27, 28, 36, 37, 41 and 42 channels.

Figure 2. NIRSTI channel and functional area division.

DownLoad: Full-Size Img PowerPoint

Figure 3. The example of drug pictures.

DownLoad: Full-Size Img PowerPoint

2.5. Near-infrared imaging theory

When light passes through a uniform, non-scattering medium, only the absorption of photons by the medium is considered. According to Beer-Lambert law, the attenuation of light intensity is expressed as:

$OD = log\frac{I}{{{I_0}}} = - \varepsilon \left( \lambda \right)cd\lg e$

(1)

Among them, ${I_0}$ is the incident light intensity, $I$ is the output light intensity, $\varepsilon \left(\lambda \right)$ is the extinction coefficient of the substance at the wavelength $\lambda$ , which is determined by the absorbing medium and the wavelength of the light, $c$ is the medium concentration, and the depth L of the penetration medium. Define the absorption coefficient as ${\mu _a}$ :

${\mu _a}(\lambda ) = \varepsilon \left( \lambda \right)c$

(2)

The total absorption coefficient in the medium can be expressed as the linear superposition of the absorption coefficient of each medium:

${\mu _a}(\lambda ) = \sum\limits_i^N {{\varepsilon _i}} \left( \lambda \right){c_i}$

(3)

The optical density can be expressed as:

$OD = log\frac{I}{{{I_0}}} = \sum\limits_i^N {{\varepsilon _i}} \left( \lambda \right){c_i}L$

(4)

The absorbance OD represents the degree of light attenuation after passing through the medium, which is related to the absorption coefficient ${\mu _a}$ of the medium, depth L of the penetration medium, and wavelength λ of the irradiated light. The available formula is as follows:

$OD = {\mu _a}(\lambda ) \cdot L$

(5)

Among them, the absorption coefficient ${\mu _a}$ can be expressed as the product of the chromophore concentration c and its extinction coefficient ε. Considering the scattering problem, a differential path factor "DPF (λ)" is generally introduced, so it can be further expressed as follows:

$OD = c \cdot \varepsilon (\lambda ) \cdot L \cdot DPF(\lambda )$

(6)

In the near-infrared band from 650 to 1000 nm, the main absorber of photons is hemoglobin. Although other chromophores also absorb light in this range, their contribution is assumed to be constant so that the change in the measured absorption signal over time can be attributed only to hemoglobin, and it can be expressed as follows:

$\Delta OD(\lambda ) = (\Delta [Hbo]{\varepsilon _{Hbo}}(\lambda ) + \Delta [Hbb]{\varepsilon _{Hbb}}(\lambda )) \cdot L \cdot DPF(\lambda )$

(7)

In the formula, [Hbo] and [Hbb] represent the concentrations of oxyhemoglobin and deoxyhemoglobin, respectively. Changes in the concentrations of oxyhemoglobin and deoxyhemoglobin can be obtained by deformation:

$\Delta [Hbo] = \frac{{{\varepsilon _{Hbb}}({\lambda _1})\frac{{\Delta OD({\lambda _2})}}{{DPF({\lambda _2})}} - {\varepsilon _{Hbb}}({\lambda _2})\frac{{\Delta OD({\lambda _1})}}{{DPF({\lambda _1})}}}}{{({\varepsilon _{Hbb}}({\lambda _1}) \cdot {\varepsilon _{Hbo}}({\lambda _2}) - {\varepsilon _{Hbb}}({\lambda _2}) \cdot {\varepsilon _{Hbo}}({\lambda _1})) \cdot L}}$

(8)

$\Delta [Hbb] = \frac{{{\varepsilon _{Hbo}}({\lambda _2})\frac{{\Delta OD({\lambda _1})}}{{DPF({\lambda _1})}} - {\varepsilon _{Hbo}}({\lambda _1})\frac{{\Delta OD({\lambda _2})}}{{DPF({\lambda _2})}}}}{{({\varepsilon _{Hbb}}({\lambda _1}) \cdot {\varepsilon _{Hbo}}({\lambda _2}) - {\varepsilon _{Hbb}}({\lambda _2}) \cdot {\varepsilon _{Hbo}}({\lambda _1})) \cdot L}}$

(9)

2.6. Experiment and data collection

We used E-prime software package (Psychology Software Tools, Pittsburgh, PA) to write the experimental paradigm, with each picture numbered. The experimental paradigm consisted of three stages.

Figures 3 and 4, are examples of drug abuse-related images and neutral images used in the experimental paradigm. Figure 5 The whole process of experimental paradigm. P means: drug picture; N means: Neutral Picture;

Figure 4. The example of neutral pictures.

DownLoad: Full-Size Img PowerPoint

Figure 5. The whole experimental structure.

DownLoad: Full-Size Img PowerPoint

The first stage of the experiment, which lasted for 10 minutes, involved the participants closing their eyes for five minutes and then leaving their eyes open for five minutes.

The second stage of the experiment, which lasted for six minutes, included the drug and neutral pictures. Each time block lasted for 10 seconds, for a total of 16 pictures, which were each displayed for 0.6 seconds. At the beginning, the first four pictures contained two drug images randomly displayed in a group, and the remaining 12 neutral images were displayed randomly. After a block had ended, a 4-second interval picture was shown, with a white background and a black cross.

The third stage of the experiment, which lasted for 4.6 minutes, a completely neutral image was shown. Each time block lasted for 10 seconds and a total of 16 pictures were shown. The picture display time was 0.6 seconds, with a 4-second interval picture shown between each block.

3. Results

3.1. Introduction to methamphetamine, heroin, and mixed drugs

Methamphetamine easily causes intense excitement, which is difficult to eradicate after addiction ^[27,28].

Heroin is a psychoanaesthetic drug. Once a person becomes addicted, their physiological reaction is intense, and they have a compulsion to seek medication ^[29,30].

"Mixed drug abusers" refers to drug users who attempt to mix two or three drugs at a time. A major feature of mixed drug users is that they are the first to be exposed to new drugs. Mixed drugs have strong psychedelic properties, which causes the body to produce neurochemicals and form a dependence on them ^[31,32,33].

3.2. CNN network design

Data on a total of 30 classified drug users were collected, each drug user containing 56 trials. Each trial corresponded to the channels of near-infrared data 0.625 seconds after the drug image appears. The whole CNN network has 20 layers, including 24 subjects in the training data, 3 in the validation data, and 3 in the testing data. Figure 6, CNN classification model of different types of drug abuse. The CNN model parameter are shown in Table 2.

Figure 6. CNN classification model of different types of drug abuse.

DownLoad: Full-Size Img PowerPoint

Table 2. CNN parameters.

Layer (type)	Output Shape	Parameter #
conv2d (Conv2D)	(None, 5, 8, 32)	96
activation (Activation)	(None, 5, 8, 32)	0
average_pooling2d	(None, 5, 4, 32)	0
conv2d_1 (Conv2D)	(None, 5, 4, 16)	2064
activation_1 (Activation)	(None, 5, 4, 16)	0
average_pooling2d_1	(None, 5, 3, 16)	0
conv2d_2 (Conv2D)	(None, 5, 3, 32)	1056
activation_2 (Activation)	(None, 5, 3, 32)	0
average_pooling2d_2	(None, 5, 2, 32)	0
conv2d_3 (Conv2D)	(None, 5, 2, 32)	2080
activation_3 (Activation)	(None, 5, 2, 32)	0
average_pooling2d_3	(None, 5, 1, 32)	0
flatten (Flatten)	(None, 160)	0
dense1 (Dense)	(None, 160)	25760
dropout (Dropout)	(None, 160)	0
Dense2 (Dense)	(None, 160)	25760
dropout_1 (Dropout)	(None, 160)	0
dense3 (Dense)	(None, 160)	25760
dropout_2 (Dropout)	(None, 160)	0
dense4 (Dense)	(None, 4)	644

| Show Table

DownLoad: CSV

3.3. EEG and NIRS data preprocessing

3.3.1. EEG and NIRS filtering

NIRS networks are designed with Butterworth filters. The expression of n-order Butterworth filter is:

${\left|\boldsymbol{H}\left(\boldsymbol{f}\right)\right|}^{\bf 2} = \frac{\bf 1}{{\bf 1}+{\left(\frac{\boldsymbol{f}}{{\boldsymbol{f}}_{\boldsymbol{c}}}\right)}^{{\bf 2}\boldsymbol{n}}} = \frac{{\bf 1}}{{\bf 1}+{\bf{ϵ}}^{{\bf 2}}{\left(\frac{\boldsymbol{f}}{{\boldsymbol{f}}_{\boldsymbol{p}}}\right)}^{{\bf 2}\boldsymbol{n}}}$

(10)

where n is the order, ${\boldsymbol{f}}_{\boldsymbol{c}}$ is the cutoff frequency, and ${\boldsymbol{f}}_{\boldsymbol{p}}$ is the passband edge frequency.

3.3.2. Convolutional layer

Convolutional layers are the core of convolutional neural networks. Its main role is to extract features from the input data. The calculation form is as follows:

${x}_{j}^{l} = f\left({\sum }_{i\in {M}_{j}}{x}_{i}^{l-1}\cdot {k}_{ij}^{l}+{b}_{j}^{l}\right)$

(11)

${x}_{j}^{l}$ is the $j$ th feature of the layer $l$ . ${k}_{ij}^{l}$ is the $j$ th feature of the layer $l$ and the $i$ th feature of the layer $l-1$ . ${b}_{j}^{l}$ is a bias parameter, $f(•)$ is the activation function.

3.3.3. Pooling layer

The calculation form is as follows:

${x}_{j}^{l} = f\left({\mathrm{\beta }}_{1}^{l}\backslash down\left({x}_{j}^{l-1}\right)+{b}_{j}^{l}\right)$

(12)

${x}_{j}^{l}$ is the $j$ th feature of the layer $l$ . ${\beta }_{1}^{l}$ is the Subsampling coefficient. ${b}_{j}^{l}$ is the bias parameter, $down(•)$ is a sub-sampling function, $f(•)$ is the activation function.

3.3.4. Normalization of data

The specific implementation process is as follows:

Input: Values of

$\mathrm{x}$ over a mini-batch:

$B=\left\{{x}_{1}\dots {x}_{m}\right\};$
Parameters to be learned:

$\gamma, \beta$
Output:

$\left\{{y}_{i}=B{N}_{\mathrm{\gamma }, \mathrm{\beta }}\left({x}_{i}\right)\right\}$

1. Calculate the mean of each mini-batch:

${\mu }_{B}=\frac{1}{m}{\sum }_{i=1}^{m}{x}_{i}$
2. Calculate the variance of each mini-batch:

${\mathrm{\sigma }}_{\mathcal{B}}^{2}\leftarrow \frac{1}{m}{\sum }_{i=1}^{m}{\left({x}_{i}-{\mathtt{μ }}_{\mathcal{B}}\right)}^{2}$
3. Normalize the data:

${\widehat{x}}_{i}=\frac{{x}_{i}-{\mu }_{B}}{\sqrt{{\sigma }_{B}^{2}+\varepsilon }}$
4. Scale and shift:

${y}_{i}=\gamma \widehat{{x}_{i}}+\beta \equiv B{N}_{\mathrm{\gamma }\mathrm{\beta }}\left({x}_{i}\right)$

| Show Table

DownLoad: CSV

3.3.5. Activation function

In this paper, the activation function uses a modified linear unit (ReLU), and the formula is as follows:

$f\left(x\right) = \mathrm{max}\left(0, x\right)$

(13)

3.3.6. Full connection layer

The calculation formula is as follows:

${h}_{w, b}\left(x\right) = \mathrm{\theta }({w}^{\text{T}}x+b)$

(14)

${h}_{w, b}\left(x\right)$ is the output value of the neuron. $x$ is the input feature vector of the neuron. $w$ is the weight. $b$ is the bias parameter $\mathrm{\theta }(\bullet)$ is the activation function.

3.3.7. Softmax layer

The softmax function formula is as follows:

${z}_{i} = \mathrm{Softmax}\left({o}_{i}\right) = \frac{\mathrm{exp}\left({o}_{i}\right)}{{\sum }_{c}\mathrm{exp}\left({o}_{c}\right)}$

(15)

${o}_{i}$ is the value of the output neuron corresponding to the Ith category

3.4. Accuracy of different brain regions

Under the same CNN network structure and parameters, there are DLPFC, VLPFC, FPC and OFC prefrontal cortical regions in the left and right hemispheres of the brain. The average accuracy of 10 times obtained is shown in the Table 3.

Table 3. Average accuracy.

Prefrontal cortex	Channel	Accuracy (%)
Left-DLPFC	1, 2, 3, 17, 18, 5, 6, 11	51–61%
Right-DLPFC	19, 20, 33, 34, 35, 38, 39, 43	56–72%
Left-VLPFC	4, 9, 10	50–60%
Right-VLPFC	40, 44, 45	40–50%
Left-FPC	7, 8, 21, 22, 12, 13, 25, 26	55–70%
Right-FPC	23, 24, 36, 37, 27, 28, 41, 42	50–60%
Left-OFC	14, 15 16, 29, 30	50–62%
Right-OFC	31, 32, 46, 47, 48	49–64%
ALL-PFC	1, 2, 3, 17, 18, 5, 6, 11, 19, 20, 33, 34, 35, 38, 39, 43, 4, 9, 10, 40, 44, 45, 7, 8, 21, 22, 12, 13, 25, 26, 23, 24, 36, 37, 27, 28, 41, 42, 14, 15, 16, 29, 30, 31, 32, , 46, 47, 48	70–77%

| Show Table

DownLoad: CSV

4. Discussion

4.1. Confusion matrix of classification accuracy of persons abusing different drugs

In this study, the accuracy rates of eight areas of the prefrontal cortex and of the entire brain were determined. Herein, the accuracy rates of all channels in terms of true-positive, true-negative, false-positive, and false-negative results are given as examples, with methamphetamine abusers labeled as 0, heroin abusers as 1, and mixed abusers as 2. Among the three categories of participants, the accuracy rate of identifying methamphetamine abuse is lower than that of heroin and mixed drugs. Further adjustments to the model can increase the uniformity of the accuracy rate. Figure 7, Confusion matrix of three types of drug abusers.

Figure 7. Confusion matrix of three types of drug abusers.

DownLoad: Full-Size Img PowerPoint

4.2. Three classification accuracy rate statistics

According to the unified CNN framework, there are 8 functional areas in the prefrontal lobe of the brain, and the correct rate statistics are shown in Figure 8. According to the statistical results, the following conclusions are drawn that the accuracy rate obtained in Left-DLPFC is lower than the Right-DLPFC prefrontal cortex. However, In VLPFC, FPC, OFC functional areas, the accuracy of the left hemisphere of the brain is higher than that of the right hemisphere.

Figure 8. The accuracy of the forehead area.

DownLoad: Full-Size Img PowerPoint

4.3. Statistical analysis of three types of drug abusers

Heroin, methamphetamine, and mixed drug abusers, through one-way ANOVA analysis revealed three types of personnel differences. The analysis results of Table 4 are as follows: Right-VLPFC, Right-OFC, there are significant differences between the three types of personnel. The differences in other functional areas are not very obvious.

Table 4. statistical analysis of drug abusers in different functional areas.

Heroin addicts Meth addicts Mixed drug addicts	Left-DLPFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			1.467	0.2327	0.01223	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.001373	2	0.0006866	F (2,237) = 1.467	P = 0.2327
		Residual (within columns)	0.1109	237	0.0004680
		Total	0.1123	239
	Right-DLPFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			2.794	0.0660	0.02267	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.001266	2	0.0006332	F (2,237) = 2.749	P = 0.0660
		Residual (within columns)	0.05459	237	0.0002303	0.05459
		Total	0.05586	239
	Left-VLPFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			0.2203	0.8032	0.01038	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.001820	2	0.0009100	F (2, 42) = 0.2203	P = 0.8032
		Residual (within columns)	0.1735	42	0.004130
		Total	0.1753	44
	Right-VLPFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			4.068	0.0243	0.1623	Yes
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.000564	2	0.0002820	F (2, 42) = 4.068	P = 0.0243
		Residual (within columns)	0.002912	42	6.933e-005
		Total	0.003476	44
	Left-FPC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			1.492	0.2293	0.02486	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.001555	2	0.0007773	F (2,117) = 1.492	P = 0.2293
		Residual (within columns)	0.06097	117	0.0005211
		Total	0.06252	119
	Right-FPC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			2.762	0.0657	0.02839	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.000312	2	0.0001562	F (2,189) = 2.762	P = 0.0657
		Residual (within columns)	0.01069	189	5.655e-005
		Total	0.01100	191
	Left-OFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			1.422	0.2446	0.01879	No
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.000153	2	7.679e-005	F (2,147) = 1.422	P = 0.2446
		Residual (within columns)	0.007941	147	5.402e-005
		Total	0.008094	149
	Right-OFC	ANOVA summary	F	P-value	R- square	(P < 0.05)
			6.930	0.0013	0.08780	Yes
		ANOVA table	SS	DF	MS	F (DFn, DFd)	P value
		Treatment (between columns)	0.000685	2	0.0003425	F (2,144) = 6.930	P = 0.0013
		Residual (within columns)	0.007118	144	4.943e-005
		Total	0.007803	146

| Show Table

DownLoad: CSV

The following results can be obtained:

1) Long-term drug abuse of drug users has caused the function of the brain to become stronger or weaker.

2) Long-term drug abuse by drug users on Right-VLPFC and Right-OFC can infer the functional damage of the cortical area.

5. Conclusions

Due to the different pathogenic mechanisms of drugs, drug users who abuse different types of drugs suffer from different brain damages. In this paper, the blood oxygen levels of 30 drug users were obtained by high-density functional near-infrared spectroscopy. The eight Brodmann areas and the entire prefrontal area of the three types of individuals were identified and classified by the designed CNN to obtain the final results: the 3-class accuracy was lower on the left side than on the right in the DLPFC, while it was higher on the left than on the right in the VLPFC, FPC, and OFC. Statistical analysis on the eight functional areas showed significant differences in the right VLPFC and right OFC, and preliminarily predictions were for the brain damages caused by abusing different drugs.

Acknowledgments

The authors thank the Shanghai Drug Rehabilitation Administration Bureau and Shanghai Qing Dong Drug Rehabilitation Center for their support, and all the people who contribute to the writing of the article. This project was supported by Key Research & Development Project of National Science and Technique Ministry of China (No. 2018YFC0807405, No. 2018YFC1312903), National Natural Science Foundation of China (No. 61976133). Defense Industrial Technology Development Program (JCKY2019413D002) and the Key Research and Development Project of Shandong (2019JZZY021010).

Conflict of interest

The authors declare that they have no conflict of interest.

References

[1]	Y. Yan, H. Ma, M. Wen, S. Dang, H. Xu, Multi-feature fusion-based mechanical fault diagnosis for on-load tap changers in smart grid with electric vehicles, IEEE Sens. J., 21 (2021), 15696-15708. https://doi.org/10.1109/JSEN.2020.3021920 doi: 10.1109/JSEN.2020.3021920
[2]	K. Wongon, K. Sunuwe, J. Jingyo, H. Kim, H. Lee, B. D. Youn, Digital twin approach for on-load tap changers using data-driven dynamic model updating and optimization-based operating condition estimation, Mech. Syst. Signal PR., 181 (2022), 1-17. https://doi.org/10.1016/j.ymssp.2022.109471 doi: 10.1016/j.ymssp.2022.109471
[3]	Q. Yang, J. Ruan, Z. Zhuang, Fault diagnosis of circuit breakers based on time–frequency and chaotic vibration analysis, IET Gener. Transm. Dis., 14 (2020), 1214–1221. https://doi.org/10.1049/iet-gtd.2019.0985 doi: 10.1049/iet-gtd.2019.0985
[4]	R. Y. Shang, C. Q. Peng, P. F. Shao, R. Fang, FFT-based equal-integral-bandwidth feature extraction of vibration signal of OLTC, Math. Biosci. Eng., 18 (2021), 1996–1980. https://doi.org/10.3934/mbe.2021102 doi: 10.3934/mbe.2021102
[5]	C. Bengtsson, Status and trends in transformer monitoring, IEEE Trans. Power deliver., 11 (1996), 1379–1384. https://doi.org/10.1109/61.517495 doi: 10.1109/61.517495
[6]	P. Kang, D. Birtwhistle.Condition monitoring of power transformer on-load tap-changers.Part I: Automatic condition diagnostics, IEE P-Gener. Transm. D., 148 (2001), 301–306. https://doi.org/10.1049/ip-gtd:20010389 doi: 10.1049/ip-gtd:20010389
[7]	P. Kang, D. Birtwhistle.Condition monitoring of power transformer on-load tap-changers.Part Ⅱ:Detection of ageing from vibration signatures, IEE P-Gener. Transm. D., 148 (2001), 307–311. https://doi.org/10.1049/ip-gtd:20010388 doi: 10.1049/ip-gtd:20010388
[8]	P. Kang, D. Birtwhistle. Condition assessment of power transformer on-load tap changers using wavelet analysis and self-organizing map: field evaluation, IEEE Trans. Power deliver., 18 (2003), 78–84. https://doi.org/10.1109/TPWRD.2002.803692 doi: 10.1109/TPWRD.2002.803692
[9]	X. Zhou, F. H. Wang, J. Fu, J. Lin, Mechanical condition monitoring of on-load tap changers based on chaos theory and k-means clustering method, Proc. CSEE, 35 (2015), 1541–1548. https://doi.org/10.13334/j.0258-8013.pcsee.2015.06.031 doi: 10.13334/j.0258-8013.pcsee.2015.06.031
[10]	J. X. Liu, G. Wang, T. Zhao, L. Zhang, Fault diagnosis of on-load tap-changer based on variational mode decomposition and relevance vector machine, Energies, 10 (2017), 946–959. https://doi.org/10.3390/en10070946 doi: 10.3390/en10070946
[11]	X. Duan, T. Zhao, T. Li, J. Liu, L. Zou, L. Zhang, Method for diagnosis of on-load tap-changer based on wavelet theory and support vector machine, J. Eng. Ny., 13 (2017), 2193–2197. https://doi.org/10.1049/joe.2017.0719 doi: 10.1049/joe.2017.0719
[12]	Q. Li, T. Zhao, Z. Li, J. Lou, Mechanical fault diagnosis of on load tap changer within power transformers based on hidden Markov model, IEEE Trans. Power deliver., 27 (2012), 596–601. https://doi.org/10.1109/TPWRD.2011.2175454 doi: 10.1109/TPWRD.2011.2175454
[13]	X. Liang, Y. Wang, H. Gu, A mechanical fault diagnosis model of on-load tap changer based on same-source heterogeneous data fusion, IEEE Trans. Instrum. Meas., 71 (2022). https://doi.org/10.1109/TIM.2021.3064808
[14]	L. Zheng, G. Liu, C. Yan, C. Jiang, et al. Improved TradaBoost and its application to transaction fraud detection, IEEE Trans. Comput. Social Syst., 7 (2020), 1304–1316. https://doi.org/10.1109/TCSS.2020.3017013 doi: 10.1109/TCSS.2020.3017013
[15]	S. Dhote., C. Vichoray, R. Pais, et al., Hybrid geometric sampling and AdaBoost based deep learning approach for data imbalance in E-commerce, Electron. Commer. Res., 20 (2020), 259–274. https://doi.org/10.1007/s10660-019-09383-2 doi: 10.1007/s10660-019-09383-2
[16]	W. Lee, C. H. Jun, J. Lee, Instance categorization by support vector machines to adjust weights in AdaBoost for imbalanced data classification, Inform. Sci., 381 (2017), 92–103. https://doi.org/10.1016/j.ins.2016.11.014 doi: 10.1016/j.ins.2016.11.014
[17]	Y. Gao, L. Gao, X. Li, S. Cao, A hierarchical training-convolutional neural network for imbalanced fault diagnosis in complex equipment, IEEE Trans. Ind. Inform., 18 (2022), 8138–8145. https://doi.org/10.1109/TⅡ.2022.3177662 doi: 10.1109/TⅡ.2022.3177662
[18]	Y. Geng, X. Y. Luo, Cost-sensitive convolutional neural networks for imbalanced time series classification, Intell. Data Anal., 23 (2019), 357–370. https://doi.org/10.3233/IDA-183831 doi: 10.3233/IDA-183831
[19]	A. Taherhnai, G. Cosma, T. T. McGinnity, AdaBoost-CNN: An adaptive boosting algorithm for convolutional neural networks to classify multi-class imbalanced datasets using transfer learning, Neurocomputing, 404 (2020), 351–366. https://doi.org/10.1016/j.neucom.2020.03.064 doi: 10.1016/j.neucom.2020.03.064
[20]	Y. Xie, G. Liu, C. Yan, C. Jiang, M. Zhou, M. Li, Learning transactional behavioral representations for credit card fraud detection, IEEE Trans. Neural Networks Learn. Syst., 2022. https://doi.org/10.1109/TNNLS.2022.3208967 doi: 10.1109/TNNLS.2022.3208967
[21]	Q. X. Zhu, X. W. Wang, N. Zhang, Novel K-Medoids based SMOTE integrated with locality preserving projections for fault diagnosis, IEEE Trans. Instrum. Meas., 71 (2022). https://doi.org/10.1109/TIM.2022.3218551
[22]	Y. Gao, Q. C. Liu, An over sampling method of unbalanced data based on ant colony clustering, IEEE Access, 9 (2021), 130990–130996. https://doi.org/10.1109/ACCESS.2021.3114443 doi: 10.1109/ACCESS.2021.3114443
[23]	J. Shen, J.C. Wu, M. Xu, D. Gan, B. An, F. Liu, A hybrid method to predict postoperative survival of lung cancer using improved SMOTE and adaptive SVM, Comput. Math. Method Med., 2021 (2021). https://doi.org/10.1155/2021/2213194 doi: 10.1155/2021/2213194
[24]	K. Hu, Z. Zhou, L. Weng, J. Liu, L. Wang, Y. Su, et al., An optimization strategy for weighted extreme learning machine based on PSO, Int. J. Pattern. Recogn., 31 (2017). https://doi.org/10.1142/S0218001417510016
[25]	Z. Z. Li, M. Huang, G. J. G. Liu, Optimizing weighted extreme learning machines for imbalanced classification and application to credit card fraud detection, Expert Syst. Appl., 175 (2021). https://doi.org/10.1016/j.eswa.2021.114750
[26]	S. Saremi, S. Z. Mirjalili, S. M. Mirjalili. Evolutionary population dynamics and grey Wolf optimizer, Neural Comput. Appl., 26 (2015), 1257–1253. https://doi.org/10.1007/s00521-014-1806-7 doi: 10.1007/s00521-014-1806-7
[27]	G. M. Komaki, V. Kayvanfar. Grey Wolf optimizer for the two-stage assembly flow shop scheduling problems with release time, J. Comput. Sci., 8 (2015), 109–120. https://doi.org/10.1016/j.jocs.2015.03.011 doi: 10.1016/j.jocs.2015.03.011
[28]	A. K. Mishra, S. R. Das, P. K. Ray, R. K. Mallick, A. Mohanty, D. K. Mishra, PSO-GWO optimized fractional order PID based hybrid shunt active power filter for power quality improvements, IEEE Access, 8 (2020), 74497–74512. https://doi.org/10.1109/ACCESS.2020.2988611 doi: 10.1109/ACCESS.2020.2988611
[29]	H. H. Zhu, G. J. Liu, M. C., Zhou, Y. Xie, Q. Kang, Dandelion algorithm with probability-based mutation, IEEE Access, 7 (2019), 97974–97985. https://doi.org/10.1109/ACCESS.2019.2927846 doi: 10.1109/ACCESS.2019.2927846
[30]	A. K. Dutta, B. Qureshi, Y. Albagory, Ma. Alsanea, M. Al Faraj, A. R. W. Sait, Optimal weighted extreme learning machine for cybersecurity fake news classification, Comput. Syst. Sci. Eng., 44 (2023), 2395–2409. https://doi.org/10.32604/csse.2023.027502 doi: 10.32604/csse.2023.027502
[31]	G. B. Allende, G. Still, Solving bilevel programs with the KKT-approach, Math. Program., 138 (2013), 309–332. https://doi.org/10.1007/s10107-012-0535-x doi: 10.1007/s10107-012-0535-x
[32]	C. Lei, S. Wan, Intelligent fault diagnosis of high-voltage circuit breakers using triangular global alignment kernel extreme learning machine, ISA Trans., 109 (2020), 368–379. https://doi.org/10.1016/j.isatra.2020.10.018 doi: 10.1016/j.isatra.2020.10.018
[33]	Z. C. Li, M. Huang, G. J. Liu, C. Jiang, A hybrid method with dynamic weighted entropy for handling the problem of class imbalance with overlap in credit card fraud detection, Expert Syst. Appl., 175 (2021), 114750. https://doi.org/10.1016/j.eswa.2021.114750 doi: 10.1016/j.eswa.2021.114750
[34]	C. B. Liu, H. F. Ke, G. Zhang, Y. Mei, H. Xu, An improved weighted extremely learning machine for imbalanced data classification, Memetic Comput., 20 (2019), 27–34. https://doi.org/10.1007/s12293-017-0236-3 doi: 10.1007/s12293-017-0236-3
[35]	L. Chen, S. Wan, L. Dou, Improving diagnostic performance of High-Voltage circuit breakers on imbalanced data using an oversampling method, IEEE Trans. Power deliver., 37 (2022), 2704–2716. https://doi.org/10.1109/TPWRD.2021.3114547 doi: 10.1109/TPWRD.2021.3114547

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Mathematical Biosciences and Engineering

Research on imbalanced data fault diagnosis of on-load tap changers based on IGWO-WELM

Related Papers:

Abstract

1. Introduction

2. Materials and methods

2.1. Participates

2.2. Subject description

2.3. Near-infrared spectroscopy technology equipment introduction

2.4. NIRSIT channel and functional area division

2.5. Near-infrared imaging theory

2.6. Experiment and data collection

3. Results

3.1. Introduction to methamphetamine, heroin, and mixed drugs

3.2. CNN network design

3.3. EEG and NIRS data preprocessing

3.3.1. EEG and NIRS filtering

3.3.2. Convolutional layer

3.3.3. Pooling layer

3.3.4. Normalization of data

3.3.5. Activation function

3.3.6. Full connection layer

3.3.7. Softmax layer

3.4. Accuracy of different brain regions

4. Discussion

4.1. Confusion matrix of classification accuracy of persons abusing different drugs

4.2. Three classification accuracy rate statistics

4.3. Statistical analysis of three types of drug abusers

5. Conclusions

Acknowledgments

Conflict of interest

References

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Mathematical Biosciences and Engineering

Research on imbalanced data fault diagnosis of on-load tap changers based on IGWO-WELM

Related Papers:

Abstract

1. Introduction

2. Materials and methods

2.1. Participates

2.2. Subject description

2.3. Near-infrared spectroscopy technology equipment introduction

2.4. NIRSIT channel and functional area division

2.5. Near-infrared imaging theory

2.6. Experiment and data collection

3. Results

3.1. Introduction to methamphetamine, heroin, and mixed drugs

3.2. CNN network design

3.3. EEG and NIRS data preprocessing

3.3.1. EEG and NIRS filtering

3.3.2. Convolutional layer

3.3.3. Pooling layer

3.3.4. Normalization of data

3.3.5. Activation function

3.3.6. Full connection layer

3.3.7. Softmax layer

3.4. Accuracy of different brain regions

4. Discussion

4.1. Confusion matrix of classification accuracy of persons abusing different drugs

4.2. Three classification accuracy rate statistics

4.3. Statistical analysis of three types of drug abusers

5. Conclusions

Acknowledgments

Conflict of interest

References

This article has been cited by:

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