
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39223198
71107
10.1038/s41598-024-71107-w
Article
Fault diagnosis method for oil-immersed transformers integrated digital twin model
Yao Haiyan 1
Zhang Xin 2
Guo Qiang 1
Miao Yufeng 1
Guan Shan guanshan1970@163.com

3
1 Hangzhou Electric Power Equipment Manufacturing Co. Ltd Yuhang Qunli Complete Sets Electricity Manufacturing Branch Electric, Hangzhou, 311000 China
2 Hangzhou Electric Power Equipment Manufacturing Co. Ltd., Hangzhou, 311000 China
3 https://ror.org/00zqaxa34 grid.412245.4 0000 0004 1760 0539 Northeast Electric Power University School of Mechanic Engineering, Jilin, 132012 China
2 9 2024
2 9 2024
2024
14 2035520 5 2024
26 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
To address the problems of low accuracy in fault diagnosis of oil-immersed transformers, poor state perception ability and real-time collaboration during diagnosis feedback, a fault diagnosis method for transformers based on the integration of digital twins is proposed. Firstly, fault sample balance is achieved through Iterative Nearest Neighbor Oversampling (INNOS), Secondly, nine-dimensional ratio features are extracted, and the correlation between dissolved gases in oil and fault types is established. Then, sparse principal component analysis (SPCA) is used for feature fusion and dimensionality reduction. Finally, the Aquila Optimizer (AO) is introduced to optimize the parameters of the Kernel Extreme Learning Machine (KELM), establishing the optimal AO-KELM diagnosis model. The final fault diagnosis accuracy reaches 98.1013%. Combining transformer digital twin models, real-time interaction mapping between physical entities and virtual space is achieved, enabling online diagnosis of transformer faults. Experimental results show that the method proposed in this paper has high diagnostic accuracy and strong stability, providing reference for the intelligent operation and maintenance of transformers.

Keywords

Transformer fault diagnosis
Digital twin
Imbalanced small sample
KELM
SPCA
Subject terms

Electrical and electronic engineering
Mechanical engineering
Jilin Provincial Development and Reform Commission innovation capacity construction fund2020C022-6 Guan Shan issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

The transformer, as the hub of power systems, its health status directly impacts the stability and reliability of the electrical system's operation. Therefore, the precise management of a transformer's health status is paramount to ensuring the steadfast and secure operation of the power grid1.

Presently, the technology of Dissolved Gas Analysis (DGA) is extensively employed in the monitoring and identification of faults within oil-insulated transformers2,3, primarily encompassing: the IEC triad ratio method4, the Rogers quadruple ratio method5, and the DUVAL triangle technique6. Despite their simplicity of operation, these approaches lack the depth of representation for fault characteristics and are limited by their capabilities, resulting in a blurred and indistinct encoding boundary, thereby leading to a low accuracy rate in fault recognition7. With the rapid advancement of artificial intelligence, eminent scholars have integrated machine learning with DGA technology, achieving notable results in the field of transformer fault detection. The literature8 optimizes the support vector machine parameters through the refinement of the scalar search algorithm, thereby augmenting both the convergence velocity and the diagnostic precision of the methodology. The literature9 proffers an SE-ELM diagnostic method, whose efficacy was validated through the verification across various datasets. The literature10 enhances the particle swarm optimization algorithm through the dynamic adjustment of inertial weights and acceleration factors, iteratively optimizing the parameters of XGBoost, thereby augmenting the model's classification acumen. Additionally, methods such as Convolutional Neural Networks11,12, Long Short-Term Memory Networks13–15, LightGBM16, and the Capsule Network17 are extensively employed.

With the advancement of big data and the Internet of Things (IoT) technologies, the Digital Twin (DT)18 technology has paved a new path for enhancing the efficiency of equipment health management. The core concept is to construct a holographic virtual twin model in the digital realm, utilizing advanced technologies such as intelligent sensing and data transmission, which accurately, comprehensively, and in real-time reflect the evolution of physical devices, achieving intelligent control over entities19–21. This technology has been extensively utilized in various sectors including aerospace, manufacturing, and healthcare.

In the field of transformer fault diagnosis, scholars both domestically and internationally have carried out extensive research. Referencing22, the study proposed a method for constructing a dual-driving twin model integrating data and models, focusing on 10 kv oil-immersed transformers. This approach enables the synchronization between the actual operating conditions of the transformer and the digital twin center. Referencing23, a digital twin fault diagnosis model was constructed based on the mechanism model and data model of transformers. Five characteristic gases extracted from DGA data were selected as input feature vectors for a CNN. Experimental results showed that the 1D-CNN model established in this study responded rapidly, had a short training time, and achieved high accuracy, thus validating the effectiveness of the model. Referencing24, a fault diagnosis model based on digital twin was constructed for transformers, taking into account their structural characteristics and operational traits. By optimizing the smoothing factor δ in a probabilistic neural network through differential evolution algorithm, the diagnostic accuracy reached an impressive 96.7%, enabling precise monitoring of the transformer's actual operating state. Reference25 conducts a statistical analysis of the operating data and state information quantity of power transformers, proposes a framework for a state evaluation system and fault detection system based on GCA-CNN, and verifies with 2000 real data cases that the model has higher accuracy and evaluation and detection effects. The literature26 establishes a high-fidelity simulation model of transformers to accurately simulate winding currents and the temperatures of different components, which can be used for the identification of early faults. However, the aforementioned research is only focused on a single dissolved gas in oil or vibration signal as the basis for fault diagnosis, but there are many factors affecting transformer faults. In the future, it may be possible to combine multi-source data for comprehensive judgment.

In light of the above context, this paper proposes a fault diagnosis method for oil-immersed transformers that integrates a digital twin model. The main contributions of the paper are divided into several parts. Part 1 mainly elaborates on the research background of the paper and the future research direction. Part 2 establishes a transformer digital twin framework, based on geometric, physical, behavioral, and rule models, to achieve interaction mapping between the virtual entity and the physical entity. Part 3 introduces the methods used in the paper, providing theoretical support for the establishment of an accurate and efficient fault diagnosis model. Part 4 addresses the issue of imbalanced small sample data that can easily lead to misjudgment of minority class samples, deeply explores the correlation between dissolved gases in oil and fault types, and eliminates the 'dimensionality catastrophe' problem, using instance data to obtain diagnostic results. Part 5 discusses and analyzes different sampling methods, different features, and different diagnostic models. Part 6 summarizes the entire paper.

Transformer fault diagnosis model fusing digital twin

Transformer digital twin framework

This article takes a 400kV oil-immersed transformer as the research object and establishes a transformer digital twin integrated digital twin technology. The constructed digital twin framework mainly includes: physical space, twin body, twin data layer and application service layer27, as shown in Fig. 1.Fig. 1 Transformer digital twin framework.

In the process of building a digital twin, the geometric model is the foundation for creating the digital twin model. Three-dimensional software such as UG and SolidWorks are used to comprehensively describe the solid model in terms of geometric dimensions, material properties, and assembly relationships. Based on prior knowledge, physical properties, and operating mechanisms, the geometric model is analyzed and tested for magnetic field, structure, and other modeling aspects, fully reflecting the intrinsic nature and operating mechanism of the transformer. Heterogeneous data from multiple sources, such as dissolved gas in oil and acoustic vibration signals, are collected using state-aware devices. Artificial intelligence algorithms integrated in the behavior model are used for processing and analysis. The derived data generated from simulation calculations are fed back to the mechanism model in real-time. At the same time, simulation data, state-aware data, as well as transformer's full life cycle process data, maintenance records, and computed derived data collectively form the twin database. Through data communication protocols and interfaces, real-time updates and interactive control between the physical entity and the digital twin are achieved, enabling visual description, real-time monitoring, analysis, diagnosis, and intelligent decision-making for the physical transformer. This provides new ideas for improving the safety and reliable operation of power transmission and transformation equipment.

The five-dimensional model of digital twin

The present work is founded on the five-dimensional model proposed by Tao Fei from Beijing Aerospace University28, culminating in the creation of a digital twin for transformers, as exemplified by Eq. (1).1 MDT=PE,VE,SS,DD,CN,

where: PE denotes the physical entity of the transformer, VE represents the virtual entity, SS signifies data, algorithms and models of the digital twin, DD stands for the twinning data of the transformer, and CN symbolizes the interaction and communication among the various components.

The acronym PE stands for transformer physical entity, an ensemble of components including the core, windings, tap-changer, and cooling equipment, it caters to the perception of contact or non-contact by state-sensing devices, embodying the interactive and responsive essence of an objective presence.

The SS represents the process of integrating data and models generated by the digital twin transformer system, thereby facilitating comprehensive monitoring of entities, diagnostic analysis of equipment failures, and predictive maintenance.

VE represents the twin model of the virtual realm, establishing the fundamental groundwork for mapping the virtual to the real. The specific composition is delineated by the formula (2) shown:2 VE=Gv,Pv,Bv,Rv,

where: Gv represents the geometric model, which uses 3D modeling software to create a comprehensive description of the geometric features of physical entities; Pv represents the physical model, which describes the physical properties and operating mechanisms of electrical equipment; Bv represents the behavior model, which combines artificial intelligence algorithms to create Bv; Rv represents the rule model, which mainly includes expert experience and rule inference based on processed historical data for optimization and deduction.

DD represents twin data, which dynamically stores relevant data of PE/VE/SS, and is an important prerequisite for ensuring intelligent operation and maintenance of transformers. The specific representation is shown in formula (3):3 DD=Dp,Dv,Ds,Dk,Df

where: Dp refers to the dynamic factor data collected through the state-aware device; Dv refers to the running parameters in the virtual model; Ds mainly refers to the functional and business service data; Dk includes expert experience, industry rules in the transformer field, and usage guidelines, etc. Df refers to the integrated transformation, interactive fusion, and other derived data of the above-mentioned data.

CN represents the data connection part, which is crucial for ensuring the interaction and updating of the elements in the digital twin model. Through data interfaces, communication protocols, etc., efficient transmission and utilization of data in the digital twin system can be achieved, enabling seamless communication and connectivity among different parts of the model. The interactive relationships of the five dimensions in the digital twin model are shown in Fig. 2.Fig. 2 Transformer digital twin five-dimensional model connection relationship.

Transformer fault diagnosis model based on optimized extreme learning machine

Iterative nearest neighbor oversampling algorithm

The iterative neighborhood oversampling29 algorithm is a sampling method designed to tackle class imbalance issues, with its principal tenet being the selection of a multitude of class-specific samples as neighbors, and then traversing all k data points within this category, scouring for the most recent unlabeled instance within each label data subset of said category until the dataset balances out or approaches close to it. Here follow the specific steps:

Assume the samples in the dataset for each tag to be r=r1,r2,⋯,rj,⋯,ra, with rjj=1,2,⋯a denoting the number of samples contained within category j. Define the sample set's imbalance factor, utilizing the standard deviation varr to symbolize the dispersal of various types of samples within the dataset, as illustrated in Eq. (4):4 IR=1a∑i=1arj-r-212

where: r-=1a∑j=1arj.

Based on the philosophy of greedy search, endeavor to identify a multitude of particular sub-samples, with the process detailed in formula (5):5 xmaxk=argmaxxk⊂XUsimxk,xj

where: xj represents the labeled data in category j. If xmaxk is the classification boundary, remove it and select the next nearest neighbor. Then, label it as category j, remove it from the unlabeled data set XU, add it to the labeled data set XL, and set rj=rj+1. Recalculate the imbalance degree until the preset value is reached, and stop iterating.

Extreme learning machine algorithm

The Kernel Extreme Learning Machine (KELM)30 is based on a single hidden layer feedforward neural network. It introduces a kernel function on top of the ELM algorithm, which maps low-dimensional data to a high-dimensional feature space, resulting in a model with stronger generalization and robustness. The specific steps are as follows:

Assume we are provided with N samples represented as xi,tii=1N, where xi=xi1,xi2,⋯,xinT∈Rn and ti=ti1,ti2,⋯,timT∈Rn denote the input vector and output function of the model respectively. In the context of a neural network with k hidden layers and an activation function gx, the number of hidden nodes is L, and the ELM model can be articulated by the formula shown in Eq. (6):6 fx=∑j=1Lβjhjx=hxβ

where: βj=βj1,βj2,⋯,βjLTj=1,2,⋯,L denotes the output weight value connecting the jth implicit layer node with the output layer node. Among these, H=hiji=1,2,⋯,N;j=1,2,⋯,L represents the output matrix of the hidden layer, and H denotes the jth column of the input x1,x2,⋯,xn corresponding to the jth hidden layer node. Within H, the jth row corresponds to the output vector of xi.

Using the least squares method to obtain the output weight values, as shown in formula (7):7 β∗=H′T

In the formula, H′ represents the generalized inverse matrix of the hidden layer output matrix H.

Introducing the kernel function mitigates the issue of randomly generated input weights and bias values, exemplified by the KELM weight output formula (8):8 β=HT1C+HHT-1T

The KELM output function as expressed in formula (9):9 fx=hβ=hxHT1C+HHT-1

When hx remains unknown, the kernel function matrix is represented by formula (10):10 ΩELM=HHT;ΩELMi,j=hxi·hxj=Kxi,xj

In the equation, Kxi,xj denotes the nuclear function, represented as:11 Kxi,xj=exp-xi-xj2σ2

The KELM model's output function expression is delineated in formula (12):12 fx=Kx,x1⋯Kx,xN1C+ΩELM-1T

Sparse principal component analysis

The sparse principal component analysis31 is a method that builds upon the principal component analysis algorithm by incorporating the LASSO penalty term, thereby enabling the matrix to be sparsely populated. By solving the regression coefficient matrix, it further transforms PCA into an optimization problem aimed at finding the optimal set of coefficients for regression. Compared to traditional PCA, SPCA excels in effectively managing the sparsity within high-dimensional data, yielding results that are more interpretative.

The SPCA algorithm is resolve into two segments: the first entails calculating the principal components via PCA; the second entails enhancing the LASSO penalty term to render the obtained solution sparse. Here follow the specific steps:

Given a n×m-variant dataset X, the feature decomposition upon normalization treatment, as expounded upon in formula (13):13 covX=XTXn-1=VΛVT

In the equation, Λ∈Rm×m represents a diagonal matrix of eigenvalues, arranged in descending order. Λ∈Rm×m is a unitary matrix with column vectors as load vectors.

Select the first k columns of the load matrix P∈Rm×k, compute the score matrix T, as shown in Eq. (14):14 T=XP

Projecting T onto X yields a new matrix X∧ that encompasses information from the corresponding principal component; the difference with X is denoted as E, as illustrated in formula (15), (16):15 X∧=TPT

16 E=X-X∧

The solution of the SPCA first reverts to the PCA model. The formula (15–16) yields the expression (17):17 X=TPT+E=XPPT+E

Ensure the main component is as near to the original data as possible, that is,it mandates E'sminimalism. Therefore, the principal component seeks resolution through formula (18):18 P∧=argmini=1∑i=1nxi-PiTPixi2

In the equation, P∧ is the solution to the minimum value of the principal matrix P.

The vectors sought by PCA are all non-zero; thus, the sparse solution is achieved by incorporating the LASSO penalty term, thereby mitigating the overfitting issue in PCA. The solution formula for sparse principal components, as displayed in formula (19), is illustrated:19 A∧,B∧=argmini=1∑i=1nxi-ABTxi2+λ∑j=1kbj2+λ1,j∑j=1kbj1SubjecttoATA=Ik×k

In this equation, matrix A denotes the expected demand matrix to be sought, while matrix B represents the demand matrix expected under the regression problem. A and B represent the m×k matrix, A∧ and B∧ the matrices to be solved for minimizing values of A and B; they are subject to the constraints bj∝Pj, λ and λ1,j being the penalty coefficients, and must adhere to λ>0. The adjusted variance, as expressed in formula (20), is indicative of:20 SΛ=diagqxXP∧n2

In the equation, the diagonal matrix interpreting variance is delineated, with P∧ representing the load matrix following the coefficients. Model contribution lies articulated in formula (21):21 CPV=∑i=1kSΛi∑i=1mΛi

Transformer fault diagnosis model process

This article, established on the premise of transformer fault imbalance within small sample sets, aims at achieving real-time and precise diagnosis through the establishment of a diagnostic model and a determined diagnostic process. The specific diagnostic process is illustrated in Fig. 3. The article employs the AO-KELM model as the diagnostic model, erecting a diagnostic process that integrates offline model training with online fault identification.Fig. 3 Transformer fault diagnosis model based on optimized kernel extreme learning machine.

⑴ Train the model offline

The article delves into the offline model training segment from three perspectives: data preprocessing, feature extraction, and model recognition.

Step 1: the preprocessing segment encompasses data INNOS's oversampling and normalization treatment. Collect the gathered DGA samples through INNOS for augmenting the minority class samples, followed by normalization treatment.

Step 2: the feature extraction section encompasses the establishment of ratio signature generation and the integration of SPCA for fusion dimensionality reduction. First, construct a multidimensional discriminant signature, delving deeply into the correlation between the ratio of dissolved gas content in oil and the type of fault. Subsequently, employ SPCA for feature fusion to acquire the optimal principal component, thereby removing redundant information, and divide the training set, validation set, and test set proportionally.

Step 3: the model identification segment encompasses the training and validation of the model. Utilizing the AO algorithm to optimize the regularization parameters C and the kernel functions within the KELM model, one verifies the model's accuracy through validation set on each iteration. Should the discrepancy between consecutive training sessions fall beneath 5%, the model training continues; otherwise, the model retraining commences anew until the prerequisite conditions are met. The ultimate establishment of the AO-KELM optimal diagnostic model.

⑵ Online fault diagnosis

Normalize the samples collected in real-time to handle and construct multi-dimensional features, employing an unencoded ratio method to input into an optimal diagnosis model directly following optimal principal component projection, thereby achieving swift recognition of transformer fault. Although the computational time for offline model training is accordingly elevated, it is merely necessary to undergo training once, with the aim of achieving online recognition and diagnosis of transformer faults as data from real-time monitoring continues to be inputted.

Case study analysis

Data source and normalization processing

Transformer insults are exacerbated by thermal electrochemical action, causing the decomposition of internal insulating materials and the dissolution of various hydrocarbon gases within the insulation oil. Distinct characteristics of gas dissolved in oil under varying fault types exist; research has demonstrated that diagnostic and classification of faults can be achieved through the use of DGA techniques32. Consequently, these five gas contents are utilized as a basis for transformer fault diagnosis in this article.

The article selected a comprehensive sample of 337 monitoring data from a particular power supply company, dividing the operating status of transformers into categories such as normal, moderate heat overload, high temperature overload, high energy discharge, low energy discharge, and local discharge, each represented by labels 1 through 6. Each type of fault is augmented with specific characteristic gases including H2, CH4, C2H4, C2H6, and C2H2; the exact number of samples for each category is detailed in Table 1. The data reveals that the majority of samples fall into the category of normal, comprising 35.63% of the total. Low-energy discharge and local discharge types account for 5.55% and 9.78% respectively, with a maximum disparity reaching 5.1:1. Such imbalanced data is prone to misidentifying samples of the minority class as normal, thereby impacting recognition accuracy. Therefore, this paper employs the INNOS algorithm to augment the minority class samples, achieving a balance in sample categories.Table 1 Category labels and sample distribution.

Status type	Category label	Sample quantity	Balanced data after processing	
Normal	1	102	102	
High temperature overheating	2	70	140	
Medium–low temperature overheating	3	45	135	
High-energy discharge	4	64	128	
Low-energy discharge	5	20	140	
Partial discharge	6	36	144	

To manifest the disparities between data prior to and after sampling, a principal component analysis is conducted upon the sample data from before and after said sampling process. Subsequently, the first two principal components are selected for visualizing the data of various types both before and after said sampling, as illustrated in Fig. 4. In Fig. 4, it becomes apparent that the data distribution trends for various types of faults, prior to and after the adoption of the INNOS sampling method, are identical, thereby underscoring the viability of the INNOS sampling approach.Fig. 4 Scatter plot of INNOS samples.

Transformer malfunction signature composition

Considering the substantial disparities among the various volatile gases, a preliminary normalization is required for each gas's abundance, as illustrated in Eq. (22):22 xi∗=xi-ximinximax-ximin

In the equation: xi and xi∗ represent features pre-normalized; ximax and ximin indicate the original minimal and maximum values.

The method of unencoded ratio analysis33 is but one among numerous techniques widely employed, utilizing the percentage ratio of key gases to either the total gas or the hydrocarbon concentration can profoundly illustrate the interconnectedness between characteristic gases and types of failures. For instance, the ratio of a singular gas to the total hydrocarbon concentration provides a more conclusive indicator of the interplay between diverse fault types; the concentrations of C2H4 and CH4 can effectively demarcate local discharge from discharge with overheating diagnosis; the percentage composition of C2H2 can determine whether a transformer has experienced thermal failure, among other determinations. The construction of this paper is predicated on the integration of pertinent literature, establishing a nine-dimensional candidate ratio signature for transformer fault diagnosis31, as delineated in Table 2, wherein THC = CH4 + C2H4 + C2H6 + C2H2, and ALL = H2 + CH4 + C2H4 + C2H6 + C2H2.Table 2 Characteristic codes and characteristic quantities of dissolved gases in oil.

Encoding number	Ratio features	Encoding number	Ratio features	
S1	CH4/H2	S6	C2H6/THC	
S2	C2H2/C2H4	S7	C2H2/THC	
S3	C2H4/C2H6	S8	(CH4 + C2H4)/THC	
S4	CH4/THC	S9	H2/ALL	
S5	C2H4/THC			

Dimensionality reduction through feature parameter fusion

To avoid the redundancy of fault-related feature information within the samples and to enhance the efficiency and precision of the diagnostic model, the SPCA method was employed for the integration of the derived rational features. The cumulative explicable variance contribution rate of each principal component is depicted in Fig. 5. It is evident from Fig. 5 that the cumulative variance contribution rate for the first six principal components reaches 90.4419%, indicating that the first five principal components can achieve more than 90% of the ability expressed by all the principal components. Hence, selecting these five principal components as inputs for the transformer fault diagnosis model is warranted.Fig. 5 Cumulative variance contribution rate.

Transformer malfunction diagnosis outcomes

The fused features derived from the SPCA extraction are delineated in a ratio of 6:2:2 to be divided into training, testing, and validation datasets. The regularization parameters C within KELM determine the learning capacity of the model and its diagnostic precision; in this paper, we employ the AO optimization algorithm to optimize C, with an introduction of the AO algorithm as delineated in literature34,35, culminating in the establishment of a diagnostic model based on SPCA-AO-KELM. Figure 6 delineates the confusion matrix diagram of the transformer fault diagnosis. It is evident from Fig. 6 that within the test set of 158 samples, 155 were correctly diagnosed, representing a total correct rate of 98.1013%. The accuracy rates for normal, high-temperature overheating, and low-energy discharge diagnoses are 100%, one case of misjudgment was found in medium–low temperature overheating, high-energy discharge, and partial discharge.Fig. 6 Transformer fault diagnosis results.

However, the precision of diagnostic accuracy alone cannot comprehensively nor efficaciously evaluate the impact of rare class faults on classification performance36,37. In this paper, we introduce classification model performance evaluation metrics derived from confusion matrices, employing accuracy (R), precision (P), and F1-score as the core components of our evaluation system. The veracity of diagnostic models for identifying various faults is assessed by the accuracy rate, the sensitivity of the model in recognizing a variety of faults is evaluated by the coverage rate, while the F1 score derived from the amalgamation of precision and recall reflects the model's classification performance amidst sample imbalance, with specific formulas denoted in the literature displayed here. The model's precision, recall, and F1-score derived from the computed graph in Fig. 6 respectively stand at 0.9816, 0.9825, and 0.9820, further underscoring the model's high fault detection accuracy and its stable nature.

Results and discussions

Comparison and analysis of different sampling methods

To verify the effectiveness of the new samples synthesized based on INNOS in improving the accuracy of transformer fault diagnosis, this paper uses unbalanced data set, random oversampling, SMOTE, and ADASYN oversampling algorithms for sample augmentation, and the diagnostic results are shown in Fig. 7. The red dots in the figure represent the samples that are correctly classified in the test set, while the circles represent the samples of the true class, and the scattered dots represent the samples that are misclassified as other classes. The more scattered sample points, the higher the misclassification rate. In Fig. 7d, the diagnostic accuracy of the original unbalanced data set without balancing processing is only 88.4058%, indicating that due to the imbalance of data in each fault category, the training of the diagnostic model is insufficient, and it is easy to misclassify minority class samples as majority class samples during classification recognition. After balancing the data set using different sampling methods, the misclassification rate of the samples decreases. The sampling method used in this paper improves the diagnostic accuracy by 7.7967%, 2.5316%, and 1.8987% compared to ADASYN, SMOTE, and random oversampling, respectively, indicating that the INNOS sampling method can effectively solve the problem of low diagnostic accuracy caused by data imbalance.Fig. 7 Diagnostic results under different sampling methods.

Qualitative and quantitative analysis with integrated features

To demonstrate the effectiveness of the SPCA feature fusion method, this study conducted analysis from two perspectives: qualitative observation and quantitative analysis. Firstly, PCA, KPCA, and SPCA were used to extract features from the constructed ratio signs. The cumulative variance contribution rate threshold was set at 90%, and the obtained principal component information is detailed in Table 3. LASSO penalty term was introduced based on PCA to constrain some loading vectors to zero, resulting in a loss of variance contribution rate. From the data in the table, it can be seen that the contribution rate of SPCA principal components is slightly lower than that of PCA and KPCA, effectively removing redundant information in the ratio features and providing a valid data foundation for subsequent classification and recognition.Table 3 Cumulative variance contribution of principal components.

Cumulative variance contribution	Contribution rate of each principal component variance	
SPCA	1-st element	2-nd element	3-rd element	4-th element	5-th element	
32.8794%	54.6637%	71.1496%	82.6964%	90.4419%	
KPCA	1-st element	2-nd element	3-rd element	4-th element	5-th element	
33.7358%	56.0409%	71.7705%	83.3737%	91.1917%	
PCA	1-st element	2-nd element	3-rd element	4-th element	5-th element	
33.2636%	55.5458%	72.4232%	83.9287%	91.4745%	

Furthermore, for the above feature extraction methods, quantitative calculations were performed. The fused features extracted by the 9-dimensional joint feature, PCA, KPCA, and SPCA were input into the diagnostic model for comparative analysis, as shown in Fig. 8. From Fig. 8a–d, it can be observed that the diagnostic accuracy is significantly improved after feature extraction. Figure 8a has a higher accuracy compared to Fig. 8b and c, which validates the superiority of the SPCA feature extraction method.Fig. 8 Diagnostic outcomes under various characteristics.

Analysis of contrastive diagnostic models

To explore the diagnostic performance of the models, three diagnostic models, ELM, KELM, and AO-ELM, were constructed for horizontal comparison. The diagnostic results are shown in Table 4. From the perspective of a single model, the introduction of a kernel function improved the diagnostic accuracy and evaluation indicators of ELM. From the perspective of optimization algorithms, the diagnostic capability of fault recognition was effectively improved after parameter optimization using the AO algorithm.Table 4 Results of fault diagnosis under various diagnostic models.

Model Name	Accuracy (%)	Recall	Precision	F1-score	
ELM	92.5098	0.9240	0.9273	0.9256	
KELM	93.1420	0.9316	0.9312	0.9314	
AO-ELM	95.0832	0.9502	0.9527	0.9514	
AO-KELM	98.1013	0.9816	0.9825	0.9820	

On the other hand, the extracted integration features are respectively inputted into the POA-SVM model proposed in Literature38, the SSA-ELM model suggested in Literature39, and the PSO-BiLSTM model introduced in Literature40 for longitudinal comparison. To circumvent the chances of chance, each model is subjected to ten-fold cross-validation, as manifested in Table 5. It is evident from Table 5 that, under conditions where the input features remain identical, the AO-KELM outperforms both the POA-SVM and POA-SVM by elevating the average accuracy by 3.23% and 2.64%, respectively, while the PSO-BiLSTM lags behind with a mere 1.8% increase in accuracy. This clearly signifies the robust stability of the AO-KELM model and its formidable classification capabilities.Table 5 Average diagnostic accuracy of different diagnostic models.

Model name	Accuracy of fault diagnosis	Accuracy variance	
Maximum (%)	Minimum (%)	Average (%)	
POA-SVM	95.36	94.87	95.15	0.62	
SSA-ELM	95.96	95.33	95.74	0.59	
PSO-BiLSTM	96.86	96.32	96.58	0.46	
AO-KELM	98.10	97.76	98.38	0.24	

Conclusion

The paper introduces an oil-immersed transformer fault diagnosis method that integrates digital twin models, providing validation through case studies, leading to the conclusions below:Build a twin mechanism model based on geometric, physical, rule, and behavior models, use real-time data to drive the fusion of data and mechanism models, complete real-time mapping between physical entities and virtual entities, and use visualization technology to express the twin in multiple dimensions, achieve intelligent diagnosis, health monitoring, and optimization decision-making for the transformer entity.

Proposed a transformer fault diagnosis model based on optimized kernel extreme learning machine, which solves the problem of misjudgment of minority class samples caused by unbalanced small samples, effectively extracts fusion features, establishes the optimal AO-KELM classifier, and achieves an accuracy of 98.1013%. By comparing with different diagnostic models, the classification performance and stability of the proposed method are verified.

Acknowledgements

Project supported by Jilin Provincial Development and Reform Commission innovation capacity construction fund (2020C022-6).

Author contributions

Haiyan Y designed the experiments and contributedmaterials/analysis tools; Xin Zhang analyzed the data and its visualization; Qiang Guo and Yufeng Miao M guided the data analysis; Shan Guan wrote the paper; All authors have reviewed the manuscript.

Data availability

The datasets generated and/or analysed during the currentstudy are not publicly availabledue [REASON WHY DATA ARENOT PUBLlC] but are availablefrom the corresponding authoron reasonable request. E-mail:guanshan1970@163.com.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Tightiz L Nasab MA Yang H An intelligent system based on optimized ANFIS and association rules for power transformer fault diagnosis ISA Trans. 2020 103 63 74 10.1016/j.isatra.2020.03.022 32197758
Tightiz, L. et al. An intelligent system based on optimized ANFIS and association rules for power transformer fault diagnosis. ISA Trans. 103, 63–74 (2020).32197758 10.1016/j.isatra.2020.03.022
2. Zhang Y Tang Y Liu Y Fault diagnosis of transformer using artificial intelligence: A review Front. Energy Res. 2022 10 1006474 10.3389/fenrg.2022.1006474
Zhang, Y. et al. Fault diagnosis of transformer using artificial intelligence: A review. Front. Energy Res. 10, 1006474 (2022).10.3389/fenrg.2022.1006474
3. Wani SA Rana AS Sohail S Advances in DGA based condition monitoring of transformers: A review Renew. Sustain. Energy Rev. 2021 149 111347 10.1016/j.rser.2021.111347
Wani, S. A. et al. Advances in DGA based condition monitoring of transformers: A review. Renew. Sustain. Energy Rev. 149, 111347 (2021).10.1016/j.rser.2021.111347
4. Malik H Mishra S Application of gene expression programming (GEP) in power transformers fault diagnosis using DGA IEEE Trans. Ind. Appl. 2016 52 6 4556 4565 10.1109/TIA.2016.2598677
Malik, H. & Mishra, S. Application of gene expression programming (GEP) in power transformers fault diagnosis using DGA. IEEE Trans. Ind. Appl. 52(6), 4556–4565 (2016).10.1109/TIA.2016.2598677
5. Lin J Ma J Zhu J Hierarchical federated learning for power transformer fault diagnosis IEEE Trans. Instrum. Meas. 2022 71 1 11
Lin, J., Ma, J. & Zhu, J. Hierarchical federated learning for power transformer fault diagnosis. IEEE Trans. Instrum. Meas. 71, 1–11 (2022).
6. Duval M A review of faults detectable by gas-in-oil analysis in transformers IEEE Electr. Insul. Mag. 2002 18 3 8 17 10.1109/MEI.2002.1014963
Duval, M. A review of faults detectable by gas-in-oil analysis in transformers. IEEE Electr. Insul. Mag. 18(3), 8–17 (2002).10.1109/MEI.2002.1014963
7. Li P Hu GM Transformer fault diagnosis based on data enhanced one-dimensional improved convolutional neural network Power Syst. Technol. 2023 47 07 2957 2967
Li, P. & Hu, G. M. Transformer fault diagnosis based on data enhanced one-dimensional improved convolutional neural network. Power Syst. Technol. 47(07), 2957–2967 (2023).
8. Zhou XH Feng YW Chen L Transformer fault diagnosis based on SVM optimized by the improved bald eagle search algorithm Power Syst. Prot. Control 2023 51 08 118 126
Zhou, X. H. et al. Transformer fault diagnosis based on SVM optimized by the improved bald eagle search algorithm. Power Syst. Prot. Control 51(08), 118–126 (2023).
9. Chen HC Zhang Y Chen M Transformer dissolved gas analysis for highly-imbalanced dataset using multi-class sequential ensembled ELM IEEE Trans. Dielectr. Electr. Insulat. 2023 10.1109/TDEI.2023.3280436
Chen, H. C., Zhang, Y. & Chen, M. Transformer dissolved gas analysis for highly-imbalanced dataset using multi-class sequential ensembled ELM. IEEE Trans. Dielectr. Electr. Insulat.10.1109/TDEI.2023.3280436 (2023).10.1109/TDEI.2023.3280436
10. Gong ZWY Rao T Wang G Fault diagnosis method of transformer based on improved particle swarm optimization XGBoost High Volt. Appar. 2023 59 08 61 69
Gong, Z. W. Y. et al. Fault diagnosis method of transformer based on improved particle swarm optimization XGBoost. High Volt. Appar. 59(08), 61–69 (2023).
11. Xu HR Wang ZY Condition evaluation and fault diagnosis of power transformer based on GAN-CNN J. Electrotechnol. Electr. Eng. Manag. 2023 6 3 8 16
Xu, H. R. & Wang, Z. Y. Condition evaluation and fault diagnosis of power transformer based on GAN-CNN. J. Electrotechnol. Electr. Eng. Manag. 6(3), 8–16 (2023).
12. Wang Z Xu H GCA-CNN based transformer digital twin model construction and fault diagnosis and condition evaluation analysis Acad. J. Comput. Inf. Sci. 2023 6 6 100 107
Wang, Z. & Xu, H. GCA-CNN based transformer digital twin model construction and fault diagnosis and condition evaluation analysis. Acad. J. Comput. Inf. Sci. 6(6), 100–107 (2023).
13. Wang L Littler T Liu X Dynamic incipient fault forecasting for power transformers using an LSTM model IEEE Trans. Dielectr. Electr. Insulat. 2023 10.1109/TDEI.2023.3253463
Wang, L., Littler, T. & Liu, X. Dynamic incipient fault forecasting for power transformers using an LSTM model. IEEE Trans. Dielectr. Electr. Insulat.10.1109/TDEI.2023.3253463 (2023).10.1109/TDEI.2023.3253463
14. Ding Y Jia M Miao Q A novel time–frequency Transformer based on self-attention mechanism and its application in fault diagnosis of rolling bearings Mech. Syst. Signal Process. 2022 168 108616 10.1016/j.ymssp.2021.108616
Ding, Y. et al. A novel time–frequency Transformer based on self-attention mechanism and its application in fault diagnosis of rolling bearings. Mech. Syst. Signal Process. 168, 108616 (2022).10.1016/j.ymssp.2021.108616
15. Zheng Q Wang R Tian X A real-time transformer discharge pattern recognition method based on CNN-LSTM driven by few-shot learning Electr. Power Syst. Res. 2023 219 109241 10.1016/j.epsr.2023.109241
Zheng, Q. et al. A real-time transformer discharge pattern recognition method based on CNN-LSTM driven by few-shot learning. Electr. Power Syst. Res. 219, 109241 (2023).10.1016/j.epsr.2023.109241
16. Yan P Chen F Zhao T Transformer fault diagnosis research based on LIF technology and IAO optimization of LightGBM Anal. Methods 2023 15 3 261 274 10.1039/D2AY01745H 36546319
Yan, P. et al. Transformer fault diagnosis research based on LIF technology and IAO optimization of LightGBM. Anal. Methods 15(3), 261–274 (2023).36546319 10.1039/D2AY01745H
17. Yang DC Liao WL Ren X Fault diagnosis of transformer based on capsule network High Volt. Eng. 2021 47 02 415 425
Yang, D. C. et al. Fault diagnosis of transformer based on capsule network. High Volt. Eng. 47(02), 415–425 (2021).
18. Grieves M Vickers J Kahlen F-J Flumerfelt S Alves A Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems Transdisciplinary Prespectives on Complex Systems 2017 Springer International Publishing 85 113
Grieves, M. & Vickers, J. Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems. In Transdisciplinary Prespectives on Complex Systems (eds Kahlen, F.-J. et al.) 85–113 (Springer International Publishing, 2017).
19. Bai XZ Zang Y Ge LJ Selection method of feature derived from dissolved gas in oil for transformers fault diagnosis High Volt. Eng. 2023 49 09 3873 3886
Bai, X. Z. et al. Selection method of feature derived from dissolved gas in oil for transformers fault diagnosis. High Volt. Eng. 49(09), 3873–3886 (2023).
20. Liu YP Liu YJ Lv FC Application prospect and key technology of digital twin in power transmission and transformation equipment High Volt. Eng. 2022 48 05 1621 1633
Liu, Y. P. et al. Application prospect and key technology of digital twin in power transmission and transformation equipment. High Volt. Eng. 48(05), 1621–1633 (2022).
21. Yang F Wu T Liao RJ Application and implementation method of digital twin in electric equipment High Volt. Eng. 2021 47 05 1505 1521
Yang, F. et al. Application and implementation method of digital twin in electric equipment. High Volt. Eng. 47(05), 1505–1521 (2021).
22. Jiang L Wang DJ Sun L Research on transformer fault diagnosis method based on digital twin J. Syst. Simulat. 2024 10.16182/j.issn1004731x.joss.23-1402
Jiang, L. et al. Research on transformer fault diagnosis method based on digital twin. J. Syst. Simulat.10.16182/j.issn1004731x.joss.23-1402 (2024).10.16182/j.issn1004731x.joss.23-1402
23. Yan ZJ Yang YF Fault diagnosis of transformers based on CNN and digital twin Comput. Digit. Eng. 2023 51 11 2758 2762
Yan, Z. J. & Yang, Y. F. Fault diagnosis of transformers based on CNN and digital twin. Comput. Digit. Eng. 51(11), 2758–2762 (2023).
24. Wang Y Zhang TH Fault diagnosis of transformers based on optimal probabilistic neural network based on digital twin Mod. Mach. Tool Autom. Manuf. Techn. 2020 11 20 23
Wang, Y. & Zhang, T. H. Fault diagnosis of transformers based on optimal probabilistic neural network based on digital twin. Mod. Mach. Tool Autom. Manuf. Techn. 11, 20–23 (2020).
25. Moutis P Alizadeh-Mousavi O Digital twin of distribution power transformer for real-time monitoring of medium voltage from low voltage measurements IEEE Trans. Power Deliv. 2020 36 4 1952 1963 10.1109/TPWRD.2020.3017355
Moutis, P. & Alizadeh-Mousavi, O. Digital twin of distribution power transformer for real-time monitoring of medium voltage from low voltage measurements. IEEE Trans. Power Deliv. 36(4), 1952–1963 (2020).10.1109/TPWRD.2020.3017355
26. Zhang LJ Sheng GG Ni ZZ Study on electrothermal characteristics of oil-immersed power transformers in early stage of interturn faults Proc. CSEE 2023 43 15 6124 6136
Zhang, L. J. et al. Study on electrothermal characteristics of oil-immersed power transformers in early stage of interturn faults. Proc. CSEE 43(15), 6124–6136 (2023).
27. Tao F Liu WR Zhang M Five-dimension digital twin model and its ten applications Comput. Integr. Manuf. Syst. 2019 25 01 1 18
Tao, F. et al. Five-dimension digital twin model and its ten applications. Comput. Integr. Manuf. Syst. 25(01), 1–18 (2019).
28. Li SW Zhang DL Huang XY Application of data feature selection and classification in mechanical fault diagnosis J. Vibrat. Shock 2020 39 02 218 222
Li, S. W. et al. Application of data feature selection and classification in mechanical fault diagnosis. J. Vibrat. Shock 39(02), 218–222 (2020).
29. Han X Ma S Shi Z A novel power transformer fault diagnosis model based on Harris-Hawks-optimization algorithm optimized kernel extreme learning machine J. Electr. Eng. Technol. 2022 17 3 1993 2001 10.1007/s42835-022-01000-x
Han, X. et al. A novel power transformer fault diagnosis model based on Harris-Hawks-optimization algorithm optimized kernel extreme learning machine. J. Electr. Eng. Technol. 17(3), 1993–2001 (2022).10.1007/s42835-022-01000-x
30. Kong DM Chen HJ Chen XY Research on oil identification method based on three-dimensional fluorescence spectroscopy combined with sparse principal component analysis and support vector machine Spectroscopy Spectral Anal. 2021 41 11 3474 3479
Kong, D. M. et al. Research on oil identification method based on three-dimensional fluorescence spectroscopy combined with sparse principal component analysis and support vector machine. Spectroscopy Spectral Anal. 41(11), 3474–3479 (2021).
31. Kim SW Kim SJ Seo HD New methods of DGA diagnosis using IEC TC 10 and related databases part l: Application of gas-ratio combinations IEEE Trans. Dielectr. Electr. Insulat. 2013 20 2 685 690 10.1109/TDEI.2013.6508773
Kim, S. W. et al. New methods of DGA diagnosis using IEC TC 10 and related databases part l: Application of gas-ratio combinations. IEEE Trans. Dielectr. Electr. Insulat. 20(2), 685–690 (2013).10.1109/TDEI.2013.6508773
32. Guo RY Peng MM Cao ZQ Fault diagnosis of power transformer based on SE-DenseNet Adv. Technol. Electr. Eng. Energy 2021 40 01 61 69
Guo, R. Y., Peng, M. M. & Cao, Z. Q. Fault diagnosis of power transformer based on SE-DenseNet. Adv. Technol. Electr. Eng. Energy 40(01), 61–69 (2021).
33. Wang K Li JZ Zhang SQ New features derived from dissolved gas Analysis for fault diagnosis of power transformers Proc. CSEE 2016 36 23 6570 6578+6625
Wang, K. et al. New features derived from dissolved gas Analysis for fault diagnosis of power transformers. Proc. CSEE 36(23), 6570–6578+6625 (2016).
34. Li GL Chen XY Li ZY Thermal error model of spindle for precision CNC machine tool based on AO-CNN J. Xi'an Jiaotong Univ. 2022 56 08 51 61
Li, G. L. et al. Thermal error model of spindle for precision CNC machine tool based on AO-CNN. J. Xi’an Jiaotong Univ. 56(08), 51–61 (2022).
35. Zhang CS Zhang JZ Qian B improved aquila optimization based on multi-strategy integration Acta Electron. Sin. 2023 51 05 1245 1255
Zhang, C. S. et al. improved aquila optimization based on multi-strategy integration. Acta Electron. Sin. 51(05), 1245–1255 (2023).
36. Wang Y Li W Zhao HS Transformer fault diagnosis fused with synthetic minority over-sampling balanced multi-classification data based on improved extreme learning machine Power Syst. Technol. 2023 47 09 3799 3807
Wang, Y. et al. Transformer fault diagnosis fused with synthetic minority over-sampling balanced multi-classification data based on improved extreme learning machine. Power Syst. Technol. 47(09), 3799–3807 (2023).
37. Tang J Hou HJ Sheng GG Oversampling and cost⁃sensitive algorithm for transformer fault diagnosis with unbalanced samples High Volt. Apparatus 2023 59 06 93 102
Tang, J. et al. Oversampling and cost⁃sensitive algorithm for transformer fault diagnosis with unbalanced samples. High Volt. Apparatus 59(06), 93–102 (2023).
38. Liu DD Wang Y Liu HQ POA-SVM transformer fault diagnosis based on ADASYN balanced data set Power Syst. Clean Energy 2023 39 08 36 44
Liu, D. D. et al. POA-SVM transformer fault diagnosis based on ADASYN balanced data set. Power Syst. Clean Energy 39(08), 36–44 (2023).
39. Wang Y Li Y Zhao HS Transformer DGA fault diagnosis method based on DBN-SSAELM Power Syst. Prot. Control 2023 51 04 32 42
Wang, Y. et al. Transformer DGA fault diagnosis method based on DBN-SSAELM. Power Syst. Prot. Control 51(04), 32–42 (2023).
40. Fan QC Yu F Xuan M Power transformer fault diagnosis based on optimized Bi-LSTM model Comput. Simul. 2022 39 11 136 140
Fan, Q. C., Yu, F. & Xuan, M. Power transformer fault diagnosis based on optimized Bi-LSTM model. Comput. Simul. 39(11), 136–140 (2022).
