Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2017 / Article
Special Issue

Advanced Control for Singular Systems with Applications

View this Special Issue

Research Article | Open Access

Volume 2017 |Article ID 3068548 | https://doi.org/10.1155/2017/3068548

Yu Ding, Qiang Liu, "Data-Driven Fault Diagnosis Method for Power Transformers Using Modified Kriging Model", Mathematical Problems in Engineering, vol. 2017, Article ID 3068548, 5 pages, 2017. https://doi.org/10.1155/2017/3068548

Data-Driven Fault Diagnosis Method for Power Transformers Using Modified Kriging Model

Academic Editor: Wanquan Liu
Received25 May 2017
Accepted20 Sep 2017
Published22 Oct 2017

Abstract

A data-driven fault diagnosis method that combines Kriging model and neural network is presented and is further used for power transformers based on analysis of dissolved gases in oil. In order to improve modeling accuracy of Kriging model, a modified model that replaces the global model of Kriging model with BP neural network is presented and is further extended using linearity weighted aggregation method. The presented method integrates characteristics of the global approximation of the neural network technology and the localized departure of the Kriging model, which improves modeling accuracy. Finally, the validity of this method is demonstrated by several numerical computations of transformer fault diagnosis problems.

1. Introduction

Transformer is one of the most important equipment in power system [1], which is mainly used to transfer electrical energy between two or more circuits through electromagnetic induction. In the course of using this equipment, some factors such as electrical, thermal, and mechanical stresses may lead to irreversible damage to the insulating material [2]. In order to improve the reliability of power supply, fault diagnosis for transformer has drawn much attention from researchers, and many fault diagnosis methods have been widely proposed during the past decades.

At present, Dissolved Gas-in-oil Analysis (DGA) is a commonly used method to identify incipient failures of transformer fault [3]. With the development of artificial intelligence and computer technology, many fault diagnosis algorithms have been proposed based on DGA, such as neural network [4, 5], fuzzy logic [6, 7], expert system [8], support vector machine [2, 9], and rough set theory [10]. Given that existing methods have their own characteristics and some limitations, effective fault diagnosis methods that integrate advantages of existing technologies to improve the modeling accuracy still remain an open area of research.

As a classic modeling technology, Kriging model combines a global model plus localized departures to construct approximation from sample data. It has been widely used in the field of Computer-Aided Engineering (CAE) [11, 12]. On the other hand, neural network technology is a well-known information processing paradigm and has been widely applied in various areas due to its advantages such as adaptive learning. In this paper, a data-driven fault diagnosis model based on Kriging model and BP neural network is constructed and then is used for transformer fault diagnosis problems based on DGA. In order to improve the modeling accuracy of Kriging model, BP neural network is used to modify the global model of Kriging model, where the modified formula is given in detail. The modified Kriging model combines global and adaptive learning abilities of neural network technology and retains the localized departures of the Kriging model in the meantime. It integrates the advantages of both methods, which thus effectively improve the modeling accuracy. Finally, some examples of transformer fault diagnosis show that the proposed method is effective and feasible.

2. Overall Design of Modified Kriging Model: A Hybrid Model

The Kriging model is an unbiased estimation model based on the minimum variance estimation of sample points and their response values. The output can be viewed as a combination of a regression model and a stochastic process [13, 14]. The regression model is equivalent to the global simulation of the sample space, and the stochastic process is equivalent to local deviation.

In order to further improve the accuracy of the Kriging model, this paper proposes a transformer fault diagnosis method that combines Kriging model and neural network technology. The structure of this hybrid model is shown in Figure 1. The main steps for constructing the hybrid model are as follows:

() Determine characteristic variables and fault types based on DGA method, and collect sample data and test data.

() According to sample data, construct BP network model.

() Construct the Kriging model based on sample data.

() The global simulation of Kriging model is modified and updated by neural network, and then the hybrid model is constructed.

3. Modeling Method of Hybrid Model

3.1. Kriging Model and Parameter Optimization

The Kriging model contains global simulation plus localized departures, and the basic principles of which can be briefly given as follows [13, 14]: set approximate function as , and the function between the response value and the independent variable of the system can be formulated as follows:where is the unknown function of interest, is the regression model that is equivalent to the global simulation, and is regression parameter; is a normal stochastic process in which the mean value is 0 and the variance is denoted as . It reflects the randomness of the response and is equivalent to partial divergence.

The covariance matrix of is formulated as follows:where R is correlation matrix; the order of matrix is . ; is the number of sample points; and are the th and the th sample points; is the correlation function between and . In this paper, we utilize the Gaussian correlation function:where is the dimension of the problem; and are the th dimensional components of the th and the th sample points, respectively; is the unknown related parameters of the interpolation model.

In general, can be replaced with a scalar . Thus, formula (3) can be formulated as

Therefore, the estimated value of test point can be given by the following equation:where is the estimate of the global simulation; is sample data response; is column vectors; is the correlation vector between observation point and sample data, which can be formulated as follows:

When is a constant, can be simplified and estimated by the following equation:

The parameter determines the accuracy of the Kriging model, which can be solved by the following optimization problem:where is variance estimation, which can be determined by the following equation:

To optimize parameter , intelligent optimization algorithms are commonly used. In this paper, a modified particle swarm optimization (MPSO) [15] is used to optimize the parameters of Kriging model. The key points of applying MSPO to perform optimization are threefold: () make as encoding in real numbers; () take (8) as the objective function; and () with respect to the constraint condition of , the commonly used penalty function method is applied.

The inertia weight and learning factors in MPSO [15] are updated as follows:where and are the initial value and the final value of inertia weight , respectively; and and and are the initial value and the final value of learning factors and , respectively; is the maximum number of iterations; is the current iteration number.

3.2. Combinations of Neural Network and Kriging Model

The mapping relationship between the characteristic variables and fault types of transformer is very complex, which increases difficulty in improving high accuracy of Kriging model. On the other hand, neural network technology, for example, BP network, is a well-known information processing paradigm with some advantages such as adaptive learning and strong adaptability. The basic principle of BP network can be found in many references such as [4, 5, 16], details of which are not introduced here. In general, the output of BP network can be formulated as follows:where are the outputs of BP network, is transfer function, are network weights, are network thresholds, and are the outputs of the upper layer node.

To improve modeling accuracy, a modified Kriging model (hybrid model) is constructed by combining Kriging model and BP neural network technology, and the overall design of which has been shown in Figure 1. More specifically, the global model of Kriging model is replaced with BP neural network, which is given by (14):

Further, this modified method can be extended using linearity weighted aggregation method, which is formulated by (15):where is the modified global model and and are weighting coefficients.

Thus, the final output of the hybrid model can be given as follows:

Obviously, the hybrid model is of generality. When and , the hybrid model becomes original Kriging model and (16) can be rewritten by (5). When and , the hybrid model can be formulated by (14), where the global model of Kriging model is replaced with BP neural network.

4. Application of Transformer Fault Diagnosis

4.1. Feature Variable and Fault Type

In general, the concentrations of five gases (H2, CH4, C2H6, C2H4, and C2H2) dissolved in transformer oil can be selected as characteristic variables based on DGA data samples. The corresponding fault types of the characteristic variables contain normal, high temperature overheating, medium temperature overheating, low temperature overheating, partial discharge, low energy discharge, and high energy discharge. In this paper, we select some DGA data published in [17, 18]. The distributions and coding of these fault data are shown in Table 1.


Fault typeCoding modeSample dataTest data

Normal1515
High temperature overheating2525
Medium temperature overheating1515
Low temperature overheating99
Partial discharge98
Low energy discharge2016
High energy discharge2023

4.2. Parameter Setting

In this paper, BP network structure is set as three-layer network. The selected sample data have 5 characteristic variables; thus the number of nodes in the input layer of the network is set as 5; the number of nodes in the output layer is set as 1; the number of hidden layer nodes is set as 8 by trial and error. The initial weights and thresholds of the network are randomly initialized, and Log-sigmoid is selected as function transfer function.

Parameters of MPSO are set as follows: , , , , , and population size . Figure 2 shows the MPSO convergence curve of objective function.

4.3. Analysis of Examples

() Table 2 shows the comparisons between the proposed method and other methods. As far as these test examples are concerned, the proposed method can effectively improve the accuracy of transformer fault diagnosis.


Test methodAverage calculation timeAccuracy rate

BP network5.06 s72.07%
SVM6.21 s75.67%
Kriging model2.49 s81.08%
Hybrid method7.84 s91.89%

() Tables 2 and 1 also show that the calculation time of presented method is averagely about 7.84 s for test data including 111 sample points (hardware configuration: CPU i5, RAM 4 G; programming software: Matlab), which demonstrates the efficiency of the presented method.

() Table 3 lists some test results using the presented method (due to limitation of paper length, the complete results are not listed here). The results show that diagnosis accuracy is basically satisfactory.


Serial numberH2CH4C2H6C2H4C2H2Fault type
Actual faultFault analysis

()935843370Middle temperature overheatingMiddle temperature overheating
()139526.8639.6Middle and low temperature overheatingMiddle temperature overheating
()19.6320.7279.2574.70High temperature overheatingHigh temperature overheating
()45779541902.4High temperature overheatingHigh temperature overheating
()2794118.14231.8High energy dischargeHigh energy discharge
()14.673.6810.542.710.2NormalNormal
()345112.2527.551.558.75Low energy dischargeLow energy discharge
()217.5404.951.867.5High energy dischargeHigh energy discharge
()1812622105280Middle and low temperature overheatingLow temperature overheating
()44.317.33.623.310.4High energy dischargeHigh energy discharge
()172.9334.1172.9812.537.7Partial dischargePartial discharge
()12.268.8613.9518.210NormalLow energy discharge
()5678181730Low temperature overheatingLow temperature overheating

5. Conclusions

In this paper, a data-driven fault diagnosis model based on Kriging model and neural network is proposed. The proposed model is based on the Kriging model and integrates neural network technology. Meanwhile, the localized departures of Kriging model are retained.

The presented hybrid model is further used for power transformer fault diagnosis problems based on DGA method. Some numerical computations of transformer fault diagnosis problems are conducted, and the results show the feasibility and efficiency of the proposed method. In addition, the presented modified Kriging model is of some potential application value in other areas such as power system and engineering machinery.

Conflicts of Interest

The authors declare that the mentioned received funding did not lead to any conflicts of interest regarding the publication of this manuscript and there are not any possible conflicts of interest in the manuscript.

Acknowledgments

This study is supported by Program for Liaoning Excellent Talents in University (Grant no. LJQ2014037) and Natural Science Foundation of Liaoning Province of China (Grant no. 20170540589).

References

  1. J. Pleite, C. Gonzalez, J. Vazquez, and A. Lazaro, “Power Transfomer Core Fault Diagnosis Using Frequency Response Analysis,” in Proceedings of the MELECON 2006 - 2006 IEEE Mediterranean Electrotechnical Conference, pp. 1126–1129, Benalmadena, Spain. View at: Publisher Site | Google Scholar
  2. S.-W. Fei and X.-B. Zhang, “Fault diagnosis of power transformer based on support vector machine with genetic algorithm,” Expert Systems with Applications, vol. 36, no. 8, pp. 11352–11357, 2009. View at: Publisher Site | Google Scholar
  3. S. S. M. Ghoneim and I. B. M. Taha, “A new approach of DGA interpretation technique for transformer fault diagnosis,” International Journal of Electrical Power & Energy Systems, vol. 81, pp. 265–274, 2016. View at: Publisher Site | Google Scholar
  4. Y. J. Sun, S. Zhang, C. X. Miao et al., “Improved BP neural network for transformer fault diagnosis,” Journal of China University of Mining & Technology, vol. 17, no. 01, pp. 138–142, 2007. View at: Google Scholar
  5. S. Seifeddine, B. Khmais, and C. Abdelkader, “Power transformer fault diagnosis based on dissolved gas analysis by artificial neural network,” in Proceedings of the 2012 1st International Conference on Renewable Energies and Vehicular Technology, REVET 2012, pp. 230–236, March 2012. View at: Publisher Site | Google Scholar
  6. S. M. Islam, T. Wu, and G. Ledwich, “A novel fuzzy logic approach to transformer fault diagnosis,” IEEE Transactions on Dielectrics and Electrical Insulation, vol. 7, no. 2, pp. 177–186, 2000. View at: Publisher Site | Google Scholar
  7. Y.-C. Huang and H.-C. Sun, “Dissolved gas analysis of mineral oil for power transformer fault diagnosis using fuzzy logic,” IEEE Transactions on Dielectrics and Electrical Insulation, vol. 20, no. 3, pp. 974–981, 2013. View at: Publisher Site | Google Scholar
  8. C. E. Lin, J. M. Ling, and C. L. Huang, “An expert system for transformer fault diagnosis using dissolved gas analysis,” IEEE Transactions on Power Delivery, vol. 8, no. 1, pp. 231–238, 1993. View at: Publisher Site | Google Scholar
  9. Y.-C. Xiao, X.-H. Chen, and H.-J. Zhu, “Application of genetic support vector machine in power transformer fault diagnosis,” Shanghai Jiaotong Daxue Xuebao/Journal of Shanghai Jiaotong University, vol. 41, no. 11, pp. 1878–1886, 2007. View at: Google Scholar
  10. A.-H. Zhou, H. Song, H. Xiao, and X.-H. Zeng, “Power transformer fault diagnosis based on integrated of rough set theory and neural network,” in Proceedings of the 2nd International Conference on Intelligent Systems Design and Engineering Applications, ISDEA 2012, pp. 1463–1465, January 2012. View at: Publisher Site | Google Scholar
  11. S. Jeong, M. Murayama, and K. Yamamoto, “Efficient optimization design method using kriging model,” Journal of Aircraft, vol. 42, no. 2, pp. 413–420, 2005. View at: Publisher Site | Google Scholar
  12. T. W. Simpson, T. M. Mauery, J. J. Korte, and F. Mistree, “Kriging models for global approximation in simulation-based multidisciplinary design optimization,” AIAA Journal, vol. 39, no. 12, pp. 2233–2241, 2001. View at: Publisher Site | Google Scholar
  13. S. Dey, T. Mukhopadhyay, and S. Adhikari, “Stochastic free vibration analyses of composite shallow doubly curved shells - A Kriging model approach,” Composites Part B: Engineering, vol. 70, no. 5, pp. 99–112, 2015. View at: Publisher Site | Google Scholar
  14. Z. Chen, S. Peng, X. Li et al., “An important boundary sampling method for reliability-based design optimization using kriging model,” Structural and Multidisciplinary Optimization, vol. 52, no. 1, pp. 55–70, 2015. View at: Publisher Site | Google Scholar
  15. Q. Liu and C. Wang, “Pipe-assembly approach for aero-engines by modified particle swarm optimization,” Assembly Automation, vol. 30, no. 4, pp. 365–377, 2010. View at: Publisher Site | Google Scholar
  16. H. M. Guo and A. Yang, “Diagnosis of transformer fault based on GA-BP neural network,” Coal Mine Machinery, vol. 36, no. 7, pp. 318–320, 2015. View at: Google Scholar
  17. Y. B. Tang, Data-Driven Fault Diagnosis and Prediction for Large-Scale Power Transformer, Central South University, Changsha, China, 2013 (Chinese).
  18. W. Gao, Study on Fault Diagnosis for Power Transformer Based on Support Vector Machine of Artificial Immune Algorithm, Taiyuan University of Technology, Taiyuan, China, 2012 (Chinese).

Copyright © 2017 Yu Ding and Qiang Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Download other formatsMore
 Order printed copiesOrder
Views694
Downloads290
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.