http://orcid.org/0000-0002-5061-1809
Figures
Abstract
Early detection of power transformer fault is important because it can reduce the maintenance cost of the transformer and it can ensure continuous electricity supply in power systems. Dissolved Gas Analysis (DGA) technique is commonly used to identify oil-filled power transformer fault type but utilisation of artificial intelligence method with optimisation methods has shown convincing results. In this work, a hybrid support vector machine (SVM) with modified evolutionary particle swarm optimisation (EPSO) algorithm was proposed to determine the transformer fault type. The superiority of the modified PSO technique with SVM was evaluated by comparing the results with the actual fault diagnosis, unoptimised SVM and previous reported works. Data reduction was also applied using stepwise regression prior to the training process of SVM to reduce the training time. It was found that the proposed hybrid SVM-Modified EPSO (MEPSO)-Time Varying Acceleration Coefficient (TVAC) technique results in the highest correct identification percentage of faults in a power transformer compared to other PSO algorithms. Thus, the proposed technique can be one of the potential solutions to identify the transformer fault type based on DGA data on site.
Citation: Illias HA, Zhao Liang W (2018) Identification of transformer fault based on dissolved gas analysis using hybrid support vector machine-modified evolutionary particle swarm optimisation. PLoS ONE 13(1): e0191366. https://doi.org/10.1371/journal.pone.0191366
Editor: Xiangtao Li, Northeast Normal University, CHINA
Received: October 13, 2017; Accepted: January 3, 2018; Published: January 25, 2018
Copyright: © 2018 Illias, Zhao Liang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: This work was supported by the Ministry of Higher Education Malaysia H-16001-D00048) to HAI and University of Malaya PG236-2016A to HAI. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Power transformer is a vital component in power system networks. Failure of power transformers can interrupt power system network operation. Thus, any fault in a transformer should be detected early. Electrical fault in a transformer occurs at high voltage and will eventually cause physical damage to the conductor and insulator of the transformer, leading to the reduction of power quality, blackouts and fire, causing a substantial propriety loss. Damage in a transformer is difficult to be repaired and the transformer replacement is very costly and requires a lot of resources. Therefore, early detection of transformer fault is imperative in the operation and maintenance process of power system networks. This is to ensure correct transformer oil maintenance, cost reduction and good quality of electricity supply to power systems.
Exposure to electrical and thermal stress causes molecules of hydrocarbon of the mineral oil decomposition and hydrogen and carbon are formed. Under high voltage, these gases can react with each other to form various gases such as ethylene (C2H4), methane (CH4), acetylene (C2H2), hydrogen (H2), and ethane (C2H6). Previous studies have revealed that as temperature increases, gases are generated in the order of H2, CH4, C2H6, C2H4 and C2H2 [1]. Overheating and corona typically lead to the insulation material decomposition [2]. Decomposition of insulation materials such as paper and cellulose in a transformer can be analysed according to the amount of carbon dioxide (CO2) and carbon monoxide (CO) present in the transformer oil. This is due to depolymerisation causes breaking of glucose ring chains in the paper. CO2, CO and H2O are emitted due to the presence of oxygen atoms in the cellulose materials.
The existing methods of detecting the incipient fault in transformer oil are IEC ratio method, Rogers ratio method, key gas method and Doernenburg ratio method. However, gas ratio usage is based on experience through correlating amount of gas concentration and the type of fault. Each of this method has disadvantages, rigorous borderline and hidden relationship [3]. For example, key gas method requires a gas of significant amount to exist in the oil sample and is unable to give a conclusion in some cases. Thus, improvement on the accuracy of the existing method to identify the fault type in transformer oil is important. Utilisation of artificial intelligence and optimisation methods has shown convincing results in power transformer modelling [4, 5]. Artificial intelligence has also been widely applied in transformer fault diagnosis and in power systems [6–9].
In An-xin Zhao’s work [10], four combustible gases and six combination of gas ratios, which correlate to six fault types were considered. The accuracy rates were calculated for 117 cases by different methods. From this work, the best methods of thermal and electrical fault diagnosis are found to be Duval Triangle and KimSW methods [11]. Each method achieves accuracy higher than 55%. However, the accuracy according to the total number of cases shows various results. Since there are many cases undistinguishable, the accuracy reduces less than 55% for Roger and Doernenburg ratio methods.
Based on the work in [12], rules of IEC Code and Roger’s ratio were modified to enhance the accuracy of the current version based on 320 samples with its actual fault type. The samples were categorised into six fault types, which are high thermal fault (Tl), low thermal fault, medium thermal fault (T2), low energy discharge (Dl), high energy discharge (D2) and partial discharge (PD). The overall accuracy of the modified Roger’s four ratios increases from 45.62% to 75.62%. For IEC Code method modification, significant variation was observed after modification for all transformer fault types, where the overall accuracy increases from 62.81% to 79.38%. Hence, the new version of Roger’s four ratios and IEC Standard Code methods have the ability to identify the transformer fault with higher accuracy than the unmodified version.
In [13], genetic algorithm (GA) and support vector machine (SVMG) were employed on power transformer fault identification, where GA was applied to optimise SVM parameters. SVM classifiers were employed to identify the no-fault state, high-energy discharge, low-energy discharge, high-temperature overheating, low- and mid-temperature overheating. From the results obtained, it was found that SVMG achieves better diagnosis results compared to the IEC method, back propagation neural network and SVM alone. Other works have also shown that optimisation method can improve the performance of the system significantly [14, 15].
PSO and SVM were employed to predict dissolved gas contents in power transformers [16]. PSO was used to optimise the SVM parameters to avoid under or over-fitting of the SVM model. It was found that the proposed method achieves better forecasting accuracy than grey model and artificial neural network (ANN) under small number of samples. In [17], SVM was employed in transformer fault diagnosis on DGA data. One-against-all, one-against-one and binary decision tree were applied. From the results, the highest accuracy was achieved by SVM one-against-one method, which is 92%.
Identification of transformer fault was also proposed using different PSO and ANN techniques [18]. The PSO optimisation methods employed were traditional PSO, evolutionary PSO and iteration PSO. From the fault identification algorithm, ANN-EPSO results in the highest correct identification percentage of transformer fault than the previously reported works and existing DGA methods. In [19], ANN was employed to classify transformer condition based 3 combustible gas ratios. Three ratios of combustible gases were applied as the input. From this method, the validation and test set errors have the same characteristics and no overfitting.
Although SVM has been applied widely in classification of gas ratio, limited amount of work has been reported on transformer fault identification using SVM combined with various optimisation techniques. It is believed that there is room for improvement in combining SVM with various optimisation techniques in identification of power transformer faults. Thus, this work proposes a hybrid SVM with different particle swarm optimisation (PSO) techniques to identify the transformer faults. Feature selection using stepwise regression was also applied prior to the SVM training for data reduction. This was done to enable only meaningful sets of data are used in the training of SVM. The effectiveness of each method was evaluated by comparing the results with the actual fault and existing methods, unoptimised SVM and previous works using ANN. A better result of the proposed method than the previously reported work will indicate that this method can be an alternative solution for transformer fault diagnosis on site.
This work is organised as follows. Section 1 is the introduction of this work, which includes problem statement and review of published related works. Section 2 describes the support vector machine and feature selection method used in this work. Section 3 explains different types of particle swarm optimisation (PSO) techniques. In Section 4, all findings and analysis are presented. Finally, Section 5 is the conclusions, which presents a summary of the key findings.
Intelligent classifier and feature selection
Support vector machine (SVM)
SVM was introduced by Vapnik and Chervonenkis, which was derived from statistical learning theory [20–22]. SVM is useful in dealing with non-linear separable cases [23]. SVM is a powerful technique used for data classification and data prediction [24]. The training of SVM was performed where the classified vector dimension has no distinct influence on the SVM performance. Thus, SVM has the capability of handling a very large feature space, giving SVM higher efficiency compared to other classification techniques especially when dealing with large amount of classification data. Since the past, SVM has been employed widely to solve many practical problems in various fields [25–28]. The flexibility of SVM makes it beneficial in transformer fault identification due to the number of features that forms the fault diagnosis basis is not limited.
In this work, radial basis function (RBF) kernel was employed. Two parameters in SVM were optimised by different PSO algorithms in this work, σ and c. σ is a RBF kernel parameter while c represents the misclassification parameter and determines the trade-off between the size and margin of slack variables [29]. A large c means a higher penalty for non-separable points. A small c is an indication that an under-fit process is occurring. Both c and σ are important as the combination of these two parameters will influence the percentage of correct fault identification by SVM.
Stepwise regression
Feature selection enables the selection of significant data for training and testing of transformer fault type using SVM. This technique prevents the use of a large amount of redundant information and insignificant features in the dataset, which often leads to greater complexity, longer run time and lower accuracy [30]. In this work, stepwise regression technique was employed to simplify the model to be interpreted by the SVM and to reduce the chance of overfitting, giving a shorter run time while maintaining high percentage of correct fault identification.
Stepwise regression is a regression-based algorithm with automatic filtering features [31]. It is utilised to select the important features of the training and testing dataset [32]. Hence, the most significant statistical features are selected by the algorithm. Stepwise regression analyses the significance of the model in term of statistical using partial F-statistic. Enabling users to determine the type of gases has the greatest influence on the fault type identification.
In this work, the forward selection characteristic of stepwise regression was utilised. Each term was removed from or added to the input feature vector with reference to the p-value of exiting or entering input data. Null-hypothesis test probability is represented by p-value with α tolerance for a term addition and β tolerance for a term removal. In this work, each input data represents a type of gas obtained from DGA. The input data were selected based on the p-value resulted from stepwise regression.
Input and output data for SVM classifier
Different PSO techniques were employed to optimise the SVM to identify transformer fault type using DGA data obtained from an electrical utility in Malaysia. The parameters of each method which give the highest percentage of correct fault identification and yield the shortest test time were selected for the optimization objective. Feature selection of training and testing data were carried out using stepwise regression to reduce the run time while maintaining a high percentage of correct fault identification.
Numbers of run were tested to examine the performance of each method. The results were compared between different PSO methods with the existing DGA method, which is IEC 60599 method. 400 data from the actual site diagnosis were used in this work. The raw data were classified into 64 cases of low and high intensity discharge each, 72 cases of thermal fault and 200 cases without fault. Table 1 shows the input (dissolved gas) and output data (fault type) used for SVM training and testing. Seventy percent of the overall data was used to train the SVM while for testing purpose, the remaining data were used.
Particle swarm optimisation techniques
Conventional PSO
PSO is an evolutionary computational algorithm to solve non-linear optimisation problems [30, 33–36]. The advantage of PSO is the PSO parameters can be empirically adjusted to optimise its performance for the best results. Fig 1 shows a PSO algorithm flowchart to optimise the performance of SVM. First, swarms were initialised randomly with velocity and initial position of every particle. The swarms are the SVM parameters, c and σ. Then, the fitness for every particle, which is the accuracy of SVM, was calculated with the initial position and velocity. After that, the fitness of every each particle was compared with its personal best pbidk. When the new fitness is better than pbidk, it is set as pbidk and Xidk or the particle’s current position. The overall best fitness is taken as the global best gbdk. Next, the updated position and velocity of every particle were calculated using
(1)
(2)
where Xidk+1 is the new position of particle i, Xidk is the previous position of particle i at k-th iteration, Vidk+1 is the new particle i velocity in d dimension, Vidk is particle i velocity at iteration k, r2 and r1 are randomly generated number between 0 and 1 and c2 and c1 are the acceleration factors. In this work, the domains of Xi are two SVM parameters, c and σ. The inertia weight, w is determined using
(3)
where kmax is the final iteration, wmin is the minimum weight and wmax is the maximum weight. If any particle moves out of the bounds, its position is set to the upper or lower boundary. The algorithm was halted when the final number of iteration was reached.
Iteration particle swarm optimisation (IPSO)
IPSO incorporates the iteration best, Ib in the existing PSO algorithm. Ib is the optimum value of fitness function by a particle in an iteration. IPSO improves the quality of the solutions and efficiency of the existing PSO [37]. The new velocity equation for each particle in IPSO is given by
(4)
where Ibdk is the best fitness obtained by any particle at k-th iteration and c3 is the stochastic acceleration weight to attract every particle towards Ibdk. c3 is calculated using
(5)
Evolutionary particle swarm optimisation (EPSO)
EPSO is a meta-heuristic algorithm that combines the concept of PSO and Evolution Strategies (ES). This algorithm was introduced by Miranda [38]. EPSO introduces a mutation operation into PSO, causing each particle to have its weight mutated. EPSO provides a procedure of explicit selection with self-adapting properties in its parameters. This allows the solution with superior characteristic to be passed down from a generation to the next generation. Hence, the equation of the updated velocity is modified to
(6)
where wi0*, wi1* and wi2* are the mutated weight and gbid* is the mutated global best position. gbid*, wi0*, wi1* and wi2* are calculated using
(7)
(8)
where j = 0, 1 and 2. N is a random number between 0 and 1 with Gaussian distribution, variance equals to 1 and zero mean. τ is the learning dispersion parameter and τ’ is the noise dispersion parameter. τ and τ’ are the learning parameters introduced in EPSO algorithm to facilitate the search for the optimum values for the desired parameters.
Modified PSO (MPSO)-Time varying acceleration coefficient (TVAC)
In MPSO-TVAC, the main function of this technique is to avoid search form converging prematurely and to enhance the convergence rate to the optimum global solution at the later search stage [39–41]. A new term rb is added into the velocity equation of PSO to improve the PSO robustness by providing additional information for every particle, where rb is selected from other particles’ pb randomly. Hence, the premature convergence can be avoided and particles’ movement is diversified. The new updated velocity for MPSO-TVAC is given by
(9)
where
(10)
(11)
(12)
c3 is the TVAC for rbest, c2f and c2i are the final and initial values of the social coefficient respectively, c2 is the social coefficient and c1 is the cognitive coefficient. c1f and c1i are the final and initial cognitive coefficient values respectively.
Results and discussion
Optimisation of SVM without stepwise regression
Table 2 shows the results obtained using different PSO algorithms from SVM that have been performed in this work. For each algorithm, different combinations of PSO parameters were tested, which include varying c1, c2, wmax and wmin to obtain the best accuracy results of SVM. Each combination of c1 and c2 were varied from 0.1 to 2.0 with a step size of 0.1. Each test was repeated for 100 times to obtain the average result. The population size was set to 50. From Table 2, it can be seen that each algorithm yields different parameters, average SVM accuracy and run time, number of convergence at first iteration and best c and σ. The accuracy of the SVM was calculated based on the percentage of correct fault type identification.
From the results obtained, the proposed SVM-MEPSO-TVAC technique yields the highest accuracy with an average accuracy of 99.50% and with an average run time of 90.8578s. It is followed by SVM-MPSO-TVAC with 99.10% accuracy, SVM-EPSO with 99.01% accuracy, SVM-IPSO with 99.00% accuracy and finally SVM-PSO with 98.88% accuracy. From 100 runs, the lowest number of run which converges at first iteration was achieved by SVM-PSO, which is 27 or 27% while the highest number of run which converges at first iteration is from SVM-MEPSO-TVAC, with 93 runs or 93%. When the percentage of convergence at first iteration is higher, this indicates that the algorithm can be run with less maximum iteration, which will reduce its run time. The shortest average run time is SVM-PSO while the longest average run time is SVM-MEPSO-TVAC.
The main advantages of PSO are simple, computation efficient and easy to be implemented. This is why the average run time is the fastest, as shown in Table 2. In PSO, the search towards the optimal solution of the parameter is guided by 2 stochastic acceleration components, the social and cognitive components. Proper setting of these components is vital to yield accurate and efficient search towards the optimum solution. If the cognitive component is higher than the social component, of individuals will be wandering excessively through the searching space. However, if the social component is higher than the cognitive component, particles will rush toward a local optimum prematurely. Hence, improvement on PSO algorithm, such as allowing the automated search of the stochastic acceleration term weighting and introduction of mutation feature has shown enhancement on the average accuracy of the SVM.
Optimisation of SVM with stepwise regression
Stepwise regression was applied on the input and output data to select gases obtained from DGA with the most dominant characteristic in transformer fault identification. The results obtained after stepwise regression are shown in Table 3. It can be seen that the data used for SVM training and testing displays similar characteristics. The p-value tests the null hypothesis, which the coefficient equals to zero. A predictor with low p-value as displayed by CO with a value of 1.0214×10−36 is a meaningful addition to the model of the selected features. A smaller p-value possessed by the gas reflects that the DGA data for that particular gas has a stronger association with the transformer fault type. In this work, stepwise regression shows that the type of gas in the order of decreasing significance towards the identification of transformer fault type for training data and testing data is CO, H2, C2H6, CH4, C2H2 and finally C2H4.
Standard error is important to access the strength of the relationship between the model made up of selected features and the response variable. Also, standard error accesses the validity of the p-values as it represents the distance that the observed values fall from the regression line in mathematical form. A smaller standard error equates a better response as the model obtained gives observations of the response variable, which is the fault type closer to the fitness line. From Table 3, it is observed that there is a small value of standard error with values less than 10−4 for all types of gases in training and testing data. With p-value and standard error showing small values, it can be deduced that the selected features have a strong relationship with the response variables, where smaller values display a stronger relationship.
The regression coefficient in Table 3 shows the change of mean in the response parameter for a unit of change in the specific predictor parameter while the other predictors are kept constant. For example, in training data, the coefficient for H2 is 0.1692×10−3. This indicates that for every unit addition in the concentration of H2, it can be expected that the overall result of the response variable increases by 0.1692×10−3.
Based on the stepwise regression results as shown in Table 3, for 3 gas input data, H2, CO and C2H6 were used as the input data for testing and training of SVM. These 3 gases are ranked at the three lowest p-values. For 4 gas input, H2, CO, CH4 and C2H6 were taken as the input gas while for 5 gas input, H2, CO, CH4, C2H2 and C2H6 were taken as the input gas. Table 4 shows the type of gases for training and testing data according to stepwise regression for different number of gas input. By decreasing the number of input data applied to SVM, the size of the kernel matrix and complexity of the computing can be reduced, hence reducing the test time.
Table 5 shows results using MEPSO-TVAC and MPSO-TVAC algorithms on SVM by using different number of gas input for 100 runs. These two algorithms were selected to be tested due to their average SVM accuracy is two highest values according to Table 2. From Table 5, when 3 gas input was used, the accuracy for SVM-MPSO-TVAC and SVM-MEPSO-TVAC is 99.02% and 99.45% each with average run time of 53.1552s and 55.0159s respectively. The number of run which converges at first iteration is 97 and 100 out of 99 for SVM-MPSO-TVAC and SVM-MEPSO-TVAC respectively. Comparing with 6 gas input data, the average run time for SVM-MPSO-TVAC and SVM-MEPSO-TVAC is 88.5753s and 90.8578s respectively but the average SVM accuracy is 99.10% and 99.50% for SVM-MPSO-TVAC and SVM-MEPSO-TVAC respectively.
Referring to Table 5, when the number of gas input used is higher, the percentage of correct fault detection (average SVM accuracy) improves with a small percentage only. However, it is obvious that the average run time increases significantly when the number of gas input used is higher due to more data are used. The number of convergence at first iteration decreases slightly when more gas input is used because the number of particles in PSO algorithm is higher. Therefore, this shows that using data reduction by stepwise regression for SVM training and testing data, the run time can be reduced significantly without affecting the accuracy results of the SVM.
From Table 5, comparison between SVM-MPSO-TVAC and SVM-MEPSO-TVAC shows that SVM-MEPSO-TVAC has higher number of convergence at first iteration and average SVM accuracy than SVM-MPSO-TVAC for different number of gas input data. However, the average run time slightly longer for SVM-MEPSO-TVAC compared to SVM-MPSO-TVAC when different number of gas input was used. Mutation in the particle weight is a critical improvement in SVM-MEPSO-TVAC over SVM-MPSO-TVAC.
Comparison with the previous works
The proposed hybrid SVM with various PSO techniques employed in this work were compared with the existing works in literature on the transformer fault identification according to dissolved gas analysis data. Table 6 shows the comparison between the proposed methods and previously developed works. It is observed that the proposed SVM-MEPSO-TVAC method results in the highest accuracy with 99.50% compared to other reported existing works.
Referring to Table 6, the IEC method yields only 75.00% accuracy. IEC method is based on the existing dissolved gas analysis (DGA) technique, which utilises three different ratios of the gas. These include CH4/H2, C2H2/C2H4 and C2H4/C2H6. This method does not depend on specific gas concentrations to exist in the transformer but it is used only when the normal limits of the individual gases have been exceeded. Hence, it is not suitable to be used in all condition of gas concentration. This is why the accuracy obtained using the IEC method in this work is low.
The accuracy of the unoptimised SVM, proposed SVM-PSO, SVM-IPSO, SVM-EPSO and SVM-MPSO-TVAC is 97.00%, 98.88%, 99.00%, 99.01% and 99.10% respectively. These are the results obtained from this work. Comparing these results with the IEC method, it shows a significant improvement in the percentage of correct prediction of the fault type, which is over 20%. Referring to results reported in [18], which applied artificial neural network (ANN) as the classifier, the accuracy results as in Table 6 show that the proposed methods using SVM is generally higher than using ANN. The accuracy result using ANN-PSO, ANN-IPSO and ANN-EPSO is 96.00%, 97.00% and 98.00% respectively.
SVM is a supervised learning machine, which uses mainly the kernel method. SVM locates the decision function from a set of labelled training data. The decision function is made by hyperplane, which segregates the training data into two groups. The solution of the classification learning problem is obtained in terms of a subset of training data, also known as support vectors. An optimal hyperplane will be selected from all the separating hyperplanes, whereby the margin of separation between itself and any training point is of maximum value. This is why SVM yields better results than ANN and the IEC method. Therefore, referring to the results shown in Table 6, it has been demonstrated that the hybrid SVM with MEPSO-TVAC algorithm proposed in this work can be an alternative solution for diagnosis of transformer fault type based on DGA in industrial practice.
Conclusions
In this work, hybrid support vector machine (SVM) with modified particle swarm optimisation (PSO) algorithms has been successfully proposed in optimising the SVM performance. In the proposed method, SVM was successfully employed to determine the transformer fault type and different algorithms of PSO were employed to optimise the SVM parameters. From results comparison, the proposed hybrid SVM with modified EPSO-Time Varying Acceleration Coefficient (TVAC) yields the best performance in terms of correct identification percentage of transformer fault compared to the current DGA method, unoptimised SVM and the reported existing works. After feature selection using stepwise regression was applied, it was found that there is a significant reduction in the training and testing time but the accuracy of SVM-MEPSO-TVAC is still high when less number of gas input was used. The proposed SVM-MEPSO-TVAC also achieves highest number of convergence at first iteration than other SVM-PSO algorithms. Hence, the proposed SVM-MEPSO-TVAC method combined with feature selection using stepwise regression can be proposed as an alternative solution for power transformer diagnosis.
Acknowledgments
The authors thank the Ministry of Higher Education Malaysia and University of Malaya, Malaysia for supporting this work through HIR research grant (grant no.: H-16001-D00048) and PPP (grant no: PG236-2016A).
References
- 1.
Wang Z. Artificial Intelligence Applications in the Diagnosis of Power Transformer Incipient Faults: Virginia Polytechnic Institute and State University; 2000.
- 2. Wei C, Tang W, Wu Q. Dissolved gas analysis method based on novel feature prioritisation and support vector machine. IET Electric Power Applications. 2014;8(8):320–8.
- 3. Zheng HB, Liao RJ, Grzybowski S, Yang LJ. Fault diagnosis of power transformers using multi-class least square support vector machines classifiers with particle swarm optimisation. IET Electric Power Applications. 2011;5(9):691–6.
- 4. Souza LM, Lemos AP, Caminhas WM, Boaventura WC. Thermal modeling of power transformers using evolving fuzzy systems. Engineering Applications of Artificial Intelligence. 2012;25(5):980–8.
- 5. Thilagar SH, Rao GS. Parameter estimation of three-winding transformers using genetic algorithm. Engineering Applications of Artificial Intelligence. 2002;15(5):429–37.
- 6. Handreck K, Dabke KP, Conlon MF. An expert system for transformer impulse test diagnosis. Engineering Applications of Artificial Intelligence. 1991;4(1):11–21.
- 7. Ma D, Liang Y, Zhao X, Guan R, Shi X. Multi-BP expert system for fault diagnosis of powersystem. Engineering Applications of Artificial Intelligence. 2013;26(3):937–44.
- 8. Srinivasan D, Cheu RL, Poh YP, Ng AKC. Automated fault detection in power distribution networks using a hybrid fuzzy—genetic algorithm approach. Engineering Applications of Artificial Intelligence. 2000;13(4):407–18.
- 9. Illias HA, Mou KJ, Bakar AHA. Estimation of Transformer Parameters from Nameplate Data by Imperialist Competitive and Gravitational Search Algorithms. Swarm and Evolutionary Computation. 2017;36:18–26.
- 10.
An-xin Z, Xiao-jun T, Zhong-hua Z, Jun-hua L, editors. The DGA interpretation method using relative content of characteristic gases and gas-ratio combinations for fault diagnosis of oil-immersed power transformers. International Symposium on Electrical Insulating Materials; 2014 1–5 June 2014.
- 11. Kim S-w, Kim S-j, Seo H-d, Jung J-r, Yang H-j, Duval M. New methods of DGA diagnosis using IEC TC 10 and related databases Part 1: application of gas-ratio combinations. IEEE Transactions on Dielectrics and Electrical Insulation. 2013;20(2):685–90.
- 12.
Taha IBM, Ghoneim SSM, Zaini HG, editors. Improvement of Rogers four ratios and IEC Code methods for transformer fault diagnosis based on Dissolved Gas Analysis. North American Power Symposium (NAPS); 2015 4–6 Oct. 2015.
- 13. Fei S-w, Zhang X-b. Fault diagnosis of power transformer based on support vector machine with genetic algorithm. Expert Systems with Applications. 2009;36(8):11352–7.
- 14.
Zhao X, Liu D, Ye D, editors. sEMG based movement quantitative estimation of joins using SVM method with gravitational search algorithm. The 27th Chinese Control and Decision Conference; 2015 23–25 May 2015.
- 15. Ing K, Mokhlis H, Illias H, Jamian J, Aman M. Optimal Daily Configuration of a Distribution Network Based on Photovoltaic Generation and System Loading Using Imperialist Competitive Algorithm and Selection Approach. Applied Mechanics and Materials. 2015;785:541–5.
- 16. Fei S-w, Wang M-J, Miao Y-b, Tu J, Liu C-l. Particle swarm optimization-based support vector machine for forecasting dissolved gases content in power transformer oil. Energy Conversion and Management. 2009;50(6):1604–9.
- 17.
Mehta AK, Sharma RN, Chauhan S, Saho S, editors. Transformer diagnostics under dissolved gas analysis using Support Vector Machine. International Conference on Power, Energy and Control; 2013 6–8 Feb. 2013.
- 18. Illias HA, Chai XR, Abu Bakar AH, Mokhlis H. Transformer Incipient Fault Prediction Using Combined Artificial Neural Network and Various Particle Swarm Optimisation Techniques. PLoS ONE. 2015;10(6):e0129363. pmid:26103634
- 19.
Zakaria F, Johari D, Musirin I, editors. Artificial neural network (ANN) application in dissolved gas analysis (DGA) methods for the detection of incipient faults in oil-filled power transformer. IEEE International Conference on Control System, Computing and Engineering; 2012 23–25 Nov. 2012.
- 20. Lo SL, Chiong R, Cornforth D. Using Support Vector Machine Ensembles for Target Audience Classification on Twitter. PLOS ONE. 2015;10(4):e0122855. pmid:25874768
- 21. Anaissi A, Goyal M, Catchpoole DR, Braytee A, Kennedy PJ. Ensemble Feature Learning of Genomic Data Using Support Vector Machine. PLOS ONE. 2016;11(6):e0157330. pmid:27304923
- 22. Van Belle V, Van Calster B, Van Huffel S, Suykens JAK, Lisboa P. Explaining Support Vector Machines: A Color Based Nomogram. PLOS ONE. 2016;11(10):e0164568. pmid:27723811
- 23. Cortes C, Vapnik V.. Support-Vector Networks. Machine Learning. 1995;20(3):273–97.
- 24. Ding S, Chen L. Intelligent Optimization Methods for High-Dimensional Data Classification for Support Vector Machines. Intelligent Information Management. 2010;2(6):354–64.
- 25. Bacha K, Souahlia S, Gossa M. Power transformer fault diagnosis based on dissolved gas analysis by support vector machine. Electric Power Systems Research. 2012;83(1):73–9.
- 26. Farquad MAH, Ravi V, Raju SB. Support vector regression based hybrid rule extraction methods for forecasting. Expert Systems with Applications. 2010;37(8):5577–89.
- 27. Liao RJ, Bian JP, Yang LJ, Grzybowski S, Wang YY, Li J. Forecasting dissolved gases content in power transformer oil based on weakening buffer operator and least square support vector machine-Markov. IET Generation, Transmission & Distribution. 2012;6(2):142–51.
- 28. Shah AM, Bhalja BR. Discrimination Between Internal Faults and Other Disturbances in Transformer Using the Support Vector Machine-Based Protection Scheme. IEEE Transactions on Power Delivery. 2013;28(3):1508–15.
- 29. Shintemirov A, Tang W, Wu QH. Power Transformer Fault Classification Based on Dissolved Gas Analysis by Implementing Bootstrap and Genetic Programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews). 2009;39(1):69–79.
- 30.
Kennedy J, Eberhart R, editors. Particle swarm optimization. IEEE International Conference on Neural Networks; 1995 Nov/Dec 1995.
- 31.
Wesolowsky GO. Multiple regression and analysis of variance: an introduction for computer users in management and economics. New York: Wiley; 1976.
- 32. Ghunem RA, Assaleh K, El-hag AH. Artificial neural networks with stepwise regression for predicting transformer oil furan content. IEEE Transactions on Dielectrics and Electrical Insulation. 2012;19(2):414–20.
- 33. Dreidy M, Mokhlis H, Mekhilef S. Application of Meta-Heuristic Techniques for Optimal Load Shedding in Islanded Distribution Network with High Penetration of Solar PV Generation. Energies. 2017;10(2):1–24.
- 34. Li D, Xu L, Li X. Full-waveform LiDAR echo decomposition based on wavelet decomposition and particle swarm optimization. Measurement Science and Technology. 2017;28(4).
- 35. Guo G, Hackney D, Pankow M, Peters K. Interrogation of a spectral profile division multiplexed FBG sensor network using a modified particle swarm optimization method. Measurement Science and Technology. 2017;28(5).
- 36. Gholami A, Honarvar F, Moghaddam HA. Modeling the ultrasonic testing echoes by a combination of particle swarm optimization and Levenberg—Marquardt algorithms. Measurement Science and Technology. 2017;28(6).
- 37. Lee TY. Operating Schedule of Battery Energy Storage System in a Time-of-Use Rate Industrial User With Wind Turbine Generators: A Multipass Iteration Particle Swarm Optimization Approach. IEEE Transactions on Energy Conversion. 2007;22(3):774–82.
- 38.
Miranda V, Fonseca N, editors. EPSO—best-of-two-worlds meta-heuristic applied to power system problems. Congress on Evolutionary Computation; 2002 2002.
- 39. Ratnaweera A, Halgamuge SK, Watson HC. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation. 2004;8(3):240–55.
- 40. Abdullah MN, Bakar AHA, Rahim NA, Mokhlis H. Modified particle swarm optimization for economic-emission load dispatch of power system operation. Turkish Journal of Electrical Engineering & Computer Sciences. 2015;23(1):2304–18.
- 41. Jamian JJ, Mokhlis H, Mustafa MW, Abdullah MN, Baharuddin MA. Comparative Learning Global Particle Swarm Optimization for Optimal Distributed Generations Output. Turkish Journal of Electrical Engineering & Computer Sciences. 2014;22(5):1323–37.
- 42. Hong-Tzer Y, Yann-Chang H. Intelligent decision support for diagnosis of incipient transformer faults using self-organizing polynomial networks. IEEE Transactions on Power Systems. 1998;13:946–52.
- 43. Huang YC. Fault identification of power transformers using genetic-based wavelet networks. IEE Proceedings-Science, Measurement and Technology. 2003;150:25–9.
- 44.
Mehta AK, Sharma RN, Chauhan S, Saho S. Transformer diagnostics under dissolved gas analysis using Support Vector Machine. International Conference on Power, Energy and Control. 2013:181–6.
- 45. Shintemirov A, Tang W, Wu QH. Power Transformer Fault Classification Based on Dissolved Gas Analysis by Implementing Bootstrap and Genetic Programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews. 2009;39:69–79.
- 46.
Setiawan NA, Sarjiya, Adhiarga Z. Power transformer incipient faults diagnosis using Dissolved Gas Analysis and Rough Set. International Conference on Condition Monitoring and Diagnosis. 2012:950–3.
- 47.
Malabanan DR, Nerves AC. Power transformer condition assessment using an immune neural network approach to Dissolved Gas Analysis. IEEE Region 10 Conference. 2014:1–6.
- 48. Hammestrom P. Neural networks at work. IEEE Spectrum. 1993.
- 49. Zhenyuan W, Yilu L, Griffin PJ. A combined ANN and expert system tool for transformer fault diagnosis. IEEE Power Engineering Society Winter Meeting. 2000;2:1261–9.