Wind Turbine Gearbox Anomaly Detection Based on Adaptive Threshold and Twin Support Vector Machines

abstractUniversum, a third class not belonging to either class of the classification problem, allows to incorporate the prior knowledge into the learning process. A lot of previous work have demonstrated that the Universum is helpful to the supervised and semi-supervised classification. Moreover, Universum has already been introduced into the support vector machine (SVM) and twin support vector machine (TSVM) to enhance the generalisation performance. To further increase the generalisation performance, we propose a least squares TSVM with Universum data (-TSVM) in this paper. Our -TSVM possesses the following advantages: first, it exploits Universum data to improve generalisation performance. Besides, it implements the structural risk minimisation principle by adding a regularisation to the objective function. Finally, it costs less computing time by solving two small-sized systems of linear equations instead of a single larger-sized quadratic programming problem. To verify the validity of our proposed algorithm, we conduct various experiments around the size of labelled samples and the number of Universum data on data-sets including seven benchmark data-sets, Toy data, MNIST and Face images. Empirical experiments indicate that Universum contributes to making prediction accuracy improved even stable. Especially when fewer labelled samples given, -TSVM is far superior to the improved LS-TSVM (ILS-TSVM), and slightly superior to the -TSVM.

Weighted Twin Support Vector Machines with Local Information and its application

KNN weighted reduced universum twin SVM for class imbalance learning

Twin support vector machine (TWSVM) and twin support vector regression (TSVR) are newly emerging efficient machine learning techniques which offer promising solutions for classification and regression challenges respectively. TWSVM is based upon the idea to identify two nonparallel hyperplanes which classify the data points to their respective classes. It requires to solve two small sized quadratic programming problems (QPPs) in lieu of solving single large size QPP in support vector machine (SVM) while TSVR is formulated on the lines of TWSVM and requires to solve two SVM kind problems. Although there has been good research progress on these techniques; there is limited literature on the comparison of different variants of TSVR. Thus, this review presents a rigorous analysis of recent research in TWSVM and TSVR simultaneously mentioning their limitations and advantages. To begin with, we first introduce the basic theory of support vector machine, TWSVM and then focus on the various improvements and applications of TWSVM, and then we introduce TSVR and its various enhancements. Finally, we suggest future research and development prospects.

Over the past decades, 1-norm techniques based on algorithms are widely used to suppress input features. Quite different from traditional 1-norm support vector machine (SVM), direct 1-norm optimization based on the primal problem of nonparallel plane classifiers like generalized proximal support vector machine, twin support vector machine (TWSVM) and least squares twin support vector machine (LSTSVM) are not capable of generating very sparse solutions that are vital for classification and can make them easier to store and faster to compute. To address the issue, in this paper, we develop a feature selection method for LSTSVM, called a feature selection method for nonparallel plane support vector machine classification (FLSTSVM), which is specially designed for strong feature suppression. We incorporate a Tikhonov regularization term to the objective of LSTSVM, and then minimize its 1-norm measure. Solution of FLSTSVM can follow directly from solving two smaller quadratic programming problems (QPPs) arising from two primal QPPs as opposed to two dual ones in TWSVM. FLSTSVM is capable of generating very sparse solutions. This means that FLSTSVM can reduce input features, for the linear case. When a nonlinear classifier is used, few kernel functions determine the classifier. In addition to having strong feature suppression, the edge of our method still lies in its faster computing time compared to that of TWSVM, Newton Method for Linear Programming SVM (NLPSVM) and LPNewton. Lastly, this algorithm is compared on public data sets, as well as an Exclusive Or (XOR) example.

Classical support vector machine (SVM) and its twin variant twin support vector machine (TWSVM) utilize the Hinge loss that shows linear behaviour, whereas the least squares version of SVM (LSSVM) and twin least squares support vector machine (LSTSVM) uses L2-norm of error which shows quadratic growth. The robust Huber loss function is considered as the generalization of Hinge loss and L2-norm loss that behaves like the quadratic L2-norm loss for closer error points and the linear Hinge loss after a specified distance. Three functional iterative approaches based on generalized Huber loss function are proposed in this paper to solve support vector classification problems of which one is based on SVM, i.e. generalized Huber support vector machine and the other two are in the spirit of TWSVM, namely generalized Huber twin support vector machine and regularization on generalized Huber twin support vector machine. The proposed approaches iteratively find the solutions and eliminate the requirements to solve any quadratic programming problem (QPP) as for SVM and TWSVM. The main advantages of the proposed approach are: firstly, utilize the robust Huber loss function for better generalization and for lesser sensitivity towards noise and outliers as compared to quadratic loss; secondly, it uses functional iterative scheme to find the solution that eliminates the need to solving QPP and also makes the proposed approaches faster. The efficacy of the proposed approach is established by performing numerical experiments on several real-world datasets and comparing the result with related methods, viz. SVM, TWSVM, LSSVM and LSTSVM. The classification results are convincing.

Truncated loss functions are robust to class noise and outliers. A robust twin bounded support vector machine is proposed in this paper that truncates the growth of its loss functions at a pre-specified point, thus, flattens the function that pre-specified score afterwards. Moreover, to make the proposed method capable of handling datasets with different imbalance ratio, cost-sensitive learning is implemented by scaling the total error of the classes based on the number of samples of each class. However, the adopted loss functions take a non-convex structure which does not always assure global optimum. To handle this issue, we suggest concave-convex procedure (CCCP) to ensure global convergence by decomposing the cost functions into additions of one convex and one concave part. The behaviour of the proposed method for varied imbalance ratio is analysed experimentally and depicted graphically. Classification performance of the proposed method in terms of AUC, F-Measure and G-Mean is compared with other related methods, viz. Hinge loss support vector machine (SVM), Ramp loss SVM (RSVM), twin SVM (TWSVM), twin bounded SVM (TBSVM), Pinball loss SVM (pin-SVM), entropy-based fuzzy SVM (EFSVM), non-parallel hyperplane Universum SVM (U-NHSVM), stochastic gradient twin support vector machine (SGTSVM), k-nearest neighbor (KNN)-based maximum margin and minimum volume hyper-sphere machine (KNN-M3VHM) and affinity and class probability-based fuzzy SVM (ACFSVM) on several real-world datasets with imbalance ratio raging from low to high. Further, to establish the significance of the proposed method in pattern classification, pair-wise statistical comparison of the methods is performed based on their average ranks on AUC. Experimental results are convincing.

The condition monitoring and fault diagnosis of power transformers plays a significant role in the safe, stable and reliable operation of the whole power system. Dissolved gas analysis (DGA) methods are widely used for fault diagnosis, however, their accuracy is limited by the selection of DGA features and the performance of fault diagnosis models, for example, the classical support vector machine (SVM), is easily affected by unbalanced training samples. This paper presents a transformer fault diagnosis model based on chemical reaction optimization and a twin support vector machine. Twin support vector machines (TWSVMs) are used as classifiers for solving problems involving unbalanced and insufficient samples. Restricted Boltzmann machines (RBMs) are used for data preprocessing to ensure the effective identification of feature parameters and improve the efficiency and accuracy of fault diagnosis. The chemical reaction optimization (CRO) algorithm is used to optimize TWSVM parameters to select the optimal training parameters. The cross-validation (CV) method is used to ensure the reliability and generalization ability of the diagnostic model. Finally, the validity of the model is verified using real fault samples and random testing.

The traditional vector-based algorithms, such as Support Vector Machine (SVM) and Twin Support Vector Machine (TSVM), have many limitations especially when tensor is considered as input matrix. In this paper, we proposed a novel algorithm with a tensor-based classification paradigm to utilize the structural information. The new proposed algorithm is called  -Twin Support Tensor Machine ( -TSTM), which is an extension of  -Twin Support Vector Machine ( -TSVM). Similarly,  -TSTM solves a pair of smaller-sized Quadratic Programming Problems (QPPs). It reduces the computational complexity substantially. Besides, we formulate  -TSTM, which separates samples in the tensor space with two non-parallel hyperplanes, and the pair of parameters ( ) have theoretical interpretation which are used to control the bounds of the fractions of support tensors and the error margins. What’s more, the structure information of data is retained by the direct use of tensor representation. The proposed  -TSTM can preferably overcome overfitting problem and deal with big data while most vector-based algorithms could hardly compare. In addition, it has better performances on high dimensional and small-sample-size (S3) problem. The efficiency and superiority of the proposed method are demonstrated by experiments on various datasets.

Sparse pinball twin support vector machines

Twin support vector machine (TWSVM) is a classical distance metric learning method for classification problems. The formulation of TWSVM criterion is based on L2-norm distance, which makes TWSVM prone to being influenced by the presence of outliers. In this paper, to develop a robust distance metric learning method, we propose a new objective for TWSVM classifier using L1-norm distance metric, termed as L1-TWSVM. The optimization strategy is to maximize the ratio of the inter-class distance dispersion to the intra-class distance dispersion by using L1-norm distance rather than L2-norm distance. Besides, we design a simple and valid iterative algorithm to solve L1-norm optimal problems, which is easy to actualize and its convergence to an optimum is theoretically ensured. The efficiency and robustness of L1-TWSVM have been validated by experiments on UCI datasets and artificial datasets. The promising experimental results indicate that our proposals outperform relevant state-of-the-art methods in all kinds of experimental settings.

PurposeAs a clean and renewable energy source, wind energy will become one of the main sources of new energy supply in the future. Relying on the stable and strong wind resources at sea, wind energy has great potential to become the primary energy. As a critical part of the wind turbine, the gearbox of a wind turbine often bears a large external load. Especially at sea, due to the effects of ocean corrosion, waves and wind, the burden of the wind turbine gearbox is greater, which brings great challenges to its reliability analysis. This study aims to systematically review the reliability research in wind turbine gearboxes and guide future research directions and challenges.Design/methodology/approachThis study systematically reviews some design requirements and reliability analysis methods for wind turbine gearboxes. Then, it summarizes previous studies on wind load uncertainty modeling methods, including the processing of wind measurement data and the summary of three different classifications of random wind speed prediction models. Finally, existing reliability analysis studies on two major parts of the gearbox are described and summarized.FindingsFirst, the basic knowledge of wind turbine gearboxes and their reliability analysis is introduced. The requirements and reliability analysis methods of wind turbine gearboxes are explained. Then, the processing methods of wind measurement data and three different random wind speed prediction models are described in detail. Furthermore, existing reliability analysis studies on two common parts of wind turbine gearboxes, gears and bearings, are summarized and classified, including a summary of bearing failure modes. Finally, three possible future research directions for wind turbine gearbox reliability analysis are discussed, namely, reliability research under the influence of multiple factors on gears, damage indicators of bearing failure modes and quantitative evaluation criteria for the overall dynamic characteristics of offshore wind turbine gearboxes and a summary is also given.Originality/valueThis paper aims to systematically introduce the relevant contents of wind turbine gearboxes and their reliability analysis. The contents of wind speed data processing, predictive modeling and reliability analysis of major components are also comprehensively reviewed, including the classification and principle introduction of these contents.

As an renewable and clean energy of the world, wind energy has gained more and more attention and its fault diagnosis becomes more and more important. The gearbox, as the kernel component of the wind turbine system, it’s robust conditions have a great influence on the whole wind turbines system. Wind turbine gearbox has complex structure, which is usually composed of solar planetary gearbox and cylindrical gearbox. In the process of operation, various kinds of faults easily occur, resulting in serious losses. Once the wind turbine gearbox is not functioning as smoothly as it could be, it may result in large economic losses for the company and owner. At the same time, the failure rate of wind turbine gearbox has always been high because of complicated mechanic structure and special motion. Therefore, the tasks of reducing the downtime and increasing the productivity of wind turbine gearbox are urgent. This paper reviewed some research results of faults diagnosis on wind turbines gearbox, such as time-frequency analysis method, vibration based methods, nondestructive testing methods, etc. Meanwhile, this paper finds out some key problems and the channel of the resolution of the issue in order to supply some information for the further research of wind turbines gearbox.

This paper is a case study of the efficiency of a 2.5 MW wind turbine gearbox including the influence of each gearbox element: gear tooth geometry, rolling bearings and oil formulation. The power loss model used to predict the gearbox efficiency was previously validated with experimental results. The calculations showed that the efficiency of a wind turbine gearbox can be improved by selecting different wind turbine gear oil formulations, modifying gear tooth geometry. The energy savings can be even more significant if both gear tooth geometry and oil formulation are adequately selected.

Twin support vector machine (TWSVM) is a new machine learning method, as opposed to solving a single quadratic programming problem in support vector machine (SVM), which generates two nonparallel hyperplanes by solving two smaller size quadratic programming problems. However, the TWSVM obtains the final classifier by giving the same importance to all training samples which may be important for classification performance. In order to address this problem, in this paper, we propose a novel entropy-based fuzzy twin bounded support vector machine (EFTBSVM) for binary classification problems. By considering the fuzzy membership value for each sample and assigning it based on the entropy value, the samples with higher class certainty are assigned to relatively larger fuzzy membership. In addition, the proposed EFTBSVM not only maintains the superior characteristics of the TWSVM but also exploits the structural risk minimization principle by introducing a regularization term. The experimental results achieved on synthetic datasets and benchmark datasets illustrate the effectiveness of the proposed method.