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For the data-driven remaining useful life (RUL) prediction for rolling bearings, the traditional machine learning-based methods generally provide insufficient feature representation and adaptive extraction. Although deep learning-based RUL prediction methods can solve these problems to some extent, they still do not yield satisfactory predictive results due to less degradation data and inconsistent data distribution among different bearings. To solve these problems, a new RUL prediction method based on deep feature representation and transfer learning is proposed in this paper. This method includes an off-line stage and an online stage. In the off-line stage, the Hilbert–Huang transform marginal spectra of the raw vibration signal of auxiliary bearings are first calculated as the input, and then contractive denoising autoencoder is introduced to extract deep features with good and stable fault representation. Second, by using the obtained deep features and Pearson’s correlation coefficient, a new health condition assessment method is proposed to divide the whole life of each bearing into a normal state and a fast-degradation state. Finally, using the extracted deep features and their RUL values, an RUL prediction model for the fast-degradation state is trained by means of a least-square support vector machine. In the online stage, a kind of transfer learning algorithm, i.e., transfer component analysis, is introduced to sequentially adjust the features of target bearing from auxiliary bearings, and then the corresponding RUL is predicted using the corrected features. Results using the PHM Challenging 2012 data set show a significant performance improvement when using the proposed method in terms of predictive accuracy and numerical stability. [ABSTRACT FROM AUTHOR]

This paper presents a new online detection approach for rolling bearing’s incipient fault based on self-adaptive deep feature matching (SDFM). This approach includes offline and online stages. At the offline stage, a new health state assessment algorithm is first proposed based on singular value decomposition (SVD) and Kurtosis criterion. Based on the assessment results, a kind of deep learning algorithm, i.e., stacked denoising autoencoder (SDAE), is introduced to extract the common deep features of normal state and early fault state. Support vector data description (SVDD) is applied to establish the offline detection model using the obtained features. At the online stage, a self-adaptive matching strategy with 1-Dimensional anchor is proposed. By utilizing the SDAE model established at offline stage, this strategy can extract more representative deep features of the target bearing via generating various proposal fragments and then determining the fault occurrence time in a self-adaptive way by feeding the online features into the SVDD model. Experiments run on the bearing data set of IEEE prognostic and health management (PHM) Challenge 2012. The results show the proposed approach has good detection performance in real time and much lower false alarm rate, with no need to acquire fault characteristic frequency in advance. [ABSTRACT FROM AUTHOR]

In many practical engineering applications, data tend to be collected in online sequential way with imbalanced class. Many traditional machine learning methods such as support vector machine and so on generally get biased classifier which leads to lower classification precision for minor class than major class. To get fast and efficient classification, a new online sequential extreme learning machine method with two-stage hybrid strategy is proposed. In offline stage, data-based strategy is employed, and the principal curve is introduced to model the distribution of minority class data. In online stage, algorithm-based strategy is employed, and a new leave-one-out cross-validation method using Sherman–Morrison matrix inversion lemma is proposed to tackle online imbalance data, meanwhile, with add-delete mechanism for updating network weights. And the rationality of this strategy is proved theoretically. The proposed method is evaluated on four UCI datasets and the real-world Macau air pollutant forecasting dataset. The experimental results show that, the proposed method outperforms the classical ELM, OS-ELM and meta-cognitive OS-ELM in terms of generalization performance and numerical stability. [ABSTRACT FROM AUTHOR]

Abstract: Multi-Input Multi-Output (MIMO) regression estimation problems widely exist in engineering fields. As an efficient approach for MIMO modeling, multi-dimensional support vector regression, named M-SVR, is generally capable of obtaining better predictions than many traditional methods. However, M-SVR is sensitive to the perturbation of hyper-parameters when facing small-scale sample problems, and most of currently used model selection methods for conventional SVR cannot be applied to M-SVR directly due to its special structure. In this paper, a fast and robust model selection algorithm for M-SVR is proposed. Firstly, a new training algorithm for M-SVR is proposed to reduce efficiently the numerical errors in training procedure. Based on this algorithm, a new leave-one-out (LOO) error estimate for M-SVR is derived through a virtual LOO cross-validation procedure. This LOO error estimate can be straightway calculated once a training process ended with less computational complexity than traditional LOO method. Furthermore, a robust implementation of this LOO estimate via Cholesky factorization is also proposed. Finally, the gradients of the LOO estimate are calculated, and the hyper-parameters with lowest LOO error can be found by means of gradient decent method. Experiments on toy data and real-life dynamical load identification problems are both conducted, demonstrating comparable results of the proposed algorithm in terms of generalization performance, numerical stability and computational cost. [Copyright &y& Elsevier]

As an effective approach for multi-input multi-output regression estimation problems, a multi-dimensional support vector regression (SVR), named M-SVR, is generally capable of obtaining better predictions than applying a conventional support vector machine (SVM) independently for each output dimension. However, although there are many generalization error bounds for conventional SVMs, all of them cannot be directly applied to M-SVR. In this paper, a new leave-one-out (LOO) error estimate for M-SVR is derived firstly through a virtual LOO cross-validation procedure. This LOO error estimate can be straightway calculated once a training process ended with less computational complexity than traditional LOO method. Based on this LOO estimate, a new model selection methods for M-SVR based on multi-objective optimization strategy is further proposed in this paper. Experiments on toy noisy function regression and practical engineering data set, that is, dynamic load identification on cylinder vibration system, are both conducted, demonstrating comparable results of the proposed method in terms of generalization performance and computational cost. [ABSTRACT FROM AUTHOR]

Abstract: Model selection plays a key role in the application of support vector machine (SVM). In this paper, a method of model selection based on the small-world strategy is proposed for least squares support vector regression (LS-SVR). In this method, the model selection is treated as a single-objective global optimization problem in which generalization performance measure performs as fitness function. To get better optimization performance, the main idea of depending more heavily on dense local connections in small-world phenomenon is considered, and a new small-world optimization algorithm based on tabu search, called the tabu-based small-world optimization (TSWO), is proposed by employing tabu search to construct local search operator. Therefore, the hyper-parameters with best generalization performance can be chosen as the global optimum based on the powerful search ability of TSWO. Experiments on six complex multimodal functions are conducted, demonstrating that TSWO performs better in avoiding premature of the population in comparison with the genetic algorithm (GA) and particle swarm optimization (PSO). Moreover, the effectiveness of leave-one-out bound of LS-SVM on regression problems is tested on noisy sinc function and benchmark data sets, and the numerical results show that the model selection using TSWO can almost obtain smaller generalization errors than using GA and PSO with three generalization performance measures adopted. [ABSTRACT FROM AUTHOR]

Most traditional approaches to load identification usually perform not very well because the inverse identification problem in most practical cases is ill-posed. In this paper, a new approach to the identification of dynamic loads based on the solution path algorithm of support vector regression is proposed. A general framework of dynamic load identification using support vector regression is derived and the corresponding identification model using solution path algorithm is established. The results of numerical and experimental tests on cylinder vibration system show that the proposed approach greatly outperforms existing methods, i.e., direct inverse identification method, ℇ-SVR and LS-SVM, in terms of identification accuracy and numerical stability. As a conclusion, the proposed approach is applicable to a wide variety of mechanical cases. [ABSTRACT FROM AUTHOR]

Abstract: In the conventional solution path algorithm of support vector regression, the ε-insensitive error of every training sample is equally penalized, which means every sample affects the generalization ability equally. However, in some cases, e.g. time series prediction or noisy function regression, the ε-insensitive error of the sample which could provide more important information should be penalized more heavily. Therefore, the weighted solution path algorithm of support vector regression is proposed in this paper. Error penalty parameter of each training sample is weighted differently, and the whole solution path is modified correspondingly. More importantly, by choosing Arc Tangent function as the prototype to generate weights with various characteristics, a heuristic weight-setting optimization algorithm is proposed to compute the optimal weights using particle swarm optimization (PSO). This method is applicable to different applications. Experiments on time series prediction and noisy function regression are conducted, demonstrating comparable results of the proposed weighted solution path algorithm and encouraging performance of the heuristic weight-setting optimization. [Copyright &y& Elsevier]

In recent years, machine learning techniques have been proven to be a promising tool for early fault detection of rolling bearings. In many actual applications, however, bearing whole-life data are not easy to be historically accumulated, while insufficient data may result in training a detection model that is not good enough. If utilizing the available data under different working conditions to facilitate model training, the data distribution of different bearings are usually quite different, which does not meet the precondition of i n d e p e n d e n t a n d i d e n t i c a l d i s t r i b u t i o n ( i. i. d ) and tends to cause performance reduction. In addition, disturbed by the unstable noise under complex conditions, most of the current detection methods are inclined to raise false alarms, so that the reliability of detection results needs to be improved. To solve these problems, a robust detection method for bearings early fault is proposed based on deep transfer learning. The method includes offline stage and online stage. In the offline stage, by introducing a deep auto-encoder network with domain adaptation, the distribution inconsistency of normal state data among different bearings can be weakened, then the common feature representation of the normal state is obtained. With the extracted common features, a new state assessment method based on the robust deep auto-encoder network is proposed to evaluate the boundary between normal state and early fault state in the low-rank feature space. By training a support vector machine classifier, the detection model is established. In the online stage, along with the data batch arriving sequentially, the features of target bearing are extracted using the common representation learnt in the offline stage, and online detection is conducted by feeding them into the SVM model. Experimental results on IEEE PHM Challenge 2012 bearing dataset and XJTU-SY dataset show that the proposed approach outperforms several state-of-the-art detection methods in terms of detection accuracy and false alarm rate. [ABSTRACT FROM AUTHOR]

By using signal processing and statistical analysis methods simultaneously, many heterogeneous features can be produced to describe the bearings fault with more comprehensive and discriminant information. At same time, there may exist redundant or irrelevant information which will instead reduce the diagnosis performance. To solve this problem, it is necessary to conduct feature selection which tries to choose the most typical and discriminant features by evaluating their effect on fault status. However, if the structural relationship between features has not been considered well, some similar or redundant features are still probably chosen, which would introduce bias into the final diagnosis model. In this paper, a new fault diagnosis method of bearings based on structural feature selection is proposed to solve the aforementioned problem. Obeying the hypothesis that the features with strong relatedness have close coefficient distance, the proposed method aims to improve diagnosis performance via determining group structure in fault features. First, a new feature selection strategy is proposed by introducing a group identification matrix. Using this matrix, two evaluation criteria about intra-group feature correlation and inter-group feature difference are constructed by means of coefficient's distance. Consequently, we get a multi-objective 0–1 integer programming problem by minimizing intra-group distance and maximizing inter-group distance simultaneously. Second, we use the multi-objective particle swarm optimization algorithm to solve this problem, and then determine the optimal group structure of features adaptively. Finally, a diagnosis model can be trained by support vector machine on the typical features extracted from these groups. Experimental results on four UCI datasets show the effectiveness of the proposed group feature selection strategy. Moreover, the experimental results on two bearing datasets (i.e., CWRU and IMS datasets) demonstrate that the proposed method can identify the inherent group structure in fault features, and then has better diagnosis performance compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract: In practical engineering, small-scale data sets are usually sparse and contaminated by noise. In this paper, we propose a new sequence of orthogonal polynomials varying with their coefficient, unified Chebyshev polynomials (UCP), which has two important properties, namely, orthogonality and adaptivity. Based on these new polynomials, a new kernel function, the unified Chebyshev kernel (UCK), is constructed, which has been proven to be a valid SVM kernel. To find the optimal polynomial coefficient and the optimal kernel, we propose an adaptive algorithm based on the evaluation criterion for adaptive ability of UCK. To evaluate the performance of the new method, we applied it to learning some benchmark data sets for regression, and compared it with other three algorithms. The experiment results show that the proposed adaptive algorithm has excellent generalization performance and prediction accuracy, and does not cost more time compared with other SVMs. Therefore, this method is suitable for practical engineering application. [Copyright &y& Elsevier]