Machinery fault diagnosis using supervised manifold learning

https://doi.org/10.1016/j.ymssp.2009.02.006Get rights and content

Abstract

Fault diagnosis is essentially a kind of pattern recognition. How to implement feature extraction and improve recognition performance is a crucial task. In this paper, a new supervised manifold learning algorithm (S-LapEig) for feature extraction is proposed first. Via combining preserving the consistency of local neighbor information and class labels information, S-LapEig can not only gain a perfect approximation of low-dimensional intrinsic geometric structure within the high-dimensional observation data, but also enhance local within-class relations. Based on S-LapEig, a novel fault diagnosis approach is proposed. The approach extracts the intrinsic manifold features from high-dimensional fault data by directly learning the data, and translates complex mode space into a low-dimensional feature space, in which pattern classification and fault diagnosis are carried out easily. Comparing with other feature extraction methods such as PCA, LDA and Laplacian eigenmaps, the proposed method obviously improves the classification performance of fault pattern recognition. The experiments on benchmark data and engineering instance demonstrate the feasibility and effectiveness of the new approach.

Introduction

The progress of artificial intelligence and computer technology greatly accelerates the development of machinery intelligent fault diagnostic techniques. For instance, many intelligent techniques have been applied in machine unit diagnosis such as self-organizing feature maps (SOM) [1], support vector machines [2], expert system, neural network, rough set and fuzzy logic, etc. The problems of these methods are in computing complexity to feature extraction, and of instability in learning process.

The other challenging problem of fault diagnosis is how to deal with the high-dimensional and nonlinear data, which are collected from the complete information of operating machinery. A large number of data provide more available information, while also increasing the problem of effective using these data, and the useful knowledge might be submerged in a large number of redundant data so as to increase difficulty of feature extraction. An approach to the problem is to apply dimensionality reduction to the data for the object of learning and classification. The purpose of dimensionality reduction is to obtain a more compact representation of the original high-dimensional data, representation that nonetheless captures all the information necessary for higher-level decision-making. There are four advantages for reducing the dimensionality of observation data: (1) to project data to a low-dimensional space so as to be able to discern data distribution; (2) to extract features from data for fault diagnosis; (3) to eliminate noise; and (4) to compress the data to reduce storage requirements. For fault feature extraction, the classical dimensionality reduction methods include principal component analysis (PCA) [3], multi-dimensional scaling (MDS) [4], linear discriminate analysis (LDA) and independent component analysis (ICA) [5]. However, these approaches have only effect on the datasets of linear structure and gauss distributing. It is difficult for us to use these methods to discover the nonlinear structure in the fault data, result in, from the angle of fault classification, low accurate fault identification or misjudgment. For traditional nonlinear mapping methods, Sammon mapping [6] and neuroscale [7], the former has iterative process that results in intensive computation, the latter uses a radial basis function network and lies in the shortcomings similar to neural network. Meanwhile, manifold learning, a new effective method of nonlinear dimensionality reduction, has attracted more and more attention recently. The approach provides a new means to intelligent fault diagnosis.

Compared with linear method, the purpose of manifold learning methods is to project the original high-dimensional data into a lower dimensional feature space by preserving the local neighborhood structure, and are effective for us to discover the intrinsic structure of nonlinear high-dimensional data to the analysis of data. At present, the representative methods include isometric mapping (ISOMAP) [8], locally linear embedding (LLE) [9], Laplacian eigenmaps [10], [11], local tangent space alignment (LTSA) [12], etc. Manifold learning can be applied mainly to image recognition and image processing. For instance, the LLE algorithm is utilized to solve face recognition problem [13], a local embedding method based on LLE and ISOMAP algorithm is presented to gain lower dimensionality from high-dimensional data and implement visualization and classification of data [14], and a recognition algorithm based on manifold learning is successfully applied to image and character recognition [15]. Furthermore, manifold learning is seldom studied in fault diagnosis field, Yang [16] proposed a method of nonlinear time series noise reduction based on principal manifold learning applied to the analysis of gearbox vibration signal with snaggletooth, which only for signal denoising.

However, manifold learning is an unsupervised learning method, and cannot be applied efficiently to supervised learning problem. To the supervised expansion of manifold learning, Ridder [17] proposed a supervised LLE method (SLLE) for classification problem. Vlachos [18] proposed a WeightedIso method based on ISOMAP for data visualization and classification. Zhang Junping [19] proposed a supervised manifold learning method unifying LLE and LDA (ULLELDA) for face recognition. Zhang Haitao [20] proposed a supervised feature extraction method called locally discriminating projection (LDP) and achieved good recognition accuracy. Jian Cheng [21] proposed a supervised kernel locality preserving projections (SKLPP) for face recognition based on locality preserving projections (LPP). Most of these methods are based on the improvement of manifold learning methods and to solve a certain task.

In this paper, aimed at the difficulty of high-dimensional nonlinear fault data, we propose a new fault classification approach based on supervised manifold learning for machinery fault diagnosis. Because of the prominent properties of considering both the local geometry information and the class information of the data, the proposed approach has efficient capability to deal with the supervised learning problem. Some experiments with our method show its feasibility and effectiveness.

The remainder of the paper is organized as following. In Section 2, the theory and methods of manifold learning are reviewed briefly. In Section 3, a new supervised manifold learning algorithm (S-LapEig) for feature extraction is proposed. The implementation steps of the algorithm are described in detail. In Section 4, we discuss the fault diagnosis strategy via utilizing S-LapEig to extract fault feature. In Section 5, the new approach is applied to pattern classification experiments with Iris data, gearbox fault data, rotor bed fault data and high-speed compressor fault data. Comparisons with other feature extraction techniques are also discussed. And finally the conclusion is given in Section 6.

Section snippets

Manifold learning

Manifold learning is a new unsupervised learning method. Its aim is to explore the intrinsic geometry information of dataset, i.e. to discover the inherent low-dimensional manifold embedded in the high-dimensional observation space. It has good performance to nonlinear reduction dimensionality.

In recent years we have seen progress in modeling nonlinear manifold learning algorithms, such as LLE, ISOMAP, Laplacian eigenmaps, and LTSA. Among these algorithms, LLE supposes the local of

Supervised manifold learning algorithm

In some fault diagnosis tasks, data are from multiple classes and the class labels are known, which can help in classification tasks. The information provided by these class labels may be used to guide the procedure of dimensionality reduction. In this paper, taking special consideration of both the local geometry information and the class information of labeled data, we present a new nonlinear dimensionality reduction method based on manifold learning theory. This can be called supervised

Supervised manifold learning for fault diagnosis

Machinery fault diagnosis is the essence of pattern recognition problem, in the process of which the feature extraction is fundamental and the recognition method is at the core. We can implement fault identification by extracting the feature of equipment operating information collected from sensors, which are often high-dimensional and nonlinear. Conventional fault diagnosis methods are good at solving the problems of linearity and weak nonlinearity, but not good at fault diagnosis of

Application experiments

To verify the feature extraction capability of the S-LapEig, we test it with four datasets: Iris data, Gearbox data, rotor test bed simulation data and high-speed compressor vibration data, which are different in numbers of samples N, dimensions D and classes C. The experiments are set up as follows: a set is randomly split into a training set (80%) and a testing set (20%). The four examples are given here with the proposed approach. For comparing the effectiveness of feature extraction with

Conclusions

In this work, a new supervised manifold learning algorithm (S-LapEig) is proposed first. Via combining preserving the consistency of local neighbor information and class labels information, the S-LapEig can effectively exploit the embedded intrinsic geometric structure in the high-dimensional nonlinear dataset. Then the proposed algorithm is introduced into fault diagnosis field to solve fault pattern classification task, and a new fault diagnosis approach based on S-LapEig is proposed. The

Acknowledgements

This research project is supported by National Hi-tech Research and Development Program of China (no. 2007AA04Z421) and National Science Foundation Grant of China (no. 50775035). Finally, the authors are grateful to the anonymous reviewers for their helpful comments and constructive suggestions.

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