Impulse Feature Extraction of Bearing Faults Based on Convolutive Nonnegative Matrix Factorization

Bearing faults are a major reason for the catastrophic breakdown of rotating machinery. Therefore, the early detection of bearing faults becomes a necessity to attain an uninterrupted and safe operation. This paper proposes a novel approach based on semi-nonnegative matrix factorization for detection of incipient faults in bearings. The semi-nonnegative matrix factorization algorithm creates a sparse, localized, part-based representation of the original data and assists to capture the fault information in bearing signals more effectively. Through semi-nonnegative matrix factorization, two bearing health indicators are derived to fulfill the desired purpose. In doing so, the paper tries to address two critical issues: (i) how to reduce the dimensionality of feature space (ii) how to obtain a definite range of the indicator between 0 and 1. Firstly, a set of time domain, frequency domain, and time–frequency domain features are extracted from the bearing vibration signals. Secondly, the feature dataset is utilized to train the semi-nonnegative matrix factorization algorithm which decomposes the training data matrix into two new matrices of lower ranks. Thirdly, the test feature vectors are projected onto these lower dimensional matrices to obtain two statistics called as square prediction error and Q2. Finally, the Bayesian inference approach is exploited to convert the two statistics into health indicators that have a fixed range between [0–1]. The application of the advocated technique on experimental bearing signals demonstrates that it can effectively predict the weak defects in bearings as well as performs better than the earlier methods like principal component analysis and locality preserving projections.

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Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition

Symmetry ◽

10.3390/sym11030354 ◽

2019 ◽

Vol 11 (3) ◽

pp. 354

Author(s):

Jing Zhou

Keyword(s):

Feature Extraction ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Recognition Rate ◽

Nonnegative Matrix ◽

Facial Feature ◽

Face Database ◽

Base Matrix ◽

Sparse Nonnegative Matrix Factorization ◽

Pca Method

Weighted nonnegative matrix factorization (WNMF) is a technology for feature extraction, which can extract the feature of face dataset, and then the feature can be recognized by the classifier. To improve the performance of WNMF for feature extraction, a new iteration rule is proposed in this paper. Meanwhile, the base matrix U is sparse based on the threshold, and the new method is named sparse weighted nonnegative matrix factorization (SWNMF). The new iteration rules are based on the smaller iteration steps, thus, the search is more precise, therefore, the recognition rate can be improved. In addition, the sparse method based on the threshold is adopted to update the base matrix U, which can make the extracted feature more sparse and concentrate, and then easier to recognize. The SWNMF method is applied on the ORL and JAFEE datasets, and from the experiment results we can find that the recognition rates are improved extensively based on the new iteration rules proposed in this paper. The recognition rate of new SWNMF method reached 98% for ORL face database and 100% for JAFEE face database, respectively, which are higher than the PCA method, the sparse nonnegative matrix factorization (SNMF) method, the convex non-negative matrix factorization (CNMF) method and multi-layer NMF method.

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