Feature Extraction Using Sparse Kernel Non-Negative Matrix Factorization for Rolling Element Bearing Diagnosis

For early fault detection of a bearing, the localized defect generally brings a complex vibration signal, so it is difficult to detect the periodic transient characteristics from the signal spectrum using conventional bearing fault diagnosis methods. Therefore, many matrix analysis technologies, such as singular value decomposition (SVD) and reweighted SVD (RSVD), were proposed recently to solve this problem. However, such technologies also face failure in bearing fault detection due to the poor interpretability of the obtained eigenvector. Non-negative Matrix Factorization (NMF), as a part-based representation algorithm, can extract low-rank basis spaces with natural sparsity from the time–frequency representation. It performs excellent interpretability of the factor matrices due to its non-negative constraints. By this virtue, NMF can extract the fault feature by separating the frequency bands of resonance regions from the amplitude spectrogram automatically. In this paper, a new feature extraction method based on sparse kernel NMF (KNMF) was proposed to extract the fault features from the amplitude spectrogram in greater depth. By decomposing the amplitude spectrogram using the kernel-based NMF model with L1 regularization, sparser spectral bases can be obtained. Using KNMF with the linear kernel function, the time–frequency distribution of the vibration signal can be decomposed into a subspace with different frequency bands. Thus, we can extract the fault features, a series of periodic impulses, from the decomposed subspace according to the sparse frequency bands in the spectral bases. As a result, the proposed method shows a very high performance in extracting fault features, which is verified by experimental investigations and benchmarked by the Fast Kurtogram, SVD and NMF-based methods.

A guide for kernel generalized regression methods for genomic-enabled prediction

The primary objective of this paper is to provide a guide on implementing Bayesian generalized kernel regression methods for genomic prediction in the statistical software R. Such methods are quite efficient for capturing complex non-linear patterns that conventional linear regression models cannot. Furthermore, these methods are also powerful for leveraging environmental covariates, such as genotype × environment (G×E) prediction, among others. In this study we provide the building process of seven kernel methods: linear, polynomial, sigmoid, Gaussian, Exponential, Arc-cosine 1 and Arc-cosine L. Additionally, we highlight illustrative examples for implementing exact kernel methods for genomic prediction under a single-environment, a multi-environment and multi-trait framework, as well as for the implementation of sparse kernel methods under a multi-environment framework. These examples are followed by a discussion on the strengths and limitations of kernel methods and, subsequently by conclusions about the main contributions of this paper.