Faculty Bibliography

Data-driven machinery fault diagnosis is important for smart industrial systems to guarantee safety and reliability. However, the conventional data-driven fault diagnosis methods rely on the expert-designed features, which greatly affect the diagnosis performances. Inspired by the sparse representation-based classification (SRC) methods which can learn discriminative sparse features adaptively, we propose a novel discriminative dictionary learning based sparse classification (DDL-SC) framework for data-driven machinery fault diagnosis. The DDL-SC framework can jointly learn a discriminative dictionary for sparse representation and an optimal linear classifier for pattern recognition, which bridges the gaps between two separate processes, dictionary learning and classifier training in traditional SRC methods. In the learning stage, to enhance the discriminability of dictionary learning, we introduce the discriminative sparse code error along with the reconstruction error and classification error into the optimization objective. In the recognition stage, we employ sparse codes of testing signals with respect to the learned discriminative dictionary as inputs of the learned classifier, and promote the recognition performance by connecting a binary hard thresholding operator with the classifier predictions. The effectiveness of DDL-SC is evaluated on the planetary bearing fault dataset and gearbox fault dataset, indicating that DDL-SC yields the recognition accuracies of 99.73% and 99.41%, respectively. Besides, the comparative studies prove the superiority of DDL-SC over several state-of-the-art methods for data-driven machinery fault diagnosis.

Non-convex sparsity-inducing penalties outperform their convex counterparts, but generally sacrifice the cost function convexity. As a middle ground, we propose the sharpening sparse regularizers (SSR) framework to design non-separable non-convex penalties that induce sparsity more effectively than convex penalties such as $\ell _1$ and nuclear norms, but without sacrificing the cost function convexity. The overall problem convexity is preserved by exploiting the data fidelity relative strong convexity. The framework constructs penalties as the difference of convex functions, namely the difference between convex sparsity-inducing penalties and their smoothed versions. We propose a generalized infimal convolution smoothing technique to obtain the smoothed versions. Furthermore, SSR recovers and generalizes several non-convex penalties in the literature as special cases. The SSR framework is applicable to any sparsity regularized least squares ill-posed linear inverse problem. Beyond regularized least squares, the SSR framework can be extended to accommodate Bregman divergence, and other sparsity structures such as low-rankness. The SSR optimization problem can be formulated as a saddle point problem, and solved by a scalable forward-backward splitting algorithm. The effectiveness of the SSR framework is demonstrated by numerical experiments in different applications.

The anisotropic total variation (TV) denoising model suppresses noise for two-dimensional signals that are vertically and horizontally piecewise constant. However, two-dimensional signals may have sparse derivatives in other directions. We propose a modification of the classical anisotropic two-dimensional TV regularizer from a spectral point of view. In the frequency domain, the TV regularizer can be considered as penalizing the high-frequency component of original signals and promoting only low-frequency components. The classical anisotropic TV, which applies l1-norm on vertical and horizontal differences, suppresses high-frequency components of the signals. The proposed operator, named Haar total variation (Haar-TV), penalizes two-dimensional signals that have more varied high-frequency regions. Furthermore, we propose non-convex penalties based on the Haar-TV operator since non-convex penalties can preserve edges and thus enhance the quality of the estimation. We derive a condition that preserves the strong convexity of the total cost function so the global minimizer can be reached.

The vibration signal of faulty rotating machinery tends to be a mixture of repetitive transients, discrete frequency components and noise. How to accurately extract the repetitive transients is a critical issue for machinery fault diagnosis. Inspired by reweighted L1 (ReL1) minimization for sparsity enhancement, a reweighted generalized minimax-concave (ReGMC) sparse regularization method is proposed to extract the repetitive transients. We utilize the generalized minimax-concave (GMC) penalty to regularize the weighted sparse representation model to overcome the underestimation deficiency of L1 norm penalty. Moreover, a new reweight strategy which is different from the reweight strategy in ReL1 for sparsity enhancement is proposed according to the statistical characteristic, i.e., squared envelope spectrum kurtosis. Then ReGMC is proposed by solving a series of weighted GMC minimization problems. ReGMC is utilized to process a simulated signal and the vibration signals of a hot-milling transmission gearbox and a run-to-failure bearing with incipient fault. The ReGMC analysis results and the comparison studies show that ReGMC can effectively extract the repetitive transients while suppressing the discrete frequency components and noise, and behaves better than GMC, improved lasso, and spectral kurtosis.

Foveal structure that is specified by the thickness, depth and the overall shape of the fovea is a promising tool to qualify and quantify retinal pathology in Parkinson's disease. To determine the model variable that is best suited for discriminating Parkinson's disease eyes from those of healthy controls and to assess correlations between impaired contrast sensitivity and foveal shape we characterized the fovea in 48 Parkinson's disease patients and 45 control subjects by optical coherence tomography (OCT). The model quantifies structural changes in the fovea of Parkinson's disease patients that are correlated with a decline in contrast sensitivity. Retinal foveal remodeling may serve as a parameter for vision deficits in Parkinson's disease. Whether foveal remodeling reflects dopaminergic driven pathology or rather both dopaminergic and non-dopaminergic pathology has to be investigated in longitudinal studies.

Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a "˜convex non-convex"™ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising.