Gaigai Cai

Bio: Gaigai Cai is an academic researcher from Soochow University (Suzhou). The author has contributed to research in topics: Sparse approximation & Feature extraction. The author has an hindex of 15, co-authored 34 publications receiving 1136 citations. Previous affiliations of Gaigai Cai include Xidian University & Xi'an Jiaotong University.

Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis

Abstract: The authors introduce an iterative algorithm, called matching demodulation transform (MDT), to generate a time-frequency (TF) representation with satisfactory energy concentration. As opposed to conventional TF analysis methods, this algorithm does not have to devise ad-hoc parametric TF dictionary. Assuming the FM law of a signal can be well characterized by a determined mathematical model with reasonable accuracy, the MDT algorithm can adopt a partial demodulation and stepwise refinement strategy for investigating TF properties of the signal. The practical implementation of the MDT involves an iterative procedure that gradually matches the true instantaneous frequency (IF) of the signal. Theoretical analysis of the MDT's performance is provided, including quantitative analysis of the IF estimation error and the convergence condition. Moreover, the MDT-based synchrosqueezing algorithm is described to further enhance the concentration and reduce the diffusion of the curved IF profile in the TF representation of original synchrosqueezing transform. The validity and practical utility of the proposed method are demonstrated by simulated as well as real signal.

Nonconvex Sparse Regularization and Convex Optimization for Bearing Fault Diagnosis

Abstract: Vibration monitoring is one of the most effective ways for bearing fault diagnosis, and a challenge is how to accurately estimate bearing fault signals from noisy vibration signals. In this paper, a nonconvex sparse regularization method for bearing fault diagnosis is proposed based on the generalized minimax-concave (GMC) penalty, which maintains the convexity of the sparsity-regularized least squares cost function, and thus the global minimum can be solved by convex optimization algorithms. Furthermore, we introduce a k-sparsity strategy for the adaptive selection of the regularization parameter. The main advantage over conventional filtering methods is that GMC can better preserve the bearing fault signal while reducing the interference of noise and other components; thus, it can significantly improve the estimation accuracy of the bearing fault signal. A simulation study and two run-to-failure experiments verify the effectiveness of GMC in the diagnosis of localized faults in rolling bearings, and the comparison studies show that GMC provides more accurate estimation results than L1-norm regularization and spectral kurtosis.

Rolling bearing fault diagnosis using an optimization deep belief network

Abstract: The vibration signals measured from a rolling bearing are usually affected by the variable operating conditions and background noise which lead to the diversity and complexity of the vibration signal characteristics, and it is a challenge to effectively identify the rolling bearing faults from such vibration signals with no further fault information. In this paper, a novel optimization deep belief network (DBN) is proposed for rolling bearing fault diagnosis. Stochastic gradient descent is used to efficiently fine-tune all the connection weights after the pre-training of restricted Boltzmann machines (RBMs) based on the energy functions, and the classification accuracy of the DBN is improved. Particle swarm is further used to decide the optimal structure of the trained DBN, and the optimization DBN is designed. The proposed method is applied to analyze the simulation signal and experimental signal of a rolling bearing. The results confirm that the proposed method is more accurate and robust than other intelligent methods.

Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations

Abstract: This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus benefit from both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.