Utilizing SVD and VMD for Denoising Non-Stationary Signals of Roller Bearings

In view of the fact that vibration signals of rolling bearings are much contaminated by noise in the early failure period, this paper presents a new denoising SVD-VMD method by combining singular value decomposition (SVD) and variational mode decomposition (VMD). SVD is used to determine the structure of the underlying model, which is referred to as signal and noise subspaces, and VMD is used to decompose the original signal into several band-limited modes. Then the effective components are selected from these modes to reconstruct the denoised signal according to the difference spectrum (DS) of singular values and kurtosis values. Simulated signals and experimental signals of roller bearing faults have been analyzed using this proposed method and compared with SVD-DS. The results demonstrate that the proposed method can effectively retain the useful signals and denoise the bearing signals in extremely noisy backgrounds.

The carrier wave design for the synthesis of non-Gaussian and non-stationary signals using the amplitude modulation method

The methods of generating stationary random signals, both Gaussian and non-Gaussian, are quite complete, but the researches on the non-stationary signals are insufficient. Especially, the current methods seldom provide mathematical bases about the kurtoses of the produced signals such that the generations of non-stationary non-Gaussian signals with the desired kurtoses are inefficient, which also decrease the flexibility of the real-time control in shaker table tests. In the article, the amplitude modulation method is employed to realize the signal synthesis. The carrier waves of the method are investigated considering the bursts overlapping situations. At first, the explicit equations between the kurtoses of the synthesized signals and the three crucial parameters (the offset, the distance between a pair of adjacent bursts and the parameter of the Beta-distributed random variables) are deduced for the carrier waves with both overlapped bursts and non-overlapped busts. Meanwhile, to solve the power spectral density variation led by the amplitude modulation method, an explicit expression of a rescaling parameter is also proposed. Furthermore, the impacts of the three parameters are investigated; the focus of the investigation is on how the kurtoses of the synthesized signals are changed by the parameters. Based on the results of the investigation, a test procedure is put forward to apply the proposed equations in a shaker table test. The control process of the test demonstrates that the real-time kurtoses control can be achieved efficiently with the help of the newly proposed equations.

Development of Time Delay Estimation Algorithm Using Fuzzy Based Optimized Iterative Unscented Kalman Filter

In radar-based applications, Time Delay Estimation (TDE) is an essential criterion. Because of non-stationary behaviour, estimating the time delay between two turbulent signals is difficult. Existing delay estimation methods such as the cross correlation technique are restricted to stationary signals. The non-stationary signals are either fractal or periodic signal. The accuracy of this method is more reliable for fractal signals than for periodic signals. With a cost function at hand it is sensible to check whether the state correction results in a cost decrease in the first place, new parameter is optimized using Fuzzy Elephant Herding Optimization (FEHO). Further this paper incorporates ADAM based neural network (ADAM-NN) model for efficient time delay estimation. The study resulted in significant improvement upto 21.5% in estimating the time delay when compared with conventional methods.

Deep state-space Gaussian processes

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.