Criterion For Blind Deconvolution Research Articles

Use of generalized Gaussian cyclostationarity for blind deconvolution and its application to bearing fault diagnosis under non-Gaussian conditions

Blind deconvolution (BD) methods can extract fault signatures from noisy observations. Among all the BD methods, maximum second-order cyclostationarity blind deconvolution (CYCBD) is an effective method for extracting weak periodic impulses related to bearing faults. CYCBD is done by maximizing the second-order cyclostationarity of a signal through the indicator of second-order cyclostationarity (ICS2, which can be calculated using the squared envelope spectrum, SES). The effectiveness of the SES is under the assumption that signals are Gaussian distributed. However, SES, ICS2 and CYCBD can be ineffective when signals are corrupted by highly leptokurtic noise.A recent study separates the detection of non-stationarity from non-Gaussianity by releasing the hypothesis of Gaussianity to generalized Gaussianity. The indicator IGGCS/GGS can detect the cyclostationarity of a signal corrupted by highly impulsive noise. In addition, it can be approximated by the β-power envelope spectrum (PES). Inspired by the relationship between IGGCS/GGS and ICS2, a blind deconvolution method by maximizing the generalized Gaussian cyclostationarity (CYCBDβ) is proposed in this study. Compared with CYCBD, the robustness of CYCBDβ against strong non-Gaussian noise increases. However, the original shape parameter estimation method has two limitations, which introduces difficulties in using IGGCS/GGS as the criterion for BD. (1) The fault period must be known in advance. (2) The fault period should be an integer for the synchronous average. In addition, a serious problem of CYCBD is that the used cyclic frequencies must match fault frequencies. Otherwise, the performance of CYCBD can be severely compromised. To better incorporate the shape parameter estimation into the BD method, the GGCS model using fault frequencies for synchronous average is proposed. In addition, a fault frequencies estimation approach has been added to the generation of the weighting matrix of CYCBDβ. Benefiting from these improvements, the proposed CYCBDβ has two advantages compared with CYCBD: (1) the robustness of CYCBDβ against strong non-Gaussian noise is higher, and (2) CYCBDβ can extract fault features when fault frequencies are unknown. The effectiveness and robustness of the method are validated using simulations and real vibration datasets.

Wind turbine bearing fault diagnosis by maximum generalised Gaussian cyclostationarity blind deconvolution

This study aims to assess the performance of IGGCS/GGS as a criterion for blind deconvolution in the detection of wind turbine bearing faults. The challenges associated with diagnosing wind turbine bearing faults include two primary issues: (1) the theoretical fault frequencies or orders may not align with the actual fault frequencies or orders, and (2) the vibration signal deviates from a Gaussian distribution. Consequently, the application of the blind deconvolution criterion ICS2, as utilized in CYCBD, may encounter difficulties due to the aforementioned reasons. To address this, the criterion is modified from ICS2 to IGGCS/GGS, and a tolerance band is introduced during the generation of the weighting matrix. These modifications aim to mitigate the impact of the aforementioned challenges. The effectiveness of the modified blind deconvolution approach, referred to as CYCBDβ, is evaluated in this study by comparing its performance against that of CYCBD using two distinct datasets from 2.0 MW wind turbines.

Blind Deconvolution of Seismic Data Based on the Spearman’s Rho

In this paper, we propose a novel seismic blind deconvolution approach based on the Spearman’s rho in the case of band-limited seismic data with a low dominant frequency and short data records. The Spearman’s rho is a measure of the dependence between two continuous random variables without the influence of the marginal distributions, by which a new criterion for blind deconvolution is constructed. The optimization program for new criterion of blind deconvolution is performed by applying Neidell’s wavelet model to the inverse filter. The noise-free and noisy synthetic data, onshore seismic trace in the Ordos Basin, and offshore stacked section in the Bohai Bay Basin examples show good results of the method.

Blind Deconvolution of Seismic Data Using f-Divergences

This paper proposes a new approach to the seismic blind deconvolution problem in the case of band-limited seismic data characterized by low dominant frequency and short data records, based on Csiszár’s f-divergence. In order to model the probability density function of the deconvolved data, and obtain the closed form formula of Csiszár’s f-divergence, mixture Jones’ family of distributions (MJ) is introduced, by which a new criterion for blind deconvolution is constructed. By applying Neidell’s wavelet model to the inverse filter, we then make the optimization program for multivariate reduce to univariate case. Examples are provided showing the good performance of the method, even in low SNR situations.

Adaptive Blind Deconvolution of Linear Channels Using Renyi's Entropy with Parzen Window Estimation

Blind deconvolution of linear channels is a fundamental signal processing problem that has immediate extensions to multiple-channel applications. In this paper, we investigate the suitability of a class of Parzen-window-based entropy estimates, namely Renyi's entropy, as a criterion for blind deconvolution of linear channels. Comparisons between maximum and minimum entropy approaches, as well as the effect of entropy order, equalizer length, sample size, and measurement noise on performance, will be investigated through Monte Carlo simulations. The results indicate that this nonparametric entropy estimation approach outperforms the standard Bell-Sejnowski and normalized kurtosis algorithms in blind deconvolution. In addition, the solutions using Shannon's entropy were not optimal either for super- or sub-Gaussian source densities.

Performance of Shalvi and Weinstein's deconvolution criteria for channels with/without zeros on the unit circle

This correspondence shows that the Shalvi and Weinstein (1994) blind deconvolution criteria are applicable for finite SNR regardless of channels having zeros on the unit circle or not. The associated deconvolution filter is stable with a nonlinear relation to the nonblind MMSE equalizer and capable of performing perfect phase equalization for finite SNR.

Criteria for blind deconvolution of multichannel linear time-invariant systems

Blind deconvolution and equalization of linear time-invariant systems have widely received attention in various fields such as data communication, image processing and geophysical data processing. Shalvi and Weinstein (1990) proposed certain criteria for blind deconvolution of nonminimum-phase linear time-invariant systems. Their work is, however, restricted to the single-channel (or scalar) case. This correspondence extends the Shalvi-Weinstein approach to the multichannel case. We propose a multistage maximization criterion and a single-stage maximization criterion for attaining multichannel blind deconvolution. Under the normalized condition specified later, they are shown to be equivalent.

Comments on "New criteria for blind deconvolution of nonminimum phase systems (channels)" [with reply

It is pointed out that certain criteria proposed in the paper by Shalvi and Weinstein (see ibid., vol.36, no.2, p.312-21, 1990) have been proposed before in the context of real-valued signals. Furthermore, it is noted that the assertion made in the paper that all local maxima of the proposed criteria correspond to the desired equalizer solution, holds true, strictly speaking, only for infinite length equalizers. There exist counterexamples which show existence of false local maxima when finite-length equalizers are used. Finally, it is also noted that in the presence of additive Gaussian noise of unknown power spectral density at the input to the equalizer (equivalently, at the channel output), it is not clear if the methods proposed in the paper will yield the desired response up to a constant gain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New criteria for blind deconvolution of nonminimum phase systems (channels)

A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this condition, several optimization criteria are proposed, and their solution is shown to correspond to the desired response. These criteria involve the computation only of second- and fourth-order moments, implying a simple tap update procedure. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the (unobserved) input sequence. It is shown that in several important cases (e.g. when the additive noise is Gaussian), the proposed criteria are essentially unaffected. >