scholarly journals Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Haibin Wang ◽  
Junbo Long ◽  
Zeliang Liu ◽  
Fang You
Keyword(s):  
Lower Order ◽  
Stable Distribution ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Outer Race ◽  
Characteristic Extraction ◽  
Distribution Process ◽  
Non Gaussian ◽  
Estimate Variance ◽  
Low Order

The generated signals generally contain a large amount of background noise when the mechanical bearing fails, and the fault signals present nonlinear and non-Gaussian feature, which have heavy tail and belong to α -stable distribution ( 1 < α < 2 ); even the background noises are also α -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under α -stable distribution environment. Two improved bispectrum methods are proposed based on fractional lower-order covariation in this paper, including fractional low-order direct bispectrum (FLODB) method, fractional low-order indirect bispectrum (FLOIDB) method. In order to decrease the estimate variance and increase the bispectral flatness, the fractional lower-order autoregression (FLOAR) model bispectrum and fractional lower-order autoregressive moving average (FLOARMA) model bispectrum methods are presented, and their calculation steps are summarized. We compare the improved bispectrum methods with the conventional methods employing second-order statistics in Gaussian and S α S distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods. Finally, we use the improved methods to estimate the bispectrum of the normal and outer race fault signal; the result indicates that they are feasible and effective for fault diagnosis.

scholarly journals Applications of Fractional Lower Order Synchrosqueezing Transform Time Frequency Technology to Machine Fault Diagnosis

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Haibin Wang ◽  
Junbo Long
Keyword(s):  
Lower Order ◽  
Signal Analysis ◽  
Stable Distribution ◽  
Signal Reconstruction ◽  
Outer Race ◽  
Time Frequency ◽  
S Transform ◽  
Synchrosqueezing Transform ◽  
Better Than ◽  
Low Order

Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha (α) stable distribution with 1<α<2 and even the noises being also α stable distribution. The conventional FSST and SSST methods degenerate and even fail under α stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under α stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SαS) distribution noise.

scholarly journals ROBUST RECURSIVE IDENTIFICATION OF HAMMERSTEIN MODELS BASED ON WEISZFALD ALGORITHM

2020 ◽  
Vol 18 (2) ◽  
pp. 127
Author(s):  
Vojislav Filipović
Keyword(s):  
Robust Statistics ◽  
Moving Average ◽  
Recursive Identification ◽  
Autoregressive Moving Average ◽  
Weighted Norm ◽  
Stochastic Disturbance ◽  
Hammerstein Models ◽  
Non Gaussian ◽  
Weighting Coefficients ◽  
Nonlinear Autoregressive

The Hammerstein models can accurately describe a wide variety of nonlinear systems (chemical process, power electronics, electrical drives, sticky control valves). Algorithms of identification depend, among other, on the assumption about the nature of stochastic disturbance. Practical research shows that disturbances, owing the presence of outliers, have a non-Gaussian distribution. In such case it is a common practice to use the robust statistics. In the paper, by analysis of the least favourable probability density, it is shown that the robust (Huber`s) estimation criterion can be presented as a sum of non-overlapping - norm and - norm criteria. By using a Weiszfald algorithm - norm criterion is converted to - norm criterion. So, the weighted - norm criterion is obtained for the identification. The main contributions of the paper are: (i) Presentation of the Huber`s criterion as a sum of - norm and - norm criteria; (ii) Using the Weiszfald algorithm  – norm criterion is converted to a weighted - norm criterion; (iii) Weighted extended least squares in which robustness is included through weighting coefficients are derived for NARMAX (nonlinear autoregressive moving average with exogenous variable) . The illustration of the behaviour of the proposed algorithm is presented through simulations.

Consistency of model selection and parameter estimation

1986 ◽  
Vol 23 (A) ◽  
pp. 127-141 ◽  
Author(s):  
Ritei Shibata
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Lower Order ◽  
Moving Average ◽  
Information Matrix ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
The Cost ◽  
The Relationship ◽  
Autoregressive Moving Average Models

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.

ASYMPTOTIC THEORY OF STATISTICAL INFERENCE FOR TIME SERIES

2002 ◽  
Vol 18 (4) ◽  
pp. 993-999
Author(s):  
Offer Lieberman
Keyword(s):  
Time Series ◽  
Statistical Inference ◽  
Asymptotic Theory ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Finite Sample ◽  
Vector Autoregressive ◽  
Time Series Econometrics ◽  
Non Gaussian ◽  
Unit Root Models

Modern time series econometrics involves a diversity of models. In addition to the more traditional vector autoregressive (VAR) and autoregressive moving average (ARMA) systems, cointegration and unit root models are in widespread use for macroeconomic data, nonlinear and non-Gaussian models are popular for financial data, and long memory models are becoming more common in both macroeconomic and financial applications. Much econometric thought relates to issues of estimation and hypothesis testing, and so, in the absence of a usable finite sample theory (as is the case for the models just mentioned), an enormous amount of effort has been given to developing adequate asymptotics for statistical inference. There is often a lag between the introduction of a new model and the development of an asymptotic theory. In consequence, applied econometricians sometimes have to estimate time series models for which no asymptotic theory is available. For instance, multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models have been in use in empirical research for a while, and practitioners have been using asymptotic normality of estimators in this model even though a theoretical justification is not available.

scholarly journals Robust Signals Detection Algorithm Based on Cyclostationarity in Impulsive Noise

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Order Statistics ◽  
Lower Order ◽  
Stable Distribution ◽  
Impulsive Noise ◽  
Detection Algorithm ◽  
Communication Signals ◽  
Alpha Stable Distribution ◽  
Fractional Lower Order Statistics ◽  
Non Gaussian ◽  
Output Snr

A robust method for detecting the communication signals impinging on an antenna with interference and non-Gaussian impulsive noise is introduced in this paper. Degradation of the conventional cyclic detector which based on max-output-SNR criterion in impulsive noise is shown both theoretically and experimentally. By fusing second-order cyclostationarity and fractional lower-order statistics, a type of cyclic fractional lower-order statistics is developed which is defined for exploiting cyclostationarity property. Then, a new robust type of detection algorithm is developed using the theory of optimal filtering based on max-output-SNR criterion and alpha-stable distribution, including the fractional lower-order cyclic matched filter, which is formulated for detecting the communication signals in the presence of interference and non-Gaussian alpha-stable distribution impulsive noise. It is shown that the new method is robust to Gaussian and non-Gaussian impulsive noises, and is immune to the interfering signals which occupy the same spectral band as that of the received signal. Simulation results show the robustness and effectiveness of the proposed algorithm.

scholarly journals Applications of Fractional Lower Order Frequency Spectrum Technologies to Bearing Fault Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-24 ◽  
Author(s):  
Junbo Long ◽  
Haibin Wang ◽  
Peng Li
Keyword(s):  
Spectral Analysis ◽  
Frequency Spectrum ◽  
Lower Order ◽  
Stable Distribution ◽  
Heavy Tails ◽  
Side Lobe ◽  
Fault Analysis ◽  
Outer Race ◽  
Bearing Fault ◽  
Analysis Methods

The traditional spectral analysis method is used to study the characteristics of bearing fault signals in frequency domain, which is reasonable and effective in general cases. However, it is proved that the fault signals have heavy tails in this paper, which are α stable distribution, and 1<α<2, and even the noises belong to α stable distribution. Then the conventional spectral analysis methods degenerate and even fail under α stable distribution environment. Several improved frequency spectral analysis methods are proposed employing fractional lower order covariation or fractional lower order covariance in this paper, including fractional lower order Blackman-Tukey covariation spectrum (FLOBTCS), fractional lower order periodogram covariation spectrum (FLOPCS), and fractional lower order welch covariation spectrum (FLOWCS). In order to suppress side lobe and improve resolution, we present novel fractional lower order autoregression (FLO-AR) and fractional lower order autoregressive moving average (FLO-ARMA) parameter model frequency spectrum methods, and the calculation steps are summarized. The proposed spectrum methods are compared with the existing methods based on second-order statistics under Gaussian and SαS distribution environments, and the results show that the new algorithms have better performance than the traditional methods. Finally, the improved methods are applied to estimate frequency spectrums of the normal and outer race fault signals, and it is demonstrated that they are effective for fault diagnosis.

Consistency of model selection and parameter estimation

1986 ◽  
Vol 23 (A) ◽  
pp. 127-141 ◽  
Author(s):  
Ritei Shibata
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Lower Order ◽  
Moving Average ◽  
Information Matrix ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
The Cost ◽  
The Relationship ◽  
Autoregressive Moving Average Models

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.

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