scholarly journals Alternative Measures of Dependence for Cyclic Behaviour Identification in the Signal with Impulsive Noise—Application to the Local Damage Detection

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1863
Author(s):  
Justyna Hebda-Sobkowicz ◽  
Jakub Nowicki ◽  
Radosław Zimroz ◽  
Agnieszka Wyłomańska
Keyword(s):  
Damage Detection ◽  
Impulsive Noise ◽  
Complex Case ◽  
Local Damage ◽  
Measures Of Dependence ◽  
Cyclic Behaviour ◽  
Dependence Measure ◽  
Alternative Measures ◽  
Heavy Tailed ◽  
Non Gaussian

The local damage detection procedures in rotating machinery are based on the analysis of the impulsiveness and/or the periodicity of disturbances corresponding to the failure. Recent findings related to non-Gaussian vibration signals showed some drawbacks of the classical methods. If the signal is noisy and it is strongly non-Gaussian (heavy-tailed), searching for impulsive behvaior is pointless as both informative and non-informative components are transients. The classical dependence measure (autocorrelation) is not suitable for non-Gaussian signals. Thus, there is a need for new methods for hidden periodicity detection. In this paper, an attempt will be made to use alternative measures of dependence used in time series analysis that are less known in the condition monitoring (CM) community. They are proposed as alternatives for the classical autocovariance function used in the cyclostationary analysis. The methodology of the auto-similarity map calculation is presented as well as a procedure for a “quality” or “informativeness” assessment of the map is proposed. In the most complex case, the most resistant to heavy-tailed noise turned out the proposed techniques based on Kendall, Spearman and Quadrant autocorrelations. Whereas in the case of the local fault disturbed by the Gaussian noise, the most efficient proved to be a commonly-known approach based on Pearson autocorrelation. The ideas proposed in the paper are supported by simulation signals and real vibrations from heavy-duty machines.

scholarly journals Measures of Dependence for α-Stable Distributed Processes and Its Application to Diagnostics of Local Damage in Presence of Impulsive Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Grzegorz Żak ◽  
Marek Teuerle ◽  
Agnieszka Wyłomańska ◽  
Radosław Zimroz
Keyword(s):  
Impulsive Noise ◽  
Complex Nature ◽  
Local Damage ◽  
Second Moment ◽  
Measures Of Dependence ◽  
Heavy Tailed Distributions ◽  
Noisy Observation ◽  
Alternative Measures ◽  
Heavy Tailed ◽  
A New Technique

Local damage detection in rotating machinery is simply searching for cyclic impulsive signal in noisy observation. Such raw signal is mixture of various components with specific properties (deterministic, random, cyclic, impulsive, etc.). The problem appears when the investigated process is based on one of the heavy-tailed distributions. In this case the classical measure can not be considered. Therefore, alternative measures of dependence adequate for such processes should be considered. In this paper we examine the structure of dependence of alpha-stable based systems expressed by means of two measures, namely, codifference and covariation. The reason for using alpha-stable distribution is simple and intuitive: signal of interest is impulsive so its distribution is heavy-tailed. The main goal is to introduce a new technique for estimation of covariation. Due to the complex nature of such vibration signals applying novel methods instead of classical ones is recommended. Classical algorithms usually are based on the assumption that theoretical second moment is finite, which is not true in case of the data acquired on the faulty components. Main advantage of our proposed algorithm is independence from second moment assumption.

Recent Developments in Vibration Based Diagnostics of Gear and Bearings Used in Belt Conveyors

2014 ◽  
Vol 683 ◽  
pp. 171-176 ◽  
Author(s):  
Jakub Obuchowski ◽  
Agnieszka Wylomańska ◽  
Radosław Zimroz
Keyword(s):  
Damage Detection ◽  
Signal To Noise Ratio ◽  
Mining Industry ◽  
Time Varying ◽  
Local Damage ◽  
Recent Developments ◽  
Specific Factors ◽  
Belt Conveyors ◽  
Non Gaussian ◽  
Short Time

Local damage detection in bearings/gearboxes is one of the most intensively explored problems in condition monitoring literature. Also for mechanical systems used in mining industry this issue might be critical due to short time local overloading of surfaces in contact in gear-pair or bearings that often happens during operation. In general, the problem of local damage detection is well defined in literature, however, specific factors related to the mining industry, require adaptation of existing methods or even developing new approaches. In the paper, some of the most promising techniques with mining machinery context are briefly re-called. The key problems identified for mining machines are: operation under time-varying load/speed conditions, presence of time varying signal to noise ratio and non-Gaussian noise (impulses that appear incidentally, randomly, not with expected cycle or cyclically, however with different cycle related to another damage). All these situations motivated us to find novel solution. The paper might be considered as brief review of recent achievements in the field rather that comprehensive, holistic description of the problem.

Bearings Fault Detection in Gas Compressor in Presence of High Level of Non-Gaussian Impulsive Noise

2013 ◽  
Vol 569-570 ◽  
pp. 473-480 ◽  
Author(s):  
Tomasz Barszcz ◽  
Radoslaw Zimroz ◽  
Jacek Urbanek ◽  
Adam Jabłoński ◽  
Walter Bartelmus
Keyword(s):  
Damage Detection ◽  
Impulsive Noise ◽  
Engineering Application ◽  
Time Domain Analysis ◽  
Time Frequency ◽  
Detection Techniques ◽  
Novel Approach ◽  
Non Gaussian ◽  
High Level ◽  
Envelope Spectrum

The paper deals with the local damage detection in rolling element bearings in presence of a high level non-Gaussian noise. In many theoretical signal processing papers and engineering application related to damage detection, a simple model of the vibration is assumed. Basically it consists of signal of interest (SOI) and some unwanted (deterministic and/or random) components masking SOI in acquired observation. So, damage detection problem has to concern filtering, decomposition or extraction issue. Unfortunately, in the most of the industrial systems mentioned unwanted sources are in fact not Gaussian, so many of de-noising techniques cannot be applied directly or at least might give unexpected results. In this paper an industrial example will be discussed and novel approach based on advanced cyclostationary-based technique will be proposed. In the paper disturbances include periodic impacts in reciprocating compressor on an oil rig. Existing classical detection techniques (statistics in time domain, analysis of envelope spectrum, time-frequency decompositions) are insufficient to perform the task due to high power of disturbance contribution in comparison to damage signature. In the proposed technique, the Spectral Coherence Density Map (SCDM) is estimated first. Next step is related to analysis of SCDM contents and selection of informative part. If informative and non-informative components lay in separate frequency regions, such selection should fix the problem immediately

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

scholarly journals Extended power-law scaling of air permeabilities measured on a block of tuff

2012 ◽  
Vol 16 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. Siena ◽  
A. Guadagnini ◽  
M. Riva ◽  
S. P. Neuman
Keyword(s):  
Power Law ◽  
Structure Functions ◽  
Self Similarity ◽  
Scaling Exponents ◽  
Multi Scale ◽  
Sample Structure ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Nonlinear Fashion ◽  
Extended Power

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

scholarly journals Robust Weighted l1,2 Norm Filtering in Passive Radar Systems

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3270 ◽  
Author(s):  
Baris Satar ◽  
Gokhan Soysal ◽  
Xue Jiang ◽  
Murat Efe ◽  
Thiagalingam Kirubarajan
Keyword(s):  
Target Detection ◽  
Impulsive Noise ◽  
Simulated Data ◽  
Real Data ◽  
Detection Performance ◽  
Passive Radar ◽  
Mobile Telecommunication ◽  
Telecommunication System ◽  
Conventional Methods ◽  
Non Gaussian

Conventional methods such as matched filtering, fractional lower order statistics cross ambiguity function, and recent methods such as compressed sensing and track-before-detect are used for target detection by passive radars. Target detection using these algorithms usually assumes that the background noise is Gaussian. However, non-Gaussian impulsive noise is inherent in real world radar problems. In this paper, a new optimization based algorithm that uses weighted l 1 and l 2 norms is proposed as an alternative to the existing algorithms whose performance degrades in the presence of impulsive noise. To determine the weights of these norms, the parameter that quantifies the impulsiveness level of the noise is estimated. In the proposed algorithm, the aim is to increase the target detection performance of a universal mobile telecommunication system (UMTS) based passive radars by facilitating higher resolution with better suppression of the sidelobes in both range and Doppler. The results obtained from both simulated data with α stable distribution, and real data recorded by a UMTS based passive radar platform are presented to demonstrate the superiority of the proposed algorithm. The results show that the proposed algorithm provides more robust and accurate detection performance for noise models with different impulsiveness levels compared to the conventional methods.

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