The spectral kurtosis: a useful tool for characterising non-stationary signals
TL;DR: A formalisation of the spectral kurtosis by means of the Wold–Cramer decomposition of “conditionally non-stationary” processes is proposed, which engenders many useful properties enjoyed by the SK.
About: This article is published in Mechanical Systems and Signal Processing.The article was published on 2006-02-01. It has received 974 citations till now.
Citations
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TL;DR: This tutorial is intended to guide the reader in the diagnostic analysis of acceleration signals from rolling element bearings, in particular in the presence of strong masking signals from other machine components such as gears.
1,858 citations
TL;DR: This communication describes a fast algorithm for computing the kurtogram over a grid that finely samples the ( f, Δ f ) plane and the efficiency of the algorithm is illustrated on several industrial cases concerned with the detection of incipient transient faults.
1,130 citations
TL;DR: In this article, the spectral kurtosis (SK) was used to detect and characterize nonstationary signals in the presence of strong masking noise and to detect incipient faults in rotating machines.
1,067 citations
TL;DR: In this article, the minimum entropy deconvolution (MED) technique was used to enhance the surveillance capability of the spectral kurtosis (SK) by using a spalled inner race bearing.
509 citations
TL;DR: In this paper, the authors proposed a method based on the kurtosis of the envelope spectrum amplitudes of the demodulated signal, rather than on the filter time signal, to detect transients with smaller signal-to-noise ratio comparing to the spectral kurtogram.
487 citations
References
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Book•
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
13,886 citations
Book•
01 Jan 2002
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
12,407 citations
01 Mar 1991
TL;DR: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher- order statistics to practical problems is demonstrated.
Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >
1,854 citations
TL;DR: In this article, the spectral kurtosis (SK) was used to detect and characterize nonstationary signals in the presence of strong masking noise and to detect incipient faults in rotating machines.
1,067 citations