Cyclostationarity: Theory and Methods - II: Contributions to the 7th Workshop on Cyclostationary Systems And Their Applications, Grodek, Poland, 2014 PDF
Preview Cyclostationarity: Theory and Methods - II: Contributions to the 7th Workshop on Cyclostationary Systems And Their Applications, Grodek, Poland, 2014
Applied Condition Monitoring Fakher Chaari · Jacek Leskow Antonio Napolitano · Radoslaw Zimroz Agnieszka Wylomanska · Anna Dudek Editors Cyclostationarity: Theory and Methods - II Contributions to the 7th Workshop on Cyclostationary Systems and Their Applications, Grodek, Poland, 2014 Applied Condition Monitoring Volume 3 Series editors Mohamed Haddar, National School of Engineers of Sfax, Tunisia Walter Bartelmus, Wrocław University of Technology, Poland Fakher Chaari, National School of Engineers of Sfax, Tunisia e-mail: [email protected] Radoslaw Zimroz, Wrocław University of Technology, Poland About this Series The book series Applied Condition Monitoring publishes the latest research and developmentsinthefieldofconditionmonitoring,withaspecialfocusonindustrial applications. It covers both theoretical and experimental approaches, as well as a range of monitoring conditioning techniques and new trends and challenges in the field. Topics of interest include, but are not limited to: vibration measurement and analysis;infrared thermography;oilanalysisandtribology;acoustic emissionsand ultrasonics;andmotorcurrentanalysis.Bookspublishedintheseriesdealwithroot cause analysis, failure and degradation scenarios, proactive and predictive tech- niques, and many other aspects related to condition monitoring. Applications con- cern different industrial sectors: automotive engineering, power engineering, civil engineering,geoengineering,bioengineering,etc.Theseriespublishesmonographs, edited books, and selected conference proceedings, as well as textbooks for advancedstudents. More information about this series at http://www.springer.com/series/13418 Fakher Chaari Jacek Leskow (cid:129) Antonio Napolitano Radoslaw Zimroz (cid:129) Agnieszka Wylomanska Anna Dudek (cid:129) Editors Cyclostationarity: Theory and Methods - II Contributions to the 7th Workshop on Cyclostationary Systems and Their Applications, Grodek, Poland, 2014 123 Editors Fakher Chaari Radoslaw Zimroz National Schoolof Engineersof Sfax Instituteof Mining Engineering Sfax Wrocław UniversityofTechnology Tunisia Wrocław Poland Jacek Leskow Instituteof Mathematics AgnieszkaWylomanska Cracow University ofTechnology Department of Mathematics Kraków Wrocław UniversityofTechnology Poland Wrocław Poland Antonio Napolitano Department of Engineering AnnaDudek Universityof Napoli“Parthenope” Department of AppliedMathematics Napoli Universityof Science andTechnology Italy Kraków Poland ISSN 2363-698X ISSN 2363-6998 (electronic) AppliedCondition Monitoring ISBN 978-3-319-16329-1 ISBN 978-3-319-16330-7 (eBook) DOI 10.1007/978-3-319-16330-7 LibraryofCongressControlNumber:2014930090 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com) Contents Simulation Study of Performance of MBB in Overall Mean Estimation Problem for APC Time Series. . . . . . . . . . . . . . . . . . . . . . 1 Anna E. Dudek and Jakub Uzar Parametric Estimation Problem for a Time Periodic Signal in a Periodic Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Khalil El Waled Damage Assessment of Rolling Element Bearing Using Cyclostationary Processing of AE Signals with Electromagnetic Interference . . . . . . . . 43 David Quezada Acuña and Cristián Molina Vicuña The Stochastic Recurrence Structure of Geophysical Phenomena. . . . . 55 I. Javors’kyj, R. Yuzefovych, I. Matsko and I. Kravets Influence of Different Signal Characteristics on PAR Model Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Agnieszka Wylomanska, Jakub Obuchowski, Radosław Zimroz and Harry Hurd Limiting Distributions for Explosive PAR(1) Time Series with Strongly Mixing Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Dominique Dehay PARMA Models with Applications in R. . . . . . . . . . . . . . . . . . . . . . . 131 Anna E. Dudek, Harry Hurd and Wioletta Wójtowicz Multidimensional Analysis of New Zealand Electricity Prices. . . . . . . . 155 Matylda Jabłońska-Sabuka and Agnieszka Wylomanska v vi Contents Imputation of Missing Observations for Heavy Tailed Cyclostationary Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Christiana Drake, Jacek Leskow and Aldo M. Garay The Dependence Structure for Symmetric α-stable CARMA(p,q) Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Agnieszka Wylomanska Introduction This book is designed for students, researchers and practitioners interested in the analysis of real datasets with nonstationary behaviour. The mentioned nonstation- aritycanbeexpressedindifferentways.Oneofthepropertiesoftheprocesswhich is strongly related to nonstationarity is the cyclostationarity. In the past decades cyclostationary processes have become very important from a practical point of view and their theoretical analysis has become a challenge for many research groups. For 7 years researchers from different centres are meeting in Gródek nad Dunajcem to analyse various aspects of practical applications and theoretical properties of nonstationary processes, especially with characteristics adequate to cyclostationary systems. The 7th Workshop on Cyclostationary Systems and Their Applications was organized during 9–12 February 2014 in Grodek nad Dunajcem (Poland). As each year, it gathered researches from Europe (France, Italy, Poland, Ukraine) and the USA. The main idea of this meeting was to bring together pure and applied researchers from different disciplines and start discussion on the possible cooper- ation in the field of the analysis and applications of cyclostationary systems. The main focus of the event was on the analysis of nonstationary signals with special importance to cyclostationary systems and their possible applications in various areas. The presentations covered recent theoretical developments for such systems and their possible applications. Periodically correlated (or cyclostationary) processes are random systems that exhibitperiodic behaviour butstill they remainrandom.Therefore, they are mixed of randomness and periodicity and are likely to have periodic or almost periodic structure. Over the last 60 years, thousands of papers in this field have been pub- lished and the class of processes which exhibits behaviour adequate to this phe- nomenon is very rich and is growing rapidly. The growing interest of researchers interestedinthisfieldiscausedbyavarietyofdifferentapplicationsinmanyareas like mechanics, vibroacoustics, economics, medicine … . Thus, understanding the needsofpractitionersandsimultaneouslypresentthemthenewtheoreticalresultsis the aim of the meetings devoted to cyclostationary systems. vii viii Introduction The chapters of this book can be divided into two groups. In the first group we can find various papers devoted to theoretical properties of cyclostationary models andprocesses.Mostofthesepapersarerelatedtoproblemsofestimationofsystems whichexhibitcyclostationary properties.The readercanfindthedescription ofthe procedureoffittingproperPARMA(periodicARMA)model,maintimeseriesused to description of cyclostationary processes as well as the theoretical aspects of parametricestimationforatime-periodicsignalwithaperiodicnoise.ThePARMA models(andtheirspecialcasePAR)arealsoexaminedinthecontextofthelimiting distribution of the appropriate coefficients. There is also a chapter in which the influence of different signal characteristics to PAR model stability is examined. In the group of chapters related to the theoretical aspects of cyclostationary models there is also a paper devoted to properties of estimators for main characteristics oftheannualanddailyrhythmicparametricmodel.Intwochapters,thereadercan findalsovariousaspectsofcyclostationarysystemswithheavy-taileddistributions. Intherecentyearsthesesystemsmorefrequentlyappearintheliteratureandcanbe regarded as an extension of the classical cyclostationary processes. The last paper whichcanbeassignedtothefirstgroupisdevotedtotheproblemofestimationfor almostperiodically(APC)timeseries.Inallofthementionedpapersthetheoretical results related to various problems adequate to cyclostationary systems are sup- ported by simulations or real data analysis. The second group of chapters is more applicable oriented. The reader can find here applications of cyclostationary char- acteristics for gearbox and bearing fault diagnosis as well as cyclostationary pro- cesses for damage assessment of rolling element bearing. The last paper contains the multidimensional analysis of ARMA models which are strongly related to the mentioned PARMA systems. The multidimensional time series are applied to the real data from the New Zealand electricity market. Simulation Study of Performance of MBB in Overall Mean Estimation Problem for APC Time Series AnnaE.DudekandJakubUzar 1 Introduction In this paper we focus on the class of nonstationary processes called almost periodicallycorrelated(APC).Timeseries{X ,t ∈Z}withfinitesecondmoments t is almost periodically correlated if it has an almost periodic mean and covariance functions.Thefunction f iscalledalmostperiodicifforeveryε >0,thereexistsa numberlε suchthatforanyintervaloflengthgreaterthanlε,thereexistsanumber pε inthisintervalsuchthat sup|f (t + pε)− f (t)|<ε. t∈Z Equivalently,almostperiodicfunctionscanbedefinedasuniformlimitsoftrigono- metricpolynomials.Formoredetailsandsomepropertiesofalmostperiodicfunc- tions we refer the reader to [2]. APC time series are frequently met in different settingse.g.vibroacoustics,communications,mechanics,signalprocessingandeco- nomics (see e.g. [1, 11, 14, 16]). However, modeling such data is not easy. The asymptoticvarianceisverydifficulttoestimateandinpracticeconstructionofthe confidenceintervalsfortheparametersofinterestisalmostimpossible.Intherecent years an alternative approach based on the resampling techniques was proposed. Thegeneralideaistosubstitutetheasymptoticquantilesbytheirbootstraporsub- samplingversions.BootstrapwasintroducedbyEfronin[9]andwasdesignedfor iiddata.Samplingwithreplacementobservationsfromtheoriginalsampleonegets its bootstrap counterparts that are used to approximate the sampling distribution. ThemostknownmodificationofIIDbootstrapfordependentdatacalledtheMov- ing Block Bootstrap (MBB) was proposed independently by Künsch in [12] and B A.E.Dudek ( )·J.Uzar AGHUniversityofScienceandTechnology,al.Mickiewicza30, 30-059Krakow,Poland e-mail:[email protected] ©SpringerInternationalPublishingSwitzerland2015 1 F.Chaarietal.(eds.),Cyclostationarity:TheoryandMethods-II, AppliedConditionMonitoring3,DOI10.1007/978-3-319-16330-7_1
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