Applied Condition Monitoring Volume 6 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: fakher.chaari@gmail.com Radoslaw Zimroz, Wrocław University of Technology, Poland
About this Series The book series Applied Condition Monitoring publishes the latest research and developments in the field of condition monitoring, with a special focus on industrial 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; oil analysis and tribology; acoustic emissions and ultrasonics; and motor current analysis. Books published in the series deal with root cause analysis, failure and degradation scenarios, proactive and predictive techniques, and many other aspects related to condition monitoring. Applications concern different industrial sectors: automotive engineering, power engineering, civil engineering, geoengineering, bioengineering, etc. The series publishes monographs, edited books, and selected conference proceedings, as well as textbooks for advanced students. More information about this series at http://www.springer.com/series/13418
Fakher Chaari Jacek Leskow Antonio Napolitano Radoslaw Zimroz Agnieszka Wylomanska Editors Cyclostationarity: Theory and Methods III Contributions to the 9th Workshop on Cyclostationary Systems and Their Applications, Grodek, Poland, 2016 123
Editors Fakher Chaari National School of Engineers of Sfax Sfax Tunisia Jacek Leskow Institute of Mathematics Cracow University of Technology Cracow Poland Antonio Napolitano Department of Engineering University of Napoli Parthenope Naples Italy Radoslaw Zimroz Institute of Mining Engineering Wrocław University of Technology Wrocław Poland Agnieszka Wylomanska Institute of Mathematics and Computer Science Wrocław University of Technology Wrocław Poland ISSN 2363-698X ISSN 2363-6998 (electronic) Applied Condition Monitoring ISBN 978-3-319-51444-4 ISBN 978-3-319-51445-1 (ebook) DOI 10.1007/978-3-319-51445-1 Library of Congress Control Number: 2017934545 Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part 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 dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this 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 herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents Weak Dependence: An Introduction Through Asymmetric ARCH Models... 1 P. Doukhan and N. Mtibaa Subsampling for Non-stationary Time Series with Long Memory and Heavy Tails Using Weak Dependence Condition... 17 Elżbieta Gajecka-Mirek and Oskar Knapik Change-Point Problem in the Fraction-Of-Time Approach... 35 Jacek Leśkow and Bartosz Stawiarski Seismic Signal Enhancement via AR Filtering and Spatial Time-Frequency Denoising... 51 Marta Polak, Jakub Obuchowski, Agnieszka Wyłomańska and Radosław Zimroz Transformed GARMA Model with the Inverse Gaussian Distribution... 69 Breno Silveira de Andrade, Jacek Leśkow and Marinho G. Andrade GARCH Process with GED Distribution.... 83 Małgorzata Wiśniewska and Agnieszka Wyłomańska A Residual Based Method for Fitting PAR Models Using Fourier Representation of Periodic Coefficients... 105 Harry Hurd Vectorial Periodically Correlated Random Processes and Their Covariance Invariant Analysis.... 121 I. Javorskyj, I. Matsko, R. Yuzefovych and O. Dzeryn Periodically Correlated Sequences with Rational Spectra and PARMA Systems.... 151 Andrzej Makagon v
vi Contents Fault Detection in Belt Conveyor Drive Unit via Multiple Source Data... 173 Piotr Kruczek, Jakub Sokołowski, Jakub Obuchowski, Mateusz Sawicki, Agnieszka Wyłomańska and Radosław Zimroz Application of Independent Component Analysis in Temperature Data Analysis for Gearbox Fault Detection.... 187 Jacek Wodecki, Pawel Stefaniak, Mateusz Sawicki and Radoslaw Zimroz Time-Frequency Identification of Nonlinear Phenomena for Mechanical Systems with Backlash... 199 Rafał Burdzik, Łukasz Konieczny, Jakub Młyńczak, Piotr Kruczek, Jakub Obuchowski and Maciej Zawisza Vibration Signal Processing for Identification of Relation Between Liquid Volume and Damping Properties in Hydraulic Dampers.... 213 Łukasz Konieczny, Rafał Burdzik, Jakub Młyńczak, Jakub Obuchowski, Piotr Kruczek and Dariusz Laskowski Modified Protrugram Method for Damage Detection in Bearing Operating Under Impulsive Load... 229 Piotr Kruczek and Jakub Obuchowski Use of Cyclostationarity Based Condition Indicators for Gear Fault Diagnosis Under Fluctuating Speed Condition... 241 Vikas Sharma and Anand Parey
Introduction It is our pleasure to present already third volume (time flies!) of the series dedicated to the cyclostationarity and applications. In recent years, there is a growing interest in modelling nonstationary signals and processes with cyclic patterns and our book is a response to that. As in the previous two volumes, we have included a wide range of papers: from quite theoretical dedicated to cyclostationary models to very applied papers studying various mechanical cyclical signals. More theoretically oriented papers are dedicated to such topics as: heavy tailed time series and processes, PAR models, rational spectra for PARMA processes, covariance invariant analysis, change point problems, subsampling for time series, fraction-of-time approach, GARMA models and weak dependence. In the present volume, there are published fifteen papers that can be divided into three groups. It should be mentioned that the groups are not separable and some articles could be classified to two or even three classes. The first group is devoted to strictly periodically correlated processes and time series. The reader can find theoretical investigations of PC models as well as their possible applications in mechanical systems. The special attention is paid to periodically autoregressive model (PARMA) and their special case PAR systems (A. Makagon and H. Hurd); however, one can find also the papers related to other processes which exhibit periodically correlated behaviour, like vectorial PC processes (I. Javors Kyj et al.). To this group, we also include the application-oriented articles where PC methodology is taken under consideration (A. Parey et al.). In the second group of papers, the reader can find the analysis of general class of stochastic processes and methods dedicated to them. In two papers, authors consider the heteroscedastic models (A. Wylomanska et al., P. Doukhan et al.); in the paper of B. Silveira de Andrade et al., the reader can find the examination of generalized autoregressive model (GARMA) with the inverse Gaussian distribution, while in M. Polak et al. paper, the autoregressive model is used in the de-noising process for seismic signals. The next two papers which belong to the second group contain statistical methods used in the analysis of nonstationary processes (J. Leskow et al., E. Gajecka-Mirek et al.). The third group includes applied studies of various mechanical systems by using stochastic and statistical methods, especially in the vii
viii Introduction context of damage detection. We highlight here the analysis of vibration signals (P. Kruczek et al., R. Burdzik et al., L. Konieczny et al.) and temperature data analysis (P. Kruczek, J. Sokolowski et al., J. Wodecki et al.). The number of papers dedicated to methods (8) and the number of papers dedicated to applications (7) represent a perfect balance we attempt to maintain throughout our meetings. Our annual meetings in a lovely small town of Grodek (80 km south-east from Krakow, Poland) are usually organized around two main topics: methods and applications. The meetings are attended by specialists that come from various countries and continents. In this volume, we present results of researchers from Europe (Poland, Ukraine and France), India, USA and Brazil. In our opinion, our series on cyclostationarity and applications is quite unique. We have succeeded in putting together mathematicians, statisticians and engineers working on cyclostationary models. And it works! We have been able to develop common language, similar approaches, complementary models and interesting applications. We hope that the reader will share our views and enthusiasm for that kind of an approach.