{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T05:28:01Z","timestamp":1771478881344,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,24]],"date-time":"2015-04-24T00:00:00Z","timestamp":1429833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61273205"],"award-info":[{"award-number":["61273205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["FRF-SD-12-028A"],"award-info":[{"award-number":["FRF-SD-12-028A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Because of the importance of damage detection in manufacturing systems and other areas, many fault detection methods have been developed that are based on a vibration signal. Little work, however, has been reported in the literature on using a recurrence plot method to analyze the vibration signal for damage detection. In this paper, we develop a recurrence plot based fault detection method by integrating the statistical process control technique. The recurrence plots of the vibration signals are derived by using the recurrence plot (RP) method. Five types of features are extracted from the recurrence plots to quantify the vibration signals\u2019 characteristic. Then, the                                                    control chart, a multivariate statistical process control technique, is used to monitor these features. The     control chart technique, however, has the assumption that all the data should follow a normal distribution. The RP based     bootstrap control chart is proposed to estimate the control chart parameters. The performance of the proposed RP based     bootstrap control chart is evaluated by a simulation study and compared with other univariate bootstrap control charts based on recurrence plot features. A real case study of rolling element bearing fault detection demonstrates that the proposed fault detection method achieves a very good performance.<\/jats:p>","DOI":"10.3390\/e17052624","type":"journal-article","created":{"date-parts":[[2015,4,24]],"date-time":"2015-04-24T10:01:59Z","timestamp":1429869719000},"page":"2624-2641","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Recurrence Plot Based Damage Detection Method by Integrating                                                    Control Chart"],"prefix":"10.3390","volume":"17","author":[{"given":"Cheng","family":"Zhou","sequence":"first","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weidong","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2978","DOI":"10.1016\/j.jsv.2010.12.021","article-title":"Statistical Analysis of Brake Squeal Noise","volume":"330","author":"Oberst","year":"2011","journal-title":"J. Sound Vib"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1016\/j.jsv.2012.04.003","article-title":"Recurrence Analysis and Phase Space Reconstruction of Irregular Vibration in Friction Brakes: Signatures of Chaos in Steady Sliding","volume":"331","author":"Wernitz","year":"2012","journal-title":"J. Sound Vib"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5358","DOI":"10.3390\/e16105358","article-title":"Research and Development of a Chaotic Signal Synchronization Error Dynamics-based Ball Bearing Fault Diagnostor","volume":"16","author":"Kuo","year":"2014","journal-title":"Entropy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1006\/mssp.2000.1299","article-title":"Fault Diagnostics Using Statistical Change Detection in the Bispectral Domain","volume":"14","author":"Parker","year":"2000","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1061\/(ASCE)0733-9399(2000)126:7(677)","article-title":"Wavelet-based Approach for Structural Damage Detection","volume":"126","author":"Hou","year":"2000","journal-title":"J. Eng. Mech"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1088\/0964-1726\/10\/3\/304","article-title":"Damage Diagnosis Using Time Series Analysis of Vibration Signals","volume":"10","author":"Sohn","year":"2001","journal-title":"Smart Mater. Struct"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1006\/mssp.2001.1462","article-title":"Artificial Neural Network Based Fault Diagnostics of Rolling Element Bearings Using Time-domain Features","volume":"17","author":"Samanta","year":"2003","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1016\/j.ymssp.2011.10.016","article-title":"Mechanical Fault Diagnosis Based on Redundant Second Generation Wavelet Packet Transform, Neighborhood Rough Set and Support Vector Machine","volume":"28","author":"Li","year":"2012","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4040","DOI":"10.1016\/j.eswa.2009.10.002","article-title":"Vibration Based Fault Diagnosis of Monoblock Centrifugal Pump Using Decision Tree","volume":"37","author":"Sakthivel","year":"2010","journal-title":"Expert Syst. Appl"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1177\/1475921704047500","article-title":"Vibration Based Condition Monitoring: A Review","volume":"3","author":"Carden","year":"2004","journal-title":"Struct. Health Monit"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1063\/1.1667631","article-title":"Machine Failure Forewarning via Phase-space Dissimilarity Measures","volume":"14","author":"Hively","year":"2004","journal-title":"Chaos"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1209\/0295-5075\/4\/9\/004","article-title":"Recurrence Plots of Dynamical Systems","volume":"4","author":"Eckmann","year":"1987","journal-title":"Europhys. Lett"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.physrep.2006.11.001","article-title":"Recurrence Plots for the Analysis of Complex Systems","volume":"438","author":"Marwan","year":"2007","journal-title":"Phys. Rep"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1088\/0967-3334\/33\/9\/1399","article-title":"Self-organized Neural Network for the Quality Control of 12-lead ECG Signals","volume":"33","author":"Chen","year":"2012","journal-title":"Physiol. Meas"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.1109\/TCSI.2006.883155","article-title":"Recurrence Plot Based Approach to the Analysis of IP-network Traffic in terms of Assessing Nonstationary Transitions over Time","volume":"53","author":"Masugi","year":"2006","journal-title":"IEEE Trans. Circuits Syst"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1109\/TDEI.2008.4591218","article-title":"Recurrence Plot Analysis of Discharge Currents in Tracking Tests of Gamma-ray Irradiated Polymers","volume":"15","author":"Du","year":"2008","journal-title":"IEEE Trans. Dielectr. Electr. Insul"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1080\/10589750802570836","article-title":"Cracked Rotor Detection by Recurrence Plots","volume":"24","author":"Litak","year":"2009","journal-title":"Nondestruct. Test. Eva"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.ymssp.2004.08.007","article-title":"Damage Detection Using Multivariate Recurrence Quantification Analysis","volume":"20","author":"Nichols","year":"2006","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.physd.2007.07.004","article-title":"Using Invariants to Change Detection in Dynamical System with Chaos","volume":"237","author":"Tykierko","year":"2008","journal-title":"Physica D"},{"key":"ref_20","unstructured":"Eisenhart, .O. (1947). Selected Techniques of Statistical Analysis, Mcgraw-Hill. Chapter II."},{"key":"ref_21","unstructured":"Bajgier, S.M. (1992, January 22\u201324). The Use of Bootstrapping to Construct Limits on Control Charts. San Francisco, CA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/00224065.1995.11979577","article-title":"Statistical Process Control via the Subgroup Bootstrap","volume":"27","author":"Seppala","year":"1995","journal-title":"J. Qual. Technol"},{"key":"ref_23","unstructured":"Kantz, H., and Schreiber, T. (1997). Nonlinear Time Series Analysis, Cambridge University Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1103\/PhysRevA.33.1134","article-title":"Independent Coordinates for Strange Attractors from Mutual Information","volume":"33","author":"Fraser","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/S0167-2789(02)00586-9","article-title":"Influence of Observational Noise on the Recurrence Quantification Analysis","volume":"171","author":"Thiel","year":"2002","journal-title":"Physica D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0375-9601(92)90426-M","article-title":"Embeddings and Delays as Derived from Quantification of Recurrence Plots","volume":"171","author":"Zbilut","year":"1992","journal-title":"Phys. Lett. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"026702","DOI":"10.1103\/PhysRevE.66.026702","article-title":"Recurrence-plot-based Measures of Complexity and their Application to Heart-rate-variability Data","volume":"66","author":"Marwan","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1080\/07408170701880845","article-title":"Statistical Monitoring of Multistage Processes Based on Engineering Models","volume":"40","author":"Xiang","year":"2008","journal-title":"IIE Trans"},{"key":"ref_29","unstructured":"Montgomery, D.C. (2003). Introduction to Statistical Quality Control, Wiley. [5th]."},{"key":"ref_30","unstructured":"Available online: http:\/\/csegroups.case.edu\/bearingdatacenter\/home."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2624\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:15Z","timestamp":1760215515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2624"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,24]]},"references-count":30,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052624"],"URL":"https:\/\/doi.org\/10.3390\/e17052624","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,24]]}}}