{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T05:48:06Z","timestamp":1768888086592,"version":"3.49.0"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,14]],"date-time":"2023-01-14T00:00:00Z","timestamp":1673654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2019YFE0105000"],"award-info":[{"award-number":["2019YFE0105000"]}]},{"name":"National Key Research and Development Program of China","award":["61973057"],"award-info":[{"award-number":["61973057"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2019YFE0105000"],"award-info":[{"award-number":["2019YFE0105000"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973057"],"award-info":[{"award-number":["61973057"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Actual industrial processes often exhibit multimodal characteristics, and their data exhibit complex features, such as being dynamic, nonlinear, multimodal, and strongly coupled. Although many modeling approaches for process fault monitoring have been proposed in academia, due to the complexity of industrial data, challenges remain. Based on the concept of multimodal modeling, this paper proposes a multimodal process monitoring method based on the variable-length sliding window-mean augmented Dickey\u2013Fuller (VLSW-MADF) test and dynamic locality-preserving principal component analysis (DLPPCA). In the offline stage, considering the fluctuation characteristics of data, the trend variables of data are extracted and input into VLSW-MADF for modal identification, and different modalities are modeled separately using DLPPCA. In the online monitoring phase, the previous moment\u2019s historical modal information is fully utilized, and modal identification is performed only when necessary to reduce computational cost. Finally, the proposed method is validated to be accurate and effective for modal identification, modeling, and online monitoring of multimodal processes in TE simulation and actual plant data. The proposed method improves the fault detection rate of multimodal process fault monitoring by about 14% compared to the classical DPCA method.<\/jats:p>","DOI":"10.3390\/s23020987","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T05:30:07Z","timestamp":1673847007000},"page":"987","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Fault Monitoring Based on the VLSW-MADF Test and DLPPCA for Multimodal Processes"],"prefix":"10.3390","volume":"23","author":[{"given":"Shu","family":"Wang","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yicheng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiarong","family":"Tong","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuqing","family":"Chang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/TIE.2014.2308133","article-title":"Data-Based Techniques Focused on Modern Industry: An Overview","volume":"62","author":"Yin","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.conengprac.2017.03.001","article-title":"Incipient Fault Detection with Smoothing Techniques in Statistical Process Monitoring","volume":"62","author":"Ji","year":"2017","journal-title":"Control. Eng. Pract."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4866","DOI":"10.1109\/TIE.2017.2668987","article-title":"Multimode Process Monitoring and Fault Detection: A Sparse Modeling and Dictionary Learning Method","volume":"64","author":"Peng","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.chemolab.2019.03.012","article-title":"Data-Driven Monitoring of Multimode Continuous Processes: A Review","volume":"189","author":"Verde","year":"2019","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Aldrich, C., and Auret, L. (2013). Unsupervised Process Monitoring and Fault Diagnosis with Machine Learning Methods, Springer.","DOI":"10.1007\/978-1-4471-5185-2"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fan, J., Wang, W., and Zhang, H. (2017, January 24\u201326). AutoEncoder Based High-Dimensional Data Fault Detection System. Proceedings of the 2017 IEEE 15th International Conference on Industrial Informatics (INDIN), Emden, Germany.","DOI":"10.1109\/INDIN.2017.8104910"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.chemolab.2014.01.009","article-title":"Fault-Relevant Principal Component Analysis (FPCA) Method for Multivariate Statistical Modeling and Process Monitoring","volume":"133","author":"Zhao","year":"2014","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.chemolab.2018.12.014","article-title":"Hybrid Independent Component Analysis (H-ICA) with Simultaneous Analysis of High-Order and Second-Order Statistics for Industrial Process Monitoring","volume":"185","author":"Zhang","year":"2019","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7009","DOI":"10.1021\/acs.iecr.7b00248","article-title":"Quality-Relevant Fault Monitoring Based on Locality-Preserving Partial Least-Squares Statistical Models","volume":"56","author":"Wang","year":"2017","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.ces.2003.09.012","article-title":"Nonlinear Process Monitoring Using Kernel Principal Component Analysis","volume":"59","author":"Lee","year":"2004","journal-title":"Chem. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0169-7439(95)00076-3","article-title":"Disturbance Detection and Isolation by Dynamic Principal Component Analysis","volume":"30","author":"Ku","year":"1995","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1002\/aic.690440712","article-title":"Multiscale PCA with Application to Multivariate Statistical Process Monitoring","volume":"44","author":"Bakshi","year":"1998","journal-title":"AIChE J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.psep.2016.01.015","article-title":"Ozone Measurements Monitoring Using Data-Based Approach","volume":"100","author":"Harrou","year":"2016","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear Dimensionality Reduction by Locally Linear Embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Balasubramanian, M., and Schwartz, E.L. (2002). The Isomap Algorithm and Topological Stability. Science, 295.","DOI":"10.1126\/science.295.5552.7a"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","article-title":"Laplacian Eigenmaps for Dimensionality Reduction and Data Representation","volume":"15","author":"Belkin","year":"2003","journal-title":"Neural Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.patcog.2011.05.014","article-title":"Supervised Optimal Locality Preserving Projection","volume":"45","author":"Wong","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1016\/j.jprocont.2012.06.008","article-title":"Local and Global Principal Component Analysis for Process Monitoring","volume":"22","author":"Yu","year":"2012","journal-title":"J. Process Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7696","DOI":"10.1021\/ie4039345","article-title":"Process Monitoring with Global\u2013Local Preserving Projections","volume":"53","author":"Luo","year":"2014","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wu, Y., Fu, Z., and Fei, J. (2020). Fault Diagnosis for Industrial Robots Based on a Combined Approach of Manifold Learning, Treelet Transform and Naive Bayes. Rev. Sci. Instrum., 91.","DOI":"10.1063\/1.5118000"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/S0967-0661(99)00038-6","article-title":"Real-Time Monitoring for a Process with Multiple Operating Modes","volume":"7","author":"Hwang","year":"1999","journal-title":"Control. Eng. Pract."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0959-1524(99)00063-3","article-title":"Performance Monitoring of a Multi-Product Semi-Batch Process","volume":"11","author":"Lane","year":"2001","journal-title":"J. Process Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.chemolab.2012.05.010","article-title":"A Novel Local Neighborhood Standardization Strategy and Its Application in Fault Detection of Multimode Processes","volume":"118","author":"Ma","year":"2012","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/j.compchemeng.2008.11.014","article-title":"An Adjoined Multi-Model Approach for Monitoring Batch and Transient Operations","volume":"33","author":"Ng","year":"2009","journal-title":"Comput. Chem. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"7025","DOI":"10.1021\/ie0497893","article-title":"Monitoring of Processes with Multiple Operating Modes through Multiple Principle Component Analysis Models","volume":"43","author":"Zhao","year":"2004","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/j.jprocont.2005.12.002","article-title":"Performance Monitoring of Processes with Multiple Operating Modes through Multiple PLS Models","volume":"16","author":"Zhao","year":"2006","journal-title":"J. Process Control"},{"key":"ref_27","unstructured":"Kosanovich, K.A., Piovoso, M.J., Dahl, K.S., MacGregor, J.F., and Nomikos, P. (July, January 29). Multi-Way PCA Applied to an Industrial Batch Process. Proceedings of the 1994 American Control Conference\u2014ACC \u201994, Baltimore, MD, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1021\/ie9502594","article-title":"Improved Process Understanding Using Multiway Principal Component Analysis","volume":"35","author":"Kosanovich","year":"1996","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1021\/ie102048f","article-title":"Multimode Process Monitoring Based on Mode Identification","volume":"51","author":"Tan","year":"2012","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Marx, B.D. (1992). A User\u2019s Guide to Principal Components. J. Am. Stat. Assoc., 87.","DOI":"10.2307\/2290670"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/j.compbiomed.2006.09.002","article-title":"An Automated Feature Extraction and Emboli Detection System Based on the PCA and Fuzzy Sets","volume":"37","author":"Xu","year":"2007","journal-title":"Comput. Biol. Med."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"113988","DOI":"10.1109\/ACCESS.2019.2935117","article-title":"Time\u2013Frequency Feature Extraction of Acoustic Emission Signals in Aluminum Alloy MIG Welding Process Based on SST and PCA","volume":"7","author":"He","year":"2019","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"102","DOI":"10.4316\/aece.2010.03017","article-title":"PCA Fault Feature Extraction in Complex Electric Power Systems","volume":"10","author":"Zhang","year":"2010","journal-title":"AECE"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1049\/iet-its.2018.5215","article-title":"Kernel PCA for Road Traffic Data Non-linear Feature Extraction","volume":"13","author":"Peng","year":"2019","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1177\/0954410016638874","article-title":"A Novel Method for Spacecraft Electrical Fault Detection Based on FCM Clustering and WPSVM Classification with PCA Feature Extraction","volume":"231","author":"Li","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"He, Q., Ding, X., and Pan, Y. (2014). Machine Fault Classification Based on Local Discriminant Bases and Locality Preserving Projections. Math. Probl. Eng., 2014.","DOI":"10.1155\/2014\/923424"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Lv, Y., Yuan, R., and Shi, W. (2018). Fault Diagnosis of Rotating Machinery Based on the Multiscale Local Projection Method and Diagonal Slice Spectrum. Appl. Sci., 8.","DOI":"10.3390\/app8040619"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Luo, H., Tang, Y.Y., Li, C., and Yang, L. (2015). Local and Global Geometric Structure Preserving and Application to Hyperspectral Image Classification. Math. Probl. Eng., 2015.","DOI":"10.1155\/2015\/917259"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Zhu, X., Zhao, J., and Xu, H. (2011, January 14\u201317). Image Retrieval Based on PCA-LPP. Proceedings of the 2011 10th International Symposium on Distributed Computing and Applications to Business, Engineering and Science, Wuxi, China.","DOI":"10.1109\/DCABES.2011.52"},{"key":"ref_40","unstructured":"Zhang, E.-H., Ma, H.-B., Lu, J.-W., and Chen, Y.-J. (2009, January 12\u201315). Gait Recognition Using Dynamic Gait Energy and PCA+LPP Method. Proceedings of the 2009 International Conference on Machine Learning and Cybernetics, Baoding, China."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Yang, Q., Ba, C., Li, C., and Wu, D. (2017, January 22\u201325). An Ensemble Fault Diagnosis Approach for Multimodal Process. Proceedings of the 2017 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xiamen, China.","DOI":"10.1109\/ICSPCC.2017.8242383"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4490","DOI":"10.1016\/j.csda.2009.07.008","article-title":"Modified Fast Double Sieve Bootstraps for ADF Tests","volume":"53","author":"Richard","year":"2009","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Worden, K., Iakovidis, I., and Cross, E.J. (2021). New Results for the ADF Statistic in Nonstationary Signal Analysis with a View towards Structural Health Monitoring. Mech. Syst. Signal Process., 146.","DOI":"10.1016\/j.ymssp.2020.106979"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1007\/s00362-017-0911-y","article-title":"Lag Truncation and the Local Asymptotic Distribution of the ADF Test for a Unit Root","volume":"60","author":"Aylar","year":"2019","journal-title":"Stat. Pap."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"13713","DOI":"10.1016\/j.ifacol.2020.12.875","article-title":"Exergy-Based Fault Detection on the Tennessee Eastman Process","volume":"53","author":"Vosloo","year":"2020","journal-title":"IFAC-Pap. Line"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Chen, D., Li, Z., and He, Z. (2013, January 25\u201327). Research on Fault Detection of Tennessee Eastman Process Based on PCA. Proceedings of the 2013 25th Chinese Control and Decision Conference (CCDC), Guiyang, China.","DOI":"10.1109\/CCDC.2013.6561084"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Li, H., and Xiao, D. (2011). Fault Diagnosis of Tennessee Eastman Process Using Signal Geometry Matching Technique. EURASIP J. Adv. Signal Process., 2011.","DOI":"10.1186\/1687-6180-2011-83"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jprocont.2021.05.007","article-title":"Monitoring Multimode Processes: A Modified PCA Algorithm with Continual Learning Ability","volume":"103","author":"Zhang","year":"2021","journal-title":"J. Process Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/2\/987\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:06:24Z","timestamp":1760119584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/2\/987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,14]]},"references-count":48,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23020987"],"URL":"https:\/\/doi.org\/10.3390\/s23020987","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,14]]}}}