A Covariate-Regulated Sparse Subspace Learning Model and Its Application to Process Monitoring and Fault Isolation

References

• Astolfi, D., Castellani, F., and Terzi, L. (2014), “Fault Prevention and Diagnosis through SCADA Temperature Data Analysis of an Onshore Wind Farm,” Diagnostyka, 15, 71–78.
   Google Scholar
• Austin, P. C., and Steyerberg, E. W. (2015), “The Number of Subjects per Variable Required in Linear Regression Analyses,” Journal of Clinical Epidemiology, 68, 627–636. DOI: 10.1016/j.jclinepi.2014.12.014.
   PubMed Web of Science ®Google Scholar
• Bahadori, M. T., Kale, D., Fan, Y., and Liu, Y. (2015), “Functional Subspace Clustering with Application to Time Series,” in International Conference on Machine Learning, PMLR, pp. 228–237.
   Google Scholar
• Bauer, E., and Kohavi, R. (1999), “An Empirical Comparison of Voting Classification Algorithms: Bagging, Boosting, and Variants,” Machine Learning, 36, 105–139.
   Web of Science ®Google Scholar
• Boyd, S., Parikh, N., and Chu, E. (2011), Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Boston and Delft: Now Publishers Inc.
   Google Scholar
• Breiman, L. (1996), “Bagging Predictors,” Machine Learning, 24, 123–140. DOI: 10.1007/BF00058655.
   Web of Science ®Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32.
   Web of Science ®Google Scholar
• Breiman, L., Friedman, J., Stone, C. J., and Olshen, R. A. (1984), Classification and Regression Trees, Boca Raton, FL: CRC Press.
   Google Scholar
• Chiou, J.-M., and Müller, H.-G. (2014), “Linear Manifold Modelling of Multivariate Functional Data,” Journal of the Royal Statistical Society, Series B, 76, 605–626. DOI: 10.1111/rssb.12038.
   Google Scholar
• Chiu, T. Y., Leonard, T., and Tsui, K.-W. (1996), “The Matrix-Logarithmic Covariance Model,” Journal of the American Statistical Association, 91, 198–210. DOI: 10.1080/01621459.1996.10476677.
   Web of Science ®Google Scholar
• Ding, F., He, S., Jones, D. E., and Huang, J. Z. (2020), “Supervised Functional PCA with Covariate Dependent Mean and Covariance Structure,” arXiv preprint arXiv:2001.11425.
   Google Scholar
• Du, J., Cao, S., Hunt, J. H., Huo, X., and Shi, J. (2019a), “Optimal Shape Control via L∞ Loss for Composite Fuselage Assembly,” arXiv preprint arXiv:1911.03592.
   Google Scholar
• Du, J., Yue, X., Hunt, J. H., and Shi, J. (2019b), “Optimal Placement of Actuators via Sparse Learning for Composite Fuselage Shape Control,” Journal of Manufacturing Science and Engineering, 141, 101004. DOI: 10.1115/1.4044249.
   Web of Science ®Google Scholar
• Dubin, J. A. and Müller, H.-G. (2005), “Dynamical Correlation for Multivariate Longitudinal Data,” Journal of the American Statistical Association, 100, 872–881. DOI: 10.1198/016214504000001989.
   Web of Science ®Google Scholar
• Ebrahimi, S., Ranjan, C., and Paynabar, K. (2020), “Monitoring and Root-Cause Diagnostics of High-Dimensional Data Streams,” Journal of Quality Technology, 54, 20–43. DOI: 10.1080/00224065.2020.1805377.
   Web of Science ®Google Scholar
• EDP Open Data (2021), “SCADA Dataset of a Wind Farm from EDP Open Data,” Available at https://opendata.edp.com/pages/homepage/, Last accessed on 2021-07-03.
   Google Scholar
• Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” Annals of Statistics, 32, 407–499.
   Web of Science ®Google Scholar
• Elhamifar, E., and Vidal, R. (2013), “Sparse Subspace Clustering: Algorithm, Theory, and Applications,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 2765–2781. DOI: 10.1109/TPAMI.2013.57.
   PubMed Web of Science ®Google Scholar
• Fox, E. B., and Dunson, D. B. (2015), “Bayesian Nonparametric Covariance Regression,” The Journal of Machine Learning Research, 16, 2501–2542.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation with the Graphical Lasso,” Biostatistics, 9, 432–441. DOI: 10.1093/biostatistics/kxm045.
   PubMed Web of Science ®Google Scholar
• Friedman, J. H. (2017), The Elements of Statistical Learning: Data Mining, Inference, and Prediction, New York: Springer Open.
   Google Scholar
• Gibberd, A. J., and Nelson, J. D. (2017), “Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso,” Journal of Computational and Graphical Statistics, 26, 623–634. DOI: 10.1080/10618600.2017.1302340.
   Web of Science ®Google Scholar
• Guo, P., Infield, D., and Yang, X. (2011), “Wind Turbine Generator Condition-Monitoring using Temperature Trend Analysis,” IEEE Transactions on Sustainable Energy, 3, 124–133. DOI: 10.1109/TSTE.2011.2163430.
   Web of Science ®Google Scholar
• Hoff, P. D., and Niu, X. (2012), “A Covariance Regression Model,” Statistica Sinica, 22, 729–753. DOI: 10.5705/ss.2010.051.
   Web of Science ®Google Scholar
• Jiang, C.-R., and Wang, J.-L. (2010), “Covariate Adjusted Functional Principal Components Analysis for Longitudinal Data,” The Annals of Statistics, 38, 1194–1226. DOI: 10.1214/09-AOS742.
   Web of Science ®Google Scholar
• Johns, J., and Woolf, B. (2006), “A Dynamic Mixture Model to Detect Student Motivation and Proficiency,” in AAAI, pp. 163–168.
   Google Scholar
• Kolar, M., and Xing, E. (2011), “On Time Varying Undirected Graphs,” in Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, JMLR Workshop and Conference Proceedings, pp. 407–415.
   Google Scholar
• Kolar, M., and Xing, E. P. (2012), “Estimating Networks with Jumps,” Electronic Journal of Statistics, 6, 2069–2106. DOI: 10.1214/12-EJS739.
   PubMed Web of Science ®Google Scholar
• Li, C.-G., You, C., and Vidal, R. (2017), “Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework,” IEEE Transactions on Image Processing, 26, 2988–3001. DOI: 10.1109/TIP.2017.2691557.
   PubMed Web of Science ®Google Scholar
• Liaw, A., and Wiener, M. (2002), “Classification and Regression by RandomForest,” R News, 2, 18–22.
   Google Scholar
• Liebl, D. (2019), “Inference for Sparse and Dense Functional Data with Covariate Adjustments,” Journal of Multivariate Analysis, 170, 315–335. DOI: 10.1016/j.jmva.2018.04.006.
   Web of Science ®Google Scholar
• Liu, W. (2013), “Gaussian Graphical Model Estimation with False Discovery Rate Control,” The Annals of Statistics, 41, 2948–2978. DOI: 10.1214/13-AOS1169.
   Web of Science ®Google Scholar
• Liu, X., Du, J., and Ye, Z.-S. (2021), “A Condition Monitoring and Fault Isolation System for Wind Turbine based on SCADA Data,” IEEE Transactions on Industrial Informatics, 18, 986–995. DOI: 10.1109/TII.2021.3075239.
   Web of Science ®Google Scholar
• Long, H., Wang, L., Zhang, Z., Song, Z., and Xu, J. (2015), “Data-Driven Wind Turbine Power Generation Performance Monitoring,” IEEE Transactions on Industrial Electronics, 62, 6627–6635. DOI: 10.1109/TIE.2015.2447508.
   Web of Science ®Google Scholar
• Mason, R. L., Tracy, N. D., and Young, J. C. (1995), “Decomposition of T 2 for Multivariate Control Chart Interpretation,” Journal of Quality Technology, 27, 99–108. DOI: 10.1080/00224065.1995.11979573.
   Web of Science ®Google Scholar
• Meinshausen, N., and Bühlmann, P. (2006), “High-Dimensional Graphs and Variable Selection with the Lasso,” Annals of Statistics, 34, 1436–1462.
   Web of Science ®Google Scholar
• Parsons, L., Haque, E., and Liu, H. (2004), “Subspace Clustering for High Dimensional Data: A Review,” ACM SIGKDD Explorations Newsletter, 6, 90–105. DOI: 10.1145/1007730.1007731.
   Google Scholar
• Paynabar, K., Zou, C., and Qiu, P. (2016), “A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis,” Technometrics, 58, 191–204. DOI: 10.1080/00401706.2015.1042168.
   Web of Science ®Google Scholar
• Pourahmadi, M. (1999), “Joint Mean-Covariance Models with Applications to Longitudinal Data: Unconstrained Parameterisation,” Biometrika, 86, 677–690. DOI: 10.1093/biomet/86.3.677.
   Web of Science ®Google Scholar
• Qiao, X., Qian, C., James, G. M., and Guo, S. (2020), “Doubly Functional Graphical Models in High Dimensions,” Biometrika, 107, 415–431. DOI: 10.1093/biomet/asz072.
   Web of Science ®Google Scholar
• Shi, Y., and Chen, N. (2019), “Phase I Analysis of Hidden Operating Status for Wind Turbine,” in 2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, pp. 1007–1011. DOI: 10.1109/IEEM44572.2019.8978833.
   Google Scholar
• Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis (Vol. 26), Boca Raton, FL: CRC Press.
   Google Scholar
• Tautz-Weinert, J., and Watson, S. J. (2016), “Using SCADA Data for Wind Turbine Condition Monitoring–A Review,” IET Renewable Power Generation, 11, 382–394. DOI: 10.1049/iet-rpg.2016.0248.
   Web of Science ®Google Scholar
• Tierney, S., Gao, J., and Guo, Y. (2014), “Subspace Clustering for Sequential Data,” in Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pp. 1019–1026.
   Google Scholar
• Vidal, E. E. R. (2009), “Sparse Subspace Clustering,” in 2009 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (Vol. 6), pp. 2790–2797.
   Google Scholar
• Wang, K., and Jiang, W. (2009), “High-Dimensional Process Monitoring and Fault Isolation via Variable Selection,” Journal of Quality Technology, 41, 247–258. DOI: 10.1080/00224065.2009.11917780.
   Web of Science ®Google Scholar
• Wang, Y.-X., and Xu, H. (2013), “Noisy Sparse Subspace Clustering,” in International Conference on Machine Learning, PMLR, pp. 89–97.
   Google Scholar
• Wei, X., Sun, J., and Wang, X. (2007), “Dynamic Mixture Models for Multiple Time-Series.” in IJCAI (Vol. 7), pp. 2909–2914.
   Google Scholar
• Westerhuis, J. A., Gurden, S. P., and Smilde, A. K. (2000), “Generalized Contribution Plots in Multivariate Statistical Process Monitoring,” Chemometrics and Intelligent Laboratory Systems, 51, 95–114. DOI: 10.1016/S0169-7439(00)00062-9.
   Web of Science ®Google Scholar
• Xiang, D., Qiu, P., and Pu, X. (2013), “Nonparametric Regression Analysis of Multivariate Longitudinal Data,” Statistica Sinica, 23, 769–789. DOI: 10.5705/ss.2011.317.
   Web of Science ®Google Scholar
• Xu, R., Wu, J., Yue, X., and Li, Y. (2020), “Online Structural Change-point Detection of High-dimensional Streaming Data via Dynamic Sparse Subspace Learning,” arXiv preprint arXiv:2009.11713.
   Google Scholar
• Zhang, C., Yan, H., Lee, S., and Shi, J. (2018a), “Multiple Profiles Sensor-based Monitoring and Anomaly Detection,” Journal of Quality Technology, 50, 344–362. DOI: 10.1080/00224065.2018.1508275.
   Web of Science ®Google Scholar
• Zhang, C., Yan, H., Lee, S., and Shi, J. (2018b), “Weakly Correlated Profile Monitoring based on Sparse Multi-Channel Functional Principal Component Analysis,” IISE Transactions, 50, 878–891.
   Web of Science ®Google Scholar
• Zhang, C., Yan, H., Lee, S., and Shi, J. (2020), “Dynamic Multivariate Functional Data Modeling via Sparse Subspace Learning,” Technometrics, 63, 370–383.
   Web of Science ®Google Scholar
• Zhang, W., and Leng, C. (2012), “A Moving Average Cholesky Factor Model in Covariance Modelling for Longitudinal Data,” Biometrika, 99, 141–150. DOI: 10.1093/biomet/asr068.
   Web of Science ®Google Scholar
• Zhao, Y., Wang, B., Mostofsky, S. H., Caffo, B. S., and Luo, X. (2021), “Covariate Assisted Principal Regression for Covariance Matrix Outcomes,” Biostatistics, 22, 629–645. DOI: 10.1093/biostatistics/kxz057.
   PubMed Web of Science ®Google Scholar
• Zheng, Y., Mao, S., Liu, S., Wong, D. S.-H., and Wang, Y.-W. (2016), “Normalized Relative RBC-based Minimum Risk Bayesian Decision Approach for Fault Diagnosis of Industrial Process,” IEEE Transactions on Industrial Electronics, 63, 7723–7732. DOI: 10.1109/TIE.2016.2591902.
   Web of Science ®Google Scholar
• Zhou, S., Lafferty, J., and Wasserman, L. (2010), “Time Varying Undirected Graphs,” Machine Learning, 80, 295–319. DOI: 10.1007/s10994-010-5180-0.
   Web of Science ®Google Scholar
• Zou, C., Jiang, W., and Tsung, F. (2011), “A Lasso-based Diagnostic Framework for Multivariate Statistical Process Control,” Technometrics, 53, 297–309. DOI: 10.1198/TECH.2011.10034.
   Web of Science ®Google Scholar
• Zou, C., and Qiu, P. (2009), “Multivariate Statistical Process Control using LASSO,” Journal of the American Statistical Association, 104, 1586–1596. DOI: 10.1198/jasa.2009.tm08128.
   Web of Science ®Google Scholar