Abstract
This paper proposes a novel improved LLE-based (local linear embedding) approach (TLLE) for solving the fault diagnosis problem of the nonlinear system. Firstly, tangent space distance is introduced to LLE approach, which can satisfy the local linearity of LLE and better preserve the local manifold features of the original data simultaneously. Then, to solve the problem of inner dimension in LLE approach is hard to estimate, the method of intrinsic dimension estimation based on fractal dimension is employed in the approach by means of linear fitting. Furthermore, a fault diagnosis scheme is presented based on the TLLE approach. We combine fault state with special distribution to complete the fault diagnosis, which can simplify the computation obviously and improve the real-time capability of the approach. Finally, numerical simulations of the TE process data are performed to illustrate the effectiveness of the proposed fault diagnosis scheme.
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Zhang, J., Swain, A.K., Nguang, S.K.: Robust Observer-Based Fault Diagnosis for Nonlinear Systems Using MATLAB. Springer, Switzerland (2016)
Gao, Z., Cecati, C., Ding, S.X.: A survey of fault diagnosis and fault-tolerant techniques: part i: fault diagnosis with model-based and signal-based approaches. IEEE Trans. Ind. Electron. 62(6), 3757–3767 (2015)
Hotelling, H.: Analysis of a complex of statistical variables into principal components. Br. J. Educ. Psychol. 24(6), 417–520 (1933)
Good, R.P., Kost, D., Cherry, G.A.: Introducing a unified PCA approach for model size reduction. IEEE Trans. Semicond. Manuf. 23(2), 201–209 (2010)
Scholkopf, B., Smola, A.J., Muller, K.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10(5), 1299–1319 (1998)
Ni, J., Zhang, C., Ren, L., Yang, S.X.: Abrupt event monitoring for water environment system based on KPCA and SVM. IEEE Trans. Instrum. Meas. 61(4), 980–989 (2012)
Yoshikazu, W.: Adaptive subset kernel principal component analysis for time-varying patterns. IEEE Trans. Neural Netw. Learn. Syst. 23(12), 1961–1973 (2012)
Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(22), 2323–2326 (2000)
Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Samuel, K., Martin, D.L.: Face Diagnosis in Gray Scale Images Using Locally Linear Embeddings. Elsevier, Amsterdam (2007)
Hadid, A., Koouropteva, O., Pietikainen, M.: Unsupervised learning using locally linear embedding: experiments with face pose analysis, pp. 111–114. In: Proceedings of the 16th International Conference on Pattern Recognition (2002)
Heureuxa, P.J., Carreaua, J., Bengioa, Y., Delalleaua, O., Yueb, S.Y.: Locally linear embedding for dimensionality reduction in QSAR. J. Comput. Aided Mol. Des. 18, 475–482 (2004)
Zhao, S., Zhu, S.A.: Face recognition by LLE dimensionality reduction. Fourth Int. Conf. Intell. Comput. Technol. Autom. 2011, 121–123 (2011)
Sun, B.Y., Zhang, X.M., Li, J., Mao, X.M.: Feature fusion using locally linear embedding for classification. IEEE Trans. Neural Netw. 21(1), 163–168 (2010)
Li, Z., Yan, X., Yuan, C., Zhao, J., Peng, Z.: A new method of nonlinear feature extraction for multi-fault diagnosis of rotor systems. Noise Vib. Worldw. 41(10), 29–37 (2010)
Ridder, D.D., Kouropteva, O., Okun, O.: Supervised Locally Linear Embedding, Joint International Conference on Artificial Neural Networks and Neural Information Processing, pp. 333–341. Springer, New York (2003)
Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. J. Mach. Learn. Res. 4(2), 119–155 (2003)
Hastie, T., Tibshirani, R.: Discriminant adaptive nearest-neighbor classification. IEEE Pattern Recognit. Mach. Intell. 243(18), 607–616 (1996)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990)
Min, W.L., Lu, L., He, X.F.: Locality pursuit embedding. Pattern Recognit. 37(4), 781–788 (2004)
K\(\acute{\rm {e}}\)gl, B.: Intrinsic dimension estimation using packing numbers, pp. 697–704. In: Advances in Neural Information Processing Systems (2002)
Grassbergel, J., Procacria, I.: Measuring the strangeness of strange attractor. Physical D 9, 189–208 (1983)
Bengio, Y., Vincent, P., Delalleau, O., Roux, N. L., Ouimet, M.: Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering, pp. 177–184. In: International Conference on Neural Information Processing Systems, MIT Press (2003)
Taylor, J.S., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Downs, J.J., Vogel, E.F.: Plant-wide industrial process control problem. Comput. Chem. Eng. 17(3), 245–255 (1993)
Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault Diagnosis and Diagnosis in Industrial Systems. Advanced Textbooks in Control and Signal Processing. Springer, London (2001)
Acknowledgements
This work is supported by National Natural Science Foundation of China under Grant 51505470 and 51605474, The State Key Laboratory of Robotics under Grant Y7C1200301.
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Zhang, W., Gao, S. & He, X. An improved LLE-based cluster security approach for nonlinear system fault diagnosis. Cluster Comput 22 (Suppl 3), 5663–5673 (2019). https://doi.org/10.1007/s10586-017-1450-y
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DOI: https://doi.org/10.1007/s10586-017-1450-y