SYNTHESIS OF FAULT ESTIMATION OBSERVER, BASED ON SPECTRAL MIMO H2 OPTIMIZATION
Abstract
This paper is devoted to slowly varying additive fault detection with implementation of the observer-filter to be designed. Sensitivity of the observer to the external disturbance is to be minimized by the choice of its parameters. There are a lot of papers, devoted to fault detection issues, but such problems with initially given spectral features of external disturbances are not a subject of serious attention, in our opinion. External disturbances, which are considered in this research, can be presented as a sum of harmonic oscillations with given central frequency (sea wave disturbance) and a constant signal (ocean currents and wind). A suppression of the polyharmonical oscillations influence is considered as H2-optimization problem, which can be solved with application of the specific spectral approach in frequency domain. This approach is based on polynomial factorization that can improve computational effectiveness of the observer design procedures. This also guaranties nonuniqueness of the optimal solution that makes possible to provide integral action of the residual signal relatively to the external disturbance for the case when at least two sensors are used. The novel algorithm of adaptive fault estimation observer analytical synthesis is proposed and its effectiveness is demonstrated by the numerical example of the fault detection process with implementation of MATLAB package.
References
[2] Chen J., Patton R.J. Robust model-based fault diagnosis for dynamic systems. Springer Science & Business Media, 2012. Vol. 3.1.
[3] Witczak M. Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems: Analytical and Soft Computing Approaches. Springer Science & Business Media, 2013. Vol. 266. DOI: https://doi.org/10.1007/978-3-319-03014-2
[4] Zanoli S.M. et al. Application of Fault Detection and Isolation Techniques on an Unmanned Surface Vehicle (USV). IFAC Proceedings Volumes. 2012; 45(27):287-292. DOI: https://doi.org/10.3182/20120919-3-IT-2046.00049
[5] Wang Y., Ma X., Qian P. Wind turbine fault detection and identification through PCA-based optimal variable selection. IEEE Transactions on Sustainable Energy. 2018. p. 1-9. DOI: https://doi.org/10.1109/TSTE.2018.2801625
[6] Janssens O. et al. Convolutional neural network based fault detection for rotating machinery. Journal of Sound and Vibration. 2016; 377:331-345. DOI: https://doi.org/10.1016/j.jsv.2016.05.027
[7] Zhang W. et al. A deep convolutional neural network with new training methods for bearing fault diagnosis under noisy environment and different working load. Mechanical Systems and Signal Processing. 2018; 100:439-453. DOI: https://doi.org/10.1016/j.ymssp.2017.06.022
[8] Isermann R. Process fault detection based on modeling and estimation methods — A survey. Automatica. 1984; 20(4):387-404. DOI: https://doi.org/10.1016/0005-1098(84)90098-0
[9] Mohanty R., Pradhan A.K. Protection of Smart DC Microgrid with Ring Configuration using Parameter Estimation Approach. IEEE Transactions on Smart Grid. 2017. DOI: https://doi.org/10.1109/TSG.2017.2708743
[10] Wang Z., Shi P., Lim C.C. H−∕ H∞ fault detection observer in finite frequency domain for linear parameter-varying descriptor systems. Automatica. 2017; 86:38-45. DOI: https://doi.org/10.1016/j.automatica.2017.08.021
[11] Chadli M., Abdo A., Ding S.X. H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system. Automatica. 2013; 49(7):1996-2005. DOI: https://doi.org/10.1016/j.automatica.2013.03.014
[12] Su X. et al. Fault detection filtering for nonlinear switched stochastic systems. IEEE Transactions on Automatic Control. 2016; 61(5):1310-1315. DOI: https://doi.org/10.1109/TAC.2015.2465091
[13] Li H. et al. Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach. Automatica. 2014; 50(7):1825-1834. DOI: https://doi.org/10.1016/j.automatica.2014.04.006
[14] Wu L., Yao X., Zheng W.X. Generalized H2 fault detection for two-dimensional Markovian jump systems. Automatica. 2012; 48(8):1741-1750. DOI: https://doi.org/10.1016/j.automatica.2012.05.024
[15] Aliev F.A., Larin V.B., Naumenko K.I. Suncev V.I. Optimization of Linear Time-Invariant Control Systems. Kiev: Naukova dumka, 1978. 327 p. (In Russian)
[16] Aliev F.A., Larin V.B. Parametrization of sets of stabilizing controllers in mechanical systems. International Applied Mechanics. 2008; 44(6):599. DOI: https://doi.org/10.1007/s10778-008-0085-3
[17] Veremey E.I. Efficient Spectral Approach to SISO Problems of H2-Optimal Synthesis. Applied Mathematical Sciences. 2015; 9(79):3897-3909. DOI: https://doi.org/10.12988/ams.2015.54335
[18] Veremey E.I. H2-Optimal Synthesis Problem with Nonunique Solution. Applied Mathematical Sciences. 2016; 10(38):1891-1905. DOI: https://doi.org/10.12988/ams.2016.63120
[19] Veremey E.I. Dynamical correction of control laws for marine ships’ accurate steering. Journal of Marine Science and Application. 2014; 13(2):127-133. DOI: https://doi.org/10.1007/s11804-014-1250-1
[20] Veremej E.I. Medium-quadratic multi-purpose optimization. SPb.: Izdatel'stvo «Saint Petersburg State University», 2017. 408 p. (In Russian)
[21] Veremey E., Sotnikova M. Spectral Approach to H∞-Optimal SISO Synthesis Problem. WSEASTrans. Syst. Control. 2014; 9(43):415-424. DOI: https://doi.org/10.12988/ams.2015.54335
[22] Veremey E. Irregular H∞-optimization of control laws for marine autopilots. Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of VF Demyanov) (CNSA), 2017. IEEE, 2017. p. 1-4. DOI: https://doi.org/10.1109/CNSA.2017.7974028.
[23] Veremey E.I., Knyazkin Y.V. Spectral H2 fault estimation observer design based on allocation of the correction effect. Journal of Theoretical and Applied Information Technology. 2017; 95(12):2776-2782. Available at: http://www.jatit.org/volumes/Vol95No12/18Vol95No12.pdf (accessed 10.02.2018).
[24] Veremey E.I., Knyazkin Y.V. Spectral H-2 optimal correction of additive fault estimation observer. Proceedings of the 6th Seminar on Industrial Control Systems-Analysis, Modeling and Computation. EDP Sciences, 2016. DOI: https://doi.org/10.1051/itmconf/20160601005
[25] Veremey E.I., Smirnov M.N., Smirnova M.A. Synthesis of stabilizing control laws with uncertain disturbances for marine vessels. Proceedings of 2015 IEEE International Conference «Stability and Control Processes» in Memory of V.I. Zubov (SCP). 2015, p. 1-3. DOI: https://doi.org/10.1109/SCP.2015.7342219

This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication policy of the journal is based on traditional ethical principles of the Russian scientific periodicals and is built in terms of ethical norms of editors and publishers work stated in Code of Conduct and Best Practice Guidelines for Journal Editors and Code of Conduct for Journal Publishers, developed by the Committee on Publication Ethics (COPE). In the course of publishing editorial board of the journal is led by international rules for copyright protection, statutory regulations of the Russian Federation as well as international standards of publishing.
Authors publishing articles in this journal agree to the following: They retain copyright and grant the journal right of first publication of the work, which is automatically licensed under the Creative Commons Attribution License (CC BY license). Users can use, reuse and build upon the material published in this journal provided that such uses are fully attributed.