Баранов С.Н. доктор физико-математических наук, генеральный директор компании ООО «Русское авиационное общество», Москва, Россия e-mail: firstname.lastname@example.org
Юрьев Г.А. кандидат физико-математических наук, доцент, заведующий научной лабораторией, Московский государственный психолого-педагогический университет, Москва, Россия ORCID: https://orcid.org/0000-0002-2960-6562 e-mail: email@example.com
Under consideration are technologies for synthesis and identification of trained hidden Markov models based on a novel statistical technique and applied in condition monitoring. The approach can be used for both con-tinuous-and discrete-time models of technical and non-technical systems. An initial rough model results from statistical multivariate analysis of observed data or their analysis by means of Kohonen self-organizing feature maps. Then it suffers proper corrections. Histograms of observed frequencies of being in different system states after the given exploitation periods are employed to train the constructed models. Free network parameters are identified by the chi-square minimum method.
Acoustic loads are the most dangerous for thin-walled aircraft structures.
These loads are wide-band (up to 5000 Hz) random process, with level varying
from 145 dB to 170 dB in different points of aircraft surface.
In practice, destructiveness of these structures can be estimated by the
changes of distributed structure stiffness, which is, in its turn, recognized
by the qualitative changes of normalized spectral structure characteristics
measured in checkpoints.
Baranov S.N. and Kuravsky L.S., “Acoustic vibrations: modeling,
optimization and diagnostics”, 2nd Edition, enlarged, Moscow: RUSAVIA, 224 pp,
Baum L.E., Petrie T., Soules G., and Weiss N., “A maximization
technique occurring in the statistical analysis of probabilistic functions of
Markov chains”, Ann. Math. Statist., Vol 41, No 1, pp 164–171, 1970.
Bendat J.S. and Piersol A.G., “Random data. Analysis and
measurement procedures”, New York: John Wiley & Sons, 1986.
Bishop Y.M.M., Fienberg S.E., and Holland P.W., “Discrete
multivariate analysis: Theory and practice”, Cambridge, MA: M. I. T. Press,
Bogdanoff J.L. and Kozin F., “Probabilistic Models of Cumulative
Damage”, New York: John Wiley & Sons, 1985.
Brousset C. and Baudrillard G., “Neural network for automating
diagnosis in aircraft inspection”, Review of Progress in Quantitative
Nondestructive Evaluation (Ed. by D.O. Thompson and D.E. Chimenti), Plenum
Press, New York, Vol 12, pp 797–802, 1993.
Cramer H., “Mathematical methods of statistics”, Princeton:
Princeton University Press, 1946.
Kuravsky L.S. and Baranov S.N., “Application of neural networks
for diagnostics and forecasting of fatigue failures of thin-walled
structures”, Neurocomputers: Design and Applications, No 12, pp 47–63, 2001 (in
Kuravsky L.S. and Baranov S.N., “Condition monitoring of the
structures suffered acoustic fatigue failure and forecasting their service
life”, Proc. Condition Monitoring 2003, Oxford, United Kingdom, pp 256-279,
Kuravsky L.S. and Baranov S.N., “Discriminant networks to solve
diagnostics problems”, Neurocomputers: Design and Applications, No 8-9, pp
3–9, 2003 (in Russian).
Kuravsky L.S. and Baranov S.N., “Neural networks in fatigue damage
recognition: diagnostics and statistical analysis”, Proc. 11th International
Congress on Sound and Vibration, St.Petersburg, Russia, pp 2929–2944,
Kuravsky L.S. and Baranov S.N., “Synthesis of Markov networks for
forecasting fatigue failures”, Proc. Condition Monitoring 2003, Oxford, United
Kingdom, pp 76–91, July 2003.
Kuravsky L.S. and Baranov S.N., “The concept of multifactor Markov
networks and its application to forecasting and diagnostics of technical
systems”, Proc. Condition Monitoring 2005, Cambridge, United Kingdom, pp
111–117, July 2005.
Kuravsky L.S., Baranov S.N., and Malykh S.B., “Neural networks to
solve the problems of forecasting, diagnostics and data analysis”, Moscow:
RUSAVIA, 2003 (in Russian).
Lawley D.N. and Maxwell A.E., “Factor analysis as a statistical
method”, London: Butterworths, 1963.
Marple S.L., Jr., “Digital spectral analysis with applications”,
New Jersey: Prentice-Hall, 1987.
Pidaparti R.M.V. and Palakal M.J., “Neural network approach to
fatigue-crack-growth predictions under aircraft spectrum loadings”, Journal of
Aircraft, Vol 32, pp 825–831, 1995.
Rabiner L.R., “A tutorial on hidden Markov models and selected
applications in speech recognition”, Proc. IEEE, Vol 77, No 2, pp 257–286,
Viterbi A.J., “Error bounds for convolutional codes and an
asymptotically optimum decoding algorithm”, IEEE Transactions on Information
Theory, Vol 13, No 2, pp.260–269, 1967.