On Nonparametric Modelling of Multidimensional Noninertial Systems with Delay

We consider the problem of noninertial objects identification under nonparametric uncertainty when a priori information about the parametric structure of the object is not available. In many applications there is a situation, when measurements of various output variables are made through significant period of time and it can substantially exceed the time constant of the object. In this context, we must consider the object as the noninertial with delay. In fact, there are two basic approaches to solve problems of identification: one of them is identification in 'narrow' sense or parametric identification. However, it is natural to apply the local approximation methods when we do not have enough a priori information to select the parameter structure. These methods deal with qualitative properties of the object. If the source data of the object is sufficiently representative, the nonparametric identification gives a satisfactory result but if there are 'sparsity' or 'gaps' in the space of input and output variables the quality of nonparametric models is significantly reduced. This article is devoted to the method of filling or generation of training samples based on current available information. This can significantly improve the accuracy of identification of nonparametric models of noninertial systems with delay. Conducted computing experiments have confirmed that the quality of nonparametric models of noninertial systems can be significantly improved as a result of original sample 'repair'. At the same time it helps to increase the accuracy of the model at the border areas of the process input-output variables definition.

Keywords

nonparametric identification; data analysis; computational modelling.

References

1. Medvedev A.V. Osnovy teorii adaptivnyh sistem [Fundamentals of the Theory of Adaptive Systems]. Krasnoyarsk, Sibirskiy gosudarstvennyy aerokosmicheskiy universitet, 2015.
2. Zagoruyko N.G. Prikladnye metody analiza dannykh i znaniy [Applied Methods of Data and Knowledge Analysis]. Novosibirsk, Sobolev Institute of Mathematics, 1999.
3. Tsypkin Ja.Z. Osnovy informatsionnoy teorii indentifikatsii [The Foundation of Information Identification Theory]. Moscow, Nauka, 1984.
4. Eykhoff P. System Identification Parameter and State Estimation. London, N.-Y., Sydney, Toronto, Wiley, 1975.
5. Vasilev V.A., Dobrovidov A.V., Koshkin G.M. Neparametricheskoe otsenivanie funktsionalov ot raspredeleniy statsionarnykh posledovatel'nostey [Nonparametric Estimation of Functionals of Distributions of Stationary Sequences]. Moscow, Nauka, 2004.
6. Hardle V. Applied Nonparametric Regression. Cambridge, Cambridge University Press, 1990. DOI: 10.1017/CCOL0521382483
7. Katkovnik V.Ya. Neparametricheskaya identifikatsiya i sglazhivanie dannykh: metod lokal'noy approksimatsii [Non-Parametric Identification and Data Smoothing: Local Approximation Method]. Moscow, Nauka, 1985.
8. Nadaraya E.A. Neparametricheskie otsenki plonosti veroyatnosti i krivoy [Non-Parametric Estimation of the Probability Density and the Regression Curve]. Tbilisi, Tbilisi University, 1983.
9. Bradley E. Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 1979, vol. 7, no. 1, pp. 1-26. DOI: 10.1214/aos/1176344552
10. Garcia-Soidan P., Menezes R., Rubinos O. Bootstrap Approaches for Spatial Data. Stochastic Environmental Research and Risk Assessment, 2014, no. 28, pp. 1207-1219. DOI: 10.1007/s00477-013-0808-9
11. Loh J., Stein M.L. Spatial Bootstrap with Increasing Observations in a Fixed Domain. Statistica Sinica, 2008, vol. 18, no 2, pp. 667-688.
12. Medvedev A.V. Neparametricheskie sistemy adaptacii [Nonparametric Adaptation Systems]. Novosibirsk, Nauka, 1983.