Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(3): 723-740

Published online May 1, 2021 https://doi.org/10.4134/JKMS.j200226

Copyright © The Korean Mathematical Society.

Estimation algorithm for physical parameters in a shallow arch

Semion Gutman, Junhong Ha, Sudeok Shon

University of Oklahoma; Korea University of Technology and Education; Korea University of Technology and Education

Abstract

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

Keywords: Shallow arch, parameter estimation, critical pairs, stability analysis, damping effect

MSC numbers: Primary 45M10, 74H55, 65Y10

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019R1F1A1058327)