Identification of structural parameters and boundary conditions using a minimum number of measurement points

doi:10.1007/s11709-020-0686-4

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (6) : 1331-1348 https://doi.org/10.1007/s11709-020-0686-4

RESEARCH ARTICLE

Identification of structural parameters and boundary conditions using a minimum number of measurement points

Ali KARIMPOUR, Salam RAHMATALLA(

)

Department of Civil and Environmental Engineering and Iowa Technology Institute, The University of Iowa, Iowa City, IA 52242, USA

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Abstract

This article proposes a novel methodology that uses mathematical and numerical models of a structure to build a data set and determine crucial nodes that possess the highest sensitivity. Regression surfaces between the structural parameters and structural output features, represented by the natural frequencies of the structure and local transmissibility, are built using the numerical data set. A description of a possible experimental application is provided, where sensors are mounted at crucial nodes, and the natural frequencies and local transmissibility at each natural frequency are determined from the power spectral density and the power spectral density ratios of the sensor responses, respectively. An inverse iterative process is then applied to identify the structural parameters by matching the experimental features with the available parameters in the myriad numerical data set. Three examples are presented to demonstrate the feasibility and efficacy of the proposed methodology. The results reveal that the method was able to accurately identify the boundary coefficients and physical parameters of the Euler-Bernoulli beam as well as a highway bridge model with elastic foundations using only two measurement points. It is expected that the proposed method will have practical applications in the identification and analysis of restored structural systems with unknown parameters and boundary coefficients.

Keywords structural model validation eigenvalue problem response surface inverse problems

Corresponding Author(s): Salam RAHMATALLA

Just Accepted Date: 20 November 2020 Online First Date: 28 December 2020 Issue Date: 12 January 2021

Cite this article:

Ali KARIMPOUR,Salam RAHMATALLA. Identification of structural parameters and boundary conditions using a minimum number of measurement points[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1331-1348.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0686-4
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I6/1331

Fig.1 Flow chart of the proposed authentic SMV process showing the eight stages and their components.

Fig.2 (a) The first model, a prismatic beam plus only rotational springs; (b) the second model, a prismatic beam plus both translational and rotational springs; (c) the third model, one span of a USA highway bridge (FHWA #33472).

Fig.3 2000 DOE obtained by the LHS technique and their correlation plots: (a) 500 samples of the first example with two system parameters; (b) 1000 samples of the second example with four system parameters; (c) 500 samples of the third example with six system parameters.

Fig.4 500 overlaid mode shapes of the first example and their statistical information for the three initial modes based on the normalized axis (x): (a) first mode shapes; (b) second mode shapes; (c) third mode shapes; (d) first mode statistics; (e) second mode statistics; (f) third mode statistics.

Fig.5 RSs of the first three pieces of modal information of the first example: (a) second mode global information normalized by first mode; (b) third mode global information normalized by first mode; (c) first mode local information MT₁; (d) second mode local information MT₂; (e) third mode local information MT₃.

Fig.6 Contour plot of the 2D domain to visualize the global and local feature intersections of the first example produced by one trial point: (a) unique domain by FGP= 0.01(1% range Criteria); (b) unique domain by FGP = 0.05(5% range criteria).

Fig.7 1000 overlaid mode shapes of the second example and their statistical information for the five initial modes based on the normalized axis (x): (a) the first mode shapes; (b) the second mode shapes; (c) the third mode shapes; (d) the fourth mode shapes; (e) the fifth mode shapes; (f) the first mode statistics; (g) the second mode statistics; (h) the third mode statistics; (i) the fourth mode statistics; (j) the fifth mode statistics.

Fig.8 Results of 1000 samples for the second example: (a) NFs variation; (b) MTs variation; (c) global information statistics; (d) local information statistics; (e) global feature bounds; (f) local feature bounds.

Fig.9 Parallel coordination plots of 1E6 samples produced by the DOE tool for the second example with FGP = 0.01; (a) whole I/O dataset plus two modes outputs; (b) selected global features by two modes; (c) selected local features by two modes; (d) whole I/O dataset plus three modes outputs; (e) selected global features by three modes; (f) selected local features by three modes; (g) whole I/O dataset plus four modes outputs; (h) selected global features by four modes; (i) selected local features by four modes.

Fig.10 First six initial bending modes of the bridge span and the contour plots of the STD of the mode shape history used to locate sensitive spots to construct MT_i: (a) first mode shape; (b) first mode STD; (c) second mode shape; (d) second mode STD; (e) third mode shape; (f) third mode STD; (g) fourth mode shape; (h) fourth mode STD; (i) fifth mode shape; (j) fifth mode STD; (k) sixth mode shape; (l) sixth mode STD.

Fig.11 Results for 500 samples of the third example: (a) NFs variation; (b) MTs variation; (c) global information statistics; (d) local information statistics; (e) global feature bounds; (f) local feature bounds.

Fig.12 Parallel coordination plots of 1E6 samples produced by the DOE tool for the third example with FGP = 0.01; (a) whole I/O dataset plus four modes outputs; (b) selected global features by four modes; (c) selected local features by four modes; (d) whole I/O dataset plus five modes outputs; (e) selected global features by five modes; (f) selected local features by five modes; (g) whole I/O dataset plus six modes outputs; (h) selected global features by six modes; (i) selected local features by six modes.

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