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Observability of modally reduced order models with unknown parameters

Maes, K., Chatzis, M.N., Vandebril, R., Lombaert, G.·2021·Mechanical Systems and Signal Processing
DOI 10.1016/j.ymssp.2020.106993
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Figures

Fig. 1 Side view (left) and cross section (right) of a simply supported steel beam, indicating the force u and possible response measurements locations ( a i : vertical acceleration i , d i : vertical displacement i ).
Fig. 1 Side view (left) and cross section (right) of a simply supported steel beam, indicating the force u and possible response measurements locations ( a i : vertical acceleration i , d i : vertical displacement i ).CC-BY-NC-ND · From the PDF
Fig. 2 (a) Amplitude and (b) phase of transfer functions H yu ( ω ) (200 modes, blue solid line), H ′ yu ( ω ) (4 modes, red dashed line), and H ′′ yu ( ω ) (4 modes with dummy mode correction, cyan dotted line) that relate displacement d 4 to force u . The contribution of the dummy mode is indicated by a black dashed line. The undamped natural frequencies are indicated by vertical dashed lines, the antiresonance frequencies of the full order model by vertical dotted lines.
Fig. 2 (a) Amplitude and (b) phase of transfer functions H yu ( ω ) (200 modes, blue solid line), H ′ yu ( ω ) (4 modes, red dashed line), and H ′′ yu ( ω ) (4 modes with dummy mode correction, cyan dotted line) that relate displacement d 4 to force u . The contribution of the dummy mode is indicated by a black dashed line. The undamped natural frequencies are indicated by vertical dashed lines, the antiresonance frequencies of the full order model by vertical dotted lines.CC-BY-NC-ND · From the PDF
Fig. 3 (a) Transfer function and (b) impulse response of a rectangular frequency domain window with ω l = 0 rad / s and ω u = 1000 × 2 π rad / s.
Fig. 3 (a) Transfer function and (b) impulse response of a rectangular frequency domain window with ω l = 0 rad / s and ω u = 1000 × 2 π rad / s.CC-BY-NC-ND · From the PDF
Fig. 4 4DOF shear building model considered in Example 3.1 and its mass, damping, and stiffness matrices.
Fig. 4 4DOF shear building model considered in Example 3.1 and its mass, damping, and stiffness matrices.CC-BY-NC-ND · From the PDF
Fig. 5 (a) Amplitude and (b) phase of transfer functions H yu ( ω ) (4 modes, blue solid line) and H ′′ yu ( ω ) (2 modes with dummy mode correction, cyan dotted line) that relate displacement x 4 to force u . The contribution of the dummy mode is indicated by a black dashed line. The undamped natural frequencies are indicated by vertical dashed lines, the antiresonance frequencies of the full order model by vertical dotted lines.
Fig. 5 (a) Amplitude and (b) phase of transfer functions H yu ( ω ) (4 modes, blue solid line) and H ′′ yu ( ω ) (2 modes with dummy mode correction, cyan dotted line) that relate displacement x 4 to force u . The contribution of the dummy mode is indicated by a black dashed line. The undamped natural frequencies are indicated by vertical dashed lines, the antiresonance frequencies of the full order model by vertical dotted lines.CC-BY-NC-ND · From the PDF
Fig. 6 Singular value spectrum of the observability matrix d O 5 for case 2, obtained using the numerical evaluation procedure discussed in Section 2.8 (blue circles) and obtained using a numerical evaluation in double precision (red squares).
Fig. 6 Singular value spectrum of the observability matrix d O 5 for case 2, obtained using the numerical evaluation procedure discussed in Section 2.8 (blue circles) and obtained using a numerical evaluation in double precision (red squares).CC-BY-NC-ND · From the PDF
Fig. 7 (a) The footbrigde in Wetteren, Belgium, (b) 3D view of the FE model developed in StaBIL, and (c) 3D view of the first calculated vertical bending mode of the side span ( f j = 2 . 76 Hz).
Fig. 7 (a) The footbrigde in Wetteren, Belgium, (b) 3D view of the FE model developed in StaBIL, and (c) 3D view of the first calculated vertical bending mode of the side span ( f j = 2 . 76 Hz).CC-BY-NC-ND · From the PDF
Fig. 8 Overview of the measurement setup for the Wetteren footbridge, with an indication of the applied (known) force u and the macro-strain measurements ϵ j .
Fig. 8 Overview of the measurement setup for the Wetteren footbridge, with an indication of the applied (known) force u and the macro-strain measurements ϵ j .CC-BY-NC-ND · From the PDF
Fig. 9 Amplitude of the transfer functions H yu ( ω ) (full order model, blue solid line), H ′ yu ( ω ) (MROM without quasi-static correction, red dashed line), and H ′′ yu ( ω ) (MROM with dummy mode correction, cyan dotted line) that relate macro-strain ϵ 1 to force u . The contribution of the torsional mode of the side span ( f j = 5 . 29 Hz) is indicated by a green dash-dotted line. The contribution of the dummy mode is indicated by a black dashed line.
Fig. 9 Amplitude of the transfer functions H yu ( ω ) (full order model, blue solid line), H ′ yu ( ω ) (MROM without quasi-static correction, red dashed line), and H ′′ yu ( ω ) (MROM with dummy mode correction, cyan dotted line) that relate macro-strain ϵ 1 to force u . The contribution of the torsional mode of the side span ( f j = 5 . 29 Hz) is indicated by a green dash-dotted line. The contribution of the dummy mode is indicated by a black dashed line.CC-BY-NC-ND · From the PDF

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Citations

Cites

  • Nonlinear controllability and observability

    Hermann, R., & Krener, A. (1977) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1977.1101601 · Cited by 2,374 · cited 1×

    “Most geometric observability methods build on the work of Hermann and Krener [3], which extends the observability test for linear systems to nonlinear analytical systems by developing the Observability Rank Condition (ORC) based on Lie algebra [4, 5].”
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Show all 1 references

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Metadata

Authors
Maes, K., Chatzis, M. N., Vandebril, R., & Lombaert, G.
Venue
Mechanical Systems and Signal Processing
Publisher
Elsevier BV
Published
2021-01
Volume
146
Pages
106993
ISSN
0888-3270
DOI
10.1016/j.ymssp.2020.106993
Cited by
15
References
1
Language
en
Licence
Funders
Fonds Wetenschappelijk Onderzoek

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