Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques

Justin Jacobs; David Najera-Flores; Adam R. Brink; Tatiana Flanagan

doi:10.1007/978-3-030-76004-5_16

Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques

Justin Jacobs, David Najera-Flores, Adam R. Brink, Tatiana Flanagan

Spatial Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.

Original language	English
Title of host publication	Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021
Editors	Ramin Madarshahian, Francois Hemez
Publisher	Springer
Pages	135-143
Number of pages	9
ISBN (Print)	9783030760038
DOIs	https://doi.org/10.1007/978-3-030-76004-5_16
State	Published - 2022
Event	39th IMAC, A Conference and Exposition on Structural Dynamics, 2021 - Virtual, Online Duration: Feb 8 2021 → Feb 11 2021

Publication series

Name	Conference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)	2191-5644
ISSN (Electronic)	2191-5652

Conference

Conference	39th IMAC, A Conference and Exposition on Structural Dynamics, 2021
City	Virtual, Online
Period	02/8/21 → 02/11/21

Funding

Acknowledgments This work was funded by Sandia National Laboratories, which is a multi-mission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

Keywords

Continuous noise
Data assimilation
Discontinuous noise
Kalman filter
Nonlinear dynamics

Access to Document

10.1007/978-3-030-76004-5_16

Cite this

Jacobs, J., Najera-Flores, D., Brink, A. R., & Flanagan, T. (2022). Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques. In R. Madarshahian, & F. Hemez (Eds.), Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 (pp. 135-143). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-030-76004-5_16

Jacobs, Justin ; Najera-Flores, David ; Brink, Adam R. et al. / Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques. Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021. editor / Ramin Madarshahian ; Francois Hemez. Springer, 2022. pp. 135-143 (Conference Proceedings of the Society for Experimental Mechanics Series).

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abstract = "Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.",

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Jacobs, J, Najera-Flores, D, Brink, AR & Flanagan, T 2022, Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques. in R Madarshahian & F Hemez (eds), Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021. Conference Proceedings of the Society for Experimental Mechanics Series, Springer, pp. 135-143, 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, Virtual, Online, 02/8/21. https://doi.org/10.1007/978-3-030-76004-5_16

Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques. / Jacobs, Justin; Najera-Flores, David; Brink, Adam R. et al.
Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021. ed. / Ramin Madarshahian; Francois Hemez. Springer, 2022. p. 135-143 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Jacobs, Justin

AU - Najera-Flores, David

AU - Brink, Adam R.

AU - Flanagan, Tatiana

PY - 2022

Y1 - 2022

N2 - Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.

AB - Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.

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Jacobs J, Najera-Flores D, Brink AR, Flanagan T. Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques. In Madarshahian R, Hemez F, editors, Data Science in Engineering, Volume 9 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021. Springer. 2022. p. 135-143. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-030-76004-5_16

Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques

Abstract

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