Neural-based models ensemble for identification of the vibrating beam system

Krzysztof Patan, Maciej Patan, Piotr Balik
Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", PMLR 255:1-13, 2024.

Abstract

The paper provides an effective machine learning-based approach to model design and implementation for the transverse vibrations of the actuated cantilever beam under the regime of nonlinear loads. In particular, the problems of reconstruction of non-linear actuation and dynamics of the beam are separately covered based on available measurement data. Little is expected from input sequences, except for application-required spectral coverage. The idea is to decompose the whole system into a serial connection of a static non-linear subsystem representing electromagnetic actuation with inherent built-in magnetic hysteresis and a non-linear dynamic subsystem approximating the spatio-temporal dynamics of the vibrating beam. Then, both components can be independently modeled in terms of dedicated neural networks: static feedforward network with augmented inputs providing the information on the signal gradient for the first subsystem and the multimodel neural ensemble with dedicated data fusion rule for the latter. In this context, a novel method is proposed here, where all candidate models are evaluated first using historical data, and based on achieved results, a proper weight is assigned to each model pointing out its contribution to the final response of the model. Each candidate model was designed using a recurrent neural network. The proposed approach provides great flexibility in model design, leading to a very high accuracy of system state estimation. In addition, the networks to be used have at most two layers with internal feedback loops, offering competitively attractive complexity. The advantage of this data-driven machine learning scheme is that incomplete knowledge of the physical model can be efficiently recovered or exchanged with the properly gathered information from input-output measurements. A physically relevant real-world application is given to illustrate the potential of the new design in the form of dynamic displacement modeling for an actuated vibrating beam system.

Cite this Paper

BibTeX
@InProceedings{pmlr-v255-patan24a, title = {Neural-based models ensemble for identification of the vibrating beam system}, author = {Patan, Krzysztof and Patan, Maciej and Balik, Piotr}, booktitle = {Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"}, pages = {1--13}, year = {2024}, editor = {Coelho, Cecı́lia and Zimmering, Bernd and Costa, M. Fernanda P. and Ferrás, Luı́s L. and Niggemann, Oliver}, volume = {255}, series = {Proceedings of Machine Learning Research}, month = {20 Oct}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v255/main/assets/patan24a/patan24a.pdf}, url = {https://proceedings.mlr.press/v255/patan24a.html}, abstract = {The paper provides an effective machine learning-based approach to model design and implementation for the transverse vibrations of the actuated cantilever beam under the regime of nonlinear loads. In particular, the problems of reconstruction of non-linear actuation and dynamics of the beam are separately covered based on available measurement data. Little is expected from input sequences, except for application-required spectral coverage. The idea is to decompose the whole system into a serial connection of a static non-linear subsystem representing electromagnetic actuation with inherent built-in magnetic hysteresis and a non-linear dynamic subsystem approximating the spatio-temporal dynamics of the vibrating beam. Then, both components can be independently modeled in terms of dedicated neural networks: static feedforward network with augmented inputs providing the information on the signal gradient for the first subsystem and the multimodel neural ensemble with dedicated data fusion rule for the latter. In this context, a novel method is proposed here, where all candidate models are evaluated first using historical data, and based on achieved results, a proper weight is assigned to each model pointing out its contribution to the final response of the model. Each candidate model was designed using a recurrent neural network. The proposed approach provides great flexibility in model design, leading to a very high accuracy of system state estimation. In addition, the networks to be used have at most two layers with internal feedback loops, offering competitively attractive complexity. The advantage of this data-driven machine learning scheme is that incomplete knowledge of the physical model can be efficiently recovered or exchanged with the properly gathered information from input-output measurements. A physically relevant real-world application is given to illustrate the potential of the new design in the form of dynamic displacement modeling for an actuated vibrating beam system.} }
Endnote
%0 Conference Paper %T Neural-based models ensemble for identification of the vibrating beam system %A Krzysztof Patan %A Maciej Patan %A Piotr Balik %B Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications" %C Proceedings of Machine Learning Research %D 2024 %E Cecı́lia Coelho %E Bernd Zimmering %E M. Fernanda P. Costa %E Luı́s L. Ferrás %E Oliver Niggemann %F pmlr-v255-patan24a %I PMLR %P 1--13 %U https://proceedings.mlr.press/v255/patan24a.html %V 255 %X The paper provides an effective machine learning-based approach to model design and implementation for the transverse vibrations of the actuated cantilever beam under the regime of nonlinear loads. In particular, the problems of reconstruction of non-linear actuation and dynamics of the beam are separately covered based on available measurement data. Little is expected from input sequences, except for application-required spectral coverage. The idea is to decompose the whole system into a serial connection of a static non-linear subsystem representing electromagnetic actuation with inherent built-in magnetic hysteresis and a non-linear dynamic subsystem approximating the spatio-temporal dynamics of the vibrating beam. Then, both components can be independently modeled in terms of dedicated neural networks: static feedforward network with augmented inputs providing the information on the signal gradient for the first subsystem and the multimodel neural ensemble with dedicated data fusion rule for the latter. In this context, a novel method is proposed here, where all candidate models are evaluated first using historical data, and based on achieved results, a proper weight is assigned to each model pointing out its contribution to the final response of the model. Each candidate model was designed using a recurrent neural network. The proposed approach provides great flexibility in model design, leading to a very high accuracy of system state estimation. In addition, the networks to be used have at most two layers with internal feedback loops, offering competitively attractive complexity. The advantage of this data-driven machine learning scheme is that incomplete knowledge of the physical model can be efficiently recovered or exchanged with the properly gathered information from input-output measurements. A physically relevant real-world application is given to illustrate the potential of the new design in the form of dynamic displacement modeling for an actuated vibrating beam system.
APA
Patan, K., Patan, M. & Balik, P.. (2024). Neural-based models ensemble for identification of the vibrating beam system. Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", in Proceedings of Machine Learning Research 255:1-13 Available from https://proceedings.mlr.press/v255/patan24a.html.

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