Tsialiamanis, G. orcid.org/0000-0002-1205-4175 and Farrar, C.R. (2024) On the detection and quantification of nonlinearity via statistics of the gradients of a black-box model. In: Brake, M.R.W., Renson, L., Kuether, R.J. and Tiso, P., (eds.) Nonlinear Structures & Systems, Volume 1: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023. 41st IMAC, A Conference and Exposition on Structural Dynamics 2023, 13-16 Feb 2023, Austin, TX United States. Conference Proceedings of the Society for Experimental Mechanics Series (CPSEMS) . Springer Nature Switzerland , pp. 1-9. ISBN 9783031369988
Abstract
Detection and identification of nonlinearity is a task of high importance for structural dynamics. On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure. On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure. Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model selected for the current application is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some of which are nonlinear. More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column. Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for “more nonlinear” scenarios.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2024 The Society for Experimental Mechanics, Inc. This is an author-produced version of a paper subsequently published in Nonlinear Structures & Systems, Volume 1: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Structural health monitoring (SHM); Structural dynamics; Nonlinear dynamics; Machine learning; Neural networks |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Mechanical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Feb 2024 11:03 |
Last Modified: | 19 Jun 2024 00:13 |
Status: | Published |
Publisher: | Springer Nature Switzerland |
Series Name: | Conference Proceedings of the Society for Experimental Mechanics Series (CPSEMS) |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-031-36999-5_1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208829 |