Chapter 3 Chapter 1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model Georgios Tsialiamanis and Charles R. Farrar Abstrac t 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. Keyword s Structural health monitoring (SHM) · Structural dynamics · Nonlinear dynamics · Machine learning · Neural networks 1.1 Introduction In the pursuit of making everyday life safer, humans have extensively tried to model the environment around them. Structures are an important part of the environment, in which humans live. They are man-made and should be safe throughout their lifetime. Structures are exposed to numerous environmental factors, which may cause them to fail. Moreover, during operation, structures are subjected to dynamic loads, which, in time, may cause failure. Such failures will most probably result in economic damage to society and may even result in loss of human lives. Therefore, for the purpose of maintaining structures safe, the field of structural health monitoring (SHM) [1] has emerged. G. Tsialiamanis ( ) Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: g.tsialiamanis@sheffield.ac.uk C. R. Farrar Engineering Institute, MS T-001, Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: farrar@lanl.gov © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_1 1 The Stress Relaxation Response of the Porcine Descending Aorta under Combined Normal and Torsional Loadings Luc Nguyen, Abdelrahman Youssef, Calvin Nguyen, Kirtan Patel, Jack Luce, Benjamin Tijerina, and Chandler C. Benjamin Abstract Understanding the mechanical properties of aortic tissue is crucial for improving future medical interventions related to cardiovascular diseases. Our group has previously investigated the uni-axial, bi-axial, and shear responses of the porcine thoracic aorta. In this study, we explore the stress relaxation of the porcine aorta under torsional shearing while maintaining a constant normal compressive load. Circular samples, measuring 0.5 inches in diameter, were extracted from the descending section of porcine thoracic aortas. Stress relaxation experiments were conducted at a constant shear strain ranging from 10 to 50% while maintaining a compressive strain ranging from 5 to 25%. We observed that the stress relaxation behavior differs between the normal and torsional shear directions. Results suggest that neither the normal or shear stress relaxation behavior of the porcine aorta is significantly influenced by the degree of compressive strain or shear strain applied. Keywords Stress relaxation· Creep· Aorta · Viscoelastic · Rheology Introduction A better framework for mechanical analysis of aortic tissue is needed to improve medical diagnosis and intervention. Current pathology for aortic diseases (such as aortic aneurysms, dissections, and stenosis) revolve around the determination of other diseases or genes that increase risk [16, 12, 20, 3]. However, the weakening of the tissue seen in aortic aneurysms and the rupture initiation seen in aortic dissections are clear signs that the pathology of aortic diseases needs to address mechanics. LucNguyen· Abdelrahman Youssef · Calvin Nguyen· Chandler C. Benjamin Department of Mechanical Engineering, Texas A&M University email: lucnguyen314@tamu.edu; abdelyoussef@tamu.edu; calvinnguyennn@tamu.edu; ccbenjamin@tamu.edu Kirtan Patel Department of Biomedical Sciences, Texas A&M University email: kpatel23@tamu.edu JackLuce Department of Biology, Texas A&M University email: jluce02@tamu.edu Benjamin Tijerina Department of Allied Health, Texas A&M University email: btijerina2@tamu.edu Chandler C. Benjamin School of Engineering Medicine, Texas A&M University Texas A&M University, College Station, TX, 77843 email: ccbenjamin@tamu.edu © The Author(s), under exclusive license to River Publishers 2025 19 Karen Kasza et al. (eds.), Mechanics of Biological Systems and Materials and the Mechanics of Composite, Hybrid & Multifunctional Materials, Vol. 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0829-9 3
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