Chapter 15 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 Effective Structural Health Monitoring of Rotating Propellers using Asynchronous Neuromorphic Tracking Guillermo Toledo, Wyatt Saeger, Fernando Moreu, David Mascarenas, Christian Torres, and Jahsyel Rojas Structural Health Monitoring (SHM) of rotating propellers has been proved crucial by preventing catastrophic failure, detecting defects early, reducing costs through predictive maintenance and prolonging the lifespan of components. Current techniques for SHM of rotating propellers generally imply high cost, complex installation and configuration or limited effectiveness across different frequency ranges. This study aims to develop and evaluate an effective and efficient Structural Health Monitoring system for rotating propellers using asynchronous neuromorphic tracking. By leveraging advanced neuromorphic cameras and real-time data processing algorithms, the proposed system offers a novel approach to measure the vibrations of the propeller. Elements involved in the displacement data acquisition include Laser Doppler Vibrometer (LDV), scanning galvanometer and Dynamic Vision Sensor (DVS). Out of plane displacement is collected using LDV, which operates through a galvanometer that ensures the laser remains fixed on a specific point on the propeller. Realtime positional data of the propeller is acquired using a neuromorphic camera, which dynamically controls the galvanometer to maintain precision. This research provides a practical and efficient solution for real-time structural health monitoring, offering valuable insights for future engineering applications. Keywords Neuromorphic camera · Propeller SHM· Tachometer · DVS· Galvanometer · LDV Introduction Structural Health Monitoring (SHM) of rotating propellers is a critical component across various industries, including wind energy [1], aerospace [2], and marine [3] applications. Effective SHM plays an important role in preventing failures, detecting defects at early stages, and reducing maintenance costs through predictive strategies. The need for continuous monitoring is fundamental, particularly for high-speed rotating elements, where structural integrity is key to ensure operational safety and efficiency. Current SHM techniques, such as accelerometers [4], optical methods [5], and motor current analysis [6], present limitations. Accelerometers, while useful for dynamic behavior analysis, have a limited scope for complex or high-frequency vibrations, and their invasive installment can disrupt the dynamics they intent to measure [4]. Optical techniques, including Guillermo Toledo Department of Mechanical Engineering, Universidad Carlos III de Madrid, Legane´s, Madrid, Spain e-mail: guille03tnf@unm.edu Guillermo Toledo· Wyatt Saeger · Fernando Moreu · Christian Torres · Jahsyel Rojas Department of Civil, Construction and Environmental Engineering, The University of New Mexico, Albuquerque, NM, USA e-mail: guille03tnf@unm.edu; wsaeger@unm.edu; fmoreu@unm.edu; christian.torres55@upr.edu; jahsyel.rojas@upr.edu David Mascarenas Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: dmascarenas@lanl.gov Christian Torres Department of Electrical Engineering, The University of Puerto Rico-Mayagu¨ez, Mayagu¨ez, PR, USA e-mail: christian.torres55@upr.edu Jahsyel Rojas Department of Software Engineering, The University of Puerto Rico-Mayagu¨ez, Mayagu¨ez, PR, USA e-mail: jahsyel.rojas@upr.edu © The Author(s), under exclusive license to River Publishers 2025 123 Brian Damiano et al. (eds.), Structural Health Monitoring & Machine Learning, Vol. 12, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0157-3 15
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