Chapter 9 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 A Comparative Study of Feature Selection Methods for Wind Turbine Gearbox Bearing Fault Prognosis Feras Abla, Mohammad Hesam Soleimani-Babakamali, Sahabeddin Rifai, Ahmad Rababah, Shawn Sheng, Ertugrul Taciroglu, Serkan Kiranyaz, and Onur Avci Abstract This paper focuses on comparing two main approaches for selecting input and target features for training a normal behavior model (NMB) using wind turbines’ SCADA data. The NMB models aid in predicting gearbox failure in wind turbine structures. In the first approach, the target feature is excluded from the input features, and in the second approach, the NBM models are trained using lagged measurements of the target feature. Historical SCADA data from a wind farm are used in this study. The SCADA data are preprocessed and used to train four sequential artificial neural network long short-term memory (LSTM) models to predict the normal behavior of the target feature. The analysis of the errors between the predicted and measured output feature indicates that the first approach is more promising in failure prognosis, and the gearbox oil temperature is found to be the optimal target feature to foreshadow deterioration in components. Keywords SCADAdata · Wind Turbine · Prognosis Introduction The continuous monitoring of wind turbine (WT) components is critical for the early detection of potential failures. Operation and maintenance (O&M) of wind farms can account for a significant portion of their lifetime expenses, with some offshore projects reporting costs as high as 30% of the total expenditure [1]. To reduce these costs, condition-based maintenance FerasAbla · Sahabeddin Rifai · Ahmad Rababah Graduate Student, Department of Civil and Environmental Engineering, Engineering Sciences Building, 1306 Evansdale Drive, West Virginia University, Morgantown, WV 26506 Corresponding author: fa00060@mix.wvu.edu e-mail: sr00090@mix.wvu.edu; ayr00002@mix.wvu.edu Mohammad Hesam Soleimani-Babakamali Postdoctoral Research Associate, Department of Civil and Environmental Engineering, 5731K Boelter Hall, University of California, Los Angeles | UCLA, Los Angeles, CA 90095 e-mail: soleimanisam92@g.ucla.edu Shawn Sheng Senior Researcher Engineer, National Renewable Energy Laboratory (NREL), Golden, Colorado, 80401 e-mail: shawn.sheng@nrel.gov Ertugrul Taciroglu Department Chair, Department of Civil and Environmental Engineering, 5731K Boelter Hall, University of California, Los Angeles, UCLA, Los Angeles, CA 90095 e-mail: etacir@ucla.edu Serkan Kiranyaz Professor, Department of Electrical Engineering, Qatar University, Doha 2713, Qatar e-mail: mkiranyaz@qu.edu.qa OnurAvci, Assistant Professor, Department of Civil and Environmental Engineering, Engineering Sciences Building, 1306 Evansdale Drive, West Virginia University, Morgantown, WV 26506 e-mail: onur.avci@mail.wvu.edu © The Author(s), under exclusive license to River Publishers 2025 67 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 9
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