Chapter 29 Non-unique Estimates in Material Parameter Identification of Nonlinear FE Models Governed by Multiaxial Material Models Using Unscented Kalman Filtering Mukesh Kumar Ramancha, Ramin Madarshahian, Rodrigo Astroza, and Joel P. Conte Abstract Bayesian nonlinear finite element (FE) model updating using input and output measurements have emerged as a powerful technique for structural health monitoring (SHM), and damage diagnosis and prognosis of complex civil engineering systems. The Bayesian approach to model updating is attractive because it provides a rigorous framework to account for and quantify modeling and parameter uncertainty. This paper employs the unscented Kalman filter (UKF), an advanced nonlinear Bayesian filtering method, to update, using noisy input and output measurement data, a nonlinear FE model governed by a multiaxial material constitutive law. Compared to uniaxial material constitutive models, multiaxial models are typically characterized by a larger number of material parameters, thus requiring parameter estimation to be performed in a higher dimensional space. In this work, the UKF is applied to a plane strain FE model of Pine Flat dam (a concrete gravity dam on King’s River near Fresno, California) to update the time-invariant material parameters of the cap plasticity model, a three-dimensional non-smooth multi-surface plasticity concrete model, used to represent plain concrete behavior. This study considers seismic input excitation and utilizes numerically simulated measurement response data. Estimates of the multi-axial material model parameters (for the single material model used in this study) are non-unique. All sets of parameter estimates yield very similar and accurate seismic response predictions of both measured and unmeasured response quantities. Keywords Non-unique estimates · Bayesian parameter estimation · Unscented Kalman filter · Nonlinear FE model · Cap plasticity model · Concrete gravity dams 29.1 Introduction Finite element (FE) model updating is an important component of structural health monitoring (SHM) of complex civil engineering systems such as dams, buildings and bridges [1]. The system response measured using sensors mounted on the real system differs from the response predicted using a mechanics-based FE model, thus raising the need for model updating. The discrepancy between measured and FE predicted responses are mainly due to noisy input and output measurements, uncertainty in model parameters and model uncertainties (the selected model class does not contain the real structure) [2]. The current state-of-the-art in model updating involves updating the system state vector and the vector of unknown parameters of the FE model using measured input and output data. This is achieved by minimizing the error between the predicted and measured responses [3]. Once updated, the FE model acts as a digital twin (or cyber model) of the real system and can thus be used for structural health monitoring, damage diagnosis and prognosis purposes. The input and output measurements pertaining to structural/civil engineering systems are often noisy and sparse (not sufficient to completely determine the unknown state and parameter vector of the FE model). In such systems, there often exists a prior knowledge (or degree of belief), expressed as prior probability distribution, about the unknown parameter vector. For example, if the parameter of interest is “the tensile strength of concrete at a certain location of the structure”, then its nominal value can be used as a mean of the prior probability distribution of that parameter. In this regard, the M. K. Ramancha ( ) · R. Madarshahian · J. P. Conte Department of Structural Engineering, Jacobs School of Engineering, University of California, San Diego, La Jolla, CA, USA e-mail: mramanch@eng.ucsd.edu; jpconte@ucsd.edu R. Astroza Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_29 257
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