A two-step method for analysis of linear systems with uncertain parameters driven by Gaussian noise |
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| Affiliation: | 1. Cornell University, Ithaca, NY 14853, USA;2. Sandia National Laboratories, Albuquerque, NM 87185-0346, USA;1. Department of Civil Engineering, King Mongkut’s University of Technology North Bangkok, Thailand;2. Department of Teacher Training in Civil Engineering, King Mongkut’s University of Technology North Bangkok, Thailand;3. Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand;1. Department of Computer Science and Artificial Intelligence, University of Granada, DICITS, iMUDS, DaSCI, 18071 Granada, Spain;1. Chung-Ang University, School of Energy Systems Engineering, Seoul, Republic of Korea;2. Kyoto University, Research Reactor Institute, Osaka, Japan |
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| Abstract: | A two-step method is proposed to find state properties for linear dynamic systems driven by Gaussian noise with uncertain parameters modeled as a random vector with known probability distribution. First, equations of linear random vibration are used to find the probability law of the state of a system with uncertain parameters conditional on this vector. Second, stochastic reduced order models (SROMs) are employed to calculate properties of the unconditional system state. Bayesian methods are applied to extend the proposed approach to the case when the probability law of the random vector is not available. Various examples are provided to demonstrate the usefulness of the method, including the random vibration response of a spacecraft with uncertain damping model. |
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| Keywords: | Bayesian analysis Monte Carlo simulation Random vibration Stochastic differential equations Stochastic reduced order models |
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