Bayesian statistics is a quintessential tool for model validation in many applications including smart materials, adaptive structures, and intelligent systems. It typically uses either experimental data or high-fidelity simulations to infer model parameter uncertainty of reduced order models due to experimental noise and homogenization of quantum or atomistic behavior. When heterogeneous data is available for Bayesian inference, open questions remain on appropriate methods to fuse data and avoid inappropriate weighting on individual data sets. To address this issue, we implement a Bayesian statistical method that begins with maximizing entropy. We show how this method can weight heterogeneous data automatically during the inference process through the error covariance. This Maximum Entropy (ME) method is demonstrated by quantifying uncertainty in 1) a ferroelectric domain structure model and 2) a finite deforming electrostrictive membrane model. The ferroelectric phase field model identifies continuum parameters from multiple density functional theory calculations. In the case of the electrostrictive membrane, parameters are estimated from both mechanical and electric displacement experimental measurements.
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ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
September 10–12, 2018
San Antonio, Texas, USA
Conference Sponsors:
- Aerospace Division
ISBN:
978-0-7918-5195-1
PROCEEDINGS PAPER
Application of the Maximum Entropy Method to Multifunctional Materials for Data Fusion and Uncertainty Quantification
Wei Gao,
Wei Gao
Florida State University, Tallahassee, FL
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William S. Oates,
William S. Oates
Florida State University, Tallahassee, FL
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Paul R. Miles,
Paul R. Miles
North Carolina State University, Raleigh, NC
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Ralph C. Smith
Ralph C. Smith
North Carolina State University, Raleigh, NC
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Wei Gao
Florida State University, Tallahassee, FL
William S. Oates
Florida State University, Tallahassee, FL
Paul R. Miles
North Carolina State University, Raleigh, NC
Ralph C. Smith
North Carolina State University, Raleigh, NC
Paper No:
SMASIS2018-7960, V002T08A003; 8 pages
Published Online:
November 14, 2018
Citation
Gao, W, Oates, WS, Miles, PR, & Smith, RC. "Application of the Maximum Entropy Method to Multifunctional Materials for Data Fusion and Uncertainty Quantification." Proceedings of the ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 2: Mechanics and Behavior of Active Materials; Structural Health Monitoring; Bioinspired Smart Materials and Systems; Energy Harvesting; Emerging Technologies. San Antonio, Texas, USA. September 10–12, 2018. V002T08A003. ASME. https://doi.org/10.1115/SMASIS2018-7960
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