Bayesian System Identification and Structural Reliability

1. Bayesian System Identification and Structural Reliability Soheil Saadat, Research Associate Mohammad N. Noori, Professor & Head Department of Mechanical & Aerospace Engineering

2. Overview • Intelligent Parameter Varying (IPV) Technique • Bayesian System Identification (BSI) Technique and Structural Reliability • Research Directions

3. Parametric Non-parametric Find “optimal” parameters of a system using “white box” models Fully derived from the first principles “White box” “Black box” • Intelligent Parameter Varying (IPV) Technique Identification Techniques   Modeling Techniques

4. Identification Techniques Parametric Non-parametric Find “optimal” functional representation of a system using “black box” models Solely based on the recorded data “White box” “Black box” Modeling Techniques • Intelligent Parameter Varying (IPV) Technique 

5. Identification Techniques Parametric Non-parametric Combines the advantages of parametric and non-parametric techniques A mixture of “white box” and “black box” models “White box” “Black box” Modeling Techniques • Intelligent Parameter Varying (IPV) Technique IPV   “Gray box”

6. Advantages 1. Does not require a priori knowledge of system constitutive non-linearities 2. Finds “optimal” functional representation of system constitutive non-linearities 3. Can detect the presence, location, and time of damage • Intelligent Parameter Varying (IPV) Technique

7. Intelligent Parameter Varying (IPV) Technique

8. Intelligent Parameter Varying (IPV) Technique

9. Intelligent Parameter Varying (IPV) Technique Identified restoring forces

10. Intelligent Parameter Varying (IPV) Technique Identified restoring forces

11. The unknown model parameters are not “estimated” but their posterior probability distributions are calculated Thus, the estimated parameters are not point estimates but probability distributions, conditional on the given data The Baye’s theorem provides the mathematical procedure, where: • Bayesian System Identification (BSI) Technique Is an statistical approach to system identification that can be applied to a wide range of dynamic systems

12. Bayesian System Identification (BSI) Technique Normalizing constant The prior pdf of model parameters The likelihood function, reflects the contribution of the measured data DN in calculating the updated posterior pdf The posterior pdf of model parameters, conditional on the given data

13. Procedure 1. Select a model class and structure 2. Define prior pdf of model parameters 3. Define the likelihood function 4. Minimize the posterior pdf with respect to model parameters • Bayesian System Identification (BSI)

14. 2D truss structure • Bayesian System Identification (BSI)

15. Research Directions 1. Application of Bayesian system identification to aerospace structure 2. Health monitoring and damage detection of aerospace structures based on real-time Bayesian system identification 3. Adaptive structural reliability analysis of aerospace structures based on real-time Bayesian system identification