1 September 4, 2003 Bayesian System Identification and Structural Reliability Soheil Saadat, Research Associate Mohammad N. Noori, Professor & Head Department of Mechanical & Aerospace Engineering

2 September 4, 2003 Overview 1.Intelligent Parameter Varying (IPV) Technique 2.Bayesian System Identification (BSI) Technique and Structural Reliability 3.Research Directions

3 September 4, Intelligent Parameter Varying (IPV) Technique Parametric Non-parametric “White box”“Black box” Find “optimal” parameters of a system using “white box” models Fully derived from the first principles Identification Techniques Modeling Techniques  

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

5 September 4, 2003 Parametric Non-parametric “White box”“Black box” Identification Techniques Modeling Techniques 1.Intelligent Parameter Varying (IPV) Technique “Gray box” IPV Combines the advantages of parametric and non-parametric techniques A mixture of “white box” and “black box” models 

6 September 4, Intelligent Parameter Varying (IPV) Technique Advantages 2. Finds “optimal” functional representation of system constitutive non-linearities 1. Does not require a priori knowledge of system constitutive non- linearities 3. Can detect the presence, location, and time of damage

7 September 4, Intelligent Parameter Varying (IPV) Technique

8 September 4, Intelligent Parameter Varying (IPV) Technique

9 September 4, Intelligent Parameter Varying (IPV) Technique Identified restoring forces

10 September 4, Intelligent Parameter Varying (IPV) Technique Identified restoring forces

11 September 4, Bayesian System Identification (BSI) Technique Is an statistical approach to system identification that can be applied to a wide range of dynamic systems 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:

12 September 4, Bayesian System Identification (BSI) Technique The posterior pdf of model parameters, conditional on the given data The likelihood function, reflects the contribution of the measured data D N in calculating the updated posterior pdf The prior pdf of model parameters Normalizing constant

13 September 4, Bayesian System Identification (BSI) Procedure 2. Define prior pdf of model parameters1. Select a model class and structure3. Define the likelihood function4. Minimize the posterior pdf with respect to model parameters

14 September 4, Bayesian System Identification (BSI) 2D truss structure

15 September 4, Research Directions 3. Adaptive structural reliability analysis of aerospace structures based on real-time Bayesian system identification 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