Post on 25-Dec-2015
transcript
September 4, 2003 1
Bayesian System Identification and Structural Reliability
Soheil Saadat, Research AssociateMohammad N. Noori, Professor & Head
Department of Mechanical & Aerospace Engineering
September 4, 2003 2
Overview
1. Intelligent Parameter Varying (IPV) Technique
2. Bayesian System Identification (BSI) Technique and Structural Reliability
3. Research Directions
September 4, 2003 3
1. 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
xy
ux,ufxx,ufx
21
xy
buaxx
Identification Techniques
Modeling Techniques
September 4, 2003 4
1. Intelligent Parameter Varying (IPV) Technique
Find “optimal” functional representation of a system using “black box” models
Solely based on the recorded data
xy
ux,ufxx,ufx
21
Parametric Non-parametric
“White box” “Black box”
Identification Techniques
Modeling Techniques
xy
x,ufx
September 4, 2003 5
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
xy
ux,ufxx,ufx
21
xy
uwx,ugxwx,ugx
2211 ,,
September 4, 2003 6
1. 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
September 4, 2003 7
1. Intelligent Parameter Varying (IPV) Technique
M 3M 2M 1
xg x1 x2 x3
gxMux,fuCuM
gii xxu
u y
k2=0
RelativeD isplacem ent
Restoring Force
k1
R elativeD isplacem ent
k1
k2=0
R estoring Force
u y
September 4, 2003 8
1. Intelligent Parameter Varying (IPV) Technique
M 3M 2M 1
xg x1 x2 x3
gxMux,fuCuM
gii xxu
u y
k2=0
RelativeD isplacem ent
Restoring Force
k1
R elativeD isplacem ent
k1
k2=0
R estoring Force
u y
September 4, 2003 11
2. Bayesian System Identification (BSI) Technique
Is an statistical approach to system identification that can be applied to a wide range of dynamic systems
NNN
NN
yuyuyu
cppp
,,...,,,, 2211
D
θθDDθ
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:
September 4, 2003 12
2. Bayesian System Identification (BSI) Technique
cppp NN θθDDθ
The posterior pdf of model parameters,conditional on the given data
The likelihood function, reflects the contributionof the measured data DN in calculating the updatedposterior pdf
The prior pdf of model parameters
Normalizing constant
September 4, 2003 13
2. Bayesian System Identification (BSI)
Procedure
2. Define prior pdf of model parameters
1. Select a model class and structure
3. Define the likelihood function
4. Minimize the posterior pdf with respect to model parameters
September 4, 2003 15
3. 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