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A final presentation for ce291f on the estimation of soil parameters using dynamic system modeling and optimization. The presentation covers objectives, system modeling, identification, approach, cost function, optimization using the adjoint method, and numerical modeling. The study focuses on a bay mud site with a vertical array system and identifies shear modulus and visco-damping coefficient.
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0 m
Fill
HoloceneBay Mud
d
7 m
16 m
31 m
44 m ene
Treasure Island Array, CA
Bay Mud
BedRock
44 m
122 m
Pleistoce
∂ ( x t ) ∂⎡ ∂ ( xt )⎤ ∂⎡ ∂ ( xt ) ⎤
2 2 μ μ μ
1D Visco-elastic shear-wave Propagation Equation
Boundary Conditions:
x t
xt x x x
xt gx t x
xt x
2
μ η
μ μ ρ
uLt uphole series
u t downhole series
∂ ux
(1)
(2a)
(2b)
(3a) 0
t
u x Initial Conditions: u x
Estimate
Visco-Damping Coefficient
(3b)
X T
obs ∫ ∫ = −
2 ( , ) ( , ) 2
1 Cost Function: min :
Subject to: PDE (1), B.C(2a,2b), I.C (3a,3b)
True value (g, η)
