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The Second Order Adjoint Analysis
Team of Stochastic Department Of Civil Engineering Chuo University Kawahara Lab.
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What is Hessian? Performance Function Taylor Expansion
: The model solution : Observation Taylor Expansion
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The First Order
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The Second Order Hessian
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Hessian Action Calculation
DFP method High computational burden EFGS method SOA ( Second Order Adjoint )
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Basic Equation Thermal Conduction Equation Initial Condition
Specific heat Density Thermal Conductivity Temperature Initial Condition
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Boundary Condition Heat Flux Error
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Uncertain Estimation via Hessian Calculation
Performance Function Exact Solution Noisy Solution
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Lagrange Multiplier Method
First Order Adjoint Variation
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First Order Adjoint (FOA)
The First Order Adjoint Equation Boundary Conditions Final Condition
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Tangent Linear Tangent Liner Problem Boundary Conditions
Initial Condition
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Second Order Adjoint (SOA)
The Second Order Adjoint Equation Boundary Conditions Final Condition
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and The Hessian Action
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Newton’s Method Gradient Hessian
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Numerical Example
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Performance Function
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Heat Flux
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Temperature
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Conclusion The calculation of the Hessian can be performed using the solution of the SOA problem. The optimal control of thermal conduction can be analyzed using Hessian.
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