An Inverse Analysis for Determining Geometric Shape and Material
Properties of an Inclusionin a Finite Body Using Boundary
Parameterization Technique and Regularization
Cheon Jong Park
A new system identification scheme based on the boundary element method is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body. To deal with the shape variation of an inclusion, the boundary parameterization technique is applied to the boundary element method. Material properties of inclusion and the coordinates of control nodes that represent the discretized boundary of inclusion are selected as system parameters.
Regularization technique is adopted to stabilize numerical instability of optimization process. The spatial regularization function that represents the square of discretized length of boundary curve is adopted to calm down the instability due to non-uniqueness of solution. The regularization term for material properties that represents the squared distance of initial guess and current value of material properties of inclusion is added to the error function to stabilize the optimization process with noisy measurement data. The gradient based regularization factor modification scheme is proposed to maximize the regularization effect.
Nonlinear constraint based on the concept of candidate group is proposed to prevent an element from crossing with the others. The optimization proceeds with linearized constraints at each iteration step. Fletcher's active set strategy is adopted to deal with inequality constraints. The sensitivity of displacement with respect to system parameters is obtained from direct differentiation of boundary integral equation. Boundary integral equation and its derivative are integrated analytically. The validity of the proposed method is demonstrated through some examples.
Boundary parameterization technique, Regularization, Regularization factor modification scheme, Direct differentiation, Sensitivity