1. System Identification and Regularization Technique
Identification of geometric shapes and material properties of inclusions in two dimensional bodies
A new system identification (SI) scheme based on the finite element method (FEM) and the boundary element method (BEM) is proposed to determine geometric shapes and elastic material properties of inclusions in a 2-D finite body. The proposed scheme is more rigorous than the previous ones since the proposed scheme can identify an arbitrary single-connected shape and material properties of an inclusion while the previous ones identify only a predefined shape of inclusions such as a crack. A weak regularity condition which minimizes the perimeter of an inclusion is imposed on minimization of least squared errors between measured and calculated responses to overcome the inherent ill-posedness of SI. A new regularization factor modification, Variable Regularization Factor Scheme (VRFS) is proposed to keep regularization effects proper and consistent. The proposed scheme can be adopted to identify foreign inclusions and to detect crack-like damage.
Determination scheme of optimal regularization parameter in nonlinear system identification
SI schemes based on minimization of least squared errors between measured and calculated responses are generally nonlinear ill-posed problems. Ill-posedness of conventional SI scheme is revealed and regularization technique is adopted to overcome numerical instabilities of ill-posed problems. It is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution. Since determination of regularization parameter is crucial to physically meaningful solution, new criterion to determine an optimal regularization parameter, named GMS (Geometric Mean Scheme) is proposed. In the GMS, the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses. The GMS was successfully employed in the SI in elastic continua when noise amplitude is in moderate range regardless of measurement and modeling error.
L1-Regularization technique for system identification of structures
Most of previous studies usually use the 2-norm of system parameters representing the discrete form of the L2-norm of the solution space as the regularization function. The regularization functions defined by the L2-norms of system parameter effectively stabilize the ill-posedness of SI. However, the regularization schemes using the 2-norm of system parameters yield smeared solutions of SI, in which information on the stiffness properties of a member is shared with other members. The smearing effect is caused by smoothing characteristics of the L2-norm. It is difficult to estimate structural properties accurately with smeared solutions of SI. A new class of regularization functions is proposed for the system identification in structures. The regularity conditions based on the L1-norm for the system property of framed and continuous structures are investigated. The discretized regularity condition is expressed by the 1-norm of the system parameters. The L1-truncated singular value decomposition (L1-TSVD) is employed to filter out noise-polluted solution components and to impose the regularity condition. The proposed L1-TSVD was successfully applied to isolate and detect damage in continuous and framed structures.
Time Domain System Identification for estimating damping and stiffness properties in structures
Recently, time domain system identification has been studied widely among the researchers due to the rapid developments in computer, sensor, and IT technologies. Time domain system identification plays an important role in the structural health monitoring assessing the integrity of civil infrastructures in real time or in near real time. The current study is focused on developing a time domain system identification scheme in which damping and stiffness properties in a structure is identified using dynamic responses measured from the structure. Rayleigh damping is adopted to simplify the damping properties of the structure and two damping coefficients are estimated through system identification. It was shown in several numerical examples that more complicated damping properties such as modal damping could be identified on the average sense in lower frequency dominated structures. Experimental studies have been performed and more experiments are planned to verify the current studies.
Excavation inverse analysis for identifying plastic-material properties
An inverse analysis is proposed to estimate material properties and geometric shapes of soil layers in the ground during the excavation processes. To analyze the elasto-plastic behaviors of soil layers, consistent tangent moduli is adopted. For an excavation analysis, we calculate the unbalanced stress defined as the difference between the stresses before and after excavation. The domain parameterization technique is adopted to treat variations of soil layers in the ground. Using the real-measured displacements along the soil wall at the current excavation step, the proposed method can predict the displacements of the soil wall at the subsequent steps.
2. Structural Damage Assessment
Damage assessment of the framed structures from static responses with statistical approach.
A damage assessment algorithm for framed structures is proposed using a system identification scheme with a regularization technique. The regularization technique is introduced to alleviate the ill-posedness of the system identification problems. A new regularization function based on the Frobenius norm of the difference between the estimated and the baseline stiffness matrix is proposed. A parameter grouping technique is adopted to locate damaged members and to overcome sparseness of measured data. A data perturbation method is employed to obtain statistical approach by a hypothesis test is presented to assess damage. The proposed algorithm can detect damage in structures more rigorously compared with the previous ones.
Damage detection of the framed structures using modal responses
An improved damage assessment algorithm is proposed using modal data based on the system identification algorithm with a regularization technique. In this algorithm, the regularization technique is introduced to overcome ill-posedness of the inverse problem. The Variable Regularized Factor Scheme(VRFS) is employed for the Frobenius norm and the Geometric Mean Scheme(GMS) is employed for the Tikhonov function to determine a regularization factor. In the optimization process, sensitivities of modal responses are required. First order sensitivity of mode shape normalized with mass matrix can be calculated by modal method. However, in the real situation, measurement data of entire DOFs cannot be obtained. Therefore, the sensitivity of the normalized mode shape by an arbitrary matrix is proposed. The Gauss-Newton Hessian is used for second order sensitivity. Statistical approach is used to estimate more reliable system parameter to overcome sparseness and noise of measurement data. The proposed algorithm could detect damage of frame and grid model successfully.
Damage detection of the framed structures using time domain system identification
Experimental studies locating the damage in framed structures are in progress. Time domain system identification scheme is used to estimate the stiffness and damping properties in the framed structure and the location and severity of the damage is determined using the properties estimated by the system identification. The relationships between damage and the changes of the damping and stiffness properties before and after damage will be investigated in the experiments.
Damage detection in continuum structures by plastic system identification technique with static responses.
A damage detection scheme by plastic SI technique in continuum structures is under research. This scheme is capable of predicting both location of damage and the mechanical behavior of the given structures.
3. Geometric Nonlinear Structural Analysis
Initial equilibrium state analysis of cable structure by Newton-Raphson method
Determining either unstrained length or tension which satisfies the given geometry in equilibrium is defined as initial equilibrium state analysis. Incremental formulation based on stiffness method is proposed. Nodal coordinates and unstrained lengths are updated simultaneously by solving the incremental equations which consist of equilibrium equations and geometric constraints.
4. Optimal Design
Optimal pile placement for minimizing differential settlements in piled raft foundation
This study presents an optimal pile placement scheme to determine the optimal location of the pile support beneath the raft which minimizes the differential settlements of the raft. An object function is defined as area of the deflected raft. RQP(Recursive Quadratic Programming) is adopted to minimize the nonlinear object function with regard to the design variables.
5. Dynamic Analysis of Periodic Structures
Multiply supported pipeline under seismic wave excitation
Dynamic behavior of a surface-mounted pipeline under seismic excitation is investigated. Pipeline is modeled as an infinitely long Euler-Bernoulli beam attached to evenly spaced ground supports.