Sungmin Baek

Hierarchical strategies of optimization for structural system identification based on the condensation method

In the system identification using finite element method (FEM), system responses of overall degree of freedoms (DOFs) are necessary. Because of the limitation of sensor and other experiment equipment, the responses of unspecified DOFs have to be contained in the design variables. This increase of the design variable makes difficult to solve the inverse problem. It is one of the solutions about the problem of limited responses that the responses of unspecified DOFs are represented by the responses of specified DOFs, using the condensation method. In the previous study, we applied iterative inverse perturbation method (IIPM) to enhance the efficiency and the solution convergence of the structural system identification problems using the condensation method. So we efficiently identify structural system through solving the optimization problem with design variables which have the same number of elements. However, if the size of problem developed to analyze practical model is increased, the number of design variables which had to be considered in solving process is extremely increased. To identify large structural system, optimization strategy to efficiently change design variables during the iteration of optimization is required. In this study, we suggest two optimization strategies which are adaptive sub-domain method and genetic concept method. Numerical examples are presented to verify the efficiency of the proposed methods and to compare with those methods.

Structural Dynamic System Condensation with Multi-level Sub-structuring Scheme in Large-scale Problem

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we improve previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In first step, the global system is recursively partitioned into a hierarchy of subdomain. And next, each uncoupled subdomains condensates by improved TLCS. After assembly process of each reduced subeigenvalue problem, eigen-solution is calculated by Lanczos method (ARPACK). Finally, Numerical examples demonstrate performance of proposed method.

Structural system identification considering the noise of system response using the optimization strategy

In this paper, the optimization strategy of structural system identification is proposed considering the noise of system responses. In the formulated optimization problem for the system identification, a huge amount of computational resources and time are required to identify the large scale structural system due to the increased design variables in proportion to the number of elements. Moreover, added design variables are necessary to consider the noise of system response obtained from experimental observations. Owing to the many design variables presenting the noise and the large area without structural change, the convergence of solution is deteriorated. In order to overcome these issues, we devise the optimization strategy that selects the significant design variables and reduces the number of design variables. The proposed method reduce required computational resources and calculation time and improve the solution convergence through the discarding the design variables that disturb the solution convergence. The efficiency of the proposed method is verified through numerical examples with pre- assumed noise.

The effective dynamic response prediction through condensation in damped system

Selection of the primary degrees of freedom (PDOFs) is a matter of great importance because it is very closely related to accuracy of the eigenpairs in dynamic condensation. In case of undamped systems, reasonable selection method of the PDOFs have been proposed; however, it cannot be extended to damped systems. Therefore, new approach is needed in selection of the PDOFs analytically. The proposed method is based on the degrees of freedom – level energy distribution. Ritz vectors to estimate energy distribution of structures are obtained by using two-side Lanczos algorithm. From them, energy distribution are calculated and then degrees of freedom corresponding to the lowest Rayleigh quotients are selected as the PDOFs. In numerical examples, results are presented for the verification of the proposed method. I. Introduction he eigenproblems of large and complex structural systems through the finite element method (FEM) require too much computation resource and time. Enormous advance in computer capability enables to compute more large scale problems. However, the effort to overcome the limitation of computational resource and shorten computational time is still under way. From this point of view, many researchers have developed efficient model reduction methods. The need for the model reduction increase more and more at various fields such as inverse problem, multi-scale, multi-physics problem. In structural dynamics, one field related to model reduction is the reduced order method (ROM). While accurate solutions in ROM can be obtained by saving the computational resource and time, it loses information related to physical coordinates after constructing the reduced system. The other research is about system condensation. The advantage of system condensation compared with ROM is to keep up the relationship between origin and reduced system. This fact means to be closely related to sensor positioning in experiments. Condensation technique in undamped systems was proposed by Guyan 1 at first. However, Guyan‟s method could not produce accurate eigenvalues because the effect of mass associated with the secondary degrees of freedom (SDOFs) is not rationally considered when constructing the reduced system matrices. Leung 2

Structural System Identification Using Iterative Improved Reduced System

In the inverse perturbation method, enormous computational resource was required to obtain reliable results, because all the unspecified DOFs were considered as unknown variables. Thus, in the present study, an iterative reduced system method is used to condense the unspecified DOFs to improve the computational efficiency as well as the solution accuracy. All the conventional reduction methods include transformation errors in the transformation matrix between the unspecified DOFs and the specified DOFs. Thus it is hard to obtain reliable and accurate solution of inverse perturbation problems by reduction methods due to the error included in the transformation matrix. This numerical trouble is resolved in the present study by adopting iterative improved reduced system (IIRS) as well as by updating the transformation matrix at every step in the inverse perturbation method. In this reduction method, system accuracy is related to the selection of the primary DOFs. The two-level condensation method (TLCS) is employed to select the proper primary DOFs for increasing accuracy and reducing iteration time. Numerical results of the present iterative inverse perturbation method (IIPM) are presented for the verification of the proposed reduced method in the inverse problem.

System Id entification by Subdomain Reduction Method

A number of approximate techniques have been developed to determine primary degrees of freedom ( DOF ) of the reduced eigenvalue problem . These schemes approximate the lower eigenvalues that represent the g lobal behavior of the structures. In general, sequential elimination can be used with reliability. But it takes excessively large amount of time to construct a reduced system. To reduce computational time and resources, two -level selection scheme combined with sub -structuring method are used . Especially, in the three - dimensional problem with relatively large number of degrees of freedom on the interface area, conventional sub -structuring techniques are not efficient because the large number of interface deg rees of freedoms is included in the final degrees of freedom in the reduction process. Therefore, to reduce computer resources and computing time, an improved sub - domain reduction method is used. In the present study, nonlinear inverse perturbation method is used to solve inverse problem. In the system reduction process, nonlinear inverse perturbation equations are derived for full system because damage effects are distributed to the whole system. This formulation is the form of optimal design problem with the objective function which is the residual error of dynamic equilibrium equations. In the traditio nal inverse problem, all the perturbation quantities of element matrices belong to the design variables. However, in the present study, design variables are limited not to all the perturbed quantities of the elements in the global domain but only to the perturbed quantities in the particular sub -domain which is expected to possess damages. The present sub -domain system identification method can provide effici ent tool in inverse problems because it requires only small number of design variables and convergence in nonlinear problem is much faster than tha t of a single global system.