• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1114-1119
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• 2002

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on 12-norm of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters for small order systems. In designing Kalman filters, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.10a
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• pp.313-318
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• 2001

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on $L_2-norm$ of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters. In designing Kalman filters for small order systems, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.175-185
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• 2014

This study presents the prediction of propagated wave profiles using the wave information at a fixed point. The fixed points can be fixed in either space or time. Wave information based on the linear wave theory can be expressed by Fredholm integral equation of the first kinds. The discretized matrix equation is usually an ill-conditioned system. Tikhonov regularization was applied to the ill-conditioned system to overcome instability of the system. The regularization parameter is calculated by using the L-curve method. The numerical results are compared with the experimental results. The analysis of the numerical computation shows that the Tikhonov regularization method is useful.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-952
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• 2011

This paper is concerned with the solution of ill-conditioned Systems of Linear Equations (SLE's) via the solution of equivalent SLE's which are well-conditioned. A matrix is rst constructed from that of the given ill-conditioned system. Then, an adequate right-hand side is computed to make up the instance of an equivalent system. Formulae and algorithms for computing an instance of this equivalent SLE and solving it will be given and illustrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.390-397
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• 1998

An approach to identifying input forces is proposed using measured structural dynamic responses and its analytical model. The identification of input forces is a reverse process and ill-conditioned problem. Its solution is unstable and generally case dependent. In this paper, the ill-condition is described considering characteristic matrix which is defined by reduced dynamic stiffness matrix. Special attention is focused on the condition number of a characteristic matrix used in the solution algorithm of this reverse process. Simple example is presented in support of the ill-condition of a reverse process.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.21-26
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• 2003

The well-conditioned observer in a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic issues such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic issues such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_2$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic issues and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.503-510
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• 2004

In this paper, the well-conditioned observer for a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic uncertainties such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic uncertainties such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_{2}$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. In stochastic viewpoints, the estimation variance represents the robustness to the stochastic uncertainties and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.431-438
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• 2001

This paper present experimental results of source identification for non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method can\`t be applied for a non-minimum phase system, the reason is that the system has ill-conditioning. Therefore, in this study to execute an effective inversion, SVD inverse technique is introduced. In a Non-minimum phase system, its system matrix may be singular or near-singular and has one more very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verified it for the practical system(cantilever beam). The experimental results show that SVD inverse technique works well for non-minimum phase system.

• The Journal of the Acoustical Society of Korea
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• v.23 no.1E
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• pp.3-9
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• 2004

An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.