• Smart Structures and Systems
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• v.4 no.3
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• pp.279-290
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• 2008

The modeling and parameter estimation of a damped one-degree-of-freedom mass-spring system is examined. This paper presents a method for estimating the system parameters (damping coefficients and natural frequency) from measured free-vibration motion of a system that is modeled to include both subcritical viscous damping and kinetic Coulomb friction. The method applies a commercially available least-squares curve-fitting software function to fit the known solution of the equations of motion to the measured response. The method was tested through numerical simulation, and it was applied to experimental data collected from a laboratory mass-spring apparatus. The mass of this apparatus translates on linear bearings, which are the primary source of light inherent damping. Results indicate that the curve-fitting method is effective and accurate for both perfect and noisy measurements from a lightly damped mass-spring system.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.88-94
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• 1997

Photographic lenses and an aspheric optical pickup-lens are designed by using damped least-squares(DLS) method. We start optimization with arbitrary initial damping factor. To improve the rate of convergence and the stability in optimization, we apply the special procedure that estimates numerical adequacy of derivative increments of variables to the DLS method. When the initial damping factor is almost equal to the median of series of eigenvalues, the convergence and the stability of the method significantly are improved. Optimized lenses have the performance of each target.

• Smart Structures and Systems
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• v.22 no.3
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• pp.315-326
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• 2018

This paper presents a novel time-domain method for the identification of plastic rotations and stiffness parameters of single-bay frames with nonlinear plastic hinges. Each plastic hinge is modelled as a pseudo-semi-rigid connection with nonlinear hysteretic moment-curvature characteristics at an element end. Through the comparison of the identified end rotations of members that are connected together, the plastic rotation that furnishes information of the locations and plasticity degrees of plastic hinges can be identified. The force consideration of the frame members may be used to relate the stiffness parameters to the elastic rotations and the excitation. The damped-least-squares method and damped-and-weighted-least-squares method are adopted to estimate the stiffness parameters of frames. A noise-removal strategy employing a de-noising technique based on wavelet packets with a smoothing process is used to filter out the noise for the parameter estimation. The numerical examples show that the proposed method can identify the plastic rotations and the stiffness parameters using measurements with reasonable level of noise. The unknown excitation can also be estimated with acceptable accuracy. The advantages and disadvantages of both parameter estimation methods are discussed.

• Economic and Environmental Geology
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• v.14 no.3
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• pp.193-201
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• 1981

The problem of automatic inversion of apparent resistivity sounding curves resulting from horizontally layered earth models is solved using the least-squares technique. This method, which makes use of damped least-squares algorithm in conjunction with digital filtering technique, is found to be speedier and more accurate than the conventional curve-matching method. Four sounding curves were chosen to test the inversion scheme. The analysis of the theoretical sounding data associated with a three-layer model illustrates clear advantages over the conventional curve-matching method. The usefulness of the inversion method is also shown when applied to the actual field data. It was found that the best fit earth models coincide with the subsurface structures confirmed by drilling.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.780-785
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• 1998

In this paper, it is shown that the conventional methods for dealing with the singularity problem of a manipulator can be generalized as a local minimization problem with differently weighted objective functions. A new damping method proposed in this article automatically determines the damping amounts for singular values, which are inversely proportional to the magnitude of the singular values. Furthermore, this can be done without explicitly computing the singular values. The proposed method can be applied to all the manipulators with revolute joints.

• Economic and Environmental Geology
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• v.27 no.5
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• pp.479-489
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• 1994

In this paper, the iterative least-squares inversion method is used to determine shapes and density contrasts of 2-D structures from the gravity data. The 2-D structures are represented by their cross-sections of N-sided polygons with density contrasts which are constant or varying with depth. Gravity data are calculated by theoretical formulas for the above structure models. The data are considered as observed ones and used for inversions. The inversions are performed by the following processes: I) polygon's vertices and density contrast are initially assumed, 2) gravity are calculated for the assumed model and error between the true (observed) and calculated gravity are determined, 3) new vertices and density contrast are determined from the error by using the damped least-squares inversion method, and 4) final model is determined when the error is very small. Results of this study show that the shape and density contrast of each model are accurately determined when the density contrast is constant or vertical density gradient is known. In case where the density gradient is unknown, the inversion gives incorrect results. But the shape and density gradient of the model are determined when the surface density contrast is known.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.363-372
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• 1993

An optimization technique with variable orthogonalization and SVD(singular value decomposition) is examined in a double-Gauss type photographic lens design and its convergence and stability are compared with ordinary least squares and DLS(damped least squares) method. It is known that there are close relationship between the stability of optimization and condition number of nomal equation, the ratio between maximum and minimum of eigenvalues. In this study, the stability is greatly improved by limiting the condition number, the SVD, as expeded. The case of DLS with small damping, orthogonalization and SVD shows the most rapid convergence and stability. It means that the unstability of DLS method with small damping is overcome by using the variable orthogonalization and SVD.

• Geophysics and Geophysical Exploration
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• v.8 no.2
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• pp.129-136
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• 2005

The damped least-squares inversion has become a most popular method in finding the solution in geophysical problems. Generally, the least-squares inversion is to minimize the object function which consists of data misfits and model constraints. Although both the data misfit and the model constraint take an important part in the least-squares inversion, most of the studies are concentrated on what kind of model constraint is imposed and how to select an optimum regularization parameter. Despite that each datum is recommended to be weighted according to its uncertainty or error in the data acquisition, the uncertainty is usually not available. Thus, the data weighting matrix is inevitably regarded as the identity matrix in the inversion. We present a new inversion scheme, in which the data weighting matrix is automatically obtained from the analysis of the data resolution matrix and its spread function. This approach, named 'extended active constraint balancing (EACB)', assigns a great weighting on the datum having a high resolution and vice versa. We demonstrate that by applying EACB to a two-dimensional resistivity tomography problem, the EACB approach helps to enhance both the resolution and the stability of the inversion process.

• Journal of Korean Ophthalmic Optics Society
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• v.1 no.1
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• pp.29-39
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• 1996

We studied the method which would determine the appropriate additive damping factor for the damped least sequres(DLS) optimization. We calculated eigenvalues of the product of the Jacobian matrix of error function by using the singular value decomposition(SVD) method. While suitable damping factor was appiled to the additive DLS by using SVD and Gaussian elimination method, the convergence and stability of the optimization process were examined in a triplet-type camera lens-system where the condition number is well conditioned. We compared the convergence and stability of merit function when median, maximum and minimum of eigenvalues were used as a damping factor in the optimization process. When damping factor is median of eigenvalue, the convergence and stability of merit function are more excellent than in the case of two other eigenvalues. Thus, we adopt the median of eigenvalues as an appropriate damping factor. Next, by using SVD and Gaussian elimination method, we compound the convergence and stability of optimization process for triplet-type camera lens-system design. In these two method; triplet-type camera lens-system in which condition number is well conditioned, has little improvement with the combination of DLS and SVD.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.121-127
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• 2001

While SVD and Gaussian elimination method were applied to the additive damped least squares(DLS), the convergence and the stability of the optimization process were examined in a triplet-type camera lens-system where the condition number is well conditioned. DLS with SVD method generated a suitable merit function but this merit function may be trapped in a local minimum by the nonlinearity of error function. Therefore, the least camera lens-system was further designed by the global optimization method is grid method, and this method is adopted to get merit function that convergent to global minimum without local minimum trapping.