• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.147-153
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• 2007

The conjugate gradient (CG) method is one of the most efficient algorithms for solving a linear system of equations. In addition to being used as a linear equation solver, it can be applied to a least-squares problem. When the CG method is applied to large-scale three-dimensional inversion of magnetotelluric data, two approaches have been pursued; one is the linear CG inversion in which each step of the Gauss-Newton iteration is incompletely solved using a truncated CG technique, and the other is referred to as the nonlinear CG inversion in which CG is directly applied to the minimization of objective functional for a nonlinear inverse problem. In each procedure we only need to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector, significantly reducing the computational requirements needed to do large-scale inversion.

• Geophysics and Geophysical Exploration
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• v.7 no.3
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• pp.207-212
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• 2004

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1679-1688
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• 1990

The method of nonlinear parameter estimation(NPE), which is a statistical and an inverse method, is used to estimate the thermal diffusivity of the porous insulation material. In order to apply the NPE method for measuring the thermal diffusivity, and algorithm for programing suitable to IBM personal computer is established, and is studied the statistical treatment of experimental data and theory of estimation. The experimental data obtained by discrete measurement using a constant heat flux technique are used to find the boundary conditions, initial conditions, and the thermal diffusivity, and then the final values are compared with the values obtained by some different methods. The results are presented as follows:(1) NPE method is used to establish the estimation of the thermal diffusivity and compared results with experimental output shows, that this method can be applicable to define the thermal diffusivity without considering hear flux types. (2) Because of all of the temperatures obtained by the discrete measurement on each steps of time are used to estimate the thermal diffusivity. Although some error in the temperature measurements of temperature are included in estimating process, its influences on the final value are minimzed in NPE method. (3) NPE method can reduce the experimental time including the time of data collecting in a few minutes and can take smaller specimen compared with steady state method. If the tube-type furnace is used, also the adjusting time of surrounding temperature can be reduced.

• Structural Engineering and Mechanics
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• v.30 no.6
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• pp.679-698
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• 2008

On marine vessels, delicate instruments such as navigation radars are normally mounted on ship masts. However the vibrations at the top of mast where the radar is mounted often cause serious deterioration in radar-tracking resolution. The most serious problem is caused by the rotational vibrations at the top of mast that may be due to wind loading, inertial loading from ship rolling and base excitations induced by the running propeller. This paper presents a method of semi-active vibration control using magneto-rheological (MR) dampers to reduce the rotational vibration of the mast. In the study, the classical optimal control algorithm, the independent modal space control algorithm and the double input - single output fuzzy control algorithm are employed for the vibration control. As the phenomenological model of an MR damper is highly nonlinear, which is difficult to analyse, a back- propagation neural network is trained to emulate the inverse dynamic characteristics of the MR damper in the analysis. The trained neural network gives the required voltage for each MR damper based on the displacement, velocity and control force of the MR damper quickly. Numerical simulations show that the proposed control methods can effectively suppress the rotational vibrations at the top of mast.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.577-582
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• 2002

Neural network can be trained to approximate an arbitrary nonlinear function of multivariate data like the mini-mill crown values in Automatic Shape Control. The trained weights of neural network can evaluate or generalize the process data outside the training vectors. Sometimes, the blind modeling of the process data is necessary to compare with the scattered analytical model of mini-mill process in isolated electro-mechanical forms. To come up with a viable model, we propose the blind neural-based range-division domain-clustering piecewise-linear modeling scheme. The basic ideas are: 1) dividing the range of target data, 2) clustering the corresponding input space vectors, 3)training the neural network with clustered prototypes to smooth out the convergence and 4) solving the resulting matrix equations with a pseudo-inverse to alleviate the ill-conditioning problem. The simulation results support the effectiveness of the proposed scheme and it opens a new way to the data analysis technique. By the comparison with the statistical regression, it is evident that the proposed scheme obtains better modeling error uniformity and reduces the magnitudes of errors considerably. Approximatly 10-fold better performance results.

• Journal of Satellite, Information and Communications
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• v.3 no.1
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• pp.15-21
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• 2008

The high peak to average power ratio (PAPR) of OFDM (Orthogonal Frequency Division Multiplexing) system introduces inevitable non-linear distortion in the transmission due to the amplifier non-linear property. This causes both in-band distortion and out of band spectrum re-growth. In this paper we tried to compensate the problem by using polynomial based pre-distortion. Estimation of both the non-linear and inverse non-linear polynomial is achieved using the Least Square Error (LSE) method. Using these parameters closed form pre-distorter can be easily created. We also used the 'partial peak cancellation and clipping' method to remove the high peak present in the non constant amplitude of the OFDM signal responsible to drive the amplifier in near saturation region for better performance of the system

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.621-638
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• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1223-1228
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• 2006

This paper presents an experimental investigation of a recently developed Kronecker Product (KP) method to determine the type, location, and intensity of structural damage from an identified state-space model of the system. Although this inverse problem appears to be highly nonlinear, the system mass, stiffness, and damping matrices are identified through a series of transformations, and with the aid of the Kronecker product, only linear operations are involved in the process. Since a state-space model can be identified directly from input-output data, an initial finite element model and/or model updating are not required. The test structure is a two-degree-of-freedom torsional system in which mass and stiffness are arbitrarily adjustable to simulate various conditions of structural damage. This simple apparatus demonstrates the capability of the damage detection method by not only identifying the location and the extent of the damage, but also differentiating the nature of the damage. The potential applicability of the KP method for structural damage identification is confirmed by laboratory test.

• Nuclear Engineering and Technology
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• v.46 no.5
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• pp.619-632
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• 2014

The Best Estimate Plus Uncertainty (BEPU) method has been widely used to evaluate the uncertainty of a best-estimate thermal hydraulic system code against a figure of merit. This uncertainty is typically evaluated based on the physical model's uncertainties determined by expert judgment. This paper introduces the application of data assimilation methodology to determine the uncertainty bands of the physical models, e.g., the mean value and standard deviation of the parameters, based upon the statistical approach rather than expert judgment. Data assimilation suggests a mathematical methodology for the best estimate bias and the uncertainties of the physical models which optimize the system response following the calibration of model parameters and responses. The mathematical approaches include deterministic and probabilistic methods of data assimilation to solve both linear and nonlinear problems with the a posteriori distribution of parameters derived based on Bayes' theorem. The inverse problem was solved analytically to obtain the mean value and standard deviation of the parameters assuming Gaussian distributions for the parameters and responses, and a sampling method was utilized to illustrate the non-Gaussian a posteriori distributions of parameters. SPACE is used to demonstrate the data assimilation method by determining the bias and the uncertainty bands of the physical models employing Bennett's heated tube test data and Becker's post critical heat flux experimental data. Based on the results of the data assimilation process, the major sources of the modeling uncertainties were identified for further model development.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.765-779
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• 2009

Quantitative condition assessment of structures has been traditionally using proof load test leading to an indication of the load-carrying capacity. Alternative approaches using ultrasonic, dynamics etc. are based on the unloaded state of the structure and anomalies may not be fully mobilized in the load resisting path and thus their effects are not fully included in the measured responses. This paper studies the effect of the load carried by a reinforced concrete beam on the assessment result of the crack damage. This assessment can only be performed with an approach based on static measurement. The crack damage is modelled as a crack zone over an area of high tensile stress of the member, and it is represented by a damage function for the simulation study. An existing nonlinear optimization algorithm is adopted. The identified damage extent from a selected high level load and a low load level are compared, and it is concluded that accurate assessment can only be obtained at a load level close to the one that creates the damage.