• Title/Summary/Keyword: least-squares problem

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Inversion of Acoustical Properties of Sedimentary Layers from Chirp Sonar Signals (Chirp 신호를 이용한 해저퇴적층의 음향학적 특성 역산)

  • 박철수;성우제
    • The Journal of the Acoustical Society of Korea
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    • v.18 no.8
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    • pp.32-41
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    • 1999
  • In this paper, an inversion method using chirp signals and two near field receivers is proposed. Inversion problems can be formulated into the probabilistic models composed of signals, a forward model and noise. Forward model to simulate chirp signals is chosen to be the source-wavelet-convolution planewave modeling method. The solution of the inversion problem is defined by a posteriori pdf. The wavelet matching technique, using weighted least-squares fitting, estimates the sediment sound-speed and thickness on which determination of the ranges for a priori uniform distribution is based. The genetic algorithm can be applied to a global optimization problem to find a maximum a posteriori solution for determined a priori search space. Here the object function is defined by an L₂norm of the difference between measured and modeled signals. The observed signals can be separated into a set of two signals reflected from the upper and lower boundaries of a sediment. The separation of signals and successive applications of the genetic algorithm optimization process reduce the search space, therefore improving the inversion results. Not only the marginal pdf but also the statistics are calculated by numerical evaluation of integrals using the samples selected during importance sampling process of the genetic algorithm. The examples applied here show that, for synthetic data with noise, it is possible to carry out an inversion for sedimentary layers using the proposed inversion method.

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Nonlinear Inference Using Fuzzy Cluster (퍼지 클러스터를 이용한 비선형 추론)

  • Park, Keon-Jung;Lee, Dong-Yoon
    • Journal of Digital Convergence
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    • v.14 no.1
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    • pp.203-209
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    • 2016
  • In this paper, we introduce a fuzzy inference systems for nonlinear inference using fuzzy cluster. Typically, the generation of fuzzy rules for nonlinear inference causes the problem that the number of fuzzy rules increases exponentially if the input vectors increase. To handle this problem, the fuzzy rules of fuzzy model are designed by dividing the input vector space in the scatter form using fuzzy clustering algorithm which expresses fuzzy cluster. From this method, complex nonlinear process can be modeled. The premise part of the fuzzy rules is determined by means of FCM clustering algorithm with fuzzy clusters. The consequence part of the fuzzy rules have four kinds of polynomial functions and the coefficient parameters of each rule are estimated by using the standard least-squares method. And we use the data widely used in nonlinear process for the performance and the nonlinear characteristics of the nonlinear process. Experimental results show that the non-linear inference is possible.

Three-dimensional Inversion of Resistivity Data (전기비저항 탐사자료의 3차원 역산)

  • Yi Myeong-Jong;Kim Jung-Ho;Cho Seong-Jun;Chung Seung-Hwan;Song Yoonho
    • Geophysics and Geophysical Exploration
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    • v.2 no.4
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    • pp.191-201
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    • 1999
  • The interpretation of resistivity data has, so far, mainly been made under the assumption that the earth is of relatively simple structure and then using one or two-dimensional inversion scheme. Since real earth structure and topography are fully three-dimensional and very complicated In nature, however, such assumptions often lead to misinterpretation of the earth structures. In such situations, three-dimensional inversion is probably the only way to get correct image of the earth. In this study, we have developed a three-dimensional inversion code using the finite element solution for the forward problem. The forward modeling algorithm simulates the real field situation with irregular topography. The inverse problem is solved iteratively using the least-squares method with smoothness constraint. Our inversion scheme employs ACB (Active Constraint Balancing) to enhance the resolving power of the inversion. Including Irregular surface topography in the inversion, we can accurately define the earth structures without artifact in the numerical tests. We could get reasonable image of earth structure by Inverting the real field data sets taken over highway bridge construction site.

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Fuzzy Inference Systems Based on FCM Clustering Algorithm for Nonlinear Process (비선형 공정을 위한 FCM 클러스터링 알고리즘 기반 퍼지 추론 시스템)

  • Park, Keon-Jun;Kang, Hyung-Kil;Kim, Yong-Kab
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.5 no.4
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    • pp.224-231
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    • 2012
  • In this paper, we introduce a fuzzy inference systems based on fuzzy c-means clustering algorithm for fuzzy modeling of nonlinear process. Typically, the generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, the fuzzy rules of fuzzy model are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process.

Simultaneous Equation Estimation in Finance and Corporate Financial Decision: Empirical Evidence from Pakistan Stock Exchange

  • AHMED, Wahab;KHAN, Hadi Hassan;RAUF, Abdul;ULHAQ, SM Nabeel;BANO, Safia;SARWAR, Bilal;HUDA, Shams ul;KHAN, Mirwaise;WALI, Ahmed;DURRANI, Maryam Najeeb
    • The Journal of Asian Finance, Economics and Business
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    • v.8 no.3
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    • pp.11-21
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    • 2021
  • In the last few years, there is growing interest in the field of simultaneous equation estimation in finance due to the endogeneity problem caused by measurement errors, simultaneity, or omitted variables. This study aims to discuss the endogeneity problem in corporate financing decisions and investigate the interrelationship of financial decision-making such as investment decision, dividend decision, and external financing decision in Pakistan Stock Exchange (PSX) using two-stage least squares (2SLS) and generalized method of moment (GMM) estimation. The Bruech-Pagan test shows that the data has no heteroskedasticity issue and 2SLS is a better approach in the context of this study as compared to the GMM approach, and internal instruments are also sufficiently strong and valid. The three financial decision-making attributes are not jointly determined, and the dividend is influenced by one-sided investment. In the emerging stock market context, external financing and investment are not inter-related and did not affect each other. The question of whether the simultaneous equation estimation can be useful in the context of the emerging stock markets and newly-growing firms remains unanswered. The inclusive evidence shows that the theoretical link in the emerging stock market is difficult to prove like in developed stock markets.

A 3D Magnetic Inversion Software Based on Algebraic Reconstruction Technique and Assemblage of the 2D Forward Modeling and Inversion (대수적 재구성법과 2차원 수치모델링 및 역산 집합에 기반한 3차원 자력역산 소프트웨어)

  • Ko, Kwang-Beom;Jung, Sang-Won;Han, Kyeong-Soo
    • Geophysics and Geophysical Exploration
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    • v.16 no.1
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    • pp.27-35
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    • 2013
  • In this study, we developed the trial product on 3D magnetic inversion tentatively named 'KMag3D'. Also, we briefly introduced its own function and graphic user interface on which especially focused through the development in the form of user manual. KMag3D is consisted of two fundamental frame for the 3D magnetic inversion. First, algebraic reconstruction technique was selected as a 3D inversion algorithm instead of least square method conventionally used in various magnetic inversion. By comparison, it was turned out that algebraic reconstruction algorithm was more effective and economic than that of least squares in aspect of both computation time and memory. Second, for the effective determination of the 3D initial and a-priori information model required in the execution of our algorithm, we proposed the practical technique based on the assemblage of 2D forward modeling and inversion results for individual user-selected 2D profiles. And in succession, initial and a-priori information model were constructed by appropriate interpolation along the strke direction. From this, we concluded that our technique is both suitable and very practical for the application of 3D magentic inversion problem.

Statistical review and explanation for Lanchester model (란체스터 모형에 대한 통계적 고찰과 해석)

  • Yoo, Byung Joo
    • The Korean Journal of Applied Statistics
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    • v.33 no.3
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    • pp.335-345
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    • 2020
  • This paper deals with the problem of estimating the log-transformed linear regression model to fit actual battle data from the Ardennes Campaign of World War II into the Lanchester model. The problem of determining a global solution for parameters and multicollinearity problems are identified and modified by examining the results of previous studies on data. The least squares method requires attention because a local solution can be found rather than a global solution if considering a specific constraint or a limited candidate group. The method of exploring this multicollinearity problem can be confirmed by a statistic known as a variance inflation factor. Therefore, the Lanchester model is simplified to avoid these problems, and the combat power attrition rate model was proposed which is statistically significant and easy to explain. When fitting the model, the dependence problem between the data has occurred due to autocorrelation. Matters that might be underestimated or overestimated were resolved by the Cochrane-Orcutt method as well as guaranteeing independence and normality.

Image alignment method based on CUDA SURF for multi-spectral machine vision application (다중 스펙트럼 머신비전 응용을 위한 CUDA SURF 기반의 영상 정렬 기법)

  • Maeng, Hyung-Yul;Kim, Jin-Hyung;Ko, Yun-Ho
    • Journal of Korea Multimedia Society
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    • v.17 no.9
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    • pp.1041-1051
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    • 2014
  • In this paper, we propose a new image alignment technique based on CUDA SURF in order to solve the initial image alignment problem that frequently occurs in machine vision applications. Machine vision systems using multi-spectral images have recently become more common for solving various decision problems that cannot be performed by the human vision system. These machine vision systems mostly use markers for the initial image alignment. However, there are some applications where the markers cannot be used and the alignment techniques have to be changed whenever their markers are changed. In order to solve these problems, we propose a new image alignment method for multi-spectral machine vision applications based on SURF extracting image features without depending on markers. In this paper, we propose an image alignment method that obtains a sufficient number of feature points from multi-spectral images using SURF and removes outlier iteratively based on a least squares method. We further propose an effective preliminary scheme for removing mismatched feature point pairs that may affect the overall performance of the alignment. In addition, we reduce the execution time by implementing the proposed method using CUDA based on GPGPU in order to guarantee real-time operation. Simulation results show that the proposed method is able to align images effectively in applications where markers cannot be used.

Spatial Analysis of the Urban Heat Island Using a 3-D City Model (3차원 도시모형을 이용한 도시열섬의 공간분석)

  • Chun, Bum-Seok;Guldmann, Jean-Michel
    • Spatial Information Research
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    • v.20 no.4
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    • pp.1-16
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    • 2012
  • There is no doubt that the urban heat island (UHI) is a mounting problem in built-up environments, due to energy retention by the surface materials of dense buildings, leading to increased temperatures, air pollution, and energy consumption. To investigate the UHI, three-dimensional (3-D) information is necessary to analyze complex sites, including dense building clusters. In this research, 3-D building geometry information is combined with two-dimensional (2-D) urban surface information to examine the relationship between urban characteristics and temperature. In addition, this research introduces spatial regression models to account for the spatial spillover effects of urban temperatures, and includes the following steps: (a) estimating urban temperatures, (b) developing a 3-D city model, (c) generating urban parameters, and (d) conducting statistical analyses using both Ordinary Least-Squares (OLS) and Spatial Regression Models. The results demonstrate that 3-D urban characteristics greatly affect temperatures and that neighborhood effects are critical in explaining temperature variations. Finally, the implications of the results are discussed, providing guidelines for policies to reduce the UHI.

The Stress Analysis of Structural Element Using Meshfree Method(RPIM) (무요소법(RPIM)을 이용한 구조 요소의 응력해석)

  • Han, Sang-Eul;Yang, Jae-Guen;Joo, Jung-Sik
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.3
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    • pp.311-319
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    • 2007
  • A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate, hollow cylinder and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.