• Title/Summary/Keyword: Ill-conditioning

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The Selection of Measurement Positions for BEM Based NAH Using a Non-conformal Hologram to Reduce the Reconstruction Error

  • Oey, Agustinus;Ih, Jeong-Guon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.1018-1021
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    • 2007
  • This paper explores the use of BEM based NAH to reconstruct the surface vibration of a plate in a rectangular finite cavity, in which the distances between sensors and the nearest points on the source surface are not equal. In such circumstances, different degree of information on propagating and non-propagating wave components will be detected by sensors at different positions, as well as the influence of measurement noise will vary significantly from the nearest points of measurement to the farthest ones. On the other hand, the condition number of the vibro-acoustic transfer function matrix relating normal surface velocities and field pressures will becomes high, numerically indicating an increase of linear dependency between rows of transfer function matrix. The combination of poor measurement and high condition number will result inaccurate reconstruction. Therefore, one approach to be investigated in this work is to select the measurement positions in such ways that reduce measurement redundancy, as it indicated by the condition number. The improvement is found to be significant in the numerical simulations utilizing two different criterions, spanning from over-determined to under-determined cases, and in the validation experiment.

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Robust finite element model updating of a large-scale benchmark building structure

  • Matta, E.;De Stefano, A.
    • Structural Engineering and Mechanics
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    • v.43 no.3
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    • pp.371-394
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    • 2012
  • Accurate finite element (FE) models are needed in many applications of Civil Engineering such as health monitoring, damage detection, structural control, structural evaluation and assessment. Model accuracy depends on both the model structure (the form of the equations) and the model parameters (the coefficients of the equations), and can be generally improved through that process of experimental reconciliation known as model updating. However, modelling errors, including (i) errors in the model structure and (ii) errors in parameters excluded from adjustment, may bias the solution, leading to an updated model which replicates measurements but lacks physical meaning. In this paper, an application of ambient-vibration-based model updating to a large-scale benchmark prototype of a building structure is reported in which both types of error are met. The error in the model structure, originating from unmodelled secondary structural elements unexpectedly working as resonant appendages, is faced through a reduction of the experimental modal model. The error in the model parameters, due to the inevitable constraints imposed on parameters to avoid ill-conditioning and under-determinacy, is faced through a multi-model parameterization approach consisting in the generation and solution of a multitude of models, each characterized by a different set of updating parameters. Results show that modelling errors may significantly impair updating even in the case of seemingly simple systems and that multi-model reasoning, supported by physical insight, may effectively improve the accuracy and robustness of calibration.

Local Minimum Problem of the ILS Method for Localizing the Nodes in the Wireless Sensor Network and the Clue (무선센서네트워크에서 노드의 위치추정을 위한 반복최소자승법의 지역최소 문제점 및 이에 대한 해결책)

  • Cho, Seong-Yun
    • Journal of Institute of Control, Robotics and Systems
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    • v.17 no.10
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    • pp.1059-1066
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    • 2011
  • This paper makes a close inquiry into ill-conditioning that may be occurred in wireless localization of the sensor nodes based on network signals in the wireless sensor network and provides the clue for solving the problem. In order to estimate the location of a node based on the range information calculated using the signal propagation time, LS (Least Squares) method is usually used. The LS method estimates the solution that makes the squared estimation error minimal. When a nonlinear function is used for the wireless localization, ILS (Iterative Least Squares) method is used. The ILS method process the LS method iteratively after linearizing the nonlinear function at the initial nominal point. This method, however, has a problem that the final solution may converge into a LM (Local Minimum) instead of a GM (Global Minimum) according to the deployment of the fixed nodes and the initial nominal point. The conditions that cause the problem are explained and an adaptive method is presented to solve it, in this paper. It can be expected that the stable location solution can be provided in implementation of the wireless localization methods based on the results of this paper.

Design of the Well-Conditioned Observer - A Linear Matrix Inequality Approach - (Well-Conditioned 관측기 설계 - A Linear Matrix Inequality Approach -)

  • Jung, Jong-Chul;Huh, Kun-Soo
    • 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.

On the Reconstruction of Pinwise Flux Distribution Using Several Types of Boundary Conditions

  • Park, C. J.;Kim, Y. H.;N. Z. Cho
    • Nuclear Engineering and Technology
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    • v.28 no.3
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    • pp.311-319
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    • 1996
  • We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

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An improved extended Kalman filter for parameters and loads identification without collocated measurements

  • Jia He;Mengchen Qi;Zhuohui Tong;Xugang Hua;Zhengqing Chen
    • Smart Structures and Systems
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    • v.31 no.2
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    • pp.131-140
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    • 2023
  • As well-known, the extended Kalman filter (EKF) is a powerful tool for parameter identification with limited measurements. However, traditional EKF is not applicable when the external excitation is unknown. By using least-squares estimation (LSE) for force identification, an EKF with unknown input (EKF-UI) approach was recently proposed by the authors. In this approach, to ensure the influence matrix be of full column rank, the sensors have to be deployed at all the degrees-of-freedom (DOFs) corresponding to the unknown excitation, saying collocated measurements are required. However, it is not easy to guarantee that the sensors can be installed at all these locations. To circumvent this limitation, based on the idea of first-order-holder discretization (FOHD), an improved EKF with unknown input (IEKF-UI) approach is proposed in this study for the simultaneous identification of structural parameters and unknown excitation. By using projection matrix, an improved observation equation is obtained. Few displacement measurements are fused into the observation equation to avoid the so-called low-frequency drift. To avoid the ill-conditioning problem for force identification without collocated measurements, the idea of FOHD is employed. The recursive solution of the structural states and unknown loads is then analytically derived. The effectiveness of the proposed approach is validated via several numerical examples. Results show that the proposed approach is capable of satisfactorily identifying the parameters of linear and nonlinear structures and the unknown excitation applied to them.

Refinement of damage identification capability of neural network techniques in application to a suspension bridge

  • Wang, J.Y.;Ni, Y.Q.
    • Structural Monitoring and Maintenance
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    • v.2 no.1
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    • pp.77-93
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    • 2015
  • The idea of using measured dynamic characteristics for damage detection is attractive because it allows for a global evaluation of the structural health and condition. However, vibration-based damage detection for complex structures such as long-span cable-supported bridges still remains a challenge. As a suspension or cable-stayed bridge involves in general thousands of structural components, the conventional damage detection methods based on model updating and/or parameter identification might result in ill-conditioning and non-uniqueness in the solution of inverse problems. Alternatively, methods that utilize, to the utmost extent, information from forward problems and avoid direct solution to inverse problems would be more suitable for vibration-based damage detection of long-span cable-supported bridges. The auto-associative neural network (ANN) technique and the probabilistic neural network (PNN) technique, that both eschew inverse problems, have been proposed for identifying and locating damage in suspension and cable-stayed bridges. Without the help of a structural model, ANNs with appropriate configuration can be trained using only the measured modal frequencies from healthy structure under varying environmental conditions, and a new set of modal frequency data acquired from an unknown state of the structure is then fed into the trained ANNs for damage presence identification. With the help of a structural model, PNNs can be configured using the relative changes of modal frequencies before and after damage by assuming damage at different locations, and then the measured modal frequencies from the structure can be presented to locate the damage. However, such formulated ANNs and PNNs may still be incompetent to identify damage occurring at the deck members of a cable-supported bridge because of very low modal sensitivity to the damage. The present study endeavors to enhance the damage identification capability of ANNs and PNNs when being applied for identification of damage incurred at deck members. Effort is first made to construct combined modal parameters which are synthesized from measured modal frequencies and modal shape components to train ANNs for damage alarming. With the purpose of improving identification accuracy, effort is then made to configure PNNs for damage localization by adapting the smoothing parameter in the Bayesian classifier to different values for different pattern classes. The performance of the ANNs with their input being modal frequencies and the combined modal parameters respectively and the PNNs with constant and adaptive smoothing parameters respectively is evaluated through simulation studies of identifying damage inflicted on different deck members of the double-deck suspension Tsing Ma Bridge.

A Study on the Management Improvement of an Academic Library Using Customer Relationship Management (CRM 기법을 이용한 대학도서관 경영개선에 관한 연구)

  • Park, Il-Jong;Yoo, Kyeong-Jong
    • Journal of the Korean Society for information Management
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    • v.36 no.2
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    • pp.31-56
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    • 2019
  • The user satisfaction and needs of an academic library were caught through a questionnaire survey in this study. The aim of this study is to draw up the CRM based plan for meeting user needs on the study. The users' demographic information, library resources & their use, homepage, services, and facilities/environment of the library were categorized in the questionnaire and analyzed for this study. The major conclusions of this study are: (1) The library resources use was the highest, and its facilities/environment was the lowest in the user satisfaction study. It also revealed that there are much necessities for the quick acquisition and dissemination of the requested material to the library users, and for the inter-library loan (ILL) services among campuses for the subscription books in the library resources use study, too; (2) There are a lot of necessities for the improvement of OPAC retrieval and the subscription books system, and menu rearrangement in the library homepage; (3) There are a lot of necessities for the plans of more frequent library event, more detailed event guidance, and more reinforcement of public relations such as SMS, push services of SDI etc. in the library user services; and (4) There are a lot of necessities for the improved policies to the complaints of library users such as the lack of common study place and lockers, air conditioning and heating problem, complaints about facilities management of restroom (lack of toilet paper), library accessibility on campus, unauthorized user management etc. in the facilities/environment of the library.