• Title/Summary/Keyword: ill-posed inverse problem

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Simultaneous identification of moving loads and structural damage by adjoint variable

  • Abbasnia, Reza;Mirzaee, Akbar;Shayanfar, Mohsenali
    • Structural Engineering and Mechanics
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    • v.56 no.5
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    • pp.871-897
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    • 2015
  • This paper presents a novel method based on sensitivity of structural response for identifying both the system parameters and input excitation force of a bridge. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The computational cost of sensitivity analyses is the main concern associated with damage detection by these methods. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. The reliable performance of the method to precisely indentify the location and intensity of all types of predetermined single, multiple and random damages over the whole domain of moving vehicle speed is shown. A comparison study is also carried out to demonstrate the relative effectiveness and upgraded performance of the proposed method in comparison to the similar ordinary sensitivity analysis methods. Moreover, various sources of error including the effects of noise and primary errors on the numerical stability of the proposed method are discussed.

A novel sensitivity method to structural damage estimation in bridges with moving mass

  • Mirzaee, Akbar;Shayanfar, Mohsenali;Abbasnia, Reza
    • Structural Engineering and Mechanics
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    • v.54 no.6
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    • pp.1217-1244
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    • 2015
  • In this research a theoretical and numerical study on a bridge damage detection procedure is presented based on vibration measurements collected from a set of accelerometers. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The approach relies on minimizing a penalty function, which usually consists of the errors between the measured quantities and the corresponding predictions attained from the model. Moving mass is an interactive model and includes inertia effects between the model and mass. This interactive model is a time varying system and the proposed method is capable of detecting damage in this variable system. Robustness of the proposed method is illustrated by correct detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparative study on common sensitivity and the proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. In addition various possible sources of error, including the effects of measurement noise and initial assumption error in stability of method are also discussed.

A hybrid-separate strategy for force identification of the nonlinear structure under impact excitation

  • Jinsong Yang;Jie Liu;Jingsong Xie
    • Structural Engineering and Mechanics
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    • v.85 no.1
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    • pp.119-133
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    • 2023
  • Impact event is the key factor influencing the operational state of the mechanical equipment. Additionally, nonlinear factors existing in the complex mechanical equipment which are currently attracting more and more attention. Therefore, this paper proposes a novel hybrid-separate identification strategy to solve the force identification problem of the nonlinear structure under impact excitation. The 'hybrid' means that the identification strategy contains both l1-norm (sparse) and l2-norm regularization methods. The 'separate' means that the nonlinear response part only generated by nonlinear force needs to be separated from measured response. First, the state-of-the-art two-step iterative shrinkage/thresholding (TwIST) algorithm and sparse representation with the cubic B-spline function are developed to solve established normalized sparse regularization model to identify the accurate impact force and accurate peak value of the nonlinear force. Then, the identified impact force is substituted into the nonlinear response separation equation to obtain the nonlinear response part. Finally, a reduced transfer equation is established and solved by the classical Tikhonove regularization method to obtain the wave profile (variation trend) of the nonlinear force. Numerical and experimental identification results demonstrate that the novel hybrid-separate strategy can accurately and efficiently obtain the nonlinear force and impact force for the nonlinear structure.

The Cross-validation of Satellite OMI and OMPS Total Ozone with Pandora Measurement (지상 Pandora와 위성 OMI와 OMPS 오존관측 자료의 상호검증 방법에 대한 분석 연구)

  • Baek, Kanghyun;Kim, Jae-Hwan;Kim, Jhoon
    • Korean Journal of Remote Sensing
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    • v.36 no.3
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    • pp.461-474
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    • 2020
  • Korea launched Geostationary Environmental Monitoring Satellite (GEMS), a UV/visible spectrometer that measure pollution gases on 18 February 2020. Because satellite retrieval is an ill-posed inverse solving process, the validation with ground-based measurements or other satellite measurements is essential to obtain reliable products. For this purpose, satellite-based OMI and OMPS total column ozone (TCO), and ground-based Pandora TCO in Busan and Seoul were selected for future GEMS validation. First of all, the goal of this study is to validate the ground ozone data using characteristics that satellite data provide coherent ozone measurements on a global basis, although satellite data have a larger error than the ground-based measurements. In the cross validation between Pandora and OMI TCO, we have found abnormal deviation in ozone time series from Pandora #29 observed in Seoul. This shows that it is possible to perform inverse validation of ground data using satellite data. Then OMPS TCO was compared with verified Pandora TCO. Both data shows a correlation coefficient of 0.97, an RMSE of less than 2 DU and the OMPS-Pandora relative mean difference of >4%. The result also shows the OMPS-Pandora relative mean difference with SZA, TCO, cross-track position and season have insignificant dependence on those variables.In addition, we showed that appropriate thresholds depending on the spatial resolution of each satellite sensor are required to eliminate the impact of the cloud on Pandora TCO.

Three-Dimensional Subsurface Resistivity Profile using Electrical Resistance Tomography for Designing Grounding Grid (접지 그리드 설계를 위한 전기 저항 단층촬영법에 기반한 지표의 3차원 저항률 분포 추정)

  • Khambampati, Anil Kumar;Kim, Kyung Youn
    • Journal of the Institute of Electronics and Information Engineers
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    • v.53 no.4
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    • pp.117-128
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    • 2016
  • Installation of earth grounding system is essential to ensure personnel safety and correct operation of electrical equipment. Earth parameters, especially, soil resistivity has to be determined in designing an efficient earth grounding system. The most common applied technique to measure soil resistance is Wenner four-point method. Implementation of this method is expensive, time consuming and cumbersome as large set of measurements with variable electrode spacing are required to obtain a one dimensional resistivity plot. It is advantageous to have a method which is of low cost and provides fast measurements. In this perspective, electrical resistance tomography (ERT) is applied to estimate subsurface resistivity profile. Electrical resistance tomograms characterize the soil resistivity distribution based on the measurements from electrodes placed in the region of interest. The nonlinear ill-posed inverse problem is solved using iterated Gauss-Newton method with Tikhonov regularization. Through extensive numerical simulations, it is found that ERT offers promising performance in estimating the three-dimensional soil resistivity distribution.

Review on the Three-Dimensional Inversion of Magnetotelluric Date (MT 자료의 3차원 역산 개관)

  • Kim Hee Joon;Nam Myung Jin;Han Nuree;Choi Jihyang;Lee Tae Jong;Song Yoonho;Suh Jung Hee
    • 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.