• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.1
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• pp.56-74
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• 2023

In order to obtain practical and high-quality satellite images containing high-frequency components, a large aperture optical system is required, which has a limitation in that it greatly increases the payload weight. As an attempt to overcome the problem, many multi-aperture optical systems have been proposed, but in many cases, these optical systems do not include high-frequency components in all directions, and making such an high-quality image is an ill-posed problem. In this paper, we use deep learning to overcome the limitation. A deep learning model receives low-quality images as input, estimates the Point Spread Function, PSF, and combines them to output a single high-quality image. We model images obtained from three rectangular apertures arranged in a regular polygon shape. We also propose the Modulation Transfer Function Loss, MTF Loss, which can capture the high-frequency components of the images. We present qualitative and quantitative results obtained through experiments.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.10
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• pp.5129-5152
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• 2016

Multi-view super-resolution (MVSR) aims to estimate a high-resolution (HR) image from a set of low-resolution (LR) images that are captured from different viewpoints (typically by different cameras). MVSR is usually applied in camera array imaging. Given that MVSR is an ill-posed problem and is typically computationally costly, we super-resolve multi-view LR images of the original scene via image fusion (IF) and blind deblurring (BD). First, we reformulate the MVSR problem into two easier problems: an IF problem and a BD problem. We further solve the IF problem on the premise of calculating the depth map of the desired image ahead, and then solve the BD problem, in which the optimization problems with respect to the desired image and with respect to the unknown blur are efficiently addressed by the alternating direction method of multipliers (ADMM). Our approach bridges the gap between MVSR and BD, taking advantages of existing BD methods to address MVSR. Thus, this approach is appropriate for camera array imaging because the blur kernel is typically unknown in practice. Corresponding experimental results using real and synthetic images demonstrate the effectiveness of the proposed method.

• 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.

• Smart Structures and Systems
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• v.21 no.4
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• pp.449-467
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• 2018

In this paper, a theoretical and numerical study on bridge simultaneous damage detection procedure for identifying both the system parameters and input excitation mass, are presented. This method is called 'Adjoint Variable Method' which is an iterative gradient-based model updating method based on the dynamic response sensitivity. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. Moving mass is a model which takes into account the inertia effects of the vehicle. This interaction model is a time varying system and proposed method is capable of detecting damage in this variable system. Robustness of proposed method is illustrated by correctly 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 comparison study of common sensitivity and proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. Various sources of errors including the effects of measurement noise and initial assumption error in stability of method are also discussed.

• Smart Structures and Systems
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• v.14 no.5
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• pp.831-845
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• 2014

This paper proposed a discrete wavelet transform based method for time-varying physical parameter identification of shear type structures. The time-varying physical parameters are dispersed and expanded at multi-scale as profile and detail signal using discrete wavelet basis. To reduce the number of unknown quantity, the wavelet coefficients that reflect the detail signal are ignored by setting as zero value. Consequently, the time-varying parameter can be approximately estimated only using the scale coefficients that reflect the profile signal, and the identification task is transformed to an equivalent time-invariant scale coefficient estimation. The time-invariant scale coefficients can be simply estimated using regular least-squares methods, and then the original time-varying physical parameters can be reconstructed by using the identified time-invariant scale coefficients. To reduce the influence of the ill-posed problem of equation resolving caused by noise, the Tikhonov regularization method instead of regular least-squares method is used in the paper to estimate the scale coefficients. A two-story shear type frame structure with time-varying stiffness and damping are simulated to validate the effectiveness and accuracy of the proposed method. It is demonstrated that the identified time-varying stiffness is with a good accuracy, while the identified damping is sensitive to noise.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.8
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• pp.2718-2731
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• 2021

In the structural health monitoring of composite materials, in order to solve the ill-posed problem of impact force reconstruction, regularization techniques are often used to deal with it. Due to the poor convergence of the traditional Tikhonov regularization method, in order to accurately reconstruct the time history of the impact force, this paper improves Tikhonov regularization method and constructs homotopy function with strong convergence. Since the optimal regularization parameters need to be found in the homotopy function, the Newton downhill method is used to find the optimal parameters and the homotopy function can be calculated, which can accurately reconstruct the time history of the impact force. In order to verify the universality of the method in this paper, impact hammers of different materials were used in the experiment in this paper to study and compare the reconstruction effect of impact time history of different impact hammers.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1000-1010
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• 2019

Image semantic segmentation and dehazing are key tasks in the computer vision. In recent years, researches in both tasks have achieved substantial improvements in performance with the development of Convolutional Neural Network (CNN). However, most of the previous works for semantic segmentation assume the images are captured in clear weather and show degraded performance under hazy images with low contrast and faded color. Meanwhile, dehazing aims to recover clear image given observed hazy image, which is an ill-posed problem and can be alleviated with additional information about the image. In this work, we propose a deep multi-task network for simultaneous semantic segmentation and dehazing. The proposed network takes single haze image as input and predicts dense semantic segmentation map and clear image. The visual information getting refined during the dehazing process can help the recognition task of semantic segmentation. On the other hand, semantic features obtained during the semantic segmentation process can provide cues for color priors for objects, which can help dehazing process. Experimental results demonstrate the effectiveness of the proposed multi-task approach, showing improved performance compared to the separate networks.

• Advances in nano research
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• v.16 no.3
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• pp.265-272
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• 2024

In this paper, the problem of static bending of axially functionally graded (AFG) nanobeam is formulated with the local stress(Lσ)- and strain-driven(εD) two-phase local/nonlocal integral models (TPNIMs). The novelty of the present study aims to compare the size-effects of nonlocal integral models on bending deflections of AFG Euler-Bernoulli nano-beams. The integral relation between strain and nonlocal stress components based on two types nonlocal integral models is transformed unitedly and equivalently into differential form with constitutive boundary conditions. Purely LσD- and εD-NIMs would lead to ill-posed mathematical formulation, and Purely εD- and LσD-nonlocal differential models (NDM) may result in inconsistent size-dependent bending responses. The general differential quadrature method is applied to obtain the numerical results for bending deflection and moment of AFG nanobeam subjected to different boundary and loading conditions. The influence of AFG index, nonlocal models, and nonlocal parameters on the bending deflections of AFG Euler-Bernoulli nanobeams is investigated numerically. A consistent softening effects can be obtained for both LσD- and εD-TPNIMs. The results from current work may provide useful guidelines for designing and optimizing AFG Euler-Bernoulli beam based nano instruments.