• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.9
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• pp.1124-1132
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• 2004

The inverse problem of determining unknown inlet temperature in thermally developing, hydrodynamically developed two phase laminar flow in a parallel plate duct is considered. The inlet temperature profile is determined by measuring temperature in the flow field. No prior information is needed for the functional form of the inlet temperature profile. The inverse convection problem is solved by minimizing the objective function with regularization method. The conjugate gradient method as iterative method and the Tikhonov regularization method are employed. The effects of the functional form of inlet temperature, the number of measurement points and the measurement errors are investigated. The accuracy and efficiency of these two methods are compared and discussed.

• Journal of Biomedical Engineering Research
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• v.18 no.3
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• pp.211-216
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• 1997

An inverse method with regularization has been developed to determine the viscoelastic properties of trabecular bone. A series of stress relaxation experiments were performed under the condition of uniaxial compression stress state. Optimization has been formulated within the framework of nonlinear least-squares and a modified Gauss-Newton method with a zeroth-order regularization technique. The stress relaxation behavior of trabecular bone was analyzed using a standard viscoelastic model. The present study clearly shows that trabecular bone exhibits typical viscoelastic stress relaxation behavior, and the obtained material parameters well represent the viscoelastic behavior of trabecular bone.

• 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.

• Coupled systems mechanics
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• v.11 no.1
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• pp.15-32
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• 2022

The comprehensive understanding of the fiber reinforced polymer behavior requires the use of advanced non-destructive testing methods due to its heterogeneous microstructure and anisotropic mechanical proprieties. In addition, the material response under load is strongly associated with manufacturing defects (e.g., voids, inclusions, fiber misalignment, debonds, improper cure and delamination). Such imperfections and microstructures induce various damage mechanisms arising at different scales before macrocracks are formed. The origin of damage phenomena can only be fully understood with the access to underlying microstructural features. This makes X-ray Computed Tomography an appropriate imaging tool to capture changes in the bulk of fibrous materials. Moreover, Digital Volume Correlation (DVC) can be used to measure kinematic fields induced by various loading histories. The correlation technique relies on image contrast induced by microstructures. Fibrous composites can be reinforced by different fiber architectures that may lead to poor natural contrast. Hence, a priori analyses need to be performed to assess the corresponding DVC measurement uncertainties. This study aimed to evaluate measurement resolutions of global and regularized DVC for glass fiber reinforced polymers with different fiber architectures. The measurement uncertainties were evaluated with respect to element size and regularization lengths. Even though FE-based DVC could not reach the recommended displacement uncertainty with low spatial resolution, regularized DVC enabled for the use of fine meshes when applying appropriate regularization.

• Korean Journal of Remote Sensing
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• v.28 no.5
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• pp.561-571
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• 2012

The MTF(Modulation Transfer Function) is one of quality assesment factors to evaluate the performance of satellite images. Image restoration is needed for MTF compensation, but it is an ill-posed problem and doesn't have a certain solution. Lots of filters were suggested to solve this problem, such as Inverse Filter(IF), Pseudo Inverse Filter(PIF) and Wiener Filter(WF). The most commonly used filter is a WF, but it has a limitation on distinguishing signal and noise. The L-curve-based Modified Wiener Filter(MWF) is a solution technique using a Tikhonov regularization method. The L-curve is used for estimating an optimal regularization parameter. The image restoration was performed with Dubaisat-1 images for PIF, WF, and MWF. It is found that the image restored with MWF results in more improved MTF by 20.93% and 10.85% than PIF and WF, respectively.

• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1611-1620
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• 2005

This paper shows the use of wavelet transformation combined with inverse acoustics to reconstruct the surface velocity of a noise source. This approach uses the boundary element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations and wavelet transformation for reconstructing the normal surface velocity field. The reconstructed field can be diverged due to the small measurement errors in the case of nearfield acoustic holography (NAH) using an inverse boundary element method. In order to avoid this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a wavelet transformation is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed vibration field. The computational speed-up is achieved, with solution time being reduced to $14.5\%$.

• Korea-Australia Rheology Journal
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• v.20 no.2
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• pp.51-58
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• 2008

This paper describes a two-step Tikhonov regularization procedure for converting the steady shear data generated by parallel-disk viscometers, in the presence of wall slip, into a shear stress-shear rate function and a wall shear stress-slip velocity functions. If the material under test has a yield stress or a critical wall shear stress below which no slip is observed the method will also provide an estimate of these stresses. Amplification of measurement noise is kept under control by the introduction of two separate regularization parameters and Generalized Cross Validation is used to guide the selection of these parameters. The performance of this procedure is demonstrated by applying it to the parallel disk data of an oil-in-water emulsion, of a foam and of a mayonnaise.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.10
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• pp.1271-1278
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• 2004

In order to measure non-intrusively velocity profile in liquid metal flow, a modified electromagnetic flowmeter was designed, which was based on electromagnetic tomography technique. Under the assumption that flow is fully-developed, axisymmetric and rectilinear, the velocity profile was reconstructed after the flowmeter equation, the first kind of Fredholm integration equation, was linearized. In reconstruction process Tikhonov regularization method with regularization parameter was used. The reconstructed velocity profile had the nearly same as turbulent flow profile which was approximately represented as log law. In addition, flowmeter output fur a fixed magnet rotation angle was linearly proportional to flow rate. When magnet rotation angle was 54$^{\circ}$, axisymmetric weight function was nearly uniform so that the flowmeter gives a constant signal for any fully-developed, axisymmetric and rectilinear profile with a constant flow rate.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.8 s.239
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• pp.903-910
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• 2005

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and finite-difference Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach that adopts the hybrid genetic algorithm as an initial value selector and uses the finite-difference Newton method as an optimization procedure.

• Smart Structures and Systems
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• v.21 no.6
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• pp.741-749
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• 2018

Structural health monitoring (SHM) systems are necessary to achieve smart predictive maintenance and repair planning as well as they lead to a safe operation of mechanical structures. In the context of vibration-based SHM the measured structural responses are employed to draw conclusions about the structural integrity. This usually leads to a mathematically illposed inverse problem which needs regularization. The restriction of the solution set of this inverse problem by using prior information about the damage properties is advisable to obtain meaningful solutions. Compared to the undamaged state typically only a few local stiffness changes occur while the other areas remain unchanged. This change can be described by a sparse damage parameter vector. Such a sparse vector can be identified by employing $L_1$-regularization techniques. This paper presents a novel framework for damage parameter identification by combining sparse solution techniques with an Extended Kalman Filter. In order to ensure sparsity of the damage parameter vector the measurement equation is expanded by an additional nonlinear $L_1$-minimizing observation. This fictive measurement equation accomplishes stability of the Extended Kalman Filter and leads to a sparse estimation. For verification, a proof-of-concept example on a quadratic aluminum plate is presented.