• Journal of Advanced Marine Engineering and Technology
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• v.36 no.2
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• pp.258-266
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• 2012

Recently, Acoustic Emission (AE) technique is widely applied to develop the early fault detection system, and the problem about a signal processing method for AE signal is mainly focused on. In the signal processing method, envelope analysis is a useful method to evaluate the rolling element bearing problems and Wavelet transform is a powerful method to detect faults occurred on gearboxes. However, exact method for AE signal is not developed yet. Therefore, in this paper, two methods, which is Hilbert transforms (HT) and Hilbert-Huang transforms (HHT), will be compared for development a signal processing method for early fault detection system by using AE. AE signals were measured through a fatigue test. HHT has better advantages than HT because HHT can show the time-frequency domain result. But, HHT needs long time to process a signal, which has a lot of data, and has a disadvantage in de-noising filter.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1299-1309
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• 2021

Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H_a,b,c under the critical index 1/2 for some parameters a, b and c. We show the unboundedness of H_a,b,c for any parameters.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.269-275
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• 2022

In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.911-929
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• 2006

A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Smart Structures and Systems
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• v.14 no.3
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• pp.445-468
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• 2014

The objective in this research is to determine the feasibility of using changes on the dynamic properties of a reinforced concrete (RC) structure to identify different levels of seismic induced damage. Damping ratio and natural frequency changes in a RC bridge column are analyzed using different signal processing techniques like Hilbert Transforms, Random Decrement and Wavelet Transforms. The data used in the analysis was recorded during a full-scale RC bridge column shake table test. The structure was subjected to ten earthquake excitations that induced different levels of inelastic demand on the column. In addition, low-intensity white noises were applied to the column in-between earthquakes. The results obtained show that the use of the damping ratio and natural frequency of vibration as damage indicators is arguable.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.499-504
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• 2004

The purpose of this study is to investigate a investigating of a floor-impact isolation system using damping materials in apartment buildings. The stiffness elastic modulus(k) by puls impact forces were calculated loss factor by Hilbert transforms. It is absolved that natural frequency was moved floor shock-absorbing materials and the impact force was reduced by floor panel. The slab was constructed by damping materials. As towards a result, the system showed inverse A 45dB by heavy weight-impact noise and inverse A 52dB by light-impact noise. High frequencies impact-noise can be reduced by upgrading naturial frequency of vibration and noise in the system.

• Structural Engineering and Mechanics
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• v.40 no.6
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• pp.745-762
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• 2011

Damage detection methodologies based on the direct examination of the nonlinear-nonstationary characteristics of the structure dynamic response may play an important role in online structural health monitoring applications. Different signal processing based damage detection methodologies have been proposed based on the uncovering of spikes in the high frequency component of the structural response obtained via Discrete Wavelet transforms, Hilbert-Huang transforms or high pass filtering. The performance of these approaches in systems subjected to different types of excitation is evaluated in this paper. It is found that in the case of random excitations, like earthquake accelerations, the effectiveness of such methodologies is limited. An alternative damage detection approach using the Continuous Wavelet Transform (CWT) is also evaluated to overcome this limitation. Using the CWT has the advantage that the central frequencies at which it operates can be defined by the user while the frequency bands of the detail functions obtained via DWT are predetermined by the sampling period of the signal.

• Smart Structures and Systems
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• v.20 no.3
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• pp.263-272
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• 2017

This paper presents the time response of a mixed vibration system with the viscous damping and the hysteretic damping. There are two ways to derive the time response of such a vibration system. One is an analytical method, using the contour integral of complex functions to compute the inverse Fourier transforms. The other is an approximate method in which the analytic functions derived by Hilbert transform are expressed in the state space representation, and only the effective eigenvalues are used to efficiently compute the transient response. The unit impulse responses of the two methods are compared and the change in the damping properties which depend on the viscous and hysteretic damping values is investigated. The results showed that the damping properties of a mixed damping vibration system do not present themselves as a linear combination of damping properties.

• Smart Structures and Systems
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• v.9 no.5
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• pp.441-459
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• 2012

Identification of vibration parameters from the analysis of the dynamic response of a structure plays a key role in current health monitoring systems. This study evaluates the capabilities of the recently developed Synchrosqueezed Wavelet Transform (SWT) to extract instant frequencies and damping values from the simulated noise-contaminated response of a structure. Two approaches to estimate the modal damping ratio from the results of the SWT are presented. The results obtained are compared to other signal processing methods based on Continuous Wavelet (CWT) and Hilbert-Huang (HHT) transforms. It was found that the time-frequency representation obtained via SWT is sharped than the obtained using just the CWT and it allows a more robust extraction of the individual modal responses than using the HHT. However, the identification of damping ratios is more stable when the CWT coefficients are employed.