• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.409-428
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• 2004

In this paper, a Holder exponent, a measure of the degree to which a signal is differentiable, is presented to detect the presence of a discontinuity and when the discontinuity occurs in a dynamic signal. This discontinuity detection has potential applications to structural health monitoring because discontinuities are often introduced into dynamic response data as a result of certain types of damage. Wavelet transforms are incorporated with the Holder exponent to capture the time varying nature of discontinuities, and a classification procedure is developed to quantify when changes in the Holder exponent are significant. The proposed Holder exponent analysis is applied to various experimental signals to reveal underlying damage causing events from the signals. Signals being analyzed include acceleration response of a mechanical system with a rattling internal part, acceleration signals of a three-story building model with a loosing bolt, and strain records of an in-situ bridge during construction. The experimental results presented in this paper demonstrate that the Holder exponent can be an effective tool for identifying certain types of events that introduce discontinuities into the measured dynamic response data.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.585-594
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• 2006

We consider a stochastic integral process represented by multiple Ito-Wiener integrals. We derive gaussian chaos which has some shift continuous function. We get continuity property of self-similar process represented by multiple integrals and finally we show that $Y_{H_t}$ (t) is continuous in t with probability one for Holder function $H_t$ of exponent $\beta$.

• Smart Structures and Systems
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• v.22 no.6
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• pp.711-725
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• 2018

Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Hence, it is highly desirable to detect and characterize the nonlinearity present in the system in order to assess the true behaviour of the structural system. Further, these identified nonlinear features can be effectively used for damage diagnosis during structural health monitoring. In this paper, we focus on the detection of the nonlinearity present in the system by confining our discussion to only a few selective time-frequency analysis and multivariate analysis based techniques. Both damage induced nonlinearity and inherent structural nonlinearity in healthy systems are considered. The strengths and weakness of various techniques for nonlinear detection are investigated through numerically simulated two different classes of nonlinear problems. These numerical results are complemented with the experimental data to demonstrate its suitability to the practical problems.

• Transactions of Materials Processing
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• v.10 no.2
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• pp.101-110
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• 2001

The thermal problem of press work is classified into two cases. First, the temperature of forming die passively rises due to the heating effect of plastic deformation. The warm forming is the second case in which the external heating is applied to the die and blank holder. So, the purpose of this study is to provide database for the forming characteristics at various temperature conditions. In this study, the tensile test was carried out for the commercial steel sheets such as SCPI and SCP3C with the thickness of 0.7mm and 1.4mm respectively. The tensile strength, total elongation, Lankford value and the flow curve have been obtained at the temperature of $25^{\circ}C$, $50^{\circ}C$, $100^{\circ}C$, $150^{\circ}C$, $200^{\circ}C$, $250^{\circ}C$ and $300^{\circ}C$, respectively. From the results, we can see that both the tensile strength and total elongation decrease as the temperature increases. In the light of anisotropy, the effect of thickness is dominant than the material specs. For the temperature dependency of flow curves, there are only small differences for the work-hardening exponent, and the strength intensity decreases monotonically as temperature increases. The present results we useful as input data for the analysis of sheet metal forming processes with the various temperature conditions.