scholarly journals Detection on Structural Sudden Damage Using Continuous Wavelet Transform and Lipschitz Exponent

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Bo Chen ◽  
Yuan-pin Kang ◽  
Peng-yun Li ◽  
Wen-ping Xie
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Damage Index ◽  
Measurement Noise ◽  
Continuous Wavelet ◽  
Frequency Range ◽  
Engineering Structures ◽  
Lipschitz Exponent ◽  
Stiffness Reduction ◽  
Detection Approach

The degradation of civil engineering structures may lead to a sudden stiffness reduction in a structure and such a sudden damage will cause a discontinuity in the dynamic responses. The detection on structural sudden damage has been actively carried out in this study. The signal singularity of the acceleration responses with sudden stiffness reduction is characterized by the coefficients of continuous wavelet transform with fine scales. A detection approach based on the CWT is proposed in terms of the decomposed detail coefficients of continuous wavelet transform to detect the damage time instant and location. The Lipschitz exponent is mathematically used to estimate the local properties of certain function and is applied to reflect the damage severity. Numerical simulation using a five-story shear building under different types of excitation is carried out to assess the validity of the proposed detection approach for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also investigated. The effects of both measurement noise intensity and frequency range on the damage detection are numerically investigated.

An Continuous Wavelet Transform-Based Detection Approach to Traffic Anomalies

2011 ◽  
Vol 130-134 ◽  
pp. 2098-2102
Author(s):  
Ding De Jiang ◽  
Cheng Yao ◽  
Zheng Zheng Xu ◽  
Peng Zhang ◽  
Zhen Yuan ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Network Traffic ◽  
Wavelet Transforms ◽  
Detection Threshold ◽  
Continuous Wavelet ◽  
Continuous Wavelet Transforms ◽  
Traffic Characteristics ◽  
Analysis Theory ◽  
Detection Approach

Anomalous traffic often has a significant impact on network activities and lead to the severe damage to our networks because they usually are involved with network faults and network attacks. How to detect effectively network traffic anomalies is a challenge for network operators and researchers. This paper proposes a novel method for detecting traffic anomalies in a network, based on continuous wavelet transform. Firstly, continuous wavelet transforms are performed for network traffic in several scales. We then use multi-scale analysis theory to extract traffic characteristics. And these characteristics in different scales are further analyzed and an appropriate detection threshold can be obtained. Consequently, we can make the exact anomaly detection. Simulation results show that our approach is effective and feasible.

scholarly journals Brain Activity Measurement during a Mental Arithmetic Task in fNIRS Signal Using Continuous Wavelet Transform

2021 ◽  
Author(s):  
Farzaneh Aliabadi Farahani ◽  
Mehrdad Dadgostar ◽  
Zahra Einalou
Keyword(s):  
Prefrontal Cortex ◽  
Wavelet Transform ◽  
Frontal Cortex ◽  
Continuous Wavelet Transform ◽  
Mental Arithmetic ◽  
Average Energy ◽  
Continuous Wavelet ◽  
Frequency Range ◽  
Arithmetic Task ◽  
Mental Arithmetic Task

Purpose: Functional Near-Infrared Spectroscopy (fNIRS) is a non-invasive imaging technology with widespread use in cognitive sciences and clinical studies. It indirectly measures neural activation by measuring alterations of oxyhemoglobin (HbO2) and deoxyhemoglobin (Hb) in tissues. This study used mental arithmetic task for analyzing the activation of the frontal cortex. Materials and methods: The fNIRS instrument was used for measuring the alterations of HbO2 and Hb in healthy subjects during the task. Then the recorded signals were filtered in the frequency range of 3 to 80 mHz. The Continuous Wavelet Transform (CWT) of each of the HbO2 and Hb signals in each channel was calculated in the intended frequency range, followed by the calculation of the energy of obtained coefficients. Finally, for the performed tasks, the average energy of each channel in each region was obtained. Then the energies of spatially symmetric channel pairs in the two hemispheres were compared using the t-test. Results: Results demonstrated that the average energy of HbO2 signal for corresponding channels in the temporal, Medial Prefrontal Cortex (MPFC), and Dorsolateral Prefrontal Cortex (DLPFC) regions had significant differences (P<0.05). Also, a significant difference was observed in the temporal, medial prefrontal, and Ventrolateral Prefrontal Cortex (VLPFC) regions for Hb signal. Conclusion: The obtained results indicate activation in both HbO2 and Hb signals in the DLPFC, temporal, and MPFC regions, considering the performance of memory and the frontal cortex under mental arithmetic tasks. Therefore, it can be concluded that this technique is effective and appropriate for analyzing alterations of brain oxygen levels during cognitive activity.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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