New decoupled wavelet bases for multiresolution structural analysis

Wang, Youming,Chen, Xuefeng,He, Yumin,He, Zhengjia Techno-Press 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.35 No.2

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

Damage detection using the improved Kullback-Leibler divergence

Tian, Shaohua,Chen, Xuefeng,Yang, Zhibo,He, Zhengjia,Zhang, Xingwu Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.3

Structural health monitoring is crucial to maintain the structural performance safely. Moreover, the Kullback-Leibler divergence (KLD) is applied usually to asset the similarity between different probability density functions in the pattern recognition. In this study, the KLD is employed to detect the damage. However the asymmetry of the KLD is a shortcoming for the damage detection, to overcoming this shortcoming, two other divergences and one statistic distribution are proposed. Then the damage identification by the KLD and its three descriptions from the symmetric point of view is investigated. In order to improve the reliability and accuracy of the four divergences, the gapped smoothing method (GSM) is adopted. On the basis of the damage index approach, the new damage index (DI) for detect damage more accurately based on the four divergences is developed. In the last, the grey relational coefficient and hypothesis test (GRCHT) is utilized to obtain the more precise damage identification results. Finally, a clear remarkable improvement can be observed. To demonstrate the feasibility and accuracy of the proposed method, examples of an isotropic beam with different damage scenarios are employed so as to check the present approaches numerically. The final results show that the developed approach successfully located the damaged region in all cases effect and accurately.

Multiple damages detection in beam based approximate waveform capacity dimension

Yang, Zhibo,Chen, Xuefeng,Tian, Shaohua,He, Zhengjia Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.5

A number of mode shape-based structure damage identification methods have been verified by numerical simulations or experiments for on-line structure health monitoring (SHM). However, many of them need a baseline mode shape generated by the healthy structure serving as a reference to identify damages. Otherwise these methods can hardly perform well when multiple cracks conditions occur. So it is important to solve the problems above. By aid of the fractal dimension method (FD), Qiao and Wang proposed a generalized fractal dimension (GFD) to detect the delamination damage. As a modification of GFD, Qiao and Cao proposed the approximate waveform capacity dimension (AWCD) technique to simplify the calculation of fractal and overcome the false peak appearing in the high mode shapes. Based on their valued work, this paper combined and applied the AWCD method and curvature mode shape data to detect multiple damages in beam. In the end, the identification properties of the AWCD for multiple damages have been verified by groups of Monte Carlo simulations and experiments.

The construction of multivariable Reissner-Mindlin plate elements based on B-spline wavelet on the interval

Zhang, Xingwu,Chen, Xuefeng,He, Zhengjia Techno-Press 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.38 No.6

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

New decoupled wavelet bases for multiresolution structural analysis

Youming Wang,Xuefeng Chen,Yumin He,Zhengjia He 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.35 No.2

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval

Xiang, Jiawei,He, Zhengjia,He, Yumin,Chen, Xuefeng Techno-Press 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.25 No.5

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

Damage detection using the improved Kullback-Leibler divergence

Shaohua Tian,Xuefeng Chen,Zhibo Yang,Zhengjia He,Xingwu Zhang 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.3

Structural health monitoring is crucial to maintain the structural performance safely. Moreover, the Kullback-Leibler divergence (KLD) is applied usually to asset the similarity between different probability density functions in the pattern recognition. In this study, the KLD is employed to detect the damage. However the asymmetry of the KLD is a shortcoming for the damage detection, to overcoming this shortcoming, two other divergences and one statistic distribution are proposed. Then the damage identification by the KLD and its three descriptions from the symmetric point of view is investigated. In order to improve the reliability and accuracy of the four divergences, the gapped smoothing method (GSM) is adopted. On the basis of the damage index approach, the new damage index (DI) for detect damage more accurately based on the four divergences is developed. In the last, the grey relational coefficient and hypothesis test (GRCHT) is utilized to obtain the more precise damage identification results. Finally, a clear remarkable improvement can be observed. To demonstrate the feasibility and accuracy of the proposed method, examples of an isotropic beam with different damage scenarios are employed so as to check the present approaches numerically. The final results show that the developed approach successfully located the damaged region in all cases effect and accurately.

Multiple damages detection in beam based approximate waveform capacity dimension

Zhibo Yang,Xuefeng Chen,Shaohua Tian,Zhengjia He 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.5

A number of mode shape-based structure damage identification methods have been verified by numerical simulations or experiments for on-line structure health monitoring (SHM). However, many of them need a baseline mode shape generated by the healthy structure serving as a reference to identify damages. Otherwise these methods can hardly perform well when multiple cracks conditions occur. So it is important to solve the problems above. By aid of the fractal dimension method (FD), Qiao and Wang proposed a generalized fractal dimension (GFD) to detect the delamination damage. As a modification of GFD, Qiao and Cao proposed the approximate waveform capacity dimension (AWCD) technique to simplify the calculation of fractal and overcome the false peak appearing in the high mode shapes. Based on their valued work, this paper combined and applied the AWCD method and curvature mode shape data to detect multiple damages in beam. In the end, the identification properties of the AWCD for multiple damages have been verified by groups of Monte Carlo simulations and experiments.

The construction of multivariable Reissner-Mindlin plate elements based on B-spline wavelet on the interval

Xingwu Zhang,Xuefeng Chen,Zhengjia He 국제구조공학회 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.38 No.6

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

Sifting process of EMD and its application in rolling element bearing fault diagnosis

Hongbo Dong,Keyu Qi,Xuefeng Chen,Yanyang Zi,Zhengjia He,Bing Li 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.8

Among the vibration-based fault diagnosis methods for rolling element bearing, the shock pulse method (SPM) combined with the demodulation method is a useful quantitative technique for estimating bearing running state. However, direct demodulation often misestimates the shock value of characteristic defect frequency. To overcome this disadvantage, the vibration signal should be decomposed before demodulation. Empirical mode decomposition (EMD) can be an alternative for preprocess bearing fault signals. However, the trouble with this method’s application is that it is time-consuming. Therefore, a novel method that can improve the sifting process’s efficiency is proposed, in which only one time of cubic spline fitting is required in each sifting process. As a consequence, the time for EMD analysis can be evidently shortened and the decomposition results simultaneously maintained at a high precision. Simulations and experiments verify that the improved EMD method, combined with SPM and demodulation analysis, is efficient and accurate and can be effectively applied in engineering practice.