• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.281-294
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• 2016

The paper is devoted to study a mesh-free analysis method of structural elements of engineering structures based on B-spline Wavelet Basis Function. First, by employing the moving-least square method and the weighted residual method to solve the structural displacement field, the control equations and the stiffness equations are obtained. And then constructs the displacement field of the structure by using the m-order B-spline wavelet basis function as a weight function. In the end, the paper selects the plane beam structure and the structure with opening hole to carry out numerical analysis of deformation and stress. The Finite Element Method calculation results are compared with the results of the method proposed, and the calculation results of the relative error norm is compared with Gauss weight function as weight function. Therefore, the clarification verified the validity and accuracy of the proposed method.

• Smart Structures and Systems
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• v.16 no.1
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• pp.47-65
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• 2015

A novel finite element (FE) model updating method based on multi-resolution analysis (MRA) is proposed. The true stiffness of the FE model is considered as the superposition of two pieces of stiffness information of different resolutions: the pre-defined stiffness information and updating stiffness information. While the resolution of former is solely decided by the meshing density of the FE model, the resolution of latter is decided by the limited information obtained from the experiment. The latter resolution is considerably lower than the former. Second generation wavelet is adopted to describe the updating stiffness information in the framework of MRA. This updating stiffness in MRA is realized at low level of resolution, therefore, needs less number of updating parameters. The efficiency of the optimization process is thus enhanced. The proposed method is suitable for the identification of multiple irregular cracks and performs well in capturing the global features of the structural damage. After the global features are identified, a refinement process proposed in the paper can be carried out to improve the performance of the MRA of the updating information. The effectiveness of the method is verified by numerical simulations of a box girder and the experiment of a three-span continues pre-stressed concrete bridge. It is shown that the proposed method corresponds well to the global features of the structural damage and is stable against the perturbation of modal parameters and small variations of the damage.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

• Smart Structures and Systems
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• v.11 no.6
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• pp.589-604
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• 2013

Identification of damage has become an evolving area of research over the last few decades with increasing the need of online health monitoring of the large structures. The visual damage detection can be impractical, expensive and ineffective in case of large structures, e.g., offshore platforms, offshore pipelines, multi-storied buildings and bridges. Damage in a system causes a change in the dynamic properties of the system. The structural damage is typically a local phenomenon, which tends to be captured by higher frequency signals. Most of vibration-based damage detection methods require modal properties that are obtained from measured signals through the system identification techniques. However, the modal properties such as natural frequencies and mode shapes are not such good sensitive indication of structural damage. Identification of damaged jacket type offshore platform members, based on wavelet packet transform is presented in this paper. The jacket platform is excited by simple wave load. Response of actual jacket needs to be measured. Dynamic signals are measured by finite element analysis result. It is assumed that this is actual response of the platform measured in the field. The dynamic signals first decomposed into wavelet packet components. Then eliminating some of the component signals (eliminate approximation component of wavelet packet decomposition), component energies of remained signal (detail components) are calculated and used for damage assessment. This method is called Detail Signal Energy Rate Index (DSERI). The results show that reduced wavelet packet component energies are good candidate indices which are sensitive to structural damage. These component energies can be used for damage assessment including identifying damage occurrence and are applicable for finding damages' location.

• Interaction and multiscale mechanics
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• v.5 no.3
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• pp.169-185
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• 2012

The concrete bridge is likely to produce fatigue cracks during long period of service due to the moving vehicular loads and the degeneration of materials. This paper deals with the time-frequency analysis of a coupled bridge-vehicle system. The bridge is modeled as an Euler beam with breathing cracks. The vehicle is represented by a two-axle vehicle model. The equation of motion of the coupled bridge-vehicle system is established using the finite element method, and the Newmark direct integration method is adopted to calculate the dynamic responses of the system. The effect of breathing cracks on the dynamic responses of the bridge is investigated. The time-frequency characteristics of the responses are analyzed using both the Hilbert-Huang transform and wavelet transform. The results of time-frequency analysis indicate that complicated non-linear and non-stationary features will appear due to the breathing effect of the cracks.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.77-91
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• 2011

A simply structural damage detection software is developed to identification damage in beams. According to linear fracture mechanics theory, the localized additional flexibility in damage vicinity can be represented by a lumped parameter element. The damaged beam is modeled by wavelet-based elements to gain the first three frequencies precisely. The first three frequencies influencing functions of damage location and depth are approximated by means of surface-fitting techniques to gain damage detection database of forward problem. Then the first three measured natural frequencies are employed as inputs to solve inverse problem and the intersection of the three frequencies contour lines predict the damage location and depth. The DLL (Dynamic Linkable Library) file of damage detection method is coded by C++ and the corresponding interface of software is coded by virtual instrument software LabVIEW. Finally, the software is tested on beams and shafts in engineering. It is shown that the presented software can be used in actual engineering structures.

• Smart Structures and Systems
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• v.20 no.2
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• pp.139-150
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• 2017

The structural strain plays a significant role in structural condition assessment of in-service bridges in terms of structural bearing capacity, structural reliability level and entire safety redundancy. Therefore, it has been one of the most important parameters concerned by researchers and engineers engaged in structural health monitoring (SHM) practices. In this paper, an SHM system instrumented on the Jiubao Bridge located in Hangzhou, China is firstly introduced. This system involves nine subsystems and has been continuously operated for five years since 2012. As part of the SHM system, a total of 166 fiber Bragg grating (FBG) strain sensors are installed on the bridge to measure the dynamic strain responses of key structural components. Based on the strain monitoring data acquired in recent two years, the strain-based structural condition assessment of the Jiubao Bridge is carried out. The wavelet multi-resolution algorithm is applied to separate the temperature effect from the raw strain data. The obtained strain data under the normal traffic and wind condition and under the typhoon condition are examined for structural safety evaluation. The structural condition rating of the bridge in accordance with the AASHTO specification for condition evaluation and load and resistance factor rating of highway bridges is performed by use of the processed strain data in combination with finite element analysis. The analysis framework presented in this study can be used as a reference for facilitating the assessment, inspection and maintenance activities of in-service bridges instrumented with long-term SHM system.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.1-8
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• 2010

The Fourier series uses a vibrating wave that possesses an amplitude that is like the one of the sine curve. Therefore, the functions used in the Fourier series do not change due to the value of the frequency and that set a limit to express irregular signals with rapid oscillations or with discontinuities in localized regions. However, the wavelet series analysis(WSA) method supplements these limits of the Fourier series by a linear combination of a suitable number of wavelets. By using the wavelet that is focused on time, it is able to give changes to the range in the cycle. Also, this enables to express a signal more efficiently that has singular configuration and that is flowing. The main objective of this study is to propose a scheme called wavelet series analysis for the application of wavelet theory to one-dimensional problems represented by the second-order elliptic equation and to evaluate theperformance of proposed scheme comparing with the finite element analysis. After a through evaluation of different types of wavelets, the HAT wavelet system is chosen as a wavelet function as well as a scaling function. It can be stated that the WSA method is as efficient as the FEA method in the case of axial bars with distributed loads, but the WSA method is more accurate than the FEA method at the singular points and its computation time is less.

• Smart Structures and Systems
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• v.19 no.2
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• pp.181-194
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• 2017

In order to investigate the interface debonding defects detection mechanism between steel tube and concrete core of concrete-filled steel tubes (CFSTs), multi-physical fields coupling finite element models constituted of a surface mounted Piezoceramic Lead Zirconate Titanate (PZT) actuator, an embedded PZT sensor and a circular cross section of CFST column are established. The stress wave initiation and propagation induced by the PZT actuator under sinusoidal and sweep frequency excitations are simulated with a two dimensional (2D) plain strain analysis and the difference of stress wave fields close to the interface debonding defect and within the cross section of the CFST members without and with debonding defects are compared in time domain. The linearity and stability of the embedded PZT response under sinusoidal signals with different frequencies and amplitudes are validated. The relationship between the amplitudes of stress wave and the measurement distances in a healthy CFST cross section is also studied. Meanwhile, the responses of PZT sensor under both sinusoidal and sweep frequency excitations are compared and the influence of debonding defect depth and length on the output voltage is also illustrated. The results show the output voltage signal amplitude and head wave arriving time are affected significantly by debonding defects. Moreover, the measurement of PZT sensor is sensitive to the initiation of interface debonding defects. Furthermore, wavelet packet analysis on the voltage signal under sweep frequency excitations is carried out and a normalized wavelet packet energy index (NWPEI) is defined to identify the interfacial debonding. The value of NWPEI attenuates with the increase in the dimension of debonding defects. The results help understand the debonding defects detection mechanism for circular CFST members with PZT technique.