Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

HYBRID WAVELET PACKET-TEAGER ENERGY OPERATOR ANALYSIS AND ITS APPLICATION FOR GEARBOX FAULT DIAGNOSIS

Based on wavelet packet decomposition （WPD） algorithm and Teager energy operator （TEO）, a novel gearbox fault detection and diagnosis method is proposed. Its process is expatiated after the principles of WPD and TEO modulation are introduced respectively. The preprocessed sigaaal is interpolated with the cubic spline function, then expanded over the selected basis wavelets. Grouping its wavelet packet components of the signal based on the minimum entropy criterion, the interpolated signal can be decomposed into its dominant components with nearly distinct fault frequency contents. To extract the demodulation information of each dominant component, TEO is used. The performance of the proposed method is assessed by means of several tests on vibration signals collected from the gearbox mounted on a heavy truck. It is proved that hybrid WPD-TEO method is effective and robust for detecting and diagnosing localized gearbox faults.

Multi-scale analysis of earthquake activity in Chinese mainland

Identifying the active and inactive period of earthquakes in Chinese mainland is of great importance for guiding mid-short term, especially short term, earthquake forecast.……

Feature Extraction by Multi-Scale Principal Component Analysis and Classification in Spectral Domain

Feature extraction of signals plays an important role in classification problems because of data dimension reduction property and potential improvement of a classification accuracy rate. Principal component analysis (PCA), wavelets transform or Fourier transform methods are often used for feature extraction. In this paper, we propose a multi-scale PCA, which combines discrete wavelet transform, and PCA for feature extraction of signals in both the spatial and temporal domains. Our study shows that the multi-scale PCA combined with the proposed new classification methods leads to high classification accuracy for the considered signals.

A NOVEL METHOD FOR NETWORK WORM DETECTION BASED ON WAVELET PACKET ANALYSIS

Objective To detect unknown network worm at its early propagation stage. Methods On the basis of characteristics of network worm attack, the concept of failed connection flow (FCT) was defined. Based on wavelet packet analysis of FCT time series, this method computed the energy associated with each wavelet packet of FCT time series, transformed the FCT time series into a series of energy distribution vector on frequency domain, then a trained K-nearest neighbor (KNN) classifier was applied to identify the worm. Results The experiment showed that the method could identify network worm when the worm started to scan. Compared to theoretic value, the identification error ratio was 5.69%. Conclusion The method can detect unknown network worm at its early propagation stage effectively.

Application of Wavelet Packet De-noising in Time-Frequency Analysis of the Local Wave Method

The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

The Ying-Qiong Basin is located on the northwestern margin of the South China Sea and at the junction of the South China Block and the Indochina Block.It is characterized by complex geological structures.The existing seismic data in the study area is sparse due to the lack of earthquake activities.Because of the limited source energy and poor coverage of seismic data,the knowledge of deep structures in the area,including the spatial distribution of deep faults,is incomplete.Contrarily,satellite gravity data cover the entire study area and can reveal the spatial distribution of faults.Based on the wavelet multi-scale decomposition method,the Bouguer gravity field in the Ying-Qiong Basin was decomposed and reconstructed to obtain the detailed images of the first-to sixth-order gravitational fields.By incorporating the known geological features,the gravitational field responses of the main faults in the Ying-Qiong Basin were identified in the detailed fields,and the power spectrum analysis yielded the depths of 1.4,8,15,26.5,and 39 km for the average burial depths of the bottom surfaces from the first-to fifth-order detailed fields,respectively.The four main faults in the Yinggehai Basin all have a large active depth range:fault A(No.1)is between 5 and 39 km,fault B is between 26.5 and 39 km,and faults C and D are between 15 and 39 km.However,the depth of active faults in the Qiongdongnan Basin is relatively shallow,mainly between 8 and 26.5 km.

Medical Image Segmentation Based on Wavelet Analysis and Gradient Vector Flow

Medical image segmentation is one of the key technologies in computer aided diagnosis. Due to the complexity and diversity of medical images, the wavelet multi-scale analysis is introduced into GVF (gradient vector flow) snake model. The modulus values of each scale and phase angle values are calculated using wavelet transform, and the local maximum points of modulus values, which are the contours of the object edges, are obtained along phase angle direction at each scale. Then, location of the edges of the object and segmentation is implemented by GVF snake model. The experiments on some medical images show that the improved algorithm has small amount of computation, fast convergence and good robustness to noise.

Influence of explosion parameters on wavelet packet frequency band energy distribution of blast vibration

Blast vibration analysis is one of the important foundations for studying the control technology of blast vibration damage.According to blast vibration live data that have been collected and the characteristics of short-time non-stationary random signals,the wavelet packet energy spectrum analysis for blast vibration signal has made by wavelet packet analysis technology and the signals were measured under different explosion parameters(the maximal section dose,the distance of blast source to measuring point and the section number of millisecond detonator).The results show that more than 95% frequency band energy of the signals s1-s8 concentrates at 0-200 Hz and the main vibration frequency bands of the signals s1-s8 are 70.313-125,46.875-93.75,15.625-93.75,0-62.5,42.969-125,15.625-82.031,7.813-62.5 and 0-62.5 Hz.Energy distributions for different frequency bands of blast vibration signal are obtained and the characteristics of energy distributions for blast vibration signal measured under different explosion parameters are analyzed.From blast vibration signal energy,the decreasing law of blast seismic waves measured under different explosion parameters was studied and the wavelet packet analysis is an effective means for studying seismic effect induced by blast.

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper,an Automated Brain Image Analysis(ABIA)system that classifies the Magnetic Resonance Imaging(MRI)of human brain is presented.The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis.The Non-Subsampled Shearlet Transform(NSST)that captures more visual information than conventional wavelet transforms is employed for feature extraction.As the feature space of NSST is very high,a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies.A combination of features that includes Gray Level Co-occurrence Matrix(GLCM)based features,Histograms of Positive Shearlet Coefficients(HPSC),and Histograms of Negative Shearlet Coefficients(HNSC)are estimated.The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers;k-Nearest Neighbor(kNN),Naive Bayes(NB)and Support Vector Machine(SVM)classifiers.The output of individual trained classifiers for a testing input is hybridized to take a final decision.The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data(REMBRANDT)database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.

Underdetermined Blind Mixing Matrix Estimation Using STWP Analysis for Speech Source Signals

Wavelet packets decompose signals in to broader components using linear spectral bisecting. Mixing matrix is the key issue in the Blind Source Separation (BSS) literature especially in under-determined cases. In this paper, we propose a simple and novel method in Short Time Wavelet Packet (STWP) analysis to estimate blindly the mixing matrix of speech signals from noise free linear mixtures in over-complete cases. In this paper, the Laplacian model is considered in short time-wavelet packets and is applied to each histogram of packets. Expectation Maximization (EM) algorithm is used to train the model and calculate the model parameters. In our simulations, comparison with the other recent results will be computed and it is shown that our results are better than others. It is shown that complexity of computation of model is decreased and consequently the speed of convergence is increased.

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

珍视向量的 multiresolution 分析的观点被介绍，有3规模的直角的珍视向量的小浪的概念是直角的珍视向量的小浪的存在上的状况借助于 paraunitary 向量过滤器银行 theory.An 算法被给的必要、足够的 proposed.A 因为构造简洁地支持的直角的珍视向量的小浪的一个班是 presented.Their 特征被讨论由操作员理论的优点，时间频率 method.Moreover ，它被看

The Biorthogonality of Multiple Vector-valued Bivariate Wavelet Packets

The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.

Novel Adaptive Beamforming Algorithm Based on Wavelet Packet Transform

An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packet theory to adaptive beamforming, a wavelet packet transform-based adaptive beamforming algorithm (WP-ABF) is proposed . This WP-ABF algorithm uses wavelet packet transform as the preprocessing, and the wavelet packet transformed signal uses least mean square algorithm to implement the ~adaptive beamforming. White noise can be wiped off under wavelet packet transform according to the different characteristics of signal and white under the wavelet packet transform. Theoretical analysis and simulations demonstrate that the proposed WP-ABF algorithm converges faster than the conventional adaptive beamforming algorithm and the wavelet transform-based beamforming algorithm. Simulation results also reveal that the convergence of the algorithm relates closely to the wavelet base and series; that is, the algorithm convergence gets better with the increasing of series, and for the same series of wavelet base the convergence gets better with the increasing of regularity.

DWPT-Based Sub-Band Analysis for FaultDetection of Rolling Element Bearings

To early detect symptoms of defective rolling element bearings, this paper introduces discrete wavelet packet transform （DWPT）-based sub-band analysis. The objective of this analysis is to explore the impacts of multiple sub-band signals by 4-level DWPTusing proper Daubechies mother wavelet on a 2.5-second acoustic emission signal. In particular, the DWPT-based sub-bandanalysis determines the most informative sub-band signal involving intrinsic information about bearing defects among theaforementioned multiple sub-band signals based on the ratio of spectral magnitudes at harmonics of the bearing＇s characteristicfrequency to those around the harmonics. This paper also verifies the efficacy of the DWPT-based sub-band analysis for seededbearing defects （i.e., a crack on the inner race, the outer race, or a roller）.

Impulse Response Identification Based on Varying Scale Orthogonal Wavelet Packet Transform

In this paper, by applying a group of specific orthogonal wavelet packet to Eykho?algorithm, a new impulse response identification algorithm based on varying scale orthogonal WPTis provided. In comparison to Eykho? algorithm, the new algorithm has better practicability andwider application range. Simulation results show that the proposed impulse response identificationalgorithm can be applied to both deterministic and random systems, and is of higher identificationprecision, stronger anti-noise interference ability and better system dynamic tracking property.