Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Satellite Image Adaptive Restoration Using Periodic Plus Smooth Image Decomposition and Complex Wavelet Packet Transforms

A satellite image adaptive restoration method was developed that avoids ringing artifacts at the image boundary and retains oriented features. The method combines periodic plus smooth image decom- position with complex wavelet packet transforms. The framework first decomposes a degraded satellite im- age into the sum of a ＂periodic component＂ and a ＂smooth component＂. The Bayesian method is then used to estimate the modulation transfer function degradation parameters and the noise. The periodic component is deconvoluted using complex wavelet packet transforms with the deconvolution result of the periodic component then combined with the smooth component to get the final recovered result. Tests show that this strategy effectively avoids ringing artifacts while preserving local image details （especially directional tex- tures） without amplifying the noise. Quantitative comparisons illustrate that the results are comparable with previous methods. Another benefit is that this approach can process large satellite images with parallel processing, which is important for practical use.

A New HFRT Algorithm Based on Maximal Overlap Discrete Wavelet Packet Transformation

The high frequency resonant technique （HFRT） algorithm is a popular technique for fault-detection and is widely applied in mechanism systems and industrial constructions. In this paper, a new HFRT algorithm based on maximal overlap discrete wavelet packet transformation （MODWPT） is developed. By the simulation test for soil embedded pipes fault-detection, it is shown that the performance of newly proposed HFRT algorithms is more sensitive to early defects than the traditional HFRT methods based on the Hilbert transform.

Ignition Pattern Analysis for Automotive Engine Trouble Diagnosis Using Wavelet Packet Transform and Support Vector Machines

Engine spark ignition is an important source for diagnosis of engine faults.Based on the waveform of the ignition pattern,a mechanic can guess what may be the potential malfunctioning parts of an engine with his/her experience and handbooks.However,this manual diagnostic method is imprecise because many spark ignition patterns are very similar.Therefore,a diagnosis needs many trials to identify the malfunctioning parts.Meanwhile the mechanic needs to disassemble and assemble the engine parts for verification.To tackle this problem,an intelligent diagnosis system was established based on ignition patterns.First,the captured patterns were normalized and compressed.Then wavelet packet transform（WPT） was employed to extract the representative features of the ignition patterns.Finally,a classification system was constructed by using multi-class support vector machines（SVM） and the extracted features.The classification system can intelligently classify the most likely engine fault so as to reduce the number of diagnosis trials.Experimental results show that SVM produces higher diagnosis accuracy than the traditional multilayer feedforward neural network.This is the first trial on the combination of WPT and SVM to analyze ignition patterns and diagnose automotive engines.

FEATURE EXTRACTION OF VIBRATION SIGNALS BASED ON WAVELET PACKET TRANSFORM

A method is proposed for the analysis of vibration signals from components ofrotating machines, based on the wavelet packet transformation (WPT) and the underlying physicalconcepts of modulation mechanism. The method provides a finer analysis and better time-frequencylocalization capabilities than any other analysis methods. Both details and approximations are splitinto finer components and result in better-localized frequency ranges corresponding to each node ofa wavelet packet tree. For the punpose of feature extraction, a hard threshold is given and theenergy of the coefficients above the threshold is used, as a criterion for the selection of the bestvector. The feature extraction of a vibration signal is accomplished by computing thereconstruction signal and its spectrum. When applied to a rolling bear vibration signal featureextraction, the proposed method can lead to be very effective.

Classification using wavelet packet decomposition and support vector machine for digital modulations

To make the modulation classification system more suitable for signals in a wide range of signal to noise rate （SNR）, a feature extraction method based on signal wavelet packet transform modulus maxima matrix （WPTMMM） and a novel support vector machine fuzzy network （SVMFN） classifier is presented. The WPTMMM feature extraction method has less computational complexity, more stability, and has the preferable advantage of robust with the time parallel moving and white noise. Further, the SVMFN uses a new definition of fuzzy density that incorporates accuracy and uncertainty of the classifiers to improve recognition reliability to classify nine digital modulation types （i.e. 2ASK, 2FSK, 2PSK, 4ASK, 4FSK, 4PSK, 16QAM, MSK, and OQPSK）. Computer simulation shows that the proposed scheme has the advantages of high accuracy and reliability （success rates are over 98% when SNR is not lower than 0dB）, and it adapts to engineering applications.

Damage Detection Methods for Offshore Platforms Based on Wavelet Packet Transform

The wavelet packet transform is used for the damage detection of offshore platforms. When some damage occurs, the dynamic response parameters of the structure will shift subtly. However, in some cases, the dynamic parameters, such as dynamic response, are not sensitive, and it is very difficult to predict the existence of damage. The present paper aims to describe how to find small damage by the use of wavelet packet transform. As the wavelet packet transform can be used to quickly find the singularity of the response signal on different scales, the acceleration signal of a damaged offshore platform in the time domain is transformed through the wavelet packet. Experimental results show that the Daubechies 4 wavelet transform can be used to detect damage.

Radar Emitter Signal Recognition Using Wavelet Packet Transform and Support Vector Machines

This paper presents a novel method for radar emitter signal recognition. First, wavelet packet transform （WPT） is introduced to extract features from radar emitter signals. Then, rough set theory is used to select the optimal feature subset with good discriminability from original feature set, and support vector machines （SVMs） are employed to design classifiers. A large number of experimental results show that the proposed method achieves very high recognition rates for 9 radar emitter signals in a wide range of signal-to-noise rates, and proves a feasible and valid method.

Motion Classification of EMG Signals Based on Wavelet Packet Transform and LS-SVMs Ensemble

This paper presents an effective method for motion classification using the surface electromyographic (sEMG) signal collected from the forearm. Given the nonlinear and time-varying nature of EMG signal, the wavelet packet transform (WPT) is introduced to extract time-frequency joint information. Then the multi-class classifier based on the least squares support vector machine (LS-SVM) is constructed and verified in the various motion classification tasks. The results of contrastive experiments show that different motions can be identified with high accuracy by the presented method. Furthermore, compared with other classifiers with different features, the performance indicates the potential of the SVM techniques combined with WPT in motion classification.

A NOVEL ALGORITHM OF MULTI-SENSOR IMAGE FUSION BASED ON WAVELET PACKET TRANSFORM

In order to enhance the image information from multi-sensor and to improve the abilities of the information analysis and the feature extraction, this letter proposed a new fusion approach in pixel level by means of the Wavelet Packet Transform (WPT). The WPT is able to decompose an image into low frequency band and high frequency band in higher scale. It offers a more precise method for image analysis than Wavelet Transform (WT). Firstly, the proposed approach employs HIS (Hue, Intensity, Saturation) transform to obtain the intensity component of CBERS (China-Brazil Earth Resource Satellite) multi-spectral image. Then WPT transform is employed to decompose the intensity component and SPOT (Systeme Pour I'Observation de la Therre ) image into low frequency band and high frequency band in three levels. Next, two high frequency coefficients and low frequency coefficients of the images are combined by linear weighting strategies. Finally, the fused image is obtained with inverse WPT and inverse HIS. The results show the new approach can fuse details of input image successfully, and thereby can obtain a more satisfactory result than that of HM (Histogram Matched)-based fusion algorithm and WT-based fusion approach.

Study of the Functions of Wavelet Packet Transform （WPT） and Continues Wavelet Transform （CWT） in Recognizing the Damage Specification

Modem and efficient methods focus on signal analysis and have drawn researchers＇ attention to it in recent years. These methods mainly include Continuous Wavelet and Wavelet Packet transforms. The main advantage of the application of these Wavelets is their capacity to analyze the signal position in different occasions and places. However, in sites with high frequencies its resolution becomes much more difficult. Wavelet packet transform is a more advanced form of continuous wavelets and can make a perfect level by level resolution for each signal. Although very few studies have been done in the field. In order to do this, in the present study, f^st there was an attempt to do a modal analysis on the structure by the ANSYS finite elements software, then using MATLAB, the wavelet was investigated through a continuous wavelet analysis. Finally the results were displayed in 2-D location-coefficient figures. In the second form, transient-dynamic analysis was done on the structure to find out the characteristics of the damage and the wavelet packet energy rate index was suggested. The results indicate that suggested index in the second form is both practical and applicable, and also this index is sensitive to the intensity of the damage.

Multicomponent Kinetic Determination by Wavelet Packet Transform Based Elman Recurrent Neural Network Method

This paper covers a novel method named wavelet packet transform based Elman recurrent neural network(WPTERNN) for the simultaneous kinetic determination of periodate and iodate. The wavelet packet representations of signals provide a local time-frequency description, thus in the wavelet packet domain, the quality of the noise removal can be improved. The Elman recurrent network was applied to non-linear multivariate calibration. In this case, by means of optimization, the wavelet function, decomposition level and number of hidden nodes for WPTERNN method were selected as D4, 5 and 5 respectively. A program PWPTERNN was designed to perform multicomponent kinetic determination. The relative standard error of prediction(RSEP) for all the components with WPTERNN, Elman RNN and PLS were 3.23%, 11.8% and 10.9% respectively. The experimental results show that the method is better than the others.

Fluorescence Discrimination and Determination Technique for Phytoplankton Composition by Coif2 Wavelet Packet

An in vivo fluorescence discrimination technique for phytoplankton population was developed by using Wavelet packet transform, cluster analysis and non-negative least squares. The technique was used to analyze water samples from different sea regions. For simulative mixtures, when dominant species account for 60%, 70%, 80%, 90% at the division level, the correct discrimination ratios (CDRs) are 83.0%, 99.1%, 99.7% and 99.9% with the relative contents of 58.5%, 68.4%, 77.7% and 86.3%, respectively; when the algae dominance are 60%, 70%, 80%, 90%, 100% at the genus level, the CDRs are 86.1%, 94.9%, 95.2%, 96.8% and 96.7%, respectively. For laboratory mixtures, the CDRs are 88.1% and 78.4% at the division and genus level, respectively. For field samples, the CDRs were 91.7% and 80% at the division and genus level, respectively (mesocosm experiments), and the CDRs were 100% and 66.7% at the division and genus level, respectively (Jiaozhou Bay). The fluorometric technique was used to estimate the phytoplankton community composition and relative abundance of different classes for the April 2010 cruise in the Yellow Sea with the results agreeing with those in published papers by other authors.

Seismic signal analysis based on the dual-tree complex wavelet packet transform

We tried to apply the dual-tree complex wavelet packet transform in seismic signal analysis. The complex wavelet packet transform (CWPT) combine the merits of real wavelet packet transform with that of complex continuous wavelet transform (CCWT). It can not only pick up the phase information of signal, but also produce better ″focal- izing″ function if it matches the phase spectrum of signals analyzed. We here described the dual-tree CWPT algo- rithm, and gave the examples of simulation and actual seismic signals analysis. As shown by our results, the dual-tree CWPT is a very effective method in analyzing seismic signals with non-linear phase.

OFDM Scheme Based on Wavelet Packet Transform-Oriented Graded Multi-Service

In this paper, a concept of image grading transmission is put forward to enhance data rate and to improve the usage of subcarriers in orthogonal frequency division multiplexing (OFDM). The idea originates from the wavelet packets representative of an image in which information is graded in terms of different priorities. The graded image facilitates more efficient use of adaptive subcarriers and bits allocation. The results of simulation in typical mobile environment prove that the output signal noise ratio (SNR) of the graded image excels that of the ungraded image by 1—2 dB under the same channel condition.

Defects Recognition of 3D Braided Composite Based on Dual-Tree Complex Wavelet Packet Transform

Textile-reinforced composites,due to their excellent highstrength-to-low-mass ratio, provide promising alternatives to conventional structural materials in many high-tech sectors. 3D braided composites are a kind of advanced composites reinforced with 3D braided fabrics; the complex nature of 3D braided composites makes the evaluation of the quality of the product very difficult. In this investigation,a defect recognition platform for 3D braided composites evaluation was constructed based on dual-tree complex wavelet packet transform( DT-CWPT) and backpropagation( BP) neural networks. The defects in 3D braided composite materials were probed and detected by an ultrasonic sensing system. DT-CWPT method was used to analyze the ultrasonic scanning pulse signals,and the feature vectors of these signals were extracted into the BP neural networks as samples. The type of defects was identified and recognized with the characteristic ultrasonic wave spectra. The position of defects for the test samples can be determined at the same time. This method would have great potential to evaluate the quality of 3D braided composites.

Matrix Expression of the Orthogonal Wavelet (Packets) Transform

Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *

A method to compress vibration signals using wavelet packet transformation combined with sub-band vector quantization

A novel compression method for mechanical vibrating signals,binding with sub-band vector quantization(SVQ) by wavelet packet transformation(WPT) and discrete cosine transformation(DCT) is proposed.Firstly,the vibrating signal is decomposed into sub-bands by WPT.Then DCT and adaptive bit allocation are done per sub-band and SVQ is performed in each sub-band.It is noted that,after DCT,we only need to code the first components whose numbers are determined by the bits allocated to that sub-band.Through an actual signal,our algorithm is proven to improve the signal-to-noise ratio(SNR) of the reconstructed signal effectively,especially in the situation of lowrate transmission.

Structural Damage Identification via Pseudo Strain Energy Density and Wavelet Packet Transform

Based on strain signals, a new time-domain methodology for detecting the beam local damage has been developed. The pseudo strain energy density （PSED） is defined and used to build two major damage indexes, the average pseudo strain energy density （APSED） and the average pseudo strain energy density rate （APSEDR）. Probability and mathematical statistics are utilized to derive a standardized damage index. Furthermore, by applying the analytic relation between the strain energy release rate and the stress intensity factor, an analytic solution of crack depth is derived. For the dynamic strain signals, the wavelet packet transform is used to pre-process measured data. Finally, a numerical simulation indicates that this method can effectively identify the damage location and its absolute severity.

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.