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.

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.

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.

Performance Evaluation of Complex Wavelet Packet Modulation (CWPM) System over Multipath Rayleigh Fading Channel

In this paper a novel multicarrier modulation system called Complex Wavelet Packet Modulation (CWPM) has been proposed. It is based on using the Complex Wavelet Transform (CWT) together with the Wavelet Packet Modulation (WPM). The proposed system has been tested for communication over flat and frequency selective Rayleigh fading channels and its performance has been compared with some other multicarrier systems. The simulation results show that the performance of the proposed CWPM system has the best performance in all types of channel considered as compared with OFDM, Slantlet based OFDM, FRAT based OFDM and WPM systems. Furthermore, the proposed scheme has less PAPR as compared with the traditional WPM multicarrier system.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

Acoustic emission source identification based on harmonic wavelet packet and support vector machine

In order to solve the fatigue damage identification problem of helicopter moving components, a new approach for acoustic emission （AE） source type identification based on the harmonic wavelet packet （HWPT） feature extraction and the hierarchy support vector machine （H-SVM） classifier is proposed. After a four-level decomposition of the HWPT, the energy feature of AE signals in different frequency bands is extracted, which overcomes the shortcomings of the traditional wavelet packet including energy leakage, and inflexible frequency band selection and different frequency resolutions on different levels. The H-SVM classifier is trained with a subset of the experimental data for known AE source types and tested using the remaining set of data. The results of pressure-off experiments on the specimens of carbon fiber materials indicate that the proposed approach can effectively implement the AE source type identification, and has a better performance in terms of computational efficiency and identification accuracy than the wavelet packet （WPT） feature extraction.

Radar Target Discrimination based on waveletPackets for Reduced data Storage

In order to storage resource of a radar recognition system, schemes for reducing data storage and for correlation discrimination of radar based on wavelet packets were proposed Experiment results at various signal-to-noise ratios were given The given.ability of the reduced data method's validity are supported by experimental results. Using optimal basis can get higher successful recognition rate using rigid wavelet basis.

Performance of STBC-MC-CDMA system based on complex wavelet packet and turbo coding

On the basis of analyzing the principle of the space-time coding technique and the multi-carrier code division multiple access （MC-CDMA） technique, adopting the turbo codes as channel coding and the optimized complex wavelet packet as multi-carrier modulation, a novel space-time block coded the MC-CDMA system based on complex wavelet packet and turbo coding is proposed, and the system bit error rate （BER） performance in the Rayleigh fading channel is investigated. The system can make full use of space-time block codes＇ transmit diversity and turbo codes＇ good ability against fading channel to improve the BER performance significantly, and it can also avoid the decrease of spectrum efficiency of conventional MC-CDMA due to inserting cyclic prefix （CP） by utilizing superior characteristics of the optimized complex wavelet packet. Simulation results show that the proposed space-time block coded MC-CDMA system based on the complex wavelet packet performs better than the conventional space-time block coded MC-CDMA （STBC-MC-CDMA） system, and slightly outperforms the STBC-MC-CDMA with CP. Moreover, the application of the space-time block coding technique concatenated with turbo codes strengthens the system ability to combat various interferences in fading channel further.

数控机床电动主轴WPD-TSNE-SVM模型故障诊断

为了提高数控机床电动主轴故障诊断效率,设计了一种WPD-TSNE-SVM组合模型。利用小波包方法分解主轴振动信号,并完成样本集TSNE降维的过程,利用SVM完成重构特征的故障分类。构建数控机床主轴信号混合特征空间向量,并进行故障诊断分析。研究结果表明:TSNE方法训练样数据形成规律分布特点,采用非线性SVM多故障分类器实现小波包混合特征的故障准确分类。根据径向基核函数建立的非线性SVM诊断方法获得更高准确率。该方法诊断轴承运行故障,获得更高维护效率,确保数控机床主轴运行稳定性。

基于EEMD-WPT的温室环境数据优化处理研究

【目的】解决温室系统中的数据采集传感器容易受到多种环境因素的干扰,从而导致数据中存在噪声的问题。【方法】提出一种集合经验模态分解(Ensemble empirical mode decomposition,EEMD)与小波包自适应阈值(Wavelet packet adaptive threshold,WPT)算法联合的数据降噪处理方法,并采用卡尔曼滤波与自适应加权平均算法对降噪后的数据进行融合。【结果】将EEMD-WPT算法应用于含噪温、湿度数据的降噪处理,相较于降噪前的数据,信噪比提升了73.08%。该算法相较于传统WPT算法具有更好的降噪效果,处理后的数据信噪比提升了40.31%,均方根误差降低了84.75%。【结论】该算法能解决数据跳动、冗余和丢失等问题,并为温室控制系统提供了有效的参数,具有较大的实际应用价值。

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.

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.

基于WPES与MEEMD的船用主机振动研究

为揭示船用长冲程低速柴油机健康状态下的振动特征,采用小波包能量谱(Wavelet Packet Energy Spectrum, WPES)和改进的总体平均经验模态分解(Modified Ensemble Empirical Mode Decomposition, MEEMD)结合的特征提取方法,对典型推进工况下低速机的表面振动信号进行3层小波包分解和重构。通过对能量占比较大的节点采用MEEMD方法进行分解,获得IMF1分量频谱。研究结果表明,在40%以下的较低发动机负荷时,各单次燃烧循环的振动波动较小,振动幅值基本一致。提升至50%以上发动机负荷时,燃烧引起振动波动明显增强。50%工况下,中高频能量占总能量的41.51%,为主要振动源。

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 sl-s8 concentrates at 0-200 Hz and the main vibration frequency bands of the signals sl-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.

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.

基于WP-ICA分析的涡旋压缩机故障特征提取方法研究

针对涡旋压缩机故障特征难以提取以及在小样本下故障类别难以区分的问题,提出了一种基于小波包能量谱与独立成分分析相结合的故障特征提取方法,结合支持向量机建立故障分类模型,实现非平稳信号的准确识别。首先对信号进行小波包分解与重构,通过重构系数获取分解后不同频带所对应的小波包能量作为故障特征值;再利用独立成分分析法对故障特征值进行优化得到特征向量值;最后构造支持向量机,输入故障特征向量进行训练和测试,可得出涡旋压缩机故障诊断的准确率。实验和仿真分析结果验证了该方法的有效性,其诊断准确率可达94.5%。

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.

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.

基于WPT-IDBO-RELM和WPT-IDMO-RELM模型的日径流预测

为提高日径流时间序列预测精度,改进正则化极限学习机(RELM)的预测性能,对比验证改进蜣螂优化(IDBO)算法和改进侏獴优化(IDMO)算法与其他算法的优化效果,提出了基于小波包变换(WPT)的WPT-IDBO-RELM和WPT-IDMO-RELM日径流时间序列预测模型。对云南省暮底河水库、马鹿塘电站入库日径流进行预测,结果表明WPT-IDBO-RELM和WPT-IDMO-RELM模型对暮底河水库日径流预测的平均绝对百分比误差分别为1.048%、1.015%,对马鹿塘电站日径流预测的平均绝对百分比误差分别为1.493%、1.478%,优于其他对比模型;IDBO、IDMO算法对标准测试函数和实例目标函数的寻优效果均优于其他对比算法,且IDBO、IDMO算法优化效果越好,RELM超参数越优,WPT-IDBO-RELM、WPT-IDMO-RELM模型预测精度越高;WPT可将日径流序列分解为分量更少、规律性更强的子序列分量,在提高预测精度的同时显著降低模型复杂度和计算规模。