The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec...The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.展开更多
The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets a...The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2（R, C^s×s） is constructed from the orthogonal multiple vector-valued wavelet packets.展开更多
In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar...In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.展开更多
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 wavel...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.展开更多
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-t...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.展开更多
2-band wavelet packets in L-2 (R-s) were constructed in [3]. In this note, a way to construct bidimensional orthonormal wavelet packets related to the dilation matrix M = ((1)(1) (1)(-1)) is obtained. M-wavelets are u...2-band wavelet packets in L-2 (R-s) were constructed in [3]. In this note, a way to construct bidimensional orthonormal wavelet packets related to the dilation matrix M = ((1)(1) (1)(-1)) is obtained. M-wavelets are used ill quincunx subsampling in two dimensions for image processing. What is more., the approach of this paper can be generalized to construct wavelet packets in L-2 (R-s) related to a general diltion matrix.展开更多
Travel-time prediction has gained significance over the years especially in urban areas due to increasing traffic congestion. In this paper, the basic building blocks of the travel-time prediction models are discussed...Travel-time prediction has gained significance over the years especially in urban areas due to increasing traffic congestion. In this paper, the basic building blocks of the travel-time prediction models are discussed, with a small review of the previous work. A model for the travel-time prediction on freeways based on wavelet packet decomposition and support vector regression (WDSVR) is proposed, which used the multi-resolution and equivalent frequency distribution ability of the wavelet transform to train the support vector machines. The results are compared against the classical support vector regression (SVR) method. Our results indicated that the wavelet reconstructed coefficient when used as an input to the support vector machine for regression performed better (with selected wavelets only), when compared with the support vector regression model (without wavelet decomposition) with a prediction horizon of 45 minutes and more. The data used in this paper was taken from the California Department of Transportation (Caltrans) of District 12 with a detector density of 2.73, experiencing daily peak hours except most weekends. The data was stored for a period of 214 days accumulated over 5-minute intervals over a distance of 9.13 miles. The results indicated MAPE ranging from 12.35% to 14.75% against the classical SVR method with MAPE ranging from 12.57% to 15.84% with a prediction horizon of 45 minutes to 1 hour. The basic criteria for selection of wavelet basis for preprocessing the inputs of support vector machines are also explored to filter the set of wavelet families for the WDSVR model. Finally, a configuration of travel-time prediction on freeways is presented with interchangeable prediction methods.展开更多
To overcome the challenges of poor real-time performance,limited scalability,and low intelligence in conventional jamming pattern recognition methods,this paper proposes a method based on Wavelet Packet Decomposition(...To overcome the challenges of poor real-time performance,limited scalability,and low intelligence in conventional jamming pattern recognition methods,this paper proposes a method based on Wavelet Packet Decomposition(WPD)and enhanced deep learning techniques.In the proposed method,an agent at the receiver processes the received signal using WPD to generate an initial Spectrogram Waterfall(SW),which is subsequently segmented using a sliding window to serve as the input for the jamming recognition network.The network employs a bilateral filter to preprocess the input SW,thereby enhancing the edge features of the jamming signals.To extract abstract features,depthwise separable convolution is utilized instead of traditional convolution,thereby reducing the network’s parameter count and enhancing real-time performance.A pyramid pooling layer is integrated before the fully connected layer to enable the network to process input SW of varying sizes,thus enhancing scalability.During network training,adaptive moment estimation is employed as the optimizer,allowing the network to dynamically adjust the learning rate and accelerate convergence.A comprehensive comparison between the proposed jamming recognition network and six other models is conducted,along with Ablation Experiments(AE)based on numerical simulations.Simulation results demonstrate that the proposed method based on WPD and enhanced deep learning achieves high-precision recognition of various jamming patterns while maintaining a favorable balance among prediction accuracy,network complexity,and prediction time.展开更多
The early impulse fault diagnosis of the gearbox in rolling mills is often difficult and labour intensive because the gearbox of that high speed machine is multi-shafting transmission system,in which many gearsets and...The early impulse fault diagnosis of the gearbox in rolling mills is often difficult and labour intensive because the gearbox of that high speed machine is multi-shafting transmission system,in which many gearsets and rolling bears work together at the same time and there are much complex frequency structure and various disturb.A new time-frequency method based on the wavelet packets technique was developed and used to extract the impact feature from signals collected from faulty data of one rolling mills gearbox.The method improves the signal to noise ration so that results obtained using this method represents features with fine resolution in both low-frequency and the high frequency bands.The results of analysis indicate the validity and the practicability of the method proposed here.展开更多
Accurate forecasting of electricity spot prices is crucial for market participants in formulating bidding strategies.However,the extreme volatility of electricity spot prices,influenced by various factors,poses signif...Accurate forecasting of electricity spot prices is crucial for market participants in formulating bidding strategies.However,the extreme volatility of electricity spot prices,influenced by various factors,poses significant challenges for forecasting.To address the data uncertainty of electricity prices and effectively mitigate gradient issues,overfitting,and computational challenges associated with using a single model during forecasting,this paper proposes a framework for forecasting spot market electricity prices by integrating wavelet packet decomposition(WPD)with a hybrid deep neural network.By ensuring accurate data decomposition,the WPD algorithm aids in detecting fluctuating patterns and isolating random noise.The hybrid model integrates temporal convolutional networks(TCN)and long short-term memory(LSTM)networks to enhance feature extraction and improve forecasting performance.Compared to other techniques,it significantly reduces average errors,decreasing mean absolute error(MAE)by 27.3%,root mean square error(RMSE)by 66.9%,and mean absolute percentage error(MAPE)by 22.8%.This framework effectively captures the intricate fluctuations present in the time series,resulting in more accurate and reliable predictions.展开更多
In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improv...In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the performance of wavelets for time-frequency localization, which makes more kinds of signals for analyzing by wavelets. Similar to the notations from the extension of 2-band wavelets to 2-band wavelet packets, the theoretic framework of M-band wavelet packets is developed, a generalization of the notations and properties of 2-band wavelet packets to that of M-band wavelet packets is made and the corresponding proofs are given.展开更多
In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline...In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.展开更多
The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding fra...The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.展开更多
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 provi...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. *展开更多
In Wavelet Packets Based Multicarrier Multicode CDMA system, the multicode (MCD) part ensures the transmission for high speed and flexible data rate, the multicarrier (MC) part ensures the flexibility of handling mult...In Wavelet Packets Based Multicarrier Multicode CDMA system, the multicode (MCD) part ensures the transmission for high speed and flexible data rate, the multicarrier (MC) part ensures the flexibility of handling multiple data rates, and wavelet packets modulation technique contributes to the mitigation of the interference problems. The CDMA system can suppress a given amount of interference. In this paper, the receiver employs suppression filter (SF) to mitigate the effect of narrow-band jammer interference and diversity techniques to reduce multiple access interference. The framework for the system and the performance evaluation are presented in terms of bit error rate (BER) over a Nakagami fading channel. Also, we investigate how the performance is influenced by various parameters, such as the number of taps of the SF, the ratio of narrow-band interference bandwidth to the spread-spectrum bandwidth, the diversity order, the fading parameter and so on. Finally, the performance of the system is compared with the performance Sinusoidal (Sin) based MC/MCD CDMA system.展开更多
In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet...In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.展开更多
In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of t...In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular, a new orthonormal basis of L2(R, Cs×s) is obtained from the matrix-valued wavelet packets.展开更多
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 un...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.展开更多
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...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.展开更多
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 comple...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.展开更多
基金the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)the Items of Xi’an University of Architecture and Technology(RC0701JC0718)
文摘The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.
基金the National Natural Science Foundation of China (10371105).
文摘The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2（R, C^s×s） is constructed from the orthogonal multiple vector-valued wavelet packets.
基金Foundation item： Supported by the Natural Science Foundation of China（10571113）
文摘In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.
基金Supported by Natural Science Foundation of Henan Province（0511013500）
文摘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.
文摘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.
基金the National Natural Science Foundation (19801005). the Youth Foundation of Beijing. the Natural Science Foundation of Beijing (
文摘2-band wavelet packets in L-2 (R-s) were constructed in [3]. In this note, a way to construct bidimensional orthonormal wavelet packets related to the dilation matrix M = ((1)(1) (1)(-1)) is obtained. M-wavelets are used ill quincunx subsampling in two dimensions for image processing. What is more., the approach of this paper can be generalized to construct wavelet packets in L-2 (R-s) related to a general diltion matrix.
文摘Travel-time prediction has gained significance over the years especially in urban areas due to increasing traffic congestion. In this paper, the basic building blocks of the travel-time prediction models are discussed, with a small review of the previous work. A model for the travel-time prediction on freeways based on wavelet packet decomposition and support vector regression (WDSVR) is proposed, which used the multi-resolution and equivalent frequency distribution ability of the wavelet transform to train the support vector machines. The results are compared against the classical support vector regression (SVR) method. Our results indicated that the wavelet reconstructed coefficient when used as an input to the support vector machine for regression performed better (with selected wavelets only), when compared with the support vector regression model (without wavelet decomposition) with a prediction horizon of 45 minutes and more. The data used in this paper was taken from the California Department of Transportation (Caltrans) of District 12 with a detector density of 2.73, experiencing daily peak hours except most weekends. The data was stored for a period of 214 days accumulated over 5-minute intervals over a distance of 9.13 miles. The results indicated MAPE ranging from 12.35% to 14.75% against the classical SVR method with MAPE ranging from 12.57% to 15.84% with a prediction horizon of 45 minutes to 1 hour. The basic criteria for selection of wavelet basis for preprocessing the inputs of support vector machines are also explored to filter the set of wavelet families for the WDSVR model. Finally, a configuration of travel-time prediction on freeways is presented with interchangeable prediction methods.
基金supported by National Natural Science Foundation of China under Grant U23A20279China Electronics Tian’ao Innovation Theory and Technology Group Fund under Grand 20221193-04-04.
文摘To overcome the challenges of poor real-time performance,limited scalability,and low intelligence in conventional jamming pattern recognition methods,this paper proposes a method based on Wavelet Packet Decomposition(WPD)and enhanced deep learning techniques.In the proposed method,an agent at the receiver processes the received signal using WPD to generate an initial Spectrogram Waterfall(SW),which is subsequently segmented using a sliding window to serve as the input for the jamming recognition network.The network employs a bilateral filter to preprocess the input SW,thereby enhancing the edge features of the jamming signals.To extract abstract features,depthwise separable convolution is utilized instead of traditional convolution,thereby reducing the network’s parameter count and enhancing real-time performance.A pyramid pooling layer is integrated before the fully connected layer to enable the network to process input SW of varying sizes,thus enhancing scalability.During network training,adaptive moment estimation is employed as the optimizer,allowing the network to dynamically adjust the learning rate and accelerate convergence.A comprehensive comparison between the proposed jamming recognition network and six other models is conducted,along with Ablation Experiments(AE)based on numerical simulations.Simulation results demonstrate that the proposed method based on WPD and enhanced deep learning achieves high-precision recognition of various jamming patterns while maintaining a favorable balance among prediction accuracy,network complexity,and prediction time.
文摘The early impulse fault diagnosis of the gearbox in rolling mills is often difficult and labour intensive because the gearbox of that high speed machine is multi-shafting transmission system,in which many gearsets and rolling bears work together at the same time and there are much complex frequency structure and various disturb.A new time-frequency method based on the wavelet packets technique was developed and used to extract the impact feature from signals collected from faulty data of one rolling mills gearbox.The method improves the signal to noise ration so that results obtained using this method represents features with fine resolution in both low-frequency and the high frequency bands.The results of analysis indicate the validity and the practicability of the method proposed here.
基金partially supported by projects funded by the National Key R&D Program of China(2022YFB2403000)the State Grid Corporation of China Science and Technology Project(522722230034).
文摘Accurate forecasting of electricity spot prices is crucial for market participants in formulating bidding strategies.However,the extreme volatility of electricity spot prices,influenced by various factors,poses significant challenges for forecasting.To address the data uncertainty of electricity prices and effectively mitigate gradient issues,overfitting,and computational challenges associated with using a single model during forecasting,this paper proposes a framework for forecasting spot market electricity prices by integrating wavelet packet decomposition(WPD)with a hybrid deep neural network.By ensuring accurate data decomposition,the WPD algorithm aids in detecting fluctuating patterns and isolating random noise.The hybrid model integrates temporal convolutional networks(TCN)and long short-term memory(LSTM)networks to enhance feature extraction and improve forecasting performance.Compared to other techniques,it significantly reduces average errors,decreasing mean absolute error(MAE)by 27.3%,root mean square error(RMSE)by 66.9%,and mean absolute percentage error(MAPE)by 22.8%.This framework effectively captures the intricate fluctuations present in the time series,resulting in more accurate and reliable predictions.
文摘In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the performance of wavelets for time-frequency localization, which makes more kinds of signals for analyzing by wavelets. Similar to the notations from the extension of 2-band wavelets to 2-band wavelet packets, the theoretic framework of M-band wavelet packets is developed, a generalization of the notations and properties of 2-band wavelet packets to that of M-band wavelet packets is made and the corresponding proofs are given.
文摘In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.
文摘The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.
文摘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. *
文摘In Wavelet Packets Based Multicarrier Multicode CDMA system, the multicode (MCD) part ensures the transmission for high speed and flexible data rate, the multicarrier (MC) part ensures the flexibility of handling multiple data rates, and wavelet packets modulation technique contributes to the mitigation of the interference problems. The CDMA system can suppress a given amount of interference. In this paper, the receiver employs suppression filter (SF) to mitigate the effect of narrow-band jammer interference and diversity techniques to reduce multiple access interference. The framework for the system and the performance evaluation are presented in terms of bit error rate (BER) over a Nakagami fading channel. Also, we investigate how the performance is influenced by various parameters, such as the number of taps of the SF, the ratio of narrow-band interference bandwidth to the spread-spectrum bandwidth, the diversity order, the fading parameter and so on. Finally, the performance of the system is compared with the performance Sinusoidal (Sin) based MC/MCD CDMA system.
文摘In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.
基金This work is partially supported by the Natural Science Foundation of Henan (0211044800).
文摘In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular, a new orthonormal basis of L2(R, Cs×s) is obtained from the matrix-valued wavelet packets.
文摘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.
基金The Natural Science Foundation of Heilongjiang Province ( No. F201018)the National Natural Science Foundation of China( No. 60901042)
文摘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.
文摘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.
