By virtue of neural network, a series of signals is extended forward and backward, as a result, two additional maxima and two additional minima are obtained at both ends of the original data set, with which the EMD de...By virtue of neural network, a series of signals is extended forward and backward, as a result, two additional maxima and two additional minima are obtained at both ends of the original data set, with which the EMD decomposition can be exactly achieved with cubic spline interpolation. Meanwhile, by using of neural network every IMF component can also be extended forward and backward, which effectively restrains the end effect, thus the veracious Hilbert spectra are achieved. Verifications of the sample signals and the actual surface elevation of sea waves show that the present extension method is relatively accurate.展开更多
Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtai...Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network(WSN), a low cost cortex-M4 F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter(ADC) working at 10 k Hz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform(FFT) and Hilbert transform(HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.展开更多
A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcati...A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.展开更多
Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller b...Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.展开更多
This paper focuses on improving the detection performance of spectrum sensing in cognitive radio(CR) networks under complicated electromagnetic environment. Some existing fast spectrum sensing algorithms cannot get sp...This paper focuses on improving the detection performance of spectrum sensing in cognitive radio(CR) networks under complicated electromagnetic environment. Some existing fast spectrum sensing algorithms cannot get specific features of the licensed users'(LUs') signal, thus they cannot be applied in this situation without knowing the power of noise. On the other hand some algorithms that yield specific features are too complicated. In this paper, an algorithm based on the cyclostationary feature detection and theory of Hilbert transformation is proposed. Comparing with the conventional cyclostationary feature detection algorithm, this approach is more flexible i.e. it can flexibly change the computational complexity according to current electromagnetic environment by changing its sampling times and the step size of cyclic frequency. Results of simulation indicate that this approach can flexibly detect the feature of received signal and provide satisfactory detection performance compared to existing approaches in low Signal-to-noise Ratio(SNR) situations.展开更多
The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time vari...The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.展开更多
By means of a sharpening of Hoelder＇s inequality, Hardy-Hilbert＇s integral inequality with parameters is improved. Some new inequalities are established,
Expounded in this survey article is a series of refinements and generalizations of Hilbert's inequalities mostly published during the years 1990 through 2002.Those inequalities concerned may be classified into sev...Expounded in this survey article is a series of refinements and generalizations of Hilbert's inequalities mostly published during the years 1990 through 2002.Those inequalities concerned may be classified into several types (discrete and integral etc.), and various related results obtained respectively by L. C. Hsu, M. Z. Gao, B. C. Yang, J. C. Kuang, Hu Ke and H. Hong et.al are described a little more precisely. Moreover, earlier and recent extensions of Hilbert-type inequalities are also stated for reference. And the new trend and the research ways are also brought forward.展开更多
Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0,1], respec...Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0,1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c 0 ∪ (Q Σ)), i.e., there is a homeomorphism h:↓USCC(X) → Q such that h(↓CC(X)) = c 0 ∪ (Q Σ), where Q = [?1,1]ω, Σ = {(x n ) n∈? ∈ Q: sup|x n | < 1} and c 0 = {(x n ) n∈? ∈ Σ: lim n→+∞ x n = 0}. Combining this statement with a result in our previous paper, we have $$ ( \downarrow USCC(X), \downarrow CC(X)) \approx \left\{ \begin{gathered} (Q,c_0 \cup (Q\backslash \Sigma )), if the set of isolanted points is dense in X, \hfill \\ (Q,c_0 ),otherwise, \hfill \\ \end{gathered} \right. $$ if X is an infinite compact metric space. We also prove that, for a metric space X, (↓USCC(X), ↓CC(X)) ≈ (Σ, c 0) if and only if X is non-compact, locally compact, non-discrete and separable.展开更多
In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equatio...In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.展开更多
Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions conce...Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.展开更多
In this paper, the structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one dep...In this paper, the structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one depending on the amplitude of the signal and another on the boundary value of an inner function. Based on this result, properties of the instantaneous frequencies of these two parts are studied, and it is found that negative instantaneous frequencies are caused by the amplitude of a signal. Finally, such conditions that an analytic signal is of positive instantaneous frequency are presented.展开更多
基金the NationalNatural Science Foundation of China (Grant No. 49976003) and the "863" Project (Grant No. 863-818-06-02).
文摘By virtue of neural network, a series of signals is extended forward and backward, as a result, two additional maxima and two additional minima are obtained at both ends of the original data set, with which the EMD decomposition can be exactly achieved with cubic spline interpolation. Meanwhile, by using of neural network every IMF component can also be extended forward and backward, which effectively restrains the end effect, thus the veracious Hilbert spectra are achieved. Verifications of the sample signals and the actual surface elevation of sea waves show that the present extension method is relatively accurate.
文摘Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network(WSN), a low cost cortex-M4 F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter(ADC) working at 10 k Hz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform(FFT) and Hilbert transform(HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.
基金This work was supported by the Strategic Research (Grant No. 7000934) from the City University of Hong Kong.
文摘A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.
基金This project is supported by National Natural Science Foundation of China (No.50205050).
文摘Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.
基金sponsored by National Basic Research Program of China (973 Program, No. 2013CB329003)National Natural Science Foundation of China (No. 91438205)+1 种基金China Postdoctoral Science Foundation (No. 2011M500664)Open Research fund Program of Key Lab. for Spacecraft TT&C and Communication, Ministry of Education, China (No.CTTC-FX201305)
文摘This paper focuses on improving the detection performance of spectrum sensing in cognitive radio(CR) networks under complicated electromagnetic environment. Some existing fast spectrum sensing algorithms cannot get specific features of the licensed users'(LUs') signal, thus they cannot be applied in this situation without knowing the power of noise. On the other hand some algorithms that yield specific features are too complicated. In this paper, an algorithm based on the cyclostationary feature detection and theory of Hilbert transformation is proposed. Comparing with the conventional cyclostationary feature detection algorithm, this approach is more flexible i.e. it can flexibly change the computational complexity according to current electromagnetic environment by changing its sampling times and the step size of cyclic frequency. Results of simulation indicate that this approach can flexibly detect the feature of received signal and provide satisfactory detection performance compared to existing approaches in low Signal-to-noise Ratio(SNR) situations.
基金National Science Foundation Grant NSF CMS CAREER Under Grant No.9996290NSF CMMI Under Grant No.0830391
文摘The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.
文摘By means of a sharpening of Hoelder＇s inequality, Hardy-Hilbert＇s integral inequality with parameters is improved. Some new inequalities are established,
文摘Expounded in this survey article is a series of refinements and generalizations of Hilbert's inequalities mostly published during the years 1990 through 2002.Those inequalities concerned may be classified into several types (discrete and integral etc.), and various related results obtained respectively by L. C. Hsu, M. Z. Gao, B. C. Yang, J. C. Kuang, Hu Ke and H. Hong et.al are described a little more precisely. Moreover, earlier and recent extensions of Hilbert-type inequalities are also stated for reference. And the new trend and the research ways are also brought forward.
基金supported by National Natural Science Foundation of China (Grant No. 10471084)
文摘Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0,1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c 0 ∪ (Q Σ)), i.e., there is a homeomorphism h:↓USCC(X) → Q such that h(↓CC(X)) = c 0 ∪ (Q Σ), where Q = [?1,1]ω, Σ = {(x n ) n∈? ∈ Q: sup|x n | < 1} and c 0 = {(x n ) n∈? ∈ Σ: lim n→+∞ x n = 0}. Combining this statement with a result in our previous paper, we have $$ ( \downarrow USCC(X), \downarrow CC(X)) \approx \left\{ \begin{gathered} (Q,c_0 \cup (Q\backslash \Sigma )), if the set of isolanted points is dense in X, \hfill \\ (Q,c_0 ),otherwise, \hfill \\ \end{gathered} \right. $$ if X is an infinite compact metric space. We also prove that, for a metric space X, (↓USCC(X), ↓CC(X)) ≈ (Σ, c 0) if and only if X is non-compact, locally compact, non-discrete and separable.
基金supported by Korea Research Foundation Grant KRF-2002-041-C00014
文摘In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.
基金Supported by the National Natural Science Foundation of China (Grant No. 60674018)
文摘Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space, Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.
基金National Natural Science Foundation of China (Grant Nos.10631080, 60873088, 10810301059)
文摘In this paper, the structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one depending on the amplitude of the signal and another on the boundary value of an inner function. Based on this result, properties of the instantaneous frequencies of these two parts are studied, and it is found that negative instantaneous frequencies are caused by the amplitude of a signal. Finally, such conditions that an analytic signal is of positive instantaneous frequency are presented.
