A joint estimation algorithm of direction of arrival (DOA), frequency, and polarization, based on fourth-order cumulants and uniform circular array (UCA) of trimmed vector sensors is presented for narrowband non-G...A joint estimation algorithm of direction of arrival (DOA), frequency, and polarization, based on fourth-order cumulants and uniform circular array (UCA) of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.展开更多
Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which kee...Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.展开更多
In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition...In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.展开更多
Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^* is defined and the three-order Hamilton's principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order...Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^* is defined and the three-order Hamilton's principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result.展开更多
The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s ...The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.展开更多
In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as c...In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.展开更多
This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the...This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.展开更多
This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters. AutoRegressive (AR), Moving Average (MA) or AutoRegressive-Moving Average (...This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters. AutoRegressive (AR), Moving Average (MA) or AutoRegressive-Moving Average (ARMA) model structure can be extracted blindly from the Third Order Cumulants (TOC) of the system output ts, where the unknown system is driven by an unobservable stationary independent identically distributed (i.i.d.) non-Gaussian signal. By means of the system order recursion, whether the system has an AR structure or has AR part of an ARMA structure is firstly investigated. MA features in the TOC domain is then applied as a threshold to decide if the system is an MA model or has MA part of an ARMA model. Numerical simulations illustrate the generality of the proposed blind structure identification methodology that may serve as a guideline for blind, linear system modeling.展开更多
Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussia...Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.展开更多
BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations ...BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.展开更多
Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experim...Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.展开更多
Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order L...Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.展开更多
Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulan...Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulant. Calculations have been derived showing that the first moment causes a shift in the peak position of the profile while the third moment affects its shape. The intensity expression has been derived on the basis of usual Cartesian coordinates and also of polar coordinates indicated by the probability of the fault and the reciprocal lattice parameter as the two axes. The expressions for the fourth cumulant have also been so derived. Here we have used three different approaches to determine methods for calculating the fourth cumulant due to stacking faults. The three forms of the equations derived here are for different coordinate systems, but will arrive at the same answers.展开更多
This paper presents an improved algorithm for classification of M-Differential Phase-Shift Keying(MDPSK) signals based on eumulant. The feature proposed in the algorithm is invariant with respect to constellation scal...This paper presents an improved algorithm for classification of M-Differential Phase-Shift Keying(MDPSK) signals based on eumulant. The feature proposed in the algorithm is invariant with respect to constellation scale, rotation, the shift and the carrier frequency offset between transmitter and receiver.The invariant property is proved theoretically.Through computer simulation the performance is evaluated and the results show that the improved classification algorithm is better and valuable in practice.展开更多
Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method t...Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their ?dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.展开更多
Although mechanical vibration is extremely complicated, each fault signal produced by it has its own inherent features, The distinction may be most prominent between the certain components hidden in those features and...Although mechanical vibration is extremely complicated, each fault signal produced by it has its own inherent features, The distinction may be most prominent between the certain components hidden in those features and the same components of normal signals. Three-order cumulant can reduce the Gaussian background noise automatically and its complex formal includes different coupling information of its signal. In the experiment, through these different coupling modes, the same coupling components are fetched from specific fault signal and normal signal, then these components are used to diagnose that certain fault. The results show that the method can fetch the most prominent distinction between normal signal and the specific fault signal, so the specific fault diagnosis by this method is satisfactory.展开更多
Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and...Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en'ors than that of the SOS-RARE from the resolution point of view.展开更多
This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularl...This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.展开更多
The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode...The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function.As an application,we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states:a mixture of vacuum and Fock states,single-photon added thermal states,and even/odd Schr¨odinger cat states.It is shown that such a criterion is faithful and effective for revealing non-Gaussianity.We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.展开更多
Due to their high density,the ilmenite-bearing cumulates(IBC)(with or without KREEP)formed during the late-stage lunar magma ocean solidification are thought to sink into the underlying lunar mantle and trigger lunar ...Due to their high density,the ilmenite-bearing cumulates(IBC)(with or without KREEP)formed during the late-stage lunar magma ocean solidification are thought to sink into the underlying lunar mantle and trigger lunar mantle overturn.Geophysical evidence implied that IBC may descend deep inside the Moon and remain as a partially molten layer at the core-mantle boundary(CMB).However,partial melting may have occurred on the mixed mantle cumulates during the sinking of IBC/KREEP and the silicate melt may be positively buoyant,thus preventing the IBC/KREEP layer from sinking to the CMB.Here,we perform thermodynamic simulation on the stability of lunar mantle cumulates at different depths mixed with different amounts of IBC/KREEP from an updated LMO model.The modeling results suggest that the sinking of IBC/KREEP will cause at least 5 wt%partial melting in the shallow(~120 km)and a much larger degree of partial melting in the deep lunar mantle(~420 km).Due to the density contrast with the surrounding mantle,IBC/KREEP-bearing melts could potentially decouple under certain conditions.The modified lunar mantle by sinking of IBC/KREEP can better explain the formation of different kinds of lunar basaltic magma than the primary lunar mantle formed through differentiation of lunar magma ocean.Sinking of IBC/KREEP back into the lunar mantle may introduce plagioclase,clinopyroxene,garnet,and incompatible radioactive elements into the deep lunar mantle,which will further affect the thermal and chemical evolution of the lunar interior.展开更多
基金This project was supported by the Graduate Innovation Laboratory of Jilin University(502039)Jilin Science Committee of China(20030519)+1 种基金the National Natural Science Foundation of China (69872012)the Foundation of Nanjing Institute of Technology.
文摘A joint estimation algorithm of direction of arrival (DOA), frequency, and polarization, based on fourth-order cumulants and uniform circular array (UCA) of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.
文摘Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.
文摘In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.
文摘Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^* is defined and the three-order Hamilton's principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result.
文摘The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.
文摘In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.
文摘This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.
基金Supported by the National Natural Science Foundation of China (No.60575006).
文摘This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters. AutoRegressive (AR), Moving Average (MA) or AutoRegressive-Moving Average (ARMA) model structure can be extracted blindly from the Third Order Cumulants (TOC) of the system output ts, where the unknown system is driven by an unobservable stationary independent identically distributed (i.i.d.) non-Gaussian signal. By means of the system order recursion, whether the system has an AR structure or has AR part of an ARMA structure is firstly investigated. MA features in the TOC domain is then applied as a threshold to decide if the system is an MA model or has MA part of an ARMA model. Numerical simulations illustrate the generality of the proposed blind structure identification methodology that may serve as a guideline for blind, linear system modeling.
文摘Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.
基金National Natural Science Foundation of China,No.72101236China Postdoctoral Science Foundation,No.2022M722900+1 种基金Collaborative Innovation Project of Zhengzhou City,No.XTCX2023006Nursing Team Project of the First Affiliated Hospital of Zhengzhou University,No.HLKY2023005.
文摘BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.
文摘Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.
文摘Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.
文摘Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulant. Calculations have been derived showing that the first moment causes a shift in the peak position of the profile while the third moment affects its shape. The intensity expression has been derived on the basis of usual Cartesian coordinates and also of polar coordinates indicated by the probability of the fault and the reciprocal lattice parameter as the two axes. The expressions for the fourth cumulant have also been so derived. Here we have used three different approaches to determine methods for calculating the fourth cumulant due to stacking faults. The three forms of the equations derived here are for different coordinate systems, but will arrive at the same answers.
基金Supported by China TRAPOYT,863 Project(2001AA123031)National Natural Science Foundation of China(No.69872028)
文摘This paper presents an improved algorithm for classification of M-Differential Phase-Shift Keying(MDPSK) signals based on eumulant. The feature proposed in the algorithm is invariant with respect to constellation scale, rotation, the shift and the carrier frequency offset between transmitter and receiver.The invariant property is proved theoretically.Through computer simulation the performance is evaluated and the results show that the improved classification algorithm is better and valuable in practice.
文摘Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their ?dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.
文摘Although mechanical vibration is extremely complicated, each fault signal produced by it has its own inherent features, The distinction may be most prominent between the certain components hidden in those features and the same components of normal signals. Three-order cumulant can reduce the Gaussian background noise automatically and its complex formal includes different coupling information of its signal. In the experiment, through these different coupling modes, the same coupling components are fetched from specific fault signal and normal signal, then these components are used to diagnose that certain fault. The results show that the method can fetch the most prominent distinction between normal signal and the specific fault signal, so the specific fault diagnosis by this method is satisfactory.
基金Project(61201381)supported by the National Nature Science Foundation of ChinaProject(YP12JJ202057)supported by the Future Development Foundation of Zhengzhou Information Science and Technology College,China
文摘Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en'ors than that of the SOS-RARE from the resolution point of view.
文摘This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.
基金Project supported by the Natural Science Foundation of Hunan Province of China(Grant No.2021JJ30535)。
文摘The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function.As an application,we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states:a mixture of vacuum and Fock states,single-photon added thermal states,and even/odd Schr¨odinger cat states.It is shown that such a criterion is faithful and effective for revealing non-Gaussianity.We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.
基金funded by the National Natural Science Foundation of China(41773052,41973058)。
文摘Due to their high density,the ilmenite-bearing cumulates(IBC)(with or without KREEP)formed during the late-stage lunar magma ocean solidification are thought to sink into the underlying lunar mantle and trigger lunar mantle overturn.Geophysical evidence implied that IBC may descend deep inside the Moon and remain as a partially molten layer at the core-mantle boundary(CMB).However,partial melting may have occurred on the mixed mantle cumulates during the sinking of IBC/KREEP and the silicate melt may be positively buoyant,thus preventing the IBC/KREEP layer from sinking to the CMB.Here,we perform thermodynamic simulation on the stability of lunar mantle cumulates at different depths mixed with different amounts of IBC/KREEP from an updated LMO model.The modeling results suggest that the sinking of IBC/KREEP will cause at least 5 wt%partial melting in the shallow(~120 km)and a much larger degree of partial melting in the deep lunar mantle(~420 km).Due to the density contrast with the surrounding mantle,IBC/KREEP-bearing melts could potentially decouple under certain conditions.The modified lunar mantle by sinking of IBC/KREEP can better explain the formation of different kinds of lunar basaltic magma than the primary lunar mantle formed through differentiation of lunar magma ocean.Sinking of IBC/KREEP back into the lunar mantle may introduce plagioclase,clinopyroxene,garnet,and incompatible radioactive elements into the deep lunar mantle,which will further affect the thermal and chemical evolution of the lunar interior.