Parameter estimation to alpha stable distribution is difficult for without a explicit probability density function. On the base of sample characteristic function,an iterative LAD parameter estimation algorithm for SaS...Parameter estimation to alpha stable distribution is difficult for without a explicit probability density function. On the base of sample characteristic function,an iterative LAD parameter estimation algorithm for SaS is discussed. The example illustrates that the algorithm is feasible and efficient.展开更多
Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the...Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.展开更多
The K-V beam through an axisymmetric uniform-focusing channel is studied using the particle-core model. The beam halo-chaos is found, and a sample function controller is proposed based on mechanism of halo formation a...The K-V beam through an axisymmetric uniform-focusing channel is studied using the particle-core model. The beam halo-chaos is found, and a sample function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. We perform multiparticle simulation to control the halo by using the sample function controller. The numerical results show that our control method is effective. We also find that the radial ion density changes when the ion beam is in the channel： not only can the halo-chaos and its regeneration be eliminated by using the sample function control method, but also the density uniformity can be found at the beam＇s centre as long as an appropriate control method is chosen.展开更多
In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-m...In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.展开更多
In this work the authors develop the n-dimensional sinc function theory in the several complex variables setting. In terms of the corresponding Paley-Wiener theorem the exact sinc interpolation and quadrature are esta...In this work the authors develop the n-dimensional sinc function theory in the several complex variables setting. In terms of the corresponding Paley-Wiener theorem the exact sinc interpolation and quadrature are established. Exponential convergence rate of the error estimates for band-limited functions in n-dimensional strips are obtained.展开更多
A novel fuzzy support vector machine based on unbalanced samples(FSVM-US)is proposed to solve the high false positive rate problem since the gyroscope output is susceptible to unmanned aerial vehicle(UAV)airborne elec...A novel fuzzy support vector machine based on unbalanced samples(FSVM-US)is proposed to solve the high false positive rate problem since the gyroscope output is susceptible to unmanned aerial vehicle(UAV)airborne electromagnetic environment and the gyroscope abnormal signal sample is rather rare.Firstly,the standard deviation of samples projection to normal vector for SVM classifier hyper plane is analyzed.The imbalance feature expression reflecting the hyper plane shift for the number imbalance between samples and the dispersion imbalance within samples is derived.At the same time,the denoising factor is designed as the exponential decay function based on the Euclidean distance between each sample and the class center.Secondly,the imbalance feature expression and denoising factor are configured into the membership function.Each sample has its own weight denoted the importance to the classifier.Finally,the classification simulation experiments on the gyroscope fault diagnosis system are conducted and FSVM-US is compared with the standard SVM,FSVM,and the four typical class imbalance learning(CIL)methods.The results show that FSVM-US classifier accuracy is 12% higher than that of the standard SVM.Generally,FSVM-US is superior to the four CIL methods in total performance.Moreover,the FSVMUS noise tolerance is also 17% higher than that of the standard SVM.展开更多
As sandstone layers in thin interbedded section are difficult to identify,conventional model-driven seismic inversion and data-driven seismic prediction methods have low precision in predicting them.To solve this prob...As sandstone layers in thin interbedded section are difficult to identify,conventional model-driven seismic inversion and data-driven seismic prediction methods have low precision in predicting them.To solve this problem,a model-data-driven seismic AVO(amplitude variation with offset)inversion method based on a space-variant objective function has been worked out.In this method,zero delay cross-correlation function and F norm are used to establish objective function.Based on inverse distance weighting theory,change of the objective function is controlled according to the location of the target CDP(common depth point),to change the constraint weights of training samples,initial low-frequency models,and seismic data on the inversion.Hence,the proposed method can get high resolution and high-accuracy velocity and density from inversion of small sample data,and is suitable for identifying thin interbedded sand bodies.Tests with thin interbedded geological models show that the proposed method has high inversion accuracy and resolution for small sample data,and can identify sandstone and mudstone layers of about one-30th of the dominant wavelength thick.Tests on the field data of Lishui sag show that the inversion results of the proposed method have small relative error with well-log data,and can identify thin interbedded sandstone layers of about one-15th of the dominant wavelength thick with small sample data.展开更多
In this note, we discuss a class of so-called generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrab...In this note, we discuss a class of so-called generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrable or Lebegue integrable on the real number line. They are in fact the generalization of the classic sinc function. Two approaches of constructing the generalized sampling functions are reviewed. Their properties such as cardinality, orthogonality, and decaying properties are discussed. The interactions of those functions and Hilbert transformer are also discussed.展开更多
This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usua...This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.展开更多
The Bayesian sampling plans for exponential distributions are studied based on type-Ⅱ hybrid censored samples. The optimal Bayesian sampling plan is derived under a general loss function which includes the sampling c...The Bayesian sampling plans for exponential distributions are studied based on type-Ⅱ hybrid censored samples. The optimal Bayesian sampling plan is derived under a general loss function which includes the sampling cost, time-consuming cost, salvage value,and decision loss. It is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. Furthermore,for the conjugate prior distribution,the closed-form formula of the Bayes decision rule can be obtained under either the linear or quadratic decision loss.展开更多
Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system mode...Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system model has a simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling systems.展开更多
Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct ...Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.展开更多
A robust H∞sampled-data stabilization problem for nonlinear dynamic positioning(DP) ships with Takagi-Sugeno(T-S) fuzzy models is discussed in this paper. Input delay approach is used to convert the sampleddata DP sh...A robust H∞sampled-data stabilization problem for nonlinear dynamic positioning(DP) ships with Takagi-Sugeno(T-S) fuzzy models is discussed in this paper. Input delay approach is used to convert the sampleddata DP ship system to a fuzzy system with time-varying delay. Adequate conditions are derived to determine the system's asymptotical stability and achieve H∞performance via Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analyzing the stabilization condition. Simulation result shows that the proposed method and the designed controller for a DP ship are effective so that the DP ship can maintain the desired position, heading and velocities in the existence of varying environment disturbances.展开更多
This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno （T-S） fuzzy model is employed to ...This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno （T-S） fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
Nonperiodic interrupted sampling repeater jamming(ISRJ)against inverse synthetic aperture radar(ISAR)can obtain two-dimensional blanket jamming performance by joint fast and slow time domain interrupted modulation,whi...Nonperiodic interrupted sampling repeater jamming(ISRJ)against inverse synthetic aperture radar(ISAR)can obtain two-dimensional blanket jamming performance by joint fast and slow time domain interrupted modulation,which is obviously dif-ferent from the conventional multi-false-target deception jam-ming.In this paper,a suppression method against this kind of novel jamming is proposed based on inter-pulse energy function and compressed sensing theory.By utilizing the discontinuous property of the jamming in slow time domain,the unjammed pulse is separated using the intra-pulse energy function diffe-rence.Based on this,the two-dimensional orthogonal matching pursuit(2D-OMP)algorithm is proposed.Further,it is proposed to reconstruct the ISAR image with the obtained unjammed pulse sequence.The validity of the proposed method is demon-strated via the Yake-42 plane data simulations.展开更多
Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained ...Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].展开更多
基金Supported by Hubei Educational Committee grant Q20091809Wuhan Polytechnic University grant 2009Y21
文摘Parameter estimation to alpha stable distribution is difficult for without a explicit probability density function. On the base of sample characteristic function,an iterative LAD parameter estimation algorithm for SaS is discussed. The example illustrates that the algorithm is feasible and efficient.
文摘Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10247005 and 70071047） and the Scientific Research Foundation of China University of Mining and Technology for the Young （Grant No 2005A037）.
文摘The K-V beam through an axisymmetric uniform-focusing channel is studied using the particle-core model. The beam halo-chaos is found, and a sample function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. We perform multiparticle simulation to control the halo by using the sample function controller. The numerical results show that our control method is effective. We also find that the radial ion density changes when the ion beam is in the channel： not only can the halo-chaos and its regeneration be eliminated by using the sample function control method, but also the density uniformity can be found at the beam＇s centre as long as an appropriate control method is chosen.
基金supported by Natural Science Foun■ion of Henan P■visial Commission of Bdusation
文摘In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.
文摘In this work the authors develop the n-dimensional sinc function theory in the several complex variables setting. In terms of the corresponding Paley-Wiener theorem the exact sinc interpolation and quadrature are established. Exponential convergence rate of the error estimates for band-limited functions in n-dimensional strips are obtained.
基金supported by the Fundamental Research Fund for the Central Universities(No.56XZA12017)
文摘A novel fuzzy support vector machine based on unbalanced samples(FSVM-US)is proposed to solve the high false positive rate problem since the gyroscope output is susceptible to unmanned aerial vehicle(UAV)airborne electromagnetic environment and the gyroscope abnormal signal sample is rather rare.Firstly,the standard deviation of samples projection to normal vector for SVM classifier hyper plane is analyzed.The imbalance feature expression reflecting the hyper plane shift for the number imbalance between samples and the dispersion imbalance within samples is derived.At the same time,the denoising factor is designed as the exponential decay function based on the Euclidean distance between each sample and the class center.Secondly,the imbalance feature expression and denoising factor are configured into the membership function.Each sample has its own weight denoted the importance to the classifier.Finally,the classification simulation experiments on the gyroscope fault diagnosis system are conducted and FSVM-US is compared with the standard SVM,FSVM,and the four typical class imbalance learning(CIL)methods.The results show that FSVM-US classifier accuracy is 12% higher than that of the standard SVM.Generally,FSVM-US is superior to the four CIL methods in total performance.Moreover,the FSVMUS noise tolerance is also 17% higher than that of the standard SVM.
文摘As sandstone layers in thin interbedded section are difficult to identify,conventional model-driven seismic inversion and data-driven seismic prediction methods have low precision in predicting them.To solve this problem,a model-data-driven seismic AVO(amplitude variation with offset)inversion method based on a space-variant objective function has been worked out.In this method,zero delay cross-correlation function and F norm are used to establish objective function.Based on inverse distance weighting theory,change of the objective function is controlled according to the location of the target CDP(common depth point),to change the constraint weights of training samples,initial low-frequency models,and seismic data on the inversion.Hence,the proposed method can get high resolution and high-accuracy velocity and density from inversion of small sample data,and is suitable for identifying thin interbedded sand bodies.Tests with thin interbedded geological models show that the proposed method has high inversion accuracy and resolution for small sample data,and can identify sandstone and mudstone layers of about one-30th of the dominant wavelength thick.Tests on the field data of Lishui sag show that the inversion results of the proposed method have small relative error with well-log data,and can identify thin interbedded sandstone layers of about one-15th of the dominant wavelength thick with small sample data.
文摘In this note, we discuss a class of so-called generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrable or Lebegue integrable on the real number line. They are in fact the generalization of the classic sinc function. Two approaches of constructing the generalized sampling functions are reviewed. Their properties such as cardinality, orthogonality, and decaying properties are discussed. The interactions of those functions and Hilbert transformer are also discussed.
基金supported by the National Natural Science Foundation of China(61374090)the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Provincethe Taishan Scholarship Project of Shandong Province
文摘This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.
基金Natural Science Foundation of Guangdong Province of China(No.2016A030307019)the Higher Education Colleges and Universities Innovation Strong School Project of Guangdong Province,China(No.2016KTSCX153)
文摘The Bayesian sampling plans for exponential distributions are studied based on type-Ⅱ hybrid censored samples. The optimal Bayesian sampling plan is derived under a general loss function which includes the sampling cost, time-consuming cost, salvage value,and decision loss. It is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. Furthermore,for the conjugate prior distribution,the closed-form formula of the Bayes decision rule can be obtained under either the linear or quadratic decision loss.
文摘Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system model has a simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling systems.
文摘Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.
基金the National Natural Science Foundation of China(No.51579114)the Project of New Century Excellent Talents of Colleges and Universities of Fujian Province(No.JA12181)the Project of Young and Middle-Aged Teacher Education of Fujian Province(No.JAT170309)
文摘A robust H∞sampled-data stabilization problem for nonlinear dynamic positioning(DP) ships with Takagi-Sugeno(T-S) fuzzy models is discussed in this paper. Input delay approach is used to convert the sampleddata DP ship system to a fuzzy system with time-varying delay. Adequate conditions are derived to determine the system's asymptotical stability and achieve H∞performance via Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analyzing the stabilization condition. Simulation result shows that the proposed method and the designed controller for a DP ship are effective so that the DP ship can maintain the desired position, heading and velocities in the existence of varying environment disturbances.
基金Project supported by the National Natural Science Foundation of China(Grant No.60974004)
文摘This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno （T-S） fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China(62001481,61890542,62071475)the Natural Science Foundation of Hunan Province(2022JJ40561)the Research Program of National University of Defense Technology(ZK22-46).
文摘Nonperiodic interrupted sampling repeater jamming(ISRJ)against inverse synthetic aperture radar(ISAR)can obtain two-dimensional blanket jamming performance by joint fast and slow time domain interrupted modulation,which is obviously dif-ferent from the conventional multi-false-target deception jam-ming.In this paper,a suppression method against this kind of novel jamming is proposed based on inter-pulse energy function and compressed sensing theory.By utilizing the discontinuous property of the jamming in slow time domain,the unjammed pulse is separated using the intra-pulse energy function diffe-rence.Based on this,the two-dimensional orthogonal matching pursuit(2D-OMP)algorithm is proposed.Further,it is proposed to reconstruct the ISAR image with the obtained unjammed pulse sequence.The validity of the proposed method is demon-strated via the Yake-42 plane data simulations.
文摘Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].
