In distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distr...In distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distributed fusion algorithms,such as the Covariance Union(CU)and Faulttolerant Generalized Convex Combination(FGCC),are only used for the point estimation case where local estimates and their associated error covariances are provided.A treatment with focus on the fault-tolerant distributed fusions of arbitrary local Probability Density Functions(PDFs)is lacking.For this problem,we first propose Kullback–Leibler Divergence(KLD)and reversed KLD induced functional Fuzzy c-Means(FCM)clustering algorithms to soft cluster all local PDFs,respectively.On this basis,two fault-tolerant distributed fusion algorithms of arbitrary local PDFs are then developed.They select the representing PDF of the cluster with the largest sum of memberships as the fused PDF.Numerical examples verify the better fault tolerance of the developed two distributed fusion algorithms.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear st...The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.展开更多
Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important in...Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.展开更多
Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the...Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.展开更多
The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the...The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.展开更多
A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in tr...A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.展开更多
Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a var...Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.展开更多
This paper derives an approximate formula for probability density function(PDF) of received signal-to-interference-and-noise ratio(SINR) at user terminal when matched filter(MF) is adopted at a base station(BS).This d...This paper derives an approximate formula for probability density function(PDF) of received signal-to-interference-and-noise ratio(SINR) at user terminal when matched filter(MF) is adopted at a base station(BS).This distribution of SINR can be used to make an analysis of average sum-rate,outage probability,and symbol error rate of massive MIMO downlink with MF at BS.From simulation,it is found that the derived approximate analytical expression for PDF of SINR is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.展开更多
研究了基于层流小火焰概念和假定beta-PDF(probability density function)的湍流预混燃烧模型.该模型采用PREMIX程序来计算层流小火焰,将计算结果表示为进程变量的函数,并利用进程变量的be-ta-PDF积分生成了用于RANS(雷诺平均Navier-Sto...研究了基于层流小火焰概念和假定beta-PDF(probability density function)的湍流预混燃烧模型.该模型采用PREMIX程序来计算层流小火焰,将计算结果表示为进程变量的函数,并利用进程变量的be-ta-PDF积分生成了用于RANS(雷诺平均Navier-Stokes)计算的PDF表.以化学当量的甲烷湍流本生火焰为算例对模型进行了计算验证,并与Zimont模型的计算结果和实验结果做了对比.结果表明,平均速度分布与实验符合的较好,温度和湍动能计算结果有待改善.本模型高估了化学反应速率,导致计算火焰比实际瘦,这是因为模型中未能考虑湍流对火焰的拉伸和弯曲效应,考虑湍流拉伸和弯曲效应的预混燃烧模型是今后进一步研究的方向.展开更多
为了使直扩系统在未知非高斯噪声模型下准确地捕获微弱直扩信号,提出一种新的基于整数最大熵概率密度函数（probability density function,PDF）估计和局部最佳检测（locally optimal detection,LOD）相结合的相关前一维幅域处理捕获方...为了使直扩系统在未知非高斯噪声模型下准确地捕获微弱直扩信号,提出一种新的基于整数最大熵概率密度函数（probability density function,PDF）估计和局部最佳检测（locally optimal detection,LOD）相结合的相关前一维幅域处理捕获方式。通过蒙特卡洛数据仿真可以发现：在非高斯噪声的情况下,基于整数最大熵PDF估计的LOD检测器的检测性能要明显优于常规平方和（Square-Sum,SS）检测器,在信噪比为-25~0 dB时分别有2.0%~99.0%的改善。从根本上改变了常规SS检测器在非高斯噪声模型下性能急剧下降甚至无法工作的现象。展开更多
A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) closure model has been devel-oped for supersonic turbulent combustion. Scalar transport equations for all species in a given che...A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) closure model has been devel-oped for supersonic turbulent combustion. Scalar transport equations for all species in a given chemical kinetic mechanism were solved, which are necessary in the supersonic combustion where the non-equilibrium chemistry is essentially involved. The clipped Gaussian PDF of temperature and multivariate ? PDF of composition were used to close the sub-grid chemical sources that appear in the conservation equations. The sub-grid variances of temperature and composition were constructed based on scale similarity approach. A semi-implicit approach based on the PDF model was proposed to tackle the resulting numerical stiffness associated with finite rate chemistry. The model was applied to simulate a supersonic, coaxial H2-air burner, where both the mean and rms (root mean square) results were compared with the experimental data. In general, good agree-ments were achieved, which indicated that the present sub-grid PDF method could work well in simulating supersonic turbu-lent combustion. Moreover, the calculation showed that the sub-grid fluctuations of temperature and major species in the combustion region were of the order of 10%-20% of their rms, while the sub-grid fluctuation of hydroxyl might be as high as 40%-50% of its rms.展开更多
基金supported in part by the Open Fund of Intelligent Control Laboratory,China(No.ICL-2023–0202)in part by National Key R&D Program of China(Nos.2021YFC2202600,2021YFC2202603)。
文摘In distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distributed fusion algorithms,such as the Covariance Union(CU)and Faulttolerant Generalized Convex Combination(FGCC),are only used for the point estimation case where local estimates and their associated error covariances are provided.A treatment with focus on the fault-tolerant distributed fusions of arbitrary local Probability Density Functions(PDFs)is lacking.For this problem,we first propose Kullback–Leibler Divergence(KLD)and reversed KLD induced functional Fuzzy c-Means(FCM)clustering algorithms to soft cluster all local PDFs,respectively.On this basis,two fault-tolerant distributed fusion algorithms of arbitrary local PDFs are then developed.They select the representing PDF of the cluster with the largest sum of memberships as the fused PDF.Numerical examples verify the better fault tolerance of the developed two distributed fusion algorithms.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金the National Natural Science Foundation of China(No.61273127)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(No.12JK0524)
文摘The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.
文摘Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.
基金supported by the National Natural Science Foundation of China(No.51390493)
文摘Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.
基金National Science and Technology Major Project of China(No.2016ZX04003001)。
文摘The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.
基金National Natural Science Foundation of China(No.61374044)Shanghai Municipal Science and Technology Commission,China(No.15510722100)+2 种基金Shanghai Municipal Education Commission,China(No.14ZZ088)Shanghai Talent Development Plan,ChinaShanghai Baoshan Science and Technology Commission,China(No.bkw2013120)
文摘A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.
基金This workis financially supported by the National Natural Science Foundation of China (Grant No.40490263 andNo.40276006)
文摘Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.
基金Supported by the National Natural Science Foundation of China(No.61271230,61301107)the Fundamental Research Funds for the Central Universities(No.30920130122004)Open Research Fund of National Mobile Communications Research Laboratory,Southeast University(No.2013D02)
文摘This paper derives an approximate formula for probability density function(PDF) of received signal-to-interference-and-noise ratio(SINR) at user terminal when matched filter(MF) is adopted at a base station(BS).This distribution of SINR can be used to make an analysis of average sum-rate,outage probability,and symbol error rate of massive MIMO downlink with MF at BS.From simulation,it is found that the derived approximate analytical expression for PDF of SINR is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.
文摘研究了基于层流小火焰概念和假定beta-PDF(probability density function)的湍流预混燃烧模型.该模型采用PREMIX程序来计算层流小火焰,将计算结果表示为进程变量的函数,并利用进程变量的be-ta-PDF积分生成了用于RANS(雷诺平均Navier-Stokes)计算的PDF表.以化学当量的甲烷湍流本生火焰为算例对模型进行了计算验证,并与Zimont模型的计算结果和实验结果做了对比.结果表明,平均速度分布与实验符合的较好,温度和湍动能计算结果有待改善.本模型高估了化学反应速率,导致计算火焰比实际瘦,这是因为模型中未能考虑湍流对火焰的拉伸和弯曲效应,考虑湍流拉伸和弯曲效应的预混燃烧模型是今后进一步研究的方向.
文摘间歇过程的优化控制依赖于过程精确的数学模型,数据驱动的建模方法是目前间歇过程模型研究中的热点问题。突破传统数据驱动建模方法中采用均方差(mean squared error,MSE)作为准则函数的思想,提出一种新颖的间歇过程数据驱动建模方法,引入了概率密度函数(probability density function,PDF)控制的概念,构造间歇过程模型误差控制系统,将模型的可调参数作为控制系统的输入,模型误差PDF的形状作为控制系统的输出,从而把开环模型参数辨识问题转化为模型误差PDF形状的闭环控制问题。通过可调参数控制模型误差PDF的空间分布状态,不仅能够保障模型精度,还可控制模型误差的空间分布状态,从而消除模型中的有色噪声。仿真实验表明,基于模型误差PDF形状的间歇过程数据驱动模型具有较好的建模精度、鲁棒性和泛化能力,为间歇过程的数据驱动建模提供了一条新途径。
基金supported by the National Natural Science Foundation of China (Grant Nos. 50906098 and 91016028)
文摘A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) closure model has been devel-oped for supersonic turbulent combustion. Scalar transport equations for all species in a given chemical kinetic mechanism were solved, which are necessary in the supersonic combustion where the non-equilibrium chemistry is essentially involved. The clipped Gaussian PDF of temperature and multivariate ? PDF of composition were used to close the sub-grid chemical sources that appear in the conservation equations. The sub-grid variances of temperature and composition were constructed based on scale similarity approach. A semi-implicit approach based on the PDF model was proposed to tackle the resulting numerical stiffness associated with finite rate chemistry. The model was applied to simulate a supersonic, coaxial H2-air burner, where both the mean and rms (root mean square) results were compared with the experimental data. In general, good agree-ments were achieved, which indicated that the present sub-grid PDF method could work well in simulating supersonic turbu-lent combustion. Moreover, the calculation showed that the sub-grid fluctuations of temperature and major species in the combustion region were of the order of 10%-20% of their rms, while the sub-grid fluctuation of hydroxyl might be as high as 40%-50% of its rms.
