The lumped time distribution functions were proposed, which can be used for describing the dynamicsystems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numer...The lumped time distribution functions were proposed, which can be used for describing the dynamicsystems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numerical analysis of the lumped time distribution functions was carried out. The method for calculating molecularweight distribution of polymer in the stable free radical polymerization and more general cases was developed basedon the lumped time distribution functions.展开更多
We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an ...We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.展开更多
Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,...Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A rea...Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A real-time measurement device is developed, the measurement spectral range of which is from ultraviolet to near infrared with 2.4-nm wavelength resolution, and the angular range is 0° - 360° in azimuth angle and 0° - 85° in zenith angle with 0.01° angle resolution. Absolute measurements of BRDF on tinfoil and ceramic tile are performed and the test materials present apparent specular reflection characteristics. The theoretical error in the experiment is about 6.05%. The BRDF measurement results are closely related to the precision of measurement platform, the sensitivity of measurement instrument, and the stability of illuminating light source.展开更多
Optimal Models for first arrival time (rH) and first arrival target total return (WH) distribution functions on MDP in continuous time are presented. Asymptotic expansions of rH and WH are derived and expressed in sim...Optimal Models for first arrival time (rH) and first arrival target total return (WH) distribution functions on MDP in continuous time are presented. Asymptotic expansions of rH and WH are derived and expressed in simple, explicit forms, and some of their properties are discussed. Two methods to find an optimal policy for distribution function of rH are given. Several necessary and sufficient conditions for the existence of the optimal policy are obtained. This result leads to that the scope of finding the optimal policy is greatly reduced. A special case is also discussed and some deep results are given.展开更多
An analytical algorithm was presented for the exact computation of the probability distribution of the project completion time in stochastic networks,where the activity durations are mutually independent and continuou...An analytical algorithm was presented for the exact computation of the probability distribution of the project completion time in stochastic networks,where the activity durations are mutually independent and continuously distributed random variables. Firstly,stochastic activity networks were modeled as continuous-time Markov process with a single absorbing state by the well-know method of supplementary variables and the time changed from the initial state to absorbing state is equal to the project completion time.Then,the Markov process was regarded as a special case of Markov skeleton process.By taking advantage of the backward equations of Markov skeleton processes,a backward algorithm was proposed to compute the probability distribution of the project completion time.Finally,a numerical example was solved to demonstrate the performance of the proposed methodology.The results show that the proposed algorithm is capable of computing the exact distribution function of the project completion time,and the expectation and variance are obtained.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 practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “...A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piece- wise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large- scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.展开更多
Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including at...Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.展开更多
In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using...In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.展开更多
After the time history of seismic motion is represented by superposition of a series of narrow frequency band wave groups, we obtain a general relation between wave group arrival time and derivative of phase spectra i...After the time history of seismic motion is represented by superposition of a series of narrow frequency band wave groups, we obtain a general relation between wave group arrival time and derivative of phase spectra in the paper. On the basis of the relation, frequency number distribution function of wave group arrival time is completely equivalent to that of phase difference spectra. Under the assumption that phase angles of seismic motionobey uniform distribution ranged from 0 to ─ 2π, a quantitative relation between intensity envelope function of seismic motion and energy distribution function with wave group arrival time has been derived in this paper. The relation illuminates inner links among Fourier amplitude spectra and derivative of phase spectra and intensity envelope function. Some examples given by the paper support the conclusions mentioned above.展开更多
The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful ...The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.展开更多
The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the ...The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.展开更多
Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive sol...Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.展开更多
Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arriva...Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.展开更多
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
文摘The lumped time distribution functions were proposed, which can be used for describing the dynamicsystems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numerical analysis of the lumped time distribution functions was carried out. The method for calculating molecularweight distribution of polymer in the stable free radical polymerization and more general cases was developed basedon the lumped time distribution functions.
文摘We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.
基金supported by National Key Research and Development Program of China(2024YFE0214000)National Natural Science Foundation of China(62173308)+3 种基金Natural Science Foundation of Zhejiang Province of China(LRG25F030002)Zhejiang Province Leading Geese Plan(2025C01056)Jinhua Science and Technology Project(2022-1-042)Natural Science Foundation of Jiangsu Province(BK20240009).
文摘Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.
基金supported by the National"863"Project of China under Grant No.2006AA704214-5.
文摘Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A real-time measurement device is developed, the measurement spectral range of which is from ultraviolet to near infrared with 2.4-nm wavelength resolution, and the angular range is 0° - 360° in azimuth angle and 0° - 85° in zenith angle with 0.01° angle resolution. Absolute measurements of BRDF on tinfoil and ceramic tile are performed and the test materials present apparent specular reflection characteristics. The theoretical error in the experiment is about 6.05%. The BRDF measurement results are closely related to the precision of measurement platform, the sensitivity of measurement instrument, and the stability of illuminating light source.
文摘Optimal Models for first arrival time (rH) and first arrival target total return (WH) distribution functions on MDP in continuous time are presented. Asymptotic expansions of rH and WH are derived and expressed in simple, explicit forms, and some of their properties are discussed. Two methods to find an optimal policy for distribution function of rH are given. Several necessary and sufficient conditions for the existence of the optimal policy are obtained. This result leads to that the scope of finding the optimal policy is greatly reduced. A special case is also discussed and some deep results are given.
基金Project(10671212) supported by the National Natural Science Foundation of ChinaProject(20050533036) supported by the Specialized Research Found for the Doctoral Program Foundation of Higher Education of China
文摘An analytical algorithm was presented for the exact computation of the probability distribution of the project completion time in stochastic networks,where the activity durations are mutually independent and continuously distributed random variables. Firstly,stochastic activity networks were modeled as continuous-time Markov process with a single absorbing state by the well-know method of supplementary variables and the time changed from the initial state to absorbing state is equal to the project completion time.Then,the Markov process was regarded as a special case of Markov skeleton process.By taking advantage of the backward equations of Markov skeleton processes,a backward algorithm was proposed to compute the probability distribution of the project completion time.Finally,a numerical example was solved to demonstrate the performance of the proposed methodology.The results show that the proposed algorithm is capable of computing the exact distribution function of the project completion time,and the expectation and variance are obtained.
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.
文摘A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piece- wise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large- scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.
基金supported by the Basic Science Center Project of the National Natural Science Foundation of China(42388102)the National Natural Science Foundation of China(42174030)+2 种基金the Special Fund of Hubei Luojia Laboratory(220100020)the Major Science and Technology Program for Hubei Province(2022AAA002)the Fundamental Research Funds for the Central Universities of China(2042022dx0001 and 2042023kfyq01)。
文摘Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.
文摘In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.
文摘After the time history of seismic motion is represented by superposition of a series of narrow frequency band wave groups, we obtain a general relation between wave group arrival time and derivative of phase spectra in the paper. On the basis of the relation, frequency number distribution function of wave group arrival time is completely equivalent to that of phase difference spectra. Under the assumption that phase angles of seismic motionobey uniform distribution ranged from 0 to ─ 2π, a quantitative relation between intensity envelope function of seismic motion and energy distribution function with wave group arrival time has been derived in this paper. The relation illuminates inner links among Fourier amplitude spectra and derivative of phase spectra and intensity envelope function. Some examples given by the paper support the conclusions mentioned above.
基金supported by the National Natural Science Foundation of China(61261046,61362038)the Natural Science Foundation of Jiangxi Province(20142BAB207006,20151BAB207013)+2 种基金the Science and Technology Project of Provincial Education Department of Jiangxi Province(GJJ14738,GJJ14739)the Research Foundation of Health Department of Jiangxi Province(20175561)the Science and Technology Project of Jiujiang University(2016KJ001,2016KJ002)
文摘The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.
基金The National Natural Science Foundation of China(No.61273119,61104068,61374038)the Natural Science Foundation of Jiangsu Province(No.BK2011253)
文摘The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China(60874114)
文摘Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.
文摘Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.
文摘In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
