An analytical approach for probabilistic evaluation of transient stability of a power system incorporating a wind farm is presented in this study. Based on the fact that the boundary of practical dynamic security regi...An analytical approach for probabilistic evaluation of transient stability of a power system incorporating a wind farm is presented in this study. Based on the fact that the boundary of practical dynamic security region(PDSR) of a power system with double fed induction generators(DFIG) can be approximated by one or few hyper-planes in nodal power injection space, transient stability criterion for given configurations of pre-fault, fault-on and post-fault of a power system is to be expressed by certain expressions of linear combination of nodal injection vector and the transient stability probability(TSP) is further obtained with a much more simplified expression than the complex integral. Furthermore, considering uncertainties of nodal injection power including wind power and load, TSP is calculated analytically by Cornish-Fisher expansion, which can provide reliable evaluation results with high accuracy and much less computing time compared with Monte Carlo simulation. TSP and its visualization can further help operators and planners be aware of the degree of stability or instability and find critical components to monitor and reinforce. Test results on the New England 10-generators and 39-buses power system show the method's effectiveness and significance for probabilistic security assessment.展开更多
Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gainin...Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gaining increasing prominence.This is primarily due to their unique properties,including low strength and loose structure.Current methods for evaluating slope stability,such as basic quality(BQ)and slope stability probability classification(SSPC),do not adequately account for the poor integrity and structural fragmentation characteristic of disintegrated dolomite.To address this challenge,an analysis of the applicability of the limit equilibrium method(LEM),BQ,and SSPC methods was conducted on eight disintegrated dolomite slopes located in Baoshan,Southwest China.However,conflicting results were obtained.Therefore,this paper introduces a novel method,SMRDDS,to provide rapid and accurate assessment of disintegrated dolomite slope stability.This method incorporates parameters such as disintegrated grade,joint state,groundwater conditions,and excavation methods.The findings reveal that six slopes exhibit stability,while two are considered partially unstable.Notably,the proposed method demonstrates a closer match with the actual conditions and is more time-efficient compared with the BQ and SSPC methods.However,due to the limited research on disintegrated dolomite slopes,the results of the SMRDDS method tend to be conservative as a safety precaution.In conclusion,the SMRDDS method can quickly evaluate the current situation of disintegrated dolomite slopes in the field.This contributes significantly to disaster risk reduction for disintegrated dolomite slopes.展开更多
This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution sy...This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calcula...Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.展开更多
In open-pit mines,pit slope as one of the important parameters affects the mine economy and total minable reserve,and it is also affected by different uncertainties which arising from many sources.One of the most crit...In open-pit mines,pit slope as one of the important parameters affects the mine economy and total minable reserve,and it is also affected by different uncertainties which arising from many sources.One of the most critical sources of uncertainty effects on the pit slope design is rock mass geomechanical properties.By comparing the probability of failure resulted from deterministic procedure and probabilistic one,this paper investigated the effects of aforesaid uncertainties on open-pit slope stability in metal mines.In this way,to reduce the effect of variance,it implemented Latin Hypercube Sampling(LHS)technique.Furthermore,a hypothesis test was exerted to compare the effects on two cases in Middle East.Subsequently,the investigation approved high influence of geomechanical uncertainties on overall pit steepness and stability in both iron and copper mines,though on the first case the effects were just over.展开更多
Delay and stability are two key factors that affect the performance of multicast data transmission in a network.However,current algorithms of tree generation hardly meet the requirements of low delay and high sta-bili...Delay and stability are two key factors that affect the performance of multicast data transmission in a network.However,current algorithms of tree generation hardly meet the requirements of low delay and high sta-bility simultaneously.Given a general network,the generation algorithm of a multicast tree with minimum delay and maximum stability is an NP-hard problem,without a precise and efficient algorithm.To address these challenges,this paper studies the generation of low-delay and high-stability multicast trees under the model of spanning tree based on stability probability,degree-constrained,edge-weighted for multicast(T-SDE).A class of algorithms was proposed which creates the multicast tree greedy on the ratio of fan-out to delay(RFD)and probability of stability of terminal to obtain a high performance in multicast.The proposed algorithms greedily select terminals with a large RFD and a high probability of stability as forwarding nodes in the generation of the multicast tree,where the larger RFD and higher stability of upstream nodes are beneficial to achieve a low transmission delay and high stability in multicast.The proposed RFD can be compatible with the original model,which can take advantage of network connectivity during the generation of a multicast tree.This paper carries out simulation experiments on Matlab R2016b to measure the performance of the proposed algorithm.Experimental results show that the proposed algorithm can provide a smaller height,higher stability,and a lower transmission delay of the resulting multicast tree than other solutions.The spanning tree of the proposed algorithms can support low transmission delay and high stability in multicast transmission.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stabi...In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.展开更多
So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It...So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.展开更多
We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions f...We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.展开更多
The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals ...The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.展开更多
A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noise...A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters.By using Itô’s differentiation rule,nonlinear damping and adaptive Backstepping procedure,the input-to-state stable controller of global stabilization in probability is developed,which guarantees that system states are bounded and the system has a robust stabilization.According to Swapping technique,we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.Transient performance of the system is estimated by the norm of error.Results of simulation show the effectiveness of the control algorithms.The modular design,which has a concise hierarchy,is more flexible and versatile than a Lyapunov-based algorithm.展开更多
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2013CB228204)the National Natural Science Foundation of China(Grant No.51407126)Tianjin Natural Science Foundation(Grant No.15JCQNJC07000)
文摘An analytical approach for probabilistic evaluation of transient stability of a power system incorporating a wind farm is presented in this study. Based on the fact that the boundary of practical dynamic security region(PDSR) of a power system with double fed induction generators(DFIG) can be approximated by one or few hyper-planes in nodal power injection space, transient stability criterion for given configurations of pre-fault, fault-on and post-fault of a power system is to be expressed by certain expressions of linear combination of nodal injection vector and the transient stability probability(TSP) is further obtained with a much more simplified expression than the complex integral. Furthermore, considering uncertainties of nodal injection power including wind power and load, TSP is calculated analytically by Cornish-Fisher expansion, which can provide reliable evaluation results with high accuracy and much less computing time compared with Monte Carlo simulation. TSP and its visualization can further help operators and planners be aware of the degree of stability or instability and find critical components to monitor and reinforce. Test results on the New England 10-generators and 39-buses power system show the method's effectiveness and significance for probabilistic security assessment.
基金supported by the National Natural Science Foundation of China(Grant No.42162026)the Applied Basic Research Foundation of Yunnan Province(Grant No.202201AT070083).
文摘Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gaining increasing prominence.This is primarily due to their unique properties,including low strength and loose structure.Current methods for evaluating slope stability,such as basic quality(BQ)and slope stability probability classification(SSPC),do not adequately account for the poor integrity and structural fragmentation characteristic of disintegrated dolomite.To address this challenge,an analysis of the applicability of the limit equilibrium method(LEM),BQ,and SSPC methods was conducted on eight disintegrated dolomite slopes located in Baoshan,Southwest China.However,conflicting results were obtained.Therefore,this paper introduces a novel method,SMRDDS,to provide rapid and accurate assessment of disintegrated dolomite slope stability.This method incorporates parameters such as disintegrated grade,joint state,groundwater conditions,and excavation methods.The findings reveal that six slopes exhibit stability,while two are considered partially unstable.Notably,the proposed method demonstrates a closer match with the actual conditions and is more time-efficient compared with the BQ and SSPC methods.However,due to the limited research on disintegrated dolomite slopes,the results of the SMRDDS method tend to be conservative as a safety precaution.In conclusion,the SMRDDS method can quickly evaluate the current situation of disintegrated dolomite slopes in the field.This contributes significantly to disaster risk reduction for disintegrated dolomite slopes.
文摘This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
基金Project(51878668)supported by the National Natural Science Foundation of ChinaProjects(2017-122-058,2018-123-040)supported by the Guizhou Provincial Department of Transportation Foundation,ChinaProject([2018]2815)supported by the Guizhou Provincial Department of Science and Technology Foundation,China。
文摘Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.
文摘In open-pit mines,pit slope as one of the important parameters affects the mine economy and total minable reserve,and it is also affected by different uncertainties which arising from many sources.One of the most critical sources of uncertainty effects on the pit slope design is rock mass geomechanical properties.By comparing the probability of failure resulted from deterministic procedure and probabilistic one,this paper investigated the effects of aforesaid uncertainties on open-pit slope stability in metal mines.In this way,to reduce the effect of variance,it implemented Latin Hypercube Sampling(LHS)technique.Furthermore,a hypothesis test was exerted to compare the effects on two cases in Middle East.Subsequently,the investigation approved high influence of geomechanical uncertainties on overall pit steepness and stability in both iron and copper mines,though on the first case the effects were just over.
基金supported by the Hainan Provincial Natural Science Foundation of China(620RC560,2019RC096,620RC562)the Scientific Research Setup Fund of Hainan University(KYQD(ZR)1877)+2 种基金the National Natural Science Foundation of China(62162021,61802092,82160345,61862020)the key research and development program of Hainan province(ZDYF2020199,ZDYF2021GXJS017)the key science and technology plan project of Haikou(2011-016).
文摘Delay and stability are two key factors that affect the performance of multicast data transmission in a network.However,current algorithms of tree generation hardly meet the requirements of low delay and high sta-bility simultaneously.Given a general network,the generation algorithm of a multicast tree with minimum delay and maximum stability is an NP-hard problem,without a precise and efficient algorithm.To address these challenges,this paper studies the generation of low-delay and high-stability multicast trees under the model of spanning tree based on stability probability,degree-constrained,edge-weighted for multicast(T-SDE).A class of algorithms was proposed which creates the multicast tree greedy on the ratio of fan-out to delay(RFD)and probability of stability of terminal to obtain a high performance in multicast.The proposed algorithms greedily select terminals with a large RFD and a high probability of stability as forwarding nodes in the generation of the multicast tree,where the larger RFD and higher stability of upstream nodes are beneficial to achieve a low transmission delay and high stability in multicast.The proposed RFD can be compatible with the original model,which can take advantage of network connectivity during the generation of a multicast tree.This paper carries out simulation experiments on Matlab R2016b to measure the performance of the proposed algorithm.Experimental results show that the proposed algorithm can provide a smaller height,higher stability,and a lower transmission delay of the resulting multicast tree than other solutions.The spanning tree of the proposed algorithms can support low transmission delay and high stability in multicast transmission.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金the National Natural Science Foundation of China (70701002,70521001)the National Basic Research Program of China (2006CB705503)the Research Grants Council of the Hong Kong Special Administrative Region (HKU7187/05E)
文摘In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.
基金Supported by the National Natural Science Foundation of China(Grant No.60574042)
文摘So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
基金Project supported by the National Natural Science Foundation of China(Nos.61873284,61473315,and 61321003)。
文摘We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301030, 11401169 and 11431014)Key Scientific Research Projects of Henan Province (Grant No. 16A110010)
文摘The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.
基金supported by the National science Foundation of Anhui(03042302)。
文摘A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters.By using Itô’s differentiation rule,nonlinear damping and adaptive Backstepping procedure,the input-to-state stable controller of global stabilization in probability is developed,which guarantees that system states are bounded and the system has a robust stabilization.According to Swapping technique,we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.Transient performance of the system is estimated by the norm of error.Results of simulation show the effectiveness of the control algorithms.The modular design,which has a concise hierarchy,is more flexible and versatile than a Lyapunov-based algorithm.
