Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to in...Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to inherent fluctuations,limited data and imperfect measurements resulting in aleatory,epistemic and measurement uncertainties of the degradation process.This paper proposes a degradation model and remaining useful life(RUL)prediction method under triple uncertainties for a category of complex equipment with multi-phase degradation and jumps.First,a multi-phase degradation model with random jumps and measurement errors is constructed based on uncertain random processes.Afterward,the analytic expression of RUL prediction considering the heterogeneity is derived by modeling the uncertainty of degradation states at change points under the concept of first hitting time.A stochastic uncertain approach is utilized for the proposed multi-phase degradation model to identify model parameters based on historical data.Furthermore,the implied degradation features are adaptively updated in online stage using similarity-based weighted stochastic uncertain maximum likelihood estimation and Kalman filtering.Finally,the effectiveness of the method is verified by simulation example and practical case.展开更多
Wireless Sensor Networks(WSNs)have hardware and software limitations and are deployed in hostile environments.The problem of energy consumption in WSNs has become a very important axis of research.To obtain good perfo...Wireless Sensor Networks(WSNs)have hardware and software limitations and are deployed in hostile environments.The problem of energy consumption in WSNs has become a very important axis of research.To obtain good performance in terms of the network lifetime,several routing protocols have been proposed in the literature.Hierarchical routing is considered to be the most favorable approach in terms of energy efficiency.It is based on the concept parent-child hierarchy where the child nodes forward their messages to their parent,and then the parent node forwards them,directly or via other parent nodes,to the base station(sink).In this paper,we present a new Energy-Efficient clustering protocol for WSNs using an Objective Function and Random Search with Jumps(EEOFRSJ)in order to reduce sensor energy consumption.First,the objective function is used to find an optimal cluster formation taking into account the ratio of the mean Euclidean distance of the nodes to their associated cluster heads(CH)and their residual energy.Then,we find the best path to transmit data from the CHs nodes to the base station(BS)using a random search with jumps.We simulated our proposed approach compared with the Energy-Efficient in WSNs using Fuzzy C-Means clustering(EEFCM)protocol using Matlab Simulink.Simulation results have shown that our proposed protocol excels regarding energy consumption,resulting in network lifetime extension.展开更多
A class of stochastic differential equations with random jump magnitudes( SDEwRJMs) is investigated. Under nonLipschitz conditions,the convergence of semi-implicit Euler method for SDEwRJMs is studied. The main purpos...A class of stochastic differential equations with random jump magnitudes( SDEwRJMs) is investigated. Under nonLipschitz conditions,the convergence of semi-implicit Euler method for SDEwRJMs is studied. The main purpose is to prove that the semi-implicit Euler solutions converge to the true solutions in the mean-square sense. An example is given for illustration.展开更多
To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the c...To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.展开更多
This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backw...This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.展开更多
基金supported by the National Key Research and Development Program of China(2021YFB3301200)the National Natural Science Foundation of China(NSFC)(U21A20483,62373040,62203042).
文摘Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to inherent fluctuations,limited data and imperfect measurements resulting in aleatory,epistemic and measurement uncertainties of the degradation process.This paper proposes a degradation model and remaining useful life(RUL)prediction method under triple uncertainties for a category of complex equipment with multi-phase degradation and jumps.First,a multi-phase degradation model with random jumps and measurement errors is constructed based on uncertain random processes.Afterward,the analytic expression of RUL prediction considering the heterogeneity is derived by modeling the uncertainty of degradation states at change points under the concept of first hitting time.A stochastic uncertain approach is utilized for the proposed multi-phase degradation model to identify model parameters based on historical data.Furthermore,the implied degradation features are adaptively updated in online stage using similarity-based weighted stochastic uncertain maximum likelihood estimation and Kalman filtering.Finally,the effectiveness of the method is verified by simulation example and practical case.
文摘Wireless Sensor Networks(WSNs)have hardware and software limitations and are deployed in hostile environments.The problem of energy consumption in WSNs has become a very important axis of research.To obtain good performance in terms of the network lifetime,several routing protocols have been proposed in the literature.Hierarchical routing is considered to be the most favorable approach in terms of energy efficiency.It is based on the concept parent-child hierarchy where the child nodes forward their messages to their parent,and then the parent node forwards them,directly or via other parent nodes,to the base station(sink).In this paper,we present a new Energy-Efficient clustering protocol for WSNs using an Objective Function and Random Search with Jumps(EEOFRSJ)in order to reduce sensor energy consumption.First,the objective function is used to find an optimal cluster formation taking into account the ratio of the mean Euclidean distance of the nodes to their associated cluster heads(CH)and their residual energy.Then,we find the best path to transmit data from the CHs nodes to the base station(BS)using a random search with jumps.We simulated our proposed approach compared with the Energy-Efficient in WSNs using Fuzzy C-Means clustering(EEFCM)protocol using Matlab Simulink.Simulation results have shown that our proposed protocol excels regarding energy consumption,resulting in network lifetime extension.
基金National Natural Science Foundations of China(Nos.11401261,11471071)Qing Lan Project of Jiangsu Province,China(No.2012)+2 种基金Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.13KJB110005)the Grant of Jiangsu Second Normal University(No.JSNU-ZY-02)the Jiangsu Government Overseas Study Scholarship,China
文摘A class of stochastic differential equations with random jump magnitudes( SDEwRJMs) is investigated. Under nonLipschitz conditions,the convergence of semi-implicit Euler method for SDEwRJMs is studied. The main purpose is to prove that the semi-implicit Euler solutions converge to the true solutions in the mean-square sense. An example is given for illustration.
基金Supported by the National Natural Science Foundation of China under Grant No 11626047the Foundation for Young Key Teachers of Chengdu University of Technology under Grant No KYGG201414
文摘To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.
基金This research is supported by the National Nature Science Foundation of China under Grant Nos 11001156, 11071144, the Nature Science Foundation of Shandong Province （ZR2009AQ017）, and Independent Innovation Foundation of Shandong University （IIFSDU）, China.
文摘This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.
