For the large number of nonlinear degradation devices existing in a project, the existing methods have not systematically studied the effects of random effect on the remaining lifetime(RL),the accuracy and efficiency ...For the large number of nonlinear degradation devices existing in a project, the existing methods have not systematically studied the effects of random effect on the remaining lifetime(RL),the accuracy and efficiency of the parameters estimation are not high, and the current degradation state of the target device is not accurately estimated. In this paper, a nonlinear Wiener degradation model with random effect is proposed and the corresponding probability density function(PDF) of the first hitting time(FHT)is deduced. A parameter estimation method based on modified expectation maximum(EM) algorithm is proposed to obtain the estimated value of fixed coefficient and the priori value of random coefficient in the model. The posterior value of the random coefficient and the current degradation state of target device are updated synchronously by the state space model(SSM) and the Kalman filter algorithm. The PDF of RL with random effect is deduced. A simulation example is analyzed to verify that the proposed method has the obvious advantage over the existing methods in parameter estimation error and RL prediction accuracy.展开更多
We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） an...We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.展开更多
The existence of random attractor family for a class of nonlinear high-order Kirchhoff equation stochastic dynamical systems with white noise is studied. The Ornstein-Uhlenbeck process and the weak solution of the equ...The existence of random attractor family for a class of nonlinear high-order Kirchhoff equation stochastic dynamical systems with white noise is studied. The Ornstein-Uhlenbeck process and the weak solution of the equation are used to deal with the stochastic terms. The equation is transformed into a general stochastic equation. The bounded stochastic absorption set is obtained by estimating the solution of the equation and the existence of the random attractor family is obtained by isomorphic mapping method. Temper random compact sets of random attractor family are obtained.展开更多
基金supported by the National Defense Foundation of China(71601183)the China Postdoctoral Science Foundation(2017M623415)
文摘For the large number of nonlinear degradation devices existing in a project, the existing methods have not systematically studied the effects of random effect on the remaining lifetime(RL),the accuracy and efficiency of the parameters estimation are not high, and the current degradation state of the target device is not accurately estimated. In this paper, a nonlinear Wiener degradation model with random effect is proposed and the corresponding probability density function(PDF) of the first hitting time(FHT)is deduced. A parameter estimation method based on modified expectation maximum(EM) algorithm is proposed to obtain the estimated value of fixed coefficient and the priori value of random coefficient in the model. The posterior value of the random coefficient and the current degradation state of target device are updated synchronously by the state space model(SSM) and the Kalman filter algorithm. The PDF of RL with random effect is deduced. A simulation example is analyzed to verify that the proposed method has the obvious advantage over the existing methods in parameter estimation error and RL prediction accuracy.
基金supported by China NSF(11271388)Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1400430)Basis and Frontier Research Project of Chongqing(cstc2014jcyj A00035)
文摘We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.
文摘The existence of random attractor family for a class of nonlinear high-order Kirchhoff equation stochastic dynamical systems with white noise is studied. The Ornstein-Uhlenbeck process and the weak solution of the equation are used to deal with the stochastic terms. The equation is transformed into a general stochastic equation. The bounded stochastic absorption set is obtained by estimating the solution of the equation and the existence of the random attractor family is obtained by isomorphic mapping method. Temper random compact sets of random attractor family are obtained.
