Weak approximation for stochastic reaction-diffusion equation near sharp interface limit

It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is crucial to develop numerical approximations whose error bounds depends on $\frac 1\epsilon$ polynomially. However, due to loss of spectral estimate of the linearized stochastic reaction-diffusion equation, how to get such error bound of numerical approximation has been an open problem. In this paper, we solve this weak error bound problem for stochastic reaction-diffusion equations near sharp interface limit. We first introduce a regularized problem which enjoys the exponential ergodicity. Then we present the regularity analysis of the regularized Kolmogorov and Poisson equations which only depends on $\frac 1{\epsilon}$ polynomially. Furthermore, we establish such weak error bound. This phenomenon could be viewed as a kind of the regularization effect of noise on the numerical approximation of stochastic partial differential equation (SPDE). As a by-product, a central limit theorem of the weak approximation is shown near sharp interface limit. Our method of proof could be extended to a number of other spatial and temporal numerical approximations for semilinear SPDEs.Comment: 58 page

A DPCA-based online fault indicator for gear faults using three-direction vibration signals

For online monitoring and identifying gear faults, a new fault indicator is proposed based on a multivariate statistical technique, dynamic principal component analysis (DPCA), under variable load conditions. In this method, a tri-axial vibration sensor is used to acquire the 3-direction vibration signals of gear in the gear box because it can pick up more abundant fault information than a single axis sensor does. By monitoring the value of the fault indicator, the running state of the gear (normal condition or faults) can be directly identified according to the set thresholds without using any other fault classification methods. To verify the effectiveness, the proposed method is applied on the QPZZ-II rotating machinery fault simulation rig in which the root crack and the tooth broken faults are introduced into the gearbox’s driving gear. Experimental results show that the fault indicator not only can effectively reveal the health state of the gear, but also is without being influenced by the load fluctuation. And, the accuracy rate of fault diagnosis is over 96 %

Exponential Integrators for Stochastic Maxwell's Equations Driven by It\^o Noise

This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is $\frac 12$ for general multiplicative noise. Combing a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be $1$ for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.Comment: 21 Page

Condition trend prediction of aero-generator based on particle swarm optimization and fuzzy integral

In order to improve and enhance the prediction accuracy and efficiency of aero-generator running trend, grasp its running condition, and avoid accidents happening, in this paper, auto-regressive and moving average model (ARMA) and least squares support vector machine (LSSVM) which are used to predict its running trend have been optimized using particle swarm optimization (PSO) based on using features found in real aero-generator life test, which lasts a long period of time on specialized test platform and collects mass data that reflects aero-generator characteristics, to build new models of PSO-ARMA and PSO-LSSVM. And we use fuzzy integral methodology to carry out decision fusion of the predicted results of these two new models. The research shows that the prediction accuracy of PSO-ARMA and PSO-LSSVM has been much improved on that of ARMA and LSSVM, and the results of decision fusion based on fuzzy integral methodology show further substantial improvement in accuracy than each particle swarm optimized model. Conclusion can be drawn that the optimized model and the decision fusion method presented in this paper are available in aero-generator condition trend prediction and have great value of engineering application

A DPCA-based online fault indicator for gear faults using three-direction vibration signals

For online monitoring and identifying gear faults, a new fault indicator is proposed based on a multivariate statistical technique, dynamic principal component analysis (DPCA), under variable load conditions. In this method, a tri-axial vibration sensor is used to acquire the 3-direction vibration signals of gear in the gear box because it can pick up more abundant fault information than a single axis sensor does. By monitoring the value of the fault indicator, the running state of the gear (normal condition or faults) can be directly identified according to the set thresholds without using any other fault classification methods. To verify the effectiveness, the proposed method is applied on the QPZZ-II rotating machinery fault simulation rig in which the root crack and the tooth broken faults are introduced into the gearbox’s driving gear. Experimental results show that the fault indicator not only can effectively reveal the health state of the gear, but also is without being influenced by the load fluctuation. And, the accuracy rate of fault diagnosis is over 96 %