The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN app...The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.展开更多
In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forwar...In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.展开更多
基金supported by the Science and Technology on Reactor System Design Technology Laboratory(No.LRSDT12023108)supported in part by the Chongqing Postdoctoral Science Foundation(No.cstc2021jcyj-bsh0252)+2 种基金the National Natural Science Foundation of China(No.12005030)Sichuan Province to unveil the list of marshal industry common technology research projects(No.23jBGOV0001)Special Program for Stabilizing Support to Basic Research of National Basic Research Institutes(No.WDZC-2023-05-03-05).
文摘The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.
基金This project is supported by National Natural Science Foundation of China (No.50605065)Natural Science Foundation Project of CQ CSTC(No.2007BB2142).
文摘In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.
