To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solut...To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-dema...The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-demanding.To assess the slope stability problems with a more desirable computational effort,many machine learning(ML)algorithms have been proposed.However,most ML-based techniques require that the training data must be in the same feature space and have the same distribution,and the model may need to be rebuilt when the spatial distribution changes.This paper presents a new ML-based algorithm,which combines the principal component analysis(PCA)-based neural network(NN)and transfer learning(TL)techniques(i.e.PCAeNNeTL)to conduct the stability analysis of slopes with different spatial distributions.The Monte Carlo coupled with finite element simulation is first conducted for data acquisition considering the spatial variability of cohesive strength or friction angle of soils from eight slopes with the same geometry.The PCA method is incorporated into the neural network algorithm(i.e.PCA-NN)to increase the computational efficiency by reducing the input variables.It is found that the PCA-NN algorithm performs well in improving the prediction of slope stability for a given slope in terms of the computational accuracy and computational effort when compared with the other two algorithms(i.e.NN and decision trees,DT).Furthermore,the PCAeNNeTL algorithm shows great potential in assessing the stability of slope even with fewer training data.展开更多
We present our results by using a machine learning(ML)approach for the solution of the Riemann problem for the Euler equations of fluid dynamics.The Riemann problem is an initial-value problem with piecewise-constant ...We present our results by using a machine learning(ML)approach for the solution of the Riemann problem for the Euler equations of fluid dynamics.The Riemann problem is an initial-value problem with piecewise-constant initial data and it represents a mathematical model of the shock tube.The solution of the Riemann problem is the building block for many numerical algorithms in computational fluid dynamics,such as finite-volume or discontinuous Galerkin methods.Therefore,a fast and accurate approximation of the solution of the Riemann problem and construction of the associated numerical fluxes is of crucial importance.The exact solution of the shock tube problem is fully described by the intermediate pressure and mathematically reduces to finding a solution of a nonlinear equation.Prior to delving into the complexities of ML for the Riemann problem,we consider a much simpler formulation,yet very informative,problem of learning roots of quadratic equations based on their coefficients.We compare two approaches:(i)Gaussian process(GP)regressions,and(ii)neural network(NN)approximations.Among these approaches,NNs prove to be more robust and efficient,although GP can be appreciably more accurate(about 30\%).We then use our experience with the quadratic equation to apply the GP and NN approaches to learn the exact solution of the Riemann problem from the initial data or coefficients of the gas equation of state(EOS).We compare GP and NN approximations in both regression and classification analysis and discuss the potential benefits and drawbacks of the ML approach.展开更多
Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of th...Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.展开更多
This paper addresses a geometric control algorithm for the attitude tracking problem of the rigid spacecraft modeled on SO(3).Considering the topological and geometric properties of SO(3),we introduced a smooth positi...This paper addresses a geometric control algorithm for the attitude tracking problem of the rigid spacecraft modeled on SO(3).Considering the topological and geometric properties of SO(3),we introduced a smooth positive attitude error function to convert the attitude tracking issue on SO(3)into the stabilization counterpart on its Lie algebra.The error transformation technique was further utilized to ensure the assigned transient and steady state performance of the attitude tracking error with the aid of a well⁃designed assigned⁃time performance function.Then,using the actor⁃critic(AC)neural architecture,an adaptive reinforcement learning approximator was constructed,in which the actor neural network(NN)was utilized to approximate the unknown nonlinearity online.A critic function was introduced to tune the next phase of the actor neural network operation for performance improvement via supervising the system performance.A rigorous stability analysis was presented to show that the assigned system performance can be achieved.Finally,the effectiveness and feasibility of the constructed control strategy was verified by the numerical simulation.展开更多
Magnetically coupled rodless cylinders are widely used in the coordinate positioning of mechanical arms,electro-static paintings,and other industrial applications.However,they exhibit strong nonlinear characteristics,...Magnetically coupled rodless cylinders are widely used in the coordinate positioning of mechanical arms,electro-static paintings,and other industrial applications.However,they exhibit strong nonlinear characteristics,which lead to low servo control accuracy.In this study,a mass-flow equation through the valve port was derived to improve the control performance,considering the characteristics of the dynamics and throttle-hole flow.Subsequently,a fric-tion model combining static,viscous,and Coulomb friction with a zero-velocity interval was proposed.In addition,energy and dynamic models were set for the experimental investigation of the magnetically coupled rodless cylin-der.A nonlinear mathematical model for the position of the magnetically coupled rodless cylinder was proposed.An incremental PID controller was designed for the magnetically coupled rodless cylinder to control this system,and the PID parameters were adjusted online using RBF neural network.The response results of the PID parameters based on the RBF neural network were compared with those of the traditional incremental PID control,which proved the superiority of the optimization control algorithm of the incremental PID parameters based on the RBF neural network servo control system.The experimental results of this model were compared with the simulation results.The average error between the established model and the actual system was 0.005175054(m),which was approximately 2.588%of the total travel length,demonstrating the accuracy of the theoretical model.展开更多
Classification of speech signals is a vital part of speech signal processing systems.With the advent of speech coding and synthesis,the classification of the speech signal is made accurate and faster.Conventional meth...Classification of speech signals is a vital part of speech signal processing systems.With the advent of speech coding and synthesis,the classification of the speech signal is made accurate and faster.Conventional methods are considered inaccurate due to the uncertainty and diversity of speech signals in the case of real speech signal classification.In this paper,we use efficient speech signal classification using a series of neural network classifiers with reinforcement learning operations.Prior classification of speech signals,the study extracts the essential features from the speech signal using Cepstral Analysis.The features are extracted by converting the speech waveform to a parametric representation to obtain a relatively minimized data rate.Hence to improve the precision of classification,Generative Adversarial Networks are used and it tends to classify the speech signal after the extraction of features from the speech signal using the cepstral coefficient.The classifiers are trained with these features initially and the best classifier is chosen to perform the task of classification on new datasets.The validation of testing sets is evaluated using RL that provides feedback to Classifiers.Finally,at the user interface,the signals are played by decoding the signal after being retrieved from the classifier back based on the input query.The results are evaluated in the form of accuracy,recall,precision,f-measure,and error rate,where generative adversarial network attains an increased accuracy rate than other methods:Multi-Layer Perceptron,Recurrent Neural Networks,Deep belief Networks,and Convolutional Neural Networks.展开更多
基金V. ACKN0WLEDGMENT This work was supported by the National Natural Sci- ence Foundation of China （No.10375024） and the Science Foundation of Hunan Educational Committee.
文摘To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
基金supported by the National Natural Science Foundation of China(Grant No.52008402)the Central South University autonomous exploration project(Grant No.2021zzts0790).
文摘The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-demanding.To assess the slope stability problems with a more desirable computational effort,many machine learning(ML)algorithms have been proposed.However,most ML-based techniques require that the training data must be in the same feature space and have the same distribution,and the model may need to be rebuilt when the spatial distribution changes.This paper presents a new ML-based algorithm,which combines the principal component analysis(PCA)-based neural network(NN)and transfer learning(TL)techniques(i.e.PCAeNNeTL)to conduct the stability analysis of slopes with different spatial distributions.The Monte Carlo coupled with finite element simulation is first conducted for data acquisition considering the spatial variability of cohesive strength or friction angle of soils from eight slopes with the same geometry.The PCA method is incorporated into the neural network algorithm(i.e.PCA-NN)to increase the computational efficiency by reducing the input variables.It is found that the PCA-NN algorithm performs well in improving the prediction of slope stability for a given slope in terms of the computational accuracy and computational effort when compared with the other two algorithms(i.e.NN and decision trees,DT).Furthermore,the PCAeNNeTL algorithm shows great potential in assessing the stability of slope even with fewer training data.
基金This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396The authors gratefully acknowledge the support of the US Department of Energy National Nuclear Security Administration Advanced Simulation and Computing Program.The Los Alamos unlimited release number is LA-UR-19-32257.
文摘We present our results by using a machine learning(ML)approach for the solution of the Riemann problem for the Euler equations of fluid dynamics.The Riemann problem is an initial-value problem with piecewise-constant initial data and it represents a mathematical model of the shock tube.The solution of the Riemann problem is the building block for many numerical algorithms in computational fluid dynamics,such as finite-volume or discontinuous Galerkin methods.Therefore,a fast and accurate approximation of the solution of the Riemann problem and construction of the associated numerical fluxes is of crucial importance.The exact solution of the shock tube problem is fully described by the intermediate pressure and mathematically reduces to finding a solution of a nonlinear equation.Prior to delving into the complexities of ML for the Riemann problem,we consider a much simpler formulation,yet very informative,problem of learning roots of quadratic equations based on their coefficients.We compare two approaches:(i)Gaussian process(GP)regressions,and(ii)neural network(NN)approximations.Among these approaches,NNs prove to be more robust and efficient,although GP can be appreciably more accurate(about 30\%).We then use our experience with the quadratic equation to apply the GP and NN approaches to learn the exact solution of the Riemann problem from the initial data or coefficients of the gas equation of state(EOS).We compare GP and NN approximations in both regression and classification analysis and discuss the potential benefits and drawbacks of the ML approach.
文摘Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.
基金the National Natural Science Foundation of China(Grant Nos.62103171,61773142)the Natural Science Foundation of Fujian Province of China(Grant Nos.2020J05095,2020J05096)the Jiangsu Provincial Double⁃Innovation Doctor Program(Grant Nos.JSSCBS20210993,JSSCBS20211009)。
文摘This paper addresses a geometric control algorithm for the attitude tracking problem of the rigid spacecraft modeled on SO(3).Considering the topological and geometric properties of SO(3),we introduced a smooth positive attitude error function to convert the attitude tracking issue on SO(3)into the stabilization counterpart on its Lie algebra.The error transformation technique was further utilized to ensure the assigned transient and steady state performance of the attitude tracking error with the aid of a well⁃designed assigned⁃time performance function.Then,using the actor⁃critic(AC)neural architecture,an adaptive reinforcement learning approximator was constructed,in which the actor neural network(NN)was utilized to approximate the unknown nonlinearity online.A critic function was introduced to tune the next phase of the actor neural network operation for performance improvement via supervising the system performance.A rigorous stability analysis was presented to show that the assigned system performance can be achieved.Finally,the effectiveness and feasibility of the constructed control strategy was verified by the numerical simulation.
基金Supported by Outstanding Young Scientists in Beijing of China(Grant No.BJJWZYJH01201910006021)Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems of China(Grant No.GZKF-202016)+2 种基金Henan Provincial Science and Technology Key Project of China(Grant Nos.202102210081,212102210050)Sub Project of Strengthening Key Basic Research Projects in the Basic Plan of the Science and Technology Commission of the Central Military Commission of China(Grant No.2019-JCJQ-ZD-120-13)Henan Provincial Fundamental Research Funds for the Universities of China(Grant No.NSFRF200403).
文摘Magnetically coupled rodless cylinders are widely used in the coordinate positioning of mechanical arms,electro-static paintings,and other industrial applications.However,they exhibit strong nonlinear characteristics,which lead to low servo control accuracy.In this study,a mass-flow equation through the valve port was derived to improve the control performance,considering the characteristics of the dynamics and throttle-hole flow.Subsequently,a fric-tion model combining static,viscous,and Coulomb friction with a zero-velocity interval was proposed.In addition,energy and dynamic models were set for the experimental investigation of the magnetically coupled rodless cylin-der.A nonlinear mathematical model for the position of the magnetically coupled rodless cylinder was proposed.An incremental PID controller was designed for the magnetically coupled rodless cylinder to control this system,and the PID parameters were adjusted online using RBF neural network.The response results of the PID parameters based on the RBF neural network were compared with those of the traditional incremental PID control,which proved the superiority of the optimization control algorithm of the incremental PID parameters based on the RBF neural network servo control system.The experimental results of this model were compared with the simulation results.The average error between the established model and the actual system was 0.005175054(m),which was approximately 2.588%of the total travel length,demonstrating the accuracy of the theoretical model.
文摘Classification of speech signals is a vital part of speech signal processing systems.With the advent of speech coding and synthesis,the classification of the speech signal is made accurate and faster.Conventional methods are considered inaccurate due to the uncertainty and diversity of speech signals in the case of real speech signal classification.In this paper,we use efficient speech signal classification using a series of neural network classifiers with reinforcement learning operations.Prior classification of speech signals,the study extracts the essential features from the speech signal using Cepstral Analysis.The features are extracted by converting the speech waveform to a parametric representation to obtain a relatively minimized data rate.Hence to improve the precision of classification,Generative Adversarial Networks are used and it tends to classify the speech signal after the extraction of features from the speech signal using the cepstral coefficient.The classifiers are trained with these features initially and the best classifier is chosen to perform the task of classification on new datasets.The validation of testing sets is evaluated using RL that provides feedback to Classifiers.Finally,at the user interface,the signals are played by decoding the signal after being retrieved from the classifier back based on the input query.The results are evaluated in the form of accuracy,recall,precision,f-measure,and error rate,where generative adversarial network attains an increased accuracy rate than other methods:Multi-Layer Perceptron,Recurrent Neural Networks,Deep belief Networks,and Convolutional Neural Networks.
