Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along th...Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.展开更多
Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In ...Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In order to avoid the unphysical motion of the interface,a novel eddy-viscosity eliminator based on sigmoid functions is designed to reduce the excessive turbulence level,and the eddy-viscosity eliminator based on polynomials is extracted from the cavitation simulations.Surface elevations by combining the eddy-viscosity eliminators and classical two-equation closure models are compared with the experiments,the ones by using the adaptive asymptotic model(AAM)and the ones by using the modified two-equation closure models.The root-mean-squared error(RMSE)is introduced to quantify the accuracies of surface elevations and the forces.The relation between the turbulence level in the transition layer and RMSEs of surface elevations is studied.Besides,the parametric analysis of the eddy-viscosity eliminators is carried out.The studies suggest that(1)the excessive turbulence level in the transition layer around the interface has a significant influence on the accuracies of surface elevations and the forces;(2)the eddy-viscosity eliminators can effectively reduce the excessive turbulence level in the transition layer to avoid the unphysical motion of the interface;(3)the k-ωSST model combined with the eddy-viscosity eliminators is appropriate for predicting surface elevations and forces in RANS simulations of sloshing flow.展开更多
This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in ...This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm.To demonstrate the validity of the algorithm,an identification test is carried out on the ship‘SWAN’with only 26 sets of test data.Furthermore,the identification effects of the least squares algorithm,original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared.Generally,the stochastic gradient algorithm is not suitable for the condition of small test data.The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2%up compared with the least squares algorithm.Then the effectiveness of the algorithm is verified by another identification test on the ship‘Galaxy’,the accuracy of parameter identification can reach more than 95%which can be used in ship motion simulation and controller design.The proposed algorithm has advantages of the small test data,fast speed and high accuracy of identification,which can be extended to other parameter identification systems with less sample data.展开更多
To get simpler operation in modified fuzzy adaptive learning control network (FALCON) in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership functi...To get simpler operation in modified fuzzy adaptive learning control network (FALCON) in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing (SA) learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells.展开更多
In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_...In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,dn,σ(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that dn,H(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that dn,σ(f)≤‖σ‖/(n+1)V(f)and dn,H(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.展开更多
In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results fo...In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11672071,11302046,and 11672072)the Fundamental Research Funds for the Central Universities(No.N150504003)
摘要Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.11802176,11802301)。
摘要Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In order to avoid the unphysical motion of the interface,a novel eddy-viscosity eliminator based on sigmoid functions is designed to reduce the excessive turbulence level,and the eddy-viscosity eliminator based on polynomials is extracted from the cavitation simulations.Surface elevations by combining the eddy-viscosity eliminators and classical two-equation closure models are compared with the experiments,the ones by using the adaptive asymptotic model(AAM)and the ones by using the modified two-equation closure models.The root-mean-squared error(RMSE)is introduced to quantify the accuracies of surface elevations and the forces.The relation between the turbulence level in the transition layer and RMSEs of surface elevations is studied.Besides,the parametric analysis of the eddy-viscosity eliminators is carried out.The studies suggest that(1)the excessive turbulence level in the transition layer around the interface has a significant influence on the accuracies of surface elevations and the forces;(2)the eddy-viscosity eliminators can effectively reduce the excessive turbulence level in the transition layer to avoid the unphysical motion of the interface;(3)the k-ωSST model combined with the eddy-viscosity eliminators is appropriate for predicting surface elevations and forces in RANS simulations of sloshing flow.
基金funded by the National Natural Science Foundation of China,grant number 51679024,51909018the Science and Technology Innovation Fundation of Dalian City,grant number 2019J12GX026+1 种基金the Fundamental Research Funds for the Central University,grant number 3132019343,3132021132the University 111 Project of China,grant number B08046.
摘要This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm.To demonstrate the validity of the algorithm,an identification test is carried out on the ship‘SWAN’with only 26 sets of test data.Furthermore,the identification effects of the least squares algorithm,original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared.Generally,the stochastic gradient algorithm is not suitable for the condition of small test data.The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2%up compared with the least squares algorithm.Then the effectiveness of the algorithm is verified by another identification test on the ship‘Galaxy’,the accuracy of parameter identification can reach more than 95%which can be used in ship motion simulation and controller design.The proposed algorithm has advantages of the small test data,fast speed and high accuracy of identification,which can be extended to other parameter identification systems with less sample data.
摘要To get simpler operation in modified fuzzy adaptive learning control network (FALCON) in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing (SA) learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells.
摘要In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,dn,σ(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that dn,H(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that dn,σ(f)≤‖σ‖/(n+1)V(f)and dn,H(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.
基金supported, in part, by the GNAMPA and the GNFM of the Italian INdAM
摘要In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.