Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to t...Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to their adaptable design.Furthermore,spine fins are introduced to improve performance in applications such as automotive radiators.They can be shaped in different ways and constructed from a collection of materials.Inspired by this,the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin.Using dimensionless terms,the proposed fin model involving a governing nonlinear ordinary differential equation(ODE)is transformed into a dimensionless form.The study uses the operational matrix with the Charlier polynomial collocation method(OMCCM)to ensure precise and computationally efficient numerical solutions for the dimensionless equation.In order to aid in the analysis of thermal performance,the importance of major parameters on the temperature profile is graphically illustrated.The main outcome of the study reveals that as the radiation-conductive,wet,and convective-conductive parameters increase,the heat transfer rate progressively improves.Conversely,the ambient temperature and internal heat generation parameters show an inverse relationship.展开更多
Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limi...Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.展开更多
The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when th...The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.展开更多
In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is a...In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.展开更多
Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolu...Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.展开更多
We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the gener...We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions.展开更多
Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with s...Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.展开更多
The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to const...The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.展开更多
The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach...The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.展开更多
The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on dif...The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on different swept angles,the experimental data from the icing wind tunnel establish the geometric link between the position of the wingspan and the shape of ice accretion at the leading edge.The correlation analysis and Sobol sensitivity are used to study the uncertainty of single variable.Simultaneously,the polynomial chaos method is employed to study the uncertainty of multiple variables.The results indicate significant correlation between the angle of attack and lift and drag coefficients.The influence of height and velocity on sensitivity is negligible,with the aerodynamic characteristics mostly dependent on the geometric attributes of the ice structure.The uncertainty propagation framework established can accurately assess the impact of swept angle on the aerodynamic parameters of the icing wing,and the predicted findings fall within a 95%confidence interval.展开更多
In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure betwe...In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.展开更多
By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials wh...By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.展开更多
We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Herm...We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.展开更多
Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate ...Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.展开更多
This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear syst...This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.展开更多
To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq...To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).展开更多
In order to optimize the crashworthy characteristic of energy-absorbing structures, the surrogate models of specific energy absorption （SEA） and ratio of SEA to initial peak force （REAF） with respect to the design...In order to optimize the crashworthy characteristic of energy-absorbing structures, the surrogate models of specific energy absorption （SEA） and ratio of SEA to initial peak force （REAF） with respect to the design parameters were respectively constructed based on surrogate model optimization methods （polynomial response surface method （PRSM） and Kriging method （KM））. Firstly, the sample data were prepared through the design of experiment （DOE）. Then, the test data models were set up based on the theory of surrogate model, and the data samples were trained to obtain the response relationship between the SEA ＆amp; REAF and design parameters. At last, the structure optimal parameters were obtained by visual analysis and genetic algorithm （GA）. The results indicate that the KM, where the local interpolation method is used in Gauss correlation function, has the highest fitting accuracy and the structure optimal parameters are obtained as： the SEA of 29.8558 kJ/kg （corresponding toa=70 mm andt= 3.5 mm） and REAF of 0.2896 （corresponding toa=70 mm andt=1.9615 mm）. The basis function of the quartic PRSM with higher order than that of the quadratic PRSM, and the mutual influence of the design variables are considered, so the fitting accuracy of the quartic PRSM is higher than that of the quadratic PRSM.展开更多
A one-dimensional non-intrusive Polynomial Chaos （PC） method is applied in Uncertainty Quantification （UQ） studies for CFD-based ship performances simulations. The uncertainty properties of Expected Value （EV） a...A one-dimensional non-intrusive Polynomial Chaos （PC） method is applied in Uncertainty Quantification （UQ） studies for CFD-based ship performances simulations. The uncertainty properties of Expected Value （EV） and Standard Deviation （SD） are evaluated by solving the PC coefficients from a linear system of algebraic equations. The one-dimensional PC with the Legendre polynomials is applied to： （1） stochastic input domain and （2） Cumulative Distribution Function （CDF） image domain, allowing for more flexibility. The PC method is validated with the Monte-Carlo benchmark results in several high-fidelity, CFD-based, ship UQ problems, evaluating the geometrical, operational and environmental uncertainties for the Delft Catamaran 372. Convergence is studied versus PC order P for both EV and SD, showing that high order PC is not necessary for present applications. Comparison is carried out for PC with/without the least square minimization when solving the PC coefficients. The least square minimization, using larger number of CFD samples, is recommended for current test cases. The study shows the potentials of PC method in Robust Design Optimization （RDO） and Reliability-Based Design Optimization （RBDO） of ship hydrodynamic performances.展开更多
The complete discrimination system for polynomial method is applied to the long-short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the ...The complete discrimination system for polynomial method is applied to the long-short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the （G~/G）-expansion method, we gain some new solutions.展开更多
To obtain a universal model solving the uncertain acoustic field in shallow water, a non-intrusive model coupled polynomial chaos expansion （PCE） method with Helmholtz equa- tion is established, in which the polynom...To obtain a universal model solving the uncertain acoustic field in shallow water, a non-intrusive model coupled polynomial chaos expansion （PCE） method with Helmholtz equa- tion is established, in which the polynomial coefficients are solved by probabilistic collocation method （PCM）. For the cases of Pekeris waveguide which have uncertainties in depth of water column, in both sound speed profile and depth of water column, and for the case of thermocline with lower limit depth uncertain, probability density functions （PDF） of transmission loss （TL） are calculated. The results show that the proposed model is universal for the acoustic propa- gation codes with high computational efficiency and accuracy, and can be applied to study the uncertainty of acoustic propagation in the shallow water en^-ironment with multiple parameters uncertain.展开更多
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/308/46。
文摘Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to their adaptable design.Furthermore,spine fins are introduced to improve performance in applications such as automotive radiators.They can be shaped in different ways and constructed from a collection of materials.Inspired by this,the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin.Using dimensionless terms,the proposed fin model involving a governing nonlinear ordinary differential equation(ODE)is transformed into a dimensionless form.The study uses the operational matrix with the Charlier polynomial collocation method(OMCCM)to ensure precise and computationally efficient numerical solutions for the dimensionless equation.In order to aid in the analysis of thermal performance,the importance of major parameters on the temperature profile is graphically illustrated.The main outcome of the study reveals that as the radiation-conductive,wet,and convective-conductive parameters increase,the heat transfer rate progressively improves.Conversely,the ambient temperature and internal heat generation parameters show an inverse relationship.
基金supported by the National Natural Science Foundation of China(Grant No.12102131).
文摘Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.
基金Project supported by the National Natural Science Foundation of China(No.12102131)the Natural Science Foundation of Henan Province of China(No.242300420248)the International Science and Technology Cooperation Project of Henan Province of China(No.242102521010)。
文摘The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(No.62102444)a Major Research Project in Higher Education Institutions in Henan Province(No.23A560015).
文摘In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.
文摘Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.
文摘We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.
文摘The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.
基金supported by the National Natural Science Foundation of China(No.92371201)the State Key Laboratory for Strength and Vibration of Mechanical Structures Program,China.Thanks to China Aerodynamics Research and Development Center for providing the experimental data.
文摘The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on different swept angles,the experimental data from the icing wind tunnel establish the geometric link between the position of the wingspan and the shape of ice accretion at the leading edge.The correlation analysis and Sobol sensitivity are used to study the uncertainty of single variable.Simultaneously,the polynomial chaos method is employed to study the uncertainty of multiple variables.The results indicate significant correlation between the angle of attack and lift and drag coefficients.The influence of height and velocity on sensitivity is negligible,with the aerodynamic characteristics mostly dependent on the geometric attributes of the ice structure.The uncertainty propagation framework established can accurately assess the impact of swept angle on the aerodynamic parameters of the icing wing,and the predicted findings fall within a 95%confidence interval.
基金Supported by the Natural Science Foundation of Hubei Province(2008CDZD47)
文摘In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.
基金Project supported by the National Natural Science Foundation of China(Grnat No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.
文摘Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.
基金supported by the National Science Fund for Distinguished Young Scholars(11125209)the National Natural Science Foundation of China(51121063 and 10702039)
文摘This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.
基金supported by the the National Science and Technology Council(Grant Number:NSTC 112-2221-E239-022).
文摘To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).
基金Project(U1334208)supported by the National Natural Science Foundation of ChinaProject(2013GK2001)supported by the Fund of Hunan Provincial Science and Technology Department,China
文摘In order to optimize the crashworthy characteristic of energy-absorbing structures, the surrogate models of specific energy absorption （SEA） and ratio of SEA to initial peak force （REAF） with respect to the design parameters were respectively constructed based on surrogate model optimization methods （polynomial response surface method （PRSM） and Kriging method （KM））. Firstly, the sample data were prepared through the design of experiment （DOE）. Then, the test data models were set up based on the theory of surrogate model, and the data samples were trained to obtain the response relationship between the SEA ＆amp; REAF and design parameters. At last, the structure optimal parameters were obtained by visual analysis and genetic algorithm （GA）. The results indicate that the KM, where the local interpolation method is used in Gauss correlation function, has the highest fitting accuracy and the structure optimal parameters are obtained as： the SEA of 29.8558 kJ/kg （corresponding toa=70 mm andt= 3.5 mm） and REAF of 0.2896 （corresponding toa=70 mm andt=1.9615 mm）. The basis function of the quartic PRSM with higher order than that of the quadratic PRSM, and the mutual influence of the design variables are considered, so the fitting accuracy of the quartic PRSM is higher than that of the quadratic PRSM.
基金Project supported by the National Natural Science Foundation of China(Grant No.50979060)
文摘A one-dimensional non-intrusive Polynomial Chaos （PC） method is applied in Uncertainty Quantification （UQ） studies for CFD-based ship performances simulations. The uncertainty properties of Expected Value （EV） and Standard Deviation （SD） are evaluated by solving the PC coefficients from a linear system of algebraic equations. The one-dimensional PC with the Legendre polynomials is applied to： （1） stochastic input domain and （2） Cumulative Distribution Function （CDF） image domain, allowing for more flexibility. The PC method is validated with the Monte-Carlo benchmark results in several high-fidelity, CFD-based, ship UQ problems, evaluating the geometrical, operational and environmental uncertainties for the Delft Catamaran 372. Convergence is studied versus PC order P for both EV and SD, showing that high order PC is not necessary for present applications. Comparison is carried out for PC with/without the least square minimization when solving the PC coefficients. The least square minimization, using larger number of CFD samples, is recommended for current test cases. The study shows the potentials of PC method in Robust Design Optimization （RDO） and Reliability-Based Design Optimization （RBDO） of ship hydrodynamic performances.
基金Project supported by the Scientific Research Fund of Education Department of Heilongjiang Province of China (Grant No.12531475)
文摘The complete discrimination system for polynomial method is applied to the long-short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the （G~/G）-expansion method, we gain some new solutions.
文摘To obtain a universal model solving the uncertain acoustic field in shallow water, a non-intrusive model coupled polynomial chaos expansion （PCE） method with Helmholtz equa- tion is established, in which the polynomial coefficients are solved by probabilistic collocation method （PCM）. For the cases of Pekeris waveguide which have uncertainties in depth of water column, in both sound speed profile and depth of water column, and for the case of thermocline with lower limit depth uncertain, probability density functions （PDF） of transmission loss （TL） are calculated. The results show that the proposed model is universal for the acoustic propa- gation codes with high computational efficiency and accuracy, and can be applied to study the uncertainty of acoustic propagation in the shallow water en^-ironment with multiple parameters uncertain.
