In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hen...In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.展开更多
A new theory developed from extended high-order sandwich panel theory(EHSAPT)is set up to assess the static response of sandwich panels by considering the geometrical and material nonlinearities simultaneously.The geo...A new theory developed from extended high-order sandwich panel theory(EHSAPT)is set up to assess the static response of sandwich panels by considering the geometrical and material nonlinearities simultaneously.The geometrical nonlinearity is considered by adopting the Green-Lagrange-type strain for the face sheets and core.The material nonlinearity is included as a piecewise function matched to the experimental stress-strain curve using a polynomial fitting technique.A Ritz technique is applied to solve the governing equations.The results show that the stress stiffening feature is well captured in the geometric nonlinear analysis.The effect of the geometric nonlinearity in the face sheets on the displacement response is more significant when the stiffness ratio of the face sheets to the core is large.The geometric nonlinearity decreases the shear stress and increases the normal stress in the sandwich core.By comparison with open literature and finite element simulations,the present nonlinear EHSAPT is shown to be sufficiently precise for estimating the nonlinear static response of sandwich beams by considering the geometric and material nonlinearities simultaneously.展开更多
In this paper,the relationship between the extended family and several mixing properties in measuretheoretical dynamical systems is investigated.The extended family eF related to a given family F can be regarded as th...In this paper,the relationship between the extended family and several mixing properties in measuretheoretical dynamical systems is investigated.The extended family eF related to a given family F can be regarded as the collection of all sets obtained as"piecewise shifted"members of F.For a measure preserving transformation T on a Lebesgue space(X,B,μ),the sets of"accurate intersections of order k"defined below are studied,Nε(A0,A1,...,Ak)=n∈Z+:μk i=0T inAiμ(A0)μ(A1)μ(Ak)<ε,for k∈N,A0,A1,...,Ak∈B and ε>0.It is shown that if T is weakly mixing(mildly mixing)then for any k∈N,all the sets Nε(A0,A1,...,Ak)have Banach density 1(are in(eFip),i.e.,the dual of the extended family related to IP-sets).展开更多
The investigation of closed form solutions for nonlinear evolution equations(NLEEs)is being an attractive subject in the different branches of mathematical and physical sciences.In this article,the enhanced(G'=G)-...The investigation of closed form solutions for nonlinear evolution equations(NLEEs)is being an attractive subject in the different branches of mathematical and physical sciences.In this article,the enhanced(G'=G)-expansion method has been applied to find the closed form solutions for NLEEs,such as the simplified MCH equation and third extended fifth order nonlinear equations which are very important in mathematical physics.Plentiful closed form solutions with arbitrary parameters are successfully obtained by this method which are expressed in terms of hyperbolic and trigonometric functions.It is shown that the obtained solutions are more general and fresh and can be helpful to analyze the NLEES in mathematical physics and engineering problems.展开更多
The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of ...The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.展开更多
In this paper, a full-order sliding mode control based on extended state observer(FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer(ESO) is ...In this paper, a full-order sliding mode control based on extended state observer(FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer(ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control. Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.展开更多
基金the National Science Fund for Distinguished Young Scholars(Grant No.51725502)the major program of the National Natural Science Foundation of China(Grant No.51490662)the National Key Research and Development Project of China(Grant No.2016YFD0701105).
文摘In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.
基金the National Natural Science Foundation of China(Grant 11432004).
文摘A new theory developed from extended high-order sandwich panel theory(EHSAPT)is set up to assess the static response of sandwich panels by considering the geometrical and material nonlinearities simultaneously.The geometrical nonlinearity is considered by adopting the Green-Lagrange-type strain for the face sheets and core.The material nonlinearity is included as a piecewise function matched to the experimental stress-strain curve using a polynomial fitting technique.A Ritz technique is applied to solve the governing equations.The results show that the stress stiffening feature is well captured in the geometric nonlinear analysis.The effect of the geometric nonlinearity in the face sheets on the displacement response is more significant when the stiffness ratio of the face sheets to the core is large.The geometric nonlinearity decreases the shear stress and increases the normal stress in the sandwich core.By comparison with open literature and finite element simulations,the present nonlinear EHSAPT is shown to be sufficiently precise for estimating the nonlinear static response of sandwich beams by considering the geometric and material nonlinearities simultaneously.
基金supported by National Natural Science Foundation of China(Grant Nos.10926038 and 11201157)Fundamental Research Funds for the Central Universities(Grant No.2012ZZ0073)
文摘In this paper,the relationship between the extended family and several mixing properties in measuretheoretical dynamical systems is investigated.The extended family eF related to a given family F can be regarded as the collection of all sets obtained as"piecewise shifted"members of F.For a measure preserving transformation T on a Lebesgue space(X,B,μ),the sets of"accurate intersections of order k"defined below are studied,Nε(A0,A1,...,Ak)=n∈Z+:μk i=0T inAiμ(A0)μ(A1)μ(Ak)<ε,for k∈N,A0,A1,...,Ak∈B and ε>0.It is shown that if T is weakly mixing(mildly mixing)then for any k∈N,all the sets Nε(A0,A1,...,Ak)have Banach density 1(are in(eFip),i.e.,the dual of the extended family related to IP-sets).
文摘The investigation of closed form solutions for nonlinear evolution equations(NLEEs)is being an attractive subject in the different branches of mathematical and physical sciences.In this article,the enhanced(G'=G)-expansion method has been applied to find the closed form solutions for NLEEs,such as the simplified MCH equation and third extended fifth order nonlinear equations which are very important in mathematical physics.Plentiful closed form solutions with arbitrary parameters are successfully obtained by this method which are expressed in terms of hyperbolic and trigonometric functions.It is shown that the obtained solutions are more general and fresh and can be helpful to analyze the NLEES in mathematical physics and engineering problems.
基金Taif University Researchers Supporting Project number(TURSP-2020/20),Taif University,Taif,Saudi Arabia。
文摘The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.
基金supported by the National Natural Science Foundation of China under Grant No.61403343the China Postdoctoral Science Foundation funded project under Grant No.2015M580521
文摘In this paper, a full-order sliding mode control based on extended state observer(FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer(ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control. Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.
