受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cram&#...受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cramér-Rao Bound,CRB),提出了一种基于克拉美罗界的小孔径阵列性能评估和构型优化方法。首先,梳理了宽带信号波达方向估计的发展历程和典型的二维阵列结构,建立了基于频带分解的标量阵列及极化敏感阵列宽带信号模型;接着,针对标量阵列,给出了宽带二维波达方向估计克拉美罗界闭式表达式;随后,推导出极化敏感阵列宽带二维波达方向估计克拉美罗界的通用框架及闭式表达式,建立了极化敏感阵列二维测向性能评估准则;最后,结合制导系统平台对阵元数量和布阵孔径的限制,提出了基于所推导克拉美罗界的二维阵型优化方法,通过构建阵型优化集合和理论性能评估,实现阵列布局的定量优化。研究结果为小孔径制导测向系统的阵列构型设计与性能评估提供了理论支撑和技术指导。展开更多
Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applyin...Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.展开更多
We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of...We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
文摘受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cramér-Rao Bound,CRB),提出了一种基于克拉美罗界的小孔径阵列性能评估和构型优化方法。首先,梳理了宽带信号波达方向估计的发展历程和典型的二维阵列结构,建立了基于频带分解的标量阵列及极化敏感阵列宽带信号模型;接着,针对标量阵列,给出了宽带二维波达方向估计克拉美罗界闭式表达式;随后,推导出极化敏感阵列宽带二维波达方向估计克拉美罗界的通用框架及闭式表达式,建立了极化敏感阵列二维测向性能评估准则;最后,结合制导系统平台对阵元数量和布阵孔径的限制,提出了基于所推导克拉美罗界的二维阵型优化方法,通过构建阵型优化集合和理论性能评估,实现阵列布局的定量优化。研究结果为小孔径制导测向系统的阵列构型设计与性能评估提供了理论支撑和技术指导。
基金Supported by the National Natural Science Foundation of China (10571035,10871141)
文摘Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.
文摘We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
