伴随方程

这就引出了，如我们将要看到的，伴随方程的概念。

This led , as we shall see , to the concept of the adjoint equation .

非线性阿贝耳积分方程的正则化求解一类非线性优化问题的伴随方程算法

A kind of adjoint equation approach for solving nonlinear optimization problems

变分同化中的伴随方程伴随方程在水汽资料四维同化中的应用I.理论

The Four-Dimension Assimilation Problem of Water Vapour by Means of the Adjoint Equation Part I. Theory

一种适用于EDA电子系统分析软件的数学伴随方程建模的新方法研究

A New Method to Establish Models by Using Mathematics Fellow Equations for EDA Software

流动方程与伴随方程均用隐式LU-SGS方法求解。

An implicit factorized LU-SGS method is applied to solve the Euler and the adjoint equations .

对Euler方程为流动模型的翼型绕流，在微分方程生成的网格中，以B样条控制顶点为设计变量，用连续伴随方程法对翼型气动外形进行数值优化设计。

Continuous adjoint formulation is employed to carry out optimization design for airfoil shape . In our work , the flow is modeled by Euler equations on arbitrary grid , and B-spline vertices are adopted as design variables in Quasi Newton optimization algorithm .

随机种群系统伴随方程解的存在唯一性

Existence and uniqueness of solutions to adjoining equation of stochastic population system

电力系统动态灵敏度计算的伴随方程方法

Adjoint equation methods for dynamic sensitivity calculation in power systems

反向积分伴随方程的时间可以缩短。

The time to integrate adjoint equations can be shortened .

将微分方程线性化，求得线性化方程的伴随方程。

The differential equations were linearized and their adjoint equations were found .

基于伴随方程的翼型数值优化设计方法研究

An Investigation of Aerodynamic Optimization Design for Airfoil Based on Adjoint Formulation

用伴随方程研究空气污染的优化控制

Study on optimal control of air pollution using adjoint equation

应用伴随方程的跨声速翼型数值优化设计

Numerical Optimization Design for Transonic Airfoils

本文在二维潮波方程的基础上，采用变分方法，给出其伴随方程。

By using the variational method , the adjoint equations are derived from the 2-D tidal equations .

对于二维连续模型，获得了连续形式的伴随方程及其边界条件。

For continuous case , the continuous adjoint equations and boundary conditions are derived for a 2-D model .

伴随方程的解若同时满足伴随不变条件就可以由之构造出系统的守恒量。

Conserved quantity of the system can be constructed through the adjoint equations ' solutions which satisfy adjoint invariance condition .

基于粒子群优化的非线性系统最小二乘支持向量机预测控制方法一类非线性优化问题的伴随方程算法

LS-SVM predictive control based on PSO for nonlinear systems A KIND OF ADJOINT EQUATION APPROACH FOR SOLVING NONLINEAR OPTIMIZATION PROBLEMS

一种确定快速最优及能控性问题伴随方程边界条件的方法&集合覆盖法

A method for determining boundary conditions of the adjoint equations for time optimal and controllability problems & the sets covering method

对一个典型的水轮机调节系统，本文导出了系统状态方程、伴随方程和梯度方程。

For a typical hydroturbine control system , the state equation , the adjoint system equation and equations for calculating gradients have been deduced .

具有不等式约束的最优控制问题已经有了成熟的理论。本文主要论证具有等式约束的最优控制问题应该满足的控制方程、伴随方程以及横截条件。

This paper analyses the control equation , the accompany equation and the cross section conditions which should satisfy the optimal control with equality constraints .

文中将伴随方程方法运用于该矩阵的计算，有效地提高了算法的效率。

Hence this paper proposes a novel approach for OTS , in which the adjoint equation method is applied to evaluate the Jacobian matrices of stability constraints functions .

对一类具有线性等式约束和一般不等式约束的非线性优化问题进行了讨论，建立了一类伴随方程算法。

A kind of nonlinear optimisation problem which has linear equal constraint and general inequal constraint conditions is discussed , and then an ad joint equation algorithm is presented .

提出了建立伴随方程的分解技术，通过二维浅水波方程的伴随方程的建立，研究了建立伴随方程的数学方法。

We put forward a decomposing technology of creating the adjoint equation . By creating the 2-D shallow-water equation , we study the mathematical method of creating the adjoint equation .

本文概述了变分同化伴随方程理论研究的重要性，讨论了变分同化原理、证明了预报模式方程的伴随方程解的特性；

This paper describes the importance of performing theoretical studies of the adjoint equation . We discuss the variational assimilation principle , and prove the characteristics of the adjoint equation .

该方法以观测值与模拟值的差的平方为目标函数的极小化问题，目标函数的梯度通过伴随方程求解。

This method is based on the minimization of an objective function measuring the difference between the observed and computed , the gradient of the objective function being computed by adjoint equations .

利用伴随方程与状态方程形式上的相似性，用数值方法实现了一种新的结构最优控制算法。

A new algorithm of optimal control to structural vibration has been realized by using state transition method which is based on the similarity between the companion equation and the state equation .

算法运用伴随方程方法处理暂态稳定约束，有效提高了计算效率。

Then an efficient penalty-based GRG ( generalized reduced gradient ) approach is used to solve the transformed problem , in which the adjoin equation method is applied to evaluate the gradien .

利用末端横截条件反向积分伴随方程，避开伴随变量的初值猜测，运用迭代法数值求解了逃逸地心引力场轨道和低轨道变轨优化。

The adjoint equations are integrated backword to avoid the initial guess of adjoint variables by means of the transversality condition . The earth escape trajectory and low orbit transfer optimization are numerically resolved by iteration method .

文中讨论了与伴随方程方法相关的、动态系统的一些基本特性，以及伴随方程的构造方法，并且给出了伴随方程方法的算法流程和数值实例。

Some details of the adjoint equations method , the algorithm flow and the numerical test result , are also elaborated in this paper . Numerical experience shows that the proposed methods can efficiently evaluate the dynamic sensitivities with high accuracy .

实际的翼型是在一个非确定性的状态范围内工作的，为此应用鲁棒控制理论建立了翼型的鲁棒气动反设计方法及数值求解过程，基本的优化器为基于伴随方程的位流优化方法。

The employed basic optimizer is the control theory based design methods . These methods need to solve the state equations as well as adjoint equations . Robust aerodynamic design can produce an airfoil which works better within the range of fly condition .