无约束优化问题的精细修正牛顿算法

针对牛顿法在求解一般非凸函数极小值过程中,迭代点处Hessian矩阵不一定正定的情况,提出了一种精细修正的牛顿法.该方法充分利用迭代点处目标函数的一阶、二阶信息,合适选取搜索方向,是最速下降法、牛顿法和已有修正牛顿法相混合的一种方法.在较弱的条件下建立了算法的全局收敛性.进一步的数值实验验证了提出的算法比以往同类算法计...     

2PL模型的EM缺失数据处理方法研究

项目反应理论(IRT)模型是教育统计与测量中一种十分重要的模型,它包含项目参数和能力参数.目前一种常用的估计IRT模型项目参数的方法是由Woodruff和Hanson(1997)应用EM算法给出的,它用于完全反应数据,而把能力参数看作缺失数据.本文将Woodruff的方法推广到处理缺失反应的情况,基本思想是把能力参数和缺失反应均看作缺失数据,再运用EM算法估计参数.通过模拟研究,在不同被试人数和不同缺失比例的情况下,本文比较了我们给出的方法和BILOG-MG软件的缺失数据处理方法的参数估计效果.结果表明,在大多数情况下,本文提出的方法能得到更好的估计.     

交叉货币百慕大式互换期权的定价

本文首先研究了涉及两种货币市场的Hull-White随机利率模型.以此为基础,本文给出了交叉货币百慕大式互换期权的定价公式.由于无法得到显式定价公式,我们使用了Least Squared Monte-Carlo(LSM)算法来确定期权的最优执行时刻.最后本文给出了数值计算方面的结果.     

Robust airfoil optimization based on improved particle swarm optimization method

A robust airfoil optimization platform is constructed based on the modified particle swarm optimization method (i.e., the second-order oscillating particle swarm method), which consists of an efficient optimization algorithm, a precise aerodynamic analysis program, a high accuracy surrogate model, and a classical airfoil parametric method. There are two improvements for the modified particle swarm method compared with the standard particle swarm method. First, the particle velocity is represented by the combination of the particle position and the variation of position, which makes the particle swarm algorithm a second-order precision method with respect to the particle position. Second, for the sake of adding diversity to the swarm and enlarging the parameter searching domain to improve the global convergence performance of the algorithm, an oscillating term is introduced to the update formula of the particle velocity. At last, taking two airfoils as examples, the aerodynamic shapes are optimized on this optimization platform. It is shown from the optimization results that the aerodynamic characteristic of the airfoils is greatly improved in a broad design range.     

高速流场气动光学RANS/DSMC混合数值模拟算法研究

提出了适用于高速流场气动光学数值模拟的RANS/DSMC混合算法.通过RANS对全局时均流场进行数值模拟,再对其中局部流场的脉动量采用DSMC进行数值模拟,以Maxwellian速度分布实现RANS宏观量信息向DSMC微观量信息的传递.采用超声速环境下尖劈模型对该混合算法进行校验,对比试验结果论证了算法的正确性.在计算...     

Test analysis of detection of damage to a complicated spatial model structure

A two-stage damage detection approach is proposed and experimentally demonstrated on a complicated spatial model structure with a limited number of measurements. In the experiment,five known damage patterns,including 3 brace damage cases and 2 joint damage cases,were simulated by removing braces and weakening beam-column connections in the structure. The limited acceleration response data generated by hammer impact were used for system identification,and modal parameters were extracted by using the eigensystem realization algorithm. In the first stage,the possible damaged locations are determined by using the damage index and the characteristics of the analytical model itself,and the extent of damage for those substructures identified at stage I is estimated in the second stage by using a second-order eigen-sensitivity approximation method. The main contribution of this paper is to test the two-stage method by using the real dynamic data of a complicated spatial model structure with limited sensors. The analysis results indicate that the two-stage approach is ableto detect the location of both damage cases,only the severity of brace damage cases can be assessed,and the reasonable analytical model is critical for successful damage detection.     

流体与结构相互作用问题的FE-SPH耦合模拟

应用有限元(FE)-光滑粒子流体动力学(SPH)耦合法模拟了具有自由表面的不可压流体与结构的相互作用问题.流体和结构分别采用SPH法和有限元法同时求解,两者在交界面处的相互作用通过接触算法进行处理.为了避免隐式计算压力,通过引入人工压缩率,将不可压流体近似为人工可压缩流体.采用FE-SPH耦合法对弹性板在随时间变化的水压作用下的变形以及倒塌水柱冲击弹性结构两个问题进行了模拟.模拟结果与实验结果以及其他已有数值结果符合良好,说明FE-SPH耦合法用于流体与结构相互作用问题的模拟是可行和有效的.     

一种新型SPH-FEM耦合算法及其在冲击动力学问题中的应用

为了充分发挥光滑粒子流体动力学方法(smoothed particle hydrodynamics,SPH)在处理大变形和有限元(finite element method,FEM)问题时计算精度高的优势,提出了一种新型SPH-FEM耦合算法.该耦合算法在大变形区域使用SPH粒子离散,其余区域使用有限元离散.在耦合界面...     

通信网络中的GPS/TDOA混合定位算法

提出了一种混合GPS/TDOA的泰勒级数-最小二乘算法,在GPS和TDOA定位方法都无法独立定位时实现了定位.算法先将GPS伪距观测方程做单差运算、消除钟差,然后与TDOA双曲线方程组合,一起进行泰勒级数展开得到组合后的线性方程组,再利用最小二乘的方法迭代估计出终端位置.验证该算法的实验结果表明,GPS伪距观测量越多时,定位精度越高;相反,由于TDOA观测量NLOS误差较大,TDOA观测量越多时,精度越差.因此实施该算法时,GPS伪距观测量作为输入应全部采用;在保证能够定位的前提下,应尽量少用TDOA观测量.试验所得混合定位结果的最大误差为231.52 m,最佳条件下所得均方根误差为33.80m,能够满足某些精度要求不高,而又必需位置信息的定位应用需求.     

基于隐马尔可夫模型的地磁匹配算法

为了在地磁特征微弱区域内实现地磁辅助导航以及提高惯性导航系统在地磁特征明显区域内的定位精度,提出了基于隐马尔可夫模型的地磁匹配算法.首先以惯性导航系统定位误差为隐状态,以实时测量的地磁强度为观测量,建立了地磁匹配的隐马尔可夫模型;其次,针对该模型,使用Viterbi算法来确定最优状态序列,给出了惯性导航系统的当前定位误差.仿真结果表明,该算法可以实现地磁辅助导航,导航误差优于EKF算法,组合导航系统的定位误差在50 m左右.