On the Convergence of Iterative Orthogonalization Processes

Polar decomposition of matrices is used here to investigate the convergence properties of iterative orthogonalization processes. It is shown that, applying this decomposition, the investigation of a general iterative process of a certain form can be reduced to the investigation of a scalar iterative process which is simple. Three known iterative orthogonalization processes, which are special cases of the general process, are analyzed, their convergence rate (order) is determined, and their range of convergence is established in terms of the spectral radius of the modulus of the matrix which is being orthogonalyzed.     

Orthogonalization of a Direction Cosine Matrix by Iterative Techniques

It is shown that the ?first inversion, transposition, and averaging? technique [1] is, assuming convergence, quadratically convergent, since it can be developed very simply by the use of quasilinearization. Only the three-dimensional case is considered; the art of matrix orthogonalization is practiced in more general settings [2] than considered here.     

Homotopy based optimal configuration space reduction for anytime robotic motion planning

Anytime sampling-based motion planning algorithms are widely used in practical applications due to limited real-time computing resources. The algorithm quickly finds feasible paths and incrementally improves them to the optimal ones. However, anytime sampling-based algorithms bring a paradox in convergence speed since finding a better path helps prune useless candidates but also introduces unrecognized useless candidates by sampling. Based on the words of homotopy classes, we propose a Homotopy class Informed Preprocessor (HIP) to break the paradox by providing extra information. By comparing the words of path candidates, HIP can reveal wasteful edges of the sampling-based graph before finding a better path. The experimental results obtained in many test scenarios show that HIP improves the convergence speed of anytime sampling-based algorithms.     

Gram-Schmidt forward-backward generalized sidelobe canceller

Addressed here is the the discrete-time and the continuous-time recursive least-squares (RLS) modified Gram-Schmidt orthogonalization (MGSO) algorithms for forward-backward (FB) generalized sidelobe cancelling (GSC) adaptive beamformers. The FB-GSC requires processing each input data twice, forward and conjugated backward, and hence its adaptation would require a rank-two update each time. This paper first derives a discrete-time rank-two-update RLS MGSO algorithm for this purpose. Then, by imposing the conjugate symmetry constraints, the backward data processing can be removed without any loss and the complex-valued algorithm can be further transformed into an equivalent real-valued algorithm Therefore, significant computation savings can be achieved. Also described here is the continuous-time RLS MGSO algorithms for the FB-GSC and the conjugate symmetric FB-GSC. Computer simulations of the FB-GSC and the forward-only GSC are presented     

Improved NSGA-Ⅱ Multi-objective Genetic Algorithm Based on Hybridization-encouraged Mechanism

To improve performances of multi-objective optimization algorithms,such as convergence and diversity,a hybridization-encour-aged mechanism is proposed and realized in elitist nondominated sorting genetic algorithm (NSGA-Ⅱ).This mechanism uses the nor-malized distance to evaluate the difference among genes in a population.Three possible modes of crossover operators-"Max Distance","Min-Max Distance",and "Neighboring-Max"-are suggested and analyzed.The mode of "Neighboring-Max",which not only takes advantage of hybridization but also improves the distribution of the population near Pareto optimal front,is chosen and used in NSGA-II on the basis of hybridization-encouraged mechanism (short for HEM-based NSGA-Ⅱ).To prove the HEM-based algorithm,several problems are studied by using standard NSGA-II and the presented method.Different evaluation criteria are also used to judge these algorithms in terms of distribution of solutions,convergence,diversity,and quality of solutions.The numerical results indicate that the application of hybridization-encouraged mechanism could effectively improve the performances of genetic algorithm.Finally,as an example in engineering practices,the presented method is used to design a longitudinal flight control system,which demonstrates the obtainability of a reasonable and correct Pareto front.     

Convergence properties of Gram-Schmidt and SMI adaptive algorithms.II

For pt.I see ibid., vol.26, no.1, p.44-56, Jan. 1990. Theorems and relationships associated with the convergence rate of the Gram-Schmidt (GS) and sampled matrix inversion (SMI) algorithms are presented. Two forms of the GS canceler are discussed: concurrent block processing and sliding window processing. It is shown (as has been stated by other researchers) that the concurrent block processed GS canceler converges rapidly to its optimal signal-to-noise ratio. However, it is also shown that the result is deceptive in that the output residue samples may be highly correlated, which would significantly degrade postdetection processing. It is demonstrated that a specific form of a sliding window GS canceler has the same convergence properties as the concurrent block processed GS canceler     

Performance of multiple-model filters and parameter-sensitivity analysis for likelihood evaluation with shock variance models

The performance of multiple-model filtering algorithms is examined for shock-variance models, which are a form of linear Gaussian switching models. The primary aim is to determine whether existing multiple-model filters are suitable for evaluating measurement likelihoods in classification applications, and under what conditions such classification models are viable. Simulation experiments are used to empirically examine the likelihood-evaluation performance of suboptimal merging and pruning algorithms as the number of state hypotheses per time step (i.e., algorithm order) increases. The second-order generalized pseudo-Bayes or (GPB(2)) algorithm is found to provide excellent performance relative to higher order GPB algorithms through order five. Likelihoods from fixed-size pruning (FSP) algorithms with increasing numbers of state hypotheses are used to validate the GPB likelihoods, and convergence of the FSP likelihoods to the GPB values is observed. These results suggest that GPB(2) is a reasonable approximation to the unrealizable optimal algorithm for classification. In all cases except very-low-noise situations, the interacting multiple model (IMM) algorithm is found to provide an adequate approximation to GPB(2). Sensitivity of likelihood estimates to certain model parameters is also investigated via a mismatch analysis. As a classification tool, the discrimination capabilities of the measurement likelihoods are tested using an idealized forced-choice experiment, both with ideal and with mismatched models     

基于遗传退火算法的电路模拟吸波材料设计

相比传统吸波材料,电路模拟吸波材料可以很好地减小材料厚度、提高吸波性能,其设计通常使用遗传算法进行优化。针对传统遗传算法的诸多不足,对交叉和变异概率进行了改进、引入了模拟退火思想作为子代接受准则并增加了算法终止准则。其中,对交叉和变异概率的改进是最大创新点。改进后的遗传算法只需进化100代即得到最优解,平均反射率为-15.0420,厚度为1.43 mm,均优于传统算法得出的结果。结果表明,改进后的遗传算法具有收敛速率快、不易陷入局部最优解等优点。     

一种对飞行参数选取的自适应方法

飞参数据的典型选取问题是单机寿命监控以及飞行品质分析中压缩数据的储存空间关键。针对飞参数据的特征,提出了一种基于ELM极限学习机的飞参数据选取的模型。利用极限学习机ELM神经网络、文化基因算法MAS优化的方式,克服了算法中存在早熟收敛和局部极小的问题。实现了对飞机不同部位载荷自适应选取不同飞行参数的效果,有效获得评估出飞参数据的重要度。验证结果表明,优化后的ELM-M模型比传统选取飞参模型的精度得到了极大提高,泛化能力增强,说明了方法的可行性、有效性。     

Practical Comparison of Iterative Matrix Orthogonalization Algorithms

In previous work several algorithms for orthogonalizing the direction cosine matrix were introduced and their convergence rate and range were theoretically investigated. Three of the most promising algorithms are examined in this paper. lt is shown that the so-called Dual Algorithm is by far superior to the other two from the point of view of speed, computer memory, accuracy, and convergence rate. lt is therefore recommended that whenever the direction cosine matrix is computed by simple numerical integration of a matrix differential equation, the Dual Algorithm be used to orthogonalize the resultant matrix.     

基于Bang-Bang控制思想的迭代学习控制算法研究

根据迭代学习控制基本原理,吸取了Bang-Bang控制的思想,提出了新的迭代学习控制算法。与常用的利用迭代误差或误差变化率进行控制率计算的算法相比,该算法只需根据迭代误差的符号即可计算控制率,不仅大大减小了计算工作量,而且增强了系统的抗干扰能力。给出了算法表达式和控制结构图,进行算法收敛性分析。仿真结果表明该算法的有效性和收敛性。     

Improved NSGA-II Multi-objective Genetic Algorithm Based on Hybridization-encouraged Mechanism

To improve performances of multi-objective optimization algorithms, such as convergence and diversity, a hybridization- encouraged mechanism is proposed and realized in elitist nondominated sorting genetic algorithm （NSGA-Ⅱ）. This mechanism uses the normalized distance to evaluate the difference among genes in a population. Three possible modes of crossover operators--＂Max Distance＂, ＂Min-Max Distance＂, and ＂Neighboring-Max＂--are suggested and analyzed. The mode of ＂Neighboring-Max＂, which not only takes advantage of hybridization but also improves the distribution of the population near Pareto optimal front, is chosen and used in NSGA-Ⅱ on the basis of hybridization-encouraged mechanism （short for HEM-based NSGA-Ⅱ）. To prove the HEM-based algorithm, several problems are studied by using standard NSGA-Ⅱ and the presented method. Different evaluation criteria are also used to judge these algorithms in terms of distribution of solutions, convergence, diversity, and quality of solutions. The numerical results indicate that the application of hybridization-encouraged mechanism could effectively improve the performances of genetic algorithm. Finally, as an example in engineering practices, the presented method is used to design a longitudinal flight control system, which demonstrates the obtainability of a reasonable and correct Pareto front.     

A Hybrid Optimization Approach for SRM FINOCYL Grain Design

This article presents a method to design and optimize 3D FINOCYL grain （FCG） configuration for solid rocket motors （SRMs）. The design process of FCG configuration involves mathematical modeling of the geometry and parametric evaluation of various independent geometric variables that define the complex configuration. Virtually infinite combinations of these variables will satisfy the requirements of mass of propellant, thrust, and burning time in addition to satisfying basic needs for volumetric loading fraction and web fraction. In order to ensure the acquisition of the best possible design to be acquired, a sound approach of design and optimization is essentially demanded. To meet this need, a method is introduced to acquire the finest possible performance. A series of computations are carried out to formulate the grain geometry in terms of various combinations of key shapes inclusive of ellipsoid, cone, cylinder, sphere, torus, and inclined plane. A hybrid optimization （HO） technique is established by associating genetic algorithm （GA） for global solution convergence with sequential quadratic programming （SQP） for further local convergence of the solution, thus achieving the final optimal design. A comparison of the optimal design results derived from SQP, GA, and HO algorithms is presented. By using HO technique, the parameter of propellant mass is optimized to the minimum value with the required level of thrust staying within the constrained burning time, nozzle and propellant parameters, and a fixed length and outer diameter of grain.     

基于粒子群和人工蜂群混合算法的气动优化设计

现代启发式智能算法存在全局与局部搜索能力的平衡问题,针对此问题,采用双种群进化策略和信息交流机制,提出一种基于粒子群算法和人工蜂群算法相结合的新型混合优化算法——MABCPSO,并分别进行函数测试和翼型的气动优化设计验证。结果表明:MABCPSO新型混合优化算法具有更好的寻优能力,相比粒子群算法和人工蜂群算法,该算法能以更少的进化代数分别提高1.7%和2.2%的减阻效果。     

演化策略用于高维故障样本集最优统计聚类分析

针对液体火箭发动机推进系统超高维故障样本数据的聚类问题 ,提出基于演化策略的最优统计聚类算法。为预防算法过早收敛 ,演化策略采用了父本适应值的动态调整值与共享函数 ,并针对超高维数据聚类提出了控制参数的适应性调整技术 ;为使算法能最终跳出局部最优死区 ,提出算法的局部调整策略。该算法用于液体火箭发动机典型故障仿真数据集分析 ,并取得了最优聚类结果。此外 ,还基于IRIS数据集比较了该算法与FKCN模糊自主聚类算法。仿真分析表明了算法在高维数据聚类分析中的优点。     

迭代动力缩聚法的收敛性分析

 利用Lyapunov矩阵方程和Riccati矩阵方程解的理论,对迭代动力缩聚法的收敛性进行了分析证明,并给出了迭代收敛的充分条件。揭示了动力缩聚法与经典的子空间迭代法的内在关系,阐明了各自的优缺点。迭代动力缩聚法实质上是子空间迭代法的变形,它需要人为选择主辅自由度,而子空间迭代法需要人为选定初始迭代向量。从理论上讲,只有主辅自由度选择满足收敛的充分条件要求,才能保证迭代结果收敛到理论上的精确解。给出了一个数值算例,对几种算法进行了对比,并验证了本文的论点。     

两种初始对准算法的比较研究

初始对准的精度作为影响惯性导航系统精度的核心因素,一直受到广泛的研究。传统初始对准算法存在对扰动敏感、对准时间长、需要小失准角假设等诸多缺陷。针对传统算法的不足,有学者最近提出了一些思路新颖的初始对准算法,如优化对准算法和基于频域分离算子的初始对准算法。本文对比研究了这两种初始对准算法的基本原理,通过摇摆台实测数据对两种算法进行了验证,对工程应用具有一定的参考价值。     

自适应差分进化算法在气动优化设计中的应用

以实数编码的差分进化（DE）算法为基础,引入种群熵估计方法分析种群个体的分散程度,自适应地调整设计变量的搜索范围。采用Navier-Stokes方程作为主控方程计算翼型气动性能,分别采用标准遗传算法（SGA）、基本DE算法和自适应差分进化（ARDE）算法作为气动性能优化算法进行了针对翼型的气动优化设计。函数测试实例表明,ARDE算法具有更好的收敛稳定性和收敛速度。并针对翼型气动优化问题的特点,分析了参数设置对ARDE算法优化结果的影响。实验结果对比表明,ARDE算法得到了更好的优化结果。     

气动设计的多目标优化算法比较研究

由于目标函数复杂且流场求解耗时,气动优化设计需要选择搜索能力强且调用目标次数少的优化算法,现有的优化算法种类很多,针对不同类型问题算法性能不同。本文将常用的多目标优化算法进行了分类总结并进行函数测试,判断各个优化算法对不同问题的收敛性和稳定性,找出适合气动优化的多目标优化算法。将该算法应用于气动优化问题当中,进行了针对翼型的气动优化设计,缩短了优化时间,取得了一定的优化效果。     

基于启发式自适应离散差分进化算法的多UCAV协同干扰空战决策

 研究了多无人作战飞机(UCAV)协同干扰空战决策(MUCJAD)问题,在干扰效能评估指标量化方法的基础上为该问题建立了优化模型。为有效求解该模型,提出一种启发式自适应离散差分进化(H-SDDE)算法。在H-SDDE算法中,设计了包含4种候选解产生策略的候选策略池,引入了候选解产生策略及其参数的自适应学习过程。此外,结合实际问题为算法设计了基于威胁度的扩展型整数编码方案、基于威胁度的启发式个体调整操作、基于约束满足的个体修复操作。在12个测试实例上进行了仿真验证,结果表明,H-SDDE算法与其他同类算法相比在求解质量和求解速度上具有明显优势,能够更好地发挥多UCAV协同干扰整体效果。