Receiver characteristics of laser altimeters with avalanchephotodiodes

The receiver characteristics of a laser altimeter system containing an avalanche photodiode photodetector are analyzed using the Gaussian approximation, the saddlepoint approximation, and a nearly exact analysis. The last two methods are shown to yield very similar results except when the background noise is extremely low and the probability of false alarm is high. However, the Gaussian approximation method is shown to cause significant errors even under relatively high levels of background noise and received signal energy     

一种金融投资模型的数值逼近方法

对一种金融模型，给出了一、二阶的Itoe-Taylor逼近的估计，并对这两种估计证明了其强收敛性，同时给出了收敛的阶数．通过比较得出Itoe-Taylor逼近阶数越高，得到的估计强收敛的阶越高。     

Implementation of the simultaneous perturbation algorithm forstochastic optimization

The need for solving multivariate optimization problems is pervasive in engineering and the physical and social sciences. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for challenging optimization problems where it is difficult or impossible to directly obtain a gradient of the objective function with respect to the parameters being optimized. SPSA is based on an easily implemented and highly efficient gradient approximation that relies on measurements of the objective function, not on measurements of the gradient of the objective function. The gradient approximation is based on only two function measurements (regardless of the dimension of the gradient vector). This contrasts with standard finite-difference approaches, which require a number of function measurements proportional to the dimension of the gradient vector. This paper presents a simple step-by-step guide to implementation of SPSA in generic optimization problems and offers some practical suggestions for choosing certain algorithm coefficients     

一种结构优化的准解析法

协同利用数学变换、高精度近似和二级逼近策略,提出了一种求解结构优化问题的准解析法。该方法通用性强,计算效率高,尤其适用于求解大型结构设计问题。方法的有效性通过不同类型的优化算例进行了验证。     

Signal Representation by Prolate Spheroidal Wave Functions

The efficiency for signal representation of the angular prolate spheroidal wave function, particularly the two sets Sol(1, t) and Sol(8, t) is discussed Six signal waveforms are considered: rectangular, triangular, trapezoidal, exponential, Gaussian, and cosine-squared. For each, a representation is made in terms of the two sets above and also the Fourier cosine functions. As the number of terms of the representation increases, the approximation gets better. A measure of the ?goodness? of the approximation is the percentage of the total signal energy represented by the finite expansion, over a fixed, finite time interval. The angular prolate spheroidal wave functions are a very efficient orthogonal set in this sense. Their principal advantage over Fourier cosine functions occurs for cases whereby only a very few terms of the expansion are to be used to approximate a signal shape.     

用于结构优化的一种新的两点近似函数

提出一种基于两点信息的近似函数,它在当前设计点能够保证原函数的函数值、一阶导数值和近似二阶导数值;在另一设计点保证原函数的一阶导数值。用该近似函数形成结构优化原问题的序列近似问题,再用约束变尺度法解近似问题。通过典型算例的计算,结果表明本方法具有较好的收敛性和较高的计算效率,适用于结构优化问题的求解     

Taylor expansion of the differential range for monostatic SAR

The polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) is based on a linear approximation for the differential range to a scatterer. We derive a second-order Taylor series approximation of the differential range. We provide a simple and concise derivation of both the far-field linear approximation of the differential range, which forms the basis of the PFA, and the corresponding approximation limits based on the second-order terms of the approximation.     

状态空间气动弹性模型及其在颤振计算中的应用

本文评述了已有的状态空间气动弹性模型,并对它们提出了一些改进意见。本文还提出了一种新的状态空间气动弹性模型。用两种机翼为例进行了颤振计算。算例表明:这种新的状态空间气动弹性模型是一种精度较高而阶数较低的模型。本文还提出了用状态空间气动弹性模型进行颤振计算时自动识别模态及自动确定颤振点的方法。     

Reachable set estimation for spacecraft relative motion based on bang-bang principle

For spacecraft formation flight, the information of relative motion reachable set is very important, which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation. In this paper, we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion. In particular, we focus on the quality of the approximation and the computational cost. Based on the bang-bang control principle, a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system. An inner approximation and an outer approximation of the reachable set for the system can be obtained. We prove that the approximation quality measured in Hausdorff distance can be guaranteed. The method is easy to implement and has low computational cost. Finally, the effectiveness of the algorithm is demonstrated by experimental simulation.     

PSO节点寻优的样条逼近微分

样条节点分布对逼近精度的影响很大,样条节点寻优模型的雅可比矩阵求解复杂。利用经典参数的PSO（粒子群算法）解算样条最优节点分布模型,以逼近残差的平方和为目标函数,每步对节点序列排序后再计算目标函数,可以提高样条逼近精度,为样条节点寻优提供了一种较好的实现方法。仿真计算表明,在一定的节点个数情况下,PSO节点寻优的逼近效果比Carl de Boor的NEWNOT程序中的方法要好。     

Investigation of the stability of inviscid compressible swirling flows

The stability of an inviscid compressible swirling flow between two concentric cylinders is analytically investigated. Two stability criteria are derived for compressible swirling flows under narrow gap approximation by an analytic method analogous to Ludwieg's method. Finally, the effect of compressibility is discussed.     

Transient Analysis of the Rectified Superconducting Alternator

A set of five differential equations is derived to describe the transient electrical behavior of a three-phase superconducting alternator connected to a full-wave thyristor bridge. The approximation of constant flux linkages for the rotor circuits is utilized to reduce the number of numerical integrations from five to two. This produces a very efficient algorithm that is quite useful for studies requiring a large number of simulations. Numerical results based on the parameters of a 10-MVA superconducting machine are included.     

工程数值优化方法研究进展

回顾与分析了工程数值优化方法研究的发展历程 ,着重介绍与讨论了优化问题的几种数学列式、近似问题的保真度与近似函数 ,以及复杂优化问题的求解策略等。指出优化问题的对偶列式变式 DFOP-V2与高精度多点近似函数和二级近似概念结合而产生的数值优化解法 ,具有通用性 ,高的计算效率 ,并易于与市场现有分析软件结合使用等显著优点     

基于Kriging模型的翼型气动性能优化设计

将基于Kriging模型的近似技术引入气动优化设计。通过计算两个测试函数的全局极值以及翼型几何形状的重构,比较了基于Kriging模型的优化方法与传统的梯度类优化方法、标准遗传算法的特点。结果表明基于近似模型的优化方法不仅全局性良好,而且有效节约了计算资源。用此方法进行了翼型的气动优化设计,目标函数为来流马赫数为0.7、攻角为3°时升阻比最大。设计结果表明,与参考翼型相比,优化翼型升阻比提高了81%,而翼型截面积减少不到1%,优化效果非常明显。     

中心刚体-柔性悬臂梁系统的动力特性研究

对中心刚体-柔性悬臂梁系统的动力特性进行研究。首先采用Hamilton原理和有限元离散化方法,给出该系统的一次近似耦合模型以及相应的KED解耦模型,然后通过数值仿真对该系统的动力特性进行研究。研究中考虑了2种情况:中心刚体的转动惯量远大于柔性悬臂梁的转动惯量的情况和中心刚体的转动惯量接近柔性悬臂梁的转动惯量的情况。研究结果显示,传统的零次近似模型在处理大范围运动为未知的刚柔耦合动力学问题时同样存在失效的可能,而一次近似模型能够对系统的动力学行为进行正确的数学描述。当中心刚体的转动惯量远大于柔性悬臂梁的转动惯量时,一次近似模型的结果与零次近似模型的结果之间存在较小偏差;但当中心刚体的转动惯量接近柔性悬臂梁的转动惯量时,零次近似模型将导致错误的结果。     

Proactive optimization of transmission power and 3D trajectory in UAV-assisted relay systems with mobile ground users

In this paper, an Unmanned Aerial Vehicle (UAV)-assisted relay communication system is studied, where a UAV is served as a flying relay to maintain a communication link between a mobile source node and a remote destination node. Specifically, an average outage probability minimization problem is formulated firstly, with the constraints on the transmission power of the source node, the maximum energy consumption budget, the transmission power, the speed and acceleration of the flying UAV relay. Next, the closed-form of outage probability is derived, under the hybrid line-of-sight and non-line-of-sight probability channel model. To deal with the formulated nonconvex optimization, a long-term proactive optimization mechanism is developed. In particular, firstly, an approximation for line-of-sight probability and a reformulation of the primal problem are given, respectively. Then, the reformulated problem is transformed into two subproblems: one is the transmission power optimization with given UAV’s trajectory and the other is the trajectory optimization with given transmission power allocation. Next, two subproblems are tackled via tailoring primal–dual subgradient method and successive convex approximation, respectively. Furthermore, a proactive optimization algorithm is proposed to jointly optimize the transmission power allocation and the three-dimensional trajectory. Finally, simulation results demonstrate the performance of the proposed algorithm under various parameter configurations.     

Stochastic structural optimization using particle swarm optimization, surrogate models and Bayesian statistics

This paper focuses on a method to solve structural optimization problems using particle swarm optimization (PSO), surrogate models and Bayesian statistics. PSO is a random/stochastic search algorithm designed to find the global optimum. However, PSO needs many evaluations compared to gradient-based optimization. This means PSO increases the analysis costs of structural optimization. One of the methods to reduce computing costs in stochastic optimization is to use approximation techniques. In this work, surrogate models are used, including the response surface method (RSM) and Kriging. When surrogate models are used, there are some errors between exact values and approximated values. These errors decrease the reliability of the optimum values and discard the realistic approximation of using surrogate models. In this paper, Bayesian statistics is used to obtain more reliable results. To verify and confirm the efficiency of the proposed method using surrogate models and Bayesian statistics for stochastic structural optimization, two numerical examples are optimized, and the optimization of a hub sleeve is demonstrated as a practical problem.     

利用差值定理降低飞行器速度和加速度拟合的截断误差

推导了差值定理及其推论,并以此作为数据拟合的有效点判据,显著降低了飞行器速度和加速度拟合的截断误差;探讨了该判据条件下滤波参数对拟合结果的影响及截断误差的判断条件,并采用实测数据对拟合效果进行了检验。     

Material deformation curve approximation in strength and stability analysis

A deformation curve approximation method applicable for materials without yield line and characterized by simple realization and a possibility of explicit representation of the stress-strain dependence is presented. The simplest approximation variant makes it possible to find critical stresses for beams or plates in the closed form.     

判断矩阵的一个恰当的校正方法

 本文首先证明了成对比较矩阵在相容性矩阵集合中的最佳逼近的存在性和不唯一性。然后通过微分同胚,把原来的非线性逼近转化成一个线性逼近,从而用投影定理获得解决。算例证明该方法简易可行。