基于模型降阶的分数阶系统动态性能研究

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具.首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统.仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能.     

基于平衡截断法的离散时间线性时滞系统的低频域模型降阶

研究在系统工作频率范围为低频区间情形下的离散时间线性时滞系统模型降阶问题. 首先根据时滞系统在零频点处传递函数的性质, 构造了一类匹配其零频响应的带有可调参数的扩展线性时滞系统, 进而在其基础上结合已有的时滞系统平衡截断法给出了新的低频模型降阶算法. 通过调节其中的设计参数, 新方法所得降阶时滞系统模型能够以任意精度逼近原系统的零频响应特性, 进而可以用于改善低频范围内的模型逼近性能. 数值算例验证了所提方法的有效性和优越性.     

Pade近似降低技术的改进

本文提出Pade逼近的一个定理，用于改进Pade近似模型降阶技术，并推广到离散模型的降阶，减少了模型降阶的计算量，提高了精度。     

带约束条件的张量积Bézier曲面最佳降多阶

为了交换和存储不同造型系统中的数据,提出一种张量积Bézier曲面带约束条件的一次降多阶算法.该算法在保角点高阶插值情形下,利用原曲面顶点数组的降维方法和最小二乘法给出了Bézier曲面的最佳降多阶逼近;在给定降阶曲面的4条边界曲线的情形下,利用最小二乘法,对原曲面减去降阶曲面的4条边界曲线后所得到的新曲面进行无约束最佳降阶逼近;将保边界插值的降阶方法应用于拼接曲面,所得到的降阶曲面为整体C0连续.数值实验和逼近理论表明,文中算法比其他算法的精度高、效率高.     

张量积Bézier曲面降阶逼近的新方法

基于 L2 范数 ,给出基于曲面间体积极小的约束优化算法 ,将 Bézier曲面的降阶问题转变为线性方程组的求解 ,并给出降阶逼近问题解的存在性证明 .文中还对逼近误差进行了分析 ,并利用曲面离散算法减少降阶逼近误差     

GC1约束的三角Bézier曲面降阶逼近研究

研究给定的n次三角Bezier曲面在L2范数下的一次降多阶的逼近问题,给出了在无约束条件下的三角Bezier曲面降阶求解的详细过程,将降阶问题转化为非线性最优化问题求解,并将降阶过程与曲面的几何连续拼接结合在一起,给出了降阶同时满足GC1拼接的实现过程.实验结果表明,该方法简单实用,降阶逼近效果好.     

H-Bézier曲线的降多阶逼近

国内外对参数曲线降阶,尤其是对Bézier曲线降阶的研究已渐趋成熟,但尚缺少对超越曲线降阶的研究.为此以能精确表示指数曲线、悬链线等超越曲线的H-Bézier曲线为载体,运用H-Bézier曲线的升阶公式,结合广义逆矩阵理论给出了H-Bézier曲线一次降多阶的逼近方法;同时估计了降阶的误差界,并建立了与Bézier曲线降阶的关系.实验结果表明,采用该方法可取得较好的逼近效果,有效地丰富了H-Bézier曲线的理论体系.     

GC~1约束的多三角Bézier曲面混合降阶逼近研究

三角曲面的降阶问题一直是CAGD领域的一个难点问题,近年来受到关注.对L2范数下多三角Bézier曲面在拼接边界满足GC1约束的降阶逼近问题进行研究,包括:1)给出了一种L2范数下单一三角Bézier曲面的一次降多阶的逼近算法;2)对两个三角Bézier曲面在拼接边界上满足GC1约束的降阶逼近算法进行研究,提出一种通过调整两个三角Bézier曲面片距离拼接边界的第2排内部控制点来满足GC1约束的降阶逼近算法;3)研究基于调整三角Bézier曲面片内部控制点的多三角曲面片在各拼接边界满足GC1约束的曲面降阶算法.算法首先按照2)中的方法,确定每两个三角Bézier曲面片在公共边界满足GC1约束的降阶逼近所需要调整的内部控制点,然后构造blending函数.通过将每个三角Bézier曲面所对应的多组控制点进行混合,形成新的混合降阶曲面的三角Bézier格式,并在理论上证明该混合三角Bézier降阶曲面片与其周边的各降阶曲面片仍保持GC1约束.实验结果表明,所提方法简单实用,逼近效果好.     

基于模型降阶的最优分数阶PID控制器设计

由于一些受控对象较为复杂或者模型系统阶次较高,使得控制器的设计变得非常困难,这会造成控制系统的鲁棒性和动态特性下降;文章在H2范数模型降阶的基础上提出一种新的降阶模型结构,它可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统,并以降阶后模型的幅频、相频和对象增益变化的鲁棒特性为约束条件进行最优分数阶PID控制器的设计;仿真实验证明,与原有闭环控制系统相比,基于模型降阶的最优分数阶PID控制器控制下的闭环系统具有更好的动态性能,并且鲁棒性较强。     

L∞范数下使用基本曲线和修正曲线的带约束Bézier曲线降阶

为避免直接求解基于L∞距离的带约束逼近的非线性最优解引起的复杂性,提出了一种把降阶逼近曲线分解为基本曲线和修正曲线的降阶方法.基本曲线利用约束Legendre多项式可得到显式解,且保证降阶后曲线满足要求的边界插值条件;修正曲线的控制顶点由降阶逼近曲线和原曲线的差定义,能够在L∞范数意义下极小化降阶逼近曲线与原曲线的误差.文中方法以简单稳定的方式实现保端点插值的一次降多阶,并达到L∞范数意义下对原曲线的近似最佳逼近.最后通过实例说明了文中方法的有效性.     

Multi-stage design space reduction and metamodeling optimization method based on self-organizing maps and fuzzy clustering

Design space exploration and metamodeling techniques have gained rapid dominance in complex engineering design problems. It is observed that the modeling efficiency and accuracy are directly associated with the design space. In order to reduce the complexity of the design space and improve modeling accuracy, a multi-stage design space reduction and metamodeling optimization methodology based on self-organizing maps and fuzzy clustering is proposed in this paper. By using the proposed three-stage optimization approach, the design space is systematically reduced to a relatively small promising region. Self-organizing maps are introduced to act as the preliminary reduction approach through analyzing the underlying mapping relations between design variables and system responses within the original samples. GK (Gustafson & Kessel) clustering algorithm is employed to determine the proper number of clusters by utilizing clustering validity indices, and sample points are clustered using fuzzy c-means (FCM) clustering method with the known number of clusters, so that the search can focus on the most promising area and be better supported by the constructed kriging metamodel. Empirical studies on benchmark problems with multi-humps and two practical nonlinear engineering design problems show the accurate results can be obtained within the reduced design space, which improve the overall efficiency significantly.     

Approximate techniques of strctural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach for the selection of the reduced basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consist of the original analyzed design and the first-order sensitivity analysis vectors.The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended.Numerical examples are presented of space truss structures. These examples demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.     

一种基于沙漏网络的多层次协同搜索方法

目前,人工智能快速发展,人们可以通过探索硬件设计空间使优秀的神经网络算法高效部署在FPGA加速器。然而,由于参数量大、操作过于复杂而导致算法与硬件难以匹配,加速效率不高。为了算法和硬件两者匹配性更强,提出了一种多层次协同搜索的方法,采用SPOS搜索策略并以检测准确率和延时为评估目标,搜索出最优神经网络架构、量化方式和硬件设计参数组合。该方法应用在姿态识别中具有优异性能的沙漏网络中,在获取候选子网络量化前、后的检测准确率的同时对硬件设计参数使用遍历搜索得到预估延时,根据目标函数获取最高得分的最优组合。为了保证获取的数据有效性,子网络需要进行重新训练、量化后重新推理得到检测准确率,获取硬件设计参数则利用基于Spinal HDL设计的加速器模板进行仿真测试得到测试延时。就平均而言,该方法比文献［1］减少了83.3%的参数,准确率只下降了0.69;比传统加速方法平均减少了33.2%参数量,准确率只下降了0.46,网络推理的测试总延时减少22.1%,在沙漏块的测试延时减少67.8%。总体而言,该协同搜索方法对于沙漏网络的优化有一定效果,比传统加速设计方法更有优势。     

Efficient design of experiments for structural optimization using significance screening

When performing structural optimization of large scale engineering problems, the choice of experiment design is important. However, classical experiment designs are developed to deal with undesired but inevitable scatter and are thus not ideal for sampling of deterministic computational responses. In this paper, a novel screening and design of computer experiments algorithm is presented. It is based on the concept of orthogonal design variable significances and is applicable for problems where design variables do not simultaneously have a significant influence on any of the constraints. The algorithm presented uses significance orthogonality to combine several one-factor-at-a-time experiments in one several-factors-at-a-time experiment. The procedure results in a reduced experiment design matrix. In the reduced experiment design, each variable is varied exactly once but several variables may be varied simultaneously, if their significances with respect to the constraints are orthogonal. Moreover, a measure of influence, as well as an influence significance threshold, is defined. In applications, the value of the threshold is left up to the engineer. To assist in this choice, a relation between model simplification, expressed in terms of the significance threshold, and computational cost is established in a screening. The relation between efficiency and loss of accuracy for the proposed approach is discussed and demonstrated. For two solid mechanics type problems studied herein, the necessary number of simulations could be reduced by 25% and 64%, respectively, with negligible losses in accuracy.     

Selection of initial designs for multi-objective optimization using classification and regression tree

One of the major challenges for solving large-scale multi-objective optimization design problems is to find the Pareto set effectively. Data mining techniques such as classification, association, and clustering are common used in computer community to extract useful information from a large database. In this paper, a data mining technique, namely, Classification and Regression Tree method, is exploited to extract a set of reduced feasible design domains from the original design space. Within the reduced feasible domains, the first generation of designs can be selected for multi-objective optimization to identify the Pareto set. A mathematical example is used to illustrate the proposed method. Two industrial applications are used to demonstrate the proposed methodology that can achieve better performances in terms of both accuracy and efficiency.     

基于径向基神经网络的语音识别技术

深入分析研究了径向基神经网络的优缺点,并对其进行了改进,分析讨论了语音识别研究中,径向基神经网络的设计原则以及特征参数等对语音识别结果的影响。将其应用于数字语音识别中,实验结果表明,基于改进型的径向基神经网络的语音识别方法有着较好的识别性能和应用效果。针对非特定人的孤立词识别,识别率可以达到90%以上。     

宽频带系统数字控制的双单片机并行实现

讨论了一种适合于宽频带系统数字控制的双单片机并行实现的算法表达及硬件结构设计。该方法可以大大缩短控制算法的运算时间，从而有利于减小控制系统的采样周期，为提高数字控制系统带宽和精度提供了保证。     

500m口径球面射电望远镜柔性馈源支撑系统仿真

为给500m口径球面射电望远镜(Five-hundred-meter Aperture Spherical radio Telescope,FAST)提供设计优化方案,对其柔性馈源支撑系统进行1:1原型虚拟样机的全程仿真.设计整个仿真模型的控制框架和控制算法;分析系统的运动学、动力学和在干扰载荷下的控制精度.整个仿真工...     

基于空间分解的参数优化径向基函数近似模型构造方法

为了进一步提高径向基函数(RBF)近似模型的精度,对其近似精度影响因素进行了深入研究.深入分析了计算机舍入误差对RBF近似精度的影响,指出矩阵条件数和形状参数同为影响RBF模型近似精度的两个重要因素.结合灵敏度分析对设计空间进行了分解,改善了矩阵条件数,增加了设计自由度,在传统基于形状参数优化的RBF近似模型的基础上,提出了基于空间分解的参数优化RBF近似模型构造方法.数值实验结果表明,在两个测试算例中,所提方法较传统基于形状参数优化的RBF近似模型构造方法的均方根误差(RMSE)分别减小了51.3%、58.0%,具有更高的近似精度.     

A novel engineering tool for creative design of fluid systems

Computational fluid dynamics is not often used early in the conceptual design stage of product development due to the lengthy computation times involved with solving complex computational fluid dynamics models. At this early stage, design options are being explored and significant changes are common, and therefore updated solutions must be found quickly to make these models effective. Because of this, computational fluid dynamics models are often reduced to analysis tools used later in the process and are used for refinement rather than for creative engineering design. This paper presents a novel method to create computational fluid dynamics models that can be used earlier in the engineering design process. The key aspects of analysis models used in the initial, creative phase of design are the ability to make changes and re-analyze the altered model quickly. Typically, computational fluid dynamics analysts choose to re-analyze the entire altered model to maintain the same level of accuracy. This can take a significant amount of time because the entire domain must be recalculated. Much of this time is devoted to fine-tuning the model, i.e., improving the accuracy of details of the domain that are sometimes non-essential to the bulk characteristics of the flowfield. However, in the early stage of the design process, decisions are often made based on the large-scale behavior of the fluid flow; fine details are often inconsequential. We have taken advantage of this premise to decrease the turnaround time required to re-analyze a computational fluid dynamics model using the Adaptive Modeling by Evolving Blocks Algorithm. The Adaptive Modeling by Evolving Blocks Algorithm is a genetic programming-based optimization program that segregates a flowfield and places minimal cost solvers in regions with simple flow dynamics while placing full-scale computational fluid dynamics solvers in the more complex regions to preserve accuracy. The program evolves the combined segregation scheme and solver placement until a reliably accurate, faster multi-solver model is found. Substantial reductions in solution times have been found in some cases. The results show an improvement in the speed of the multi-solver when compared with a single-model solution with no significant loss of accuracy.