非线性最优化问题的一种混合解法

把BFGS方法与混沌优化方法相结合,基于混沌变量提出一种求解具有变量边界约束非线性最优化问题的混合优化方法。混合算法兼顾了混沌优化全局搜索能力强和BFGS方法收敛速度快的优点,成为一种求解非凸优化问题全局最优的有效方法。算例表明,当混沌搜索的次数达到一定数量时,混合优化方法可以保证算法收敛到全局最优解,且计算效率比混沌优化方法有很大提高。     

A Newton multigrid framework for optimal control of fluid–structure interactions

Optimization and Engineering - In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is...     

ERT技术图像重建算法研究

两相流参数测量中,电阻层析成像技术的图像重建算法可归为两大类,即直接法和迭代法。对常用的几种图像重建算法进行了比较性研究,结果表明:直接法速度快,但重建图像质量不理想,仅可作定性分析;迭代法总体上说重建图像质量较高,但速度较慢。当增加像素数以提高重建图像分辨率时,直接法重建图像耗时增量较小,迭代型算法中改进的Newton-Raphson算法、BFGS算法由于目标函数的Hessian矩阵维数增加,计算时间大大增加,而改进的BFGS算法因简化了Hessian矩阵及其逆矩阵的计算,时间增量则较小。     

On Quasi-Newton methods in fast Fourier transform-based micromechanics

This work is devoted to investigating the computational power of Quasi-Newton methods in the context of fast Fourier transform (FFT)-based computational micromechanics. We revisit FFT-based Newton-Krylov solvers as well as modern Quasi-Newton approaches such as the recently introduced Anderson accelerated basic scheme. In this context, we propose two algorithms based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, one of the most powerful Quasi-Newton schemes. To be specific, we use the BFGS update formula to approximate the global Hessian or, alternatively, the local material tangent stiffness. Both for Newton and Quasi-Newton methods, a globalization technique is necessary to ensure global convergence. Specific to the FFT-based context, we promote a Dong-type line search, avoiding function evaluations altogether. Furthermore, we investigate the influence of the forcing term, that is, the accuracy for solving the linear system, on the overall performance of inexact (Quasi-)Newton methods. This work concludes with numerical experiments, comparing the convergence characteristics and runtime of the proposed techniques for complex microstructures with nonlinear material behavior and finite as well as infinite material contrast.     

油品混合粘度合成方法的试验研究

依据国家标准对46#机械油、白油以及两者按不同比例混合之后的油品粘度进行了实验测试.运用BFGS算法和全局最优化相结合的方法对试验数据进行拟合,得出了粘度计算模型.实验结果表明,通过将两种不同粘度的油品混合获得所需粘度的方法是可行的,粘度的计算模型具有一定的精度,拟合误差绝大部分数据可控制在±2%以内,可以作为粘度控制模型.     

Numerical Analysis of Secondary Cooling in Continuous Slab Casting

In the present study, a numerical optimization program has been developed for predicting the optimal secondary cooling patterns in a continuous slab caster. Optimization strategy using Broydon-Fletcher-Goldfarb-Shanno （13FGS） method is carried out by determining the constant heat transfer coefficients in each spray zone, which could satisfy the casting conditions and metallurgical criteria specified by the engineer. From the present results, it is found that even a slight variation in the pouring temperature, allowable surface temperature, and casting speed could give rise to the changes in the cooling pattern throughout the spray zones.     

基于等参元的三维电阻抗成像的数值模拟和分析

对于电阻抗成像的数学模型,本文用等参元方法将对应的椭圆型方程离散化,把成像问题转化为非线性优化问题,给出了目标函数梯度及近似Hesee阵的计算公式;提出了伪单元刚度矩阵的概念,给出了利用其在迭代过程中的不变性来提高计算效率的方法：分别用BFGS校正拟Newton算法和Goldfeld修正Gauss-Newton算法对三维成像问题进行了一系列数值模拟实验,证实了算法的有效性,指出了其中存在的问题。     

基于傅里叶变换的点衍射干涉术

在相移算法的点衍射干涉术的基础上,提出了基于傅里叶变换的点衍射干涉测量术.基于傅里叶变换的点衍射干涉测量术是一种建立在点光源衍射干涉理论基础上的测量方法,它采用傅里叶条纹分析方法来求解干涉条纹的相位分布,运用基于BFGS的拟牛顿算法进行三坐标的迭代计算,确定点光源的三维空间坐标.通过计算机模拟实验,验证了该方法在有噪声干扰的情况下,可以有效降低干扰噪声对测量的影响.     

基于相位差法的波前检测技术

基于相位差法的波前检测技术,主要是利用在焦面和离焦位置上同时采集的一对图像,对光瞳上的波前相位分布进行恢复,同时也可以对目标进行恢复。与哈特曼波前传感器和剪切干涉仪等波前检测技术相比,相位差法具有光路简单、易于实现的特点,同时可以采用扩展目标作为参考源,主要适用于对实时性要求不高的领域。在计算机模拟大气湍流和成像系统的基础上,我们使用有限内存拟牛顿法对波前相位和目标进行了恢复。模拟研究结果表明,相位差法可以较准确的恢复出波前相位,并且最优化的离焦波面差为一个波长。     

An efficient multilevel solution scheme for large scale non-linear systems

We present a new approach for the fast, efficient solution of large systems of non-linear equations arising from the finite element discretization. The proposed non-linear solver builds on the advantages of the popular methods of solution that are currently being employed, while eliminating most of their undesirable features. It combines the well-known BFGS method with the FAS version of the multigrid method, introduced by Brandt,¹ to form a fast, efficient solution method for non-linear problems. We present numerical performance studies that are indicative of the convergence properties as well as the stability of the new method.     

混合遗传算法在结构动力反演中的应用研究

研究了输入荷载未知条件下的结构参数识别及荷载反演问题,该问题最终归结为一个非线性的优化问题求解,根据目标函数、约束条件的具体特性,采用BFGS算法作为局部搜索算子,构造了基于浮点编码的混合遗传算法。针对系统输入未知的激励特性,采用分解反演的计算策略,从而提高了动力反演中混合遗传算法的稳健性和收敛速度。数值算例表明,这种方法具有很好的参数识别精度及荷载反演效果,对测试噪声有较强的适应能力。     

Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers

Various non‐linear equation solvers are adapted to handle linear constraints via the Lagrange‐multiplier technique. This adaptation process turns out to be quite straightforward for Newton–Raphson methods and rank‐two Quasi–Newton methods (BFGS and DFP), but rather more involved for Broyden method. In fact, two Broyden methods can be obtained: the standard one and a modified one, better adapted to the Lagrange‐multiplier environment. Some numerical examples are used to assess the relative performance of the various adapted solvers. These tests illustrate the superiority of the modified Broyden method over the standard one. Copyright © 1999 John Wiley & Sons, Ltd.     

钴湿法冶炼萃取过程质量指标的软测量

利用基于物料衡算关系的机理模型、基于萃取平衡关系的半经验模型以及基于径向基函数-偏最小二乘法的萃余液的pH值预测模型,提出了一种钴湿法冶炼萃取过程质量指标软测量建模方法.机理模型用以描述过程的整体特性;半经验模型利用拟牛顿变尺度方法对其中未知参数进行估计,并用以逼近机理模型中的萃取平衡关系;基函数-偏最小二乘法则用来预测萃余液pH值.将所建立的软测量模型应用于实际钴湿法冶炼生产过程中,结果表明,该方法具有良好的预测精度.     

Adaptive split spectrum processing using a neural network

The polarity thresholding algorithm for split spectrum processing (SSP) is known to work well once properly tuned. However, there are several problems related to the finding of the right split parameters such as the number of filters and the information carrying spectral range. Here we show that the polarity thresholding method can be formulated as a multilayer perceptron (MLP) neural network with binary neurons and binary input signals operating in feedforward mode. Then the method is generalized to process nonbinary data using an adaptive MLP with graded neurons. Experiments with real ultrasonic NDE signals are presented using the conventional backpropagation optimization algorithm (BP) and a second order optimization method (BFGS) with exact line search. Finally, alternative adaptive algorithms based on a decomposition of the network into single neurons or linear discriminants are briefly discussed.     

An E-type Temperature Sensor for Upper Air Meteorology

An E-type high-precision temperature sensor, which is adopted for upper air meteorology, was proposed in this paper. A computational fluid dynamics(CFD) method was implemented to analyze temperature rise induced by solar radiation at different altitudes and solar radiation intensities. A temperature rise correction equation was obtained by fitting the CFD results using a Broyden-Fletcher-Goldfarb-Shanno(BFGS) method. To verify the performance of the temperature sensor, an experimental platform was constructed. Through simulations and experiments, the relationship among the altitude, solar radiation intensity and radiation temperature rise was obtaned. The root-mean-square error(RMSE) between the temperature rise derived from the correction equation and that derived from the experiments is 0.013 K. The sample determination coefficient r2 of the solar radiation error correction equation is 0.9975.     

Symmetry preserving algorithm for large displacement frictionless contact by the pre‐discretization penalty method

A three‐dimensional contact algorithm based on the pre‐discretization penalty method is presented. Using the pre‐discretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation of the problem and allows an easy incorporation of higher‐order elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. The proposed algorithm utilizes the BFGS method modified for constrained non‐linear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders. Copyright © 2004 John Wiley & Sons, Ltd.     

采用混合粒子群算法实现匹配追踪算法

针对匹配追踪信号稀疏分解的巨大计算量问题,在具有全局优化能力的粒子群算法基础上,提出了一种结合BFGS(Broyden、Fletcher、Goldfarb和Shanno)方法和变异操作的混合粒子群算法实现信号匹配追踪分解。利用BFGS方法增强了算法的局部开发能力,加快了信号特征提取速度;通过变异操作控制种群多样性以避免早熟收敛,增强了算法全局探测能力,提高了信号特征提取精度。通过与单一粒子群算法和遗传算法实现仿真信号匹配追踪分解的结果进行对比,证明了使用混合粒子群算法的匹配追踪分解能够快速准确提取信号特征参数。最后,将该算法应用于某内圈损伤轴承振动信号中的冲击特征提取,结果表明该算法在工程应用中具有一定的准确性和实用性。     

An adaptive model order reduction with Quasi‐Newton method for nonlinear dynamical problems

Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error. Copyright © 2015 John Wiley & Sons, Ltd.     

Crack identification based on optimization methods using harmonic elastic waves

The current paper presents a theoretical study of the identification of cracks in an elastic medium based on optimization methods using harmonic elastic waves. A generalized crack model was used to determine the elastodynamic behaviour of an arbitrarily located and oriented crack subjected to a plane harmonic wave. Sensitivity analysis was conduced to evaluate the variation of stress and strain fields with various crack parameters using the direct differential method (DDM). These general results were then used to identify an unknown crack from known strain components at discrete locations. The BFGS optimization scheme based on the sensitivity analysis was used to determine the length, the orientation and the position of the crack. Numerical simulation was conducted and the results were presented to show the effectiveness of the sensitivity analysis and the optimization method. It was observed that starting from a set of arbitrarily determined initial values, the length, position and the orientation of the crack can be accurately determined.