Classic and inverse compositional Gauss-Newton in global DIC

Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss-Newton implementation of finite element DIC is proposed as a cost-effective and mathematically sound alternative to this approximation.     

波动方程初至双差走时层析反演

对于有限频带的地震信号,地震波绝对走时受到震源子波的波形特征、走时测量准则等多种因素的影响,提高走时测量的精度有助于增加反演结果的可靠性.为降低绝对走时测量误差对反演的影响,采用双差走时代替绝对走时,并将其与Rytov近似导出的相位延迟敏感度核函数相结合,构造有限频带地震波的双差走时敏感度核函数.针对初至双差走时层析反...     

A Joint TDOA/FDOA Lo calization Algorithm Using Bi-iterative Method with Optimal Step Length

In order to improve the estimation accuracy of multi-station joint Time difference of arrive/ Frequency difference of arrive (TDOA/FDOA) location with Bi-Iterative method, a solution for the position of target with Gauss-Newton optimal step length is proposed in this paper. First, get the initial estimation of target based on Two-stage weighted least-squares (TSWLS) algorithm, and then alternately solve the position and velocity of the target with Bi-Iterative method. In this paper, Gauss-Newton method is applied to iteratively solve the target position, including the detailed equations of the descending direction and the optimal iterative step length in each iterative process. Simulations are carried out to examine the algorithm's performance by comparing it with TSWLS method and Gauss-Newton method regardless of the step length. The results show that when Gauss noise variance is small, the estimation accuracy is close to Cramer Rao lower bound (CRLB) and the proposed method performs better than the other two methods. In addition, because the model which includes the position and velocity of the observation station and the target is in line with the over-the-horizon reality scene in this paper, our research has certain practical value.     

基于混合微分进化算法的生化过程动态参数估计(英文)

Determination of the optimal model parameters for biochemical systems is a time consuming iterative process. In this study, a novel hybrid differential evolution (DE) algorithm based on the differential evolution technique and a local search strategy is developed for solving kinetic parameter estimation problems. By combining the merits of DE with Gauss-Newton method, the proposed hybrid approach employs a DE algorithm for identifying promising regions of the solution space followed by use of Gauss-Newton method to determine the optimum in the identified regions. Some well-known benchmark estimation problems are utilized to test the efficiency and the robustness of the proposed algorithm compared to other methods in literature. The comparison indicates that the present hybrid algorithm outperforms other estimation techniques in terms of the global searching ability and the convergence speed. Additionally, the estimation of kinetic model parameters for a feed batch fermentor is carried out to test the applicability of the proposed algorithm. The result suggests that the method can be used to estimate suitable values of model parameters for a complex mathematical model.     

难加工材料高速切削过程中切削力的非线性特征规律析因研究

综合应用析因试验设计与拉丁超立方抽样试验设计,对难加工材料马氏体不锈钢进行了高速铣削试验。在分析其切削力的非线性特征规律基础上,建立了高速切削难加工材料工艺中切削力与背吃刀量、每齿进给量和切削速度之间的非线性数学模型。试验结果表明,高速切削难加工材料时,背吃刀量和每齿进给量之间的交互作用对切削力有显著影响;切削力与切削用量间确实存在非线性特征规律;切削用量对切削力的影响效应随切削用量的变化而发生改变。     

电磁传播电阻率测井快速稳定的混合反演方法

多参数阵列电磁传播电阻率测井(EPRL)资料的反演问题具有较强的非线性和多值性.高斯-牛顿法是求解这类问题的有效方法之一,但其反演的稳定性与精度对初值有较强的依赖性.微分进化算法可以有效地避开对初值的依赖性且其反演稳定性很好,但耗时量大效率较低.在高斯-牛顿法和微分进化算法的基础上发展了一种混合反演方法,即先用微分进化算法筛选得到好的初值,然后再用高斯-牛顿法反演得到最优解.经过一些资料的反演实践,表明该混合反演方法是一种快速、稳定、有效的反演方法.     

非线性平方和函数极小化的两种方法及其收敛性质

本文给出了求平方和函数极小化问题的两种改进方法,并讨论了它们的收敛性质,最后的数值例子也说明了算法是有效的.     

Spreadsheet template approach for nonlinear regression estimation

Industrial Engineers may encounter variables which are nonlinearly related such that the relationship cannot be transformed to one which is linear in the unknown parameters. One instance where this can occur is a learning curve which approaches a non-zero asymptote. This paper presents a spreadsheet template for implementing the Gauss-Newton Method for solving such nonlinear regression estimation problems.     

Robust Parameter Estimation in Dynamic Systems

In this paper we present a practical method for robust parameter estimation in dynamic systems. In our study we follow the very successful approach for solving optimization problems in dynamic systems, namely the boundary value problem (BVP) approach. The suggested method combines multiple shooting for parameterizing dynamics, a flexible realization of the BVP principle, with a fast Gauss-Newton algorithm for solving the resulting constrained l ₁ problem. We give an overview of the theoretical background as well as the details of a numerical implementation. We discuss why the Gauss-Newton algorithm, which is known to perform well mainly on well-conditioned problems, is appropriate for parameter estimation problems, while quasi-Newton methods have only limited use for parameter estimation. The method is implemented on the basis of the direct multiple shooting method as implemented in PARFIT, thus inheriting all basic properties of PARFIT such as numerical stability, reliability and efficiency. The new code has been successfully applied to real-life parameter estimation problems in enzyme and chemical kinetics.     

高斯-牛顿法在模拟特征分析测试参数优化中的应用

普通的模拟特征分析测试方法直接根据采集的VI曲线进行故障判定,无法自动调整测试参数,测试人员需要手动调整测试参数,这样严重影响测试工作效率。以容性器件为例,根据模拟特征分析原理建立故障前后信号差异的目标函数,依据被测器件参数利用改进的高斯-牛顿迭代法对测试信号进行自动灵敏度调整,计算机仿真结果表明,该方法有效,且优化参数对电流信号差异的提升尤为明显。