A hybrid homogeneously weighted moving average control chart for process monitoring: Discussion

The sensitivity of a monitoring scheme depends on many factors including the variance of the charting statistic which is very important in the computation of the control limits. This paper discusses the computation of the variance of the recently proposed hybrid homogeneously weighted moving average (HHWMA) $\overline{X}$ scheme which was based on an incorrect assumption. The correct variance is used to evaluate the run-length characteristics of the HHWMA $\overline{X}$ scheme. It is observed that the incorrect variance has a significant impact on the sensitivity (or performance) of the HHWMA $\overline{X}$ scheme.     

A hybrid homogeneously weighted moving average control chart for process monitoring

Several modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ₁ and λ₂ . The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.     

Weighted Superposition Attraction (WSA): A swarm intelligence algorithm for optimization problems – Part 2: Constrained optimization

This paper is the second one of the two papers entitled “Weighted Superposition Attraction (WSA) Algorithm”, which is about the performance evaluation of the WSA algorithm in solving the constrained global optimization problems. For this purpose, the well-known mechanical design optimization problems, design of a tension/compression coil spring, design of a pressure vessel, design of a welded beam and design of a speed reducer, are selected as test problems. Since all these problems were formulated as constrained global optimization problems, WSA algorithm requires a constraint handling method for tackling them. For this purpose we have selected 6 formerly developed constraint handling methods for adapting into WSA algorithm and analyze the effect of the used constraint handling method on the performance of the WSA algorithm. In other words, we have the aim of producing concluding remarks over the performance and robustness of the WSA algorithm through a set of computational study in solving the constrained global optimization problems. Computational study indicates the robustness and the effectiveness of the WSA in terms of obtained results, reached level of convergence and the capability of coping with the problems of premature convergence, trapping in a local optima and stagnation.     

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

毒品滥用流行病模型的稳定性分析

现有毒品滥用流行病模型假设吸毒者康复后对毒品拥有永久"免疫"力，而忽视了其再次成为毒品易感者的可能性。针对这一问题，通过考虑社区治疗和隔离治疗两种措施，分析了毒品滥用人群的演化过程，提出了基于暂时"免疫"力的毒品滥用流行病模型，并计算了模型的基本再生数，讨论了模型平衡点的存在性和稳定性。当基本再生数小于1时，模型存在一个局部渐进稳定的无毒平衡点；当基本再生数大于1时，模型存在唯一的地方病平衡点，并利用几何方法证明了地方病平衡点的全局稳定性；当基本再生数等于1时，如果满足一定条件，模型出现后向分支现象。数值模拟验证了上述所有结果。研究结果表明提高隔离治疗率、改善社区治疗效果和降低接触传染率可以有效抑制毒品滥用的流行。     

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.     

On global Hessenberg based methods for solving Sylvester matrix equations

In the first part of this paper, we investigate the use of Hessenberg-based methods for solving the Sylvester matrix equation $AX+XB=C$. To achieve this goal, the Sylvester form of the global generalized Hessenberg process is presented. Using this process, different methods based on a Petrov–Galerkin or on a minimal norm condition are derived. In the second part, we focus on the SGl-CMRH method which is based on the Sylvester form of the Hessenberg process with pivoting strategy combined with a minimal norm condition. In order to accelerate the SGl-CMRH method, a preconditioned framework of this method is also considered. It includes both fixed and flexible variants of the SGl-CMRH method. Moreover, the connection between the flexible preconditioned SGl-CMRH method and the fixed one is studied and some upper bounds for the residual norm are obtained. In particular, application of the obtained theoretical results is investigated for the special case of solving linear systems of equations with several right-hand sides. Finally, some numerical experiments are given in order to evaluate the effectiveness of the proposed methods.     

移动机器人路径规划方法研究

移动机器人技术研究中的一个重要领域是路径规划技术，它分为基于模型的环境已知的全局路径规划和基于传感器的环境未知的局部路径规划。综述了移动机器人路径规划技术的发展现状指出了各种方法的优点与不足，最后对移动机器人路径规划技术的发展趋势进行了展望。