Covariance matrix adapted evolution strategy algorithm-based solution to dynamic economic dispatch problems

This article presents a covariance matrix adapted evolution strategy (CMAES) algorithm to solve dynamic economic dispatch (DED) problems. The DED is an extension of the conventional economic dispatch problem, in which optimal settings of generator units are determined with a predicted load demand over a period of time. In this article, the applicability and validity of the CMAES algorithm is demonstrated on three DED test systems with a sequential decomposition approach. The results obtained using the CMAES algorithm are compared with results obtained using the real-coded genetic algorithm, the Nelder–Mead simplex method, and other methods from the literature. To compare the performance of the various algorithms, statistical measures like best, mean, worst, standard deviation, and mean computation time over 20 independent runs are taken. The effect of population size on the performance of the CMAES algorithm is also investigated. The simulation experiments reveal that the CMAES algorithm performs better in terms of fuel cost and solution consistency. Karush–Kuhn–Tucker conditions are applied to the solutions obtained using the CMAES algorithm to verify optimality. It is found that the obtained results satisfy the Karush–Kuhn–Tucker conditions and confirm optimality.     

基于分块DCT和Tucker分解的彩色图像数字水印

提出了一种通过分块DCT和Tucker分解将水印信息同时嵌入彩色图像R、G、B通道的离散余弦变换(DCT)直流系数中的水印算法。首先对彩色图像R、G、B通道进行8×8分块DCT,然后将各分块系数矩阵的直流系数分量构成三阶张量,再经过Tucker分解后获得核心张量,通过在核心张量中嵌入水印信息使得水印信息同时扩散到三通道的直流系数中。通过实验表明,该算法对于压缩、噪声、滤波、缩放等攻击具有一定的鲁棒性。与传统的基于YCbCr颜色空间的算法比较,该算法具有更好的不可见性。     

关于多目标分式规划问题

本文对一般情况的多目标分式规划问题，给出了比较全面的最优性条件和对偶结果，把Ｋｕｈｎ－Ｔｕｃｋｅｒ型最优性条件和Ｍｏｎｄ－Ｗｅｉｒ型对偶的结果推广到更一般的情况     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.     

基于张量Tucker分解的发动机故障诊断

传统的发动机故障诊断方法通常基于向量模式进行数据特征的提取,可能丢失数据之间的结构信息及破坏数据间相关性。针对此问题,提出了一种张量模式下提取发动机数据特征的方法,构建了“信号类别×曲轴转角×转速”的三阶张量形式的发动机状态样本,基于交替投影的思想,使用HOSVD-HOOI张量Tucker分解的联立求解算法,对数据特征进行提取。分别以不进行数据特征提取和基于张量Tucker分解进行数据特征提取两种情况,对发动机正常工作、单缸失火和轴系不对中三种状态下的实验数据进行处理,并分别采用网格参数优化法、遗传算法、粒子群算法对分类模型中的参数进行优化。以预测准确率和模型学习时间为评价指标进行对比分析,实验结果表明,基于张量Tucker分解的发动机数据特征提取及诊断方法预测准确率更高,分类模型学习时间更短。     

A bi-level optimization model for operation of distribution networks with micro-grids

Active distribution grids (ADGs) consist of several distributed generations (DGs) and controllable loads (CLs). These resources are utilized in the form of several microgrids (MGs) which in turn facilitate managing of ADGs. Therefore, the problem of distribution company (DISCO) and MGs operation requires a hierarchical decision-making framework. An attempt is made in this paper to model such framework as a bi-level optimization problem. In the proposed bi-level model, the objective of the upper level (leader) problem is to maximize the profit of DISCO, and the objective of the lower level (follower) problems is to minimize the cost of MGs. The resulting model is a nonlinear bi-level problem which is transformed into a linear single-level problem through Karush–Kuhn–Tucker (KKT) conditions and dual theory. Since the proposed model creates a retail electricity market in distribution grid, two frameworks are considered for this market: various and uniform retail electricity prices. To illustrate the effectiveness of the model, a hypothetical distribution grid is considered as the case study. The impacts of the market price and various demand levels of MGs on the results are investigated in two scenarios.     

基于超图正则化非负Tucker分解的图像聚类算法

针对非负张量分解应用于图像聚类时忽略了高维数据内部几何结构的问题,在经典的张量非负Tucker分解的基础上,添加超图正则项以尽可能多地保留原始数据的内在几何结构信息,提出一种基于超图正则化非负Tucker分解模型HGNTD。通过构造超图刻画数据内部样本间的高阶关系,提高几何结构描述的准确性,针对超图正则化非负张量分解模型,基于交替非负最小二乘法,设计快速有效的超图正则化非负Tucker分解算法求解所给模型,证明算法在非负的条件下是收敛的,最终将算法应用于图像聚类。在Yale和COIL两个常用公开数据集上的实验结果表明,相对于k-means、非负矩阵分解、图正则化非负矩阵分解、非负Tucker分解和图正则化非负Tucker分解等算法,超图正则化非负Tucker分解算法聚类准确度提升了8.6%~11.4%,归一化互信息提升了2.0%~7.5%,具有更好的聚类效果。     

一种新的基于张量表示和分解的多声道音频信号压缩方法(英文)

Multichannel audio signal is more difficult to be compressed than mono and stereo ones.A novel multichannel audio signal compression method based on tensor representation and decomposition is proposed in this paper.The multichannel audio is represented with 3-order tensor space and is decomposed into core tensor with three factor matrices in the way of channel,time and frequency.Only the truncated core tensor is transmitted which will be multiplied by the pre-trained factor matrices to reconstruct the original tensor space.Objective and subjective experiments have been done to show a very noticeable compression capability with an acceptable output quality.The novelty of the proposed compression method is that it enables both high compression capability and backward compatibility with limited signal distortion to the hearing.     

Linear algebra for tensor problems

By a tensor problem in general, we mean one where all the data on input and output are given (exactly or approximately) in tensor formats, the number of data representation parameters being much smaller than the total amount of data. For such problems, it is natural to seek for algorithms working with data only in tensor formats maintaining the same small number of representation parameters—by the price of all results of computation to be contaminated by approximation (recompression) to occur in each operation. Since approximation time is crucial and depends on tensor formats in use, in this paper we discuss which are best suitable to make recompression inexpensive and reliable. We present fast recompression procedures with sublinear complexity with respect to the size of data and propose methods for basic linear algebra operations with all matrix operands in the Tucker format, mostly through calls to highly optimized level-3 BLAS/LAPACK routines. We show that for three-dimensional tensors the canonical format can be avoided without any loss of efficiency. Numerical illustrations are given for approximate matrix inversion via proposed recompression techniques.      

Evolutionary algorithm solution and KKT based optimality verification to multi-area economic dispatch

This paper is aimed at exploring the performance of the various evolutionary algorithms on multi-area economic dispatch (MAED) problems. The evolutionary algorithms such as the Real-coded Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adapted Evolution Strategy (CMAES) are considered. To determine the efficiency and effectiveness of various EAs, they are applied to three test systems; including 4, 10 and 120 unit power systems are considered. The optimal results obtained using various EAs are compared with Nelder–Mead simplex (NMS) method and other relevant methods reported in the literature. To compare the performances of various EAs, statistical measures like best, mean, worst, standard deviation and mean computation time over 20 independent runs are taken. The simulation experiments reveal that CMAES algorithm performs better in terms of solution quality and consistency. Karush–Kuhn–Tucker (KKT) conditions are applied to the solutions obtained using EAs to verify optimality. It is found that the obtained results are satisfying the KKT conditions and confirm the optimality. Also, the effectiveness of KKT error based stopping criterion is demonstrated.