State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

Outer Trust-Region Method for Constrained Optimization

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the ""greediness phenomenon"" of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

An approach to multi-fidelity optimization of aeroengine compression systems

The aerodynamic design of turbomachinery presents the design optimisation community with a number of exquisite challenges. Chief among these are the size of the design space and the extent of discontinuity therein. This discontinuity can serve to limit the full exploitation of high-fidelity computational fluid dynamics (CFD): such codes require detailed geometric information often available only sometime after the basic configuration of the machine has been set by other means. The premise of this paper is that it should be possible to produce higher performing designs in less time by exploiting multi-fidelity techniques to effectively harness CFD earlier in the design process, specifically by facilitating its participation in configuration selection. The adopted strategy of local multi-fidelity correction, generated on demand, combined with a global search algorithm via an adaptive trust region is first tested on a modest, smooth external aerodynamic problem. Speed-up of an order of magnitude is demonstrated, comparable to established techniques applied to smooth problems. A number of enhancements aimed principally at effectively evaluating a wide range of configurations quickly is then applied to the basic strategy, and the emerging technique is tested on a generic aeroengine core compression system. A similar order of magnitude speed-up is achieved on this relatively large and highly discontinuous problem. A five-fold increase in the number of configurations assessed with CFD is observed. As the technique places constraints neither on the underlying physical modelling of the constituent analysis codes nor on first-order agreement between those codes, it has potential applicability to a range of multidisciplinary design challenges. © 2012 by Jerome Jarrett and Tiziano Ghisu.

监控式水下机械手及相关技术的研究

水下机械手作为水下机器人通用作业工具得到广泛地应用，目前水下机械手的主要操作方式为主从方式。虽然主从方式具有操作直观，灵活的特点，但难于完成需要精确定位，轨迹控制的水下作用，如海洋石油钻井平台导管架的检查作用。为了扩展水下机器人的作业能力，提高水下作业智能化程度，沈阳自动化所承担国家863课题“水下虚拟遥操作与监控机械手系统”关键技术的研究工作。作者参加了此课题的研究工作，以Schilling水下机械手为研究对象，深入研究机械手的作用功能，对机械手的逆运动学，焊缝空间轨迹规划作了深入的研究，形成本文阐述的主要内容。由于Schilling水下机械手各关节之间的连接参数中存在多个偏距，其运动学逆解不能简单由解析方式给出。机械手进行控制与轨迹规划等操作必须找到一种快速求解的方法。本篇文章得出一种基于信赖域法的机械手运动学逆解算法。由于该算法具有收敛速度快的特点，故可以被应用于在线求解机械手运动学逆解；由于没有直接求解二阶导数，故不存在奇异解的问题。经理论分析和实验证明该方法在解决水下监控机械手在线跟踪水下结构物空间轨迹的技术问题具有较好的效果。作为课题的实际应用背景的导管架焊缝曲面为一复杂的空间曲面。为了实现课题的研究目标，本课题不仅要求解焊缝的轨迹，而且要给出其法线方向。对于这样一个问题，用空间解析几何和微分几何方法是很难求解的，本文给出了一种基于B样条参数曲面及曲面求交的方法，具有速度快，通用性强的优点。

Analysis of full-waveform LiDAR data for classification of an orange orchard scene

Full-waveform laser scanning data acquired with a Riegl LMS-Q560 instrument were used to classify an orange orchard into orange trees, grass and ground using waveform parameters alone. Gaussian decomposition was performed on this data capture from the National Airborne Field Experiment in November 2006 using a custom peak-detection procedure and a trust-region-reflective algorithm for fitting Gauss functions. Calibration was carried out using waveforms returned from a road surface, and the backscattering coefficient c was derived for every waveform peak. The processed data were then analysed according to the number of returns detected within each waveform and classified into three classes based on pulse width and c. For single-peak waveforms the scatterplot of c versus pulse width was used to distinguish between ground, grass and orange trees. In the case of multiple returns, the relationship between first (or first plus middle) and last return c values was used to separate ground from other targets. Refinement of this classification, and further sub-classification into grass and orange trees was performed using the c versus pulse width scatterplots of last returns. In all cases the separation was carried out using a decision tree with empirical relationships between the waveform parameters. Ground points were successfully separated from orange tree points. The most difficult class to separate and verify was grass, but those points in general corresponded well with the grass areas identified in the aerial photography. The overall accuracy reached 91%, using photography and relative elevation as ground truth. The overall accuracy for two classes, orange tree and combined class of grass and ground, yielded 95%. Finally, the backscattering coefficient c of single-peak waveforms was also used to derive reflectance values of the three classes. The reflectance of the orange tree class (0.31) and ground class (0.60) are consistent with published values at the wavelength of the Riegl scanner (1550 nm). The grass class reflectance (0.46) falls in between the other two classes as might be expected, as this class has a mixture of the contributions of both vegetation and ground reflectance properties.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Preliminary leaf area index estimates from airborne small footprint full-waveform LiDAR data

This study has compared preliminary estimates of effective leaf area index (LAI) derived from fish-eye lens photographs to those estimated from airborne full-waveform small-footprint LiDAR data for a forest dataset in Australia. The full-waveform data was decomposed and optimized using a trust-region-reflective algorithm to extract denser point clouds. LAI LiDAR estimates were derived in two ways (1) from the probability of discrete pulses reaching the ground without being intercepted (point method) and (2) from raw waveform canopy height profile processing adapted to small-footprint laser altimetry (waveform method) accounting for reflectance ratio between vegetation and ground. The best results, that matched hemispherical photography estimates, were achieved for the waveform method with a study area-adjusted reflectance ratio of 0.4 (RMSE of 0.15 and 0.03 at plot and site level, respectively). The point method generally overestimated, whereas the waveform method with an arbitrary reflectance ratio of 0.5 underestimated the fish-eye lens LAI estimates.

Uma investigação da influência do parâmetro de barreira na solução do problema de fluxo de potência ótimo

Pós-graduação em Engenharia Elétrica - FEB

Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.