There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Economic Control of Quality of Manufactured Product.

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

ABSTRACT This research work draws insight on developing a novel digital hydraulic pitch system for a large-scale wind turbine. Digital hydraulic pitching can be appropriate for wind turbine application due to its high response, high power-to-weight ratio, and robustness. To perform digital pitch control, a machine learning-based robust digital pitch controller was designed and implemented in the developed real-time test setup. The proposed real-time test setup consist of sub-systems such as digital hydraulic system hardware, real-time interface, robust digital pitch controller, and 5 MW benchmark wind turbine model. Real-time testing was conducted on proposed controller using the developed test setup. Robustness test exhibited robust pitch control tracking when subjected to high wind gusts/fluctuations. In this test, the proposed controller reduced the pitch control error (mean absolute) by 68.10% and 51.75% when compared to feed forward and Elman controller, respectively. Subsequently, a power regulation test was performed on the proposed controller under real-time turbulence wind speed. Relative to the feed-forward and Elman controller, the proposed controller regulates power close to the rated value and improved the mean generator power by 3.39%, and 3.72%, respectively. A comparative study conducted with existing controllers (in the literature) demonstrate the superior performance of the proposed controller. This study reports that intelligent digital pitching action of proposed controller generates power close to rated power when compared to existing controllers in the literature.

Real-Time testing of novel robust digital pitch controller for digital hydraulic pitch system in wind turbine

Identifying multiple models from both static and dynamic data is an important problem in several engineering fields. Clustering based on Euclidean distance measure has been proposed to solve this problem. However, since Euclidean distance is not directly related to model fidelity, these approaches can lead to suboptimal results even when the number of models is known. In this work, through a three step algorithm that includes initialization, prediction error based fuzzy clustering and model rationalization, we evaluate the possibility of uncovering multiple model structures from data. The three step algorithm is also assessed for the identification of piecewise auto regressive exogenous systems with unknown number of models and their (unknown)orders. The basic approach can be extended for trend analysis and generalized principal component analysis.

Evaluation of prediction error based fuzzy model clustering approaches for multiple model learning

Interacting coalescence avalanches in a 2D droplet assembly

Optimum use of available energy sources is essential for cost effective and sustainable growth. Fuel cells - due to their ability in efficiently extracting energy from fuels - have gained considerable attention among the various energy conversion alternatives. Systems researchers working in the field of fuel cells have been focusing on optimal stack design and the attendant modeling aspects. In a power network where multiple fuel cell stacks combine together to achieve the required power, it is not enough to focus only on the optimal design of the stacks. While operating the stacks, the problem of optimal sharing of power between the different stacks in a power network is another important problem that needs to be addressed. This optimal power sharing problem is the focus of this paper. We will describe a novel solution approach for this optimization problem, which through prior off-line computations reduces the on-line optimization task to one of solving simple equations. Another major significance of this new approach is that unlike the conventional optimizers, global optimum is guaranteed using this approach. The proposed algorithm uses a data-based model between the voltage and current for optimization. To account for changes in the system characteristics with time, a model updater algorithm that updates the data-based model using newly available data and the previous model is proposed.

Optimal Power Sharing Control in Networked Fuel Cell Stacks

Though signed directed graphs (SDG) have been widely used for modeling control loops, due to lack of adequate understanding of SDG-based steady state process modeling, special and cumbersome methods are used to analyze control loops. In this article, we discuss a unified SDG model for control loops (proposed by Maurya et al. (2002 b ) ), in which both disturbances (sensor bias etc.) as well as structural faults (sensor failure etc.) can be easily modeled. Various fault scenarios such as external disturbances, sensor bias, controller failure etc. have been discussed. Two case studies are presented to show the utility of the SDG model for fault diagnosis. A tank-level control system is used as first case study. The second case study deals with fault diagnosis of a multi-stream controlled CSTR.

Raghunathan Rengaswamy

Papers

Real-Time testing of novel robust digital pitch controller for digital hydraulic pitch system in wind turbine

Evaluation of prediction error based fuzzy model clustering approaches for multiple model learning

Interacting coalescence avalanches in a 2D droplet assembly

Optimal Power Sharing Control in Networked Fuel Cell Stacks

Consistent malfunction diagnosis inside control loops using signed directed graphs