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

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

An Introduction to MultiAgent Systems.

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

Bibliographical review on reconfigurable fault-tolerant control systems

A robust recursive zonotopic set-membership approach for remaining useful life forecasting with application to linear parameter-varying systems is proposed in this paper. The proposed approach addresses systems with degraded components formulated as a system-level prognostics problem. Thus, the critical degraded components of the system are augmented to the states resulting a nonlinear system that is reformulated as a linear parameter-varying model. Hence, joint estimation of states and parameters is adopted in a zonotopic set-membership scheme with an optimal linear matrix inequality-based tuning and assuming unknown-but-bounded noises and uncertainties. As a result, a recursive zonotopic set-membership approach is proposed for remaining useful life forecasting based on the prediction of the failure precursors of degraded systems. Finally, this approach is tested on a DC-DC converter case study with unknown degradation behaviors, and the obtained results show the estimation and the forecasting accuracy of this methodology. 

Recursive zonotopic set-membership approach for system-level prognostics with application to linear parameter-varying systems.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/acs.2878

To the Special Issue (Section) “Fault Diagnosis and Fault‐Tolerant Control of Wind Turbine Systems”

This chapter presents a sensor placement method for the classifier-based approaches for leak localization in water distribution networks introduced in the previous chapter. The proposed approach formulates the sensor placement problem as a binary optimization problem. Because of the complexity of the problem, it is solved by applying genetic algorithms. In order to reduce the number of sensor configurations to test, a binary matrix that identifies pairs of sensors providing similar information is added as a constraint. The sensors are placed in an optimal way, which maximizes the accuracy of the leak localization . The proposed approach is first illustrated by means of the application to an academic example based on the reduced version of the Hanoi water distribution network . A more realistic case study is then proposed based on the Limassol district metered area.

Sensor Placement for Classifier-Based Leak Localization in Water Distribution Networks

This work describes and validate a Linear Parameter Varying (LPV) model of a real benchmark of wind power system. With a nonlinear model of this process, the use of identification and control concepts for linear model as developed in the literature isn't useful to be used. So that, the nonlinear systems are approximated to Linear Time Invariant (LTI) systems, that is a local approximation of real system. To take account of the nonlinearity and using the linear approaches developed, a linear parameter varying modeling is required. The nonlinear model is transformed to an LPV one using the automated generation method for affine LPV representations. This method consists of generating an LPV model where the nonlinearities are hidden in the vector of parameters. Then, this transformation method is applied to a wind turbine system to get an LPV model for this benchmark system. Finally, the implementation of this LPV benchmark model on Matlab is done and good results are obtained since the LPV simulation responses achieve the nonlinear system model ones that prove the effectiveness and performance of this modeling approach.

Validation of wind turbine LPV model

This paper presents a machine learning method for optimal pressure sensor placement in water distribution networks. The proposed approach considers annealing meta-heuristics, and it is focused on the optimal placement of the sensors to perform leak localization. Unlike other works, this method considers a limited number of sensors to be placed and some restrictions on critical nodes that can be excluded or preselected. The approach is based on minimizing a cost function; this cost function is assigned as the leak location error, which varies depending on the subset of nodes where the sensors are assigned and the configuration of the leak location method. A leak localization technique based on k-NN classifiers was used, and during the minimization of the cost function, classifier hyperparameters were simultaneously optimized. The proposed method was tested on the Hanoi water distribution network programmed in MATLAB.

Vicenç Puig

Papers

Recursive zonotopic set-membership approach for system-level prognostics with application to linear parameter-varying systems.

To the Special Issue (Section) “Fault Diagnosis and Fault‐Tolerant Control of Wind Turbine Systems”

Sensor Placement for Classifier-Based Leak Localization in Water Distribution Networks

Validation of wind turbine LPV model

Pressure Sensor Placement for Leak Localization Using Simulated Annealing with Hyperparameter Optimization