Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Online Model Learning of Buildings Using Stochastic Hybrid Systems Based on Gaussian Processes

Dynamical models are essential for model-based control methodologies which allow smart buildings to operate autonomously in an energy and cost efficient manner. However, buildings have complex thermal dynamics which are affected externally by the environment and internally by thermal loads such as equipment and occupancy. Moreover, the physical parameters of buildings may change over time as the buildings age or due to changes in the buildings’ configuration or structure. In this paper, we introduce an online model learning methodology to identify a nonparametric dynamical model for buildings when the thermal load is latent (i.e., the thermal load cannot be measured). The proposed model is based on stochastic hybrid systems, where the discrete state describes the level of the thermal load and the continuous dynamics represented by Gaussian processes describe the thermal dynamics of the air temperature. We demonstrate the evaluation of the proposed model using two-zone and five-zone buildings. The data for both experiments are generated using the EnergyPlus software. Experimental results show that the proposed model estimates the thermal load level correctly and predicts the thermal behavior with good performance

Data driven discovery of cyber physical systems

Cyber-physical systems embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, and intelligent manufacturing. Cyber-physical systems have proved resistant to modeling due to their intrinsic complexity arising from the combination of physical and cyber components and the interaction between them. This study proposes a general framework for discovering cyber-physical systems directly from data. The framework involves the identification of physical systems as well as the inference of transition logics. It has been applied successfully to a number of real-world examples. The novel framework seeks to understand the underlying mechanism of cyber-physical systems as well as make predictions concerning their state trajectories based on the discovered models. Such information has been proven essential for the assessment of the performance of cyber- physical systems; it can potentially help debug in the implementation procedure and guide the redesign to achieve the required performance

Regularized System Identification

This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book

Uma avaliação crítica sobre técnicas baseadas em PCA para detecção de falhas em processos da indústria química

The aim of this dissertation was to study, develop and implement chemical process monitoring systems. In order to understand the limitations of Data Driven modeling techniques, classical techniques based on Principal Component Analysis (PCA) and related procedures were adopted as a starting point. It was sought to build a critical view of the classical methods of process monitoring. Data Driven models are quite limited, since previously learned models do not fit necessarily well new operating regions, whose data were not available during the modeling phase. In addition, it is possible to conclude that the techniques based on data currently available, such as PCA and its variants, do not have the capacity to actually model the dynamic behavior of a process. This was the main motivation for the study of Recurrence Plots. Based on the concept of recurrence, a new technique was developed to monitor processes with multiple operational points. A new control chart was proposed to monitor processes with multiple operation points, based on the Frobenius Norm. Many other aspects related to process monitoring, such as variable selection, preprocessing and removal of spurious values, were not addressed in this work, but are of fundamental importance for industrial application. Finally, it is important to note that, although the proposed monitoring methodology has been inspired by the concept of recurrence, it, in fact, is not able to reconstruct the phase space of the process.O objetivo desta dissertação foi estudar, desenvolver e implementar sistemas de monitoramento de processos químicos. Para compreender as limitações das técnicas de modelagem baseadas em dados, adotaram-se como ponto de partida as técnicas clássicas, como a Análise de Componentes Principais (PCA) e técnicas correlatas. Buscou-se construir uma visão crítica dos métodos clássicos usados para monitoramento de processos. Modelos baseados em dados são bastante limitados, já que modelos previamente aprendidos não se adaptam necessariamente bem a novas regiões de operação, cujos dados não estavam disponíveis durante a fase de modelagem. Além disso, é possível concluir que as técnicas baseadas em dados disponíveis atualmente, como PCA e suas variantes, não apresentam capacidade de realmente modelar o comportamento dinâmico de um processo. Esta foi a principal motivação para o estudo dos Gráficos de Recorrência. A partir do conceito de recorrência, foi desenvolvida uma nova técnica para monitoramento de processos com múltiplos pontos operacionais. Foi proposta uma nova carta de controle para acompanhamento de processos com múltiplos pontos de operação, fundamentada na Norma de Frobenius. Muitos outros aspectos relacionados ao tema de monitoramento, tais como seleção de variáveis, preprocessamento e remoção de valores espúrios, não foram abordados no trabalho, mas são de fundamental importância para a aplicação industrial. Finalmente, é importante ressaltar que, embora a metodologia de monitoramento proposta tenha sido inspirada no conceito de recorrência, ela, de fato, não é capaz de reconstruir o espaço de fases do processo