Online tracking of a drifting parameter of a time series

We propose an online algorithm for tracking a multivariate time-varying parameter of a time series. The algorithm is driven by a gain function. Under assumptions on the gain function, we derive uniform error bounds on the tracking algorithm in terms of chosen step size for the algorithm and on the variation of the parameter of interest. We give examples of a number of different variational setups for the parameter where our result can be applied, and we also outline how appropriate gain functions can be constructed. We treat in some detail the tracking of time varying parameters of an AR($d$) model as a particular application of our method

Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control

Simultaneously accurate and reliable tracking control for quadrotors in complex dynamic environments is challenging. As aerodynamics derived from drag forces and moment variations are chaotic and difficult to precisely identify, most current quadrotor tracking systems treat them as simple `disturbances' in conventional control approaches. We propose a novel, interpretable trajectory tracker integrating a Distributional Reinforcement Learning disturbance estimator for unknown aerodynamic effects with a Stochastic Model Predictive Controller (SMPC). The proposed estimator `Constrained Distributional Reinforced disturbance estimator' (ConsDRED) accurately identifies uncertainties between true and estimated values of aerodynamic effects. Simplified Affine Disturbance Feedback is used for control parameterization to guarantee convexity, which we then integrate with a SMPC. We theoretically guarantee that ConsDRED achieves at least an optimal global convergence rate and a certain sublinear rate if constraints are violated with an error decreases as the width and the layer of neural network increase. To demonstrate practicality, we show convergent training in simulation and real-world experiments, and empirically verify that ConsDRED is less sensitive to hyperparameter settings compared with canonical constrained RL approaches. We demonstrate our system improves accumulative tracking errors by at least 70% compared with the recent art. Importantly, the proposed framework, ConsDRED-SMPC, balances the tradeoff between pursuing high performance and obeying conservative constraints for practical implementationsComment: 16 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2205.0715

Sensitivity and discovery potential of the proposed nEXO experiment to neutrinoless double beta decay

The next-generation Enriched Xenon Observatory (nEXO) is a proposed experiment to search for neutrinoless double beta ($0\nu\beta\beta$) decay in $^{136}$Xe with a target half-life sensitivity of approximately $10^{28}$ years using $5\times10^3$ kg of isotopically enriched liquid-xenon in a time projection chamber. This improvement of two orders of magnitude in sensitivity over current limits is obtained by a significant increase of the $^{136}$Xe mass, the monolithic and homogeneous configuration of the active medium, and the multi-parameter measurements of the interactions enabled by the time projection chamber. The detector concept and anticipated performance are presented based upon demonstrated realizable background rates.Comment: v2 as publishe

A Stability Principle for Learning under Non-Stationarity

We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while keeping the cumulative bias within an acceptable range relative to the stochastic error. Our theory showcases the adaptability of this approach to unknown non-stationarity. The regret bound is minimax optimal up to logarithmic factors when the population losses are strongly convex, or Lipschitz only. At the heart of our analysis lie two novel components: a measure of similarity between functions and a segmentation technique for dividing the non-stationary data sequence into quasi-stationary pieces.Comment: 47 pages, 1 figur

Power System Transients: Impacts of Non-Ideal Sensors on Measurement-Based Applications

The power system is comprised of thousands of lines, generation sources, transformers, and other equipment responsible for servicing millions of customers. Such a complex apparatus requires constant monitoring and protection schemes capable of keeping the system operational, reliable, and resilient. To achieve these goals, measurement is a critical role in the continued functionality of the power system. However, measurement devices are never completely reliable, and are susceptible to inherent irregularities; imparting potentially misleading distortions on measurements containing high-frequency components. This dissertation analyzes some of these effects, as well as the way they may impact certain applications in the grid that utilize these kinds of measurements. This dissertation first presents background on existing measurement technologies currently in use in the power grid, with extra emphasis placed on point-on-wave (PoW) sensors, those designed to capture oscillographic records of voltage and current signals. Next, a waveform “playback” system, developed at Oak Ridge National Laboratory’s Distributed Energy Communications \& Control (DECC) laboratory was used for comparisons between various line-post-monitor PoW sensors when subjected to different high-frequency current disturbances. Each of the three sensors exhibited unique quirks in these spectral regions, both in terms of harmonic magnitude and phase angle. A goodness-of-fit metric for comparing an ideal reference sensor with the test sensors was adopted from the literature and showed the extremes to which two test sensors vastly under performed when compared to the third. The subsequent chapter analyzes these behaviors under a statistical lens, using kernel density estimation to fit probability density functions (PDFs) to error distributions at specific harmonic frequencies resulting from sensor frequency response distortions. The remaining two chapters of the dissertation are concerned with resultant effects on applications that require high-frequency transient data. First, a detection algorithm is presented, and its performance when subjected to statistical errors inherent in these sensors is quantified. The dissertation culminates with a study on an artificial intelligence (AI) technique for estimating the location of capacitor switching transients, as well as learning prediction intervals that indicate the level of uncertainty present in the data caused by sensor frequency response irregularities

Improving Hoeffding Trees

Modern information technology allows information to be collected at a far greater rate than ever before. So fast, in fact, that the main problem is making sense of it all. Machine learning offers promise of a solution, but the field mainly focusses on achieving high accuracy when data supply is limited. While this has created sophisticated classification algorithms, many do not cope with increasing data set sizes. When the data set sizes get to a point where they could be considered to represent a continuous supply, or data stream, then incremental classification algorithms are required. In this setting, the effectiveness of an algorithm cannot simply be assessed by accuracy alone. Consideration needs to be given to the memory available to the algorithm and the speed at which data is processed in terms of both the time taken to predict the class of a new data sample and the time taken to include this sample in an incrementally updated classification model. The Hoeffding tree algorithm is a state-of-the-art method for inducing decision trees from data streams. The aim of this thesis is to improve this algorithm. To measure improvement, a comprehensive framework for evaluating the performance of data stream algorithms is developed. Within the framework memory size is fixed in order to simulate realistic application scenarios. In order to simulate continuous operation, classes of synthetic data are generated providing an evaluation on a large scale. Improvements to many aspects of the Hoeffding tree algorithm are demonstrated. First, a number of methods for handling continuous numeric features are compared. Second, tree prediction strategy is investigated to evaluate the utility of various methods. Finally, the possibility of improving accuracy using ensemble methods is explored. The experimental results provide meaningful comparisons of accuracy and processing speeds between different modifications of the Hoeffding tree algorithm under various memory limits. The study on numeric attributes demonstrates that sacrificing accuracy for space at the local level often results in improved global accuracy. The prediction strategy shown to perform best adaptively chooses between standard majority class and Naive Bayes prediction in the leaves. The ensemble method investigation shows that combining trees can be worthwhile, but only when sufficient memory is available, and improvement is less likely than in traditional machine learning. In particular, issues are encountered when applying the popular boosting method to streams

Influent generator : towards realistic modelling of wastewater flowrate and water quality using machine-learning methods

Depuis que l'assainissement des eaux usées est reconnu comme un des objectifs de développement durable des Nations Unies, le traitement et la gestion des eaux usées sont devenus plus importants que jamais. La modélisation et la digitalisation des stations de récupération des ressources de l'eau (StaRRE) jouent un rôle important depuis des décennies, cependant, le manque de données disponibles sur les affluents entrave le développement de la modélisation de StaRRE. Cette thèse vis e à faire progresser la modélisation des systèmes d'assainissement en général, et en particulier en ce qui concerne la génération dynamique des affluents. Dans cette étude, différents générateurs d'affluent (GA), qui peuvent fournir un profil d'affluent dynamique, ont été proposés, optimisés et discutés. Les GA développés ne se concentrent pas seulement sur le débit, les solides en suspension et la matière organique, mais également sur les substances nutritives telles que l'azote et le phosphore. En outre, cette étude vise à adapter les GA à différentes applications en fonction des différentes exigences de modélisation. Afin d'évaluer les performances des GA d'un point de vue général, une série de critères d'évaluation de la qualité du modèle est décrite. Premièrement, pour comprendre la dynamique des affluents, une procédure de caractérisation des affluents a été développée et testée pour une étude de cas à l'échelle pilote. Ensuite, pour générer différentes séries temporelles d'affluent, un premier GA a été développé. La méthodologie de modélisation est basée sur l'apprentissage automatique en raison de ses calculs rapides, de sa précision et de sa capacité à traiter les mégadonnées. De plus, diverses versions de ce GA ont été appliquées pour différents cas optimisées en fonction des disponibilités d'études et ont été des données (la fréquence et l'horizon temporel), des objectifs et des exigences de précision. Les résultats démontrent que : i) le modèle GA proposé peut être utilisé pour générer d'affluents dynamiques réalistes pour différents objectifs, et les séries temporelles résultantes incluent à la fois le débit et la concentration de polluants avec une bonne précision et distribution statistique; ii) les GA sont flexibles, ce qui permet de les améliorer selon différents objectifs d'optimisation; iii) les GA ont été développés en considérant l'équilibre entre les efforts de modélisation, la collecte de données requise et les performances du modèle. Basé sur les perspectives de modélisation des StaRRE, l'analyse des procédés et la modélisation prévisionnelle, les modèles de GA dynamiques peuvent fournir aux concepteurs et aux modélisateurs un profil d'affluent complet et réaliste, ce qui permet de surmonter les obstacles liés au manque de données d'affluent. Par conséquent, cette étude a démontré l'utilité des GA et a fait avancer la modélisation des StaRRE en focalisant sur l'application de méthodologies d'exploration de données et d'apprentissage automatique. Les GA peuvent donc être utilisés comme outil puissant pour la modélisation des StaRRE, avec des applications pour l'amélioration de la configuration de traitement, la conception de procédés, ainsi que la gestion et la prise de décision stratégique. Les GA peuvent ainsi contribuer au développement de jumeaux numériques pour les StaRRE, soit des système intelligent et automatisé de décision et de contrôle.Since wastewater sanitation is acknowledged as one of the sustainable development goals of the United Nations, wastewater treatment and management have been more important then ever. Water Resource Recovery Facility (WRRF) modelling and digitalization have been playing an important role since decades, however, the lack of available influent data still hampers WRRF model development. This dissertation aims at advancing the field of wastewater systems modelling in general, and in particular with respect to the dynamic influent generation. In this study, different WRRF influent generators (IG), that can provide a dynamic influent flow and pollutant concentration profile, have been proposed, optimized and discussed. The developed IGs are not only focusing on flowrate, suspended solids, and organic matter, but also on nutrients such as nitrogen and phosphorus. The study further aimed at adapting the IGs to different case studies, so that future users feel comfortable to apply different IG versions according to different modelling requirements. In order to evaluate the IG performance from a general perspective, a series of criteria for evaluating the model quality were evaluated. Firstly, to understand the influent dynamics, a procedure of influent characterization has been developed and experimented at pilot scale. Then, to generate different realizations of the influent time series, the first IG was developed and a data-driven modelling approach chosen, because of its fast calculations, its precision and its capacity of handling big data. Furthermore, different realizations of IGs were applied to different case studies and were optimized for different data availabilities (frequency and time horizon), objectives, and modelling precision requirements. The overall results indicate that: i) the proposed IG model can be used to generate realistic dynamic influent time series for different case studies, including both flowrate and pollutant concentrations with good precision and statistical distribution; ii) the proposed IG is flexible and can be improved for different optimization objectives; iii) the IG model has been developed by considering the balance between modelling efforts, data collection requirements and model performance. Based on future perspectives of WRRF process modelling, process analysis, and forecasting, the dynamic IG model can provide designers and modellers with a complete and realistic influent profile and this overcomes the often-occurring barrier of shortage of influent data for modelling. Therefore, this study demonstrated the IGs' usefulness for advanced WRRF modelling focusing on the application of data mining and machine learning methodologies. It is expected to be widely used as a powerful tool for WRRF modelling, improving treatment configurations and process designs, management and strategic decision-making, such as when transforming a conventional WRRF to a digital twin that can be used as an intelligent and automated system