Clouds, p-boxes, fuzzy sets, and other uncertainty representations in higher dimensions

Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information

Uncertainty modeling in higher dimensions

Moderne Design Probleme stellen Ingenieure vor mehrere elementare Aufgaben. 1) Das Design muss die angestrebten Funktionalitäten aufweisen. 2) Es muss optimal sein in Hinsicht auf eine vorgegebene Zielfunktion. 3) Schließlich muss das Design abgesichert sein gegen Unsicherheiten, die nicht zu Versagen des Designs führen dürfen. All diese Aufgaben lassen sich unter dem Begriff der robusten Design Optimierung zusammenfassen und verlangen nach computergestützten Methoden, die Unsicherheitsmodellierung und Design Optimierung in sich vereinen. Unsicherheitsmodellierung enthält einige fundamentale Herausforderungen: Der Rechenaufwand darf gewisse Grenzen nicht überschreiten; unbegründete Annahmen müssen so weit wie möglich vermieden werden. Die beiden kritischsten Probleme betreffen allerdings den Umgang mit unvollständiger stochastischer Information und mit hoher Dimensionalität. Der niedrigdimensionale Fall ist gut erforscht, und es existieren diverse Methoden, auch unvollständige Informationen zu verarbeiten. In höheren Dimensionen hingegen ist die Anzahl der Möglichkeiten derzeit sehr begrenzt. Ungenauigkeit und Unvollständigkeit von Daten kann schwerwiegende Probleme verursachen - aber die Lage ist nicht hoffnungslos. In dieser Dissertation zeigen wir, wie man den hochdimensionalen Fall mit Hilfe von "Potential Clouds" in ein eindimensionales Problem übersetzt. Dieser Ansatz führt zu einer Unsicherheitsanalyse auf Konfidenzregionen relevanter Szenarien mittels einer Potential Funktion. Die Konfidenzregionen werden als Nebenbedingungen in einem Design Optimierungsproblem formuliert. Auf diese Weise verknüpfen wir Unsicherheitsmodellierung und Design Optimierung, wobei wir außerdem eine adaptive Aktualisierung der Unsicherheitsinformationen ermöglichen. Abschließend wenden wir unsere Methode in zwei Fallstudien an, in 24, bzw. in 34 Dimensionen.Modern design problems impose multiple major tasks an engineer has to accomplish. 1) The design should account for the designated functionalities. 2) It should be optimal with respect to a given design objective. 3) Ultimately the design must be safeguarded against uncertain perturbations which should not cause failure of the design. These tasks are united in the problem of robust design optimization giving rise to the development of computational methods for uncertainty modeling and design optimization, simultaneously. Methods for uncertainty modeling face some fundamental challenges: The computational effort should not exceed certain limitations; unjustified assumptions must be avoided as far as possible. However, the most critical issues concern the handling of incomplete information and of high dimensionality. While the low dimensional case is well studied and several methods exist to handle incomplete information, in higher dimensions there are only very few techniques. Imprecision and lack of sufficient information cause severe difficulties - but the situation is not hopeless. In this dissertation, it is shown how to transfer the high-dimensional to the one-dimensional case by means of the potential clouds formalism. Using a potential function, this enables a worst-case analysis on confidence regions of relevant scenarios. The confidence regions are weaved into an optimization problem formulation for robust design as safety constraints. Thus an interaction between optimization phase and worst-case analysis is modeled which permits a posteriori adaptive information updating. Finally, we apply our approach in two case studies in 24 and 34 dimensions, respectively

SensorCloud: Towards the Interdisciplinary Development of a Trustworthy Platform for Globally Interconnected Sensors and Actuators

Although Cloud Computing promises to lower IT costs and increase users' productivity in everyday life, the unattractive aspect of this new technology is that the user no longer owns all the devices which process personal data. To lower scepticism, the project SensorCloud investigates techniques to understand and compensate these adoption barriers in a scenario consisting of cloud applications that utilize sensors and actuators placed in private places. This work provides an interdisciplinary overview of the social and technical core research challenges for the trustworthy integration of sensor and actuator devices with the Cloud Computing paradigm. Most importantly, these challenges include i) ease of development, ii) security and privacy, and iii) social dimensions of a cloud-based system which integrates into private life. When these challenges are tackled in the development of future cloud systems, the attractiveness of new use cases in a sensor-enabled world will considerably be increased for users who currently do not trust the Cloud.Comment: 14 pages, 3 figures, published as technical report of the Department of Computer Science of RWTH Aachen Universit

A methodology for controlling the consequences of demand variability in the design of manufacturing systems

Today's unprecedented demand changes flood the global market. Staying competitive is now a matter of responding quickly and cost-effectively to variability. To address this paradigm, flexibility is a key aspect to tackle. Studies show that integrating flexibility in design of systems increases their performance by 25%, yet application procedures are still not very well established. This dissertation proposes a solution methodology for this problem. Aiming control of demand variability consequences, an integrated approach of optimization, screening, and simulation modelling has been developed. Applied to a case study in the furniture manufacturing industry, the methodology highlighted numerous opportunities of improvement in the manufacturing site. Indeed, by applying a flexible design, the overall performance goals were reached and a plan of action was initiated.The results support the proposed methodology as a viable solution for the problem addressed, nevertheless future success involves more than the pure application of this procedure, as flexibility is also a way of thinking

An Integrated Multi-Time-Scale Modeling for Solar Irradiance Forecasting Using Deep Learning

For short-term solar irradiance forecasting, the traditional point forecasting methods are rendered less useful due to the non-stationary characteristic of solar power. The amount of operating reserves required to maintain reliable operation of the electric grid rises due to the variability of solar energy. The higher the uncertainty in the generation, the greater the operating-reserve requirements, which translates to an increased cost of operation. In this research work, we propose a unified architecture for multi-time-scale predictions for intra-day solar irradiance forecasting using recurrent neural networks (RNN) and long-short-term memory networks (LSTMs). This paper also lays out a framework for extending this modeling approach to intra-hour forecasting horizons thus, making it a multi-time-horizon forecasting approach, capable of predicting intra-hour as well as intra-day solar irradiance. We develop an end-to-end pipeline to effectuate the proposed architecture. The performance of the prediction model is tested and validated by the methodical implementation. The robustness of the approach is demonstrated with case studies conducted for geographically scattered sites across the United States. The predictions demonstrate that our proposed unified architecture-based approach is effective for multi-time-scale solar forecasts and achieves a lower root-mean-square prediction error when benchmarked against the best-performing methods documented in the literature that use separate models for each time-scale during the day. Our proposed method results in a 71.5% reduction in the mean RMSE averaged across all the test sites compared to the ML-based best-performing method reported in the literature. Additionally, the proposed method enables multi-time-horizon forecasts with real-time inputs, which have a significant potential for practical industry applications in the evolving grid.Comment: 19 pages, 12 figures, 3 tables, under review for journal submissio