A note on the connection between nonextensive entropy and hh-derivative

In order to study as a whole the major part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus. This new entropy, $S_{h,h'}$, is proved to describe the non-extensive systems and recover several types of the well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann\,--\,Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.Comment: 6 pages, 1 figur

Apply Active Learning in Short-term Data-driven Building Energy Modeling

In the United States, the buildings sector accounted for about 41% of primary energy consumption. Building control and operation strategies have a great impact on building energy efficiency and the development of building-grid integration. For better building control, and for buildings to be better integrated with the grid operation, high fidelity building energy forecasting model that can be used for short-term and real-time operation is in great need. With the wide adoption of building automation system (BAS) and Internet of things (IoT), massive measurements from sensors and other sources are continuously collected which provide data on equipment and building operations. This provides a great opportunity for data-driven building energy modeling. However, data-driven approach is heavily dependent on data, while the collected operation data are often constrained to limited applicability (or termed as “bias” in this paper) because most of the building operation data are generated under limited operational modes, weather conditions, and very limited setpoints (often one or two fixed values, such as a constant zone temperature setpoint). For nonlinear systems, a data-driven model generated from biased data has poor scalabilities (when used for a different building) and extendibility (when used for different weather and operation conditions). The fact impedes the development of data-driven forecasting model as well as model-based control in buildings. The design of task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation is termed as active learning in machine learning. The purpose is to choose or generate informative training data, either to defy data bias or to reduce labeling cost (when doing experiments in building is too expensive). Research on applying active learning in building energy modeling is relatively unexplored. From the few existing researches, most of them only consider single operational setpoint, which is impractical for most real buildings where multiple setpoints in chillers, air handling units and air-conditioning terminals are used for building operation and control. Moreover, disturbances, especially weather and occupancy, in most cases are not considered. In this research, a nonlinear fractional factorial design combined with block design is applied as the active learning strategy to generate building operation (setpoints) schedule. The data generated on operation schedule will be used as training data for building energy modeling. The testbed is a virtual DOE reference large-size office building with hierarchical setpoints: zone temperature setpoint, supply air static pressure setpoint and chiller leaving water temperature setpoint. D-Optimal will be used as the nonlinear fractional factorial design algorithm, and its parameters are further compared and discussed. At the same time, block design will be applied to divide different weather and occupancy into four blocks. And D-Optimal design will be applied in each block, in which way the disturbance will be taken into consideration. Results show that compared with normal operation data and data generated by full factorial design, the proposed active learning method can increase model accuracy in validation and testing period, indicating its effectiveness to improve model generalization

The long-lasting optical afterglow plateau of short burst GRB 130912A

The short burst GRB 130912A was detected by Swift, Fermi satellites and several ground-based optical telescopes. Its X-ray light curve decayed with time normally. The optical emission, however, displayed a long term plateau, which is the longest one in current short GRB observations. In this work we examine the physical origin of the X-ray and optical emission of this peculiar event. We find that the canonical forward shock afterglow emission model can account for the X-ray and optical data self-consistently and the energy injection model that has been widely adopted to interpret the shallowly-decaying afterglow emission is not needed. We also find that the burst was born in a very-low density interstellar medium, consistent with the compact object merger model. Significant fractions of the energy of the forward shock have been given to accelerate the non-thermal electrons and amplify the magnetic fields (i.e., $\epsilon_{\rm e}\sim 0.37$ and $\epsilon_{\rm B}\sim 0.16$, respectively), which are much larger than those inferred in most short burst afterglow modeling and can explain why the long-lasting optical afterglow plateau is rare in short GRBs.Comment: 5 pages, 2 figure