III: Small: From Real-Time Sensor Data Streams to Continuous Data Fields Models: Formal Foundations and Computational Challenges

如今，大量传感器数据流是由高频和近实时的传感器数据自动收集产生的。该项目旨在通过使用一组建立现场代数的运算符，以现场数据模型的形式创建一个总体表示，从而提高实时流数据、历史数据流和模型模拟的分析潜力。例如，最好把场解释为磁场；磁场中每个点的磁力都可以确定，因此磁场被认为是连续的。同样，空气污染或洪水等环境现象在空间和时间上被认为是连续的，尽管它们是在有限的、离散的时空位置用传感器采样的。该项目开发了场代数，这是一种直观的，但数学上定义的形式主义，将现实世界的现象表示为场，并将分析需求表示为对场的规范操作。现场模型再次将现象表示为连续实体，并且该实现隐藏了其时空连续性是基于实时测量流的动态计算的事实。将传感器数据流扩展到领域是变革性的，因为很少有领域科学家对单个传感器的读数感兴趣。允许科学家使用高级抽象将显著增强他们的分析任务，例如发现对现实世界中发生的变化、趋势或意外事件的见解。该项目将在数学上整合字段和数据流，以便两者之间的映射得到很好的定义。现场数据模型是由一个创新的计算框架的发展来补充的，该计算框架用于综合和分析基于大量高通量、实时传感器数据流的现场，并用于创建动态的连续表示。该框架提供了新颖的算法，以确保现场操作人员能够吸收大量传感器数据流的吞吐量，同时仍然可以近乎实时地计算复杂的分析结果。该项目将使我们能够在极端天气事件、环境灾害或化学事故等情况下立即作出反应，并根据准确及时的信息组织响应工作，从而造福社会；这将有助于更好地保护公众利益。该项目的研究通过将传感器数据流抽象为地理字段，为传感器数据流提供了正式的基础，并建立了一个可扩展的计算框架，可以在大量传感器数据流上近乎实时地计算现场操作员。本文对具有域递归定义和一组域算子的域代数进行了形式化。领域代数和数据流在它们的数学基础水平上正式集成。形式域代数作为数据类型层次结构实现，并与流数据模型集成。同时，开发了一个计算框架，通过计算组件扩展数据流引擎，以基于递归或转置字段定义来估计时空字段，并对字段上的复杂谓词进行评估，为实时和历史字段的共同分析奠定了基础。该项目的成果将通过科学出版物、开源软件以及在线培训教程和课程进行分发。该项目的网站（https://silvianittel.wordpress.com/from-streams-to-fields-nsf/）将提供对该项目的结果的访问。

Massive sensor data streams are created from the automatic collection of sensor data in high frequency and in near real-time today. This project aims to advance the analytical potential of live-streamed data, historical data streams, and model simulations by creating an overarching representation in the form of the field data model with a set of operators that establish the field algebra. A field is best explained as, for example, a magnetic field; the magnetic force can be determined for each point in a magnetic field and the field is therefore considered to be continuous. Similarly, environmental phenomena such as air pollution or flooding are considered continuous in space and time although they are sampled at limited, discrete time-space locations with sensors. This project develops the field algebra, which is an intuitive, yet mathematically defined formalism to represent real-world phenomena as fields and to express analytical needs as canonical operations over fields. The field model represents phenomena as continuous entities again, and the implementation hides the fact that their spatio-temporal continuity is calculated on-the-fly based on real-time measurements streams. Extending sensor data streams to fields is transformative, as rarely a domain scientist is interested in the readings of individual sensors. Allowing scientists to work with high-level abstractions will significantly enhance their analytical tasks such as finding insights about changes, trends, or unexpected events happening in the real world. The project will integrate fields and data streams mathematically so that mappings between both are well defined. The field data model is complemented by the development of an innovative computational framework for synthesizing and analyzing fields based on very large numbers of high throughput, real-time sensor data streams, and for creating continuous representations on-the-fly. This framework provides novel algorithms to assure that the field operators can absorb the throughput of very large numbers of sensor data streams, yet still compute complex analytical results in near real-time. This project will benefit our society by enabling us to react to situations such as extreme weather events, environmental disasters or chemical accidents immediately, and organize response effort based on accurate and timely information; this will help to protect the public interests better. The research in this project develops a formal foundation for sensor data streams by abstracting them as geographic fields, and a scalable computational framework that computes field operators on massive numbers of sensor data streams in near real-time. In this research, the field algebra, with a recursive definition of fields and a set of field operators are formalized. The field algebra and data streams are formally integrated on the level of their mathematical foundations. The formal field algebra is implemented as a data type hierarchy and integrated with stream data models. At the same time, a computational framework is developed that extends data stream engines with computational components to estimate spatio-temporal fields based on recursive or transposed field definitions, and the evaluation of complex predicates over fields, which lays the foundation for co-analyzing live and historic fields. The results of this project will be distributed via scientific publications, open source software, and online training tutorials and classes. The project web site (https://silvianittel.wordpress.com/from-streams-to-fields-nsf/) will provide access to the results of this project.