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从高频且近乎实时的传感器数据自动收集中产生的。该项目旨在通过创建具有建立字段代数的一组运算符的字段数据模型形式的总体表示来提高实时流数据、历史数据流和模型模拟的分析潜力。例如，最好地将场解释为磁场；可以确定磁场中每个点的磁力，因此该场被认为是连续的。同样，空气污染或洪水等环境现象被认为在空间和时间上是连续的，尽管它们是用传感器在有限的、离散的时空位置进行采样的。这个项目开发了域代数，它是一种直观的、但在数学上定义的形式主义，将现实世界的现象表示为域，并将分析需求表达为域上的规范运算。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动态计算的事实。将传感器数据流扩展到领域具有变革性，因为很少有领域科学家对单个传感器的读数感兴趣。允许科学家进行高层次的抽象工作将显著增强他们的分析任务，例如对真实世界中发生的变化、趋势或意外事件进行洞察。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。现场数据模型的补充是开发一种创新的计算框架，用于基于大量高吞吐量、实时传感器数据流合成和分析场，并用于动态创建连续表示。该框架提供了新的算法，以确保现场操作员能够吸收大量传感器数据流的吞吐量，同时仍能近实时地计算复杂的分析结果。这一项目将造福我们的社会，使我们能够立即对极端天气事件、环境灾难或化学事故等情况做出反应，并根据准确和及时的信息组织应对工作，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场，为传感器数据流建立了一个形式化的基础，并建立了一个可扩展的计算框架，可以近实时地计算大量传感器数据流上的场算子。在这项研究中，形式化地定义了域的递归定义和域的运算符集。域代数和数据流在它们的数学基础上被正式地结合在一起。形式字段代数以数据类型层次结构的形式实现，并与流数据模型集成。同时，开发了一个计算框架，该框架扩展了数据流引擎的计算组件，以基于递归或转置的字段定义来估计时空场，并对场上的复杂谓词进行求值，为实时场和历史场的联合分析奠定了基础。该项目的成果将通过科学出版物、开放源码软件以及在线培训教程和课程分发。项目网站(https://silvianittel.wordpress.com/from-streams-to-fields-nsf/)将提供对该项目成果的访问。

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.