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At least 739 records · Page 41

Next Generation System Analysis Model: Recently Added Features and Future Plans

To better enable informed decision-making regarding the back-end of the nuclear fuel cycle, the Integrated Waste Management System (IWMS) program within the U.S. Department of Energy, Office of Nuclear Energy (DOE-NE) has been sponsoring the development and application of system analysis tools capable of analyzing various system options for the management of spent nuclear fuel (SNF) and high-level radioactive waste (HLW).With these tools, IWMS architecture analyses are being conducted to support the future deployment of a comprehensive nuclear waste management system that considers all major back-end aspects of the nuclear fuel cycle (i.e., transportation, storage, and disposal). The Next Generation System Analysis Model (NGSAM) is an agent-based simulation software tool expressly designed to be capable of modeling features within various IWMS architectures. NGSAM imports data from Oak Ridge National Laboratory (ORNL)’s unified database (e.g., historic assembly information, thermal profiles for assembly heat, and at-reactor dry storage loadings) to ensure that each simulation initializes with a realistic representation of the state of commercial SNF in the U.S. Recent major enhancements implemented into NGSAM in the period since NGSAM was last presented at the WM2019 conference include: • Tracking of railroad escort car acquisition and buffer car acquisition • The addition of heavy haul truck (HHT) and barge routes for some sites, as well as support for user-defined inter-modal routes • Updates to the logic that checks the transportation cask thermal limit maps prior to package transport • An allocation method that predicts when reactor sites would pack assemblies from their spent fuel pools for dry storage, and prioritizes shipments directly from the pools of those reactor sites in the preceding periods (before the predicted loadings to dry storage), thus reducing the number of casks loaded into dry storage at reactor sites • The addition of “reactor site family” operational limits to restrict the number of loads of SNF taken from the pool and from dry storage at a given reactor site each year • Added support for multiple canister loading map options and packages with multiple compatible transportation overpacks • Updates to the handling of non-commercial SNF, including a new database that contains data to support the updates • Updates to allow analysis of hypothetical scenarios which include repackaging at reactor sites, e.g., for possible comparative analysis with other scenarios • Implementation of additional output reports, or modification of existing ones • The ability to generate and implement user edits via the NGSAM website • The ability to model loading SNF from pool storage at an interim storage facility (ISF) into dry storage at the ISF • The ability to model consolidating SNF from different existing storage containers at a DOE site into the same DOE standard canister • The ability to model transferring SNF casks from one transportation mode to another, e.g., from HHT to rail, referred to as transloading. These new features have improved NGSAM capabilities and users’ experience with the model. Preliminary NGSAM requirements for modeling advanced reactor fuels, reprocessing, treatment, and conditioning were considered, and this paper describes them at a high level. Other nuclear fuel cycle system analysis tools developed under sponsorship of DOE-NE, like the VISION code developed at Idaho National Laboratory, might be better suited for initial high-level analysis of those technologies and advanced fuel cycles. As technologies are developed and system concepts evolve, NGSAM could provide value by providing more detailed modeling of transport, storage, and disposal of spent fuel and wastes from advanced reactors and advanced fuel cycles at the fuel element and waste container level.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Machine Learning Digital Twin for Lithium Ion Battery State of Health Predictions

A digital twin system has been established to model the long term degradation of the state of health of lithium ion batteries. Two data streams result from the computational model of the system and from the physical experiment measurements. A machine learning pipeline has been developed at the nexus of these data streams. Leveraging the unique data sources in multiple transfer learning approaches has lead to the development of multiple cell specific machine learning digital twins. Our discussion on this first of its kind technology will cover challenges in data ingestion, scalability, architecture and orchestration, and research findings.

25 - ENERGY STORAGE↗

Clinical Decision Support - Concepts of Operation

We are entering a new era in space exploration to return to the moon and explore Mars. These ambitious goals will require significant changes to in-flight and habitat medical care due to constraints on mass, volume, power, crew time and medical evacuation capabilities. These constraints make it absolutely necessary to develop transformative solutions using new technologies. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) pushes the boundary of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit by identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses the gap Medical-701 within the Inflight Medical Conditions risk: Enhance medical capabilities within an exploration medical system. For long-duration, deep space missions, computational and data resources will play an important role in maintaining crew health, wellness and performance where the crew will need to be more self-reliant. The aim of the CDS project is to develop and provide recommended requirements for an in-vehicle CDSS that acts as an assistant for delivering optimal health and performance and medical care during exploration missions. The CDSS is envisioned as a software-based tool that will augment a crewmembers’ knowledge, skills and abilities to assist in decision-making and crew health and performance (CHP) management thus increasing CHP systems capabilities. The human interface will be context aware and lessen the cognitive load to assimilate and use information as well as combine large disparate data sets in such a manner that provides the crew with actionable insight to decisions related to crew medical, health and performance management. Crew autonomy will be provided through a CDS that presents knowledge and data in a context aware manner to augment a crew members’ knowledge, skills and abilities during the process of observation, orientation, decisions and action. The CDS project addresses the need for crew members to operate independently during long duration space exploration missions that require medical Levels of Care (LoC) V, the highest level specified by NASA-STD-3001 and described in more detail by the ExMC interpretation of LoC document (NASA/TM-2017-219290), where significant changes to in-flight and habitat medical care necessitate increasing crew autonomy in decision making and task performance. The CDS project will develop and test a series of iterative and increasingly more complex system prototypes. These annual demonstrations of the data system integration with the crew health and performance domain will inform exploration medical system requirements for an on-board Clinical Decision Support System (CDSS) through a series of use cases that guide CDS prototype functionality. CDS concepts are based on ExMC Concept of Operations documents (presented separately) and will highlight architecture extensibility to other more complex analyses and tests using core crew health and performance integrated data management, processing and visualization capabilities. This approach also establishes how externally developed analyses and approaches could be added to expand a clinical decision support system and thus highlight how a comprehensive system can be commercially and/or globally developed. The CDS project will build upon the concept of an integrated data management approach based on the Medical Data Architecture (MDA) project to more fully address challenges associated with in-flight and habitat medical, health and performance care due to constraints on mass, volume, power, crew time and medical evacuation capabilities required for medical LoC V. These requirements will be derived through systems engineering approaches and software prototype developments over the course of the multi-year CDS project to address crew health and performance decision-making and task performance, often autonomously executed by the crew, in a manner that is consistent with the appropriate medical level of care for the mission. This presentation will provide an overview of the vision for the CDS project and highlight the initial accomplishments in project planning, implementation and requirements identification in fiscal year 2020.

clinical decision support↗

Clinical Decision Support - Overview and Update

We are entering a new era in space exploration to return to the moon and explore Mars. These ambitious goals will require significant changes to in-flight and habitat medical care due to constraints on mass, volume, power, crew time and medical evacuation capabilities. These constraints make it absolutely necessary to develop transformative solutions using new technologies. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) pushes the boundary of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit by identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses the gap Medical-701 within the Inflight Medical Conditions risk: Enhance medical capabilities within an exploration medical system. For long-duration, deep space missions, computational and data resources will play an important role in maintaining crew health, wellness and performance where the crew will need to be more self-reliant. The aim of the CDS project is to develop and provide recommended requirements for an in-vehicle CDSS that acts as an assistant for delivering optimal health and performance and medical care during exploration missions. The CDSS is envisioned as a software-based tool that will augment a crewmembers’ knowledge, skills and abilities to assist in decision-making and crew health and performance (CHP) management thus increasing CHP systems capabilities. The human interface will be context aware and lessen the cognitive load to assimilate and use information as well as combine large disparate data sets in such a manner that provides the crew with actionable insight to decisions related to crew medical, health and performance management. Crew autonomy will be provided through a CDS that presents knowledge and data in a context aware manner to augment a crew members’ knowledge, skills and abilities during the process of observation, orientation, decisions and action. The CDS project addresses the need for crew members to operate independently during long duration space exploration missions that require medical Levels of Care (LoC) V, the highest level specified by NASA-STD-3001 and described in more detail by the ExMC interpretation of LoC document (NASA/TM-2017-219290), where significant changes to in-flight and habitat medical care necessitate increasing crew autonomy in decision making and task performance. The CDS project will develop and test a series of iterative and increasingly more complex system prototypes. These annual demonstrations of the data system integration with the crew health and performance domain will inform exploration medical system requirements for an on-board Clinical Decision Support System (CDSS) through a series of use cases that guide CDS prototype functionality. CDS concepts are based on ExMC Concept of Operations documents (presented separately) and will highlight architecture extensibility to other more complex analyses and tests using core crew health and performance integrated data management, processing and visualization capabilities. This approach also establishes how externally developed analyses and approaches could be added to expand a clinical decision support system and thus highlight how a comprehensive system can be commercially and/or globally developed. The CDS project will build upon the concept of an integrated data management approach based on the Medical Data Architecture (MDA) project to more fully address challenges associated with in-flight and habitat medical, health and performance care due to constraints on mass, volume, power, crew time and medical evacuation capabilities required for medical LoC V. These requirements will be derived through systems engineering approaches and software prototype developments over the course of the multi-year CDS project to address crew health and performance decision-making and task performance, often autonomously executed by the crew, in a manner that is consistent with the appropriate medical level of care for the mission. This presentation will provide an overview of the vision for the CDS project and highlight the initial accomplishments in project planning, implementation and requirements identification in fiscal year 2020.

clinical decision support system↗

Integrating Engineering Data Systems for NASA Spaceflight Projects

NASA has a large range of custom-built and commercial data systems to support spaceflight programs. Some of the systems are re-used by many programs and projects over time. Management and systems engineering processes require integration of data across many of these systems, a difficult problem given the widely diverse nature of system interfaces and data models. This paper describes an ongoing project to use a central data model with a web services architecture to support the integration and access of linked data across engineering functions for multiple NASA programs. The work involves the implementation of a web service-based middleware system called Data Aggregator to bring together data from a variety of systems to support space exploration. Data Aggregator includes a central data model registry for storing and managing links between the data in disparate systems. Initially developed for NASA's Constellation Program needs, Data Aggregator is currently being repurposed to support the International Space Station Program and new NASA projects with processes that involve significant aggregating and linking of data. This change in user needs led to development of a more streamlined data model registry for Data Aggregator in order to simplify adding new project application data as well as standardization of the Data Aggregator query syntax to facilitate cross-application querying by client applications. This paper documents the approach from a set of stand-alone engineering systems from which data are manually retrieved and integrated, to a web of engineering data systems from which the latest data are automatically retrieved and more quickly and accurately integrated. This paper includes the lessons learned through these efforts, including the design and development of a service-oriented architecture and the evolution of the data model registry approaches as the effort continues to evolve and adapt to support multiple NASA programs and priorities.

Carvalho, Robert E.↗

Neuromorphic Computing, Architectures, Models, and Applications. A Beyond-CMOS Approach to Future Computing, June 29-July 1, 2016, Oak Ridge, TN

The White House and Department of Energy have been instrumental in driving the development of a neuromorphic computing program to help the United States continue its lead in basic research into (1) Beyond Exascale—high performance computing beyond Moore’s Law and von Neumann architectures, (2) Scientific Discovery—new paradigms for understanding increasingly large and complex scientific data, and (3) Emerging Architectures—assessing the potential of neuromorphic and quantum architectures. Neuromorphic computing spans a broad range of scientific disciplines from materials science to devices, to computer science, to neuroscience, all of which are required to solve the neuromorphic computing grand challenge. In our workshop we focus on the computer science aspects, specifically from a neuromorphic device through an application. Neuromorphic devices present a very different paradigm to the computer science community from traditional von Neumann architectures, which raises six major questions about building a neuromorphic application from the device level. We used these fundamental questions to organize the workshop program and to direct the workshop panels and discussions. From the white papers, presentations, panels, and discussions, there emerged several recommendations on how to proceed.

97 MATHEMATICS AND COMPUTING↗

Engineering data management: Experience and projections

Experiences in developing a large engineering data management system are described. Problems which were encountered are presented and projected to future systems. Business applications involving similar types of data bases are described. A data base management system architecture proposed by the business community is described and its applicability to engineering data management is discussed. It is concluded that the most difficult problems faced in engineering and business data management can best be solved by cooperative efforts.

Jefferson, D. K.↗

Lightning Instrumentation at KSC

This report summarizes lightning phenomena with a brief explanation of lightning generation and lightning activity as related to KSC. An analysis of the instrumentation used at launching Pads 39 A&B for measurements of lightning effects is included with alternatives and recommendations to improve the protection system and upgrade the actual instrumentation system. An architecture for a new data collection system to replace the present one is also included. A novel architecture to obtain lightning current information from several sensors using only one high speed recording channel while monitoring all sensors to replace the actual manual lightning current recorders and a novel device for the protection system are described.

Colon, Jose L.↗

The problem analysis of data processing performance in nuclear power plant computerized information and control system - 288

This paper is based on the data processing performance problems of operating command delay and system display not updating real-time for nuclear power plant computerized information and control system. The plant computerized information and control system is responsible for monitoring and controlling the plant operation, and it is a key part in the plant DCS system. Its data processing performance will affect the operation stability of nuclear power plant. The architecture, hardware configuration and data communication for plant computerized information and control system among the different levels in DCS are described. The main reasons affecting data processing performance in different signal channels are analyzed according to the plant load test results. The CPU load curves for real time server and central processing server are displayed, although the detailed cause for operating command delay and system display not updating realtime are not found, central processing server load is heavier than real time server which remind us to analyze the data processing of software resource scheduling deeply. So the resource distribution problem of software execution task is also analyzed according to CPU load test results. This paper provides the optimization analysis for data processing performance, and it is available and effective according to the latest test results. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Milestone M7 Report: Reducing Excess Data Movement Part 2

This milestone evaluates techniques to measure and, if possible, reduce data movement across all levels of the memory hierarchy, focusing on CPU/GPU page level data movement and on intra-GPU memory hierarchy. We quantitatively evaluate the efficacy of the techniques in reducing data movement and measure how performance tracks data movement reduction. We study a small collection of benchmarks and proxy mini-apps that run on advanced pre-exascale GPUs and on the Accelsim GPU simulator. Our approach has two thrusts: to measure advanced data movement reduction directives and techniques on the newest available GPUs, and to evaluate our benchmark set on simulated GPUs configured with architectural refinements to reduce data movement. We primarily evaluated NVidia-based architectures due to the unavailability of AMD GPU hardware and tools until very recently.

97 MATHEMATICS AND COMPUTING↗

Enhanced Control, Optimization, and Integration of Distributed Energy Applications (ECO-IDEA)

With support from the U.S. Department of Energy Solar Energy Technologies Office, the National Renewable Energy Laboratory (NREL) partnered with Xcel Energy, Schneider Electric, Varentec, and Electric Power Research Institute (EPRI) to meet the goals of the Enabling Extreme Real-Time Grid Integration of Solar Energy (ENERGISE) program. This project developed and validated an innovative data-enhanced hierarchical control architecture that enables the efficient, reliable, resilient, and secure operation of future distribution systems with a high penetration of distributed energy resources like solar energy. The architecture enables a hybrid control approach where a centralized control layer is complemented by distributed control algorithms for solar inverters and autonomous control of grid edge devices. It is fully interoperable and includes all the cybersecurity aspects necessary for reliable and secure system operation. The hybrid approach can seamlessly integrate multiple voltage-regulation technologies, both at central and grid-edge levels, which enables reliable and efficient system operation in the face of unpredictable conditions. The overarching goal of the Eco-Idea project is to develop, validate, and deploy a unique and innovative Data-Enhanced Hierarchical Control (DEHC) architecture that comprehensively addresses the formidable challenges associated with proliferation of high penetration of distributed PV such as reverse power flows, transients from variability of PV systems, feeder load balancing, and voltage stability. These issues are exposing the weaknesses of existing grid operations and controls - including, but not limited to, lack of grid situational awareness, heuristic and slow-acting control actions, latency of control for emergency situations, and points of failure in communications. The proposed architecture will comprehensively resolve the deficiencies of current operational settings - where monitoring and control solutions proposed across industry and academia may not be interoperable and may not coexist in the same system - and will enable an efficient, reliable, resilient, and secure operation of future distribution systems with penetration of solar energy well beyond current limits. The DEHC architecture was developed and validated rigorously through hardware-in-loop simulations in the laboratory environment and deployed on the field.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The goldstone real-time connected element interferometer

Connected element interferometry (CEI) is a technique of observing a celestial radio source at two spatially separated antennas and then interfering the received signals to extract the relative phase of the signal at the two antennas. The high precision of the resulting phase delay data type can provide an accurate determination of the angular position of the radio source relative to the baseline vector between the two stations. This article describes a recently developed connected element interferometer on a 21-km baseline between two antennas at the Deep Space Network's Goldstone, California, tracking complex. Fiber-optic links are used to transmit the data to a common site for processing. The system incorporates a real-time correlator to process these data in real time. The architecture of the system is described, and observational data are presented to characterize the potential performance of such a system. The real-time processing capability offers potential advantages in terms of increased reliability and improved delivery of navigational data for time-critical operations. Angular accuracies of 50-100 nrad are achievable on this baseline.

Edwards, C., Jr.↗

A Comparison Between Publish-and-Subscribe and Client-Server Models in Distributed Control System Networks

The BIO-Plex control system requires real-time, flexible, and reliable data delivery. There is no simple "off-the-shelf 'solution. However, several commercial packages will be evaluated using a testbed at ARC for publish- and-subscribe and client-server communication architectures. Point-to-point communication architecture is not suitable for real-time BIO-Plex control system. Client-server architecture provides more flexible data delivery. However, it does not provide direct communication among nodes on the network. Publish-and-subscribe implementation allows direct information exchange among nodes on the net, providing the best time-critical communication. In this work Network Data Delivery Service (NDDS) from Real-Time Innovations, Inc. ARTIE will be used to implement publish-and subscribe architecture. It offers update guarantees and deadlines for real-time data delivery. Bridgestone, a data acquisition and control software package from National Instruments, will be tested for client-server arrangement. A microwave incinerator located at ARC will be instrumented with a fieldbus network of control devices. BridgeVIEW will be used to implement an enterprise server. An enterprise network consisting of several nodes at ARC and a WAN connecting ARC and RISC will then be setup to evaluate proposed control system architectures. Several network configurations will be evaluated for fault tolerance, quality of service, reliability and efficiency. Data acquired from these network evaluation tests will then be used to determine preliminary design criteria for the BIO-Plex distributed control system.

Boulanger, Richard P., Jr.↗

NAECON 87; Proceedings of the IEEE National Aerospace and Electronics Conference, Dayton, OH, May 18-22, 1987. Volumes 1, 2, 3, & 4

The present conference discusses topics in VLSI components and their packaging, signal processing, uses of cartographic data, data transmission, advanced avionics architectures, fiber-optics, information control and display, image processing, airborne radar and fire control, navigation, air data, Kalman filtering, power generation and control, spacecraft power structures, aircraft flying qualities, flight management, fault-tolerant computer architectures, actuation technologies, self-repairing flight control system technology, multivariable control, stability and control methods, and AFTI/F-16 flight test reports. Also discussed are the ADA/JOVIAL language and its applications, software acquisition and testing, advanced software concepts, software management, computer graphics and visual systems softwear, ADA in embedded avionics, 16- and 32-bit architectures, voice interaction applications, human/machine systems analysis, human factors and AI, mental workloads and displays, pilot acceleration protection research, communications system technology, space communications, reliability and maintainability, managerial techniques, engineering management, EM compatibility and nuclear hardening, expert systems, AI language/knowledge representation, expert system implementation, machine vision/optical processing, and advanced AI concepts and architectures.

Avionics↗

Architecture of a large object-oriented database for remotely sensed data

Attention is given to the proposed Intelligent Information Fusion System (IIFS) within the framework of the Intelligent Data Management project at NASA-Goddard. IIFS is to use connectionist architectures to extract high-level attributes from incoming sensor images, and then send those characterizations and their associated ephemeris and ancillary image data to a large object-oriented database which will serve as the master catalog of sensor data. Important issues facing this project include the choice of rapid-access data structures (RADSs) for cataloging images by their high-level characterization, the implementation of efficient spatial data structures for cataloging images by their scene location, the automated population of such a database from a continuous stream of incoming ephemeris and ancillary data, and the translation and optimization of natural-language database queries so that RADSs are employed when appropriate.

Dorfman, Erik↗

Geospatial Data Platform for All

Spatiotemporal data has evolved in scale due to augmented use in cross-domain applications. Simultaneously, there is substantial growth in the availability of Geographic Information Systems (GIS) data provided by the United States Geological Survey (USGS) along with other federal, state, county, or local agencies through open-data portals and public access APIs. However, data availability does not equate with accessibility. Large-scale analyses and applications require robust, performant data management with co-location of data storage and computing. The insufficiency of data management infrastructure compels researchers to adopt ad hoc project- specific GIS data storage solutions (e.g., copying data to High-Performance computer file systems). As an ad hoc storage strategy does not scale, it hampers cross-domain analyses causing difficulty in data reuse and utilizing existing code bases. Furthermore, GIS data is complex and requires expertise to analyze and manipulate due to its intricate data structures and data-specific projection transformations. Despite the challenges, we recognize that derived GIS data products, e.g., satellite or LIDAR-based images, can be used in downstream applications such as AI by domain, but non-GIS experts. To address the data needs and overcome the challenges, we are working towards a GIS Data Platform focused on efficient data storage, data discovery and access, and an API to enable common workflows. We propose a knowledge-graph (KG) approach for data discovery, whereby datasets are semantically linked to higher- level constructs such as projects and research areas. The semantic data links enable researchers to explore datasets in a top-down approach by specifying relevant and meaningful terms (assists in finding hidden data). An advantage is that the nodes and edges in a knowledge graph create built-in semantic documentation. Deeper spatiotemporal connections between data sources can be encoded via Graph Neural Networks (GNN) (Zhang et al., 2021). The KG approach can be extended to integrate the data itself in a Virtual KG (VKG). Our work will derive inspiration from large-scale VKG efforts that have been undertaken or are currently underway as part of the OpenStreetMap project (Ding et al., 2021). For DOE Data Days, we share the proposed geospatial data platform hybrid (cloud/on-prem) architecture, our work-to-date on storing, retrieving, and transforming LiDAR and raster data relevant to two important NREL use-cases, including the Renewable Energy Potential (reV) Model, and present our proposal for a KG based data discovery engine.

data platform↗

Developing the Next Generation of Science Data System Engineers

At Goddard, engineers and scientists with a range of experience in science data systems are needed to employ new technologies and develop advances in capabilities for supporting new Earth and Space science research. Engineers with extensive experience in science data, software engineering and computer-information architectures are needed to lead and perform these activities. The increasing types and complexity of instrument data and emerging computer technologies coupled with the current shortage of computer engineers with backgrounds in science has led the need to develop a career path for science data systems engineers and architects.The current career path, in which undergraduate students studying various disciplines such as Computer Engineering or Physical Scientist, generally begins with serving on a development team in any of the disciplines where they can work in depth on existing Goddard data systems or serve with a specific NASA science team. There they begin to understand the data, infuse technologies, and begin to know the architectures of science data systems. From here the typical career involves peermentoring, on-the-job training or graduate level studies in analytics, computational science and applied science and mathematics. At the most senior level, engineers become subject matter experts and system architect experts, leading discipline-specific data centers and large software development projects. They are recognized as a subject matter expert in a science domain, they have project management expertise, lead standards efforts and lead international projects. A long career development remains necessary not only because of the breadth of knowledge required across physical sciences and engineering disciplines, but also because of the diversity of instrument data being developed today both by NASA and international partner agencies and because multidiscipline science and practitioner communities expect to have access to all types of observational data.This paper describes an approach to defining career-path guidance for college-bound high school and undergraduate engineering students, junior and senior engineers from various disciplines.

Next Generation of Science↗

Traffic information computing platform for big data

Big data environment create data conditions for improving the quality of traffic information service. The target of this article is to construct a traffic information computing platform for big data environment. Through in-depth analysis the connotation and technology characteristics of big data and traffic information service, a distributed traffic atomic information computing platform architecture is proposed. Under the big data environment, this type of traffic atomic information computing architecture helps to guarantee the traffic safety and efficient operation, more intelligent and personalized traffic information service can be used for the traffic information users.

97 MATHEMATICS AND COMPUTING↗