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At least 487 records · Page 27

Medium- and Heavy-Duty Vehicle Electrification: An Assessment of Technology and Knowledge Gaps

The objective of this assessment was to leverage current medium- and heavy-duty vehicle (MHDV) data and information to evaluate the state of commercial vehicle electrification technologies, including the following: 1. Assessment and inventory of current MHDV electrification architectures; 2. Identification and assessment of MHDV component technologies; 3. Assessment of potential performance and cost drivers; and, 4. Identification of R&D gaps where appropriate R&D and technology would accelerate commercial vehicle electrification. These gaps include shortfalls in technology, gaps in data, and inadequate knowledge and understanding. To inform this study, the National Renewable Energy Laboratory–Oak Ridge National Laboratory team examined the open literature; conducted workshops; assessed and analyzed data on more than 175 electrified MHDVs, including vehicle and powertrain specifications; and conducted one-on-one meetings with industry representatives. This systems-level information was concatenated and parsed with respect to key characteristics such as battery energy, power, and range compared across vehicle classes. Operational data of many conventional vehicles were also examined to help determine the requirements on electrified vehicle attributes such as range. Previous studies on the total cost of ownership of electrified MHDVs were reviewed to determine where improvements in technologies (efficiency, cost, maintenance) were needed to accelerate adoption. The team also assessed the state of the art in electric drivetrains for component specifications and challenges for the commercial vehicle sector, including electric machines, power electronics, and off-board high-power charging systems (extreme fast charging and beyond). The goal of this analysis was to identify the barriers to widespread adoption of commercial vehicle electrification technologies and prioritize the research and development gaps that need to be overcome to accelerate significant market penetration of these technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Energy Improvements of Fire Station 71

Since 2018, the City of Shawnee, Kansas has completed two phases of the State of Kansas Facility Conservation Improvement Program (FCIP), an initiative that guarantees operational cost and energy savings through targeted construction improvements on City facilities and infrastructure. The City is currently in the third phase of this FCIP, where one of the projects included an investment in energy improvements for Fire Station 71 (FS 71). The City partnered with Navitas, an Energy Service Company (ESCO), to implement a Photovoltaic Solar Array on FS71. The purpose of this project was to invest in sustainable building improvements with Energy Conservation Measures (ECM) to bring cost savings to the City and to provide sustainable benefits to the residents of Shawnee. In the first task of the project, Navitas collaborated with the City of Shawnee and the Community Development Department to determine the optimal layout and schedule for the installation of the solar array on FS 71. In the second task of the project, Navitas installed the 99.8 kW DC Photovoltaic solar array system. This system installation comprised of racking, inverters, optimizers, load center, and disconnect, which were all installed at a total ECM price of $\$$247,948. The third task focused on start-up and commissioning of the array. Navitas installed a real-time data analytics information management system integrated with utility meters, which evaluates the operations of the utility system and verifies operation of equipment and ensures optimum operation for energy efficiency. In the final task of this project, this analytics system was used for monitoring and verification, which will continue to be used to evaluate the success of the project for the coming years. The primary goal of the project was to install the 99.8 kW DC PV solar array at FS 71 to demonstrate the viability of solar energy systems in essential municipal facilities. Fire stations are energy demanding structures, as they require a constant intake of power and have a high baseline energy usage. The success of solar arrays on a fire station exemplifies their energy efficiency and effectiveness and displays their potential for application on other city facilities. By installing a solar array at such a facility, the City sought not only to offset electricity usage but also to serve as a model for ECMs in other municipal facilities and infrastructure projects. From an economic standpoint, this project demonstrates the feasibility of renewable energy at the municipal level. The total project cost of $\$$247,948 was split evenly between city funds and award funding, minimizing financial risk while ensuring guaranteed long-term savings. Any excess savings that are beyond the guaranteed minimums remain with the city, which enables future investment in sustainable energy initiatives. This project provides many benefits to the public. In addition to reducing the environmental footprint of city operations, it lowers taxpayer-funded utility spending and improves the energy security of a critical facility. The knowledge gained from this implementation motivates the City to focus on similar efforts across other public facilities in future FCIP phases and other City projects.

14 SOLAR ENERGY↗

A Multi-Dimensional Benefit Assessment of Automated Mobility Platforms (AMP) for Large Facilities

Automated Mobility Platform (AMP) is a general term for intelligently managed passenger mobility systems that leverage automation and electrification to improve system performance and sustainability through the integration of real-time data streams with advanced decision-making processes tailored for use in large facilities. Using airports as an example, the rapid growth in air travel demand has led to facility expansions and congested terminals, which directly impacts equity (e.g., increased challenges for passengers with reduced mobility [PRMs]) and sustainability - both of which are important metrics often neglected during the engineering design process. Therefore, to evaluate systems and inform critical decisions more effectively, a holistic evaluation framework is proposed that includes equity, sustainability, and infrastructure perspectives - referred to as a multidimensional benefit assessment. More specifically, the following analysis focuses on: (1) mobility, with emphasis on travel time and accessibility within an airport, contrasting existing systems with the proposed AMP system; (2) equity analysis, specifically to the PRM community, but with an eye to the whole of society; (3) energy consumption and greenhouse gas (GHG) emissions associated with intra-airport mobility, comparing and contrasting modes as well as impacts on overall airport operations efficiency; and (4) fundamental changes in building design enabled by AMPs for larger and more flexible, functional, and energy-efficient structures.

ADVANCED PROPULSION SYSTEMS↗

Hybrid Floating Solar Photovoltaics-Hydropower Systems: Benefits and Global Assessment of Technical Potential

Floating solar photovoltaics (FPV) is an emerging, and increasingly viable, application of photovoltaics (PV) in which systems are sited directly on waterbodies. Despite growing market interest, FPV system deployment is nascent, and potential adopters remain concerned about the technology, the benefits it offers, the advantages to pairing it in hybrid systems (such as with hydropower), and how to analyze technical potential. To support decision making, we provide a review of associated benefits of hybrid FPV-hydropower system operation and a novel, geospatial approach to assess the global technical potential of these systems employing publicly available, global datasets. We identify significant potential globally for FPV hybridized with hydropower ranging from 3.0?TW to 7.6?TW (4,251?TWh to 10,616?TWh annual generation), based on the assumptions made. We detail operational benefits that these hybrid systems may provide that could be quantified in future modeling and/or analyses of existing or planned hybrid systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DAWN: Dashboard for Agricultural Water Use and Nutrient Management—A Predictive Decision Support System to Improve Crop Production in a Changing Climate

Abstract Climate change presents huge challenges to the already-complex decisions faced by U.S. agricultural producers, as seasonal weather patterns increasingly deviate from historical tendencies. Under USDA funding, a transdisciplinary team of researchers, extension experts, educators, and stakeholders is developing a climate decision support Dashboard for Agricultural Water use and Nutrient management (DAWN) to provide Corn Belt farmers with better predictive information. DAWN’s goal is to provide credible, usable information to support decisions by creating infrastructure to make subseasonal-to-seasonal forecasts accessible. DAWN uses an integrated approach to 1) engage stakeholders to coproduce a decision support and information delivery system; 2) build a coupled modeling system to represent and transfer holistic systems knowledge into effective tools; 3) produce reliable forecasts to help stakeholders optimize crop productivity and environmental quality; and 4) integrate research and extension into experiential, transdisciplinary education. This article presents DAWN’s framework for integrating climate–agriculture research, extension, and education to bridge science and service. We also present key challenges to the creation and delivery of decision support, specifically in infrastructure development, coproduction and trust building with stakeholders, product design, effective communication, and moving tools toward use.

Meteorology & Atmospheric Sciences↗

Stakeholder Engagement Review Meeting Summary Report

Sustainability in the context of the Light Water Reactor Sustainability (LWRS) Program is the ability to maintain the safe and economic operation of the existing fleet of nuclear power plants now and in the future. It has two objectives with respect to long-term operations: (1) to provide science and technology-based solutions to industry to safely enhance the economical operation of power reactors; and (2) to manage the aging of systems, structures, and components (SSCs) so that nuclear power plants can continue to operate safely and cost-effectively.

42 ENGINEERING↗

Latest Development to the Mass Tracking System (MTG)

This poster informs about the ongoing development project of the Mass Tracking System (MTG) taking place in Fuels Conditioning Complex at MFC. The information is about the MTG utilization, the possible complications in the future with the system and the solution for those complication. Furthermore, the poster reports about the progress and the future plans of the project after brief insight on how the MTG operates in the facility. Essentially, the project is separated in three different phases starting with the back-end development focusing on conversion and migration phases and finalizing with the front-end development of the website phase to provide FCF with versatile and efficient system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multi Time-scale Imputation aided State Estimation in Distribution System

With the transition to a smart grid, we are witnessing a significant growth in sensor deployments and smart metering infrastructure in the distribution system. However, information from these sensors and meters are typically unevenly sampled at different time-scales and are incomplete. It is critical to effectively aggregate these information sources for situational awareness. In order to reconcile the heterogeneous multi-scale time-series data, we present a multi-task Gaussian process framework. This framework exploits the spatio-temporal correlation across the time-series data to impute data at any desired timescale while providing confidence bounds on the imputations. The value of the imputed data for distribution system operation is illustrated via a matrix completion based state estimation strategy. Results on the IEEE 37 bus distribution system reveals the superior performance of the proposed approach relative to linear interpolation approaches.

Dahale, Shweta↗

Waste Compliance and Tracking System (WCATS) User Guide (Release 2)

This manual has been written to provide a general reference of the usage of WCATS. Because WCATS is designed to be used at many different kinds of facilities, much of the usage of the application is driven by the metadata configuration of the system. General usage of the system and the different types of tasks provided is included in this document, but custom usage and an exhaustive list of configuration options will not be provided. This manual is not intended to be a replacement for detailed work procedures or desk instructions, and it will not include configuration details such as service unit names, waste stream numbers for selection, etc. Any use of such information in this document is only provided as an example.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

U.S. Department of Energy-National Lab Equity Summit: Grid Planning and Operations (Workshop Report)

This report summarizes the U.S. DOE and national laboratories equity summit that was held on February 5, 2024, and focused on grid planning and operations. The objectives of the summit were to connect DOE and lab researchers working on grid-related equity issues, share information on current and planned grid-related equity projects and initiatives, and inspire and educate participants by hearing from our panelists about solutions and challenges to integrating equity in grid planning and operations. The summit included two panels of industry leaders. The first was a state and community perspectives panel that included representatives from a state public utility commission (Oregon Public Utility Commission), a state energy office (Washington Department of Commerce), a state utility consumer advocate (Connecticut Consumer Counsel), and industry consultants (Elevated Engagement and ArkSpring Consulting). Panelists shared successes they have seen, critical challenges related to equity and grid planning and operations, and other considerations. The second panel addressed utility perspectives and included representatives from two utilities (Commonwealth Edison and Tacoma Power), the National Rural Electric Cooperative (NRECA), and a former utility employee and legal consultant. Panelists discussed the role of the utility concerning equity, the most significant technical and data modeling needs and opportunities, and the role the labs could help advance equity in grid planning and operations. There was also a session on partner organization presentations. Argonne National Laboratory made a short presentation on the Grid Modernization Laboratory Consortium (GMLC) project they are leading on equity-informed power system planning. NARUC, NASEO, and the Clean Energy States Alliance, as partners of the GMLC project also shared updates on relevant activities and resources. During the summit, there were two rounds of lightning presentations by national labs and DOE highlighting research that addresses equity and grid planning and operations (Tables 5 and 6 and slides in the Appendix). The goal of the lightning rounds was to share information between participants to encourage collaboration and leverage ongoing research at labs and DOE. The summit included two interactive exercises where summit participants shared their perspectives on relevant equity projects and initiatives (Table 2), key challenges regarding equity and grid planning and operations (Table 3), and promising innovations or progress (Table 4). At the end of the session, participants were asked to share essential insights from the event (Table 7) and an action they plan to take as a result of the event. Participants agreed that the event was useful in helping them share and learn from each other. The project team plans to use the information from the summit as a starting point to help inform future research and technical assistance. In 2026, another Equity Summit will be held (virtually or in person) as part of the same project to help raise awareness and disseminate research and resources completed during the project's duration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Joint Topology Identification and State Estimation in Unobservable Distribution Grids

Many distribution system operations (e.g., state estimation, control, fault detection/localization) rely on the assumption that the underlying topology is accurately defined. In general, topology identification is a challenging problem in distribution systems as these systems are unobservable with a very limited number of available measurements. In this paper, we tackle this problem by designing a compressive sensing framework that jointly estimates the systems states and network topology via an integrated mixed integer nonlinear program (MINLP) formulation. Here, two reformulations of the original MINLP problems are investigated. Firstly, in order to remove the nonlinearity in the MINLP formulation, a mixed integer linear programming (MILP) problem that employs auxiliary variables is derived. Furthermore, to achieve a faster solution, convex relaxation of the original formulation is derived. Finally, using a Markovian model for topology changes, prior information about system topology is used to improve topology identification particularly when a limited amount of measurements is available. Simulation results on IEEE 37-bus test feeder and IEEE 123-bus test feeder illustrate the efficiency and scalability of the proposed approaches from both state estimation and topology identification point of view (even with 30% of available data).

42 ENGINEERING↗

Iridium Surface Oxide Affects the Nafion Interface in Proton-Exchange-Membrane Water Electrolysis

Proton-exchange-membrane water electrolyzer (PEMWE) catalyst layers consist of aggregates of catalyst particles (typically iridium) and ionomer (typically Nafion). Prior work suggests that the oxide form of Ir affects the kinetics of the oxygen-evolution reaction. However, because most catalyst-benchmarking studies are conducted ex situ in liquid electrolytes, it remains unclear how the ionomer is influenced by the catalyst oxide and affects overall cell performance. Using a suite of experimental techniques, we conduct fundamental investigations into model ink (catalyst and ionomer dispersed in solution) and thin-film systems to inform cell-level overpotential analysis as a function of three forms of Ir (metallic Ir m , oxyhydroxide IrOOH, and oxide IrO 2 ). Furthermore, nafion on Ir m has a high degree of phase separation and higher swelling, likely improving the ionic conductivity. Additionally, Nafion binds most strongly to IrOOH, likely yielding reduced kinetic overpotentials. These findings highlight the intricacies of the ionomer/Ir interface and provide insight into all catalyst-layer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating the Interplay between Trajectory Segmentation and Mode Inference Error

Travel behavior changes are essential to transportation decarbonization. Travel diaries, consisting of sequences of trips between places, are typically used to instrument human travel behavior. However, these diaries are only as accurate as the underlying methods used to construct them. Travel diary algorithms have been a popular research topic since the advent of Global Positioning System tracking surveys. These algorithms have typically been validated using prompted recall of presegmented trips, thus disregarding the continuity of mode inference. Phone operating systems have adopted battery-conserving techniques, but the resulting data collection errors have not been studied extensively. We introduce a framework to evaluate the accuracy of trip length computations and mode inference by analyzing continuous mode-segmented trajectories for groups of trips. We then use the framework to identify the input data quality and the impact of postprocessing. Our primary inputs to this evaluation are MobilityNet, a public dataset containing information from three artificial timelines covering 15 different travel modes, and sample open-source travel diary creation algorithms from the OpenPATH project. Our framework concretely shows that the variance of the distance error drops from (0.217, 0.0848) to (o.011, 0.0407) (Android, iOS) after postprocessing. Similarly, the weighted F-scores for mode inference increase from (0.25, 0.29) to (0.60, 0.74) (iOS, Android) between random forest and geographic information system-based models. We hope that this standardized method will be adapted to evaluate other, potentially proprietary, travel diary algorithms. Finally, the results can be used to understand and improve the state of the art in the travel diary creation field.

33 ADVANCED PROPULSION SYSTEMS↗

Hydrogen Storage for Flexible Fossil Fuel Power Generation: Integration of Underground Hydrogen Storage with Gas Turbine (Final Report)

As the nation continues to encourage, through market structures and financial incentives, the proliferation of intermittent renewable electricity, how to optimize the ever-changing electric grid and identify means to retain and improve resilience, while ensuring continued reductions in GHG emissions, will be critical. According to Bloomberg, wind & solar generated 10.5% of US electricity in 2020 and that percentage continues to grow. In support of expanding renewable energy use, and to address its intermittent nature, this project will develop the Hydrogen Storage for Flexible Fossil Fuel Power Generation platform that is dispatchable, reliable, repeatable and have the ability to produce zero or negative carbon power while interfacing with geology capable of CO2 and hydrogen storage. GTI Energy (GTIE) and team members Illinois State Geological Survey (ISGS), Mitsubishi Heavy Industries America (MHIA), Ameren Illinois, Hexagon Purus, and the Low Carbon Resources Initiative (LCRI) completed a Phase I Conceptual Study under contract DE-FE0032012 for Hydrogen Storage for Flexible Fossil Fuel Power Generation: Integration of Underground Hydrogen Storage with Gas Turbine. The Hydrogen Storage for Flexible Fossil Fuel Power Generation platform addresses the intermittent nature of the expanding use of Variable Renewable Energy (VRE) generation. The low cost of the electricity (COE) generated results in greater dispatch and more operation at higher power levels (higher efficiency), fewer short intervals, and fewer start/stop cycles. The reliable, resilient system can produce zero carbon power and store hydrogen. It will demonstrate hydrogen storage in geologic formations like those used in natural gas underground storage thus enabling large scale storage of hydrogen in sedimentary strata across the United States rather than in geographically restricted salt caverns. The Phase I study confirmed the system is feasible and generates power at lower cost than other low carbon approaches. The demonstration defines the pathway for broad commercial application and will accelerate the development of larger systems suitable for centralized utility scale electricity production. The study advanced the maturity of the H 2 storage-based system with flexible power generation by completing a Pre-FEED study (Phase II). The Pre-FEED focused on the selected Energy Farm on the University of Illinois Urbana-Champaign (UIUC) site that includes above ground and underground hydrogen storage, low-carbon hydrogen production (GTI’s Compact Hydrogen Generator, CHG) with underground CO2 sequestration, and a 40-MW class gas turbine. The Pre-FEED addressed the entire system and its interconnection to the natural gas and electric grid and mitigation of key risks, such as storage behavior, load-following, and system operation. During Phase 1 of the project, the team completed key tasks, which moved the entire demonstration project, specific components and approaches closer to commercialization. These Phase I Accomplishments include: Completing System Requirements Review; Completing System Layout and Modeling - Heat & Mass Balance and Process Flow Diagram; Completing modelling of 9 turbine performance cases; Evaluating rock strata for underground storage of hydrogen and sequestration of carbon dioxide; Completing initial modelling of underground storage of hydrogen and withdrawal with evaluation of loss and water production; Identifying roadable storage for above ground hydrogen storage; Identifying existing electrical infrastructure for receiving/delivering electricity; Identifying existing gas supply infrastructure for receiving natural gas; Document concept design/development plans in required reports. Conclusions: The 12-month Feasibility study in Phase I study was completed and confirmed the system is feasible and generates power at lower cost than other low carbon approaches and even lower cost than the reference NGCC plant without carbon capture when taking advantage of 45Q carbon credits. The study enabled the fidelity of the concept to be improved and allowed identification of the requirements for the system. Defining the individual system and component requirements was performed via the system requirements review with the whole team. These requirements were then incorporated into and iterated with our Heat & Mass Balance process model and process flow diagrams were generated to reflect the overall system. This information was then used to complete the TEA and show economic feasibility. Large scale non-salt geologic storage of hydrogen is an enabling technology for a hydrogen-fired turbine that can be retrofitted into large-scale electric generating units (EGU). Our demonstration will include 428 MWh or ~4 hours full load of hydrogen storage (above and underground). Carbon capture inherent to the CHG process can capture 90% CO 2 (with upgrades to >98%). This system provides a COE of 23% savings relative to an NGCC with a post combustion amine system. Our proposed storage system decouples carbon capture and hydrogen production from power production; therefore, we expect our proposed system’s efficiency and variable COE to be superior resulting in overall higher dispatch and reduced deep cycling. Our demonstration will be full to multi-day hydrogen storage and has the potential for longer (seasonal) duration commercially. The demonstration defines the pathway for broad commercial application and will accelerate the development of larger systems suitable for centralized utility scale electricity production.

03 NATURAL GAS↗

A Multi-Dimensional Benefit Assessment of Automated Mobility Platforms (AMP) for Large Facilities: Mobility, Energy, Equity, and Facility Management & Design

The goal of the automated mobility platforms (AMPs) initiative is to raise the bar of service regarding equity and sustainability for public mobility systems that are crucial to large facilities, and doing so using electrified, energy efficient technology. Using airports as an example, the rapid growth in air travel demand has led to facility expansions and congested terminals, which directly impacts equity (e.g., increased challenges for Passengers with Reduced Mobility [PRMs]) and sustainability - both of which are important metrics often overlooked during the engineering design process. Therefore, to evaluate systems and inform critical near- and long-term decisions more effectively, a holistic evaluation framework is proposed focused on four key areas: (1) mobility, with emphasis on travel time and accessibility within an airport, (2) environment, focused on energy consumption and greenhouse gas (GHG) emissions associated with intra-airport mobility, (3) equity, specifically to the PRM community, but with an eye to the whole of society, and (4) built environment, or the fundamental changes in building design enabled by different mobility systems for larger and more flexible, functional, and energy-efficient structures. Below, AMPs are defined, and each metric is discussed further, all with a focus on airport mobility.

ADVANCED PROPULSION SYSTEMS↗

The Challenges of Using Real-Time Detection Systems: From Data Gathering to Actionable Information [Slides]

This session will discuss challenges and real life examples associated with Real-Time Detection Systems (RTDS) used in exposure assessment strategies. This first presentation will provide an overview of RTDS as used as part of an overall exposure assessment strategy and to document regulatory compliance. Managing OH consequences has been problematic when it comes to actionable information gleaned from sensor data. The judgement of regulatory entities, can be at odds with IH practitioners implementing an exposure strategy that creates exposure profiles and judges workplace exposures.

61 RADIATION PROTECTION AND DOSIMETRY↗

Holistic Measurement Driven Resilience: Combining Operational Fault and Failure Measurements and Fault Injection for Quantifying Fault Detection, Propagation and Impact. Final report

For HPC systems to date, application resilience to faults and failures has been accomplished by the brute- force method of checkpoint/restart, which allows an application to make forward progress in the face of system and application faults, errors, and failures independent of root cause or end result. It has remained the primary resilience mechanism because we lack a way to identify faults and anticipate consequences early enough to take meaningful mitigating action. However, checkpoint/restart implementations put a tremendous burden on system resources and on the applications themselves and is becoming less feasible at scale. Because we have not yet operated at scales at which checkpoint/restart fails to provide forward progress, despite increasing costs, vendors have had little motivation to provide the instrumentation necessary for early identification of faults and failures. However, as we move from petascale to exascale, component mean time to failure (MTTF) will render the existing techniques ineffectual and/or too expensive. Furthermore, fault recovery mechanisms such as failover and/or error correction introduce performance inconsistency. Instrumentation allowing early indication of problems and tools to enable use of such information by systems, operating systems, and applications offer an alternative, more scalable and less costly solution. In the HMDR project, we built on our experience and expertise developed and accumulated over years of research on design, monitoring, measurement, and assessment of resilient computing systems. Analysis of field data on the current and past generations of extreme-scale systems revealed several challenges that, if not addressed in increasingly larger and more complex systems, may hinder the effectiveness of future exascale computing systems. Specifically, i) file systems and interconnects in current-generation large-scale systems already operate at the margins of resiliency, including consistent performance, and may not scale to larger deployments; ii) automated, software-based failover mechanisms are frequently inadequate and can introduce wider failures, such that failures during recovery may lead to system/application failures, including system-wide outages; and iii) silent data corruption represents a critical fault mode and will require efficient detection mechanisms if next-generation applications are to take full advantage of exascale hardware. To address the above challenges, we assembled a team of world-renowned experts in resilient extreme- scale computing from the University of Illinois (Electrical and Computer Engineering, Computer Science, and NCSA), SNL, LANL, NERSC, and Cray. Our team includes representatives from centers that house many of the largest HPC resources in the world, both today and over the coming years. The team has a unique track record of research in i) system and application failure characterization based on the analysis of field data, ii) data-driven design of fault/error detection mechanisms, and iii) experimental characterization of system/application resiliency. The team includes system owners/operators who provide continuous data collection and access and ensure installation of appropriate analysis tools.

97 MATHEMATICS AND COMPUTING↗