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At least 181 records · Page 10

Incorporating new locations into a hydrodynamic model using ArcGIS Pro

ALGE3D is a 3-D hydrodynamic model developed at the Savannah River National Laboratory to predict pollutant dispersion. The model has several predefined locations incorporated, however adding new locations into ALGE3D is manually intensive and time-consuming. In the event of an emergency, ALGE3D can only be used if an event occurs at one of the predefined locations incorporated into the GUI. This project focuses on streamlining the integration of new locations into ALGE3D by utilizing tools in ArcGIS Pro. The Stream Order tool was used to delineate streams and assign them an order, using the Strahler method, versus manually defining these streams in Microsoft Excel. This work advances development to turn ALGE3D into a product for emergency response use by allowing the user to incorporate a new location into ALGE3D quickly, should an event occur at a location that is not already predefined.

54 ENVIRONMENTAL SCIENCES↗

Modifications to Sandia's MDT and WNTR tools for ERMA

ERMA is leveraging Sandia’s Microgrid Design Toolkit (MDT) [1] and adding significant new features to it. Development of the MDT was primarily funded by the Department of Energy, Office of Electricity Microgrid Program with some significant support coming from the U.S. Marine Corps. The MDT is a software program that runs on a Microsoft Windows PC. It is an amalgamation of several other software capabilities developed at Sandia and subsequently specialized for the purpose of microgrid design. The software capabilities include the Technology Management Optimization (TMO) application for optimal trade-space exploration, the Microgrid Performance and Reliability Model (PRM) for simulation of microgrid operations, and the Microgrid Sizing Capability (MSC) for preliminary sizing studies of distributed energy resources in a microgrid.

97 MATHEMATICS AND COMPUTING↗

Homomorphic Encryption for Machine Learning and Artificial Intelligence Applications

Third-party and expert analysis is a cost-effective solution for solving specialized problems or processing large datasets related to reactor structural health monitoring and nondestructive evaluation. However, when handling proprietary information, third-party and expert analysts pose a privacy risk. To address this challenge, Homomorphic Encryption (HE) permits arithmetic operations on encrypted data without exposing the underlying data. Implementations of Machine Learning (ML) and Artificial Intelligence (AI) algorithms using HE greatly enhances the capabilities of third-party analysts while maintaining a low security risk. This paper details current success in applying Principal Component Analysis (PCA) and Fully Connected Neural Networks (NN) using the Microsoft SEAL implementation of the popular CKKS Fully Homomorphic Encryption (FHE) algorithm. The MNIST Handwritten Dataset is analyzed as a proof-of-concept demonstration of the implementations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SCO#1197 Addendum #4 OSR Characterization Database (Test Report)

A test plan was developed and approved in June of 2022. Testing was successfully performed to verify the functions of Version 2.0 of the OSR Characterization database. Checks verified that data remains consistent to tests previously performed using Microsoft Access® 2003, 2010 and 2016.

97 MATHEMATICS AND COMPUTING↗

Development of a Cloud-based Application to Enable a Scalable Risk-informed Predictive Maintenance Strategy at Nuclear Power Plants

Light-water reactor operations and maintenance (O&M) costs are prohibitively high, thus contributing to the premature decommissioning of nuclear power plants (NPPs). This is partly due to how the equipment is monitored. In recent years, cloud computing has emerged as a dominant technology by virtue of its low costs, computing and storage adaptability, and ability to host applications over numerous types of virtual infrastructures. Cloud computing can be a cost-effective alternative to onsite storage and diagnostics. This paper conducts a techno-economic assessment of a provisional cloud deployment architecture for a NPP predictive monitoring (PdM) system. The cloud-based monitoring system would enable maintenance and diagnostics (M&D) analysts and other authorized plant users to remotely monitor equipment functionality so as to enable PdM practices and early detection of faults. The Microsoft Azure cloud platform is included in the proposed cloud architecture to provide data processing and storage, sensor device networking, and database management; however, this analysis could be extended to other cloud computing service providers as well. For the techno-economic assessment, technical feasibility is measured in terms of network performance metrics such as response time, latency, and throughput, whereas economic feasibility is measured in terms of operational costs and capital expenditures. Finally, this report covers certain regulatory and security aspects that may concern licensees looking to implement cloud computing. The report focuses on the integration of sensor database storage, the application of cloud resources to PdM, and the identification of technological and economic hurdles associated with moving to a cloud-computing-based architecture.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A Cybersecurity Threat Profile for a Connected Lighting System

In anticipation of improved energy performance and cost savings, cities and building owners are increasingly considering “smart lighting initiatives” that aim to convert their collection of simple luminaires (i.e., lighting fixtures) into an intelligent connected lighting system (CLS) capable of remotely monitoring energy consumption and fault conditions, and possibly implementing adaptive lighting schemes. The U.S. Department of Energy (DOE) has set an national goal of tripling the energy efficiency and demand flexibility of the buildings sector by 2030, relative to 2020 levels 1. It is forecast that connected lighting systems can contribute to that goal by delivering 125 TWh of annual energy savings by 2035 2, equivalent to the annual output of 50 typical (500 MW) power plants. However, these energy savings and the DOE goal are put at significant risk if connected technologies are not adopted due to real or perceived cybersecurity concerns. Connected IoT devices such as these have historically been rife with vulnerabilities which sometimes put security considerations secondary to functionality and operability. What are the cybersecurity threats that will impact these systems, as formerly banal luminaires transition into intelligent connected devices that collect information about themselves, their surrounding environment, and possibly us? In this paper we analyze a threat profile performed on a fault-detection use case for streetlights. A threat profile establishes security requirements, justifies security measures, yields actionable controls, and effectively communicates risk to stakeholders. This effort provides critical information for making threat-based decisions to increase security at a reasonable cost, and can effectively be used by development teams, software architects, and managers to make cybersecurity a part of their ongoing culture of awareness, training, and prevention. This leads to more secure systems and better-understood security. On-premise, cloud, and hybrid architectures with different authentication mechanisms were modeled and later categorized using the Microsoft STRIDE framework. An analysis of the recommended controls for each threat was performed to determine which controls could and should be put in place by manufacturers or third-party suppliers, and which controls need to be left up the end-user to implement. Fifty-seven threats were identified. Among our key findings: (1) 65% (37/57) of the threats did not involve the luminaires, but rather the other components needed to communicate with and manage them; (2) 63% (36/57) of the threats could have been mitigated through manufacturer-implemented defensive techniques or “controls”; and (3) 23% (13/57) of the threats were dependent on the network configuration. Recommendations based on the results of this work are made to key stakeholder groups. Notably, lighting technology developers are advised to address all threats that can be reasonably controlled with baked-in technology solutions (e.g., encryption or authentication controls), and employ some form of secure supply chain management and tracking where other parts (e.g., sensors, microprocessors) of a luminaire must also be built and manufactured with the proper security controls in place. Developers should also review threats involving assets not developed in-house to understand how connectivity with other devices will affect their product during system operation and determine if a compensating control for a defense-in-depth strategy will be needed. Finally, those interested in deploying CLS should compare the differences between cloud and on-premise models to determine which is more suitable for their needs and the abilities of their security team.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Incentivizing Cold-Climate Efficiency in Juneau (Final Report)

This is the final technical report for the DOE EERE BTO project Incentivizing Cold-Climate Efficiency in Juneau. The project implemented a community energy campaign to deploy heat pumps and efficiency for residents of Juneau, in Southeast Alaska. The project helped Juneau make progress towards its renewable energy goal of reaching 80% renewable energy for space heating by 2045. The Incentivizing Cold-Climate Efficiency in Juneau (ICE-Juneau) project began in 2020 and concluded three years later in 2023. During that time, a group of implementation partners and a research advisory team instituted a beneficial electrification campaign to promote energy savings and carbon reduction in residences of Juneau, Alaska. The campaign, Thermalize Juneau, focused on the installation of single head ductless mini-split heat pumps along with other efficiency upgrades. Thermalize Juneau was the first campaign of its kind in Alaska. After several months of planning, registration opened to the public in early 2021, and over the course of six months 164 participants enrolled. Campaign staff provided education to homeowners on heat pumps and efficiency, and each participant received a one-on-one heat pump assessment using a custom Microsoft Excel-based calculator that estimated energy savings for their residence based on building characteristics and past utility bills. Participants could also obtain a free energy audit from one of the two local energy auditors to further inform their decision. A heat pump installer, electrician, and builder were selected via a competitive RFP process. Participants who felt ready to install a heat pump or other efficiency upgrades received a site visit and custom quote from each of these contractors free of charge, and if they still felt energy upgrades were right for them, could move forward with an individual contract. Participants received a $400 heat pump installation rebate, offered by the installer if 40 heat pump installations occurred through the campaign. Overall, the campaign facilitated 75 heat pump installations (including participants that went with another contractor or heat pump model) and 30 efficiency upgrades (including participants that went with another builder or did DIY upgrades). The campaign created 3 new jobs as the heat pump installer hired an administrative assistant and two apprentices over the course of the campaign. It also helped Juneau work toward achieving its renewable energy goal of 80% renewable energy for space heating by 2045 by upgrading houses from fuel oil to heat pumps powered by the hydropower electric grid. Researchers conducted four surveys to inform Thermalize Juneau and future energy campaigns. The first surveyed existing and prospective heat pump owners in Juneau to identify barriers the campaign could address and inform recruitment efforts. Entry and exit surveys provided information on participant demographics, goals, outcomes, and suggestions for improving future campaigns. And a final survey of community members who had not participated in Thermalize Juneau gave insight on ways future campaigns could include a greater diversity of participants so they could realize similar benefits. Researchers also used pre-campaign energy modeling to predict energy savings, which was then compared to the savings estimated through aggregation of heat pump assessments and energy audits, and later to actual energy savings of 10 participants who installed a heat pump and were able to provide complete energy use data sets. In addition to energy savings, and to assist the electric utility in future planning efforts, researchers analyzed the overall change in electric use across participants with energy data and heat pump installations. They also completed a life cycle cost analysis, showing positive net present values for those displacing a fuel oil appliance, and a more mixed case for those switching from electric baseboard. This project proved the feasibility of energy campaigns, with a goal of beneficial electrification, in cold, remote locations. The Thermalize Juneau team compiled a Guidebook to Thermalize Campaigns, available online. In addition to documenting what occurred in Alaska’s first thermalize campaign, it provides tips and resources for other communities wishing to implement a similar program.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Verification Testing of OLI Systems Mixed Solvent Electrolyte Model for the Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 ) System to High Ionic Strength at 25°C

This technical report summarizes model verification results and summary statistics for 41 evaporite mineral solubility cases evaluated by Savannah River National Laboratory using OLI Systems’ aqueous electrolyte thermodynamic modeling software. The 41 verification cases containing a total of 60 solubility curves comprise mineral solubility data from low to high ionic strength at 25°C for the eight-component system Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 O as reported by Harvie et al. (1984). Thermodynamic calculations were executed using OLI Systems’ Stream Analyzer computation module within the OLI Studio software platform (Ver. 11.0, Rev. 11.0.1.9). The Mixed Solvent Electrolyte (MSE) thermodynamic framework was chosen for this investigation because of its superiority in modeling high ionic-strength inorganic salt solutions and actinide redox chemistry and solubility, both of which are relevant to the geological repository conditions at the Waste Isolation Pilot Plant in Carlsbad, New Mexico. Mineral solubility data in various inorganic salt solutions were digitized and extracted from figures generated by Harvie et al. (1984). For each of the 60 solubility curves, a case-specific chemistry model and input file were generated in OLI Studio using OLI Stream Analyzer and the MSE (H 3 O + ion) public databank provided by OLI Systems. Model simulation results were exported to Microsoft Excel to calculate summary statistics and to generate graphs comparing the OLI model predictions to the solubility data. Summary statistics include residuals (model – data) and concordance (accuracy × precision, where precision is indicated by the Pearson correlation coefficient and accuracy accounts for bias and scale differential). Private databanks were not developed, and activity coefficient model regressions were not performed to improve OLI model fits to the data. Of the 41 model verification plots, 83% have a mean of the percent residuals less than or equal to 25%. Similarly, 75% display a concordance greater than or equal to 0.75. Only seven of the 41 verification plots fail to show good agreement between the model and data. Of these seven, three are relevant to the WIPP repository because they involve the Mg-OH-Cl-SO 4 -CO 3 aqueous system. The remaining four address salt solubilities at the pH extremes (strong acid and strong base). It should be noted that in two of the three Mg-OH-Cl-SO 4 -CO 3 system cases, the regressed Harvie et al. (1984) solubility curve also deviated from the data. Lack of agreement between the OLI model-predicted solubility curves and the data is attributable to one or more of the following: specific solid species are not included in the OLI MSE databank; there is significant variation among the different solubility datasets chosen by Harvie et al. (1984); the OLI MSE model’s thermodynamic parameters were determined using different solubility datasets; and the activity coefficient parameters for certain relevant ion-ion and ion-molecule pairs have not been optimized via data regression. Two recommendations for future work are to (1) evaluate solubility data for the Mg-OH-Cl-SO 4 -CO 3 system at high ionic strength and, if necessary, develop a private OLI MSE database that includes missing species and, where necessary, regressed standard state properties and interaction parameters; (2) perform similar verification testing of the OLI model for actinide solubility data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Evaluating the Cloud for Capability Class Leadership Workloads

Cloud platforms offer a variety of benefits that are very appealing for a large scale HPC facility with a diverse and dynamic user base and workload set. At the same time, there is cause for concern about transitioning to the cloud. Incorporating cloud resources into existing HPC facilities or even fully transitioning to a cloud deployment poses significant challenges at the technical, organizational, and economic levels. Regardless, based on current trends it is highly likely that cloud platforms will become an integral component of many HPC centers in some form. To gain a better understanding of both the limitations and capabilities of current cloud infrastructures we evaluated the public offerings of the three leading cloud platforms (Amazon Web Services, Microsoft Azure, and Google Cloud Platform) using a selection of representative application workloads from our facility. Our findings show that while current HPC offerings are still nascent, significant progress is being made to address the present shortcomings. At the same time, significant challenges and questions remain about whether HPC cloud offerings will be able to deliver the full range of expected benefits.

97 MATHEMATICS AND COMPUTING↗

Assessment of Cloud-Based Applications Enabling a Scalable Risk-Informed Predictive Maintenance Strategy Across the Nuclear Fleet

The current light water reactor fleet uses time-based or failure-based maintenance strategies to achieve high-capacity factors. But to make nuclear more competitive in the energy market, these reactors could utilize emerging technologies in terms of artificial intelligence (AI) and cloud computing to enable a cost-effective, predictive maintenance strategy. This report examines the feasibility of cloud computing for the nuclear industry’s needs in terms of the cloud’s computing capabilities, feasibility, and regulatory concerns. The technical viability of cloud computing was analyzed using one year worth of data from a boiling water reactor’s safety relief valve. Models were hosted on a local desktop, Idaho National Laboratory’s high-performance computer, and Microsoft Azure. Data was loaded, processed, and two types of models were trained in an A/B fashion. Based on the speed at which these actions were completed, it was used to determined that cloud computing has adequate computing resources. Additionally, the computing power can scale with the demanded load. To enable cloud computing in the existing fleet, additional sensors, networks, and other requirements must be implemented to ensure a smooth transition from current maintenance strategies. However, there is a benefit as the plant no longer needs manage their own servers, software, cybersecurity, and IT support staff. Many of these features can be offloaded on to the cloud provider. A comprehensive analysis was completed that showed the current annual cost of operating is more expensive than using cloud computing resources. Lastly, the regulatory framework does not explicitly address AI or autonomous control. Currently, the NRC and other regulatory bodies are evaluating providing guidance to address gaps rather than new regulations to address the use of AI and ML. But since many of the AI applications are focused on non-safety related applications, such as balance-of-plant components, they will likely have little or no regulatory restrictions or necessary approvals. Demonstrating how AI can improve maintenance and operation of these non-safety related systems seems like the likely path forward for implementing AI and cloud computing resources inside nuclear power plants (NPPs).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

PRO-X Research Reactor Database Status

The PRO-X Research Reactor Database is a functioning tool that can be used to quickly view attributes of past, current, and future research reactors. It contains all data found in the IAEA Research Reactor Database and entries generated from the M3 fuel conversion program. Additionally, it can be downloaded to any computer with the ability to run Microsoft ACCESS. Several research reactor attributes visible to the user have a limited amount of information, much of which is available and vetted for entry into the database. However, the necessary resources have not been allocated to add this information to the data tables. A change management system has also been developed to track changes to the database. This would need to be incorporated into the database program prior to data table modification in order to ensure proper management of the changes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Integrated Risk-Informed Condition Based Maintenance Capability and Automated Platform: Technical Report 1

Due to continuing global energy market trends, driven heavily by the abundant preserves of natural gas, there is an immediate need to reduce costs associated with operation and maintenance (O&M) for the current domestic nuclear power industry and for future reactor developments. This is to ensure that nuclear power generation remains an economically competitive and viable option in the energy market. O&M costs include labor-intensive preventive maintenance (PM) programs, which involve manually-performed inspection, calibration, testing, and maintenance of plant assets at periodic frequency and time-based replacement of assets, irrespective of their condition. This has resulted in an expensive, labor-centric business model to achieve high capacity factors. Fortunately, there are technologies (advanced sensors, data analytics, and risk assessment methodologies) that can enable the transition from a labor-centric business model to a technology-centric business model. The technology-centric business model will result in a significant reduction of PM activities, laying the foundation for real-time condition assessment of plant assets, reducing overall labor and part costs. To enable this transition, PKMJ Technical Services LLC is partnering with the U.S. Department of Energy’s Idaho National Laboratory (operated by the Battelle Energy Alliance, LLC) and the Public Services Enterprise Group (PSEG) Nuclear, LLC in the Integrated Risk-Informed Condition-Based Maintenance Capability and Automated Platform Project. In this report, the configuration of a digital cloud platform using Microsoft Azure is discussed, data from the PSEG Salem Nuclear Generating Station Units 1 & 2 are imported into a digital cloud platform, and the data is used for an evaluation of several key areas: cost impact analysis, risk-informed model development, and preventive maintenance strategy optimization. First, the cost impact analysis reviews which plant assets are potential good candidates for condition-based monitoring. Next, INL utilized the data in their local environment to develop the risk-informed model; which provides estimates of failure rates and probability of failures of assets based upon their past performance. The developed model is performed on assets selected from the cost impact analysis. Lastly, engineers assess the preventive maintenance strategy for the selected assets at PSEG against maintenance strategies in the nuclear industry for similar assets to potentially identify acceptable justification for the extension of current maintenance frequencies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Verification and Validation of the PLTEMP/ANL Code for Thermal-Hydraulic Analysis of Experimental and Test Reactors, Volume 1

This is Volume 1 of a two-volume document that collects the verification and validation (V&V) works done for the PLTEMP/ANL code during the years of its development and improvement. Volume 1 describes the V&V of sixteen capabilities of the PLTEMP/ANL code that were identified by research reactor analysts as frequently used in their thermal-hydraulic analysis. Volume 2 describes the V&V of developments and improvements since the release of PLTEMP/ANL Version 4.3. Each chapter of the document focuses on verifying or validating a specific part of the software that calculates a specific phenomenon, e.g., channel flow calculation, coolant property calculation, heat transfer calculation, and flow instability calculation. Software verification is performed by comparing the code with hand calculation, Microsoft spreadsheet calculation, Mathematica calculation, or MATLAB calculation. The software validation is done by comparing the code with experimental data or a widely tested code like the RELAP5 code. In addition, some PLTEMP/ANL V&V works that are available in the open literature are simply cited in Volume 1 of the document. PLTEMP/ANL has been used in the safety analysis reports of several US and foreign research reactors licensed and converted from highly enriched uranium fuel to low-enriched uranium fuel. A list of such reactors is given in Volume 1 of the document.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification and Validation of the PLTEMP/ANL Code for Thermal-Hydraulic Analysis of Experimental and Test Reactors, Volume 2

This is Volume 2 of a two-volume document that collects the verification and validation (V&V) works done for the PLTEMP/ANL code during the years of its development and improvement. Volume 1 describes the V&V of sixteen capabilities of the PLTEMP/ANL code that were identified by research reactor analysts as frequently used in their thermal-hydraulic analysis. Volume 2 describes the V&V of developments and improvements since the release of PLTEMP/ANL Version 4.3. Each chapter of the document focuses on verifying or validating a specific part of the software that calculates a particular phenomenon, e.g., channel flow calculation, coolant property calculation, heat transfer calculation, and flow instability calculation. Software verification is performed by comparing the code with a hand calculation, Microsoft spreadsheet calculation, Mathematica calculation, or MATLAB calculation. The software validation is achieved by comparing the code with experimental data or a widely tested code like the RELAP5 code. In addition, some PLTEMP/ANL V&V works that are available in the open literature are simply referenced in Volume 1 of the document. PLTEMP/ANL has been used in safety analysis reports of several US and foreign research reactors licensed and converted from highly enriched uranium fuel to low-enriched uranium fuel. A list of such reactors is given in Volume 1 of the document.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Clear Sky Toolkit: Decision Support User Guide

The Clear Sky Decision Support Template is a Microsoft Excel-based resource that enables users to screen and prioritize critical facilities for the addition of solar + storage. The Decision Support Template consolidates and streamlines the most relevant resources from the emergency management discipline, the electric utility sector, and national energy research institutions to assist in further site analysis and decision-making. The Decision Support Template is intended for use by local government and private sector decision-makers who aim to mitigate the effects of power outages on critical infrastructure, understand the potential for deploying photovoltaic (PV) and storage solutions on critical facilities, and align emergency management planning processes and utility needs with community resilience objectives. The Decision Support Template is divided into five modules that provide a structured, step-by-step approach users can follow and apply to unique circumstances. This process guides a more thorough and accurate assessment of a site's potential to accommodate a solar + storage system, provide grid benefits to utilities, and support community resilience and disaster mitigation for the broader region. After identifying potentially viable and preferred sites for solar + storage using the Decision Support Template, users should conduct a more detailed evaluation and consultation with a solar professional.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

AMPP-4 Tank Tracking Tools

The Material Recovery & Recycle group (AMPP-4) Tank Tracking Tools are Microsoft Excel-based tools used to visualize the liquid levels in the tanks used by teams within AMPP-4. The tools rely on reports generated by the Tracking Hydrogen Accumulation in Aqueous Operations spreadsheet to provide daily data of the volume occupied by radioactive liquid waste (RLW). This set-up allows for rapid-response in viewing historical (from October 2024) and current data in thermometer-type charts.

97 MATHEMATICS AND COMPUTING↗

Decision and Control of Complex Systems – A Data-Drive Framework

During the project period, we have collaborated with other team members and developed novel algorithms for novelty detection, continual learning, and graph learning algorithms for dynamic systems. The results are documented in publications and meeting notes. Moreover, we leverage virtual collaboration tools (such as Basecamp, Microsoft Teams and Zoom) for technical exchanges. Our research on novelty detection was published at AAAI 2022 and Lecture Notes in Artificial Intelligence, Springer Nature. The newly developed algorithms were successfully applied to realistic cases, including thermal data from buildings at Pacific Northwest National Lab and microelectronic data provided by GlobalFoundries. Multiple publications have been produced from this project, in collaboration with other team members. Three PhD students were supported in this project to conduct their research.

42 ENGINEERING↗

Scaling a Podman Container Factory in the Cloud

This technical report describes an implementation of a scalable continuous integration/continuous deployment infrastructure using Microsoft Azure™ and GitLab™ resources. We utilize GitLab continuous integration podman executors to provide rootless container operations in both privileged and unprivileged modes of operation. We utilize the GitLab Fleeting plugin for Azure to manage the scaling of continuous integration execution resources. This creates a scalable, rootless, and isolate continuous integration/continuous deployment job execution infrastructure.

97 MATHEMATICS AND COMPUTING↗