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At least 325 records · Page 18

Resilient Disaster Recovery Logistics of Distribution Systems: Co-Optimize Service Restoration With Repair Crew and Mobile Power Source Dispatch

Repair crews (RCs) and mobile power sources (MPSs) are critical resources for distribution system (DS) outage management after a natural disaster. However, their logistics have not been well investigated. We propose a resilient scheme for disaster recovery logistics to co-optimize DS restoration with the dispatch of RCs and MPSs. A novel co-optimization model is formulated to route RCs and MPSs in the transportation network, schedule them in the DS, and reconfigure the DS for microgrid formation coordinately, etc. The model incorporates different timescales of DS restoration and RC/MPS dispatch, the coupling of transportation and power networks, etc. To ensure radiality of the DS with variable physical structure and MPS allocation, we also model topology constraints based on the concept of spanning forest. The model is convexified equivalently and linearized into a mixed-integer linear programming. To reduce its computation time, preprocessing methods are proposed to preassign a minimal set of repair tasks to depots and reduce the number of candidate nodes for MPS connection. Resilient recovery strategies thus are generated to enhance service restoration, especially by dynamic formation of microgrids that are powered by MPSs and topologized by repair actions of RCs and network reconfiguration of the DS. Case studies demonstrate the proposed methodology.

Disaster recovery logistics↗

Assessing Effects of Climate and Technology Uncertainties in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.

numerical methods↗

Cryogenic Curation of Lunar Samples Returned to Earth

Future lunar missions may collect samples that have been preserved at sub-freezing or even cryogenic temperatures. For such samples, the study of volatiles and temperature-sensitive minerals will have high priority. Valuable geochemical and mineralogical information will be lost if such samples are allowed to reach ambient temperatures on Earth. The ability to store, document, subdivide, and transport extraterrestrial geologic samples while maintaining sub-freezing or cryogenic temperatures, possibly as low as 40 K, is required for the complete scientific study of samples from cold environments. A lunar cryogenic sample return mission might require a combination of passive cooling during collection and cruise and active cooling during and after re-entry for maintaining desired temperatures. Once on Earth, cryocontainment must be maintained through delivery to a cryogenic chamber in the curatorial facility. This cryogenic curation chamber would include cameras and robotic manipulators for preliminary examination, subdivision of samples, and specialized sample allocation containers for shipment to laboratories world-wide. This presentation describes the planning and feasibility of cryogenic curation with current technologies developed for the superconductor industry. In addition, significant advanced research and development would be required to tailor some of these technologies to the task of sample return and long term curation of lunar samples at low temperatures in order to preserve their scientific integrity.

Calaway, Michael J.↗

Multilevel Monte Carlo Estimators For Derivative-Free Optimization Under Uncertainty

Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. Here, in this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.

97 MATHEMATICS AND COMPUTING↗

Sensitivity and Uncertainty Workflow of Full System SIERRA Models Supporting High Consequence Applications

Credibility of end-to-end CompSim (Computational Simulation) models and their agile execution requires an expressive framework to describe, communicate and execute complex computational tool chains representing the model. All stakeholders from system engineering and customers through model developers and V&V partners need views and functionalities of the workflow representing the model in a manner that is natural to their discipline. In the milestone and in this report we define workflow as a network of computation simulation activities executed autonomously on a distributed set of computational platforms. The FY19 ASC L2 Milestone (6802) for the Integrated Workflow (IWF) project was designed to integrate and improve existing capabilities or develop new functionalities to provide a wide range of stakeholders a coherent and intuitive platform capable of defining and executing CompSim modeling from analysis workflow definition to complex ensemble calculations. The main goal of the milestone was to advance the integrated workflow capabilities to support the weapon system analysts with a production deployment in FY20. Ensemble calculations supporting program decisions include sensitivity analysis, optimization and uncertainty quantification. The goal of the L2 milestone aligned with the ultimate goal of the IWF project is to foster cultural and technical shift toward and integrated CompSim capability based on automated workflows. Specific deliverables were defined in five broad categories: 1) Infrastructure, including development of distributed-computing workflow capability, 2) integration of Dakota (Sandia's sensitivity, optimization and UQ engine) with SAW (Sandia Analysis Workbench), 3) ARG (Automatic Report Generator introspecting analysis artifacts and generating human-readable extensible and archivable reports), 4) Libraries and Repositories aiding capability reuse, and 5) Exemplars to support training, capturing best practices and stress testing of the platform. A set of exemplars was defined to represent typical weapon system qualification CompSim projects. Analyzing the required capabilities and using the findings to plan implementation of required capabilities ensured optimal allocation of development resources focused on production deployment after the L2 is completed. It was recognized early that the end-to-end modeling applications pose a considerable number of diverse risks, and a formal risk tracking process was implemented. The project leveraged products, capabilities and development tasks of IWF partners. SAW, Dakota, Cubit, Sierra, Slycat, and NGA (NexGen Analytics, a small business) contributed to the integrated platform developed during this milestone effort. New products delivered include: a) NGW (Next Generation Workflow) for robust workflow definition and execution, b) Dakota wizards, editor and results visualization, and c) the automatic report generator ARG. User engagement was initiated early in the development process eliciting concrete requirements and actionable feedback to assure that the integrated CompSim capability will have high user acceptance and impact. The current integrated capabilities have been demonstrated and are continually being tested by a set of exemplars ranging from training scenarios to computationally demanding uncertainty analyses. The integrated workflow platform has been deployed on both SRN (Sandia Restricted Network) and SCN (Sandia Classified Network). Computational platforms where the system has been demonstrated span from Windows (Creo the CAD platform chosen by Sandia) to Trinity HPC (Sierra and CTH solvers). Follow up work will focus on deployment at SNL and other sites in the nuclear enterprise (LLNL, KCNSC), training and consulting support to democratize the analysis agility, process health and knowledge management benefits the NGW platform provides.

97 MATHEMATICS AND COMPUTING↗

Creating Innovative Frameworks to Spur Cultural Change at NASA Armstrong Flight Research Center

Changing the culture of an organization is a monumental task that often takes years and has no set formula. Steps can be taken, however, to spur cultural change by creating spaces and infrastructure to serve as the initial driving force. An innovation space and a bicycle sharing (bike share) program were implemented at the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) (Edwards, California) with a vision toward connecting Center personnel, fostering collaboration and innovation, retaining newer employees, promoting flexibility, and improving the culture and workplace atmosphere. This paper discusses the steps taken, challenges faced, novel culture-change-focused design elements, lessons learned, acquired metrics, and how these initiated cultural change at AFRC. For both the innovation space and the bike share program, funding was negotiated and provided through the NASA Convergent Aeronautics Solutions (CAS) project, which was seeking to improve the innovation and collaboration capabilities at each of the four NASA aeronautics Centers. Key stakeholders across AFRC from upper management, facilities, safety, engineering, and procurement were identified early in the process and were consulted and included throughout execution to ensure that any encountered roadblocks could be easily navigated. Research was then conducted by attending conferences and visiting culture-changing organizations both inside and outside United States Government agencies. Distilling the research, identifying available space, and deciding on specific design elements for the space was conducted by a subset of individuals of diverse backgrounds to enable quick, effective decision-making. Decisions were made with the intent to increase usage and diversity of users of the space; care was taken to ensure a well-crafted atmosphere that would foster the desired culture change. The allocated physical space required major structural modifications, new furniture, and new capabilities that would bring people in. Decisions and desires underwent a rapid reiterative process in order to stay within budget and short deadlines, while holding firm to what was seen as fundamental elements of an innovation space. The framework for cultural change being established, the more difficult task began: incubating the desired culture. Intentional workday use of the innovation space was encouraged, and organized events coordinated in order to truly foster culture change. Such incubation supports the organic spread of culture change to all areas of AFRC. This framework was complemented and expanded by the implementation of the bike share program. Steps for implementation included bike selection based on lessons learned, creating bike stations and signage, implementing bike share rules, and building a volunteer maintenance infrastructure. A novel user-reporting feedback system at each bike station is a low-impact method of capturing usage metrics. Due to the nature of the work conducted at AFRC, the bike share program and feedback system were negotiated and vetted through various organizations including legal, safety, and operations. The innovation space and the bike share program together are an effective initial framework for innovation and collaboration. Culture change takes time, but the innovation space and the bike share program are already showing signs of making a positive impact on the AFRC workforce.

rooms↗

Workload-Matched Adaptive Automation Support of Air Traffic Controller Information Processing Stages

Adaptive automation (AA) has been explored as a solution to the problems associated with human-automation interaction in supervisory control environments. However, research has focused on the performance effects of dynamic control allocations of early stage sensory and information acquisition functions. The present research compares the effects of AA to the entire range of information processing stages of human operators, such as air traffic controllers. The results provide evidence that the effectiveness of AA is dependent on the stage of task performance (human-machine system information processing) that is flexibly automated. The results suggest that humans are better able to adapt to AA when applied to lower-level sensory and psychomotor functions, such as information acquisition and action implementation, as compared to AA applied to cognitive (analysis and decision-making) tasks. The results also provide support for the use of AA, as compared to completely manual control. These results are discussed in terms of implications for AA design for aviation.

Kaber, David B.↗

SAS4A/SASSYS-1 Code Improvements for FY2016

SAS4A/SASSYS-1 is a simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced reactors. This report summarizes ongoing tasks to modernize the SAS4A/SASSYS-1 code system to improve internal data management, update several other code modules, and add new features. Code modernization activities focused on eliminating legacy data management in the balance-of-plant module, which was the only module that still used non-portable data allocation. Code extensions include the development of a new axial expansion model that can accurately account for non-uniform or heterogeneous fuel compositions. The most significant accomplishment is the addition of uncertainty quantification capabilities for transient simulations using the Dakota toolkit from Sandia National Laboratory. The motivation for performing these updates stems from the relevance of SAS4A/SASSYS-1 to a number of U.S. Department of Energy programs as well as domestic and international collaborations. External collaborations have also produced improvements in the SAS4A/SASSYS-1 code, and these are summarized in this report. SAS4A/SASSYS-1 has a growing user base that continues to strengthen the promotion of advanced reactor concepts such as sodium cooled fast reactors. Additional users will help solidify DOE’s leadership role in fast reactor safety both domestically and in international collaborations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Autonomous Fueling System for Heavy-Duty Fuel Cell Electric Trucks

The motivation for this project stemmed from the challenges associated with rapidly refueling heavy-duty hydrogen fuel cell electric trucks (FCETs). Current manual refueling processes for fast refueling involve large, heavy equipment (e.g., hoses three times heavier than standard) and pose ergonomic risks and potential for equipment damage. The goal was to develop and test an autonomous fueling system to improve ergonomics, enhance safety, increase equipment durability through design improvements, and potentially speed up the fueling process. This project aimed to add to the understanding of autonomous systems in the context of heavy-duty hydrogen refueling, evaluating the technical effectiveness of potential concepts. A successfully developed system would benefit the public by facilitating the adoption of zero-emission heavy-duty transport, reducing reliance on manual labor for a physically demanding task, and potentially improving the safety and efficiency of hydrogen refueling infrastructure. The major accomplishment during the project's active period was the completion of the system-level architecture task. This involved establishing a detailed list of system requirements covering interfaces, environmental conditions, regulatory compliance, industry standards, safety, security, performance capabilities, and optional features. Five key use cases for the autonomous system were also identified. However, due to internal restructuring at Nikola, the necessary resources could not be allocated to continue the project. Consequently, Nikola opted to discontinue the project. The award was mutually terminated by Nikola and the DOE.

08 HYDROGEN↗

Distributed multiport memory architecture

A multiport memory architecture is diclosed for each of a plurality of task centers connected to a command and data bus. Each task center, includes a memory and a plurality of devices which request direct memory access as needed. The memory includes an internal data bus and an internal address bus to which the devices are connected, and direct timing and control logic comprised of a 10-state ring counter for allocating memory devices by enabling AND gates connected to the request signal lines of the devices. The outputs of AND gates connected to the same device are combined by OR gates to form an acknowledgement signal that enables the devices to address the memory during the next clock period. The length of the ring counter may be effectively lengthened to any multiple of ten to allow for more direct memory access intervals in one repetitive sequence. One device is a network bus adapter which serially shifts onto the command and data bus, a data word (8 bits plus control and parity bits) during the next ten direct memory access intervals after it has been granted access. The NBA is therefore allocated only one access in every ten intervals, which is a predetermined interval for all centers. The ring counters of all centers are periodically synchronized by DMA SYNC signal to assure that all NBAs be able to function in synchronism for data transfer from one center to another.

Kohl, W. H.↗

mdtmFTP and its evaluation on ESNET SDN testbed

In this paper, to address the high-performance challenges of data transfer in the big data era, we are developing and implementing mdtmFTP: a high-performance data transfer tool for big data. mdtmFTP has four salient features. First, it adopts an I/O centric architecture to execute data transfer tasks. Second, it more efficiently utilizes the underlying multicore platform through optimized thread scheduling. Third, it implements a large virtual file mechanism to address the lots-of-small-files (LOSF) problem. In conclusion, mdtmFTP integrates multiple optimization mechanisms, including–zero copy, asynchronous I/O, pipelining, batch processing, and pre-allocated buffer pools–to enhance performance. mdtmFTP has been extensively tested and evaluated within the ESNET 100G testbed. Evaluations show that mdtmFTP can achieve higher performance than existing data transfer tools, such as GridFTP, FDT, and BBCP.

97 MATHEMATICS AND COMPUTING↗

Reference H Cycle 3 Stability, Control, and Flying Qualities Batch Assessments

This work is an update of the assessment completed in February of 1996, when a preliminary assessment report was issued for the Cycle 2B simulation model. The primary purpose of the final assessment was to re-evaluate each assessment against the flight control system (FCS) requirements document using the updated model. Only a limited number of final assessments were completed due to the close proximity of the release of the Langley model and the assessment deliverable date. The assessment used the nonlinear Cycle 3 simulation model because it combines nonlinear aeroelastic (quasi-static) aerodynamic with hinge moment and rate limited control surface deflections. Both Configuration Aerodynamics (Task 32) and Flight Controls (Task 36) were funded in 1996 to conduct the final stability and control assessments of the unaugmented Reference H configuration in FY96. Because the two tasks had similar output requirements, the work was divided such that Flight Controls would be responsible for the implementation and checkout of the simulation model and Configuration Aerodynamics for writing Madab "script' files, conducting the batch assessments and writing the assessment report. Additionally, Flight Controls was to investigate control surface allocations schemes different from the baseline Reference H in an effort to fulfill flying qualities criteria.

Henderson, Dennis K.↗

Flightspeed Integral Image Analysis Toolkit

The Flightspeed Integral Image Analysis Toolkit (FIIAT) is a C library that provides image analysis functions in a single, portable package. It provides basic low-level filtering, texture analysis, and subwindow descriptor for applications dealing with image interpretation and object recognition. Designed with spaceflight in mind, it addresses: Ease of integration (minimal external dependencies) Fast, real-time operation using integer arithmetic where possible (useful for platforms lacking a dedicated floatingpoint processor) Written entirely in C (easily modified) Mostly static memory allocation 8-bit image data The basic goal of the FIIAT library is to compute meaningful numerical descriptors for images or rectangular image regions. These n-vectors can then be used directly for novelty detection or pattern recognition, or as a feature space for higher-level pattern recognition tasks. The library provides routines for leveraging training data to derive descriptors that are most useful for a specific data set. Its runtime algorithms exploit a structure known as the "integral image." This is a caching method that permits fast summation of values within rectangular regions of an image. This integral frame facilitates a wide range of fast image-processing functions. This toolkit has applicability to a wide range of autonomous image analysis tasks in the space-flight domain, including novelty detection, object and scene classification, target detection for autonomous instrument placement, and science analysis of geomorphology. It makes real-time texture and pattern recognition possible for platforms with severe computational restraints. The software provides an order of magnitude speed increase over alternative software libraries currently in use by the research community. FIIAT can commercially support intelligent video cameras used in intelligent surveillance. It is also useful for object recognition by robots or other autonomous vehicles

Thompson, David R.↗

Optimal dispatch for participation of electric vehicles in frequency regulation based on area control error and area regulation requirement

In this study, optimal strategies are proposed for electric vehicles in charging stations to participate in the secondary frequency regulation, while considering their charging demands. In order to fairly allocate the dispatch from the control center among electric vehicles according to their charging demands, two optimal real-time strategies are proposed, respectively based on area control error and area regulation requirement. With the proposed strategies, the expected charging of electric vehicles is optimally tracked in real time by using the regulation task from the control center. Simulations on a two-area interconnected power grid show that the proposed two strategies can respectively lead to a 12.66% and 16.78% frequency deviation reduction and a 13.76% and 9.86% generator regulation reduction. At the same time, the charging demands of EVs can also be ensured.

33 ADVANCED PROPULSION SYSTEMS↗

Management by Trajectory Trade Study of Roles and Responsibilities Between Participants and Automation Report

This report describes a trade study of roles and responsibilities associated with the Management by Trajectory (MBT) concept. The MBT concept describes roles, responsibilities, and information and automation requirements for providing air traffic controllers and managers the ability to quickly generate, evaluate and implement changes to an aircraft's trajectory. In addition, the MBT concept describes mechanisms for imposing constraints on flight operator preferred trajectories only to the extent necessary to maintain safe and efficient traffic flows, and the concept provides a method for the exchange of trajectory information between ground automation systems and the aircraft that allows for trajectory synchronization and trajectory negotiation. The participant roles considered in this trade study include: airline dispatcher, flight crew, radar controller, traffic manager, and Air Traffic Control System Command Center (ATCSCC) traffic management specialists. The proposed allocation of roles and responsibilities was based on analysis of several use cases that were developed for this purpose as well as for walking through concept elements. The resulting allocation of roles and responsibilities reflects both increased automation capability to support many aviation functions, as well as increased flexibility to assign responsibilities to different participants - in many cases afforded by the increased automation capabilities. Note that the selection of participants to consider for allocation of each function is necessarily rooted in the current environment, in that MBT is envisioned as an evolution of the National Airspace System (NAS), and not a revolution. A key feature of the MBT allocations is a vision for the traffic management specialist to take on a greater role. This is facilitated by the vision that separation management functions, in addition to traffic management functions, will be carried out as trajectory management functions. This creates an opportunity for flexibility, allowing the traffic management specialist to carry out tasks that today can only be carried out by the controller currently in contact with the aircraft. This additional tasking for the traffic management specialist comes with requirements for workload management. An increased role for the Data-side (D-side) controller relative to the Radar-side (R-side) controller is a potential approach to mitigating workload for the traffic management specialist, as the D-side controller would have similar ability to perform separation management functions in what today might be considered the "trajectory management" timeframe. This analysis did not distinguish between the D-side and R-side controllers since in many cases the R-side controller works unassisted.

Fernandes, Alicia D.↗

Exploring New Frontiers in Space Communications: Enhancing Delay Tolerant Networking through Cloud and Containerization

The High-rate Delay Tolerant Networking (HDTN) project at NASA Glenn Research Center has developed software that enables more flexible, reliable, and efficient space internetworking by using modern computing techniques such as cloud services, microservices, network function virtualization, software defined networking, and a distributed architecture. HDTN is built upon the Bundle Protocol and related convergence layers which have been developed to mitigate the challenges of the space networking environment including long delays, asymmetric data rates, and intermittent connectivity. The HDTN implementation employs asynchronous message processing tasks which allow for non-blocking operations as well as deployment in both centralized and distributed architectures. This paper investigates deploying HDTN in a containerized approach on the NASA Goddard’s Mission Cloud Platform using Amazon Web Services Elastic Compute Cloud (EC2). Commercial cloud computing will lower operating costs, provide flexible resource allocation, and allow for interconnectivity between multiple NASA centers as well as external partners. Containerization using Docker will enable greater portability and scalability for HDTN to be deployed into a variety of environments. We discuss possible NASA missions and use-cases such as the Laser Communications Relay Demonstration (LCRD) where the services provided by HDTN (reliable transport, high-rate message processing, and store-and-forward capabilities) will be enhanced through cloud computing and containerization. In addition, we describe the HDTN architecture and possible microservice-based networking approaches that can be obtained via HDTN’s configuration capabilities. Finally, we detail the EC2 specifications needed to achieve data rates greater than 1 Gbps to support optical communication missions such as LCRD.

Blake LaFuente↗

Conceptual Design Report for the I2 Instrumentation Experiment in ATRC

The US Department of Energy In-Pile Instrumentation (I2) program is tasked with developing advanced sensors for in-pile service as well as supporting the engineering required to implement existing nuclear sensor technologies in US high-power test reactors. The ATRC instrumentation test has been conceived to address both of these missions, specifically with respect to neutron flux measurements. Space has been allocated in the test for Self-Powered Neutron Detectors (SPNDs), fission chambers, and Micro-Pocket Fission Detectors (MPFDs). The real-time flux readings obtained from these instruments will be compared with time integrated data obtained from passive neutron dosimetry (i.e., “flux” wires). This work will be complementary to data obtained from the TREAT MIMIC-N experiment. This experiment is expected to support instrumentation efforts related to the proposed Medium-I loop and to instrumenting loop experiments conducted in the ATR center flux trap. While the MIMIC-N experiment was conducted in a dry environment, the ATRC I-19 experiment will be conducted in an aqueous environment, similar to the center flux trap loop experiments but will take place at ambient temperature and pressure, and at a much lower neutron flux. One of the challenges of the ATRC I-19 experiment will be low amplitude signals produced by the sensors in the low neutron fluxes of ATRC. However, related work conducted several years ago in ATRC was able to reliably detect signals using a similar instrument set.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Use of Dynamic Models and Operational Architecture to Solve Complex Navy Challenges

The United States Navy established 8 Maritime Operations Centers (MOC) to enhance the command and control of forces at the operational level of warfare. Each MOC is a headquarters manned by qualified joint operational-level staffs, and enabled by globally interoperable C41 systems. To assess and refine MOC staffing, equipment, and schedules, a dynamic software model was developed. The model leverages pre-existing operational process architecture, joint military task lists that define activities and their precedence relations, as well as Navy documents that specify manning and roles per activity. The software model serves as a "computational wind-tunnel" in which to test a MOC on a mission, and to refine its structure, staffing, processes, and schedules. More generally, the model supports resource allocation decisions concerning Doctrine, Organization, Training, Material, Leadership, Personnel and Facilities (DOTMLPF) at MOCs around the world. A rapid prototype effort efficiently produced this software in less than five months, using an integrated process team consisting of MOC military and civilian staff, modeling experts, and software developers. The work reported here was conducted for Commander, United States Fleet Forces Command in Norfolk, Virginia, code N5-0LW (Operational Level of War) that facilitates the identification, consolidation, and prioritization of MOC capabilities requirements, and implementation and delivery of MOC solutions.

Grande, Darby↗