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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5

Characterization and Optimization of the Fitting of Quantum Correlation Functions

This case study presents a characterization and optimization of an application code for extracting parton distribution functions from high energy electron-proton scattering data. Profiling this application code reveals that the phase-space density computation accounts for 93% of the overall execution time for a single iteration on a single core. When executing multiple iterations in parallel on a multicore system, the application spends 78% of its overall execution time idling due to load imbalance. We address these issues by first transforming the application code from Python to C++ and then tackling the application load imbalance via a hybrid scheduling strategy that combines dynamic and static scheduling. These techniques result in a 62% reduction in CPU idle time and a 2.46x speedup in overall execution time per node. In addition, the typically enabled power-management mechanisms in supercomputers (e.g., AMD Turbo Core, Intel Turbo Boost, and RAPL) can significantly impact intra-node scalability when more than 50% of the CPU cores are used. This finding underscores the importance of understanding system interactions with power management, as they can adversely impact application performance, and highlights the necessity of intra-node scaling tests to identify performance degradation that inter-node scaling tests might otherwise overlook.

Chuang, Pi-Yueh [Virginia Tech,Dept. of Computer S↗

TA-16-0303 Crystal Grow Lab Renovation

The LANL High Explosives (HE) Crystal Lab at TA-40 Building 12 is a unique, and nearly the sole, national resource for the growth and sample preparation of large HE single crystals and related materials. This work has outgrown is current facility and is in dire need of both additional space and modern lab technology. The goal of this project is to renovate the 1950’s era building TA-16-303 to accommodate these operations and successfully relocate them from TA-40-12. Phase 1 of this project, completed in May of 2018, was to de-energize the facility and perform cleanup / remediation activities. Phase 2, the actual renovation of the facility, is currently underway and scheduled to achieve Occupancy by September of 2020.

99 GENERAL AND MISCELLANEOUS↗

Laser Powder Bed Fusion Additive Manufacture Nb1Zr Development

Next generation fission and fusion nuclear reactors require materials that can withstand operating temperatures greater than 500 °C, neutron irradiation doses of up to 200 displacements per atom (dpa), and potentially corrosive coolants such as the alkali liquid metals sodium, lithium, and NaK (Na33K eutectic alloy). Refractory alloys, such as Nb1Zr (Nb-1wt%Zr) and Molybdenum alloy TZM (Mo-0.5wt%Ti-0.08wt%Zr) have been traditionally considered viable candidates for advanced fission and fusion reactor concepts. However, it is relatively difficult to generate complex geometries of interest from these alloys using traditional manufacturing methods. In addition, there needs to be a concentrated effort to address refractory metal challenges at elevated temperature operation. In order to generate complex geometries of interest, modern manufacturing techniques are considered to increase the technological readiness level (TRL), cost-effectiveness, and schedule savings. This work focused on the continued development of laser powder bed fusion (L-PBF) additive manufacturing (AM) to improve both design flexibility, evaluate microstructure and properties, and ultimately accelerate the TRL and qualification of these processes and alloys for components to potentially be put into service. Niobium alloy Nb1Zr was identified through a down-selection process outlined in previous reports as a candidate to develop in L-PBF AM. Historically, Nb1Zr had been explored for high temperature fast spectrum fission reactors for both terrestrial and space applications. Molybdenum alloy TZM has also been considered for these reactor concepts due to exceptional high-temperature strength, creep resistance, and stability under irradiation. L-PBF AM of TZM has previously been investigated at LANL under the Microreactor program, NASA, ORNL, and in academia. However, due to the crack prone nature of TZM, L-PBF AM of TZM resulted in significant microcracking and additional development is required to pursue viable maturation. Other AM methods have been found to be more successful in printing TZM, and those alternatives approaches are discussed in this effort. The efforts detailed in this report focused on continued development of Nb1Zr through L-PBF and development of TZM via L-PBF and electron powder bed fusion (E-PBF). The objective of this work was to further the development of these AM techniques for the chosen refractory alloys, elucidating and addressing associated challenges through characterization of several demonstration builds. At LANL, Nb1Zr builds were completed using an EOS M290 and M400 machines, and a refractory alloy-dedicated L-PBF system, the Xact Metal XM200G, was installed. The XM200G primary purpose was to do the Nb1Zr parameter development process; however, due to difficulties associated with the machine installation and qualification process, it was decided to pivot development to the larger M400 and M290 machines. Although the supply of Nb1Zr powder was limited, it was sufficient to generate sub-scale metallographic specimens for the purpose of parameter development. This was first accomplished on the EOS M400 then the M290 due to machine schedule availability. Further development of TZM has been initiated at the University of Texas El Paso (UTEP) under contract with LANL to use both a heated build envelope L-PBF machine and E-PBF machine that have been found in the literature to mitigate microcracking. UTEP was provided with TZM powder and build plates to support parallel TZM parameter development across both machines. As part of the contract, UTEP will also be conducting microstructural characterization once optimized process parameters have been identified. The optimized process parameters for each machine will be used to generate a series of metallographic, mechanical, and surface finish specimens for subsequent characterization and testing. In the next section, we provide a detailed discussion of the methodology used for investigating the feasibility of leveraging these alloys for use in advanced reactor applications.

36 MATERIALS SCIENCE↗

Exploring Grid-Interactive Efficient Building Strategies for Laboratories Through Energy Modeling

Laboratories are often overlooked in demand flexibility research due to constraints on their operations as mission critical facilities, despite the major role they play in an organization's emissions. Laboratories consume 3-4 times more energy than a typical office building and are commonly the largest energy users on any campus. Consequently, most laboratories in the United States are significant contributors to their organization's carbon footprint if their energy needs are met through the combustion of fossil fuels. As part of the initiative to decarbonize laboratories, this report documents an analysis on specifically grid-interactive efficient building (GEB) opportunities for reducing energy costs and emissions associated with laboratory operations. The goal of this initiative was to provide a case study and guidance on how to use OpenStudio and REopt as modeling tools for GEB technologies and strategies in laboratory environments across different climate zones in the United States. The analysis found that efficiency-based GEB strategies had the most significant impact on laboratory operations, while load-shedding and load-shifting GEB strategies produced smaller results. The culmination of these approaches applied across all five climate zones generated on average: 1) 28% energy cost savings and 30% greenhouse gas (GHG) emissions reductions, and 2) 4% enhanced energy cost savings under a time-of-use (TOU) pricing schedule compared to traditional pricing schemes. Grid-interactive efficiency building measures were found to produce the greatest energy savings in both electricity and natural gas, particularly in regions with high electrical loads, such as warm climates for cooling. Laboratories that had high levels of natural gas consumption, meanwhile, experienced the greatest emission reductions. The report concludes with an analysis on the opportunities for flexible loads in lab spaces and how small-scale measures in addition to opaque pricing structures for peak demand could become barriers to demand flexibility planning. The report also explores how electrifying laboratory buildings with heat pumps could reduce energy costs and GHG emissions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Continuous-time look-ahead flexible ramp scheduling in real-time operation

This paper develops a novel continuous-time look-ahead optimization model for co-optimizing balancing energy and flexible ramp products in real-time power systems operation. In addition, a continuous-time day-ahead operation model is developed to commit and schedule an adequate subset of generating units for providing balancing energy and ramping requirements in real-time operation. The up and down flexible ramp products are defined as continuous-time decision trajectories that continuously supply the real-time up and down ramping requirements of the system. The deliverability of flexible ramp products is secured through reserving the respective power requirements in generation capacity constraints of generating units. A function space solution method is proposed to reduce the dimensionality of day-ahead and real-time models through projecting them into finite-dimensional function spaces spanned by Bernstein polynomials, where the real-time operation decisions are modeled with a higher accuracy level than day-ahead decisions. Simulations are conducted on the IEEE-RTS system using CAISO load data, and the numerical results showcase the effectiveness of the proposed model in supplying the energy and flexible ramp requirements and avoiding ramping scarcity in the system, while reducing the operation costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Long-Length SiC/SiC Tube Irradiation Experiment at LWR Temperatures Inserted into HFIR

This report describes the pre-irradiation characterization and successful assembly of a High Flux Isotope Reactor (HFIR) irradiation experiment designed to assess radiation-induced lateral bowing of silicon carbide fiber–reinforced, silicon carbide matrix composite (SiC/SiC) components under a radial fast neutron flux gradient at representative light-water reactor (LWR) temperatures of approximately 300 °C. The over-arching goal of this work is to validate thermomechanical models of SiC/SiC composite fuel assembly distortion used to predict the extent of lateral bowing and dose at which bowing reaches a maximum value. Ultimately, these models are used to ensure that fuel assembly distortion does not block coolant channels, interfere with control rod/blade movements, and/or impact local reactivity. The experiment contains six cladding tube specimens that are approximately 558.5 mm long with representative pressurized water reactor (PWR) outer and inner diameters of 9.5 mm and 7.5 mm, respectively. The specimens were thoroughly characterized prior to irradiation using traditional dimensional inspection and surface profilometry so that these measurements can later be compared with similar measurements that will be made post-irradiation to determine radiation-induced deformations. Furthermore, fine engraving markers were inscribed along the outer surfaces of the specimen and mapped using analytic photography and a three-dimensional stage. This technique allowed for accurate measurements of the marker spacings, which can be compared with similar measurements that will be made post-irradiation to provide local radiation-induced strain mapping. A light curtain optical micrometer was also employed to measure the pre-irradiation bowing of each specimen. The experiment was successfully assembled and inserted into position VXF-19 for HFIR cycle 516, which began May 12, 2026. The experiment will be removed after cycle 519, which is currently scheduled to end in December 2026.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Exploring the Use of Novel Spatial Accelerators in Scientific Applications

Driven by the need to find alternative accelerators which can viably replace GPUs in next-generation Supercomputing systems, this paper proposes a methodology to enable agile application/hardware co-design. The application-first methodology provides the ability to come up with design of accelerators while working with real-world workloads, available accelerators, and system software. The iterative design process targets a set of kernels in a workload for performance estimates that can prune the design space for later phases of detailed architectural evaluations. To this effect, in this paper, a novel data-parallel device model is introduced that simulates the latency of performance-sensitive operations in an accelerator including data transfers and kernel computation using multi-core CPUs. The use of off-the-shelf simulators, such as pre-RTL simulator Aladdin or multiple tools available for exploring the design of deep neural network accelerators (e.g., Timeloop) is demonstrated for evaluation of various accelerator designs using applications with realistic inputs. Examples of multiple device configurations that are instantiable in a system are explored to evaluate the performance benefit of deploying novel accelerators. The proposed device is integrated with a programming model and system software to potentially explore the impacts of high-level programming languages/compilers and low-level effects such as task scheduling on multiple accelerators. We analyze our methodology for a set of applications that represent high-performance computing (HPC) and graph analytics. The applications include a computational chemistry kernel realized using tensor contractions, triangle counting, GraphSAGE and Breadth-first Search. These applications include kernels such as dense matrix-dense matrix multiplication, sparse matrix-spare matrix multiplication, and sparse matrix-dense vector multiplication. Our results indicate potential performance benefits and insights for system design by including accelerators that realize these kernels along-side general purpose accelerators.

AI, codesign, Accelerated Computing, Modeling and ↗

Bayesian Structural Time Series for Behind-the-Meter Photovoltaic Disaggregation

Distributed photovoltaic (PV) generation often occurs ``behind the meter": a grid operator can only observe the net load, which is the sum of the gross load and distributed PV generation. This lack of observability poses a challenge to system operation at both bulk level and distribution level. The lack of real-time or near-future disaggregated estimates of gross load and PV generation will lead to over scheduling of energy production and regulation reserves, reliability constraints violations, wear and tear of controller devices, and potentially cascading failures of a system. In this paper we propose the use of a Bayesian Structural Time Series (BSTS) model with local solar irradiance measurements to disaggregate the summed PV generation and gross load signals at a downstream measurement site. BSTSs are a highly expressive model class that blends classic time series models with the powerful Bayesian state space estimation framework. Disaggregation is done probabilistically, which automatically quantifies the uncertainties of the estimated PV generation and gross load consumption. Depending on the data availability in real-time, it can be used to disaggragate PV and gross load at customer site, or can be used at the feeder level. In this paper, we focus on solving the problem at feeder level. We compare the performance of a BSTS model as well as a handful of state-of-the-art methods on a Pecan Street AMI dataset, using the National Solar Radiation Database (NSRDB) to estimate local irradiance.

bayesian structural time series↗

How Many Trip Requests Could We Support? An Activity-Travel Based Vehicle Scheduling Approach

In a world of ever-changing travel behavior and ever-increasing modal options, is vital to have integrated models that could capture the interactions between supply and demand layers of travel. Addressing this need, we propose three different versions of network representation and mathematical models for the activity-based vehicle routing problem to connect activity-travel graphs of passengers (demand layer) to spatio-temporal networks of vehicles (supply layer). Versions I and II are arc-based, while version III is path-based. In version I, we introduce the concept of activity-travel graphs for passengers. For vehicles, we construct space–time networks and add a new dimension, called “under-service state”, to track the execution status of trip requests at any location and time. In version II, we reduce the complexity of the network structure by eliminating the state dimension and some other modifications in the structure of the passengers’ and vehicles’ network. Although both versions can capture various behavioral constraints of the activity-based vehicle routing problem (e.g., mandatory and optimal activities, duration of activities, chain of activities, preferred starting and ending times of activities), due to the high level of complexity of the network structure, both versions can only solve small-sized problems. To tackle the computational complexity, we propose a path-based network representation in version III, and to make a balance between the disutility of passengers and vehicles, we present a tolled user equilibrium problem. Mathematical models are coded in C and GAMS and implemented on real-world Phoenix regional transportation network with more than 39 million trip requests, which demonstrate the effectiveness of the proposed solution for the original and restricted master problems.

33 ADVANCED PROPULSION SYSTEMS↗

Prototype College Building Energy Model: Building Characteristics and Energy Simulation Results

The US Department of Energy supports the development of commercial building energy codes and standards. To support commercial building energy research activities and the development of commercial building energy codes and standards, continuous efforts have been made to convert 16 prototype building models, which cover 80% of US commercial building floor space, to OpenStudio prototype buildings. Additionally, the suite of prototype building models was expanded to include the addition of new building prototype models (e.g., courthouse, college building). Multiple sources, including databases, documented projects, and personal communications, were used to define the prototype college building, and a 4-story with 69,063 ft 2 building was considered as the prototype college building to represent an average-sized college building in the United States. To represent realistic occupancy schedules and increase the granularity of information, actual class reservation schedules were collected and used. This report documents the building and system characteristics of the prototype college building model combined with climate-specific and construction vintage–specific requirements for the building envelope and systems from ASHRAE Standard 90.1. The energy simulation results are presented for 4 construction vintages (2004, 2007, 2010, and 2013) and 15 ASHRAE climate zones. The site energy use intensity of the college building was compared with 2012 Commercial Building Energy Consumption Survey (CBECS) and ENERGY STAR data to verify the simulation results. The site energy use intensity of the college building ranged from 60 to 202.4 kBtu/ft 2 , and compared with the energy use intensities of Commercial Building Energy Consumption Survey (122.9 kBtu/ft 2 ) and ENERGY STAR (84.3 kBtu/ft 2 ) data, the prototype college building results are in a reasonable range.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Emerging Technologies for Improved Plug Load Management Systems: Learning Behavior Algorithms and Automatic and Dynamic Load Detection

Plug loads are responsible for a significant portion of the energy consumed in commercial buildings, yet their distributed and ever-changing nature makes them one of the most challenging building end uses to manage. Plug load management systems exist today that utilize smart plugs to meter and control devices at the outlet level, however, their uptake has been relatively slow in part due to the significant labor required for installation and maintenance. Learning behavior algorithms and automatic and dynamic load detection have been identified as two technology areas that could accelerate the adoption of plug load management systems by reducing these labor demands and providing additional energy efficiency and non-energy benefits. Learning behavior algorithms learn occupant behavior and adjust plug load management systems accordingly, allowing for the automatic creation of optimized control schedules. Automatic and dynamic load detection allows a plug load management system to identify devices as they are plugged in to a building and keeps the system up to date as devices are moved throughout a building. In this paper, we present our findings with respect to the current state of these two technologies based on a review of existing research and patents, as well as a series of interviews with companies working in the plug load space. We have found that, as of now, no commercialized solutions exist for these plug load technologies and that more work is needed to bring them to market. In addition, we summarize our findings related to the technology challenges, market barriers, drivers, and opportunities for these technologies moving forward.

30 DIRECT ENERGY CONVERSION↗

Distributionally Robust Decision Making Leveraging Conditional Distributions

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

Chen, Yuxiao↗

Methodology for Exploring Water and Hydropower Operating Criteria That Simultaneously Improve Economic and Environmental Considerations

Despite the reliability and flexibility of hydropower, the operation of hydroelectric power plants may have significant impacts on the downstream river system, including its water stage, sediment transport, and water temperature, ultimately affecting the ecology. To address these challenges, there is a need to identify water scheduling patterns that improve both hydropower economics and the environment relative to current operations. This paper presents a new methodology to explore promising operational criteria/rules that can achieve such improvements. Typical environmental impact statements and relicensing processes generally perform detailed site-specific analyses of a few alternatives that focus on reservoir water release operating rules and their associated environmental impacts. In contrast, the methodology presented in this article uses a widely applicable approach that explores a much larger solution space. This large set of potential alternatives can be represented in a multidimensional space for which one axis represents the economic value and the other axis quantify individual environmental impacts (e.g., sediment transport and fish growth), and they are explored via two approaches: a Monte Carlo simulation that identifies “win–win” alternatives and a multi-objective optimization problem that identifies Pareto-optimal alternatives.

13 HYDRO ENERGY↗

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow

Computational simulations have become central to the seismic analysis and design of major infrastructure over the past several decades. Most major structures are now “proof tested” virtually through representative simulations of earthquake-induced response. More recently, with the advancement of high-performance computing (HPC) platforms and the associated massively parallel computational ecosystems, simulation is beginning to play a role in increased understanding and prediction of ground motions for earthquake hazard assessments. However, the computational requirements for regional-scale geophysics-based ground motion simulations are extreme, which has restricted the frequency resolution of direct simulations and limited the ability to perform the large number of simulations required to numerically explore the problem parametric space. In this article, recent developments toward an integrated, multidisciplinary earth science-engineering computational framework for the regional-scale simulation of both ground motions and resulting structural response are described with a particular emphasis on advancing simulations to frequencies relevant to engineered systems. This multidisciplinary computational development is being carried out as part of the US Department of Energy (DOE) Exascale Computing Project with the goal of achieving a computational framework poised to exploit emerging DOE exaflop computer platforms scheduled for the 2022–2023 timeframe.

58 GEOSCIENCES↗

Punzi-loss: a non-differentiable metric approximation for sensitivity optimisation in the search for new particles

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling, based on the minimisation of a figure-of-merit related function typical of particle physics, a Punzi-loss function, and the neural network that utilises this loss function a Punzi-net. We show that the Punzi-net outperforms standard multivariate analysis techniques and generalises well to mass hypotheses for which it was not trained. This is achieved by training a single classifier that provides a coherent and optimal classification of all signal hypotheses over the whole search space. Our result constitutes a complementary approach to fully differentiable analyses in particle physics. We implemented this work using PyTorch and provide users full access to a public repository containing all the codes and a training example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Radiation Hardened Engineered Substrates for Time and Space Resolution

Low Gain Avalanche Diodes (LGADs) have become sensors of choice for fast timing of minimum ionizing particles. The current generation of these devices suffer from only moderate radiation hardness, low fill factor, and limited design options. Cactus Materials Inc. proposes to develop sensors with gain layer implants buried beneath the surface which will, with AC coupling developed by Brookhaven National Laboratory (BNL) and University of California Santa Cruz (UC Santa Cruz) solve these problems. Fermilab has a major role in the CMS timing upgrade using the current generation of LGADs and development of AC-coupled, buried layer LGADs will solve some of the central problems inherent in this technology. Annex B included a two-year work plan, deliverables, schedule and funding for the project’s SBIR Phase II award to develop and test prototype LGADs utilizing wafer bonding technology and epitaxial growth, that will allow for fabrication of radiation hard AC coupled devices with 100% fill factor and adjustable operating point.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Development and Application of a Risk Analysis Toolkit for Plant Resources Optimization

This report summarizes the R&D activities of the Risk Informed Asset Management (RIAM) project during fiscal year 2020 (FY20). This project focuses on the development of methods designed to optimize plant operations (e.g., maintenance/replacement schedule, optimal maintenance posture) provided system/component health/cost data. This project development lives in cooperation with the Plant Health Management (PHM) project which focuses on the development of methods that integrate component health data and propagate such information at the system level to evaluate most relevant sources of risk. This year’s activities for the RIAM project focused on the continuation of schedule optimization algorithms developed in FY19. While in FY19 we focused on both deterministic and stochastic capital budgeting methods, in FY20 we moved forward by implementing two versions of schedule optimization methods. The first one reformulates the capital budgeting problem in a distributionally robust form which allows the user to rely on data directly rather than proposing a distribution from the data itself. The second version reformulates the capital budgeting explicitly using risk measures as variables to maximize/minimize. Lastly, we focused on the development of methods designed to identify the optimal maintenance posture based on the Pareto Frontier analysis. Rather than performing a tradeoff analysis (i.e., identify the absolute best posture), the Pareto Frontier analysis performs a trade space exploration approach (i.e., identify value and costs of several postures and have the analyst perform the task of imposing desired value and cost constraints). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space.

97 MATHEMATICS AND COMPUTING↗