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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 55 records · Page 3

Long-term variability in immersion-mode marine ice-nucleating particles from climate model simulations and observations

Abstract. Ice-nucleating particles (INPs) in the Southern Ocean (SO) atmosphere have significant impacts on cloud radiative and microphysical properties. Yet, INP prediction skill in climate models remains poorly understood, in part because of the lack of long-term measurements. Here we show, for the first time, how model-simulated INP concentrations compare with year-round INP measurements during the Macquarie Island Cloud Radiation Experiment (MICRE) campaign from 2017–2018. We simulate immersion-mode INP concentrations using the Energy Exascale Earth System Model version 1 (E3SMv1) by combining simulated aerosols with recently developed deterministic INP parameterizations and the native classical nucleation theory (CNT) for mineral dust in E3SMv1. Because MICRE did not collect aerosol measurements of super-micron particles, which are more effective ice nucleators, we evaluate the model's aerosol fields at other high-latitude sites using long-term in situ observations of dust and sea spray aerosol. We find that the model underestimates dust and overestimates sea spray aerosol concentrations by 1 to 2 orders of magnitude for most of the high-latitude sites in the Southern Hemisphere. We next compare predicted INP concentrations with concentrations of INPs collected on filter samples (typically for 2 or 3 d) and processed offline using the Colorado State University ice spectrometer (IS) in immersion freezing mode. We find that when deterministic parameterizations for both dust and sea spray INPs are used, simulated INPs are within a factor of 10 of observed INPs more than 60 % of the time during summer. Our results also indicate that the E3SM's current treatment of mineral dust immersion freezing in the SO is impacted by compensating biases – an underprediction of dust amount was compensated by an overprediction of its effectiveness as INPs. We also perform idealized droplet freezing experiments to quantify the implications of the time-dependent behavior assumed by the E3SM's CNT-parameterization and compare with the ice spectrometer observations. We find that the E3SM CNT 10 s diagnostic used in this study is a reasonable approximation of the exact formulation of CNT, when applied to ice spectrometer measurements in low-INP conditions similar to Macquarie Island. However, the linearized 10 s diagnostic underestimates the exact formula by an order of magnitude or more in places with high-INP conditions like the Sahara. Overall, our findings suggest that it is important to correct the biases in E3SM's simulated dust life cycle and update E3SM's INP parameterizations. INP prediction errors of 2 to 3 orders of magnitude can have considerable impacts on the simulated cloud and radiative properties in global climate models. On comparing INP concentrations during MICRE against ship-based campaigns, Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS) and Antarctic Circumnavigation Expedition (ACE), we find that INPs from the latter are significantly higher only in regions closer to Macquarie Island. This alludes to the fact that physical, chemical and biological processes affecting INP concentrations as stimulated by the island could be partly responsible for the high INP concentrations observed at Macquarie Island during the MICRE campaign. Therefore, improvements to both aerosol simulation and INP parameterizations are required to adequately simulate INPs and their cloud impacts in E3SM. It will be helpful to include a parallel measurement of the size-resolved aerosol composition and explore opportunities for long-term measurement platforms in future field campaigns studying INP sources in remote marine regions.

54 ENVIRONMENTAL SCIENCES↗

A Convolutional Neural Network Model for Battery Capacity Fade Curve Prediction using Early Life Data

Herein, early prediction of battery performance degradation trends can facilitate research of new materials and cell designs, rapid deployment of batteries in real-world applications, timely replacement of batteries in critical applications, and even the secondary use market. In this study, we design a convolutional neural network model to predict the entire battery capacity fade curve - a critical indicator of battery performance degradation - using first 100 cycles of data (~ three weeks of testing). We use the discharge voltage-capacity curves as input to the model and automate the feature extraction process through the convolutional layers of the network. Our approach can predict the per cycle capacity fade rate and rollover cycle (knee point) in the capacity fade curve, which indicate the onset of rapid capacity decay. On the publicly available graphite/LiFePO 4 battery dataset, optimized networks predict the capacity fade curves, rollover cycle, and end of life with 3.7% (worst-case), 19%, and 17% mean absolute percentage errors, respectively.

25 ENERGY STORAGE↗

Feedstock to Function (F2F) v1

The Feedstock to Function (F2F) tool was designed to help scientists and companies explore viable biofuels and bioproducts early in the R&D cycle to support more productive experimentation, while reducing early-stage exploration from months/years to days/weeks (feedstock-to-function.lbl.gov). The tool focuses on using machine learning to predict biomass-derived molecule properties, while evaluating the cost, benefits, and risks of promising molecules for sustainable aviation fuels. The tool successfully predicts (within 15% of experimental values) high-throughput aviation properties for over 10,000 molecules while enabling users to explore new possibilities and opportunities rapidly and effortlessly. It also links to lightweight life-cycle analysis and techno-economic tools for cost and emissions analyses. Predicted molecule properties include melting point, boiling point, flash point, yield sooting index, and heat of combustion. To date, F2F is more expansive and outperforms several other molecule property prediction models while enabling users (scientists, companies, and policy makers) to explore new possibilities and opportunities rapidly and effortlessly. F2F provides the foundation for developing an adaptive computational tool that predicts properties, cost, benefits, and risk of promising new and uncertified alternative jet fuel pathways and their blending effects.

Rapp, Vi↗

Resilience and economics of microgrids with PV, battery storage, and networked diesel generators

Current designs and assessments of microgrids have ignored component reliability, leading to significant errors in predicting a microgrid’s performance while islanded. Existing life cycle cost studies on hybrid microgrids—which combine photovoltaics (PV), battery storage and networked emergency diesel generators—also have not identified all the potential economic opportunities. Reducing the number of emergency diesel generators through reliance on PV and battery, retail bill savings, and demand response and wholesale market revenue streams are all important. This paper provides a new statistical methodology that calculates the impact of distributed energy reliability and variability on a microgrid’s performance and a novel use of the optimization platform REopt to explore multiple cost savings and revenue streams. We examine the impacts for microgrids in California, Maryland, and New Mexico and show that a hybrid microgrid is a more resilient and cost-effective solution than a diesel-only system. Under realistic conditions, a hybrid microgrid can provide higher system reliability when islanded and have a lower life cycle cost under multiple market conditions than a traditional diesel generator-based system. The improved performance of the hybrid system is resilient to conditions experienced over the last 20 years in solar irradiance and sees little degradation in performance immediately after a hurricane. The cost savings to provide this more resilient backup power system as compared to a diesel-only microgrid are significant. The net present cost for a hybrid microgrid is 19% lower in New Mexico and 35% lower in Maryland than a diesel-only microgrid. In California, the net present cost of the hybrid microgrid is negative because, unlike a diesel-only microgrid, a hybrid microgrid has lower life cycle costs than the power costs without a microgrid.

25 ENERGY STORAGE↗

DNA Viral Diversity, Abundance, and Functional Potential Vary across Grassland Soils with a Range of Historical Moisture Regimes

Soil viruses are abundant, but the influence of the environment and climate on soil viruses remains poorly understood. Here, we addressed this gap by comparing the diversity, abundance, lifestyle, and metabolic potential of DNA viruses in three grassland soils with historical differences in average annual precipitation, low in eastern Washington (WA), high in Iowa (IA), and intermediate in Kansas (KS). Bioinformatics analyses were applied to identify a total of 2,631 viral contigs, including 14 complete viral genomes from three deep metagenomes (1 terabase [Tb] each) that were sequenced from bulk soil DNA. An additional three replicate metagenomes (~0.5 Tb each) were obtained from each location for statistical comparisons. Identified viruses were primarily bacteriophages targeting dominant bacterial taxa. Both viral and host diversity were higher in soil with lower precipitation. Viral abundance was also significantly higher in the arid WA location than in IA and KS. More lysogenic markers and fewer clustered regularly interspaced short palindromic repeats (CRISPR) spacer hits were found in WA, reflecting more lysogeny in historically drier soil. More putative auxiliary metabolic genes (AMGs) were also detected in WA than in the historically wetter locations. The AMGs occurring in 18 pathways could potentially contribute to carbon metabolism and energy acquisition in their hosts. Structural equation modeling (SEM) suggested that historical precipitation influenced viral life cycle and selection of AMGs. The observed and predicted relationships between soil viruses and various biotic and abiotic variables have value for predicting viral responses to environmental change.

59 BASIC BIOLOGICAL SCIENCES↗

Aerosol Chemical Speciation Monitor (ACSM) Composition-Dependent Collection Efficiency (CDCE) Value-Added Product Report

Aerosol particles influence the Earth’s radiation balance directly by absorbing and scattering light and indirectly by influencing cloud formation, properties, and lifetimes. Measurements of aerosol particle optical properties, mass loading, size distributions, microphysical properties, cloud formation properties, and chemical composition are important for understanding the aerosol life cycle and for validating earth system models that predict these quantities. The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s Aerosol Observing System (AOS) is a highly instrumented platform that measures many of these aerosol properties in situ. The Aerodyne aerosol chemical speciation monitor (ACSM) is a baseline instrument deployed in the AOS. The ACSM provides a quantitative measurement of aerosol particle chemical composition for non-refractory (operationally defined as components that evaporate on the 600ºC vaporizer) aerosol components in real time. Standard output is the mass concentration of particulate organics, nitrate, sulfate, chloride, and ammonium. One well-known limitation to the accuracy of the ACSM data is in evaluating the fraction of the ambient aerosol particles that are detected by the instrument. This quantity is referred to as the collection efficiency (CE) and is often less than unity. This is attributed to particles rebounding after impaction onto the heated vaporizer rather than being trapped, volatilized rapidly, and detected. Other factors, such as divergence of the aerosol particle beam, may also impact CE, but the particle rebound effect is the dominant factor. Scientists will sometimes assume CE = 0.5 (i.e., one half of sampled particles are detected) for ambient particles collected during field missions. However, parameterizations have been developed that express CE as a function of the measured chemical composition, referred to as the composition-dependent collection efficiency (CDCE). The physical explanation for a CDCE, supported by laboratory studies, is that rebound from the vaporizer is a function of the particle phase, with liquid-like particles “sticking” to the vaporizer and solid-like or crystalline particles “bouncing” from the vaporizer. Thus, particles with compositions are liquids-like under the measurement conditions (e.g., certain organics, acidic particles, particles enriched in nitrate) have CE close to unity while crystalline or solid particles (e.g., deliquesced ammonium sulfate) have lower CE. This value-added product (VAP) implements the procedure described by Middlebrook et al. (2012) to correct the ACSM data for the composition-dependent collection efficiency. Applying this parameterization improves the accuracy of the ACSM data and brings them into better agreement with other co-located aerosol measurements.

54 ENVIRONMENTAL SCIENCES↗

Scanning Mobility Particle Sizer (SMPS)-Aerodynamic Particle Sizer (APS) Merged Size Distribution (mergedsmpsaps) Value-Added Product Report

Aerosol particles influence the Earth’s radiation balance directly by absorbing and scattering light and indirectly by influencing cloud formation, properties, and lifetimes. Measurements of aerosol particle optical properties, mass loading, size distributions, microphysical properties, cloud formation properties, and chemical composition are important for understanding the aerosol life cycle and for validating earth system models that predict these quantities. The Atmospheric Radiation Measurement (ARM) user facility’s Aerosol Observing System (AOS) is a highly instrumented platform designed to house instruments that measure many of these aerosol properties in situ. Currently, ARM operates at least four different instruments that measure a portion of the ambient aerosol size distribution. Most users are interested in the entire size distribution or a portion of the size distribution that extends across the measurement range of multiple instruments. However, merging these distributions is not trivial as the instruments employ different measurement principals and, in most cases, report data as a function of different representations of the aerosol diameter.

54 ENVIRONMENTAL SCIENCES↗

Auto-BLAST (AutoBLAST) [SWR-20-93]

Battery life modeling often involves a lot of manual parameter fitting and is not easy for users to adopt the model and use it. To reduce the difficulties for users to adopt battery lifetime models, an automatic battery lifetime modeling analysis and simulation tool suite, Auto-BLAST, has been developed. Auto-BLAST includes a lithium-loss-base life model, a battery electric model, and an algorithm which automatically fits all key parameters in the electric and life models using user provided data. The models and algorithm are packaged into two user-friendly GUIs, Auto-LifeMod, for easy battery life prognostic model fitting and Auto-LifeSim, for easy battery lifetime simulation. The lithium-loss-based life model adopts a similar model framework that models degradations using aging rate models, using battery cycling data to predict battery degradation and expected lifetime. The electric model is an equivalent circuit model which simulates battery voltage responses based on current/power demand profiles. The auto-fitting algorithm uses the user-input data to generate custom battery life model(s). Two GUIs, wrapping around the life model and the auto-fitting algorithm, provide friendly interfaces for users to generate a life model and use it for case study. One GUI requires summary data from accelerated battery life degradation tests as an input and produces battery life models predicting (a) capacity degradation, and (b) resistance growth of the battery. The GUI displays the electrical model response and the input experimental data against the life model predictions with fitted model parameters and fitting error. The GUI also generates an output file to save the fitted model parameters. The second GUI uses the life model from the first GUI and a user-defined battery cycling profile to predict battery lifetime degradation and expected lifetime. Predicted capacity and resistance vs. time are plotted in the GUI and saved to output file. There is a user guide for both GUIs

Mishra, Partha↗

Task 3.1: Research and Development Guiding Technoeconomic Analysis and Life-Cycle Assessment

Technologies under development aim to increase yields of desired end products, reduce overall raw material costs, and/or develop more energy-efficient strategies for product recovery. Techno-economic analysis (TEA) and life-cycle assessments (LCA) help assure that economic and sustainability predictions of the technologies are unbiased and compelling and provide guidance to experimentalists on areas that need focus. Building on previous work, the performance-advantaged bioproducts and bioprocessing separations project (SepCon) continues to use the integrated TEA and LCA to evaluate and guide technologies under development and target challenges relevant to the industry and the Bioenergy Technologies Office (BETO) priority pathways. The analysis team aims to provide credible, unbiased assessments for each technology under development, with ongoing assessments to guide experimental teams. Additionally, the team also supports journal publications highlighting key findings.

biofuels↗

A Combined Computational and Mathematical Analysis of Interconnect Fatigue Potential in Photovoltaic Modules

A finite element model of a 60-cell monocrystalline silicon glass-polymer photovoltaic module was simulated with ±1.0 kPa and ±2.4 kPa loads applied to the glass to calculate the deformation under load. Cell-to-cell displacements were used to approximate interconnect strain and stress. A mathematical fatigue cycle life relation was fitted to data for the interconnect material (copper), to generate a life prediction at each interconnect location based on the local stress means, reversal extents, and amplitudes. Interconnect stress was found to be significantly asymmetric about zero despite symmetric positive and negative module loads due to laminate thickness offsets about the neutral plane and the effects of module framing. Cycle life results indicated that interconnect fatigue failure was unlikely to occur over a 30-year lifetime of conservative wind and snow load cycles since the typical cell design feature of leaving some unconstrained length between the cell edge and first solder pad increases the effective gauge length and decreases the stress levels below the material endurance limit. Follow-up analyses found that 3.6 mm and 6.4 mm were the minimum unconstrained lengths required to survive the assumed lifetime of wind and snow cycles, respectively, confirming that typical industrial module constructions with 8–15 mm unconstrained lengths should survive conservatively. Notably, large magnitude, low-cycle snow loading was consistently the limiting factor requiring a longer unconstrained interconnect length. Finally, insights and workflows from this study inform module interconnection design limits for survival against mechanical fatigue in deployment environments.

14 SOLAR ENERGY↗

A Tanks-in-Series Approach to Estimate Parameters for Lithium-Ion Battery Models

Advanced Battery Management Systems (BMS) play a vital role in monitoring, predicting, and controlling the performance of lithium-ion batteries. BMS employing sophisticated electrochemical models can help increase battery cycle life and minimize charging time. However, in order to realize the full potential of electrochemical model-based BMS, it is critical to ensure accurate predictions and proper model parameterization. The accuracy of the predictions of an electrochemical model is dependent on the accuracy of its parameters, the values of which might change with battery cycling and aging. Parameter estimation for an electrochemical model is generally challenging due to the nonlinear nature and computational complexity of the model equations. To this end, this work utilizes the recently proposed Tanks-in-Series model for Li-ion batteries (J.Electrochem. Soc., 167, 013534 (2020)) to perform parameter estimation. The Tanks-in-Series approach allows for substantially faster parameter estimation compared to the original pseudo two-dimensional (p2D) model. The objective of this work is thus to demonstrate the gain in computational efficiency from the Tanks-in-Series approach. A sensitivity analysis of model parameters is also performed to benchmark the fidelity of the Tanks-in-Series model.

25 ENERGY STORAGE↗

Battery Performance, Thermal, and Life Modeling for Southern California Edison (Cooperative Research and Development Final Report)

The objective of this project is to develop battery performance models, thermal models and life models for SCE to use in simulation and analysis of grid services involving energy storage. NREL will fit the models to three separate chemistries using test data provided by SCE. The dataset for each chemistry will include electrical, thermal and aging response to different temperatures and cycling conditions, measured under a variety of cell-level and module-level experiments described in SCE test protocol documents. Once tuned to a test dataset, the battery system model software will provide predictions of battery energy and power loss, and thus cycle and calendar life, for any energy storage grid service power profile of interest to SCE. The automated battery life modeling and simulation tool can also be applied to any other grid battery systems as long as necessary input data is available to accelerate battery model development and battery lifetime analysis.

25 ENERGY STORAGE↗

DATA DRIVEN APPROACH TO ANALYZING THE IMPACT OF POWER PLANT CYCLING ON AIR PREHEATER DEGRADATION AND REMAINING USEFUL LIFE

Due to the increased penetration of renewable energy generation sources, and fluctuations of the oil and gas prices, modern coal burning power plants deal with increased variability in the demand for power generation. These varying demands result in their intermittent under-capacity operation (cycling). Periodical ramping down and back up to follow the daily power demands causes damages to the plant components reducing its operational life. In this paper we analyze the impact of cycling on a rotary Ljungstrom air preheater (APH) unit installed at a coal fire power plant in the US. An inefficient air preheater can significantly impact boiler performance. Due to the repeated boiler’s hot-cold start, the APH experiences fluctuating operating conditions that result in accelerated degradation mechanisms, such as dew-point corrosion, fouling/deposition plugging, and air heater leakage.The analysis in this paper utilizes field data related to APH basket replacement, and the number of cycles experienced by the boiler to model the life expectancy of the baskets. The data-driven model enables preventive maintenance strategies for the APH by predicting how long the APH baskets will last in a probabilistic sense. The analysis showed that an increase in cycling for a fixed operation time can reduce the APH basket remaining useful life by about 30%.

Sharma, Himanshu↗

C-FOG: Life of Coastal Fog

C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that integrates across processes (e.g., air–sea–land interactions, environmental flow, aerosol transport, and chemistry), dynamics (two-phase flow and turbulence), microphysics (nucleation, droplet characterization), and thermodynamics (heat transfer and phase changes) through field observations and modeling. Central to C-FOG was a field campaign in eastern Canada from 1 September to 8 October 2018, covering four land sites in Newfoundland and Nova Scotia and an adjacent coastal strip transected by the Research Vessel Hugh R. Sharp . An array of in situ, path-integrating, and remote sensing instruments gathered data across a swath of space–time scales relevant to fog life cycle. Satellite and reanalysis products, routine meteorological observations, numerical weather prediction model (WRF and COAMPS) outputs, large-eddy simulations, and phenomenological modeling underpin the interpretation of field observations in a multiscale and multiplatform framework that helps identify and remedy numerical model deficiencies. An overview of the C-FOG field campaign and some preliminary analysis/findings are presented in this paper.

58 GEOSCIENCES↗

Data Driven Approach to Analyzing The Impact of Power Plant Cycling on Air Preheater Degradation and Remaining Useful Life

Due to the increased penetration of renewable energy generation sources, and fluctuations of the oil and gas prices, modern coal burning power plants deal with increased variability in the demand for power generation. These varying demands result in their intermittent under-capacity operation (cycling). Periodical ramping down and back up to follow the daily power demands causes damages to the plant components reducing its operational life. In this paper we analyze the impact of cycling on a rotary Ljungstrom air preheater (APH) unit installed at a coal fire power plant in the US. An inefficient air preheater can significantly impact boiler performance. Due to the repeated boiler’s hot-cold start, the APH experiences fluctuating operating conditions that result in accelerated degradation mechanisms, such as dew-point corrosion, fouling/deposition plugging, and air heater leakage. The analysis in this paper utilizes field data related to APH basket replacement, and the number of cycles experienced by the boiler to model the life expectancy of the baskets. The data-driven model enables preventive maintenance strategies for the APH by predicting how long the APH baskets will last in a probabilistic sense. Furthermore, the analysis showed that an increase in cycling for a fixed operation time can reduce the APH basket remaining useful life by about 30%.

20 FOSSIL-FUELED POWER PLANTS↗

Comparing the economic performance of ice storage and batteries for buildings with on-site PV through model predictive control and optimal sizing

Integrating renewable energy and energy storage systems provides a way of operating the electrical grid system more energy efficiently and stably. Thermal storage and batteries are the most common devices for integration. However, it is not clear which integrated storage system performs better in terms of overall economics. Ice storage has low initial and maintenance costs, but there is an efficiency penalty for charging of storage and it can only shift electrical loads associated with building cooling requirements. A battery's round-trip efficiency, on the contrary, is quite consistent and batteries can be used to shift both HVAC and non-HVAC loads. However, batteries have greater initial costs and a shorter life. Finally, this research presents a tool, using model predictive control and optimal sizing, and provides a case study for comparing life-cycle economics of battery and ice storage systems for commercial buildings that have chillers for cooling and an on-site photovoltaic system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

CondiDiag1.0: a flexible online diagnostic tool for conditional sampling and budget analysis in the E3SM atmosphere model (EAM)

Abstract. Numerical models used in weather and climate prediction take into account a comprehensive set of atmospheric processes (i.e., phenomena) such as the resolved and unresolved fluid dynamics, radiative transfer, cloud and aerosol life cycles, and mass or energy exchanges with the Earth's surface. In order to identify model deficiencies and improve predictive skills, it is important to obtain process-level understanding of the interactions between different processes. Conditional sampling and budget analysis are powerful tools for process-oriented model evaluation, but they often require tedious ad hoc coding and large amounts of instantaneous model output, resulting in inefficient use of human and computing resources. This paper presents an online diagnostic tool that addresses this challenge by monitoring model variables in a generic manner as they evolve within the time integration cycle. The tool is convenient to use. It allows users to select sampling conditions and specify monitored variables at run time. Both the evolving values of the model variables and their increments caused by different atmospheric processes can be monitored and archived. Online calculation of vertical integrals is also supported. Multiple sampling conditions can be monitored in a single simulation in combination with unconditional sampling. The paper explains in detail the design and implementation of the tool in the Energy Exascale Earth System Model (E3SM) version 1. The usage is demonstrated through three examples: a global budget analysis of dust aerosol mass concentration, a composite analysis of sea salt emission and its dependency on surface wind speed, and a conditionally sampled relative humidity budget. The tool is expected to be easily portable to closely related atmospheric models that use the same or similar data structures and time integration methods.

58 GEOSCIENCES↗

Build-to-Replace Strategy to Reduce Operations and Maintenance Costs for Advanced Reactors

This paper targets the reduction of fixed operations and maintenance (O&M) costs for advanced reactor (AR) designs. This goal will be severely constrained if the underlying assumptions of O&M approaches and practices are not questioned and reexamined, especially today when changes can be implemented effectively and efficiently. Achieving a reduction in AR O&M costs requires a completely new way of thinking -a paradigm shift- not through incremental, technology-focused approaches alone. Here, we address this challenge by evaluating the impact of moving to a shorter design life for major structures, systems, and components and shorter, more predictable refurbishment cycles as modeled by the commercial airline industry: the build-to-replace approach. This paper provides a brief overview of this different mindset to O&M applied to ARs and it provided a set of analytical tools based on multi-objective optimization to identify the benefits of such an approach. In conclusion, we provide a direct example analysis of a build-to-replace scenario by identifying and evaluating scenarios for reduced system and component lifetimes and associated replacement and refurbishment schedules to evaluate impacts on O&M costs and other lifecycle elements, such as structure, system, and component reliability.

97 - MATHEMATICS AND COMPUTING↗