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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

NASA Tech Briefs, October 2010

Topics covered include: Hybrid Architecture Active Wavefront Sensing and Control; Carbon-Nanotube-Based Chemical Gas Sensor; Aerogel-Positronium Technology for the Detection of Small Quantities of Organic and/or Toxic Materials; Graphene-Based Reversible Nano-Switch/Sensor Schottky Diode; Inductive Non-Contact Position Sensor; High-Temperature Surface-Acoustic-Wave Transducer; Grid-Sphere Electrodes for Contact with Ionospheric Plasma; Enabling IP Header Compression in COTS Routers via Frame Relay on a Simplex Link; Ka-Band SiGe Receiver Front-End MMIC for Transponder Applications; Robust Optimization Design Algorithm for High-Frequency TWTs; Optimal and Local Connectivity Between Neuron and Synapse Array in the Quantum Dot/Silicon Brain; Method and Circuit for In-Situ Health Monitoring of Solar Cells in Space; BGen: A UML Behavior Network Generator Tool; Platform for Post-Processing Waveform-Based NDE; Electrochemical Hydrogen Peroxide Generator; Fabrication of Single, Vertically Aligned Carbon Nanotubes in 3D Nanoscale Architectures; Process to Create High-Fidelity Lunar Dust Simulants; Lithium-Ion Electrolytes Containing Phosphorous-Based, Flame-Retardant Additives; InGaP Heterojunction Barrier Solar Cells; Straight-Pore Microfilter with Efficient Regeneration; Determining Shear Stress Distribution in a Laminate; Self-Adjusting Liquid Injectors for Combustors; Handling Qualities Prediction of an F-16XL-Based Reduced Sonic Boom Aircraft; Tele-Robotic ATHLETE Controller for Kinematics - TRACK; Three-Wheel Brush-Wheel Sampler; Heterodyne Interferometer Angle Metrology; Aligning Astronomical Telescopes via Identification of Stars; Generation of Optical Combs in a WGM Resonator from a Bichromatic Pump; Large-Format AlGaN PIN Photodiode Arrays for UV Images; Fiber-Coupled Planar Light-Wave Circuit for Seed Laser Control in High Spectral Resolution Lidar Systems; On Calculating the Zero-Gravity Surface Figure of a Mirror; Optical Modification of Casimir Forces for Improved Function of Micro- and Nano-Scale Devices; Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems; Core and Off-Core Processes in Systems Engineering; Digital Reconstruction Supporting Investigation of Mishaps; and Template Matching Approach to Signal Prediction.

Source record↗
NASA NTRS2021

Machine Learning Models to Predict Cognitive Impairment of Rodents Subjected to Space Radiation

This research uses machine-learned computational analyses to predict the cognitive performance impairment of rats induced by irradiation. The experimental data in the analyses is from a rodent model exposed to ≤ 15 cGy of individual Galactic Cosmic Radiation (GCR) ions: 4He, 16O, 28Si, 48Ti, or 56Fe, expected for a Lunar or Mars mission. This work investigates rats at a subject-based level and uses performance scores taken before irradiation to predict impairment in Attentional Set-shifting (ATSET) data post-irradiation. Here, the worst performing rats of the control group define the impairment thresholds based on population analyses via cumulative distribution functions, leading to the labeling of impairment for each subject. A significant finding is the exhibition of a dose-dependent increasing probability of impairment for 1 to 10 cGy of 28Si or 56Fe in the Simple Discrimination (SD) stage of the ATSET, and for 1 to 10 cGy of 56Fe in the Compound Discrimination (CD) stage. On a subject-based level, implementing Machine Learning (ML) classifiers such as the Gaussian Naïve Bayes, Support Vector Machine, and Artificial Neural Networks identifies rats that have a higher tendency for impairment after GCR exposure. The algorithms employ the experimental prescreenperformance scores as multidimensional input features to predict each rodent’s susceptibility to cognitive impairment due to space radiation exposure. The receiver operating characteristic and the precision-recall curves of the ML models show a better prediction of impairment when 56Feis the ion in question in both SD and CD stages. They, however, do not depict impairment due to 4Hein SD and 28Siin CD, suggesting no dose-dependent impairment response in these cases. One key finding of our study is that prescreen performance scores can be used to predict the ATSET performance impairments. This result is significant to crewed space missions as it supports the potential of predicting an astronaut’s impairment in a specific task before spaceflight through the implementation of appropriately trained ML tools. Future research can focus on constructing ML ensemble methods to integrate the findings from the methodologies implemented in this study for morerobust predictionsof cognitive decrements due to space radiation exposure.

space radiation↗
NASA NTRS2011

Predictive Models of Duration of Ground Delay Programs in New York Area Airports

Initially planned GDP duration often turns out to be an underestimate or an overestimate of the actual GDP duration. This, in turn, results in avoidable airborne or ground delays in the system. Therefore, better models of actual duration have the potential of reducing delays in the system. The overall objective of this study is to develop such models based on logs of GDPs. In a previous report, we described descriptive models of Ground Delay Programs. These models were defined in terms of initial planned duration and in terms of categorical variables. These descriptive models are good at characterizing the historical errors in planned GDP durations. This paper focuses on developing predictive models of GDP duration. Traffic Management Initiatives (TMI) are logged by Air Traffic Control facilities with The National Traffic Management Log (NTML) which is a single system for automated recoding, coordination, and distribution of relevant information about TMIs throughout the National Airspace System. (Brickman, 2004 Yuditsky, 2007) We use 2008-2009 GDP data from the NTML database for the study reported in this paper. NTML information about a GDP includes the initial specification, possibly one or more revisions, and the cancellation. In the next section, we describe general characteristics of Ground Delay Programs. In the third section, we develop models of actual duration. In the fourth section, we compare predictive performance of these models. The final section is a conclusion.

Kulkarni, Deepak↗
DOE OSTI2020

Sensitivity evaluation of the Kudryavtsev permafrost model

Modeling is an important way to assess current and future permafrost spatial distribution and dynamics, especially in data poor areas like the Arctic region. Here, we evaluate a physics-based analytical model, Kudryavtsev's active layer model, which is widely used because it has relatively few data requirements. This model was recently incorporated into a component modeling toolbox, allowing for coupled modeling of permafrost and geomorphic processes over geological timescales. However, systematic quantitative assessment of the influence of its controlling parameters on permafrost temperature and active layer thickness predictions has not been undertaken before. In this work, we investigate the sensitivity of the Kudryavtsev's active layer model by Monte Carlo simulations to generate probability distributions for input parameters and compare predictions with a comprehensive benchmark dataset of in-situ permafrost observations over entire Alaska. Predicted permafrost surface temperature is highly dependent on mean annual air temperature (r = 0.78 on average), annual temperature amplitude (–0.41), and winter-averaged snow thickness (0.30). Uncertainty of predicted permafrost temperature is relatively small (RMSE = 1 °C), when air temperature and snow depth are well constrained. Similarly, RMSE between simulated and observed ALT at stations is ~0.08 m. However, under given air temperature and snow conditions, soil water content bias can significantly affect modeled active layer thickness (RMSE = 0.1 m or 40% of the observed active layer thickness). If soil water content has a large bias, improvements in other parameters may not significantly improve the active layer predictions of the Kudryavtsev's model.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2003

GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows

With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.

Source record↗
DOE OSTI2022

Hierarchical Model-Free Transactive Control of Building Loads to Support Grid Services

Residential buildings consume 4.4 quads of electricity annually, approximately 37% of the total electricity consumption in the United States. This represents a vast resource that can be used for demand management and other ancillary services. This project aims to develop a robust, scalable hierarchical transactional control mechanism incorporating elements of model-free control (MFC) and game theory to harness buildings to provide ancillary services to the grid. This approach is being taken to address the challenges of incorporating traditional transactional control schemes into existing buildings. The challenges include small individual building sizes requiring aggregation of many buildings, unpredictable energy usage that makes model identification difficult, and satisfying the sensitive occupant comfort constraints. In the proposed approach, by separating the control mechanism into two layers above and below the load aggregator, MFC can be used below the aggregator to modulate flexible building loads in response to pricing signals with guaranteed performance. This allows the burden of identifying an accurate model of the system to be shifted to the above-aggregator layer, where fluctuations in individual building usage have less impact on predicted building system behavior. Game theory concepts can then be used to determine pricing curves and control signals among regional aggregators. Managing this control in a game-theoretic approach will allow us to build in financial incentives that increase customer engagement. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable on small, embedded devices. In a broader sense, developing a strategy capable of effectively incorporating residential and small commercial buildings will allow greater throughput of existing and emerging grid services in addition to future transactive energy grid management methods. Using MFC within a hierarchical control architecture will allow the shifting of existing forecasting challenges to an aggregate level, where dynamics are slower and more predictable. This will enable a smooth interface between the grid services requests of utilities and the reliable control required by participating buildings. MFC, which supports distributed control architecture, permits a scalable solution that can be deployed to neighborhood-size systems as well as individual buildings. This project focuses on three objectives: (1) developing the mathematical framework, algorithm toolkit, and software toolset of the two-layer transactive control testbed; (2) developing a scalable solution for application over many residential and small-size commercial buildings with sparse distributed communication; and (3) field testing and implementation on hardware of the control strategies developed in the previous two objectives. The research and development activities are focused and designed to be impactful within the relevant 2025 targets timeframe. An open-source control framework for exploiting variability and dispatchability of building loads will be delivered as the outcome of the project. This capability enables greater participation of loads in electricity markets and ancillary services that are both useful for the utility and financially beneficial for building owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

C{sub 2}N{sub 2} Vertical Profile in Titan’s Stratosphere

In this paper, we present the first measurements of the vertical distribution of cyanogen (C{sub 2}N{sub 2}) in Titan’s lower atmosphere at different latitudes and seasons, using Cassini’s Composite Infrared Spectrometer far-infrared data. We also study the vertical distribution of three other minor species detected in our data: methylacetylene (C{sub 3}H{sub 4}), diacetylene (C{sub 4}H{sub 2}), and H{sub 2}O, in order to compare them to C{sub 2}N{sub 2}, but also to get an overview of their seasonal and meridional variations in Titan’s lower stratosphere from 85 km to 225 km. We measured an average volume mixing ratio of C{sub 2}N{sub 2} of 6.2±0.8×10{sup −11} at 125 km at the equator, but poles exhibit a strong enrichment in C{sub 2}N{sub 2} (up to a factor 100 compared to the equator), greater than what was measured for C{sub 3}H{sub 4} or C{sub 4}H{sub 2}. Measuring C{sub 2}N{sub 2} profiles provides constraints on the processes controlling its distribution, such as bombardment by Galactic Cosmic Rays which seem to have a smaller influence on C{sub 2}N{sub 2} than predicted by photochemical models.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1979

An improved Woodward's panel method for calculating leading-edge and side-edge suction forces at subsonic and supersonic speeds

Woodward's panel method for subsonic and supersonic flow was improved by employing control points determined by exactly matching two-dimensional pressure at a finite number of points. The results show great improvement in the predicted pressure distribution of a flapped airfoil. With the paneling scheme of cosine law in both chordwise and spanwise directions, the method is shown to accurately predict leading edge and side edge suction forces of various configurations in subsonic and supersonic flow.

Lan, C. E.↗
NASA NTRS1991

Application of laminar flow control to high-bypass-ratio turbofan engine nacelles

Recently, the concept of the application of hybrid laminar flow to modern commercial transport aircraft was successfully flight tested on a Boeing 757 aircraft. In this limited demonstration, in which only part of the upper surface of the swept wing was designed for the attainment of laminar flow, significant local drag reduction was measured. This paper addresses the potential application of this technology to laminarize the external surface of large, modern turbofan engine nacelles which may comprise as much as 5-10 percent of the total wetted area of future commercial transports. A hybrid-laminar-flow-control (HLFC) pressure distribution is specified and the corresponding nacelle geometry is computed utilizing a predictor/corrector design method. Linear stability calculations are conducted to provide predictions of the extent of the laminar boundary layer. Performance studies are presented to determine potential benefits in terms of reduced fuel consumption.

Wie, Y. S.↗
NASA NTRS1999

Applications of Constituent Data Assimilation Systems

Organizations in Europe, Australia, and the United States have recently broadened constituent assimilation activities beyond that water vapor, which has been assimilated for years in the numerical weather prediction community. Many of these activities have focused on ozone, with some efforts focused on the entire suite of reactive constituents that control the ozone distribution. This talk will draw from results from the near real-time ozone data assimilation system being run by NASA's Data Assimilation Office. This system utilizes ozone observations from both the TOMS and the SBUV instrument to generate global synoptic maps of ozone. The initial application of this product is to provide ozone fields to assist in the atmospheric corrections' that are necessary for the retrieval of information from other NASA instruments. The validation of the ozone assimilation system shows that the assimilated product agrees well with independent HALOE and ozonesonde observations. This suggests that the product is of sufficient quality to be extended to other applications. This talk will enumerate these other applications and present initial results from exploratory research. The applications being considered include estimates of tropospheric ozone, provision of ozone fields for interactive retrievals, use of analysis increments from the assimilation to evaluate model performance, and development of long-term consistent three-dimensional global ozone fields. The results from the exploratory studies are promising, and help demonstrate how assumptions made in the p development of the ozone assimilation impact the other applications. For instance, RMS errors in the current product are large near the tropopause, which is sensitive to the specification of vertical correlation functions, which in turns impacts the amount of ozone analyzed to be in the troposphere. How these sensitivities impact the different applications will also be discussed.

Rood, Richard B.↗
NASA NTRS2000

Results from NASA's Near Real Time Ozone Data Assimilation Systems

Organizations in Europe, Australia, and the United States have recently broadened constituent assimilation activities beyond water vapor, which has been assimilated for years in the numerical weather prediction applications. Many of these activities have focused on ozone, with some efforts focused on the entire suite of reactive constituents that control the ozone distribution. This talk will draw from results from the near real-time ozone data assimilation system being run by NASA's Data Assimilation Office. This system utilizes ozone observations from both the TOMS and the SBUV instrument to generate global synoptic maps of ozone. The initial application of this product is to provide ozone fields to assist in the atmospheric corrections' that are necessary for the retrieval of information from other NASA instruments. The validation of the ozone assimilation system shows that the assimilated product agrees well with independent HALOE and ozonesonde observations. Aside from providing a global synoptic map, there is verifiable geophysical information at higher vertical resolution than either of the date types input into the system. This talk will establish the validation results and enumerate applications of the ozone data assimilation system. Results from exploratory research will be presented. The applications being considered include estimates of tropospheric ozone, provision of ozone fields for interactive retrievals, use of analysis increments from the assimilation to evaluate model performance, and development of long-term consistent three-dimensional global ozone fields. The results from the exploratory studies are promising, and help demonstrate how assumptions made in the development of the ozone assimilation impact the other applications. For instance, RMS errors in the current product are large near the tropopause, which is sensitive to the specification of vertical correlation functions, which in turns impacts the amount of ozone analyzed to be in the troposphere. How these sensitivities impact the different applications will also be discussed.

Rood, Richard B.↗
NASA NTRS2018

Predictive Thermal Control (PTC) Technology to Enable Thermally Stable Telescopes

Validate models that predict thermal optical performance of real mirrors and structure based on their structural designs and constituent material properties, i.e. CTE distribution, thermal conductivity, thermal mass, etc.. Derive thermal system stability specifications from science-driven wavefront-stability requirement. Demonstrate utility of PTC system for achieving thermal stability.

Space Mirror Technology↗
NASA NTRS1990

Oceanic upper mixed layer depth determination by the use of satellite data

A method has been developed to determine the oceanic daily mean mixed layer depth from satellite observations and a mixed layer thermal inertia (MLTI) model. The algorithms were developed to use remotely-sensed values of sea surface temperature, albedo, and surface wind speeds to calculate the thermal inertia and to predict changes in subsurface diurnal mixed layer depth. The MLTI model, based on a mixed layer model of the upper ocean, has been used to simulate the diurnal mixing process and thermal inertia distribution in the Sargasso Sea around 34 deg N, 70 deg W. Sea surface temperature and albedo have been obtained from the NOAA7-AVHRR images. Surface wind speeds have been derived from the Scanning Multichannel Microwave Radiometer (SMMR) aboard Nimbus 7. Image processing was performed for images gathered between June and July 1982. The daily mean mixed layer depths predicted by the MLTI model agree well with data gathered at the LOTUS mooring located in the Sargasso Sea. This suggests that vertical mixing is the dominant physical process that controls the thermal inertia distribution in the midocean, far from major current systems, and that remote sensing is a promising tool to study such upper ocean processes.

Yan, Xiao-Hai↗
DOE OSTI2024

Simulation Evaluation of a Large-Scale Implementation of Virtual-Phase Link-Based Model Predictive Control

Traffic congestion is a serious problem in the US, and traffic signal control is one of the effective solutions to congestion. Previous research on model predictive control (MPC)-based traffic signal control showed substantial benefits over conventional methods. This study focused on implementing MPC over a large-scale network with complex intersections and the impact of cycle length, network size, and imperfect state estimation on performances. This study implemented a virtual phase link (VPL)-based model predictive control method which used the number of vehicles in each VPL as input state variables and was suitable for National Electrical Manufacturing Association (NEMA) ring-barrier control. To test the impact of network size, the performance of distributed MPC (36 intersections in the network are divided into five subnetworks) was compared with that of MPC over the full network for a set of cycle lengths. To test the impact of imperfect state estimation, we synthetically infused estimation error and developed two scenarios, MPC-error and MPC-error narrow, which had higher and lower estimation errors, respectively. The performance of these MPC methods was compared with that of the existing time-of-day (TOD) method and an offline method that used Webster's method for split and MULTIBAND for cycle length and offset optimization. Trajectory and linkwise signal performance measures were collected from the simulation to evaluate performance. The distributed MPC method with perfect state estimation had the lowest delay and highest energy efficiency of all the methods. The performance of MPC decreased as the prediction inaccuracy increased. MPC-error had 7% and 11% more delay than MPC-error narrow in the morning and evening peaks, respectively. Overall, simulation results suggest that even with imperfect state estimation, MPC methods will outperform offline methods significantly.

large-scale simulation↗
DOE OSTI2023

Standardized Data to Improve Understanding and Modeling of Soil Nitrogen at Continental Scale

Abstract Nitrogen (N) is a key limiting nutrient in terrestrial ecosystems, but there remain critical gaps in our ability to predict and model controls on soil N cycling. This may be in part due to lack of standardized sampling across broad spatial–temporal scales. Here, we introduce a continentally distributed, publicly available data set collected by the National Ecological Observatory Network (NEON) that can help fill these gaps. First, we detail the sampling design and methods used to collect and analyze soil inorganic N pool and net flux rate data from 47 terrestrial sites. We address methodological challenges in generating a standardized data set, even for a network using uniform protocols. Then, we evaluate sources of variation within the sampling design and compare measured net N mineralization to simulated fluxes from the Community Earth System Model 2 (CESM2). We observed wide spatiotemporal variation in inorganic N pool sizes and net transformation rates. Site explained the most variation in NEON’s stratified sampling design, followed by plots within sites. Organic horizons had larger pools and net N transformation rates than mineral horizons on a sample weight basis. The majority of sites showed some degree of seasonality in N dynamics, but overall these temporal patterns were not matched by CESM2, leading to poor correspondence between observed and modeled data. Looking forward, these data can reveal new insights into controls on soil N cycling, especially in the context of other environmental data sets provided by NEON, and should be leveraged to improve predictive modeling of the soil N cycle.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2008

Elastic-Plastic Fracture Mechanics Analysis of Critical Flaw Size in ARES I-X Flange-to-Skin Welds

NASA's Ares 1 Upper Stage Simulator (USS) is being fabricated from welded A516 steel. In order to insure the structural integrity of these welds it is of interest to calculate the critical initial flaw size (CIFS) to establish rational inspection requirements. The CIFS is in turn dependent on the critical final flaw size (CFS), as well as fatigue flaw growth resulting from transportation, handling and service-induced loading. These calculations were made using linear elastic fracture mechanics (LEFM), which are thought to be conservative because they are based on a lower bound, so called elastic, fracture toughness determined from tests that displayed significant plasticity. Nevertheless, there was still concern that the yield magnitude stresses generated in the flange-to-skin weld by the combination of axial stresses due to axial forces, fit-up stresses, and weld residual stresses, could give rise to significant flaw-tip plasticity, which might render the LEFM results to be non-conservative. The objective of the present study was to employ Elastic Plastic Fracture Mechanics (EPFM) to determine CFS values, and then compare these values to CFS values evaluated using LEFM. CFS values were calculated for twelve cases involving surface and embedded flaws, EPFM analyses with and without plastic shakedown of the stresses, LEFM analyses, and various welding residual stress distributions. For the cases examined, the computed CFS values based on elastic analyses were the smallest in all instances where the failures were predicted to be controlled by the fracture toughness. However, in certain cases, the CFS values predicted by the elastic-plastic analyses were smaller than those predicted by the elastic analyses; in these cases the failure criteria were determined by a breakdown in stress intensity factor validity limits for deep flaws (a greater than 0.90t), rather than by the fracture toughness. Plastic relaxation of stresses accompanying shakedown always increases the calculated CFS values compared to the CFS values determined without shakedown. Thus, it is conservative to ignore shakedown effects.

Chell, G. Graham↗
NASA NTRS2011

Multiple Damage Progression Paths in Model-Based Prognostics

Model-based prognostics approaches employ domain knowledge about a system, its components, and how they fail through the use of physics-based models. Component wear is driven by several different degradation phenomena, each resulting in their own damage progression path, overlapping to contribute to the overall degradation of the component. We develop a model-based prognostics methodology using particle filters, in which the problem of characterizing multiple damage progression paths is cast as a joint state-parameter estimation problem. The estimate is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control mechanism that maintains an uncertainty bound around the hidden parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump, to which we apply our model-based prognostics algorithms. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the chosen approach when multiple damage mechanisms are active

Daigle, Matthew↗
NASA NTRSDate not supplied

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗