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DOE OSTI2022

Artificial Intelligence/Machine Learning Technologies for Advanced Reactors (Workshop Summary Report)

A workshop on artificial intelligence and machine learning (AI/ML) for advanced reactors (AR) was held October 5-6, 2021. The workshop was to be attended in-person at ANL but COVID restrictions forced the workshop to go virtual. The objectives of the workshop were to identify the most promising AI/ML opportunities for improving advanced reactor design, optimizing plant performance, and enhancing economic competitiveness and to develop an understanding of the scientific, engineering and licensing challenges facing their application. The workshop planning committee included GAIN, EPRI and NEI and members of three national laboratories (ANL, INL, and ORNL). The workshop was attended by more than 200 individuals representing academic and scientific institutions and the nuclear power industry. The definition put forth for an AI/ML system was one that perceives its environment and takes actions that maximize its chance of achieving its goals. In this report AI/ML refers to next generation algorithms that include deep learning, statistical analysis and data analytics and associated scientific computing and their potential application to the design, licensing, operation and maintenance of ARs. These methods typically incorporate models built from process data and may also include data generated by simulations that represent the behavior of a system. The workshop was organized in response to the growing interest in application of AI/ML for improving the economic competitiveness of nuclear energy. Increasingly more resources are being allocated to investigating the benefits of AI/ML methods. The DOE created the Artificial Intelligence & Technology Office to promote their development. And within the Office of Nuclear Energy, resources have been allocated to explore and understand the potential benefits of AI/ML. Additionally, the national laboratories are strategically positioned with DOE computing facilities such as Summit, Perlmutter, Aurora and Frontier that support large-scale simulations, hybrid HPC models with AI surrogates, and the exploration of new types of generative models emerging from multi-model data streams and sources. The workshop was organized with members of the AR community to understand the effort and to identify the level of interest and progress in this emerging technology. The workshop discussions focused on identifying opportunities for AI/ML across diverse areas of the nuclear industry and identifying current scientific and engineering challenges for advanced reactors that might be addressed through transformational uses of AI/ML. Discussion panels focused on four high-interest technical domains for advanced reactors: design, maintenance and operations, energy storage, and materials. The results of those discussions are summarized in this report. This includes opportunities that were identified for exploiting AI techniques and methods to improve the efficacy and efficiency of reactor analysis and to improve the operation and optimization of advanced reactors. Advanced reactor developers expressed an interest in learning more about AI/ML methods and their application. This included understanding whether ML methods can provide an advantage over existing nonlinear data regression methods for collapsing high-fidelity simulation results into faster running models. A consensus emerged that AR advances planned for the next decade will benefit from the use of AI/ML tools. The need exists to understand and model complex systems across length scales and modalities. AI/ML is a tool for discovery that can yield a set of engineering principles for use by nuclear engineers, licensing bodies, and operators to solve problems in plant design, safety analyses, autonomous operation, and predictive maintenance. While AI/ML represents a new set of tools, an awareness by the nuclear community of the full potential is still in the early stages so there is a need to increase awareness. It appears that the wide-spread adoption of AI/ML tools for ARs would be facilitated by future educational workshops that describe foundational methods and capabilities and describe successful applications.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1993

Design of partially supervised classifiers for multispectral image data

A partially supervised classification problem is addressed, especially when the class definition and corresponding training samples are provided a priori only for just one particular class. In practical applications of pattern classification techniques, a frequently observed characteristic is the heavy, often nearly impossible requirements on representative prior statistical class characteristics of all classes in a given data set. Considering the effort in both time and man-power required to have a well-defined, exhaustive list of classes with a corresponding representative set of training samples, this 'partially' supervised capability would be very desirable, assuming adequate classifier performance can be obtained. Two different classification algorithms are developed to achieve simplicity in classifier design by reducing the requirement of prior statistical information without sacrificing significant classifying capability. The first one is based on optimal significance testing, where the optimal acceptance probability is estimated directly from the data set. In the second approach, the partially supervised classification is considered as a problem of unsupervised clustering with initially one known cluster or class. A weighted unsupervised clustering procedure is developed to automatically define other classes and estimate their class statistics. The operational simplicity thus realized should make these partially supervised classification schemes very viable tools in pattern classification.

Jeon, Byeungwoo↗

NASA NTRS2016

Further Development and Assessment of a Broadband Liner Optimization Process

The utilization of advanced fan designs (including higher bypass ratios) and shorter engine nacelles has highlighted a need for increased fan noise reduction over a broader frequency range. Thus, improved broadband liner designs must account for these constraints and, where applicable, take advantage of advanced manufacturing techniques that have opened new possibilities for novel configurations. This work focuses on the use of an established broadband acoustic liner optimization process to design a variable-depth, multi-degree of freedom liner for a high speed fan. Specifically, in-duct attenuation predictions with a statistical source model are used to obtain optimum impedance spectra over the conditions of interest. The predicted optimum impedance information is then used with acoustic liner modeling tools to design a liner aimed at producing impedance spectra that most closely match the predicted optimum values. The multi-degree of freedom design is carried through design, fabrication, and testing. In-duct attenuation predictions compare well with measured data and the multi-degree of freedom liner is shown to outperform a more conventional liner over a range of flow conditions. These promising results provide further confidence in the design tool, as well as the enhancements made to the overall design process.

Nark, Douglas M.↗

NASA NTRS1980

Parametric study of variation in cargo-airplane performance related to progression from current to spanloader designs

A parametric analysis was made to investigate the relationship between current cargo airplanes and possible future designs that may differ greatly in both size and configuration. The method makes use of empirical scaling laws developed from statistical studies of data from current and advanced airplanes and, in addition, accounts for payload density, effects of span distributed load, and variations in tail area ratio. The method is believed to be particularly useful for exploratory studies of design and technology options for large airplanes. The analysis predicts somewhat more favorable variations of the ratios of payload to gross weight and block fuel to payload as the airplane size is increased than has been generally understood from interpretations of the cube-square law. In terms of these same ratios, large all wing (spanloader) designs show an advantage over wing-fuselage designs.

Toll, T. A.↗

NASA NTRS1976

The promise of air cargo: System aspects and vehicle design

The current operation of the air cargo system is reviewed. An assessment of the future of air cargo is provided by: (1) analyzing statistics and trends, (2) by noting system problems and inefficiencies, (3) by analyzing characteristics of 'air eligible' commodities, and (4) by showing the promise of new technology for future cargo aircraft with significant improvements in costs and efficiency. The following topics are discussed: (1) air cargo demand forecasts; (2) economics of air cargo transport; (3) the integrated air cargo system; (4) evolution of airfreighter design; and (5) the span distributed load concept.

Whitehead, A. H., Jr.↗

NASA NTRS1982

Interconnect fatigue design for terrestrial photovoltaic modules

The results of comprehensive investigation of interconnect fatigue that has led to the definition of useful reliability-design and life-prediction algorithms are presented. Experimental data indicate that the classical strain-cycle (fatigue) curve for the interconnect material is a good model of mean interconnect fatigue performance, but it fails to account for the broad statistical scatter, which is critical to reliability prediction. To fill this shortcoming the classical fatigue curve is combined with experimental cumulative interconnect failure rate data to yield statistical fatigue curves (having failure probability as a parameter) which enable (1) the prediction of cumulative interconnect failures during the design life of an array field, and (2) the unambiguous--ie., quantitative--interpretation of data from field-service qualification (accelerated thermal cycling) tests. Optimal interconnect cost-reliability design algorithms are derived based on minimizing the cost of energy over the design life of the array field.

Mon, G. R.↗

DOE OSTI2020

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2(r)$ or its corresponding structure factor $\textit{S(k)}$ is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including $\textit{d}$-dimensional Gaussian structure factors, $\textit{d}$-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the $\textit{d}$-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. In this work, our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for $g_2(r)$ and $\textit{S(k)}$ associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Statistically Driven Metabolite and Lipid Profiling of Patients from the Undiagnosed Diseases Network

Advancements in molecular separations coupled with mass spectrometry have enabled large-scale metabolome analyses for clinical cohorts. A population of interest for metabolome profiling are patients with rare disease for which abnormal metabolic signatures may yield clues into the genetic bases, as well as mechanistic drivers of the disease and possible treatment options. We undertook the metabolome profiling of a large cohort of patients with mysterious conditions characterized through the Un-diagnosed Diseases Network (UDN). Due to the size and enrollment procedures, collection of the metabolomes for UDN pa-tients took place over three years. We describe the study design to adjust for measurements collected over a long time-scale and how this enabled statistical analyses to summarize the metabolome of individual patients. We demonstrate the removal of time-based batch effects, overall statistical characteristics of the UDN population, and two case-studies of interest that demonstrate the utility of metabolome profiling for rare diseases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2019

NASA’s Orbital Debris JAO/ES-MCAT Optical Telescope Facility on Ascension Island

The NASA Orbital Debris Program Office has a long-standing optical program begun over three and a half decades ago in 1984, designed to observe the Earth-orbiting environment with optical telescopes. Photometrically calibrated optical data provides a statistical sample for input to NASA models of the debris population for understanding the current and future debris environment around the Earth. Tracked objects and orbits allow for analysis of break-up events. Both known (correlated target in the SSN catalogue, or CT) and unknown (uncorrelated target, or UCT) objects are of interest to better understand how to protect current spacecraft and design more robust future operational satellites, and advise on how policies and practices can lead to protecting the environment itself for future generations. In 2015, a joint NASA JSC – Air Force Research Labs (AFRL) project culminated in the installation of the 1.3-meter Eugene Stansbery Meter Class Autonomous Telescope, ES-MCAT (a.k.a. MCAT) on Ascension Island. This DFM Engineering designed telescope provides nearly five-times greater light-collecting power than its predecessor, the 0.6-m MODEST telescope, and faster tracking capabilities by both the telescope and the 7-m ObservaDome. This allows for all orbital regimes to be easily within reach, ranging from low Earth to geosynchronous orbits. Extensive testing and commissioning activities of this custom system led to successfully reaching Initial Operational Capability in 2018, and the facility is currently on track to reach Full Operational Capability. The John Africano Observatory (JAO) comprises the primary 1.3-m ES-MCAT facility, the adjacent tower platform with a 0.4-m telescope, a sophisticated suite of weather instruments, and custom software by Euclid Research for autonomously running the entire system, including monitoring the weather and hardware, tasking all components, and collecting, processing, and analyzing the data. The mission of JAO and MCAT will be discussed, including survey and tracking tasking, a full discussion of data calibration, and both optics and weather-dependent performance.

Lederer, S. M.↗

NASA NTRS2005

Advanced Vibration Analysis Tool Developed for Robust Engine Rotor Designs

Min, James B.↗

NASA NTRS2007

Directed Design of Experiments (DOE) for Determining Probability of Detection (POD) Capability of NDE Systems (DOEPOD)

This viewgraph presentation reviews some of the issues that people who specialize in Non destructive evaluation (NDE) have with determining the statistics of the probability of detection. There is discussion of the use of the binominal distribution, and the probability of hit. The presentation then reviews the concepts of Directed Design of Experiments for Validating Probability of Detection of Inspection Systems (DOEPOD). Several cases are reviewed, and discussed. The concept of false calls is also reviewed.

Generazio, Ed↗

NASA NTRS1989

Photon statistical limitations for daytime optical tracking

Tracking of interplanetary spacecraft equipped with optical communication systems by using astrometric instruments is being investigated by JPL. Existing instruments are designed to work at night and, for bright sources, are limited by tropospheric errors. To provide full coverage of the solar system, astrometric tracking instruments must either be capable of daytime operation or be space-based. The integration times necessary for the ground-based daytime photon statistical errors to reach a given accuracy level (5 to 50 nanoradians) were computed for an ideal astrometric instrument. The required photon statistical integration times are found to be shorter than the tropospheric integrations times for the ideal detector. Since the astrometric need not be limited by photon statistics even under daytime conditions, it may be fruitful to investigate instruments for daytime optical tracking.

Folkner, W. M.↗

NASA NTRS2004

Reduced-Order Blade Mistuning Analysis Techniques Developed for the Robust Design of Engine Rotors

The primary objective of this research program is to develop vibration analysis tools, design tools, and design strategies to significantly improve the safety and robustness of turbine engine rotors. Bladed disks in turbine engines always feature small, random blade-to-blade differences, or mistuning. Mistuning can lead to a dramatic increase in blade forced-response amplitudes and stresses. Ultimately, this results in high-cycle fatigue, which is a major safety and cost concern. In this research program, the necessary steps will be taken to transform a state-of-the-art vibration analysis tool, the Turbo-Reduce forced-response prediction code, into an effective design tool by enhancing and extending the underlying modeling and analysis methods. Furthermore, novel techniques will be developed to assess the safety of a given design. In particular, a procedure will be established for using eigenfrequency curve veerings to identify "danger zones" in the operating conditions--ranges of rotational speeds and engine orders in which there is a great risk that the rotor blades will suffer high stresses. This work also will aid statistical studies of the forced response by reducing the necessary number of simulations. Finally, new strategies for improving the design of rotors will be pursued. Several methods will be investigated, including the use of intentional mistuning patterns to mitigate the harmful effects of random mistuning, and the modification of disk stiffness to avoid reaching critical values of interblade coupling in the desired operating range. Recent research progress is summarized in the following paragraphs. First, significant progress was made in the development of the component mode mistuning (CMM) and static mode compensation (SMC) methods for reduced-order modeling of mistuned bladed disks (see the following figure). The CMM method has been formalized and extended to allow a general treatment of mistuning. In addition, CMM allows individual mode mistuning, which accounts for the realistic effects of local variations in blade properties that lead to different mistuning values for different mode types (e.g., mistuning of the first torsion mode versus the second flexural mode). The accuracy and efficiency of the CMM method and the corresponding Turbo-Reduce code were validated for an example finite element model of a bladed disk.

Min, James B.↗

NASA NTRS2023

Plug20 Test Report: Particle Image Velocimetry (PIV) Measurements

This report provides turbulent flow statistics made using particle image velocimetry (PIV) for several internally mixed exhaust systems with external plugs (Plug20 designs). The tests were conducted at the NASA Glenn Research Center’s Aero-Acoustic Propulsion Laboratory (AAPL) in May and June 2022. The corresponding acoustic data for the configurations and flows presented in this report can be found in an earlier Technical Memorandum, NASA/TM-20210010291, “Plug20 Test Report.” The Plug20 nozzle family was designed to represent commercial supersonic vehicles in the 2025 to 2035 timeframe with a bypass ratio around 4, having an internal mixer, with and without an external plug to improve nacelle boattail drag and shock. The flow conditions measured represent engine cycles for commercial supersonic aircraft at takeoff, having pressure ratios of 2.0 and heated fan and core streams, measured both with and without a flight stream surrounding the plume. A few unheated flow conditions were also tested to tie results to other baseline test results. The PIV measurements in both streamwise and cross-stream planes are described, along with brief analysis to visually catalog the contents and confirm their validity. In this analysis, the streamwise PIV is found to match benchmark datasets within its experimental error. However, the cross-stream turbulent quantities measured by two systems do not match each other or the streamwise measurements in amplitude—caution is required when using the cross-stream data. Data acquired and included in this report are (1) velocity statistics of the plumes in both a streamwise and several cross-stream planes, and (2) the hot nozzle geometry. Tabular forms of the data and computer-aided design (CAD) files of the hot geometry are presented as supplemental files described in Appendix A (TM-20230006779SUPPL1.zip) and Appendix B (TM-20230006779SUPPL2.zip).

Turbulence↗

DOE OSTI2021

ATOMIC Simulations and Experimental Data for CaCO3 Mixtures

This data consists of simulations and experimental measurements of laser-induced breakdown spectroscopy (LIBS). The simulations are produced by ATOMIC, a general purpose plasma modeling and kinetics code that has been designed to compute emission (or absorption) spectra from plasmas [1] and are used to develop a statistical characterization of matrix effects. Our overall suite of simulations includes contains several sets of simulations: training and validation sets of simulations for three and four element mixtures of calcium, carbon, oxygen, and nitrogen (included to account for atmosphere) along with simulations of the individual elements. The 4-element simulations include the mixture of all four elements mentioned and for each of the four individual elements. The 3-element simulations include output for the mixture of calcium, carbon, oxygen and for these three individual elements. The training data were produced using a 600-run design, shown in Figure 1, that varies input parameters temperature (T), electron density (Ne), and proportion of the elements calcium, carbon, oxygen, and nitrogen (Ca; C; O; N) for the 4 element output. The 3-element output includes all parameters except for the proportion of nitrogen. The element proportions (all the variables but T and Ne) sum to one and are unused in the single-element simulations. The validation data was produced with a 80-run design shown in Figure 2. The training and validation simulation outputs for the 4-element simulations for the mixture and for the single element calcium are shown as sample simulations in Figures 3 and 4 respectively. The simulations produce spectra over a range of 190nm - 950nm that roughly mimics the range collected by the SciAps Z-300 LIBS instrument that was used for the experimental data. The measured spectra for a CaCO3 (which may include contribution from Earth's atmosphere) in the experiment is shown in in Figure 5. All files are kept in directories whose names indicate the elemental composition (CaCO3, Ca, C, O, or N), number of elements (3 or 4), and purpose (training, which is not labeled in the file name, or validation) with file names numbered to indicate the line in the design files used to produce the simulation. The designs are provided as text files with names indicating their purpose. The experimental data is provided as a CSV file. [1] J Colgan, EJ Judge, DP Kilcrease, and JE Barefield II. Ab-initio modeling of an iron laser-induced plasma: Comparison between theoretical and experimental atomic emission spectra. Spectrochimica Acta Part B: Atomic Spectroscopy, 97:65{73}, 2014.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

The Challenger tragedy was caused by an Apollo mistake, terminating risk analysis

NASA’s view of risk changed between early Apollo and the Space Shuttle. Risk was a known serious problem at the beginning of Apollo and the risk estimates were disturbingly high. To avoid public concern, risk analysis was discontinued. Risk analysis was avoided in Shuttle, leading to an unnecessarily risky design. The immediate cause of the Challenger tragedy was the mistaken decision to launch in cold weather. The fundamental cause was the high risk of the Shuttle design. Before Challenger, management thought and testified that the probability of an accident was 1 in 100,000. After Challenger, Probabilistic Risk Analysis (PRA) found a roughly 1 in 100 chance of a Shuttle failure. The recent Orion design uses the safer Apollo approach, with a hardened capsule, launch abort escape, and the crew placed above the rocket tanks and engines. During Apollo it was estimated that, “assuming all elements from propulsion to rendezvous and life support were done as well or better than ever before, that 30 astronauts would be lost before 3 were returned safely to the Earth.” The chance of astronaut survival was only 10%. After the Apollo 1 tragedy, the awareness of risk led to an intense focus on achieving safety. “The only possible explanation for the astonishing success – no losses in space and on time – was that every participant at every level in every area far exceeded the norm of human capabilities.” During Apollo, a NASA PRA found that the chance of success was “less than 5 percent.” The NASA Administrator felt that “the numbers could do irreparable harm,” and discontinued numerical risk assessment. This led to decreasing understanding of risk. The head of Apollo reliability and safety decided, “Statistics don’t count for anything,” and that risk is reduced by “attention taken in design.” The great and initially unexpected success of Apollo appeared to validate the neglect of PRA. Continuing to neglect the mathematical estimation of risk led Shuttle into a high risk design that produced tragic results. The initial design of the Shuttle emphasized increasing capability and reducing cost without analysis or even mention of risk. A retired NASA official stated, “some NASA people began to confuse desire with reality. … One result was to assess risk in terms of what was thought acceptable without regard for verifying the assessment. … Note that under such circumstances real risk management is shut out.” Not computing risk led to removing launch abort, removing crew escape, selecting less reliable Solid Rocket Boosters, placing the crew compartment next to the rocket boosters, and accepting more stressed shielding tile designs. Accepting these specific risks directly caused the shuttle disasters. The Challenger tragedy is frequently taught as a case of management failure. The focus is on the Challenger launch decision hours before, which is a dramatic example of bad management. However, the true cause of the Challenger disaster occurred decades earlier in the Apollo era. When the easily predictable failures occurred, failure investigations focused on how they might have been avoided. The Shuttle was cancelled after the space station was completed because of its high risk. The ultimate cause of the Shuttle tragedies was the choice by the Apollo-era NASA administrator to avoid a negative public reaction to realistic risk analysis.

Harry W. Jones↗

NASA NTRS2023

Effect of Loading Rate on the Open Hole Compression Strength of Quasi-Isotropic Carbon/Epoxy Laminates

This study was undertaken to examine how well the 0.05 inch/min loading rate typically used to develop allowables for open hole compression strength of carbon/epoxy laminates represents structures that may experience a much lower loading rate (such as civil engineering structures) or a much higher loading rate (such as a rocket interstage at liftoff). The Composite Materials Handbook-17 (CMH-17) suggests developing strength allowables at the coupon level (lowest level of the “building block” approach) and using a rigorous statistical analysis to arrive at a strength allowable upon which the structure is to be further designed at higher levels of the building block pyramid. But do these coupon level tests truly represent meaningful stresses at which the composite in the final structure can withstand considering the effects of loading rate? Open hole compression (OHC) strength was chosen for this study since most structures are designed to some damage tolerance criteria and OHC strength testing is rather simple to perform. A quasi-isotropic lay-up was chosen since this is a very common lay-up sequence. The results show that for structures that experience a very small loading rate (0.0005 in/min) the allowables developed at the standard 0.05 in/min loading rate are higher than what the composite can withstand at this lower loading rate. Conversely, at a high loading rate of 10 in/min the strength values found at the standard test rate of 0.05 in/min are slightly lower and not “in family” using the statistics suggested in CMH-17. These results question if standardized test rates are reliable, at least to the fidelity of being “in family” per CMH-17. Some creep rupture tests were also performed to demonstrate that OHC strength values could be lower than the slowest test speed used in this study (0.0005 in/min).

open hole compression strength↗

NASA NTRS1999

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗