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Development Strategies for Uncertainty Quantification to Enable Aircraft Certification by Analysis

Aircraft Certification by Analysis (CbA) is a broad term that describes the process by which engineering analysis tools are used to supplement flight testing to demonstrate compliance with regulatory requirements. For each requirement that is to be met through this process, the analysis tools must be sufficiently accurate to ensure that an equivalent level of safety is obtained as if the aircraft to be certified had been flight tested for the requirement. In recent decades, the ability of analysis tools to accurately predict aircraft performance has improved dramatically, leading to increasing interest and limited early adoption of Certification by Analysis across the aerospace industry. However, rigorously demonstrating the credibility of analysis tools remains a challenge for many types of certification requirements, yet is necessary for widespread adoption of CbA approaches in the future. The field of uncertainty quantification is well-suited to address this problem, but will require substantial advances in order to achieve the ambitious industry goals for Certification by Analysis. The objective of this position paper is to highlight gaps in the current technical and programmatic state of uncertainty quantification. Four main categories – Mindset & Awareness, Tools & Capabilities, Data and Benchmarks for V&V, and Applied Research & Established Processes – will be introduced. Each of these categories contains several shortcomings and impediments which, if overcome, will enable more widespread possibilities for Certification by Analysis in the 2040-2050 timeframe.

Uncertainty Quantification↗

NASA NTRS1977

Analysis of laser fluorosensor systems for remote algae detection and quantification

The development and performance of single- and multiple-wavelength laser fluorosensor systems for use in the remote detection and quantification of algae are discussed. The appropriate equation for the fluorescence power received by a laser fluorosensor system is derived in detail. Experimental development of a single wavelength system and a four wavelength system, which selectively excites the algae contained in the four primary algal color groups, is reviewed, and test results are presented. A comprehensive error analysis is reported which evaluates the uncertainty in the remote determination of the chlorophyll a concentration contained in algae by single- and multiple-wavelength laser fluorosensor systems. Results of the error analysis indicate that the remote quantification of chlorophyll a by a laser fluorosensor system requires optimum excitation wavelength(s), remote measurement of marine attenuation coefficients, and supplemental instrumentation to reduce uncertainties in the algal fluorescence cross sections.

Browell, E. V.↗

NASA NTRS1982

Psychoacoustic considerations for helicopter noise quantification: Metrics, human response and criteria

The purpose of this paper is to examine several aspects of helicopter noise quantification from the standpoint of psychoacoustics. Noise metrics in common use to describe far-field aircraft noise and the noise characteristics which they consider are discussed. Some findings of recent psychoacoustic research related specifically to helicopter noise quantification are presented. Criteria for the accuracy of noise metrics to quantify helicopter noise are discussed. Finally, the prospects for improved metrics and research needed to develop and validate improved metrics or existing metrics are discussed.

Powell, C. A.↗

NASA NTRS1992

Rapid detection and quantification of features such as damage or flaws in composite and metallic structures

An apparatus, system, and method for non-destructible evaluation (NDE) of a material use thermography to rapidly detect and/or generally locate a feature such as, for example, damage or a defect in the material. The apparatus, system, and method also use ultrasound to specifically locate the feature in the material for quantification and/or evaluation either by an operator or by an external device suited for such purpose. Accordingly, the apparatus, system and method are particularly useful for NDE in applications such as the analysis of the structure of an aircraft, for example, in which the scale of the material to be analyzed is large, thus requiring the rapid NDE afforded by thermography, and in which quantification and/or evaluation of a feature must be performed with precision, thus requiring the relatively high-resolution NDE afforded by ultrasound.

Farley, Gary L.↗

NASA NTRS1995

Coral Pigments: Quantification Using HPLC and Detection by Remote Sensing

Widespread coral bleaching (loss of pigments of symbiotic dinoflagellates), and the corresponding decline in coral reef health worldwide, mandates the monitoring of coral pigmentation. Samples of the corals Porites compressa and P. lobata were collected from a healthy reef at Puako, Hawaii, and chlorophyll (chl) a, peridinin, and Beta-carotene (Beta-car) were quantified using reverse-phase high performance liquid chromatography (HPLC). Detailed procedures are presented for the extraction of the coral pigments in 90% acetone, and the separation, identification, and quantification of the major zooxanthellar pigments using spectrophotometry and a modification of the HPLC system described by Mantoura and Llewellyn (1983). Beta-apo-8-carotenal was found to be inadequate as in internal standard, due to coelution with chl b and/or chl a allomer in the sample extracts. Improvements are suggested, which may result in better resolution of the major pigments and greater accuracy in quantification. Average concentrations of peridinin, chl a, and Beta-car in corals on the reef were 5.01, 8.59, and 0.29, micro-grams/cm(exp 2), respectively. Average concentrations of peridinin and Beta-car did not differ significantly between the two coral species sampled; however, the mean chl a concentration in P. compressa specimens (7.81 ,micro-grams/cm(exp 2) was significantly lower than that in P. lobata specimens (9.96 11g/cm2). Chl a concentrations determined spectrophotometrically were significantly higher than those generated through HPLC, suggesting that spectrophotometry overestimates chl a concentrations. The average ratio of chl a-to-peridinin concentrations was 1.90, with a large (53%) coefficient of variation and a significant difference between the two species sampled. Additional data are needed before conclusions can be drawn regarding average pigment concentrations in healthy corals and the consistency of the chl a/peridinin ratio. The HPLC pigment concentration values contribute to the limited database of pigment concentrations in healthy corals, from which quantitative definitions of 'healthy' vs. 'bleached' coral may emerge. They also serve as ground-truth, corresponding to fluorescence data collected from the reef at Puako using airborne remote sensing of laser induced fluorescence. Fluorescence spectra from several overflights using the NASA AOL (airborne oceanographic lidar) system show consistent chlorphyll fluorescence peaks around 685 nm, as well as consistence peaks in the 400-600 nm range which may emanate from granules in the coral tissue. These data, along with results from previous studies of coral fluorescence, suggest that remote sensing of laser-induced fluorescence may become a rapid and efficient means of monitoring coral pigmentation and coral reef bleaching.

Cottone, Mary C.↗

NASA NTRS1998

Quantification of mitral regurgitation by automated cardiac output measurement: experimental and clinical validation

OBJECTIVES: To develop and validate an automated noninvasive method to quantify mitral regurgitation. BACKGROUND: Automated cardiac output measurement (ACM), which integrates digital color Doppler velocities in space and in time, has been validated for the left ventricular (LV) outflow tract but has not been tested for the LV inflow tract or to assess mitral regurgitation (MR). METHODS: First, to validate ACM against a gold standard (ultrasonic flow meter), 8 dogs were studied at 40 different stages of cardiac output (CO). Second, to compare ACM to the LV outflow (ACMa) and inflow (ACMm) tracts, 50 normal volunteers without MR or aortic regurgitation (44+/-5 years, 31 male) were studied. Third, to compare ACM with the standard pulsed Doppler-two-dimensional echocardiographic (PD-2D) method for quantification of MR, 51 patients (61+/-14 years, 30 male) with MR were studied. RESULTS: In the canine studies, CO by ACM (1.32+/-0.3 liter/min, y) and flow meter (1.35+/-0.3 liter/min, x) showed good correlation (r=0.95, y=0.89x+0.11) and agreement (deltaCO(y-x)=0.03+/-0.08 [mean+/-SD] liter/min). In the normal subjects, CO measured by ACMm agreed with CO by ACMa (r=0.90, p < 0.0001, deltaCO=-0.09+/-0.42 liter/min), PD (r=0.87, p < 0.0001, deltaCO=0.12+/-0.49 liter/min) and 2D (r=0.84, p < 0.0001, deltaCO=-0.16+/-0.48 liter/min). In the patients, mitral regurgitant volume (MRV) by ACMm-ACMa agreed with PD-2D (r= 0.88, y=0.88x+6.6, p < 0.0001, deltaMRV=2.68+/-9.7 ml). CONCLUSIONS: We determined that ACM is a feasible new method for quantifying LV outflow and inflow volume to measure MRV and that ACM automatically performs calculations that are equivalent to more time-consuming Doppler and 2D measurements. Additionally, ACM should improve MR quantification in routine clinical practice.

Non-NASA Center↗

NASA NTRS2007

The Roles of Verification, Validation and Uncertainty Quantification in the NASA Standard for Models and Simulations

The National Aeronautics and Space Administration (NASA) recently issued an interim version of the Standard for Models and Simulations (M&S Standard) [1]. The action to develop the M&S Standard was identified in an internal assessment [2] of agency-wide changes needed in the wake of the Columbia Accident [3]. The primary goal of this standard is to ensure that the credibility of M&S results is properly conveyed to those making decisions affecting human safety or mission success criteria. The secondary goal is to assure that the credibility of the results from models and simulations meets the project requirements (for credibility). This presentation explains the motivation and key aspects of the M&S Standard, with a special focus on the requirements for verification, validation and uncertainty quantification. Some pilot applications of this standard to computational fluid dynamics applications will be provided as illustrations. The authors of this paper are the members of the team that developed the initial three drafts of the standard, the last of which benefited from extensive comments from most of the NASA Centers. The current version (number 4) incorporates modifications made by a team representing 9 of the 10 NASA Centers. A permanent version of the M&S Standard is expected by December 2007. The scope of the M&S Standard is confined to those uses of M&S that support program and project decisions that may affect human safety or mission success criteria. Such decisions occur, in decreasing order of importance, in the operations, the test & evaluation, and the design & analysis phases. Requirements are placed on (1) program and project management, (2) models, (3) simulations and analyses, (4) verification, validation and uncertainty quantification (VV&UQ), (5) recommended practices, (6) training, (7) credibility assessment, and (8) reporting results to decision makers. A key component of (7) and (8) is the use of a Credibility Assessment Scale, some of the details of which were developed in consultation with William Oberkampf, David Peercy and Timothy Trocano of Sandia National Laboratories. The focus of most of the requirements, including those for VV&UQ, is on the documentation of what was done and the reporting, using the Credibility Assessment Scale, of the level of rigor that was followed. The aspects of one option for the Credibilty Assessment Scale are (1) code verification, (2) solution verification, (3) validation, (4) predictive capability, (5) technical review, (6) process control, and (7) operator and analyst qualification.

Zang, Thomas A.↗

NASA NTRS2014

Advanced Modeling and Uncertainty Quantification for Flight Dynamics; Interim Results and Challenges

As part of the NASA Vehicle Systems Safety Technologies (VSST), Assuring Safe and Effective Aircraft Control Under Hazardous Conditions (Technical Challenge #3), an effort is underway within Boeing Research and Technology (BR&T) to address Advanced Modeling and Uncertainty Quantification for Flight Dynamics (VSST1-7). The scope of the effort is to develop and evaluate advanced multidisciplinary flight dynamics modeling techniques, including integrated uncertainties, to facilitate higher fidelity response characterization of current and future aircraft configurations approaching and during loss-of-control conditions. This approach is to incorporate multiple flight dynamics modeling methods for aerodynamics, structures, and propulsion, including experimental, computational, and analytical. Also to be included are techniques for data integration and uncertainty characterization and quantification. This research shall introduce new and updated multidisciplinary modeling and simulation technologies designed to improve the ability to characterize airplane response in off-nominal flight conditions. The research shall also introduce new techniques for uncertainty modeling that will provide a unified database model comprised of multiple sources, as well as an uncertainty bounds database for each data source such that a full vehicle uncertainty analysis is possible even when approaching or beyond Loss of Control boundaries. Methodologies developed as part of this research shall be instrumental in predicting and mitigating loss of control precursors and events directly linked to causal and contributing factors, such as stall, failures, damage, or icing. The tasks will include utilizing the BR&T Water Tunnel to collect static and dynamic data to be compared to the GTM extended WT database, characterizing flight dynamics in off-nominal conditions, developing tools for structural load estimation under dynamic conditions, devising methods for integrating various modeling elements into a real-time simulation capability, generating techniques for uncertainty modeling that draw data from multiple modeling sources, and providing a unified database model that includes nominal plus increments for each flight condition. This paper presents status of testing in the BR&T water tunnel and analysis of the resulting data and efforts to characterize these data using alternative modeling methods. Program challenges and issues are also presented.

Hyde, David C.↗

NASA NTRS2014

Uncertainty Quantification and Certification Prediction of Low-Boom Supersonic Aircraft Configurations

The primary objective of this work was to develop and demonstrate a process for accurate and efficient uncertainty quantification and certification prediction of low-boom, supersonic, transport aircraft. High-fidelity computational fluid dynamics models of multiple low-boom configurations were investigated including the Lockheed Martin SEEB-ALR body of revolution, the NASA 69 Delta Wing, and the Lockheed Martin 1021-01 configuration. A nonintrusive polynomial chaos surrogate modeling approach was used for reduced computational cost of propagating mixed, inherent (aleatory) and model-form (epistemic) uncertainty from both the computation fluid dynamics model and the near-field to ground level propagation model. A methodology has also been introduced to quantify the plausibility of a design to pass a certification under uncertainty. Results of this study include the analysis of each of the three configurations of interest under inviscid and fully turbulent flow assumptions. A comparison of the uncertainty outputs and sensitivity analyses between the configurations is also given. The results of this study illustrate the flexibility and robustness of the developed framework as a tool for uncertainty quantification and certification prediction of low-boom, supersonic aircraft.

West, Thomas K., IV↗

NASA NTRS2014

Updates of the KArLE Experiment: New Libs Calibration Under High Vacuum for the Quantification of Potassium in Basalt for In Situ Geochronology

In planetary exploration, in situ absolute geochronology is one of the main important measurements that needs to be accomplished. Until now, on Mars, the age of the surface is only determined by crater density counting, which gives relative ages. These ages can have a lot of uncertainty as they depend on many parameters. More than that, the curves must be ties to absolute ages. Thus far, only the lost lander Beagle 2 was designed to conduct absolute geochronology measurements, though some recent attempts using MSL Curiosity show that this investigation is feasible and should be strongly encouraged for future flight. Experimental: The Potassium (K)-Argon Laser Experiment (KArLE) is being developed at MSFC through the NASA Planetary Instrument Definition and Development Program (PIDDP). The goal of this experiment is to provide in situ geochronology based on the K-Ar method. A laser ablates a rock under high vacuum, creating a plasma which is sensed by an optical spectrometer to do Laser Induced Breakdown Spectroscopy (LIBS). The ablated material frees gases, including radiogenic 40Ar,which is measured by a mass spectrometer (MS). As the potassium is a content and the 40Ar is a quantity, the ablated mass needed in order to relate them. The mass is given by the product of the ablated volume by the density of this material. So we determine the mineralogy of the ablated material with the LIBS spectra and images and calculate its density. The volume of the pit is measured by using microscopy. LIBS measurement of K under high vacuum: Three independant projects [1, 2, 3] including KArLE, are developing geochronological instruments based on this LA-LIBS-MS method. Despite several differences in their setup, all of them have validated the methods with analyses and ages. However, they all described difficulties with the LIBS measurements of K [3,4]. At ambient pressure, the quantification of K by LIBS on geological materials can be accurate [5]. However the protocol of the LA-LIBS-MS experiment required hundreds of shots under high vacuum in order to free enough 40Ar* to be measured by the QMS. This long duration of ablation may induces significant changes in the LIBS spectra. The pressure may increases by orders of magnitudewithin the chamber and the laser pit geometry can change the effectiveness of ablation and intensity of plasma light received. These effects introduce variation between the first and last spectra and so the quantification of K is more complex. The ablation of one crater can give, depending on the protocol of acquisition, from tens to hundreds of spectra. Protocol and results: We are in the process of further characterizing the variation introduced into LIBS spectra by the use of hundreds of laser shots, and definining a protocol that can be used to ensure accuracy and reporoducibility in the results.We are using natural rock powder standards fused in a furnace, as well as mars analog samples with known K content. We will show the result of the calibration and some new statistical approaches in order to apprehend the effects of the long time ablation on rocks under high vacuum.

Devismes, D.↗

NASA NTRS2014

Instantaneous Wavenumber Estimation for Damage Quantification in Layered Plate Structures

This paper illustrates the application of instantaneous and local wavenumber damage quantification techniques for high frequency guided wave interrogation. The proposed methodologies can be considered as first steps towards a hybrid structural health monitoring/ nondestructive evaluation (SHM/NDE) approach for damage assessment in composites. The challenges and opportunities related to the considered type of interrogation and signal processing are explored through the analysis of numerical data obtained via EFIT simulations of damage in CRFP plates. Realistic damage configurations are modeled from x-ray CT scan data of plates subjected to actual impacts, in order to accurately predict wave-damage interactions in terms of scattering and mode conversions. Simulation data is utilized to enhance the information provided by instantaneous and local wavenumbers and mitigate the complexity related to the multi-modal content of the plate response. Signal processing strategies considered for this purpose include modal decoupling through filtering in the frequency/wavenumber domain, the combination of displacement components, and the exploitation of polarization information for the various modes as evaluated through the dispersion analysis of the considered laminate lay-up sequence. The results presented assess the effectiveness of the proposed wavefield processing techniques as a hybrid SHM/NDE technique for damage detection and quantification in composite, plate-like structures.

Mesnil, Olivier↗

NASA NTRS2014

Guided Wave Delamination Detection and Quantification With Wavefield Data Analysis

Unexpected damage can occur in aerospace composites due to impact events or material stress during off-nominal loading events. In particular, laminated composites are susceptible to delamination damage due to weak transverse tensile and inter-laminar shear strengths. Developments of reliable and quantitative techniques to detect delamination damage in laminated composites are imperative for safe and functional optimally-designed next-generation composite structures. In this paper, we investigate guided wave interactions with delamination damage and develop quantification algorithms by using wavefield data analysis. The trapped guided waves in the delamination region are observed from the wavefield data and further quantitatively interpreted by using different wavenumber analysis methods. The frequency-wavenumber representation of the wavefield shows that new wavenumbers are present and correlate to trapped waves in the damage region. These new wavenumbers are used to detect and quantify the delamination damage through the wavenumber analysis, which can show how the wavenumber changes as a function of wave propagation distance. The location and spatial duration of the new wavenumbers can be identified, providing a useful means not only for detecting the presence of delamination damage but also allowing for estimation of the delamination size. Our method has been applied to detect and quantify real delamination damage with complex geometry (grown using a quasi-static indentation technique). The detection and quantification results show the location, size, and shape of the delamination damage.

Tian, Zhenhua↗

NASA NTRS2014

Compositional Solution Space Quantification for Probabilistic Software Analysis

Probabilistic software analysis aims at quantifying how likely a target event is to occur during program execution. Current approaches rely on symbolic execution to identify the conditions to reach the target event and try to quantify the fraction of the input domain satisfying these conditions. Precise quantification is usually limited to linear constraints, while only approximate solutions can be provided in general through statistical approaches. However, statistical approaches may fail to converge to an acceptable accuracy within a reasonable time. We present a compositional statistical approach for the efficient quantification of solution spaces for arbitrarily complex constraints over bounded floating-point domains. The approach leverages interval constraint propagation to improve the accuracy of the estimation by focusing the sampling on the regions of the input domain containing the sought solutions. Preliminary experiments show significant improvement on previous approaches both in results accuracy and analysis time.

Monte Carlo Methods↗

NASA NTRS2009

Quantification of Trace Chemicals Using Vehicle Cabin Atmosphere Monitor

A system to monitor the concentrations of trace chemicals in cabin atmosphere is one of the most critical components in long-duration human flight missions. The Vehicle Cabin Atmosphere Monitor (VCAM) is a miniature gas chromatograph mass spectrometer system to be used to detect and quantify trace chemicals in the International Space Station. We developed an autonomous computational process to quantify trace chemicals for use in VCAM. The process involves the design of a measured signal quantification scheme, the construction of concentration curves (i.e. the relationship between concentration and ion count measured by VCAM), the decision rule of applying high- or low-gain concentration curves, and the detection of saturation, low-signals, and outliers. When the developed quantification process is applied, the average errors of concentration for most of trace chemicals are found to be between 14% and 66%.

Lee, Seungwon↗

NASA NTRS2016

Uncertainty Reduction using Bayesian Inference and Sensitivity Analysis: A Sequential Approach to the NASA Langley Uncertainty Quantification Challenge

This paper presents a computational framework for uncertainty characterization and propagation, and sensitivity analysis under the presence of aleatory and epistemic un- certainty, and develops a rigorous methodology for efficient refinement of epistemic un- certainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Uncertainty Quantification Challenge (NASA-LUQC) problem that deals with uncertainty analysis of a generic transport model (GTM). First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation specified in the NASA-LUQC is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refine- ment methodology, where epistemic variables for refinement are not identified all-at-once. Instead, only one variable is first identified, and then, Bayesian inference and global sensi- tivity calculations are repeated to identify the next important variable. This procedure is continued until all 4 variables are identified and the refinement in the system-level perfor- mance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained, and then applied to the NASA Langley Uncertainty Quantification Challenge problem.

Uncertainty↗

NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗

NASA NTRS2017

Summary Findings from the AVT-191 Project to Assess Sensitivity Analysis and Uncertainty Quantification Methods for Military Vehicle Design

A NATO symposium held in Greece in 2008 identified many promising sensitivity analysis and uncertainty quantification technologies, but the maturity and suitability of these methods for realistic applications was not clear. The NATO Science and Technology Organization, Task Group AVT-191 was established to evaluate the maturity and suitability of various sensitivity analysis and uncertainty quantification methods for application to realistic vehicle development problems. The program ran from 2011 to 2015, and the work was organized into four discipline-centric teams: external aerodynamics, internal aerodynamics, aeroelasticity, and hydrodynamics. This paper summarizes findings and lessons learned from the task group.

Benek, John A.↗

NASA NTRS2017

Overview of the AVT-191 Project to Assess Sensitivity Analysis and Uncertainty Quantification Methods for Military Vehicle Design

A NATO symposium held in 2008 identified many promising sensitivity analysis and un-certainty quantification technologies, but the maturity and suitability of these methods for realistic applications was not known. The STO Task Group AVT-191 was established to evaluate the maturity and suitability of various sensitivity analysis and uncertainty quantification methods for application to realistic problems of interest to NATO. The program ran from 2011 to 2015, and the work was organized into four discipline-centric teams: external aerodynamics, internal aerodynamics, aeroelasticity, and hydrodynamics. This paper presents an overview of the AVT-191 program content.

Benek, John A.↗