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NASA NTRS1987

Finite element methods in probabilistic mechanics

Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.

Liu, Wing Kam↗

NASA NTRS2004

Reliability Assessment Approach for Stirling Convertors and Generators

Stirling power conversion is being considered for use in a Radioisotope Power System for deep-space science missions because it offers a multifold increase in the conversion efficiency of heat to electric power. Quantifying the reliability of a Radioisotope Power System that utilizes Stirling power conversion technology is important in developing and demonstrating the capability for long-term success. A description of the Stirling power convertor is provided, along with a discussion about some of the key components. Ongoing efforts to understand component life, design variables at the component and system levels, related sources, and the nature of uncertainties is discussed. The requirement for reliability also is discussed, and some of the critical areas of concern are identified. A section on the objectives of the performance model development and a computation of reliability is included to highlight the goals of this effort. Also, a viable physics-based reliability plan to model the design-level variable uncertainties at the component and system levels is outlined, and potential benefits are elucidated. The plan involves the interaction of different disciplines, maintaining the physical and probabilistic correlations at all the levels, and a verification process based on rational short-term tests. In addition, both top-down and bottom-up coherency were maintained to follow the physics-based design process and mission requirements. The outlined reliability assessment approach provides guidelines to improve the design and identifies governing variables to achieve high reliability in the Stirling Radioisotope Generator design.

Shah, Ashwin R.↗

NASA NTRS2015

Integrated Medical Model (IMM) Project Verification, Validation, and Credibility (VVandC)

The Integrated Medical Model (IMM) Project supports end user requests by employing the Integrated Medical Evidence Database (iMED) and IMM tools as well as subject matter expertise within the Project. The iMED houses data used by the IMM. The IMM is designed to forecast relative changes for a specified set of crew health and mission success risk metrics by using a probabilistic model based on historical data, cohort data, and subject matter expert opinion. A stochastic approach is taken because deterministic results would not appropriately reflect the uncertainty in the IMM inputs. Once the IMM was conceptualized, a plan was needed to rigorously assess input information, framework and code, and output results of the IMM, and ensure that end user requests and requirements were considered during all stages of model development and implementation, as well as lay the foundation for external review and application. METHODS: In 2008, the Project team developed a comprehensive verification and validation (VV) plan, which specified internal and external review criteria encompassing 1) verification of data and IMM structure to ensure proper implementation of the IMM, 2) several validation techniques to confirm that the simulation capability of the IMM appropriately represents occurrences and consequences of medical conditions during space missions, and 3) credibility processes to develop user confidence in the information derived from the IMM. When the NASA-STD-7009 (7009) [1] was published, the Project team updated their verification, validation, and credibility (VVC) project plan to meet 7009 requirements and include 7009 tools in reporting VVC status of the IMM. Construction of these tools included meeting documentation and evidence requirements sufficient to meet external review success criteria. RESULTS: IMM Project VVC updates are compiled recurrently and include updates to the 7009 Compliance and Credibility matrices. Reporting tools have evolved over the lifetime of the IMM Project to better communicate VVC status. This has included refining original 7009 methodology with augmentation from the HRP NASA-STD-7009 Guidance Document working group and the NASA-HDBK-7009 [2]. End user requests and requirements are being satisfied as evidenced by ISS Program acceptance of IMM risk forecasts, transition to an operational model and simulation tool, and completion of service requests from a broad end user consortium including operations, science and technology planning, and exploration planning. IMM v4.0 is slated for operational release in the FY015 and current VVC assessments illustrate the expected VVC status prior to the completion of customer lead external review efforts. CONCLUSIONS: The VVC approach established by the IMM Project of incorporating Project-specific recommended practices and guidelines for implementing the 7009 requirements is comprehensive and includes the involvement of end users at every stage in IMM evolution. Methods and techniques used to quantify the VVC status of the IMM Project represented a critical communication tool in providing clear and concise suitability assessments to IMM customers. These processes have not only received approval from the local NASA community but have also garnered recognition by other federal agencies seeking to develop similar guidelines in the medical modeling community.

Walton, M.↗

NASA NTRS1992

A probabilistic fracture mechanics approach for structural reliability assessment of space flight systems

A probabilistic fracture mechanics approach for predicting the failure life distribution due to subcritical crack growth is presented. A state-of-the-art crack propagation method is used in a Monte Carlo simulation to generate a distribution of failure lives. The crack growth failure model expresses failure life as a function of stochastic parameters including environment, loads, material properties, geometry, and model specification errors. A stochastic crack growth rate model that considers the uncertainties due to scatter in the data and mode misspecification is proposed. The rationale for choosing a particular type of probability distribution for each stochastic input parameter and for specifying the distribution parameters is presented. The approach is demonstrated through a probabilistic crack growth failure analysis of a welded tube in the Space Shuttle Main Engine. A discussion of the results from this application of the methodology is given.

Sutharshana, S.↗

NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗

DOE OSTI2022

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Reliability and Creep/Fatigue Analysis of a CMC Component

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight and enable higher operating temperatures requiring less cooling; thus leading to increased engine efficiencies. There is a need for convenient design tools that can accommodate various loading conditions and material data with their associated uncertainties to estimate the minimum predicted life as well as the failure probabilities of a structural component. This paper presents a review of the life prediction and probabilistic analyses performed for a CMC turbine stator vane. A computer code, NASALife, is used to predict the life of a 2-D woven silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC) turbine stator vane due to a mission cycle which induces low cycle fatigue and creep. The output from this program includes damage from creep loading, damage due to cyclic loading and the combined damage due to the given loading cycle. Results indicate that the trends predicted by NASALife are as expected for the loading conditions used for this study. In addition, a combination of woven composite micromechanics, finite element structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Results indicate that reducing the scatter in proportional limit strength of the vane material has the greatest effect in improving the overall reliability of the CMC vane.

Murthy, Pappu L. N.↗

NASA NTRS2016

Model Based Mission Assurance: NASA's Assurance Future

Model Based Systems Engineering (MBSE) is seeing increased application in planning and design of NASA’s missions. This suggests the question: what will be the corresponding practice of Model Based Mission Assurance (MBMA)? Contemporaneously, NASA’s Office of Safety and Mission Assurance (OSMA) is evaluating a new objectives based approach to standards to ensure that the Safety and Mission Assurance disciplines and programs are addressing the challenges of NASA’s changing missions, acquisition and engineering practices, and technology. MBSE is a prominent example of a changing engineering practice. We use NASA’s objectives-based strategy for Reliability and Maintainability as a means to examine how MBSE will affect assurance. We surveyed MBSE literature to look specifically for these affects, and find a variety of them discussed (some are anticipated, some are reported from applications to date). Predominantly these apply to the early stages of design, although there are also extrapolations of how MBSE practices will have benefits for testing phases. As the effort to develop MBMA continues, it will need to clearly and unambiguously establish the roles of uncertainty and risk in the system model. This will enable a variety of uncertainty-based analyses to be performed much more rapidly than ever before and has the promise to increase the integration of CRM (Continuous Risk Management) and PRA (Probabilistic Risk Analyses) even more fully into the project development life cycle. Various views and viewpoints will be required for assurance disciplines, and an over-arching viewpoint will then be able to more completely characterize the state of the project/program as well as (possibly) enabling the safety case approach for overall risk awareness and communication.

Evans, John↗

NASA NTRS2013

Probabilistic Modeling of the Renal Stone Formation Module

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

kidney stones↗

DOE OSTI2025

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operations (SUMMER-GO): Project Final Report

The Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operation (SUMMER-GO) project was recently completed through a collaboration among the National Renewable Energy Laboratory, Maxar, the Electric Reliability Council of Texas (ERCOT), the University of Texas at Dallas, the University of California Berkeley, and the University of Colorado Boulder. The project made significant advances in probabilistic solar power forecasting, both through the development of Bayesian model averaging methods for ensemble forecasting and in bringing these and other advancements into practice with Maxar's delivery of operational forecasts to ERCOT. In addition to creating more reliable solar power forecasts, the project developed methods for their utilization in power system operations. These include the development of risk-aware unit commitment and economic dispatch algorithms and methods to reformulate probabilistic forecasts to be used in these power system operational models. Dynamic power system reserve methods were also developed, which have been shown in silico to create economic savings and reliability improvements on an ERCOT-like system as well as financial savings in the ERCOT system through more granular consideration of the uncertainty associated with solar power forecasts. Finally, a situational awareness tool to help grid operators better understand solar power forecast uncertainty in daily operations was developed and extensively vetted.

14 SOLAR ENERGY↗

DOE OSTI2024

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗

DOE OSTI2026

AI/ML-Enhanced Wind Forecasts for Reducing Uncertainty in Prescribed Fire Planning

Prescribed fire is a vital tool for ecosystem management and wildfire risk reduction but its escalation is constrained by overly conservative burn windows because of uncertainties, for instance, in wind forecasts. This review describes the state of the art in weather product use by fire/smoke models and identifies three priority research gaps that artificial intelligence/machine learning (AI/ML) is well positioned to address: (1) spatial and temporal downscaling to meter-scale, sub-hourly wind fields; (2) bias correction for systematic model errors in complex terrain; and (3) robust uncertainty quantification to inform ensemble-based simulations. Emerging AI/ML techniques offer promising frameworks to address all three challenges. By providing high-resolution, bias-corrected, and probabilistic wind fields, AI/ML-enhanced forecasts will allow for expanded burn windows, improved ignition strategy design and a reduced reliance on expert intuition, especially when a prescribed fire is introduced into new areas.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1993

Probabilistic simulation of concurrent engineering of propulsion systems

Technology readiness and the available infrastructure is assessed for timely computational simulation of concurrent engineering for propulsion systems. Results for initial coupled multidisciplinary, fabrication-process, and system simulators are presented including uncertainties inherent in various facets of engineering processes. An approach is outlined for computationally formalizing the concurrent engineering process from cradle-to-grave via discipline dedicated workstations linked with a common database.

Chamis, C. C.↗

NASA NTRSDate not supplied

Analysis of Alternative Architectures for Cargo Lunar Landers

NASA’s Human Landing System (HLS) program has been working with commercial partners to develop human-class lunar landers to return the first American woman and next American man to the lunar surface in the mid 2020’s. In an effort to expand human presence beyond low Earth orbit, NASA’s Artemis program aims to facilitate a sustainable, long-term human presence in cis-lunar space. A component of this will require significant infrastructure to be delivered to the lunar surface. Delivering this infrastructure will require a significant lander capability that has yet to be developed. A thorough understanding of cargo lunar lander architectures is required such that select alternatives can be identified that best support the Artemis program’s objective of sustainability. The goal of this study is to aid NASA and its partners in the understanding of the cargo lunar lander trades space, as well as identify potential robust alternatives. The results will support NASA as it moves forward with key activities such as requirements formulation, agency strategic planning, and potential cargo lunar lander procurements. The study builds off of recent work performed by the Human Landing System program’s Architecture and Systems Analysis group to encompass a broad trade space of cargo lunar lander architecture alternatives. The current trade space as depicted by the morphological matrix and mission graph in Fig. 1 and Fig. 2, respectively, includes key alternative options that have become highly relevant due to current HLS activities and include on-orbit refueling, active cryogenic fluid management, Earth orbit aggregation, and global lunar access. The authors believe that there is also a statistically relevant impact of lander-payload configuration on the primary structure of the vehicle that could greatly impact alternative selection. Because of this, several conceptual lander-payload configurations will be evaluated to determine the level of impact. The current set of conceptual configurations are shown in Fig. 3 and Fig. 4. To aid the conceptual evaluation of these configurations, a catalogue of notional payloads has been developed that represent a wide range of masses and volumes that are expected to be delivered in support of a sustained human lunar presence, including pressurized and unpressurized rovers, surface habitats, power systems, and other support infrastructure. In order to execute this study in a timely fashion, a similar approach to that utilized in a similar 2019 study focused on 2024 human lunar sorties will be employed [1]. The team utilized a novel architecture synthesis framework currently being developed by NASA/MSFC to evaluate over 600,000 lunar lander architectures over a two month time frame [2]. From this large data set, varying ground rules and assumptions were applied as filters to explore the trade space to identify alternatives which exhibited robustness, as measured by launch vehicle payload margin, to absorb the natural growth that occurs during design maturation. The set of Earth-Moon system Delta-Vs assumed from the 2019 study, shown in Fig. 5, will be repurposed to accelerate model formulation for this effort. Additionally, current efforts in collaboration with the Georgia Institute of Technology’s Aerospace System Design Lab will be integrated to provide probabilistic modeling of the cargo lunar lander architectures to aid in identifying robust design alternatives [3]. The approach will help minimize potential impacts due to large levels of uncertainty inherent to pre phase-A conceptual design. By leveraging these past and present studies and partnerships, a highly detailed set of data can be generated in a short time period to aid NASA in the coming years to support the goal of a sustained human lunar presence.

Architectures↗

DOE OSTI2021

METHODOLOGY AND APPLICATION OF PHYSICAL SECURITY EFFECTIVENESS BASED ON DYNAMIC FORCE-ON-FORCE MODELING

This paper describes ongoing work within the Light Water Reactor Sustainability (LWRS) Program at Idaho National Laboratory (INL) to optimize security and cost of nuclear power plants (NPPs). It reviews the conservatisms in conventional physical security posture and regulations. It introduces the dynamic risk assessment tool developed at INL, Event Modeling Risk Assessment using Linked Diagrams (EMRALD). The dynamic assessment methodology leverages EMRALD to process results of force-on-force (FOF) simulations and crediting safety mitigation actions from probabilistic risk assessment (PRA) models as well as diverse and flexible coping strategies (FLEX) mitigation strategies. Timing information from these simulations are compared against the available time to perform mitigations obtained from Reactor Excursion and Leak Analysis Program (RELAP5) simulations. To illustrate the methodology, a station blackout (SBO) attack scenario was modeled in commercially available FOF simulation tools. The simulation results provide valuable insights into possible attack outcomes and as the probabilistic risk of a core damage event given these outcomes. Safety mitigation procedures were modeled in EMRALD, and were dependent on the attack outcomes by considering human operator uncertainties. RELAP5 simulations incorporating human and hardware uncertainties were performed to estimate the distribution of time-to-core damage. The results demonstrate that, even in the extreme case of a successful adversarial attack, plant mitigation strategies provide significantly high-likelihood of preventing radiological release. The proposed modeling and simulation framework of integrating FLEX equipment with FOF models enables the NPPs to credit FLEX portable equipment in the plant security posture, resulting in an efficient and optimized physical security.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2017

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation.

Warner, James E.↗

NASA NTRS2009

Probabilistic Estimation of Critical Flaw Sizes in the Primary Structure Welds of the Ares I-X Launch Vehicle

The primary structure of the Ares I-X Upper Stage Simulator (USS) launch vehicle is constructed of welded mild steel plates. There is some concern over the possibility of structural failure due to welding flaws. It was considered critical to quantify the impact of uncertainties in residual stress, material porosity, applied loads, and material and crack growth properties on the reliability of the welds during its pre-flight and flight. A criterion--an existing maximum size crack at the weld toe must be smaller than the maximum allowable flaw size--was established to estimate the reliability of the welds. A spectrum of maximum allowable flaw sizes was developed for different possible combinations of all of the above listed variables by performing probabilistic crack growth analyses using the ANSYS finite element analysis code in conjunction with the NASGRO crack growth code. Two alternative methods were used to account for residual stresses: (1) The mean residual stress was assumed to be 41 ksi and a limit was set on the net section flow stress during crack propagation. The critical flaw size was determined by parametrically increasing the initial flaw size and detecting if this limit was exceeded during four complete flight cycles, and (2) The mean residual stress was assumed to be 49.6 ksi (the parent material s yield strength) and the net section flow stress limit was ignored. The critical flaw size was determined by parametrically increasing the initial flaw size and detecting if catastrophic crack growth occurred during four complete flight cycles. Both surface-crack models and through-crack models were utilized to characterize cracks in the weld toe.

Pai, Shantaram S.↗