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NASA NTRS2000

An Approach to Experimental Design for the Computer Analysis of Complex Phenomenon

The ability to make credible system assessments, predictions and design decisions related to engineered systems and other complex phenomenon is key to a successful program for many large-scale investigations in government and industry. Recently, many of these large-scale analyses have turned to computational simulation to provide much of the required information. Addressing specific goals in the computer analysis of these complex phenomenon is often accomplished through the use of performance measures that are based on system response models. The response models are constructed using computer-generated responses together with physical test results where possible. They are often based on probabilistically defined inputs and generally require estimation of a set of response modeling parameters. As a consequence, the performance measures are themselves distributed quantities reflecting these variabilities and uncertainties. Uncertainty in the values of the performance measures leads to uncertainties in predicted performance and can cloud the decisions required of the analysis. A specific goal of this research has been to develop methodology that will reduce this uncertainty in an analysis environment where limited resources and system complexity together restrict the number of simulations that can be performed. An approach has been developed that is based on evaluation of the potential information provided for each "intelligently selected" candidate set of computer runs. Each candidate is evaluated by partitioning the performance measure uncertainty into two components - one component that could be explained through the additional computational simulation runs and a second that would remain uncertain. The portion explained is estimated using a probabilistic evaluation of likely results for the additional computational analyses based on what is currently known about the system. The set of runs indicating the largest potential reduction in uncertainty is then selected and the computational simulations are performed. Examples are provided to demonstrate this approach on small scale problems. These examples give encouraging results. Directions for further research are indicated.

Rutherford, Brian↗

NASA NTRS2003

Probabilistic Evaluation of Advanced Ceramic Matrix Composite Structures

The objective of this report is to summarize the deterministic and probabilistic structural evaluation results of two structures made with advanced ceramic composites (CMC): internally pressurized tube and uniformly loaded flange. The deterministic structural evaluation includes stress, displacement, and buckling analyses. It is carried out using the finite element code MHOST, developed for the 3-D inelastic analysis of structures that are made with advanced materials. The probabilistic evaluation is performed using the integrated probabilistic assessment of composite structures computer code IPACS. The affects of uncertainties in primitive variables related to the material, fabrication process, and loadings on the material property and structural response behavior are quantified. The primitive variables considered are: thermo-mechanical properties of fiber and matrix, fiber and void volume ratios, use temperature, and pressure. The probabilistic structural analysis and probabilistic strength results are used by IPACS to perform reliability and risk evaluation of the two structures. The results will show that the sensitivity information obtained for the two composite structures from the computational simulation can be used to alter the design process to meet desired service requirements. In addition to detailed probabilistic analysis of the two structures, the following were performed specifically on the CMC tube: (1) predicted the failure load and the buckling load, (2) performed coupled non-deterministic multi-disciplinary structural analysis, and (3) demonstrated that probabilistic sensitivities can be used to select a reduced set of design variables for optimization.

Abumeri, Galib H.↗

NASA NTRS1993

Specifying design conservatism: Worst case versus probabilistic analysis

Design conservatism is the difference between specified and required performance, and is introduced when uncertainty is present. The classical approach of worst-case analysis for specifying design conservatism is presented, along with the modern approach of probabilistic analysis. The appropriate degree of design conservatism is a tradeoff between the required resources and the probability and consequences of a failure. A probabilistic analysis properly models this tradeoff, while a worst-case analysis reveals nothing about the probability of failure, and can significantly overstate the consequences of failure. Two aerospace examples will be presented that illustrate problems that can arise with a worst-case analysis.

Miles, Ralph F., Jr.↗

NASA NTRS1991

Probabilistic evaluation of SSME structural components

The application is described of Composite Load Spectra (CLS) and Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) family of computer codes to the probabilistic structural analysis of four Space Shuttle Main Engine (SSME) space propulsion system components. These components are subjected to environments that are influenced by many random variables. The applications consider a wide breadth of uncertainties encountered in practice, while simultaneously covering a wide area of structural mechanics. This has been done consistent with the primary design requirement for each component. The probabilistic application studies are discussed using finite element models that have been typically used in the past in deterministic analysis studies.

Rajagopal, K. R.↗

NASA NTRS2012

A Markov Chain Approach to Probabilistic Swarm Guidance

This paper introduces a probabilistic guidance approach for the coordination of swarms of autonomous agents. The main idea is to drive the swarm to a prescribed density distribution in a prescribed region of the configuration space. In its simplest form, the probabilistic approach is completely decentralized and does not require communication or collabo- ration between agents. Agents make statistically independent probabilistic decisions based solely on their own state, that ultimately guides the swarm to the desired density distribution in the configuration space. In addition to being completely decentralized, the probabilistic guidance approach has a novel autonomous self-repair property: Once the desired swarm density distribution is attained, the agents automatically repair any damage to the distribution without collaborating and without any knowledge about the damage.

Markov chain↗

NASA NTRSDate not supplied

Adopting an Objectives-Driven Assurance Case Approach for Achieving Space Flight Mission Planetary Protection Objectives

Traditionally, the National Aeronautics and Space Administration (NASA) has utilized prescriptive technical and process requirements to ensure safety and mission assurance performance objectives for planetary protection are achieved during space flight missions. While prescriptive requirements may be easier to communicate and manage throughout the systems engineering process, the highly constrained nature of prescriptive requirements can limit the ability to take advantage of cost-saving opportunities and offer limited ability to explore other options or alternative designs, processes, and methods. It can also be difficult to develop prescriptive requirements for objectives that are probabilistic in nature or that cannot be satisfied by direct verification. In contrast, the development of an assurance case allows for a compelling, comprehensible, and valid argument to be developed with supporting evidence that shows safety and mission assurance objectives have been satisfied. Analogous to how patent applications are constructed for inventions, an assurance case has a high-level claim of meeting a safety and mission assurance objective, followed by a more specific set of sub-claims and technical evidence which supports the claims. The objectives-driven assurance case approach allows for a better understanding and exploration of the trade space, more flexibility to balance trades, and the ability to realize and implement technical and process innovations for resource, time, and cost savings. The assurance case is a living case that evolves over the entire program life cycle. Recently, NASA’s Office of Planetary Protection (OPP) has adopted the assurance case approach as an acceptable methodology for demonstrating avoidance of contamination of target solar system bodies explored by NASA space flight missions. This methodology has been incorporated into NASA’s new technical standard for planetary protection and is currently being utilized by the Mars Sample Return campaign for safe sample containment during sample return.

Assurance Case↗

NASA NTRS2002

Reliability Analysis of Brittle Material Structures - Including MEMS(?) - With the CARES/Life Program

Brittle materials are being used, or considered, for a wide variety of high tech applications that operate in harsh environments, including static and rotating turbine parts. thermal protection systems, dental prosthetics, fuel cells, oxygen transport membranes, radomes, and MEMS. Designing components to sustain repeated load without fracturing while using the minimum amount of material requires the use of a probabilistic design methodology. The CARES/Life code provides a general-purpose analysis tool that predicts the probability of failure of a ceramic component as a function of its time in service. For this presentation an interview of the CARES/Life program will be provided. Emphasis will be placed on describing the latest enhancements to the code for reliability analysis with time varying loads and temperatures (fully transient reliability analysis). Also, early efforts in investigating the validity of using Weibull statistics, the basis of the CARES/Life program, to characterize the strength of MEMS structures will be described as as well as the version of CARES/Life for MEMS (CARES/MEMS) being prepared which incorporates single crystal and edge flaw reliability analysis capability. It is hoped this talk will open a dialog for potential collaboration in the area of MEMS testing and life prediction.

Nemeth, Noel N.↗

NASA NTRS2010

Applying Monte Carlo Simulation to Launch Vehicle Design and Requirements Analysis

This Technical Publication (TP) is meant to address a number of topics related to the application of Monte Carlo simulation to launch vehicle design and requirements analysis. Although the focus is on a launch vehicle application, the methods may be applied to other complex systems as well. The TP is organized so that all the important topics are covered in the main text, and detailed derivations are in the appendices. The TP first introduces Monte Carlo simulation and the major topics to be discussed, including discussion of the input distributions for Monte Carlo runs, testing the simulation, how many runs are necessary for verification of requirements, what to do if results are desired for events that happen only rarely, and postprocessing, including analyzing any failed runs, examples of useful output products, and statistical information for generating desired results from the output data. Topics in the appendices include some tables for requirements verification, derivation of the number of runs required and generation of output probabilistic data with consumer risk included, derivation of launch vehicle models to include possible variations of assembled vehicles, minimization of a consumable to achieve a two-dimensional statistical result, recontact probability during staging, ensuring duplicated Monte Carlo random variations, and importance sampling.

Hanson, J. M.↗

NASA NTRS2015

Simulation of Liquid Rocket Engine Failure Propagation Using Self-Evolving Scenarios

Traditional probabilistic risk assessment approaches often require failure scenarios to be explicitly defined through event sequences that are then quantified as part of the integrated analysis. This approach becomes difficult when failure propagation paths change as a function of the system operation. Additionally, if the propagation paths represent interactions among even a modest number of components, the scenario count becomes combinatorially intractable. This paper presents an alternate approach for quantifying the probability of failure propagation in such a case. Rather than explicitly defining scenario sequences, simple physical models are created for each of the components. In this way, only the physical states and rules of component interactions must be defined, rather than event sequences for each individual scenario. Initiating failures are introduced into the system, either randomly or as defined by relative likelihood, and the failures cascade through the system via the interaction rules. This process is repeated using Monte Carlo methods and, as a result, the most probable scenarios “self-evolve” in terms of both sequence path and frequency. This approach was applied to failures occurring in the engine compartment of a space launch vehicle with four liquid rocket engines and four high-pressure helium tanks. Each engine was modeled with key components, such as turbomachinery, combustion chamber, propellant lines, and additional support systems. Three test cases were conducted with different high-energy engine failures. End results of interest included an additional engine-out failure and tank burst, which represent the loss-of-mission (LOM) and loss-of-crew (LOC) failure environments, respectively. Observations show that almost every scenario outcome is unique and that many scenarios involve complex chain reactions that are difficult to predict. This validates the usefulness of the modeling approach in assessing the overall risks to the crew during a launch vehicle abort.

Rocket Engine↗

NASA NTRS2014

Preliminary Structural Sensitivity Study of Hypersonic Inflatable Aerodynamic Decelerator Using Probabilistic Methods

Acceptance of new spacecraft structural architectures and concepts requires validated design methods to minimize the expense involved with technology validation via flighttesting. This paper explores the implementation of probabilistic methods in the sensitivity analysis of the structural response of a Hypersonic Inflatable Aerodynamic Decelerator (HIAD). HIAD architectures are attractive for spacecraft deceleration because they are lightweight, store compactly, and utilize the atmosphere to decelerate a spacecraft during re-entry. However, designers are hesitant to include these inflatable approaches for large payloads or spacecraft because of the lack of flight validation. In the example presented here, the structural parameters of an existing HIAD model have been varied to illustrate the design approach utilizing uncertainty-based methods. Surrogate models have been used to reduce computational expense several orders of magnitude. The suitability of the design is based on assessing variation in the resulting cone angle. The acceptable cone angle variation would rely on the aerodynamic requirements.

Lyle, Karen H.↗

NASA NTRS2002

Probabilistic Design of a Plate-Like Wing to Meet Flutter and Strength Requirements

An approach is presented for carrying out reliability-based design of a metallic, plate-like wing to meet strength and flutter requirements that are given in terms of risk/reliability. The design problem is to determine the thickness distribution such that wing weight is a minimum and the probability of failure is less than a specified value. Failure is assumed to occur if either the flutter speed is less than a specified allowable or the stress caused by a pressure loading is greater than a specified allowable. Four uncertain quantities are considered: wing thickness, calculated flutter speed, allowable stress, and magnitude of a uniform pressure load. The reliability-based design optimization approach described herein starts with a design obtained using conventional deterministic design optimization with margins on the allowables. Reliability is calculated using Monte Carlo simulation with response surfaces that provide values of stresses and flutter speed. During the reliability-based design optimization, the response surfaces and move limits are coordinated to ensure accuracy of the response surfaces. Studies carried out in the paper show the relationship between reliability and weight and indicate that, for the design problem considered, increases in reliability can be obtained with modest increases in weight.

Stroud, W. Jefferson↗

NASA NTRS2012

Deployment Analysis of a Simple Tape-Spring Hinge Using Probabilistic Methods

Acceptance of new deployable structures architectures and concepts requires validated design methods to minimize the expense involved with technology validation flight testing. Deployable concepts for large lightweight spacecraft include booms, antennae, and masts. This paper explores the implementation of probabilistic methods in the design process for the deployment of a strain-energy mechanism, specifically a simple tape-spring hinge. Strain-energy mechanisms are attractive for deployment in very lightweight systems because they do not require the added mass and complexity associated with motors and controllers. However, designers are hesitant to include free deployment, strain-energy mechanisms because of the potential for uncontrolled behavior. In the example presented here, the tapespring cross-sectional dimensions have been varied and a target displacement during deployment has been selected as the design metric. Specifically, the tape-spring should reach the final position in the shortest time with the minimal amount of overshoot and oscillations. Surrogate models have been used to reduce computational expense. Parameter values to achieve the target response have been computed and used to demonstrate the approach. Based on these results, the application of probabilistic methods for design of a tape-spring hinge has shown promise as a means of designing strain-energy components for more complex space concepts.

Lyle, Karen H.↗

NASA NTRS2010

Overview of Graphical User Interface for ARRBOD (Acute Radiation Risk and BRYNTRN Organ Dose Projection)

Solar particle events (SPEs) pose the risk of acute radiation sickness (ARS) to astronauts, because organ doses from large SPEs may reach critical levels during extra vehicular activities (EVAs) or lightly shielded spacecraft. NASA has developed an organ dose projection model of Baryon transport code (BRYNTRN) with an output data processing module of SUMDOSE, and a probabilistic model of acute radiation risk (ARR). BRYNTRN code operation requires extensive input preparation, and the risk projection models of organ doses and ARR take the output from BRYNTRN as an input to their calculations. With a graphical user interface (GUI) to handle input and output for BRYNTRN, these response models can be connected easily and correctly to BRYNTRN in a user friendly way. The GUI for the Acute Radiation Risk and BRYNTRN Organ Dose (ARRBOD) projection code provides seamless integration of input and output manipulations required for operations of the ARRBOD modules: BRYNTRN, SUMDOSE, and the ARR probabilistic response model. The ARRBOD GUI is intended for mission planners, radiation shield designers, space operations in the mission operations directorate (MOD), and space biophysics researchers. Assessment of astronauts organ doses and ARS from the exposure to historically large SPEs is in support of mission design and operation planning to avoid ARS and stay within the current NASA short-term dose limits. The ARRBOD GUI will serve as a proof-of-concept for future integration of other risk projection models for human space applications. We present an overview of the ARRBOD GUI product, which is a new self-contained product, for the major components of the overall system, subsystem interconnections, and external interfaces.

Kim, Myung-Hee Y.↗

NASA NTRS1988

NESSUS (Numerical Evaluation of Stochastic Structures Under Stress)/EXPERT: Bridging the gap between artificial intelligence and FORTRAN

The development of a probabilistic structural analysis methodology (PSAM) is described. In the near-term, the methodology will be applied to designing critical components of the next generation space shuttle main engine. In the long-term, PSAM will be applied very broadly, providing designers with a new technology for more effective design of structures whose character and performance are significantly affected by random variables. The software under development to implement the ideas developed in PSAM resembles, in many ways, conventional deterministic structural analysis code. However, several additional capabilities regarding the probabilistic analysis makes the input data requirements and the resulting output even more complex. As a result, an intelligent front- and back-end to the code is being developed to assist the design engineer in providing the input data in a correct and appropriate manner. The type of knowledge that this entails is, in general, heuristically-based, allowing the fairly well-understood technology of production rules to apply with little difficulty. However, the PSAM code, called NESSUS, is written in FORTRAN-77 and runs on a DEC VAX. Thus, the associated expert system, called NESSUS/EXPERT, must run on a DEC VAX as well, and integrate effectively and efficiently with the existing FORTRAN code. This paper discusses the process undergone to select a suitable tool, identify an appropriate division between the functions that should be performed in FORTRAN and those that should be performed by production rules, and how integration of the conventional and AI technologies was achieved.

Fink, Pamela K.↗

NASA NTRS1999

Lunar Meteorites and Implications for Compositional Remote Sensing of the Lunar Surface

Lunar meteorites (LMs) are rocks found on Earth that were ejected from the Moon by impact of an asteroidal meteoroid. Three factors make the LMs important to remote-sensing studies: (1) Most are breccias composed of regolith or fragmental material; (2) all are rocks that resided (or breccias composed of material that resided) in the upper few meters of the Moon prior to launch and (3) most apparently come from areas distant from the Apollo sites. How Many Lunar Locations? At this writing (June 1999), there are 18 known lunar meteorite specimens. When unambiguous cases of terrestrial pairing are considered, the number of actual LMs reduces to 13. (Terrestrial pairing is when a single piece of lunar rock entered Earth's atmosphere, but multiple fragments were produced because the meteoroid broke apart on entry, upon hitting the ground or ice, or while being transported through the ice.) We have no reason to believe that LMs preferentially derive from any specific region(s) of the Moon; i.e., we believe that they are samples from random locations. However, we do not know how many different locations are represented by the LMs; mathematically, it could be as few as 1 or as many as 13. The actual maximum is < 13 because in some cases a single impact appears to have yielded more than one LM. Yamato 793169 and Asuka 881757 are considered "source-crater paired" or "launch paired" because they are compositionally and petrographically similar to each other and distinct from the others, and both have similar cosmic-ray exposure (CRE) histories. The same can be said of QUE 94281 and Y 793274. Thus the 13 meteorites probably represent a maximum of 11 locations on the Moon. The minimum number of likely source craters is debated and in flux as new data for different isotopic systems are obtained. Conservatively, considering CRE data only, a minimum of about 5 impacts is required. Compositional and petrographic data offer only probabilistic constraints. An extreme, but not unreasonable viewpoint, is that such data offer no constraint. For example, if one were to cut up the Apollo 17 landing site (which was selected for its diversity) into softball-sized pieces, some of those pieces (e.g., sample 70135) would be crystalline mare basalts like Y 793169 whereas others (e.g., sample 73131 would be feldspathic regolith breccias like MAC 88104/ 88105. However, nature is not so devious. Warren argues that LMs come from craters of only a few kilometers in diameter. If so, even though CRE data allow, for example, that ALHA 81005 and Y 791197) were launched simultaneously from the same crater, the probability is nevertheless low because the two meteorites are compositionally and mineralogically distinct. Thus, within the allowed range (5-11) for the number of locations represented by the LMs, values at the high end of the range are probably more likely. Mare Meteorites: Three LMs consist almost entirely of mare basalt. Two, Y 793169 and Asuka 881757, are unbrecciated, low-Ti, crystalline rocks that are compositionally and mineralogically similar (but not identical) to each other; they probably derive from a single lunar-mare location. The third, EET 87521/96008, is a fragmental breccia consisting predominantly of VLT mare basalt. Thus, these LMs probably represent only two lunar mare locations. The basaltic LMs have mineral and bulk compositions distinct from Apollo mare basalts. The petrography of Calcalong Creek has not been described in detail, but compositionally it is unique in that it corresponds to a mixture (breccia) of about one-half feldspathic material (i.e., the mean composition of the feldspathic lunar meteorites, below), one-fourth KREEP norite, one-fourth VLT mare basalt (like EET 87521), and 1% CI chondrite. With 4 micro g/g Th and correspondingly high concentrations of other incompatible elements, it is the only lunar meteorite that is likely to have come from within the Procellarum KREEP Terrane (PKT). Yamato 793274 and QUE 94281 are together distinct in being fragmental breccias containing subequal parts of feldspathic highland material and VLT mare basalt. Jolliff et al. estimate a mare to highland ratio of 54:46 for QUE 94281 and 62:38 for Y 793274; this difference is well within the range observed for soils collected only centimeters apart (in cores) at interface site like Apollo 15 and 17 [11]. Although the two meteorites were found on opposite sides of Antarctica, they are probably launch-paired. The strongest evidence is that the pyroclastic glass spherules that occur in both are of two compositional groups and the two groups are essentially the same in both meteorites. Yamato 791197 is nominally a feldspathic lunar meteorite (below), but among FLMs, it probably contains the highest abundance of clasts and glasses of mare derivation. As a consequence, its composition is at the high-Fe, low-Mg end of the range for FLMs and is not included in the FLM average of Table 1. Its composition is consistent with about 10% mare-derived material. Similarly, the two small (Y 82) pieces of Y 82192/82193186032 are more mafic than the large (Y 86) piece, probably as a result of about 7% mare-derived material. All Apollo missions went to areas in or near the PKT, and, consequently, all Apollo regolith samples are contaminated with Th-rich material from the PKT. At the nominally "typical" highland site, Apollo 16, about 30% of the regolith (<1-mm fines) is Th-rich ejecta from the Imbrium impact and about 6% is mare material probably derived from mare basins. Thus Apollo 16 regolith is not typical of the highlands. Among Apollo rocks, the compositions of the FLMs correspond most closely to the feldspathic granulitic breccias of Apollo 16 and 17. (Additional information is contained in original)

Korotev, R. L.↗

NASA NTRS2016

Application of Interval Predictor Models to Space Radiation Shielding

This paper develops techniques for predicting the uncertainty range of an output variable given input-output data. These models are called Interval Predictor Models (IPM) because they yield an interval valued function of the input. This paper develops IPMs having a radial basis structure. This structure enables the formal description of (i) the uncertainty in the models parameters, (ii) the predicted output interval, and (iii) the probability that a future observation would fall in such an interval. In contrast to other metamodeling techniques, this probabilistic certi cate of correctness does not require making any assumptions on the structure of the mechanism from which data are drawn. Optimization-based strategies for calculating IPMs having minimal spread while containing all the data are developed. Constraints for bounding the minimum interval spread over the continuum of inputs, regulating the IPMs variation/oscillation, and centering its spread about a target point, are used to prevent data over tting. Furthermore, we develop an approach for using expert opinion during extrapolation. This metamodeling technique is illustrated using a radiation shielding application for space exploration. In this application, we use IPMs to describe the error incurred in predicting the ux of particles resulting from the interaction between a high-energy incident beam and a target.

Crespo, Luis G.↗

NASA NTRS2018

Demonstration of Probabilistic Sensitivity Analyses Tools on the Structural Response of a Representative Inflatable Space Structure

This work provides an initial step toward demonstrating a probabilistic numerical simulation capability to support trade studies and the development of a certification plan for inflatable space habitats. This study concentrates on interpreting the results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities for a novel inflatable airlock concept, specifically the Non‐Axisymmetric Inflatable Pressure Structure (NAIPS) that was designed and tested under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. A brief overview of the finite element model is provided along with the probabilistic sensitivity analysis approach. The sensitivity studies required a model that was numerically stable and efficient enough that hundreds of simulations could be completed in the allotted time. Therefore, the existing full model was simplified by: extracting a quarter symmetry section of the dome; focusing on a single inflation pressure; and replacing the non‐linear material stress‐strain curves with linear, isotropic materials defined by elastic moduli. Responses of interest include the sensitivity of various structural component loads to material properties, cord lengths, inflation pressure and friction. Multiple sensitivity studies were completed and three are reported here. The first study focused on utilizing wide input parameter ranges to provide an opportunity to assess numerical robustness. The next two studies narrowed the parameter ranges to enable focus on understanding uncertainty at a fixed operating condition. The completion of the sensitivity studies improved understanding of the interdependence of multiple inputs on the responses. In addition, numerical stability of the simulations over wide parameter ranges, shows the feasibility of incorporating uncertainty‐based methods in the design and certification of inflatable space habitats. With the experience and trust gained, it is anticipated that these same methods will be applied to nonlinear, orthotropic models in the future.

Lyle, Karen H.↗

NASA NTRS2018

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Brown, Andrew M.↗