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At least 415 records · Page 23

Probabilistic Risk Assessment of a Light Water Reactor Coupled with a High-Temperature Electrolysis Hydrogen Production Plant

This paper presents recent updates on the Level 1 Probabilistic Risk Assessment (PRA) of Light Water Reactors (LWRs) coupled with a hydrogen production plant. It provides the overview of past results on the PRA for Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) coupled to a 1150 MW High Temperature Electrolysis Facility (HTEF), as well as the latest research results for a smaller 100 MW HTEF facility. Differences between the two HTEF designs are listed. Key differences include the amount and quality of diverted LWR steam, complexity of the Heat Extraction System (HES), and the electrical power source for the HTEF plant. A Failure Mode and Effect Analysis (FMEA) was conducted for the new HTEF design, and the LWR PRA models were modified in the SAPHIRE risk assessment tool to account for the newly identified risk contributors. These include the steam loss event at the HES system, the electrical overcurrent event at the HTEF facility and at the transmission line from the LWR plant, and the hydrogen detonation event at the HTEF facility. The coupling of LWRs with a 100 MW HTEF increases the frequency of several initiating events. For the reference PWR, the largest frequency increase is for the steam line break event at 5.5%. While for the reference BWR, the largest frequency increase is for the switchyard-related Loss of Offsite Power (LOOP) event at 0.11%. The overall plant risk increases by 6.56% and 0.03% for PWR and BWR reference plants respectively. It is found that these risk metrics satisfy the safety criteria of both 10 CFR 50.59 and Regulatory Guide 1.174 licensing pathways.

08 HYDROGEN↗

Integrating static PRA information with risk informed safety margin characterization (RISMC) simulation methods

The overall objective of the project was to develop a computationally feasible and user-friendly mechanized process to integrate traditional probabilistic risk assessment (PRA) and dynamic PRA (DPRA) results. Starting with the systematic identification of items in an existing PRA that need dynamic augmentation, the project used a generic 4-loop pressurized reactor (PWR) and 3-loop PWR as example plants. Station blackout (SBO) and large break loss of coolant accident SBLOCA) were selected as the example initiating events. Using the traditional event-tree (ET)/fault-tree (FT) methodology augmented by dynamic evet tree approach, the potential consequences of the initiating events were simulated with RELAP-3D and MELCOR/RASCAL codes to cover Level 1 through Level 3 of PRA. RAVEN and ADAPT software were used to generate Level 1 simulations with RELAP-3D and Level 2/3 simulations with MELCOR (Level 2)/RASCAL (Level 3), respectively. Example branching conditions (BCs) for SBO included AC power recovery time, valve repair failure time, reactor coolant pump leak time/break size and emergency power supply duration to a total of 9. Example BCs for LOCA included off-site power recovery time, diesel generator power recovery time, auxiliary feed water system operation time, safety relief valve failure to open upon demand, reactor coolant pump seal break time and size to a total of 21. Each RELAP-3D simulation (9,587 scenarios) was labelled OK or Core Damage based on the maximum allowed peak clad temperature (2,100oF). Each MELCOR simulation (4610 scenarios) was labeled as Bin over 10rem or Bin 0-10rem based on the dose at the site boundary. The scenarios were clustered based on the criteria above using the mean shift methodology. Classical PRA (CPRA) and DPRA results were compared to identify the ET sequences that need DPRA augmentation. Several approaches were proposed for the incorporation of these sequences into CPRA using clustering with the mean shift methodology, restructuring the CPRA ETs by adding new BCs/sequences, and using the concept of a limit surface. Procedures for decision making regarding the possible consequences of an initiating event (e.g. core damage or not, site evacuation or not) were developed using a convolutional neural network (CNN), a recurrent neural network (RNN) and a transformer neural network (TNN). The project has led to two PhD degrees, three archival journal papers and five refereed conference proceedings.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Modeling Predictive Maintenance for NuScale’s Condensate and Feedwater System Using EMRALD

Event Modeling Risk Assessment using Linked Diagrams (EMRALD) is used to model of NuScale’s feedwater and condenser system to capture component degradation and repairing process. To model the reliability of the components, a three-stage failure rate is used contrary to a constant rate leading to component failure. Results from EMRALD will be used to compare different maintenance strategies to reduce system downtime. The outcome of the project will assist in maximizing remaining useful life of the overall system and increasing the availability and revenue of the plant.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Scatter in Carbon/Silicon Carbide (C/SiC) Composites Quantified

Carbon-fiber-reinforced silicon carbide matrix (C/SiC) composites processed by chemical vapor infiltration are candidate materials for aerospace thermal structures. Carbon fibers can retain properties at very high temperatures, but they are known to have poor oxidation resistance in adverse, high-temperature environments. Nevertheless, the combination of CVI-SiC matrix with higher stiffness and oxidation resistance, the interfacial coating, and additional surface-seal coating provides the necessary protection to the carbon fibers, and makes the material viable for high-temperature space applications operating under harsh environments. Furthermore, C/SiC composites, like other ceramic matrix composites (CMCs), exhibit graceful non-catastrophic failure because of various inherent energy dissipating mechanisms. The material exhibits nonlinearity in deformation even at very low stress levels. This is the result of the severe matrix microcracking present in the as processed composite because of large differences between the coefficients of thermal expansion of the fiber and the matrix. Utilization of these advanced composites in next generation space vehicles will require innovative structural configurations, updated materials, and refined analyses. Structural safety issues for these vehicles are in direct competition with performance and cost. One would have to quantify the uncertainties associated with the design using formal probabilistic methods. Specifically four fundamental aspects on which analyses are based-- (1) loading conditions, (2) material behavior, (3) geometrical configurations, and (4) structural connections between the composite components and baseline structure--are stochastic in nature. A direct way to formally account for uncertainties is to develop probabilistic structural analysis methods where all participating variables are described by appropriate probability density functions. The present work, however, focuses on analyzing the stochastic material behavior of these advanced composites using formal probabilistic analysis methods. Often, some of the desirable property characteristics that allow composites to offer advantages over conventional structural materials (like tailoring of composite properties) and the complexity are in fact responsible for their greater statistical variability and the requirements for more characterization tests. Composite properties are anisotropic as well, having different properties in different directions. This means that characterization of a property such as stiffness--which will vary greatly depending on the orientation of the fiber relative to the direction of the testing--must be repeated for several different directions and loading conditions. The fabrication process for composites also introduces statistical variations in properties and geometry. A composite part is produced in a number of steps, each of which introduces statistical variability. The matrix is usually produced from a combination of raw materials; and the fiber, which has its own set of properties, is often coated or surface treated, introducing yet another source of variability.

Murthy, Pappu L. N.↗

RAVEN User Manual

RAVEN is a generic software framework to perform parametric and probabilistic analysis based on the response of complex system codes. The initial development was aimed to provide dynamic risk analysis capabilities to the Thermo-Hydraulic code RELAP-7, currently under development at the Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose probabilistic and uncertainty quantification platform, capable to agnostically communicate with any system code. This agnosticism includes providing Application Programming Interfaces (APIs). These APIs are used to allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by inputs files or via python interfaces. RAVEN is capable of investigating the system response, and investigating the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused to- ward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. The development of RAVEN has started in 2012, when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework became stronger. RAVEN principal assignment is to provide the necessary software and algorithms in order to employ the concept developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just the individuation of the frequency of an event potentially leading to a system failure, but the closeness (or not) to key safety-related events. Hence, the approach is interested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. for an important process such as peak pressure in a pipe) is exceeded under certain conditions. The initial development of RAVEN has been focused on providing dynamic risk assessment capability to RELAP-7, currently under development at the INL and, likely, future replacement of the RELAP5-3D code. Most the capabilities that have been implemented having RELAP-7 as principal focus are easily deployable for other system codes. For this reason, several side activates are currently ongoing for coupling RAVEN with soft- ware such as RELAP5-3D, etc. The aim of this document is the explanation of the input requirements, focalizing on the input structure.

97 MATHEMATICS AND COMPUTING↗

An Initial Assessment of the Design Margins of Different ASME Section III, Division 5 Design Rules

This report develops a method for assessing the design margin of the ASME Section III, Division 5 Class A design rules, focusing on a definition of margin as the ratio between the actual, expected component life and the ASME design life. Full inelastic finite element simulations with a complete damage model capturing the available creep, creep-fatigue, fatigue, and tension test failure data produce the expected component lives, which can then be compared to corresponding ASME design calculations. The focus of this particular work is on Alloy 617 and the ASME creep-fatigue design rules, but the approach is general and could be applied to other design limits and to other materials. A margin assessment of a representative Alloy 617 component shows the ASME creep-fatigue design rules applied to this component have a margin of 10 on design life. The report describes several challenges in completing a more comprehensive margin assessment of the ASME rules, in particular challenges in developing probabilistic assessment methods for high temperature structural components. The report details these challenge and discusses the immediate possibilities of the deterministic margin assessment method developed here.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Bayesian and HRA-Aided Method for the Novel Reliability Analysis of Software

Technological advancements and nuclear power plant modernization has inspired considerable research in the areas of safety and reliability, yet there remains a lack of consensus for the reliability assessment of digital instrumentation and control (I&C) systems. Motivated by the lack of consensus for reliability analysis methods, this work employs a novel framework that incorporates Bayesian, human reliability, and common-cause failure (CCF) modeling techniques. The novel framework allows the use of state-of-the-art or classical modeling techniques when accounting for human and CCF effects on system reliability. The Bayesian and HRA-Aided Method for the Reliability Analysis of Software (BAHAMAS) is demonstrated by a case study for the quantification of software hazards found in a previous analysis of a digital reactor trip system. The results demonstrate the ability of BAHAMAS to account for human activities during the software development life cycle and their influence on software reliability. BAHAMAS is a flexible tool for extending the coverage of conventional probabilistic risk assessments to include modernized digital I&C systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Constellation Probabilistic Risk Assessment (PRA): Design Consideration for the Crew Exploration Vehicle

Managed by NASA's Office of Safety and Mission Assurance, a pilot probabilistic risk analysis (PRA) of the NASA Crew Exploration Vehicle (CEV) was performed in early 2006. The PRA methods used follow the general guidance provided in the NASA PRA Procedures Guide for NASA Managers and Practitioners'. Phased-mission based event trees and fault trees are used to model a lunar sortie mission of the CEV - involving the following phases: launch of a cargo vessel and a crew vessel; rendezvous of these two vessels in low Earth orbit; transit to th$: moon; lunar surface activities; ascension &om the lunar surface; and return to Earth. The analysis is based upon assumptions, preliminary system diagrams, and failure data that may involve large uncertainties or may lack formal validation. Furthermore, some of the data used were based upon expert judgment or extrapolated from similar components~systemsT. his paper includes a discussion of the system-level models and provides an overview of the analysis results used to identify insights into CEV risk drivers, and trade and sensitivity studies. Lastly, the PRA model was used to determine changes in risk as the system configurations or key parameters are modified.

Prassinos, Peter G.↗

Enhancement of risk informed validation framework for external hazard scenario

In recent years, the U.S. Nuclear Regulatory Commission (USNRC) and the International Atomic Energy Agency (IAEA) have developed methodologies to assess the vulnerabilities of nuclear plants against site specific extreme hazards. In many cases, advanced simulation tools are being considered to simulate multi-physics, multi-scale phenomena and to evaluate vulnerability of nuclear facilities. The credibility of advanced simulation tools is assessed based on a formal verification, validation, and uncertainty quantification procedure. One of the key limitations in validation is the lack of relevant experimental data at system-level. This limitation leads to a decrease in the confidence of system-level risk predictions. Therefore, a robust validation framework is needed to formalize the confidence in predictive capability of advanced simulation results. Additionally, this study enhances the existing risk informed validation methodology, originally proposed by Kwag et al. [1] and Bodda et al. [2], by developing additional attributes and a new set of validation indicies for a complete and wider applicability of the framework. In this manuscript, the methodology to identify the critical path that leads to the system-level failure is illustrated. The overall validation is checked for completeness and consistency by comparing the critical path for both the system-level simulation and experimental models. The applicability of the code for an intended application is represented in terms of various maturity levels and helps in the process of decision making.

42 ENGINEERING↗

Reliability approach to rotating-component design

A probabilistic methodology for designing rotating mechanical components using reliability to relate stress to strength is explained. The experimental test machines and data obtained for steel to verify this methodology are described. A sample mechanical rotating component design problem is solved by comparing a deterministic design method with the new design-by reliability approach. The new method shows that a smaller size and weight can be obtained for specified rotating shaft life and reliability, and uses the statistical distortion-energy theory with statistical fatigue diagrams for optimum shaft design. Statistical methods are presented for (1) determining strength distributions for steel experimentally, (2) determining a failure theory for stress variations in a rotating shaft subjected to reversed bending and steady torque, and (3) relating strength to stress by reliability.

Kececioglu, D. B.↗

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

A Probabilistic Design Method Applied to Smart Composite Structures

A probabilistic design method is described and demonstrated using a smart composite wing. Probabilistic structural design incorporates naturally occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, structure geometry and control-related parameters. Probabilistic sensitivity factors are computed to identify those parameters that have a great influence on a specific structural reliability. Two performance criteria are used to demonstrate this design methodology. The first criterion requires that the actuated angle at the wing tip be bounded by upper and lower limits at a specified reliability. The second criterion requires that the probability of ply damage due to random impact load be smaller than an assigned value. When the relationship between reliability improvement and the sensitivity factors is assessed, the results show that a reduction in the scatter of the random variable with the largest sensitivity factor (absolute value) provides the lowest failure probability. An increase in the mean of the random variable with a negative sensitivity factor will reduce the failure probability. Therefore, the design can be improved by controlling or selecting distribution parameters associated with random variables. This can be implemented during the manufacturing process to obtain maximum benefit with minimum alterations.

Shiao, Michael C.↗

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. Finally, the methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

97 MATHEMATICS AND COMPUTING↗

Quantifying Medical Risk on a Long Duration Lunar Mission: A Demonstration of NASA’s IMPACT Tradespace Analysis Tool

Background NASA’s human exploration spaceflight missions to the Moon and Mars present unprecedented challenges for in-mission medical care. The distance from Earth will mean increased mission durations, communication delays, limited to no resupply opportunities, and constraints on the medical evacuation of astronauts. Mass, volume, power, and data will be limited while higher demands will be placed on the crew to manage medical care. NASA’s Moon to Mars exploration strategy lays out increasingly complex Artemis missions both in terms of duration and operations. In these more challenging deep space missions, it is important to quantitatively estimate the human medical risk to inform a traditional heuristic approach to medical risk. Prior tools have been developed for missions in low Earth orbit, but a new tool is required to plan for future exploration missions. Methods IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a risk assessment tool developed by NASA to advance exploration mission medical system design by quantitatively estimating mission medical risk. IMPACT v1.0 includes a novel evidence library baselined to exploration environments; an expanded list of 119 medical conditions; the addition of medical resources; and the ability for rapid and iterative analysis. Medical system risk estimates include loss of crew life, consideration of the need for return to definitive care (medical evacuation), and an estimate of crew time affected due to medical conditions. A notional long duration lunar orbit and lunar surface design reference mission (DRM) was chosen with a 4-astronaut crew to represent a sustained exploration Artemis mission. Results/Discussion Overall, IMPACT successfully quantified medical risk and derived an optimized medical system to support crew on a long duration lunar mission. In this DRM, the calculated loss of crew life from a medical event was 0.008 events per mission, risk of potential need for evacuation was 0.30 events per mission, and cumulative crew time affected by medical conditions was 103 days. The medical conditions that most contributed to overall medical risk were decompression sickness, trauma conditions, and respiratory failure. The conditions that had the largest effects on crew performance included musculoskeletal injuries and lunar dust exposure. The IMPACT-generated medical system included resources that target the most common and highest risk conditions. This systematic analysis demonstrates the value of the IMPACT tool in medical system design for human exploration spaceflight missions.

Missions to Mars↗

Quantifying Medical Risk on a Long Duration Lunar Mission: A Demonstration of NASA’s IMPACT Tradespace Analysis Tool

Background NASA’s human exploration spaceflight missions to the Moon and Mars present unprecedented challenges for in-mission medical care. The distance from Earth will mean increased mission durations, communication delays, limited to no resupply opportunities, and constraints on the medical evacuation of astronauts. Mass, volume, power, and data will be limited while higher demands will be placed on the crew to manage medical care. NASA’s Moon to Mars exploration strategy lays out increasingly complex Artemis missions both in terms of duration and operations. In these more challenging deep space missions, it is important to quantitatively estimate the human medical risk to inform a traditional heuristic approach to medical risk. Prior tools have been developed for missions in low Earth orbit, but a new tool is required to plan for future exploration missions. Methods IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a risk assessment tool developed by NASA to advance exploration mission medical system design by quantitatively estimating mission medical risk. IMPACT v1.0 includes a novel evidence library baselined to exploration environments; an expanded list of 119 medical conditions; the addition of medical resources; and the ability for rapid and iterative analysis. Medical system risk estimates include loss of crew life, consideration of the need for return to definitive care (medical evacuation), and an estimate of crew time affected due to medical conditions. A notional long duration lunar orbit and lunar surface design reference mission (DRM) was chosen with a 4-astronaut crew to represent a sustained exploration Artemis mission. Results/Discussion Overall, IMPACT successfully quantified medical risk and derived an optimized medical system to support crew on a long duration lunar mission. In this DRM, the calculated loss of crew life from a medical event was 0.008 events per mission, risk of potential need for evacuation was 0.30 events per mission, and cumulative crew time affected by medical conditions was 103 days. The medical conditions that most contributed to overall medical risk were decompression sickness, trauma conditions, and respiratory failure. The conditions that had the largest effects on crew performance included musculoskeletal injuries and lunar dust exposure. The IMPACT-generated medical system included resources that target the most common and highest risk conditions. This systematic analysis demonstrates the value of the IMPACT tool in medical system design for human exploration spaceflight missions.

Missions to Mars↗

Degradation in interfacial shear strength of carbon fiber/ vinyl ester composites due to long-term exposure to seawater using push-out tests

Here, in this study, single fiber (~7-μm diameter) push-out tests are conducted to evaluate hygrothermal effects on the interfacial shear strength (IFSS) of carbon fiber/vinyl ester (CF/VE) composites. Hygrothermal conditioning is achieved by saturating samples in simulated seawater at 40 °C for two years. An investigation has been conducted on the preparation, validity, and interpretation of the push-out test results. First, the authors present a polishing methodology that results in thin films of CF/VE composites in the thickness range of 15–120 μm and produces an average 41.2% drop in IFSS due to long-term hygrothermal exposure. Using scanning electron microscopy (SEM), we show that during the push-out tests, the failure initiates locally at the zone of minimum bond strength at the bottom (away from the indenter), then propagates along the length of the interface. The influence of radial tensile stresses originating due to bending is found to be negligible. Using the SEM imaging of the pushed-out fibers, we validate the failure of the interface to be the primary source of failure. The associated results are found to depend on the thickness of the interface. We then reevaluate the results using the Weibull distribution, knowing that the failure mechanism is analogous to the weakest link theory. The results show a 25.5% drop in the IFSS of the CFVE composite, measured at an infinitesimal scale due to long-term to hygrothermal conditioning at 40 °C. A significant drop in IFSS was observed after reheating above glass transition temperature (T g ) and cooling.

36 MATERIALS SCIENCE↗

Toward Failure Modeling In Complex Dynamic Systems: Impact of Design and Manufacturing Variations

When designing vehicle vibration monitoring systems for aerospace devices, it is common to use well-established models of vibration features to determine whether failures or defects exist. Most of the algorithms used for failure detection rely on these models to detect significant changes during a flight environment. In actual practice, however, most vehicle vibration monitoring systems are corrupted by high rates of false alarms and missed detections. Research conducted at the NASA Ames Research Center has determined that a major reason for the high rates of false alarms and missed detections is the numerous sources of statistical variations that are not taken into account in the. modeling assumptions. In this paper, we address one such source of variations, namely, those caused during the design and manufacturing of rotating machinery components that make up aerospace systems. We present a novel way of modeling the vibration response by including design variations via probabilistic methods. The results demonstrate initial feasibility of the method, showing great promise in developing a general methodology for designing more accurate aerospace vehicle vibration monitoring systems.

Tumer, Irem Y.↗

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Mason, Brian H.↗