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Global/local methods for probabilistic structural analysis

A probabilistic global/local method is proposed to reduce the computational requirements of probabilistic structural analysis. A coarser global model is used for most of the computations with a local more refined model used only at key probabilistic conditions. The global model is used to establish the cumulative distribution function (cdf) and the Most Probable Point (MPP). The local model then uses the predicted MPP to adjust the cdf value. The global/local method is used within the advanced mean value probabilistic algorithm. The local model can be more refined with respect to the g1obal model in terms of finer mesh, smaller time step, tighter tolerances, etc. and can be used with linear or nonlinear models. The basis for this approach is described in terms of the correlation between the global and local models which can be estimated from the global and local MPPs. A numerical example is presented using the NESSUS probabilistic structural analysis program with the finite element method used for the structural modeling. The results clearly indicate a significant computer savings with minimal loss in accuracy.

Millwater, H. R.

Progressive matrix cracking in off-axis plies of a general symmetric laminate

A generalized shear-lag model is derived to determine the average through-the-thickness stress state present in a layer undergoing transverse matrix cracking, by extending the method of Lee and Daniels (1991) to a general symmetric multilayered system. The model is capable of considering cracking in layers of arbitrary orientation, states of general in-plane applied loading, and laminates with a general symmetric stacking sequence. The model is included in a computer program designed for probabilistic laminate analysis, and the results are compared to those determined with the ply drop-off technique.

Thomas, David J.

Implementation of probabilistic design methodology at Tennessee State University

The fact that Deterministic Design Method no longer satisfies most design needs calls for methods that will cope with the high trend in technology. The advance in computer technology has reduced the rigors that normally accompany many design analysis methods that account for uncertainties in design parameters. Probabilistic Design Methodology (PDM) is beginning to make impact in engineering design. This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to this method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used for this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. Since this method is new to the students, its introduction into the engineering curriculum is to be in stages. These range from the introduction of PDM and its software to the applications. While this program is being developed for its eventual inclusion into the engineering curriculum, some graduate and undergraduate students are already carrying out some projects using this method. As the students are increasing their understanding on PDM, they are at the same time applying it to some common design problems. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Brakes; Design of Heat Exchangers Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere

Implementation of Probabilistic Design Methodology at Tennessee State University

Engineering Design is one of the most important areas in engineering education. Deterministic Design Methodology (DDM) is the only design method that is taught in most engineering schools. This method does not give a direct account of uncertainties in design parameters. Hence, it is impossible to quantify the uncertainties in the response and the actual safety margin remains unknown. The desire for a design methodology tha can identify the primitive (random) variables that affect the structural behavior has led to a growing interest on Probabilistic Design Methodology (PDM). This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to the method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used of this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. A research in technology transfer through course offering in PDM is in effect a Tennessee State University. The aim is to familiarize students with the problem of uncertainties in engineering design. Included in the paper are some projects on PDM carried out by some students and faculty. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Shafts; Design of Statistically Indeterminate Frame Structures; Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere

NASA Tech Briefs, May 2010

Topics covered include: Instrument for Analysis of Greenland's Glacier Mills Cryogenic Moisture Apparatus; A Transportable Gravity Gradiometer Based on Atom Interferometry; Three Methods of Detection of Hydrazines; Crossed, Small-Deflection Energy Analyzer for Wind/Temperature Spectrometer; Wavefront Correction for Large, Flexible Antenna Reflector; Novel Micro Strip-to-Waveguide Feed Employing a Double-Y Junction; Thin-Film Ferro Electric-Coupled Microstripline Phase Shifters With Reduced Device Hysteresis; Two-Stage, 90-GHz, Low-Noise Amplifier; A 311-GHz Fundamental Oscillator Using InP HBT Technology; FPGA Coprocessor Design for an Onboard Multi-Angle Spectro-Polarimetric Imager; Serrating Nozzle Surfaces for Complete Transfer of Droplets; Turbomolecular Pumps for Holding Gases in Open Containers; Triaxial Swirl Injector Element for Liquid-Fueled Engines; Integrated Budget Office Toolbox; PLOT3D Export Tool for Tecplot; Math Description Engine Software Development Kit; Astronaut Office Scheduling System Software; ISS Solar Array Management; Probabilistic Structural Analysis Program; SPOT Program; Integrated Hybrid System Architecture for Risk Analysis; System for Packaging Planetary Samples for Return to Earth; Offset Compound Gear Drive; Low-Dead-Volume Inlet for Vacuum Chamber; Simple Check Valves for Microfluidic Devices; A Capillary-Based Static Phase Separator for Highly Variable Wetting Conditions; Gimballing Spacecraft Thruster; Finned Carbon-Carbon Heat Pipe with Potassium Working Fluid; Lightweight Heat Pipes Made from Magnesium; Ceramic Rail-Race Ball Bearings; Improved OTEC System for a Submarine Robot; Reflector Surface Error Compensation in Dual-Reflector Antennas; Enriched Storable Oxidizers for Rocket Engines; Planar Submillimeter-Wave Mixer Technology with Integrated Antenna; Widely Tunable Mode-Hop-Free External-Cavity Quantum Cascade Laser; Non-Geiger-Mode Single-Photon Avalanche Detector with Low Excess Noise; Using Whispering-Gallery-Mode Resonators for Refractometry; RF Device for Acquiring Images of the Human Body; Reactive Collision Avoidance Algorithm; Fast Solution in Sparse LDA for Binary Classification; Modeling Common-Sense Decisions in Artificial Intelligence; Graph-Based Path-Planning for Titan Balloons; Nanolaminate Membranes as Cylindrical Telescope Reflectors; Air-Sea Spray Airborne Radar Profiler Characterizes Energy Fluxes in Hurricanes; Large Telescope Segmented Primary Mirror Alignment; and Simplified Night Sky Display System.

Source record

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability

And the Human Saves the Day or Maybe They Ruin It, The Importance of Humans in the Loop

Flying a mission in space requires a massive commitment of resources, and without the talent and commitment of the people involved in this effort we would never leave the atmosphere of Earth as safely as we have. When we use the phrase "humans in the loop", it could apply to almost any endeavor since everything starts with humans developing a concept, completing the design process, building or implementing a product and using the product to achieve a goal or purpose. Narrowing the focus to spaceflight, there are a variety of individuals involved throughout the preparations for flight and the flight itself. All of the humans involved add value and support for program success. The paper discusses the concepts of human involvement in technological programs, how a Probabilistic Risk Assessment (PRA) accounts for the human in the loop for potential missions using a technique called Human Reliability Analysis (HRA) and the tradeoffs between having a human in the loop or not. Human actions can increase or decrease the overall risk via initiating events or mitigating them, thus removing the human from the loop doesn't always lowers the risk.

DeMott, Diana L.

NASA Overview

This viewgraph presentation provides information on computer programs for the application of probabilistics in aerospace design. The presentation defines risk, and lists probabilistic tools which can take risk into account. It then lists current and future examples of NASA aerospace technology program support which utilize probabilistic methods. Current examples include turbofan engines, combustor liners, life estimation, the analysis of rotors and blades, and shuttle ground operations. The 2nd Generation Reusable Launch Vehicle is one of the future areas of support. The presentation also suggests other future uses of probabilistic tools in aerospace design, and optimal methods for their implementation.

Rusick, Jeff

Probabilistic Finite Element Development

The probabilistic finite element computer program known as Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is being developed for the analysis of critical structural components for reusable space propulsion systems. First year efforts involve the formulation of the probabilistic analysis strategy and the development of a probabilistic linear analysis code. The ultimate goal of the 3-year program is the development of a finite element code capable of performing nonlinear dynamic analysis of structures having stochastic material properties, geometry, and boundary conditions and subjected to random loading. Three levels of sophistication are envisioned for the stochastic description of the structural problem, namely: (1) homogeneous random variable for stiffness, mass, damping, and external loading; (2) stochastic characterization of variables at the element level, with specified interelement correlations; and (3) stochastic interpolation of variables within a finite element. Two alternative probabilistic analysis methods will be developed, allowing for all three levels of modeling sophistication.

Nagtegaal, J.

Assessment Of Advanced Concentrator Photovoltaic Modules

Computer program developed to estimate probabilistically total and component costs to end users of concentrating photovoltaic arrays in 1990's. Based on modified version of SIMRAND program, Simulation of Research and Development projects, -to estimate total cost of system for large number of module designs. Module design that yields minimum cost for total system then chosen as preferred design. To obtain distribution of expected module costs, simulation performed. Component estimates made by SIMRAND include efficiency of module and costs of cell, assembly of cells, lenses, and modules. Written in FORTRAN 77.

Borden, C. S.

Planning Amidst Uncertainty: Identifying Core CCS Infrastructure Robust to Storage Uncertainty

Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO2 emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO2 processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from 15% to 0% is observed to lead to an 83.7% reduction in CO2 processing capacity and a 77.1% decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions.

Olson, Daniel

CARES/Life Used for Probabilistic Characterization of MEMS Pressure Sensor Membranes

Microelectromechanical systems (MEMS) devices are typically made from brittle materials such as silicon using traditional semiconductor manufacturing techniques. They can be etched (or micromachined) from larger structures or can be built up with material deposition processes. Maintaining dimensional control and consistent mechanical properties is considerably more difficult for MEMS because feature size is on the micrometer scale. Therefore, the application of probabilistic design methodology becomes necessary for MEMS. This was demonstrated at the NASA Glenn Research Center and Case Western Reserve University in an investigation that used the NASA-developed CARES/Life brittle material design program to study the probabilistic fracture strength behavior of single-crystal SiC, polycrystalline SiC, and amorphous Si3N4 pressurized 1-mm-square thin-film diaphragms. These materials are of interest because of their superior high-temperature characteristics, which are desirable for harsh environment applications such as turbine engine and rocket propulsion system hot sections.

Nemeth, Noel N.

Probabilistic structural analysis methods development for SSME

The development of probabilistic structural analysis methods is a major part of the SSME Structural Durability Program and consists of three program elements: composite load spectra, probabilistic finite element structural analysis, and probabilistic structural analysis applications. Recent progress includes: (1) the effects of the uncertainties of several factors on the HPFP blade temperature pressure and torque, (2) the evaluation of the cumulative distribution function of structural response variables based on assumed uncertainties on primitive structural variables, and (3) evaluation of the failure probability. Collectively, the results obtained demonstrate that the structural durability of critical SSME components can be probabilistically evaluated.

Chamis, C. C.

Probabilistic structural analysis: Introductory remarks

The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra models, (2) computational probabilistic structural analysis methods, and (3) probabilistic constitutive relationships. The development of the probabilistic structural analysis methodology is a joint program of NASA Lewis in-house and sponsored research. The objective of this session is to illustrate recent progress on the application of this methodology to determine the reliability of structural components for rocket propulsion systems. The session contains descriptions of and progress reports on the following specific activities: (1) The NESSUS computer code, (2) approximate methods, (3) advanced methods, (4) composite load spectra applications, (5) probabilistic fracture mechanisms, and (6) probability of failure and risk analysis. Collectively, the progress to date demonstrates that the structural durability of hot engine structural components can be effectively evaluated in a formal probabilistic/reliability framework.

Chamis, Christos C.

Commercialization of NESSUS: Status

A plan was initiated in 1988 to commercialize the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) probabilistic structural analysis software. The goal of the on-going commercialization effort is to begin the transfer of Probabilistic Structural Analysis Method (PSAM) developed technology into industry and to develop additional funding resources in the general area of structural reliability. The commercialization effort is summarized. The SwRI NESSUS Software System is a general purpose probabilistic finite element computer program using state of the art methods for predicting stochastic structural response due to random loads, material properties, part geometry, and boundary conditions. NESSUS can be used to assess structural reliability, to compute probability of failure, to rank the input random variables by importance, and to provide a more cost effective design than traditional methods. The goal is to develop a general probabilistic structural analysis methodology to assist in the certification of critical components in the next generation Space Shuttle Main Engine.

Thacker, Ben H.

Overview of Structural Response: Probabilistic Structural Analysis

Advanced analysis methods are required to predict accurately the structural response (static, transient, cyclic, etc.) and accompanying local stresses in space propulsion system components operating in a fatigue environment consisting of complex thermal and mechanical load spectra. The probabilistic approach to structural response consists of the following program elements: (1) composite load spectra, (2) probabilistic structural analysis methods development, (3) probabilitic finite element theory, (4) probabilistic structural analysis application, (5) structural tailoring of turbopump blades, (6) unified theory of dynamic creep buckling/ratcheting, (7) creep buckling/ratcheting analyzer, and (8) nonlinear COBSTRAN development. Research activities on all of these program elements (except the creep buckling/ratcheting analyzer) are under way.

Chamis, C. C.

Probabilistic Analysis and Density Parameter Estimation Within Nessus

This NASA educational grant has the goal of promoting probabilistic analysis methods to undergraduate and graduate UTSA engineering students. Two undergraduate-level and one graduate-level course were offered at UTSA providing a large number of students exposure to and experience in probabilistic techniques. The grant provided two research engineers from Southwest Research Institute the opportunity to teach these courses at UTSA, thereby exposing a large number of students to practical applications of probabilistic methods and state-of-the-art computational methods. In classroom activities, students were introduced to the NESSUS computer program, which embodies many algorithms in probabilistic simulation and reliability analysis. Because the NESSUS program is used at UTSA in both student research projects and selected courses, a student version of a NESSUS manual has been revised and improved, with additional example problems being added to expand the scope of the example application problems. This report documents two research accomplishments in the integration of a new sampling algorithm into NESSUS and in the testing of the new algorithm. The new Latin Hypercube Sampling (LHS) subroutines use the latest NESSUS input file format and specific files for writing output. The LHS subroutines are called out early in the program so that no unnecessary calculations are performed. Proper correlation between sets of multidimensional coordinates can be obtained by using NESSUS' LHS capabilities. Finally, two types of correlation are written to the appropriate output file. The program enhancement was tested by repeatedly estimating the mean, standard deviation, and 99th percentile of four different responses using Monte Carlo (MC) and LHS. These test cases, put forth by the Society of Automotive Engineers, are used to compare probabilistic methods. For all test cases, it is shown that LHS has a lower estimation error than MC when used to estimate the mean, standard deviation, and 99th percentile of the four responses at the 50 percent confidence level and using the same number of response evaluations for each method. In addition, LHS requires fewer calculations than MC in order to be 99.7 percent confident that a single mean, standard deviation, or 99th percentile estimate will be within at most 3 percent of the true value of the each parameter. Again, this is shown for all of the test cases studied. For that reason it can be said that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ; furthermore, the newest LHS module is a valuable new enhancement of the program.

Godines, Cody R.