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Method for defining limit loads uses probability distribution of largest load occurring during given time intervals. Method is compatible with both deterministic and probabilistic structural design criteria. It also rationally accounts for fact that longer structure is exposed to random loading environment, greater is possibility that it will experience extreme load.
A multiyear program is performed with the objective to develop generic load models with multiple levels of progressive sophistication to simulate the composite (combined) load spectra that are induced in space propulsion system components, representative of Space Shuttle Main Engines (SSME), such as transfer ducts, turbine blades, and liquid oxygen (LOX) posts. Progress of the first year's effort includes completion of a sufficient portion of each task -- probabilistic models, code development, validation, and an initial operational code. This code has from its inception an expert system philosophy that could be added to throughout the program and in the future. The initial operational code is only applicable to turbine blade type loadings. The probabilistic model included in the operational code has fitting routines for loads that utilize a modified Discrete Probabilistic Distribution termed RASCAL, a barrier crossing method and a Monte Carlo method. An initial load model was developed by Battelle that is currently used for the slowly varying duty cycle type loading. The intent is to use the model and related codes essentially in the current form for all loads that are based on measured or calculated data that have followed a slowly varying profile.
Heuristic-path-planner method reduces computing time. Probability of successful motion of robot through region of space obtained from geometric model and captures effects of objects in region and kinematics of robot arm. Information used to guide on-line search and results, in most cases, in successful determination of path within reasonably short time.
The premise to be tested in this analysis is whether cost economics may accrue by delivering more landers designed to lower reliability of operation (compared to fewer landers of higher reliability) to obtain a desired probability of achieving a given number of lander successes. Generally, the application in mind is a network of penetrators, although the analysis may apply as well to other small lander concepts or even to simple rovers. The method of analysis is based on a probabilistic model of lander success and a related probabilistic model of project cost including the lander, spacecraft carrier, and integration, but not launch or operations costs. Quantitative results are obtained in a normalized and parametric fashion. Sensitivity to the assumed model parameters is also examined.
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
The goal of this NASA-funded research is to advance research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction methods for improved aerospace and aircraft propulsion system components. Reliability methods are used to quantify response uncertainties due to inherent uncertainties in design variables. In this report, several reliability methods are applied to a series pipe network. The observed responses are the head delivered by a main pump and the line head at a desired flow rate. The probability that the flow rate in the line will be less than a specified minimum will be discussed.
The goal of this NASA-funded research is to advance research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction methods for improved aerospace and aircraft propulsion system components. Reliability methods are used to quantify response uncertainties due to inherent uncertainties in design variables. In this report, several reliability methods are applied to a parallel pipe network. The observed responses are the head delivered by a main pump and the head values of two parallel lines at certain flow rates. The probability that the flow rates in the lines will be less than their specified minimums will be discussed.
This report validates and documents the detailed features and practical application of the framework for software intensive digital systems risk assessment and risk-informed safety assurance presented in the NASA PRA Procedures Guide for Managers and Practitioner. This framework, called herein the "Context-based Software Risk Model" (CSRM), enables the assessment of the contribution of software and software-intensive digital systems to overall system risk, in a manner which is entirely compatible and integrated with the format of a "standard" Probabilistic Risk Assessment (PRA), as currently documented and applied for NASA missions and applications. The CSRM also provides a risk-informed path and criteria for conducting organized and systematic digital system and software testing so that, within this risk-informed paradigm, the achievement of a quantitatively defined level of safety and mission success assurance may be targeted and demonstrated. The framework is based on the concept of context-dependent software risk scenarios and on the modeling of such scenarios via the use of traditional PRA techniques - i.e., event trees and fault trees - in combination with more advanced modeling devices such as the Dynamic Flowgraph Methodology (DFM) or other dynamic logic-modeling representations. The scenarios can be synthesized and quantified in a conditional logic and probabilistic formulation. The application of the CSRM method documented in this report refers to the MiniAERCam system designed and developed by the NASA Johnson Space Center.
Accounting for uncertainty when calibrating expensive computational models is a common challenge faced by scientists and engineers. Often Bayesian techniques are adopted to estimate a probability density function over the model parameters given noisy empirical data. The methods used to perform this type of probabilistic calibration are computationally prohibitive in that they require a large number of evaluations of the expensive model. In these cases, surrogate modeling -- that is, using a fast-to-evaluate, lower fidelity stand-in for the original computational model -- may be the only option to alleviate this computational burden. However, the upfront cost of generating training data to build a surrogate model can itself be expensive. As such, it is important to be judicious when selecting training points at which the full-fidelity model is evaluated. Here, an active learning approach is proposed that enables efficient selection of training points using approximate samples of the calibrated parameter probability density function. In this way, the training points can be concentrated in regions where the calibration algorithm requires high model accuracy.
A mission reliability estimation method has been designed to translate mission requirements into choices of robot modules in order to configure a multi-robot team to have high reliability at minimal cost. In order to build cost-effective robot teams for long-term missions, one must be able to compare alternative design paradigms in a principled way by comparing the reliability of different robot models and robot team configurations. Core modules have been created including: a probabilistic module with reliability-cost characteristics, a method for combining the characteristics of multiple modules to determine an overall reliability-cost characteristic, and a method for the generation of legitimate module combinations based on mission specifications and the selection of the best of the resulting combinations from a cost-reliability standpoint. The developed methodology can be used to predict the probability of a mission being completed, given information about the components used to build the robots, as well as information about the mission tasks. In the research for this innovation, sample robot missions were examined and compared to the performance of robot teams with different numbers of robots and different numbers of spare components. Data that a mission designer would need was factored in, such as whether it would be better to have a spare robot versus an equivalent number of spare parts, or if mission cost can be reduced while maintaining reliability using spares. This analytical model was applied to an example robot mission, examining the cost-reliability tradeoffs among different team configurations. Particularly scrutinized were teams using either redundancy (spare robots) or repairability (spare components). Using conservative estimates of the cost-reliability relationship, results show that it is possible to significantly reduce the cost of a robotic mission by using cheaper, lower-reliability components and providing spares. This suggests that the current design paradigm of building a minimal number of highly robust robots may not be the best way to design robots for extended missions.
Probabilistic Risk Assessment (PRA) is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in complex technological systems for the purpose of cost-effectively improving their safety and performance. NASA's objective is to better understand and effectively manage risk, and thus more effectively ensure mission and programmatic success, and to achieve and maintain high safety standards at NASA. NASA intends to use risk assessment in its programs and projects to support optimal management decision making for the improvement of safety and program performance. In addition to using quantitative/probabilistic risk assessment to improve safety and enhance the safety decision process, NASA has incorporated quantitative risk assessment into its system safety assessment process, which until now has relied primarily on a qualitative representation of risk. Also, NASA has recently adopted the Risk-Informed Decision Making (RIDM) process [1-1] as a valuable addition to supplement existing deterministic and experience-based engineering methods and tools. Over the years, NASA has been a leader in most of the technologies it has employed in its programs. One would think that PRA should be no exception. In fact, it would be natural for NASA to be a leader in PRA because, as a technology pioneer, NASA uses risk assessment and management implicitly or explicitly on a daily basis. NASA has probabilistic safety requirements (thresholds and goals) for crew transportation system missions to the International Space Station (ISS) [1-2]. NASA intends to have probabilistic requirements for any new human spaceflight transportation system acquisition. Methods to perform risk and reliability assessment in the early 1960s originated in U.S. aerospace and missile programs. Fault tree analysis (FTA) is an example. It would have been a reasonable extrapolation to expect that NASA would also become the world leader in the application of PRA. That was, however, not to happen. Early in the Apollo program, estimates of the probability for a successful roundtrip human mission to the moon yielded disappointingly low (and suspect) values and NASA became discouraged from further performing quantitative risk analyses until some two decades later when the methods were more refined, rigorous, and repeatable. Instead, NASA decided to rely primarily on the Hazard Analysis (HA) and Failure Modes and Effects Analysis (FMEA) methods for system safety assessment.
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.
This paper presents a semi-analytic method for computing frequency dependent means, variances, and failure probabilities for arbitrarily large-order closed-loop dynamical systems possessing a single uncertain parameter or with multiple highly correlated uncertain parameters. The approach will be shown to not suffer from the same computational challenges associated with computing failure probabilities using conventional FORM/SORM techniques. The approach is demonstrated by computing the probabilistic frequency domain performance of an optimal feed-forward disturbance rejection scheme.
An investigation was conducted to determine the influence of combined loading criteria on the space shuttle structural performance. The study consisted of four primary phases: Phase (1) The determination of the sensitivity of structural weight to various loading parameters associated with the space shuttle. Phase (2) The determination of the sensitivity of structural weight to various levels of loading parameter variability and probability. Phase (3) The determination of shuttle mission loading parameters variability and probability as a function of design evolution and the identification of those loading parameters where inadequate data exists. Phase (4) The determination of rational methods of combining both deterministic time varying and probabilistic loading parameters to provide realistic design criteria. The study results are presented.
A methodology was presented so that realistic attrition prediction could aid in selecting an optimum design option for minimizing the effects of updated loads on the Space Shuttle Solid Rocket Booster (SRB) aft skirt. The updated loads resulted in water impact attrition rates greater than 10 percent for the aft skirt structure. Adding weight to reinforce the aft skirt was undesirable. The refined method treats the occurrences of the load distribution probabilistically, radially and longitudinally, with respect to the critical structural response.
Optimizing spacecraft attitude determination systems that use onboard star trackers requires analysis and evaluation of some probabilistic aspects of system design. This paper discusses methods of constructing or compiling optimum star catalogs, which are defined as uniform distributions on a sphere. Both local and global measures of uniformity on a sphere are defined. Application of these methods and measures to a specific problem is also discussed. In addition, Poisson models of star tracker acquisition probabilities are formulated to provide a useful analytical basis for designing and optimizing attitude determination systems. These analytical models and methods lead to rapid and realistic quantitative results, and should therefore facilitate making system performance trades. Use of such methods should also reduce the need for performing tedious computer simulations to obtain analogous results.
These slides describe the data analysis methods that are used to determine inputs for probabilistic risk models supporting the Space Shuttle Program. Other applications can follow a similar path probably using different data sources. Statistical approaches are different and not addressed here. Topics included here: 1) Prior Distribution; 2) Likelihood Data; 3) Bayesian Updating; and 4) Uncertainty and Error. Note: This is a high-level discussion and is not intended to be a tutorial.
An autonomous vehicle patrols a large region, during which an algorithm receives measurements of detected potential objects within its sensor range. The goal of the algorithm is to track all objects in the region over time. This problem differs from traditional multi-target tracking scenarios because the region of interest is much larger than the sensor range and relies on the movement of the sensor through this region for coverage. The goal is to know whether anything has changed between visits to the same location. In particular, two kinds of alert conditions must be detected: (1) a previously detected object has disappeared and (2) a new object has appeared in a location already checked. For the time an object is within sensor range, the object can be assumed to remain stationary, changing position only between visits. The problem is difficult because the upstream object detection processing is likely to make many errors, resulting in heavy clutter (false positives) and missed detections (false negatives), and because only noisy, bearings-only measurements are available. This work has three main goals: (1) Associate incoming measurements with known objects or mark them as new objects or false positives, as appropriate. For this, a multiple hypothesis tracker was adapted to this scenario. (2) Localize the objects using multiple bearings-only measurements to provide estimates of global position (e.g., latitude and longitude). A nonlinear Kalman filter extension provides these 2D position estimates using the 1D measurements. (3) Calculate the probability that a suspected object truly exists (in the estimated position), and determine whether alert conditions have been triggered (for new objects or disappeared objects). The concept of a probability of existence was created, and a new Bayesian method for updating this probability at each time step was developed. A probabilistic multiple hypothesis approach is chosen because of its superiority in handling the uncertainty arising from errors in sensors and upstream processes. However, traditional target tracking methods typically assume a stationary detection volume of interest, whereas in this case, one must make adjustments for being able to see only a small portion of the region of interest and understand when an alert situation has occurred. To track object existence inside and outside the vehicle's sensor range, a probability of existence was defined for each hypothesized object, and this value was updated at every time step in a Bayesian manner based on expected characteristics of the sensor and object and whether that object has been detected in the most recent time step. Then, this value feeds into a sequential probability ratio test (SPRT) to determine the status of the object (suspected, confirmed, or deleted). Alerts are sent upon selected status transitions. Additionally, in order to track objects that move in and out of sensor range and update the probability of existence appropriately a variable probability detection has been defined and the hypothesis probability equations have been re-derived to accommodate this change. Unsupervised object tracking is a pervasive issue in automated perception systems. This work could apply to any mobile platform (ground vehicle, sea vessel, air vehicle, or orbiter) that intermittently revisits regions of interest and needs to determine whether anything interesting has changed.