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Desensitizing microcircuits to variations in temperature and performance parameters - computer aided sensitivity analysis
The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.
Human exploration missions to Mars or other destinations in the solar system require large quantities of propellant to enable the transportation of required elements from Earth's sphere of influence to Mars. Current and proposed launch vehicles are incapable of launching all of the requisite mass on a single vehicle; hence, multiple launches and in-space aggregation are required to perform a Mars mission. This study examines the potential of reusable chemical propulsion stages based in cis-lunar space to meet the transportation objectives of the Evolvable Mars Campaign and identifies cis-lunar propellant supply requirements. These stages could be supplied with fuel and oxidizer delivered to cis-lunar space, either launched from Earth or other inner solar system sources such as the Moon or near Earth asteroids. The effects of uncertainty in the model parameters are evaluated through sensitivity analysis of key parameters including the liquid propellant combination, inert mass fraction of the vehicle, change in velocity margin, and change in payload masses. The outcomes of this research include a description of the transportation elements, the architecture that they enable, and an option for a campaign that meets the objectives of the Evolvable Mars Campaign. This provides a more complete understanding of the propellant requirements, as a function of time, that must be delivered to cis-lunar space. Over the selected sensitivity ranges for the current payload and schedule requirements of the 2016 point of departure of the Evolvable Mars Campaign destination systems, the resulting propellant delivery quantities are between 34 and 61 tonnes per year of hydrogen and oxygen propellant, or between 53 and 76 tonnes per year of methane and oxygen propellant, or between 74 and 92 tonnes per year of hypergolic propellant. These estimates can guide future propellant manufacture and/or delivery architectural analysis.
To document model parameter uncertainties and to automate sensitivity analyses for numerical simulation codes, a natural-language-based method to specify tolerances has been developed. With this new method, uncertainties are expressed in a natural manner, i.e., as one would on an engineering drawing, namely, 5.25 +/- 0.01. This approach is robust and readily adapted to various application domains because it does not rely on parsing the particular structure of input file formats. Instead, tolerances of a standard format are added to existing fields within an input file. As a demonstration of the power of this simple, natural language approach, a Monte Carlo sensitivity analysis is performed for three disparate simulation codes: fluid dynamics (LAURA), radiation (HARA), and ablation (FIAT). Effort required to harness each code for sensitivity analysis was recorded to demonstrate the generality and flexibility of this new approach.
This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.
Nuclear electric propulsion (NEP) is a promising option towards enabling missions to Mars and is an area of interest for NASA’s Space Nuclear Propulsion project. This project is currently investigating technology development opportunities for an NEP vehicle. Physics-based modeling can be used in the early stages of technology development to gain understanding of the effects of technology and performance assumptions on the system performance and mass. This information can then inform technology maturation planning for near term development. By using a Brayton power conversion model and vehicle mass model for megawatt class NEP applications, a sensitivity analysis is performed to assess the impact of individual components’ performance on the power conversion system performance and system mass. A Monte Carlo simulation is also used to determine the variability in system mass based on uncertainty within the modeling parameters. The sensitivity analysis shows a high sensitivity to power conversion inlet temperature, compressor inlet temperature, and recuperator performance. A Monte Carlo analysis suggests a range of -10% to +15% for a 90% confidence interval on system mass based on the uncertainties in the model inputs.
An elastic-poroelastic simulation of ultrasound inspection for lithium-metal batteries is presented and compared to empirical reflection spectra measured during battery cycling. Simulated reflection spectra were obtained using a two-dimensional (2D) plane strain model, comprised of dozens of individual microns-thick layers within a Li-metal pouch cell. The simulated reflection spectra were then compared to ultrasonic reflection spectra measurements taken intermittently during cell cycling. A sensitivity analysis and parameter calibration were performed for the pristine pouch cell simulation prior to cycling, providing a baseline to account for difficult to measure poroelastic material parameters. Then, the reduction in solid Li anode thickness and corresponding growth into a mossy lithium layer was modeled to represent aging conditions. Results from both simulations and empirical inspections show similar trends in through-thickness resonance frequencies due to cell aging.
One important thrust in NASA s space exploration vision is to improve the safety and reliability of future launch vehicles. A quantitative reliability model is an essential technical tool to evaluate launch vehicle reliability and to enhance launch vehicle configuration down selection and detailed designs. A quantitative reliability model that supports NASA's thrust has been developed and implemented in an MS Excel spreadsheet. The model addresses key reliability parameters, and provides for sensitivity analysis of various vehicle designs. This paper presents the specific elements of the model and examples of selected sensitivity analysis results. Reliability input parameters in the model include the following: 1. Main propulsion element failure probability; 2. Propulsion element catastrophic failure fraction (Cf). This is defined as the ratio of probability of uncontained failures over sum of probability of uncontained failures and contained failures); 3. Engine-out design vs. no-engine-out design; 4. Engine with redlines vs. no redlines; 5. Different levels of health management system implementation; 6. Launch Escape System (LES) reliability; and 7. Power level correlation with reliability. The sensitivity results will illustrate the impact of each of the above parameters on several reliability metrics: Loss of Mission (LOM), LOV (Loss of Vehicle) and Loss of Crew (LOC).
A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.
The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.
The present investigation is concerned with a sensitivity analysis of the Decelerated Steep Approach and Landing (DSAL) maneuver to on-board and ground-based navigation system parameters. The Instrument Meteorological Conditions (IMC) DSAL maneuver involves decelerating to zero range rate while tracking the localizer and glideslope. The considered study investigated the performance of the navigation systems using Constant Deceleration Profile (CDP) guidance and a six degrees glideslope trajectory. A closed-loop computer simulation of the UH1H helicopter DSAL system was developed for the sensitivity analysis. Conclusions on system performance parameter sensitivity are discussed.
An acute reduction in oxygen (O2) delivery to a tissue is generally associated with a decrease in phosphocreatine, increases in ADP, NADH/NAD, and inorganic phosphate, increased rates of glycolysis and lactate production, and reduced rates of pyruvate and fatty acid oxidation. However, given the complexity of the human bioenergetic system and its components, it is difficult to determine quantitatively how cellular metabolic processes interact to maintain ATP homeostasis during stress (e.g., hypoxia, ischemia, and exercise). Of special interest is the determination of mechanisms relating tissue oxygenation to observed metabolic responses at the tissue, organ, and whole body levels and the quantification of how changes in tissue O2 availability affect the pathways of ATP synthesis and the metabolites that control these pathways. In this study, we extend a previously developed mathematical model of human bioenergetics to provide a physicochemical framework that permits quantitative understanding of O2 as a metabolic regulator. Specifically, the enhancement permits studying the effects of variations in tissue oxygenation and in parameters controlling the rate of cellular respiration on glycolysis, lactate production, and pyruvate oxidation. The whole body is described as a bioenergetic system consisting of metabolically distinct tissue/organ subsystems that exchange materials with the blood. In order to study the dynamic response of each subsystem to stimuli, we solve the ordinary differential equations describing the temporal evolution of metabolite levels, given the initial concentrations. The solver used in the present study is the packaged code LSODE, as implemented in the NASA Lewis kinetics and sensitivity analysis code, LSENS. A major advantage of LSENS is the efficient procedures supporting systematic sensitivity analysis, which provides the basic methods for studying parameter sensitivities (i.e., changes in model behavior due to parameter variation). Sensitivity analysis establishes relationships between model predictions and problem parameters (i.e., initial concentrations, rate coefficients, etc). It helps determine the effects of uncertainties or changes in these input parameters on the predictions, which ultimately are compared with experimental observations in order to validate the model. Sensitivity analysis can identify parameters that must be determined accurately because of their large effect on the model predictions and parameters that need not be known with great precision because they have little or no effect on the solution. This capability may prove to be important in optimizing the design of experiments, thereby reducing the use of animals. This approach can be applied to study the metabolic effects of reduced oxygen delivery to cardiac muscle due to local myocardial ischemia and the effects of acute hypoxia on brain metabolism. Other important applications of sensitivity analysis include identification of quantitatively relevant pathways and biochemical species within an overall mechanism, when examining the effects of a genetic anomaly or pathological state on energetic system components and whole system behavior.
Ultrareliable fault-tolerant onboard digital systems for spacecraft intended for long mission life exploration of the outer planets are under development. The design of systems involving self-repair and fault-tolerance leads to the companion problem of quantifying and evaluating the survival probability of the system for the mission under consideration and the constraints imposed upon the system. Methods have been developed to (1) model self-repair and fault-tolerant organizations; (2) compute survival probability, mean life, and many other reliability predictive functions with respect to various systems and mission parameters; (3) perform sensitivity analysis of the system with respect to mission parameters; and (4) quantitatively compare competitive fault-tolerant systems. Various measures of comparison are offered. To automate the procedures of reliability mathematical modeling and evaluation, the CARE (computer-aided reliability estimation) program was developed. CARE is an interactive program residing on the UNIVAC 1108 system, which makes the above calculations and facilitates report preparation by providing output in tabular form, graphical 2-dimensional plots, and 3-dimensional projections. The reliability estimation of fault-tolerant organization by means of the CARE program is described.
Area Array microelectronic packages with small pitch and large I/O counts are now widely used in microelectronics packaging. The impact of various package design and materials/process parameters on reliability has been studied through extensive literature review. Reliability of Ceramic Column Grid Array (CCGA) package assemblies has been evaluated using JPL thermal cycle test results (-50(deg)/75(deg)C, -55(deg)/100(deg)C, and -55(deg)/125(deg)C), as well as those reported by other investigators. A sensitivity analysis has been performed using the literature da to study the impact of design parameters and global/local stress conditions on assembly reliability. The applicability of various life-prediction models for CCGA design has been investigated by comparing model's predictions with the experimental thermal cycling data. Finite Element Method (FEM) analysis has been conducted to assess the state of the stress/strain in CCGA assembly under different thermal cycling, and to explain the different failure modes and locations observed in JPL test assemblies.
In the present design methodology for nonlinear systems containing parameter uncertainty, a generalized sensitivity analysis is incorporated which employs parameter space sampling and statistical inference. For the case of a system with j adjustable and k nonadjustable parameters, this methodology (which includes an adaptive random search strategy) is used to determine the combination of j adjustable parameter values which maximize the probability of those performance indices which simultaneously satisfy design criteria in spite of the uncertainty due to k nonadjustable parameters.
Takeoff and landing performance models require low-speed aerodynamic and thrust characteristics that are difficult to predict in the conceptual design stage. Although an empirical approach can be utilized to predict takeoff and landing performance, this approach is inadequate for aircraft incorporating novel technologies and design such as those proposed for regional air mobility aircraft. The focus of this paper is to understand the sensitivity of takeoff and landing distance to aerodynamic, propulsive, and other parameters of interest for regional air mobility class vehicles. The aerodynamic and propulsive characteristics are generated and modified using simplified approximations based on fundamental physics and integrated into the equations of motion to calculate takeoff and landing distances. The most impactful parameters for takeoff and landing were those related to propulsion and the lift curve. Additional impactful parameters for landing included braking coefficient, approach angle, and wing incidence. Lesser impact was observed for the parameters describing the low-speed drag polar.
This paper presents an uncertainty analysis of the Single-Vector Force Balance Calibration System (SVS). This study is focused on the uncertainty involved in setting the independent variables during the calibration experiment. By knowing the uncertainty in the calibration system, the fundamental limits of the calibration accuracy of a particular balance can be determined. A brief description of the SVS mechanical system is provided. A mathematical model is developed to describe the mechanical system elements. A sensitivity analysis of these parameters is carried out through numerical simulations to assess the sensitivity of the total uncertainty to the elemental error sources. These sensitivity coefficients provide valuable information regarding the relative significance of the elemental sources of error. An example calculation of the total uncertainty for a specific balance is provided. Results from this uncertainty analysis are specific to the Single-Vector System, but the approach is broad in nature and therefore applicable to other measurement and calibration systems.
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