On some stability aspects of bandlimited signal models.
Band limited signal model stability from sensitivity approach using mathematical and engineering methods
Yao, K.↗
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Using MathCad to Evaluate Exact Integral Formulations of Spacecraft Orbital Heats for Primitive Surfaces at Any Orientation
With the advent of high speed computing Monte Carlo ray tracing techniques has become the preferred method for evaluating spacecraft orbital heats. Monte Carlo has its greatest advantage where there are many interacting surfaces. However Monte Carlo programs are specialized programs that suffer from some inaccuracy, long calculation times and high purchase cost. A general orbital heating integral is presented here that is accurate, fast and runs on MathCad, a generally available engineering mathematics program. The integral is easy to read, understand and alter. The integral can be applied to unshaded primitive surfaces at any orientation. The method is limited to direct heating calculations. This integral formulation can be used for quick orbit evaluations and spot checking Monte Carlo results.
Pinckney, John↗
Polar Plate Theory for Orthogonal Anisotropy
Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to-weight and stiffness-to-weight ratios. However, because of the anisotropic behavior of composites, determining the response on a macroscopic scale is challenging. This is particularly evident in the evaluation of the governing differential equations of a circular disk with the fibers of the lamina oriented with rectilinear orthogonality. This includes any situation involving a composite plate of circular geometry in which out-of-plane displacements due to load are desired, such as fastener pull through loading of a composite plate. Current analysis techniques use numerical methods with rectilinear coordinate systems to solve problems with circular geometry. These analyses over predict plate stiffness by 20% and underpredict failure by 70%. Consequently, there is a need to transform classical composite plate theory to a polar coordinate system. In order to better analyze structures with circular geometries the classical composite plate equations are transformed into the plate equations for a rectilinearly anisotropic composite in polar coordinates. A composite plate is typically a laminate of fibers in rectilinear directions. Subsequent to the lay-tip the necessary geometry is cut out of a rectangular plate. In a similar manner, the derivation of the plate equation starts with the fundamental definitions of strain, displacement and curvature and incorporates the material property angular dependence into the equilibrium equations for a differential polar element. In the transformed state, the stiffness coefficients are no longer constant, adding to the complexity of the governing differential equations. This paper discusses the new derivation and evaluation of the plate equations for a circular composite disk with orthogonal rectilinear anisotropy. The resultant new three partial differential equations, which describe the circular anisotropic plate, can be used to evaluate out-of-plane displacements for given load conditions in design of composite Structures. Without the formation of these unique plate equations, design of such structures is not a precise engineering accomplishment due to the lack of precise design tools. Such structures are over designed to compensate and costly tests need to be performed after production to validate safety. Though impossible to present the mathematical solution within the limits of this paper, the application of the newly derived plate equation in its orthotropic form for a balanced symmetric laminate compared favorably with test results and surpassed the results of standard numerical methods. Within the limitations of the problem foundation the predictive model provides a mechanism for establishing out-of-plane deflection levels for a circular composite plate. Future work in this area should include incorporating the circular composite plate equations in Finite Element Models. The new anisotropic polar plate equations call be utilized as a design tool so that the design more accurately meets the requirements, thus taking full advantage of the weight savings of composites. These accomplishments have not previously been presented to the engineering community nor ever proposed to the IAF. Should the proposed paper be accepted for presentation, attendance is assured.
Bailey, Michelle D.↗
An Application of Retroduction to Analyzing and Testing the Backing off of Nuts and Bolts During Dynamic Loading
The method of retroduction, adapted from the doctoral thesis of Dr. A. Croce, relies on a process of dialectic questioning that begins with the information sought, proceeds to Given items (either in the form of dimensions or limits of research). and to Known mathematical forms of analysis in design or to principles of study in research. Finally, analysis and synthesis are used to abstract the dielectic questions and to arrive at the information desired. This method is used to solve the engineering design problem of a beam and to determine why bolts and nuts vibrate apart. Both mathematical analysis and dialectic logical analysis are utilized. Results are provided of tests conducted to check the retroductive study of why and how nuts back off.
Kerley, James J.↗
Overcoming the Bellman's curse of dimensionality in large optimization problems
Decomposition of large problems into a hierarchic pyramid of subproblems was proposed in the literature as a means for optimization of engineering systems too large for all-in-one optimization. This decomposition was established heuristically. The dynamic programming (DP) method due to Bellman was augmented with an optimum sensitivity analysis that provides a mathematical basis for the above decomposition, and overcomes the curse of dimensionality that limited the original formulation of DP. Numerical examples are cited.
Sobieszczanski-Sobieski, Jaroslaw↗
MSFC-TVC | TB-03: Derivation of Thrust Vector Control (TVC) Actuator-Force / Gimbal-Torque Transformation Matrix
Thrust vector control (TVC) systems for rocket engine propulsion traditionally use a simple linear relationship to convert between actuator forces and torques about the engine gimbal’s center-of-rotation (COR). As shown in Equation (1), the torque about the gimbal COR is proportional to the applied actuator force and the TVC moment arm (MA)—the perpendicular distance between the TVC actuator’s line-of-action (LOA) and the engine gimbal’s COR. While this fundamental relationship remains valid and accurate in a two-dimensional (2D), one-degree-of-freedom (1-DOF) context—particularly in its non-linear formulation as described in the ER63 Technical Bulletin TB-02 (Derivation of Thrust Vector Control (TVC) Engine-Gimbal / Actuator Moment-Arm Geometry)—it becomes limited when extended to three-dimensional (3D), two-degree-of-freedom (2-DOF) analyses. In 3D, out-of-plane angular displacements can arise, causing the gimbaled engine plane-of-motion to become non-coplanar with the respective actuator plane-of-motion. Such misalignments occur due to the rod-end (RE) and/or tail-stock (TE) mounting geometry of individual TVC actuators. These geometric complexities lead to inaccuracies in calculating engine torques and corresponding actuator forces if only the traditional TVC MA relationship is employed. For higher gimbal angular displacements (e.g., greater than 5 degrees), these inaccuracies become more pronounced, necessitating a more robust mathematical framework. This document presents a comprehensive 3D (2-DOF) derivation of a transformation matrix that accurately converts between gimbaled engine torques and TVC actuator forces. By incorporating the necessary geometric and rotational considerations, this new approach corrects the limitations of the traditional TVC MA method. Subsequent sections compare the newly formulated approach to the traditional method, demonstrating its enhanced accuracy and reliability for a broad range of gimbaled engine conditions.
Thrust Vector Control↗
Uncertainty and Intelligence in Computational Stochastic Mechanics
Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.
Ayyub, Bilal M.↗
Automated Reuse of Scientific Subroutine Libraries through Deductive Synthesis
Systematic software construction offers the potential of elevating software engineering from an art-form to an engineering discipline. The desired result is more predictable software development leading to better quality and more maintainable software. However, the overhead costs associated with the formalisms, mathematics, and methods of systematic software construction have largely precluded their adoption in real-world software development. In fact, many mainstream software development organizations, such as Microsoft, still maintain a predominantly oral culture for software development projects; which is far removed from a formalism-based culture for software development. An exception is the limited domain of safety-critical software, where the high-assuiance inherent in systematic software construction justifies the additional cost. We believe that systematic software construction will only be adopted by mainstream software development organization when the overhead costs have been greatly reduced. Two approaches to cost mitigation are reuse (amortizing costs over many applications) and automation. For the last four years, NASA Ames has funded the Amphion project, whose objective is to automate software reuse through techniques from systematic software construction. In particular, deductive program synthesis (i.e., program extraction from proofs) is used to derive a composition of software components (e.g., subroutines) that correctly implements a specification. The construction of reuse libraries of software components is the standard software engineering solution for improving software development productivity and quality.
Lowry, Michael R.↗
Users manual for Streamtube Curvature Analysis: Analytical method for predicting the pressure distribution about a nacelle at transonic speeds, volume 1
The computer program, Streamtube Curvature Analysis, is described for the engineering user and for the programmer. The user oriented documentation includes a description of the mathematical governing equations, their use in the solution, and the method of solution. The general logical flow of the program is outlined and detailed instructions for program usage and operation are explained. General procedures for program use and the program capabilities and limitations are described. From the standpoint of the grammar, the overlay structure of the program is described. The various storage tables are defined and their uses explained. The input and output are discussed in detail. The program listing includes numerous comments so that the logical flow within the program is easily followed. A test case showing input data and output format is included as well as an error printout description.
Keith, J. S.↗
Design and Experimental Verification of Deployable/Inflatable Ultra-Lightweight Structures
Because launch cost of a space structural system is often proportional to the launch volume and mass and there is no significant gravity in space, NASA's space exploration programs and various science missions have stimulated extensive use of ultra-lightweight deployable/inflatable structures. These structures are named here as Highly Flexible Structures (HFSs) because they are designed to undergo large displacements, rotations, and/or buckling without plastic deformation under normal operation conditions. Except recent applications to space structural systems, HFSs have been used in many mechanical systems, civil structures, aerospace vehicles, home appliances, and medical devices to satisfy space limitations, provide special mechanisms, and/or reduce structural weight. The extensive use of HFSs in today's structural engineering reveals the need of a design and analysis software and a database system with design guidelines for practicing engineers to perform computer-aided design and rapid prototyping of HFSs. Also to prepare engineering students for future structural engineering requires a new and easy-to- understand method of presenting the complex mathematics of the modeling and analysis of HFSs. However, because of the high flexibility of HFSs, many unique challenging problems in the modeling, design and analysis of HFSs need to be studied. The current state of research on HFSs needs advances in the following areas: (1) modeling of large rotations using appropriate strain measures, (2) modeling of cross-section warpings of structures, (3) how to account for both large rotations and cross- section warpings in 2D (two-dimensional) and 1D structural theories, (4) modeling of thickness thinning of membranes due to inflation pressure, pretension, and temperature change, (5) prediction of inflated shapes and wrinkles of inflatable structures, (6) development of efficient numerical methods for nonlinear static and dynamic analyses, and (7) filling the gap between geometrically exact elastic analysis and elastoplastic analysis. The objectives of this research project were: (1) to study the modeling, design, and analysis of deployable/inflatable ultra-lightweight structures, (2) to perform numerical and experimental studies on the static and dynamic characteristics and deployability of HFSs, (3) to derive guidelines for designing HFSs, (4) to develop a MATLAB toolbox for the design, analysis, and dynamic animation of HFSs, and (5) to perform experiments and establish an adequate database of post-buckling characteristics of HFSs.
Pai, P. Frank↗
A mathematical model of the maximum power density attainable in an alkaline hydrogen/oxygen fuel cell
A mathematical model of a hydrogen/oxygen alkaline fuel cell is presented that can be used to predict the polarization behavior under various power loads. The major limitations to achieving high power densities are indicated and methods to increase the maximum attainable power density are suggested. The alkaline fuel cell model describes the phenomena occurring in the solid, liquid, and gaseous phases of the anode, separator, and cathode regions based on porous electrode theory applied to three phases. Fundamental equations of chemical engineering that describe conservation of mass and charge, species transport, and kinetic phenomena are used to develop the model by treating all phases as a homogeneous continuum.
Kimble, Michael C.↗
Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints
The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples.
Patnaik, Surya↗
Space Shuttle Main Engine performance analysis
For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.
Santi, L. Michael↗
Computer method for design of acoustic liners for turbofan engines
A design package is presented for the specification of acoustic liners for turbofans. An estimate of the noise generation was made based on modifications of existing noise correlations, for which the inputs are basic fan aerodynamic design variables. The method does not predict multiple pure tones. A target attenuation spectrum was calculated which was the difference between the estimated generation spectrum and a flat annoyance-weighted goal attenuated spectrum. The target spectrum was combined with a knowledge of acoustic liner performance as a function of the liner design variables to specify the acoustic design. The liner design method at present is limited to annular duct configurations. The detailed structure of the liner was specified by combining the required impedance (which is a result of the previous step) with a mathematical model relating impedance to the detailed structure. The design procedure was developed for a liner constructed of perforated sheet placed over honeycomb backing cavities. A sample calculation was carried through in order to demonstrate the design procedure, and experimental results presented show good agreement with the calculated results of the method.
Minner, G. L.↗
Improve Data Mining and Knowledge Discovery Through the Use of MatLab
Data mining is widely used to mine business, engineering, and scientific data. Data mining uses pattern based queries, searches, or other analyses of one or more electronic databases/datasets in order to discover or locate a predictive pattern or anomaly indicative of system failure, criminal or terrorist activity, etc. There are various algorithms, techniques and methods used to mine data; including neural networks, genetic algorithms, decision trees, nearest neighbor method, rule induction association analysis, slice and dice, segmentation, and clustering. These algorithms, techniques and methods used to detect patterns in a dataset, have been used in the development of numerous open source and commercially available products and technology for data mining. Data mining is best realized when latent information in a large quantity of data stored is discovered. No one technique solves all data mining problems; challenges are to select algorithms or methods appropriate to strengthen data/text mining and trending within given datasets. In recent years, throughout industry, academia and government agencies, thousands of data systems have been designed and tailored to serve specific engineering and business needs. Many of these systems use databases with relational algebra and structured query language to categorize and retrieve data. In these systems, data analyses are limited and require prior explicit knowledge of metadata and database relations; lacking exploratory data mining and discoveries of latent information. This presentation introduces MatLab(R) (MATrix LABoratory), an engineering and scientific data analyses tool to perform data mining. MatLab was originally intended to perform purely numerical calculations (a glorified calculator). Now, in addition to having hundreds of mathematical functions, it is a programming language with hundreds built in standard functions and numerous available toolboxes. MatLab's ease of data processing, visualization and its enormous availability of built in functionalities and toolboxes make it suitable to perform numerical computations and simulations as well as a data mining tool. Engineers and scientists can take advantage of the readily available functions/toolboxes to gain wider insight in their perspective data mining experiments.
Shaykhian, Gholam Ali↗
Improve Data Mining and Knowledge Discovery through the use of MatLab
Data mining is widely used to mine business, engineering, and scientific data. Data mining uses pattern based queries, searches, or other analyses of one or more electronic databases/datasets in order to discover or locate a predictive pattern or anomaly indicative of system failure, criminal or terrorist activity, etc. There are various algorithms, techniques and methods used to mine data; including neural networks, genetic algorithms, decision trees, nearest neighbor method, rule induction association analysis, slice and dice, segmentation, and clustering. These algorithms, techniques and methods used to detect patterns in a dataset, have been used in the development of numerous open source and commercially available products and technology for data mining. Data mining is best realized when latent information in a large quantity of data stored is discovered. No one technique solves all data mining problems; challenges are to select algorithms or methods appropriate to strengthen data/text mining and trending within given datasets. In recent years, throughout industry, academia and government agencies, thousands of data systems have been designed and tailored to serve specific engineering and business needs. Many of these systems use databases with relational algebra and structured query language to categorize and retrieve data. In these systems, data analyses are limited and require prior explicit knowledge of metadata and database relations; lacking exploratory data mining and discoveries of latent information. This presentation introduces MatLab(TradeMark)(MATrix LABoratory), an engineering and scientific data analyses tool to perform data mining. MatLab was originally intended to perform purely numerical calculations (a glorified calculator). Now, in addition to having hundreds of mathematical functions, it is a programming language with hundreds built in standard functions and numerous available toolboxes. MatLab's ease of data processing, visualization and its enormous availability of built in functionalities and toolboxes make it suitable to perform numerical computations and simulations as well as a data mining tool. Engineers and scientists can take advantage of the readily available functions/toolboxes to gain wider insight in their perspective data mining experiments.
Shaykahian, Gholan Ali↗
Advances in space radiation shielding codes
Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary concept to the final design. For the last few decades, we have pursued deterministic solutions of the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard Finite Element Method (FEM) geometry common to engineering design methods. A single ray trace in such geometry requires 14 milliseconds and limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given.
manned↗
Structural Reliability Analysis and Optimization: Use of Approximations
This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.
Grandhi, Ramana V.↗