Requirements decomposition analysis
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Requirements decomposition analysis
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flowdown↗
SNoGloDe: A Structured Nonlinear Global Decomposition Solver
Large-scale optimization problems often require decomposition strategies and customized algorithms to achieve optimal solutions within a reasonable time. Building on the work of Cao and Zavala (2019) for solving nonlinear two-stage stochastic programs to global optimality, we implement and extend their approach. We generalize to optimization problems reformulated with a block-angular constraint structure (e.g., temporal decomposition). Our framework, written in Python using Pyomo, is highly customizable and enables parallel execution of the decomposition. SNoGloDe allows tailored branching strategies, lower bounding problems, and candidate generators to leverage problem-specific knowledge. To demonstrate effectiveness, we compare SNoGloDe’s performance with Gurobi on a temporally decomposed produced water case study.
algorithms↗
Reliability-Aware Requirements Development for Autonomy Software
Autonomy is the ability of a system to make decisions and take actions in the presence of uncertainty. Validating autonomy, therefore, is a matter of validating that the system makes intelligent decisions even when there might be discrepancies between the observed and the expected state of the world as well as when the possible outcome of each of the possible courses of action is uncertain. During the requirements engineering phase, the functions, including those that are required to be autonomous and their expected behavior are specified. However, in the case of autonomous software system, it is challenging to specify all possible scenarios that the software may encounter. Additionally, since autonomous behaviors cannot always be fully predetermined, it is difficult to reason about their completeness and correctness. While these challenges are also faced with non-autonomous system, they are more prevalent for autonomous system due to their complexity and emergent behavior. Our efforts have been three-fold. On one hand, we have developed a goal-based method for requirements decomposition. We have embedded this approach into a higher-level systems engineering framework and then developed methods for decision and reliability analysis within this framework. And finally, we use simulation analysis to validate the more theoretical methods and provide a feedback mechanism. The decision analysis approach (DA) helps in identifying and mitigating the run-time risks, by bringing to the forefront the uncertainties, decisions, interactions, and other factors that may cause autonomous software to make erroneous decisions. The DA framework is used to quantify, for each decision that the software can make, failure risk due to uncertainties. The information about the key decisions and circumstances that can cause autonomous system to make incorrect decisions are used to generate test scenarios to be run in a simulator to ensure that the system can handle error-prone circumstances. The results or outcomes from decisions, based on the simulated scenarios, can then be leveraged to further gain insight of the assured system. We combine a goal-based approach with simulation analysis to facilitate requirements development for autonomous systems and further provide a method for run-time systems level reliability considerations during the autonomous software development process. The DA and the reliability analysis methods provide a formalism for the consideration of uncertainty in the run time decision-making process for autonomous software. This formalism considers the uncertainty involved in the outcome of different courses of action, in terms of performance and cost, as well as a method to consider the system level reliability implications. System level reliability considerations for autonomous software decision making contribute to the satisfaction of the system level goals over the lifecycle of a given mission. We demonstrate our approach using a hypothetical rover path planning example. The requirements for our rover simulator are based on existing literature about Mars rovers and lessons learned from real world observations at JPL. The specifics of the autonomy design for the Mars rovers, that have not been previously cleared for external release, are not used for our demonstrations.
Lindvall, Mikael↗
An efficient design sensitivity analysis of eigenvectors
Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.
Ting, T.↗
Drag and Lift Forces Between a Rotating Conductive Sphere and a Cylindrical Magnet
Modeling the interaction between a non-uniform magnetic field and a rotating conductive object allows study of the drag force which is used in applications such as eddy current braking and linear induction motors as well as the transition to a repulsive force that is the basis for magnetic levitation systems. Here, we study the interaction between a non-uniform field generated by a cylindrical magnet and a rotating conductive sphere. Each eddy current in the sphere generates a magnetic field which in turn generates another eddy current, eventually feeding back on itself. A two step mathematics process is developed to find a closed form solution in terms of only two eddy currents. However, the complete solution requires decomposition of the magnetic field into a summation of spherical harmonics, making it more suitable for a graduate level electromagnetism lecture or lab. Finally, the forces associated with these currents are calculated and then verified experimentally.
Nurge, Mark A.↗
Human Systems Integration: Requirements and Functional Decomposition
This deliverable was intended as an input to the Access 5 Policy and Simulation Integrated Product Teams. This document contains high-level pilot functionality for operations in the National Airspace System above FL430. Based on the derived pilot functions the associated pilot information and control requirements are given.
Berson, Barry↗
A new algorithm for the integration of exponential and logarithmic functions
An algorithm for symbolic integration of functions built up from the rational functions by repeatedly applying either the exponential or logarithm functions is discussed. This algorithm does not require polynomial factorization nor partial fraction decomposition and requires solutions of linear systems with only a small number of unknowns. It is proven that if this algorithm is applied to rational functions over the integers, a computing time bound for the algorithm can be obtained which is a polynomial in a bound on the integer length of the coefficients, and in the degrees of the numerator and denominator of the rational function involved.
Rothstein, M.↗
Multi-Scale Modeling for Plasma-Enhanced Ammonia Decomposition over Carbides and Nitrides
Ammonia is a carbon-free hydrogen carrier, but its decomposition typically requires high temperatures over costly Ru-based catalysts due to the large barrier for N≡N bond formation. We develop a multiscale framework combining density functional theory, zero-dimensional plasma kinetics, and microkinetic modeling to elucidate how non-thermal plasma (NTP) enables low-temperature NH 3 decomposition over Co-based carbides and nitrides, benchmarked against Ru and Co. Under thermal conditions, all catalysts are limited by N≡N bond formation, with Co 3 C(001) most active owing to its negatively charged surface, strong N* binding, and low activation barriers of N≡N bond formation. Plasma-induced vibrational excitation of NH 3 and its reactive radicals promotes a radical-driven •NH 2 –N* coupling pathway that dominates on Co 3 C(001) and Co 3 N(001), shifting the rate-limiting step to NH 3 (v1) dissociation, increasing turnover frequencies by up to 6 orders of magnitude, and reducing the temperature needed to reach a turnover frequency of 5 s –1 from >680 °C (Ru and Co under thermal condition) to 267 °C (Co 3 C) and 415 °C (Co 3 N). These results identify Co-based carbides and nitrides as promising plasma-active catalysts for energy-efficient hydrogen production from ammonia.
ammonia decomposition↗
New evidence favoring multilevel decomposition and optimization
The issue of the utility of multilevel decomposition and optimization remains controversial. To date, only the structural optimization community has actively developed and promoted multilevel optimization techniques. However, even this community acknowledges that multilevel optimization is ideally suited for a rather limited set of problems. It is warned that decomposition typically requires eliminating local variables by using global variables and that this in turn causes ill-conditioning of the multilevel optimization by adding equality constraints. The purpose is to suggest a new multilevel optimization technique. This technique uses behavior variables, in addition to design variables and constraints, to decompose the problem. The new technique removes the need for equality constraints, simplifies the decomposition of the design problem, simplifies the programming task, and improves the convergence speed of multilevel optimization compared to conventional optimization.
Padula, Sharon L.↗
Integrated design and manufacturing for the high speed civil transport
In June 1992, Georgia Tech's School of Aerospace Engineering was awarded a NASA University Space Research Association (USRA) Advanced Design Program (ADP) to address 'Integrated Design and Manufacturing for the High Speed Civil Transport (HSCT)' in its graduate aerospace systems design courses. This report summarizes the results of the five courses incorporated into the Georgia Tech's USRA ADP program. It covers AE8113: Introduction to Concurrent Engineering, AE4360: Introduction to CAE/CAD, AE4353: Design for Life Cycle Cost, AE6351: Aerospace Systems Design One, and AE6352: Aerospace Systems Design Two. AE8113: Introduction to Concurrent Engineering was an introductory course addressing the basic principles of concurrent engineering (CE) or integrated product development (IPD). The design of a total system was not the objective of this course. The goal was to understand and define the 'up-front' customer requirements, their decomposition, and determine the value objectives for a complex product, such as the high speed civil transport (HSCT). A generic CE methodology developed at Georgia Tech was used for this purpose. AE4353: Design for Life Cycle Cost addressed the basic economic issues for an HSCT using a robust design technique, Taguchi's parameter design optimization method (PDOM). An HSCT economic sensitivity assessment was conducted using a Taguchi PDOM approach to address the robustness of the basic HSCT design. AE4360: Introduction to CAE/CAD permitted students to develop and utilize CAE/CAD/CAM knowledge and skills using CATIA and CADAM as the basic geometric tools. AE6351: Aerospace Systems Design One focused on the conceptual design refinement of a baseline HSCT configuration as defined by Boeing, Douglas, and NASA in their system studies. It required the use of NASA's synthesis codes FLOPS and ACSYNT. A criterion called the productivity index (P.I.) was used to evaluate disciplinary sensitivities and provide refinements of the baseline HSCT configuration. AE6352: Aerospace Systems Design Two was a continuation of Aerospace Systems Design One in which wing concepts were researched and analyzed in more detail. FLOPS and ACSYNT were again used at the system level while other off-the-shelf computer codes were used for more detailed wing disciplinary analysis and optimization. The culmination of all efforts and submission of this report conclude the first year's efforts of Georgia Tech's NASA USRA ADP. It will hopefully provide the foundation for next year's efforts concerning continuous improvement of integrated design and manufacturing for the HSCT.
Source record↗
An analysis of bipropellant neutralization for spacecraft refueling operations
Refueling of satellites on orbit with storable propellants will involve venting part or all of the pressurant gas from the propellant tanks. This gas will be saturated with propellant vapor, and it may also have significant amounts of entrained fine droplets of propellant. The two most commonly used bipropellants, monomethyl hydrazine (MMH) and nitrogen tetroxide (N2O4), are highly reactive and toxic. Various possible ways of neutralizing the vented propellants are examined. The amount of propellant vented in a typical refueling operation is shown to be in the range of 0.2 to 5% of the tank capacity. Four potential neutralization schemes are examined: chemical decomposition, chemical reaction, condensation and adsorption. Chemical decomposition to essentially inert materials is thermodynamically feasible for both MMH and N2O4. It would be the simplest and easiest neutralization method to implement. Chemical decomposition would require more complex control. Condensation would require a refrigeration system and a very efficent phase separator. Adsorption is likely to be much heavier. A preliminary assessment of the four neutralization shemes is presented, along with suggested research and development plans.
Kauffman, David↗
Optimization-based design of control systems for flexible structures
The purpose of this presentation is to show that it is possible to use nonsmooth optimization algorithms to design both closed-loop finite dimensional compensators and open-loop optimal controls for flexible structures modeled by partial differential equations. An important feature of our approach is that it does not require modal decomposition and hence is immune to instabilities caused by spillover effects. Furthermore, it can be used to design control systems for structures that are modeled by mixed systems of coupled ordinary and partial differential equations.
Polak, E.↗
Non-seasonal Gravitational Effects of Interannual Meteorological Oscillations in Atmosphere and Ocean
Via mass transport, the interannual meteorological oscillations (ENSO, NAO, etc.) produce slight variations in the global gravitational field, which can be observed by satellite laser ranging (SLR) and anticipated space missions such as GRACE. The meteorological oscillation modes are identified using empirical orthogonal function and principal component decomposition using de-seasoned surface fields produced from the 40-years of NCEP reanalysis. This decompositional analysis requires an accounting for issues associated with area-weighting and non-zero mean. The atmospheric contributions to gravitational variation, mode by mode and in combinations, are then computed via regional integration. To address the corresponding oceanic contributions, we examine the output of the numerical POCM ocean circulation model (1992-1998) in two ways: ocean bottom pressure field and ocean surface topography minus steric effect. The resulting lowest-degree Stokes coefficients for both NCEP reanalysis and POCM are then compared with space geodetic SLR observations, to identify the importance of each meteorological oscillations in gravitational variation signals.
Chao, Benjamin F.↗
Compositional Specification of Software Architecture
This paper describes our experience using parameterized algebraic specifications to model properties of software architectures. The goal is to model the decomposition of requirements independent of the style used to implement the architecture. We begin by providing an overview of the role of architecture specification in software development. We then describe how architecture specifications are build up from component and connector specifications and give an overview of insights gained from a case study used to validate the method.
Penix, John↗
The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise
The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.
Dunn, M. H.↗
Efficient Streaming Dynamic Mode Decomposition
We propose a reformulation of the streaming dynamic mode decomposition method that requires maintaining a single orthonormal basis, thereby reducing computational redundancy. The proposed efficient streaming dynamic mode decomposition method results in a constant-factor reduction in computational complexity and memory storage requirements. Numerical experiments on representative canonical dynamical systems show that the enhanced computational efficiency does not compromise the accuracy of the proposed method.
97 MATHEMATICS AND COMPUTING↗
An intelligent decomposition approach for efficient design of non-hierarchic systems
The design process associated with large engineering systems requires an initial decomposition of the complex systems into subsystem modules which are coupled through transference of output data. The implementation of such a decomposition approach assumes the ability exists to determine what subsystems and interactions exist and what order of execution will be imposed during the analysis process. Unfortunately, this is quite often an extremely complex task which may be beyond human ability to efficiently achieve. Further, in optimizing such a coupled system, it is essential to be able to determine which interactions figure prominently enough to significantly affect the accuracy of the optimal solution. The ability to determine 'weak' versus 'strong' coupling strengths would aid the designer in deciding which couplings could be permanently removed from consideration or which could be temporarily suspended so as to achieve computational savings with minimal loss in solution accuracy. An approach that uses normalized sensitivities to quantify coupling strengths is presented. The approach is applied to a coupled system composed of analysis equations for verification purposes.
Bloebaum, Christina L.↗