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At least 73 records · Page 4

Exact and Approximate Probabilistic Symbolic Execution

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Symbolic Execution↗

An improved digital algorithm for fast amplitude approximations of quadrature pairs

A computationally fast algorithm for approximating the amplitude (A) of a quadrature pair (I,Q) has been discovered. The piecewise linear formula, the unbiased estimate of A=X+1/8y when X or = 3Y and 7/8X + 1/2Y when X or = 3Y applies where X is congruent to the maximum absolute value of (I,Q) and Y is congruent to the minimum absolute value of (I,Q). This algorithm has been proven to be far more accurate then currently used approximations. An immediate application is the wideband digital spectrum analyzer under development for monitoring radio frequency interference at Deep Space Network stations.

Levitt, B. K.↗

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Desideri, J. A.↗

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.

Murphy, P. C.↗

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Bless, Robert R.↗

Approximation concepts for numerical airfoil optimization

An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems.

Vanderplaats, G. N.↗

An approximate factorization solution of the Navier-Stokes equations for transonic flow using body-fitted coordinates with application to NACA 64A010 airfoils

The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.

Copper, G. K.↗

Propagating Qualitative Values Through Quantitative Equations

In most practical problems where traditional numeric simulation is not adequate, one need to reason about a system with both qualitative and quantitative equations. In this paper, we address the problem of propagating qualitative values represented as interval values through quantitative equations. Previous research has produced exponential-time algorithms for approximate solution of the problem. These may not meet the stringent requirements of many real time applications. This paper advances the state of art by producing a linear-time algorithm that can propagate a qualitative value through a class of complex quantitative equations exactly and through arbitrary algebraic expressions approximately. The algorithm was found applicable to Space Shuttle Reaction Control System model.

Kulkarni, Deepak↗

On recent advances and future research directions for computational fluid dynamics

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Baker, A. J.↗

An approximation based global optimization strategy for structural synthesis

A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.

Sepulveda, A. E.↗

Study of the mapping of Navier-Stokes algorithms onto multiple-instruction/multiple-data-stream computers

Implicit approximate-factored algorithms have certain properties that are suitable for parallel processing. A particular computational fluid dynamics (CFD) code, using this algorithm, is mapped onto a multiple-instruction/multiple-data-stream (MIMD) computer architecture. An explanation of this mapping procedure is presented, as well as some of the difficulties encountered when trying to run the code concurrently. Timing results are given for runs on the Ames Research Center's MIMD test facility which consists of two VAX 11/780's with a common MA780 multi-ported memory. Speedups exceeding 1.9 for characteristic CFD runs were indicated by the timing results.

Eberhardt, D. S.↗

Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Schiess, J. R.↗

On Benchmarking Quantum Heuristics

Present an outline of important aspects for benchmarking quantum algorithms, in particular quantum heuristics. Using quantum approximate optimization algorithm as an example, we demonstrate how the choice of cost Hamiltonian, of mixer, and of initial states can affect the performance. We also discuss how realistic aspects of near-term quantum hardware will influence the algorithm performance.

Wang, Zhihui↗

A Prototype Hail Detection Algorithm and Hail Climatology Developed with the Advanced Microwave Sounding Unit (AMSU)

In previous studies published in the open literature, a strong relationship between the occurrence of hail and the microwave brightness temperatures (primarily at 37 and 85 GHz) was documented. These studies were performed with the Nimbus‐7 SMMR, the TRMM Microwave Imager (TMI) and most recently, the Aqua AMSR‐E sensor. This lead to climatologies of hail frequency from TMI and AMSR‐E, however, limitations include geographical domain of the TMI sensor (35 S to 35 N) and the overpass time of the Aqua satellite (130 am/pm local time), both of which reduce an accurate mapping of hail events over the global domain and the full diurnal cycle. Nonetheless, these studies presented exciting, new applications for passive microwave sensors. Since 1998, NOAA and EUMETSAT have been operating the AMSU‐A/B and the MHS on several operational satellites: NOAA‐15 through NOAA‐19; MetOp‐A and ‐B. With multiple satellites in operation since 2000, the AMSU/MHS sensors provide near global coverage every 4 hours, thus, offering a much larger time and temporal sampling than TRMM or AMSR‐E. With similar observation frequencies near 30 and 85 GHz and additionally three at the 183 GHz water vapor band, the potential to detect strong convection associated with severe storms on a more comprehensive time and space scale exists. In this study, we develop a prototype AMSU‐based hail detection algorithm through the use of collocated satellite and surface hail reports over the continental U.S. for a 12‐year period (2000‐2011). Compared with the surface observations, the algorithm detects approximately 40 percent of hail occurrences. The simple threshold algorithm is then used to generate a hail climatology that is based on all available AMSU observations during 2000‐11 that is stratified in several ways, including total hail occurrence by month (March through September), total annual, and over the diurnal cycle. Independent comparisons are made compared to similar data sets derived from other satellite, ground radar and surface reports. The algorithm was also applied to global land measurements for a single year and showed close agreement with other satellite based hail climatologies. Such a product could serve as a prototype for use with a future geostationary based microwave sensor such as NASA's proposed PATH mission.

Ferraro, Ralph↗

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

Holst, Terry L.↗