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An algorithm developed and incorporated into BOPACE for improving the convergence and accuracy of the inelastic stress-strain calculations is discussed. The implementation of separation of strains in the residual-force iterative procedure is defined. The elastic-plastic quantities used in the strain-space algorithm are defined and compared with previous quantities.
The high-performance computing (HPC) landscape is quickly changing to systems where most of the performance comes from specialized chips, specifically graphics processing units (GPUs). Such GPU systems are throughput machines, where efficient use of the GPU often requires code refactoring to expose a few orders of magnitude more fine grain parallelism than was previously used on the CPU. Recent modifications to OVERFLOW, an overset, structured grid, computational fluid dynamics flow solver, written in Fortran will be presented. These modifications include both code modernization efforts and algorithmic changes to enable OVERFLOW to efficiently utilize GPUs. Many of these algorithmic changes would likely also be applicable for other structured grid, stencil-based codes wanting to utilize GPUs. The capabilities that have been ported to run on the GPUs are presented, along with the performance gains of the GPU version relative the CPU version of OVERFLOW.
The high-performance computing (HPC) landscape is quickly changing to systems where most of the performance comes from specialized chips, specifically graphics processing units (GPUs). Such GPU systems are throughput machines, where efficient use of the GPU often requires code refactoring to expose a few orders of magnitude more fine grain parallelism than was previously used on the CPU. Recent modifications to OVERFLOW, an overset, structured grid, computational fluid dynamics flow solver, written in Fortran will be presented. These modifications include both code modernization efforts and algorithmic changes to enable OVERFLOW to efficiently utilize GPUs. Many of these algorithmic changes would likely also be applicable for other structured grid, stencil-based codes wanting to utilize GPUs. The capabilities that have been ported to run on the GPUs are presented, along with the performance gains of the GPU version relative the CPU version of OVERFLOW.
The development and evaluation of a fault-tolerant system for the Redundant Strapdown Inertial Measurement Unit (RSDIMU) being developed and evaluated by the NASA Langley Research Center was continued. The RSDIMU consists of four two-degree-of-freedom gyros and accelerometers mounted on the faces of a semi-octahedron which can be separated into two halves for damage protection. Compensated and uncompensated fault-tolerant system failure decision algorithms were compared. An algorithm to compensate for sensor noise effects in the fault-tolerant system thresholds was evaluated via simulation. The effects of sensor location and magnitude of the vehicle structural modes on system performance were assessed. A threshold generation algorithm, which incorporates noise compensation and filtered parity equation residuals for structural mode compensation, was evaluated. The effects of the fault-tolerant system on navigational accuracy were also considered. A sensor error parametric study was performed in an attempt to improve the soft failure detection capability without obtaining false alarms. Also examined was an FDI system strategy based on the pairwise comparison of sensor measurements. This strategy has the specific advantage of, in many instances, successfully detecting and isolating up to two simultaneously occurring failures.
The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent triangulations and matrix multiplications demand that access to the terms in the coefficient matrices be unbiased. Reliance on virtual memory (paging) operating systems with no special considerations for localized data access is not adequate. Specific data structures must be designed that accommodate the needs of the numerical algorithm yet eliminate unnecessary paging. An implementation of the subspace iteration method using hypermatrix data structures is presented. Use of hypermatrices is shown to provide unbiased and localized data access. The various modifications to the conventional formulation are described and an example problem illustrates the potential benefits of the hypermatrix formulation. Possibilities for adapting hypermatrix data structures to new supercomputer architectures are discussed.
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
A methodology is presented for simulating a docking process involving a rigid body and an unrestrained nonuniform beam in orbit, and the issues that must be faced in the course of producing any such simulation are discussed. An algorithm is produced for the simulation of motions of the unrestrained structure, which necessitates the use of a structural analysis program for the purpose of constructing modal functions. An impulse problem then is solved in order to discover the changes that take place in certain variables in the course of the docking. This information is utilized to determine the initial values of variables used to characterize postdocking motions of the system under consideration, and an algorithm for simulating these motions is created, in which a structural analysis program is again used to produce modal functions. Finally, an extension of the methodology to the simulation of the docking of a rigid body with more complex orbiting structures is discussed.
This paper describes a new hardware volume rendering algorithm for time-varying data. The algorithm uses the Time-Space Partitioning (TSP) tree data structure to identify regions within the data that have spatial or temporal coherence. By using this coherence, the rendering algorithm can improve performance when the volume data is larger than the texture memory capacity by decreasing the amount of textures required. This coherence can also allow improved speed by appropriately rendering flat-shaded polygons instead of textured polygons, and by not rendering transparent regions. To reduce the polygonization overhead caused by the use of the hierarchical data structure, we introduce an optimization method using polygon templates. The paper also introduces new color-based error metrics, which more accurately identify coherent regions compared to the earlier scalar-based metrics. By showing experimental results from runs using different data sets and error metrics, we demonstrate that the new methods give substantial improvements in volume rendering performance.
This report covers work conducted under grant NAG1-1562 for the NASA High Performance Computing and Communications Program (HPCCP) from December 7, 1993, to December 31, 1997. The objective of the research was to develop new multidisciplinary design optimization (MDO) techniques which exploit parallel computing to reduce the computational burden of aircraft MDO. The design of the High-Speed Civil Transport (HSCT) air-craft was selected as a test case to demonstrate the utility of our MDO methods. The three major tasks of this research grant included: development of parallel multipoint approximation methods for the aerodynamic design of the HSCT, use of parallel multipoint approximation methods for structural optimization of the HSCT, mathematical and algorithmic development including support in the integration of parallel computation for items (1) and (2). These tasks have been accomplished with the development of a response surface methodology that incorporates multi-fidelity models. For the aerodynamic design we were able to optimize with up to 20 design variables using hundreds of expensive Euler analyses together with thousands of inexpensive linear theory simulations. We have thereby demonstrated the application of CFD to a large aerodynamic design problem. For the predicting structural weight we were able to combine hundreds of structural optimizations of refined finite element models with thousands of optimizations based on coarse models. Computations have been carried out on the Intel Paragon with up to 128 nodes. The parallel computation allowed us to perform combined aerodynamic-structural optimization using state of the art models of a complex aircraft configurations.
One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.
A method is presented for locating physical damage or change in a structure using experimentally measured mass and stiffness matrices. The approach uses a recently developed algorithm for transforming a state-space realization into a second order structural model with physical displacements as the generalized coordinates. This is accomplished by first rotating a state-space model of the identified structural dynamics into modal coordinates and approximating the mass normalized modal vectors for the output measurement set. Next, the physical mass, damping and stiffness matrices are synthesized directly from the measured modal parameters. This yields experimental mass and stiffness matrices for the structure without the use of a finite element model or a numerical search. The computed mass and stiffness are asymptotically equivalent to a static condensation of the global physical coordinate model. Techniques for solving the inverse connectivity problem are then developed whereby it is possible to assess the stiffness in a region of the structure bounded by several sensors. Applications to both simulated data and experimental data are used to discuss the effectiveness of the approach.
To reduce oscillatory hub loads in forward flight, a structural optimization analysis of a hingeless helicopter rotor has been developed and applied. The aeroelastic analysis of the rotor is based on a finite element method in space and time, and linked with automated optimization algorithms. For the optimization analysis two types of structural representation are used: a generic stiffness-distribution and a single-cell thin-walled beam. For the first type, the design variables are nonstructural mass and its placement, chordwise center of gravity offset from the elastic axis, and stiffness. For the second type, width, height and thickness of spar are used as design variables. For the behavior constraints, frequency placement, autorotational inertia and aeroelastic stability of the blade are included. The required sensitivity derivatives are obtained using a direct analytical approach. An optimum oscillatory hub load shows a 25-77 percent reduction for the generic blade, and 30-50 percent reduction for the box-beam.
The transmission zeros of a large space structure can be computed by the general-purpose algorithm of A. Emami-Naeini and P. Van Dooren (1982). However, careful use of the special form of the equations of motion of structural dynamics leads to a new method that is about twice as fast as theirs when applied to a damped structure, and at least 60 times as fast for an undamped one.
Global Precipitation Mission (GPM)retrieval algorithm validation requires datasets characterizing the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (FOV;<10 km). Collection of this data provides a means to assess retrieval errors related to beam filling and algorithm PSD assumptions. Hence, GPM Ground Validation is developing a deployable network of precipitation gauges and disdrometers to provide fine-scale measurements of PSD and precipitation accumulation variability. These observations will be combined with dual-frequency, polarimetric, and profiling radar data in a bootstrapping fashion to extend validated PSD measurements to a large coverage domain. Accordingly, a total of 24 Parsivel disdrometers(PD), 5 3rd-generation 2D Video Disdrometers (2DVD), 70 tipping bucket rain gauges (TBRG),9 weighing gauges, 7 Hot-Plate precipitation sensors (HP), and 3 Micro Rain Radars (MRR) have been procured. In liquid precipitation the suite of TBRG, PD and 2DVD instruments will quantify a broad spectrum of rain rate and PSD variability at sub-kilometer scales. In the envisioned network configuration 5 2DVDs will act as reference points for 16 collocated PD and TBRG measurements. We find that PD measurements provide similar measures of the rain PSD as observed with collocated 2DVDs (e.g., D0, Nw) for rain rates less than 15 mm/hr. For heavier rain rates we will rely on 2DVDs for PSD information. For snowfall we will combine point-redundant observations of SWER distributed over three or more locations within a FOV. Each location will contain at least one fenced weighing gauge, one HP, two PDs, and a 2DVD. MRRs will also be located at each site to extend the measurement to the column. By collecting SWER measurements using different instrument types that employ different measurement techniques our objective is to separate measurement uncertainty from natural variability in SWER and PSD. As demonstrated using C3VP polarimetric radar, gauge, and 2DVD/PD datasets these measurements can be combined to bootstrap an area wide SWER estimate via constrained modification of density-diameter and radar reflectivity-snowfall relationships. These data will be combined with snowpack, airborne microphysics, radar, radiometer, and tropospheric sounding data to refine GPM snowfall retrievals. The gauge and disdrometer instruments are being developed to operate autonomously when necessary using solar power and wireless communications. These systems will be deployed in numerous field campaigns through 2016. Planned deployment of these systems include field campaigns in Finland (2010), Oklahoma (2011), Canada (2012) and North Carolina (2013). GPM will also deploy 20 pairs of TBRGs within a 25 km2 region along the Virginia coast under NASA NPOL radar coverage in order to quantify errors in point-area rainfall measurements.
This paper considers the pre and post buckling behavior of general structures exposed to high temperature fields for long durations wherein creep effects become significant. The solution to this problem is made possible through the use of closed upper bounding constraint surfaces which enable the development of a new time stepping algorithm. This permits the stable and efficient solution of structural problems which exhibit indefinite tangent properties. Due to the manner of constraining/bounding successive iterates, the algorithm developed herein is largely self adaptive, inherently stable, sufficiently flexible to handle geometric material and boundary induced nonlinearity, and can be incorporated into either finite element or difference simulations. To illustrate the capability of the procedure, as well as, the physics of creep induced pre and post buckling behavior, the results of several numerical experiments are included.
A recurrent multilayer perceptron network topology is used in the identification of nonlinear dynamic systems from only the input/output measurements. The identification is performed in the discrete time domain, with the learning algorithm being a modified form of the back propagation (BP) rule. The recurrent dynamic network (RDN) developed is applied for the total core reactivity prediction of a spacecraft reactor from only neutronic power level measurements. Results indicate that the RDN can reproduce the nonlinear response of the reactor while keeping the number of nodes roughly equal to the relative order of the system. As accuracy requirements are increased, the number of required nodes also increases, however, the order of the RDN necessary to obtain such results is still in the same order of magnitude as the order of the mathematical model of the system. It is believed that use of the recurrent MLP structure with a variety of different learning algorithms may prove useful in utilizing artificial neural networks for recognition, classification, and prediction of dynamic systems.
Logic programming allows structuring code in terms of predicates or relations, rather than functions. Although logic programming languages present advantages in terms of declarativeness and conciseness, the introduction of static types has not become part of most popular logic programming languages, increasing the difficulty of testing and debugging of logic programming code. This paper demonstrates how to implement logic programming in Haskell, thus empowering logic programs with types, and functional programs with relations or predicates. We do so by combining three ideas. First, we use extensible types to generalize a type by a parameter type function. Second, we use a sum type as an argument to introduce optional variables in extensible types. Third, we implement a unification algorithm capable of working with any data structure, provided that certain operations are implemented for the given type. We demonstrate our proposal via a series of increasingly complex examples inspired by educational texts in logic programming, and leverage the host language's features to make new notation convenient for users, showing that the proposed approach is not just technically possible but also practical.
Recently there has emerged a new class of sensors, called spatial filters, for structures which respond over a significant gauge length. Examples include piezoelectric laminate PVDF film, modal domain optical fiber sensors, and holographic sensors. These sensors have a unique capability in that they can be fabricated to locally alter their sensitivity to the measurand. In this paper we discuss how these sensors can be used for the implementation of control algorithms for the suppression of acoustic radiation from flexible structures. Based on this relationship between the total power radiated to the far field to the modal velocities of the structure, we show how the sensor placement to optimize the control algorithm to suppress the radiated power.