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NASA NTRS2012

Wavespace-Based Coherent Deconvolution

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Bahr, Christopher J.↗

NASA NTRS2012

Analysis of Phoenix Anomalies and IV and V Findings Applied to the GRAIL Mission

Analysis of patterns in IV&V findings and their correlation with post-launch anomalies allowed GRAIL to make more efficient use of IV&V services . Fewer issues. . Higher fix rate. . Better communication. . Increased volume of potential issues vetted, at lower cost. . Hard to make predictions of post-launch performance based on IV&V findings . Phoenix made sound fix/use as-is decisions . Things that were fixed eliminated some problems, but hard to quantify. . Broad predictive success in one area, but inverse relationship in others.

Gravity Recovery and Interior Laboratory (GRAIL)↗

NASA NTRS1987

Exact finite element method analysis of viscoelastic tapered structures to transient loads

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Spyrakos, Constantine Chris↗

NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗

NASA NTRS2006

Stochastic Evolutionary Algorithms for Planning Robot Paths

A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.

Fink, Wolfgang↗

NASA NTRS1995

Combustion and structure formation in SHS processes under microgravity conditions: SHS plans for microgravity experiments

This paper outlines ISMAN suggestions for the joint NASA-RSA project 'Combustion and Structure formation in SHS Processes under Microgravity Conditions'. The basic ideas of this work naturally follow from our almost 30-year experience in the field of SHS. As a matter of fact, we have already obtained some results in the following two directions closely related to the microgravity problem. One is the studies on SHS processes in the field of centrifugal forces. These studies aimed at the intensification of gravity-sensitive SHS processes in multicomponent highly caloric systems forming melts at high overloads (up to 2000 g). In other words, these studies had the objectives that are inverse to those in the microgravity studies. The second group of results directly relates to the microgravity problem and the project under consideration. These experiments played the important role in establishing links between SHS and microgravity.

Merzhanov, A. G.↗

NASA NTRS1986

SMI adaptive antenna arrays for weak interfering signals

The performance of adaptive antenna arrays in the presence of weak interfering signals (below thermal noise) is studied. It is shown that a conventional adaptive antenna array sample matrix inversion (SMI) algorithm is unable to suppress such interfering signals. To overcome this problem, the SMI algorithm is modified. In the modified algorithm, the covariance matrix is redefined such that the effect of thermal noise on the weights of adaptive arrays is reduced. Thus, the weights are dictated by relatively weak signals. It is shown that the modified algorithm provides the desired interference protection.

Gupta, Inder J.↗

NASA NTRS1989

A direct-inverse transonic wing-design method in curvilinear coordinates including viscous-interaction

Progress in the direct-inverse wing design method in curvilinear coordinates has been made. A spanwise oscillation problem and proposed remedies are discussed. Test cases are presented which reveal the approximate limits on the wing's aspect ratio and leading edge wing sweep angle for a successful design, and which show the significance of spanwise grid skewness, grid refinement, viscous interaction, the initial airfoil section and Mach number-pressure distribution compatibility on the final design. Furthermore, preliminary results are shown which indicate that it is feasible to successfully design a region of the wing which begins aft of the leading edge and terminates prior to the trailing edge.

Ratcliff, Robert R.↗

NASA NTRS2001

Aerosol Profile Retrievals from Integrated Dual Wavelengths Space Lidar ESSP3-CENA and Spectral Radiance MODIS Data

The ESSP3-CENA space mission (formally PICASSO-CENA) will provide continues global observations with a two wavelength lidar. The attenuated backscattering coefficients measured by the lidar, have valuable information about the vertical distribution of aerosol particles and their sizes. However the information cannot be mapped into unique aerosol physical properties. Infinite number of physical solutions with different attenuations through the atmosphere can reconstruct the same two wavelength backscattered profile measured from space. Spectral radiance measured by MODIS simultaneously with the ESSP3 data can constrain the problem and resolve this ambiguity to a large extent. Sensitivity study shows that inversion of the integrated MODIS+ESSP3 data can derive the vertical profiles of the fine and coarse modes mixed in the same atmospheric column in the presence of moderate calibration uncertainties and electronic noise (approx. 10%). We shall present the sensitivity study and results from application of the technique to measurements in the SAFARI-2000 and SHADE experiments.

Kaufman, Yoram↗

NASA NTRS2018

Magnetic Helicity Condensation and the Solar Cycle

Solar filaments exhibit a global chirality pattern where dextral/sinistral filaments, corresponding to negative/ positive magnetic helicity, are dominant in the northern/southern hemisphere. This pattern is opposite to the sign of magnetic helicity injected by differential rotation along east–west oriented polarity inversion lines, posing a major conundrum for solar physics. A resolution of this problem is offered by the magnetic helicity-condensation model of Antiochos. To investigate the global consequences of helicity condensation for the hemispheric chirality pattern, we apply a temporally and spatially averaged statistical approximation of helicity condensation. Realistic magnetic field configurations in both the rising and declining phases of the solar cycle are simulated. For the helicity-condensation process, we assume convective cells consisting of positive/negative vorticities in the northern/southern hemisphere that inject negative/positive helicity. The magnitude of the vorticity is varied as a free parameter, corresponding to different rates of helicity injection. To reproduce the observed percentages of dominant and minority filament chiralities, we find that a vorticity of magnitude 2.5 x 10(exp −6)/s is required. This rate, however, is insufficient to produce the observed unimodal profile of chirality with latitude. To achieve this, a vorticity of at least 5 x 10(exp −6)/s is needed. Our results place a lower limit on the small-scale helicity injection required to dominate differential rotation and reproduce the observed hemispheric pattern. Future studies should aim to establish whether the helicity injection rate due to convective flows and/or flux emergence across all latitudes of the Sun is consistent with our results.

Mackay, Duncan H.↗

NASA NTRS2018

Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab® autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation.

Acheson, Michael J.↗

NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

An optimization capability is developed for acoustic scattering and shielding of installed propellers and rotors, based on a spacetime Galerkin time domain boundary element method (TDBEM). The time domain approach is particularly suitable for efficient simulation of transient, rotating, and broadband noise sources such as propellers. The use of algorithmic differentiation allows efficient evaluation of design sensitivities required for gradient-based design optimization with a large number of design variables. We present a validation exercise for the coherent broadband scattering capability against an analytical solution, showing excellent agreement. We then demonstrate the optimization tool on a series of inverse design cases with broadband and rotating sources, as well as an optimization problem for a propeller-wing configuration. The results show good performance for optimization problems with the characteristics of realistic installed propeller configurations.

Maks J Groom↗

NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

Maks J Groom↗

NASA NTRS1992

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗

NASA NTRS1985

Numerical Techniques for Scattering from Submerged Objects

To represent the final results in terms of matrices, one expands all appropriate physical quantities in terms of partial wave basis states. This includes expansions for the incident and scattered fields and the surface quantities. The method then utilizes the Huygen-Poincare integral representation for both the exterior and interior solutions, leading to the required matrix equations. One thus deals with matrix equations, the complexity of which depends on the nature of the problem. It is shown that in general a transition matrix T can be obtained relating the incident field A with the scattered field f having the form T = PQ(-1), where f = TA. The structure of Q can be quite complicated and can itself be composed of other matrix inversions such as arise from layered objects. Recent improvements in this method appropriate for a variety of physical problems are focused on, and on their implementation. Results are outlined from scattering simulations for very elongated submerged objects and resonance scattering from elastic solids and shells. The final improvement concerns eigenfunction expansions of surface terms, arising from solution of the interior problem, obtained via a preconditioning technique. This effectively reduces the problem to that of obtaining eigenvalues of a Hermitian operator. This formalism is reviewed for scattering from targets that are rigid, sound-soft, acoustic, elastic solids, elastic shells, and elastic layered objects. Two sets of the more interesting results are presented. The first concerns scattering from elongated objects, and the second to thin elastic spheroids.

Werby, M. F.↗

NASA NTRS1989

Totally parallel multilevel algorithms for sparse elliptic systems

The fastest known algorithms for the solution of a large elliptic boundary value problem on a massively parallel hypercube all require O(log(n)) floating point operations and O(log(n)) distance-1 communications, if massively parallel is defined to mean a number of processors proportional to the size n of the problem. The Totally Parallel Multilevel Algorithm (TPMA) that has, as special cases, four of these fast algorithms is described. These four algorithms are Parallel Superconvergent Multigrid (PSMG), Robust Multigrid, the Fast Fourier Transformation (FFT) based Spectral Algorithm, and Parallel Cyclic Reduction. The algorithm TPMA, when described recursively, has four steps: (1) project to a collection of interlaced, coarser problems at the next lower level; (2) apply TPMA, recursively, to each of these lower level problems, solving directly at the lowest level; (3) interpolate these approximate solutions to the finer grid, and to verage them to form an approximate solution on this grid; and (4) refine this approximate solution with a defect-correction step, using a local approximate inverse. Choice of the projection operator (P), the interpolation operator (Q), and the smoother (S) determines the class of problems on which TPMA is most effective. There are special cases in which the first three steps produce an exact solution, and the smoother is not needed (e.g., constant coefficient operators).

Frederickson, Paul O.↗

NASA NTRS2024

Harnessing Collaborative Learning Automata to Guide Multi-objective Optimization based Inverse Analysis for Structural Damage Identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

Yang Zhang↗

NASA NTRS1973

Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.

Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.

Gupta, K. K.↗