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At least 19 records

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NASA NTRS2024

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

Yang Zhang↗

NASA NTRS1992

Superresolution via sparsity constraints

The problem of recovering a measure mu supported on a lattice of span Delta is considered under the condition that measurements are only available concerning the Fourier Transform at frequencies of Omega or less. If Omega is much smaller than the Nyquist frequency pi/Delta and the measurements are noisy, then stable recovery of mu is generally impossible. It is shown here that if, in addition, it is known that mu satisfies certain sparsity constraints, then stable recovery is possible. This finding validates practical efforts in spectroscopy, seismic prospecting, and astronomy to provide superresolution by imposing support limitations in reconstruction.

Donoho, David L.↗

NASA NTRS2018

Combining Sparsity DEM Inversions with Event Tracking for AIA Data

We introduce a modified version of the ASGARD code (Automated Selection and Grouping of events in A/A Regional Data). Originally written to detect and group brightenings ("events") in the AIA EUV channels, it now includes the sparsity DEM inversion method and instead detects emission measure enhancements in different temperature bins. Ultimately, the goal is to automatically determine heating and cooling rates in different coronal structures.

Bethge, Christian↗

NASA NTRS1978

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗

NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗

NASA NTRS1992

Eigenstructure assignment approach for structural damage detection

In this work, a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage. The algorithm is based on the partial inverse problem, in that only partial spectral information is required. The technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment. Algorithms to enhance mode shape assignability and to preserve sparsity in the damaged FEM are developed. The sparsity preservation is of particular importance when considering damage detection in trusslike structures. Several examples are presented to highlight the key points made within the paper.

Zimmerman, David C.↗

NASA NTRS1992

An inverse problem approach for structural damage detection - Finite element model refinement

In this work, a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage. This same algorithm is also useful in terms of finite element model refinement. The algorithm is based on the partial inverse problem, in that only partial spectral information is required. The technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment. Algorithms to enhance mode shape assignability and to preserve sparsity in the updated model are developed. The sparsity preservation is of particular importance when considering damage detection in truss-like structures. Several examples are presented which highlight the key points made within the paper.

Zimmerman, D. C.↗

NASA NTRS2016

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

aircraft↗

NASA NTRS1972

Study of propellant dynamics in a shuttle type launch vehicle

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Jones, C. E.↗

NASA NTRS1973

Sparse matrix methods based on orthogonality and conjugacy

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Lawson, C. L.↗

NASA NTRS1972

Elimination on sparse symmetric systems of a special structure.

Consideration of the problem of finding a permutation of rows and columns and an algorithm for solving ordered systems of linear algebraic equations with sparse matrices having a certain regular structure. Two approaches to the solution of this problem, in which the sparsity is used to some extent, are outlined. One of them is a very general approach where optimal (or nearly optimal) ordering is sought and the algorithm for solving the ordered system treats the matrix element by element to perform only necessary operations. The other approach involves the use of band matrices. After comparing these two approaches, a third approach is then suggested which involves the use of pipe matrices, and a means of ordering the rows and columns to obtain this type of matrix is presented. Examples of matrices reordered by the proposed procedure are cited.

Segethova, J.↗

NASA NTRS1974

The role of solar local time in polar cap magnetic variations

The role of the earth's main field in controlling the morphology of magnetic disturbance is usually accounted for by use of invariant latitude and MLT (magnetic local time) as a coordinate system. Magnetic disturbance from ionospheric currents is also controlled by ionospheric conductivity. At high latitudes, where SLT (solar local time) can be very different from MLT, the use of only MLT can give misleading results. In particular, those diurnal magnetic variations in the polar cap that change characteristics between interplanetary magnetic sectors have a tendency to peak near noon SLT rather than noon MLT at Alert, where noon MLT and noon SLT differ by more than 10 hours. Because of the sparsity of magnetic observatories it is not possible to completely separate SLT and MLT effects.

Langel, R. A.↗

NASA NTRS1975

Sparse matrix techniques applied to modal analysis of multi-section duct liners

A simplified procedure is presented for analysis of ducts with discretely nonuniform properties. The analysis uses basis functions as the generalized coordinates. The duct eigenfunctions are approximated by finite series of these functions. The emphasis is on solution of the resulting large sparse set of linear equations. Characteristics of sparse matrix algorithms are outlined and some criteria for application are established. Analogies with structural methods are used to illustrate variations which can increase efficiency in generating values for design optimization routines. The effects of basis function selection, number of eigenfunctions and identification and ordering of equations on the sparsity and solution stability are included.

Arnold, W. R.↗

NASA NTRS1976

Evidence of Archaean life - A brief appraisal

Attention is called to the question of whether the meagerness of the Archaean fossil record is a function of a sparsity of preserved, cratonal, fossiliferous facies, or whether the abrupt break in the known fossil record near the Archaean-Proterozoic boundary reflects a major event in biological evolution. The paper then reviews the currently available geochemical and paleobiological data on Archaean biota. The occurrence of stromatolites in the Archaean, and the carbon isotopic composition of Archaean organic matter, both suggest strongly the existence of an Archaean biota. The presence of relatively abundant and morphologically complex microorganisms in deposits of early Proterozoic age seems to be certain evidence for a prior episode of Archaean evolution.

Schopf, J. W.↗

NASA NTRS1977

Numerical analysis of free vibrations of damped rotating structures

This paper is concerned with the efficient numerical solution of damped and undamped free vibration problems of rotating structures. While structural discretization is achieved by the finite element method, the associated eigenproblem solution is effected by a combined Sturm sequence and inverse iteration technique that enables the computation of a few required roots only without having to compute any other. For structures of complex configurations, a modal synthesis technique is also presented, which is based on appropriate combinations of eigenproblem solution of various structural components. Such numerical procedures are general in nature, which fully exploit matrix sparsity inherent in finite element discretizations, and prove to be most efficient for the vibration analysis of any damped rotating structure, such as rotating machineries, helicopter and turbine blades, spinning space stations, among others.

Gupta, K. K.↗

NASA NTRS1978

The Lanczos algorithm with selective orthogonalization

A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al.

Parlett, B. N.↗

NASA NTRS1978

Some recent advances in numerical methods in structural dynamics

The purpose of this paper is to present some recent developments in the area of numerical dynamic analysis of large structural systems. The first part of the paper is devoted to the finite dynamic element method, a new concept in the discretization of a continuum, the adoption of which effects considerable reduction in the number of degrees of freedom for a required solution accuracy, when compared with the usual finite element method. This is followed by a brief description of eigenproblem solution techniques, for the free vibration analysis of both rotating and nonrotating structures, that fully exploit the associated matrix sparsity. Together, these techniques constitute a powerful tool for the free vibration and subsequent dynamic response analysis of complex practical structures.

Gupta, K. K.↗

NASA NTRS1980

Plan of research for integrated soil moisture studies. Recommendations of the Soil Moisture Working Group

Soil moisture information is a potentially powerful tool for applications in agriculture, water resources, and climate. At present, it is difficult for users of this information to clearly define their needs in terms of accuracy, resolution and frequency because of the current sparsity of data. A plan is described for defining and conducting an integrated and coordinated research effort to develop and refine remote sensing techniques which will determine spatial and temporal variations of soil moisture and to utilize soil moisture information in support of agricultural, water resources, and climate applications. The soil moisture requirements of these three different application areas were reviewed in relation to each other so that one plan covering the three areas could be formulated. Four subgroups were established to write and compile the plan, namely models, ground-based studies, aircraft experiments, and spacecraft missions.

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