Discrete analog of an iterative method for inverse eigenvalue problems for Jacobi matrices
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Barcilon, V.↗
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Results for “inverse methods”
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Approximation methods for inverse problems involving the vibration of beams with tip bodies
Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.
Rosen, I. G.↗
A multi-point inverse airfoil design method based on conformal mapping
An exact method of multipoint inverse airfoil design for incompressible flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise which must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in the angular coordinate, specification of the velocity in terms of arc length is handled through the multidimensional Newton iteration as well. The current formulation sets the stage for a more general multipoint inverse airfoil design method in which it will be possible to specify the velocity distribution, some boundary-layer development, or the surface geometry along a segment.
Selig, Michael S.↗
Deep-Focusing Time-Distance Helioseismology
Much progress has been made by measuring the travel times of solar acoustic waves from a central surface location to points at equal arc distance away. Depth information is obtained from the range of arc distances examined, with the larger distances revealing the deeper layers. This method we will call surface-focusing, as the common point, or focus, is at the surface. To obtain a clearer picture of the subsurface region, it would, no doubt, be better to focus on points below the surface. Our first attempt to do this used the ray theory to pick surface location pairs that would focus on a particular subsurface point. This is not the ideal procedure, as Born approximation kernels suggest that this focus should have zero sensitivity to sound speed inhomogeneities. However, the sensitivity is concentrated below the surface in a much better way than the old surface-focusing method, and so we expect the deep-focusing method to be more sensitive. A large sunspot group was studied by both methods. Inversions based on both methods will be compared.
Duvall, T. L., Jr.↗
Radio-holographic methods for inversion of radio occultation experiments on Venus
No abstract provided
Bocanegra-Bahamon, Tatiana↗
Radio-holographic methods for inversion of radio occultation experiments on Venus
No abstract provided
Bocanegra-Bahamon, Tatiana↗
Dynamic Force Reconstruction of Transient Flap Control Force Experiments in a Hypersonic Wind Tunnel
This work details the design of a sliced-cone model with a flap embedded within the slice. The flap is controlled by a fast acting servo to simulate a control force of a hypersonic vehicle. Design considerations such as sensor placement, expected loading, servo arm selection, and cavity temperatures are detailed in this work. Such a design imparts a dynamic response of the test article and as such, dynamic force measurement methodologies are required to reconstruct the control forcing. Three methods are of particular interest: the Sum of Weighted Accelerations Technique, Time Domain Deconvolution Method, and Frequency Domain Inverse Method. Novel versions of each method have been applied to this dataset to improve the reconstruction accuracy.
dynamic balance↗
Dynamic Force Reconstruction of Transient Flap Control Force Experiments in a Hypersonic Wind Tunnel
This work details the design of a sliced-cone model with a flap embedded within the slice. The flap is controlled by a fast acting servo to simulate a control force of a hypersonic vehicle. Design considerations such as sensor placement, expected loading, servo arm selection, and cavity temperatures are detailed in this work. Such a design imparts a dynamic response of the test article and as such, dynamic force measurement methodologies are required to reconstruct the control forcing. Three methods are of particular interest: the Sum of Weighted Accelerations Technique, Time Domain Deconvolution Method, and Frequency Domain Inverse Method. Novel versions of each method have been applied to this dataset to improve the reconstruction accuracy.
dynamic balance↗
A Nonlocal-Gradient Descent Method for Inverse Design in Nanophotonics
Local-gradient-based optimization approaches lack nonlocal exploration abilityrequired for escaping from local minima when searching non-convex landscapes.A directional Gaussian smoothing (DGS) approach was recently proposed in [29]and used to define a truly nonlocal gradient, referred to as the DGS gradient, inorder to enable nonlocal exploration in high-dimensional black-box optimization.Promising results show that replacing the traditional local gradient with the nonlocalDGS gradient can significantly improve the performance of gradient-based methodsin optimizing highly multi-modal loss functions. However, the current DGS methodis designed for unbounded and uncontrained optimization problems, making itinapplicable to real-world engineering optimization problems where the tuningparameters are often bounded and the loss function is usually constrained byphysical processes. In this work, we propose to extend to the DGS approachto the constrained inverse design framework in order to find better optima ofmulti-modal loss functions. A series of adaptive strategies for smoothing radiusand learning rate updating are developed to improve the computational efficiencyand robustness. Our methodology is demonstrated by an example of designing ananoscale wavelength demultiplexer, and shows superior performance compared tothe state-of-the-art approaches. By incorporating volume constraints, the optimizeddesign achieves an equivalently high performance but significantly reduces theamount of material usage.
Bi, Sirui↗
A Generalized Stress Inversion Approach With Application to Residual Stress Estimation
In this work develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.
42 ENGINEERING↗
A finite-difference method for transonic airfoil design.
This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.
Steger, J. L.↗
An inverse problem design method for branched and unbranched axially symmetrical ducts
This paper concerns the potential flow design of axially symmetrical ducts of both circular and annular cross section with or without wall suction or blowing slots. The objective of the work was to develop a method by which such ducts could be designed with directly prescribed wall pressure variation. Previous axially symmetrical design methods applied only to circular cross sectional ducts and required that the pressure distribution be prescribed along the duct centerline and not along the duct wall. The present method uses an inverse problem approach which extends the method of Stanitz to the axially symmetrical case, and an approximation is used to account for the stagnation point in branched duct designs. Two examples of successful designs of diffusers with suction slots are presented.
Nelson, C. D.↗
Comparison of forward and inverse cam generation methods for the design of cam-linkage mechanisms
This paper presents a comparison between the forward and inverse cam generation methods applied to the design of a multi-lobed cam-rocker slider mechanism for function generation. In the forward method, the cam profile is specified directly and then the linkage output is determined using kinematics. In the inverse method, the trajectory of the output link is specified first and then the cam profile is determined using inverse linkage kinematics. First, the cam-linkage mechanism is introduced, and relevant kinematic equations are presented. Then, the cam generation methods are thoroughly explained. Here, the two cam generation methods are applied to a case study of a hydraulic motor using a multi-lobed cam and multiple linkage mechanisms. While the forward method has direct control of the cam shape, the inverse method has direct control of the linkage output and offers an advantage in calculation speed. For the mechanism selected, the cam designed with the inverse method achieved a reduction of at least 50.97% in the torque ripple when compared to the cam designed with the forward method.
42 ENGINEERING↗
Experimental implementation of the modified independent modal space control method
An experimental realization of a modified independent modal space control (MIMSC) method to control the vibration of a flexible cantilevered beam is presented. In its operation the method relies on the use of one piezoelectric actuator to control several vibration modes through a time-sharing strategy. The effectiveness of the MIMSC method in damping out the beam vibration is demonstrated by comparing the results with those obtained by other modal control methods. Two methods are considered, the independent modal space control method and the pseudo-inverse method. The feasibility of the MIMSC method as a viable alternative for controlling large flexible structures with a very small number of actuators is emphasized.
Baz, A.↗
The source and distribution of Galactic positrons
The oriented scintillation spectrometer experiment (OSSE) observations of the Galactic plane and the Galactic center region were combined with observations acquired with other instruments in order to produce a map of the Galactic 511 keV annihilation radiation. Two mapping techniques were applied to the data: the maximum entropy method, and the basis pursuit inversion method. The resulting maps are qualitatively similar and show evidence for a central bulge and a weak galactic disk component. The weak disk is consistent with that expected from positrons produced by the decay of radioactive Al-26 in the interstellar medium. Both maps suggest an enhanced region of emission near l = -4 deg, b = 7 deg, with a flux of approximately 50 percent of that of the bulge. The existence of this emission appears significant, although the location is not well determined. The source of this enhanced emission is presently unknown.
Purcell, W. R.↗
Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis
An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.
Carlson, Leland A.↗
Stochastic Reconstruction of Thermal Protection Material Properties from Arc-Jet Experiments
Material response models are used to assess reliability using variances in the bond-line temperature predictions based on uncertainties in trajectory, aerothermal environment, and material properties. A key deficiency in the current approach is that input uncertainties are too often subjective, empirical, or ad-hoc, and are not rigorously linked to the arc-jet test data used to develop the TPS material model. While materials such as PICA are well understood, future missions may require more novel materials such as HEEET where unknown uncertainties have real consequences on the ability to assess reliability. A quantifiable estimate of reliability requires an iterative methodology where the parameters driving the variance in bond-line temperature (for example) are systematically identified. A test campaign to collect data or develop new models can then be identified to reduce those input uncertainties. A Bayesian inference loop defines these connections mathematically, i.e., prior knowledge about uncertainty is updated based on observation. While these concepts are well known (and often applied intuitively in a non-rigorous approach), only recent advances in reduced-order modelling have made them computationally viable methods for engineering. By replacing deterministic inverse methods with stochastic approaches, the hope is new materials proposed for future missions can more rapidly be developed with a greater understanding of the TPS material reliability. Two additional steps for the analysis of arc jet test data are discussed. The first is ability to construct a reduced-order model using material response simulations (Icarus/US3D) of the arc-jet test articles, and the second is the inclusion of this surrogate model in the Bayesian inversion process. Both capabilities will be demonstrated using prior PICA arc-jet test data. The quality of a surrogate model will be investigated and the variances on the calibrated material properties will be compared to our current understanding of the PICA material model.
Material response↗
Total ozone and aerosol optical depths inferred from radiometric measurements in the Chappuis absorption band
A second-derivative smoothing technique, commonly used in inversion work, is applied to the problem of inferring total columnar ozone amounts and aerosol optical depths. The application is unique in that the unknowns may be solved for directly without employing standard inversion methods. It is shown, however, that by employing inversion constraints, better solutions are normally obtained. The method is quite versatile and able to deal with varying total ozone and various aerosol size distributions. The technique is applied first in simulation, then to 119 days of measurements taken in Tucson, Arizona, that are compared to TOMS values for the same dates. The technique is also applied to two measurements taken at Mauna Loa, Hawaii, for which Dobson ozone values are available in addition to the TOMS values, and the results agree to within 15 percent. It is also shown through simulations that additional information can be obtained from measurements outside the Chappuis band. This approach reduces the bias and spread of the estimated total ozone and is unique in that it uses measurements from both the Chappuis and Huggins absorption bands.
Flittner, D. E.↗