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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Minimal inversion, command matching and disturbance decoupling in multivariable systems

The present treatment of the related problems of minimal inversion and perfect output control in linear multivariable systems uses a simple analytical expression for the inverse of a square multivariate system's transfer-function matrix to construct a minimal-order inverse of the system. Because the poles of the minimal-order inverse are the transmission zeros of the system, necessary and sufficient conditions for the inverse system's stability are simply stated in terms of the zero polynomial of the original system. A necessary and sufficient condition for the existence of the required controllers is that the plant zero polynomial be neither identical to zero nor unstable.

Seraji, H.↗
NASA NTRS1991

Application of direct inverse analogy method (DIVA) and viscous design optimization techniques

A direct-inverse approach to the transonic design problem was presented in its initial state at the First International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-1). Further applications of the direct inverse analogy (DIVA) method to the design of airfoils and incremental wing improvements and experimental verification are reported. First results of a new viscous design code also from the residual correction type with semi-inverse boundary layer coupling are compared with DIVA which may enhance the accuracy of trailing edge design for highly loaded airfoils. Finally, the capabilities of an optimization routine coupled with the two viscous full potential solvers are investigated in comparison to the inverse method.

Greff, E.↗
NASA NTRS1993

Non-recursive augmented Lagrangian algorithms for the forward and inverse dynamics of constrained flexible multibodies

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.

Bayo, Eduardo↗
NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗
NASA NTRS1999

Preview-Based Stable-Inversion for Output Tracking

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is non-causal - hence the inverse has to be pre-computed using a pre-specified desired-output trajectory. This requirement for pre-specification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Zou, Qing-Ze↗
NASA NTRS1985

Shoot inversion-induced ethylene in Pharbitis nil induces the release of apical dominance by restricting shoot elongation

Shoot inversion induces outgrowth of the highest lateral bud (HLB) adjacent to the bend in the stem in Pharbitis nil. In order to determine whether or not ethylene produced by shoot inversion plays a direct role in promoting or inhibiting bud outgrowth, comparisons were made of endogenous levels of ethylene in the HLB and HLB node of plants with and without inverted shoots. That no changes were found suggests that the control of apical dominance does not involve the direction action of ethylene. This conclusion is further supported by evidence that the direct application of ethylene inhibitors or ethrel to inactive or induced lateral buds has no significant effect on bud outgrowth. The hypothesis that ethylene evolved during shoot inversion indirectly promotes the outgrowth of the highest lateral bud (HLB) in restricting terminal bud (TB) growth is found to be supported by the following observations: (1) the restriction of TB growth appears to occur before the beginning of HLB outgrowth; (2) the treatment of the inverted portion of the shoot with AgNO3, an inhibitor of ethylene action, dramatically eliminates both the restriction of TB growth and the promotion of HLB outgrowth which usually accompany shoot inversion; and (3) the treatment of the upper shoot of an upright plant with ethrel mimics shoot inversion by retarding upper shoot growth and inducing outgrowth of the lateral bud basipetal to the treated region.

NASA Discipline Plant Biology↗
NASA NTRS2009

Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

Tangborn, Andrew↗
NASA NTRS2019

Implementation and Testing of Inverse Kinematics on Robotic Arm

COSIE (Coronal Spectrographic Imager in the Extreme Ultraviolet) is a proposed solar tracking ISS imaging payload that will help bridge the theoretical gap between the physics of the low corona and the heliosphere. This scientific instrument requires high pointing accuracy, on the order of arc seconds. The instrument is mounted on to a three revolute joint robotic arm in order to track the roll, pitch and yaw motion of the Sun. The goal of this project is to construct a prototype model of the robotic arm and implement the proposed analytical inverse kinematics algorithm. In robotics, the inverse kinematics problem is solving for the set of joint angles that achieve the desired end effect or location and/or orientation. In this case, orientation is the focus. Depending on the configuration, multiple sets of joint angle solutions may exist. Due to the complexity of robotics, typically iterative methods are used to solve for the joint angle solution sets. However, in this case, an analytical solution exists. A small robotic arm representative of the full size hardware was constructed. The inverse kinematics algorithm, originally in MATLAB/Simulink, was converted into C in order to interface with the motors. This C software was implemented on a Windows PC and micro-controller, and serial communication between the two was established, allowing the motors to be directly controlled by the inverse kinematics algorithm. Testing the inverse kinematics on a physical system will allow the validity and accuracy of the analytic solution to be verified.

Franz, Carter↗
NASA NTRS2019

Is There an Optimal CO2 Partial Column for Flux Inversions?

The fidelity of flux estimates from an atmospheric inversion depends on the ability of atmospheric transport models to simulate the measured quantity. For species such as CO2, with surface fluxes and a large network of surface measurements, this means correctly simulating the dynamics of the planetary boundary layer (PBL), which is one of the most uncertain aspects of atmospheric transport modeling. In contrast, the simulated total column average mole fraction of CO2 (XCO2) is largely insensitive to simulated PBL dynamics. Therefore, measurements of XCO2 provided by current and future short wave infrared (SWIR) greenhouse gas (GHG) satellites such as GOSAT and the OCO family would seem to be more appropriate to flux inversions, as far as minimizing transport model errors (the "noise") is concerned. Unfortunately, the flux-induced variation of CO2 (the "signal") is the largest within the PBL and smallest in XCO2. Therefore, assimilating XCO2 as opposed to PBL CO2 need not give us the strongest "signal to noise" in flux inversions. Recent work on GOSAT and OCO2 retrievals suggest that SWIR satellite spectra may be used to estimate a lower partial column CO2, which could be assimilated in a flux inversion, instead of XCO2.Here we report on a study to assess whether there is an optimal partial column average CO2, intermediate between PBL CO2 and XCO2, whose assimilation might yield the best signal to noise in flux inversions, where (as before) "signal" is the flux-induced variation and "noise" is the error in transport modeling. We simulate atmospheric CO2 with five different global transport models and a common surface CO2 flux over ten years. We consider the spread across the five models to be a proxy for transport model error (the "noise"), and the common variation of CO2 in all five models to be a proxy for the "signal". We compare these signals and noises at different spatiotemporal scales for different partial column specifications to investigate whether there exists an optimal partial column that has large surface flux-driven variations and yet is relatively insensitive to errors in transport models. Finally, we comment on the feasibility of estimating such a partial column from current and future SWIR GHG satellites in the light of recent work on vertically resolved CO2 from current SWIR GHG satellites.

Basu, Sourish↗
NASA NTRS2021

Inversion of Magnetic Measurements of the Swarm A Satellite of the Bangui Magnetic Anomaly

We wanted to make a satellite altitude magnetic anomaly map of the large magnetic anomaly in the Central African Republic, the Bangui magnetic anomaly, with data from the Swarm satellites. In the first part of our study, we summarize the earlier investigations and their interpretation. In the second we discuss our data processing applied to produce a magnetic anomaly map. We used the IGRF 12th to remove the long-wavelength regional anomalies. We will use an inverse procedure, which always requires a solution of the direct problem, and a horizontal polygonal prism given in the Descartes coordinate system. For this, reason the total magnetic anomaly was transformed into the Descartes coordinate system. The magnetization and its direction were used from our previous paper. The inverse problem is solved by the Simplex procedure. Our selected polygon has 14 geometrical parameters however, the inverse problem that is the numerical determination of the minimum problem is solved in the 14 dimensions. The result of our inverse problem was the 12 horizontal coordinates and the two upper and lower data of the polygon. The origin of the Bangui anomaly has been discussed in several scientific reports, either as a deep crustal tectonic feature or the result of a large external impactor. However, according to our inversion computations we cannot make any unambiguous finding for the origin of this feature. The inaccuracy in our total anomaly map is given by the Gaussian error propagation.

KI Kis↗
DOE OSTI2017

Selecting an Informative/Discriminating Multivariate Response for Inverse Prediction

The inverse prediction is important in a variety of scientific and engineering applications, such as to predict properties/characteristics of an object by using multiple measurements obtained from it. Inverse prediction can be accomplished by inverting parameterized forward models that relate the measurements (responses) to the properties/characteristics of interest. Sometimes forward models are computational/science based; but often, forward models are empirically based response surface models, obtained by using the results of controlled experimentation. For empirical models, it is important that the experiments provide a sound basis to develop accurate forward models in terms of the properties/characteristics (factors). And while nature dictates the causal relationships between factors and responses, experimenters can control the complexity, accuracy, and precision of forward models constructed via selection of factors, factor levels, and the set of trials that are performed. Recognition of the uncertainty in the estimated forward models leads to an errors-in-variables approach for inverse prediction. The forward models (estimated by experiments or science based) can also be used to analyze how well candidate responses complement one another for inverse prediction over the range of the factor space of interest. Furthermore, one may find that some responses are complementary, redundant, or noninformative. Simple analysis and examples illustrate how an informative and discriminating subset of responses could be selected among candidates in cases where the number of responses that can be acquired during inverse prediction is limited by difficulty, expense, and/or availability of material.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems

Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Uncertainty reduction in residual stress measurements by an optimised inverse solution using nonconsecutive polynomials

Many destructive methods for measuring residual stresses such as the slitting method require an inverse analysis to solve the problem. The accuracy of the result as well as an uncertainty component (the model uncertainty) depends on the basis functions used in the inverse solution. The use of a series expansion as the basis functions for the inverse solution was analysed in a previous work for the particular case where functions orders grew consecutively. The present work presents a new estimation of the model uncertainty and a new improved methodology to select the final basis functions for the case where the basis is composed of polynomials. Including nonconsecutive polynomial orders in the basis generates a larger space of possible solutions to be evaluated and allows the possibility to include higher-order polynomials. The paper includes a comparison with two other inverse analyses methodologies applied to synthetically generated data. With the new methodology, the final error is reduced and the uncertainty estimation improved.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification

Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. Furthermore, the velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

58 GEOSCIENCES↗
DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method

In this study, an efficient Bayesian framework equipped with a multivariate adaptive regression spline (MARS) technique is developed to alleviate computational burdens encountered in a conventional Bayesian inversion of a geothermal prospect. Fast MARS models are developed from training dataset generated by CPU-intensive hydrothermal models and used as surrogate of high-fidelity physical models in Markov Chain Monte Carlo (MCMC) sampling. This Bayesian inference with MARS-enabled MCMC method is used to reduce prior estimates of uncertainty in structural or characteristic hydrothermal flow parameters of the model to posterior distributions. A geothermal prospect near Superstition Mountain in Imperial County of California in USA is used to illustrate the proposed framework and demonstrate the computational efficiency of MARS-based Bayesian inversion. The developed MARS models are also used to efficiently drive calculation of Sobol’ total sensitivity indices. Furthermore, only top sensitive parameters are included in Bayesian inference to further improve the computational efficiency of inversion. Sensitivity analysis also confirms that water circulation through high permeable structures, rather than heat conduction through impermeable granite, is the primary heat transfer method. The presented framework is demonstrated an efficient tool to update knowledge of geothermal prospects by inversing field data. Although only thermal data is used in this study, other type of data, such as flow and transport observations, can be jointly used in this method for underground hydrocarbon reservoirs.

15 GEOTHERMAL ENERGY↗