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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Factorizations of hyperpower family of iterative methods via least squares approach

A new method for finding proper factorizations of the hyperpower family of iterative methods for computing generalized inverses is proposed. The method is based on numerical optimization of an appropriate least squares problem. An iterative method in a non-normalized form for finding the generalized outer inverses with prescribed range and null space of any given complex matrix is proposed and considered. Computational complexity and convergence of the method are studied. Several numerical experiments are also presented.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Optimization and mechanisms of mistuning in cascades

In the present inverse design procedure for the optimum mistuning of a high bypass ratio shroudless fan that is modeled as a cascade of blades (each with a single torsional degree-of-freedom), linearized supersonic aerodynamic theory is used to compute the unsteady aerodynamic forces in the 'influence coefficient' form at a typical blade section. The mistuning pattern is then numerically optimized in order to achieve a specified increase in the aeroelastic stability margin with a minimum amount of mistuning. If the blades are self-damped, an optimized mistuning pattern can be found that achieves a given stability margin for a much lower level of mistuning than required for the alternate mistuning pattern, which requires only two blade frequencies and is relatively insensitive to implementation errors.

Crawley, E. F.↗
DOE OSTI2022

Image-domain DAS 3D VSP elastic transmission tomography

SUMMARY Full-wavefield elastic imaging of active-source seismic data acquired by downhole receivers commonly offers higher-resolution subsurface images in the vicinity of a borehole compared to conventional surface seismic data sets, which can lack higher-frequency wavefield components due to longer travel paths and increased attenuation. An increasingly used approach for downhole acquisition is vertical seismic profiling (VSP), which has become more attractive when coupled with distributed acoustic sensing (DAS) using optical fibres installed in wells. The main difficulty for generating high-quality images with full-wavefield imaging tools for DAS VSP data, though, is the need for an accurate velocity model. To build plausible velocity models using active-source DAS VSP data, we adopt a 3-D image-domain elastic transmission tomography technique, originally developed for surface-recorded passive (microseismic) data, by exchanging the source and receiver positions (i.e. reciprocity) to mimic a passive-seismic surface monitoring scenario. The inversion approach exploits various images for each source constructed through time-reverse imaging (TRI) of downgoing P- and S-wave first-arrival waveforms. The TRI process uses the kinetic term of the (extended) PS energy imaging condition that exhibits sufficient sensitivity to velocity model errors. The method automatically updates the P- and S-wave velocity models to optimize image focusing via adjoint-state inversion. We illustrate the efficacy of the adopted elastic inversion technique using an active-source DAS 3-D VSP field data set acquired in the North Slope of Alaska. The numerical experiments demonstrate that the inverted elastic velocity models can be further used in full-wavefield acoustic/elastic imaging algorithms to obtain accurate subsurface images.

Oren, Can (ORCID:000000019534265X)↗
DOE OSTI2014

Beamlet based direct aperture optimization for MERT using a photon MLC

Purpose: A beamlet based direct aperture optimization (DAO) for modulated electron radiotherapy (MERT) using photon multileaf collimator (pMLC) shaped electron fields is developed and investigated. Methods: The Swiss Monte Carlo Plan (SMCP) allows the calculation of dose distributions for pMLC shaped electron beams. SMCP is interfaced with the Eclipse TPS (Varian Medical Systems, Palo Alto, CA) which can thus be included into the inverse treatment planning process for MERT. This process starts with the import of a CT-scan into Eclipse, the contouring of the target and the organs at risk (OARs), and the choice of the initial electron beam directions. For each electron beam, the number of apertures, their energy, and initial shape are defined. Furthermore, the DAO requires dose–volume constraints for the structures contoured. In order to carry out the DAO efficiently, the initial electron beams are divided into a grid of beamlets. For each of those, the dose distribution is precalculated using a modified electron beam model, resulting in a dose list for each beamlet and energy. Then the DAO is carried out, leading to a set of optimal apertures and corresponding weights. These optimal apertures are now converted into pMLC shaped segments and the dose calculation for each segment is performed. For these dose distributions, a weight optimization process is launched in order to minimize the differences between the dose distribution using the optimal apertures and the pMLC segments. Finally, a deliverable dose distribution for the MERT plan is obtained and loaded back into Eclipse for evaluation. For an idealized water phantom geometry, a MERT treatment plan is created and compared to the plan obtained using a previously developed forward planning strategy. Further, MERT treatment plans for three clinical situations (breast, chest wall, and parotid metastasis of a squamous cell skin carcinoma) are created using the developed inverse planning strategy. The MERT plans are compared to clinical standard treatment plans using photon beams and the differences between the optimal and the deliverable dose distributions are determined. Results: For the idealized water phantom geometry, the inversely optimized MERT plan is able to obtain the same PTV coverage, but with an improved OAR sparing compared to the forwardly optimized plan. Regarding the right-sided breast case, the MERT plan is able to reduce the lung volume receiving more than 30% of the prescribed dose and the mean lung dose compared to the standard plan. However, the standard plan leads to a better homogeneity within the CTV. The results for the left-sided thorax wall are similar but also the dose to the heart is reduced comparing MERT to the standard treatment plan. For the parotid case, MERT leads to lower doses for almost all OARs but to a less homogeneous dose distribution for the PTV when compared to a standard plan. For all cases, the weight optimization successfully minimized the differences between the optimal and the deliverable dose distribution. Conclusions: A beamlet based DAO using multiple beam angles is implemented and successfully tested for an idealized water phantom geometry and clinical situations.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2022

P- and L-Band Retrieval of Subsurface Soil Moisture and Temperature Profiles as First-Order Polynomial Function

This paper demonstrates the potential use of P and L band passive measurements to determine root zone soil moisture (SM) and soil temperature(ST). SM and ST data have been taken as a function of depth during the NASA GSFC PLEX19 experiment in the summer of 2019 at Beltsville, MD, USA. Using these data, a coherent model has been used to compute H and V brightness temperatures at frequencies of 0.8 and 1.4 GHz with an observation angle of 35 degrees. These synthetic brightness data are then used to estimate the SM and ST profiles which are represented by linear polynomials. The inversion problem is formulated as a least square problem that is solved by a global optimization method known as the Adaptive Simulated Annealing(ASA) method. Four inversion examples having different SM and ST profiles are presented. Selected results show that the standard deviation between the retrieved and measured data is less than 0.077 cm3/cm3 for SM, and 2.245 °C for ST.

Ming Li↗
NASA NTRS1983

Optimal mistuning for enhanced aeroelastic stability of transonic fans

An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom.

Hall, K. C.↗
DOE OSTI2018

Parallel multiple-chain DRAM MCMC for large-scale geosteering inversion and uncertainty quantification

Geosteering is the proactive control of a wellbore placement based on the downhole measurements, aiming at maximizing economic production from the well. We report the recent development of azimuthal resistivity logging-whiledrilling (LWD) tools have a much larger depth of detection, thus sets higher demands for geosteering inversion as more unknown parameters need to be taken into account in the earth model to be inverted. For complicated nonlinear problems, traditional deterministic inversion methods are more likely to be trapped near local optima. In general, Markov chain Monte Carlo (MCMC) inversion methods are more capable of finding the global optimal solution and providing additional uncertainty analyses by sampling from the target distribution. However, MCMC methods usually have the problem of slow convergence. Even though optimization methods like delayed rejection (DR) and adaptive Metropolis (AM) were proposed to speed up the convergence, using MCMC methods to solve geosteering inversion problems may still incur unacceptable time cost. To reduce the sampling cost of MCMC methods, we use parallel multiple-chain DRAM MCMC methods to solve geosteering inverse problems and estimate the corresponding uncertainty. A clustering method, density-based spatial clustering of applications with noise (DBSCAN), is applied to select the best solution among many results. Lastly, the simulation results show that running many relatively short MCMC chains for one problem can obtain a similar result as running a long single chain. Besides, avoiding communications between multiple Markov chains during the sampling process yields almost linear scalability.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Optimization as a Tool for Consistency Maintenance in Multi-Resolution Simulation

The need for new approaches to the consistent simulation of related phenomena at multiple levels of resolution is great. While many fields of application would benefit from a complete and approachable solution to this problem, such solutions have proven extremely difficult. We present a multi-resolution simulation methodology that uses numerical optimization as a tool for maintaining external consistency between models of the same phenomena operating at different levels of temporal and/or spatial resolution. Our approach follows from previous work in the disparate fields of inverse modeling and spacetime constraint-based animation. As a case study, our methodology is applied to two environmental models of forest canopy processes that make overlapping predictions under unique sets of operating assumptions, and which execute at different temporal resolutions. Experimental results are presented and future directions are addressed.

TEMPORAL RESOLUTION↗
DOE OSTI2019

Multidimensional sum-up rounding for integer programming in optimal experimental design

Here we present a numerical method for approximating the solution of convex integer programs stemming from optimal experimental design. The statistical setup consists of a Bayesian framework for linear inverse problems for which the direct relationship is described by a discretized integral equation. Specifically, we aim to find the optimal sensor placement from a set of candidate locations where data are collected with measurement error. The convex objective function is a measure of the uncertainty, described here by the trace or log-determinant of the posterior covariance matrix, for the discretized linear inverse problem solution. The resulting convex integer program is relaxed, producing a lower bound. An upper bound is obtained by extending the sum-up rounding approach to multiple dimensions. For this extension, we analyze its accuracy as a function of the discretization mesh size for a rectangular domain. We show asymptotic optimality of the integer solution defining the upper bound for different experimental design criteria (A- and D-optimal), by proving the convergence to zero of the gap between the upper and lower bounds as the mesh size goes to zero. The technique is illustrated on a two-dimensional gravity surveying problem for both A-optimal and D-optimal sensor placement where our designs yield better results compared with a thresholding rounding approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

TH-A-9A-06: Inverse Planning of Gamma Knife Radiosurgery Using Natural Physical Models

Purpose: Treatment-planning systems rely on computer intensive optimization algorithms in order to provide radiation dose localization. We are investigating a new optimization paradigm based on natural physical modeling and simulations, which tend to evolve in time and find the minimum energy state. In our research, we aim to match physical models with radiation therapy inverse planning problems, where the minimum energy state coincides with the optimal solution. As a prototype study, we have modeled the inverse planning of Gamma Knife radiosurgery using the dynamic interactions between charged particles and demonstrate the potential of the paradigm. Methods: For inverse planning of Gamma Knife radiosurgery: (1) positive charges are uniformly placed on the surface of tumors and critical structures. (2) The Gamma Knife dose kernels of 4mm, 8mm and 16mm radii are modeled as geometric objects with variable charges. (3) The number of shots per each kernel radii is obtained by solving a constrained integer-linear problem. (4) The shots are placed into the tumor volume and move under electrostatic forces. The simulation is performed until internal forces are zero or maximum iterations are reached. (5) Finally, non-negative least squares (NNLS) is used to calculate the beam-on times for each shot. Results: A 3D C-shaped tumor surrounding a spherical critical structure was used for testing the new optimization paradigm. These tests showed that charges spread out evenly covering the tumor while keeping distance from the critical structure, resulting in a high quality plan. Conclusion: We have developed a new paradigm for dose optimization based on the simulation of physical models. As prototype studies, we applied electrostatic models to Gamma Knife radiosurgery and demonstrated the potential of the new paradigm. Further research and fine-tuning of the model are underway. NSF CBET-0853157.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-232: Custom High-Dose-Rate Brachytherapy Surface Mold Applicators: The Importance Source to Skin Distance

Purpose: Surface mold applicators can be customized to fit irregular skin surfaces that are difficult to treat with other radiation therapy techniques. Optimal design of customized HDR skin brachytherapy is not well-established. We evaluated the impact of applicator thickness (source to skin distance) on target dosimetry. Methods: 27 patients had 34 treated sites: scalp 4, face 13, extremity 13, and torso 4. Custom applicators were constructed from 5–15 mm thick thermoplastic bolus molded over the skin lesion. A planar array of plastic brachytherapy catheters spaced 5–10 mm apart was affixed to the bolus. CT simulation was used to contour the target volume and to determine the prescription depth. Inverse planning simulated annealing followed by graphical optimization was used to plan and deliver 40–56 Gy in 8–16 fractions. Target coverage parameters (D90, Dmean, and V100) and dose uniformity (V110–200, D0.1cc, D1cc, and D2cc) were studied according to target depth (<5mm vs. ≥5mm) and applicator thickness (5–10mm vs. ≥10mm). Results: The average prescription depth was 4.2±1.5mm. The average bolus thickness was 9.2±2.4mm. The median CTV volume was 10.0 cc (0.2–212.4 cc). Similar target coverage was achieved with prescription depths of <5mm and ≥5mm (Dmean = 113.8% vs. 112.4% and D90 = 100.2% vs. 98.3%). The <5mm prescription depth plans were more uniform (D0.1cc = 131.8% vs. 151.8%). Bolus thickness <10mm vs. ≥10mm plans also had similar target coverage (Dmean = 118.2% vs. 110.7% and D90 = 100.1% vs. 99.0%). Applicators ≥10mm thick, however, provide more uniform target dosimetry (D0.1cc = 146.9% vs. 139.5%). Conclusion: Prescription depth is based upon the thickness of the lesion and upon the clinical needs of the patient. Applicators ≥10mm thick provide more dose uniformity than 5–10mm thick applicators. Applicator thickness is an important variable that should be considered during treatment planning to achieve optimal dose uniformity.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

We present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. Here, we address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.

42 ENGINEERING↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
NASA NTRS1987

Polynomial compensation, inversion, and approximation of discrete time linear systems

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Baram, Yoram↗
DOE OSTI2020

Multiple-objective Reinforcement Learning for Inverse Design and Identification

The aim of inverse chemical design is to develop new molecules with given optimized molecular properties or objectives. Recently, generative deep learning (DL) networks are considered as the state-of-the-art in inverse chemical design and have achieved early success in generating molecular structures with desired properties in the pharmaceutical and material chemistry fields. However, satisfying a large number (> 10 objectives) of molecular objectives is a limitation of current generative models. To improve the model’s ability to handle a large number of molecule design objectives, we developed a Reinforcement Learning (RL) based generative framework to optimize chemical molecule generation. Our use of Curriculum Learning (CL) to fine-tune the pre-trained generative network allowed the model to satisfy up to 21 objectives and increase the generative network’s robustness. The experiments show that the proposed multiple-objective RL-based generative model can correctly identify unknown molecules with an 83% to 100% success rate, compared to the baseline approach of 0%. Additionally, this proposed generative model is not limited to just chemistry research challenges; we anticipate that problems that utilize RL with multiple objectives will benefit from this framework.

reinforcement learning, generative model, inverse ↗
NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

The current aviation revolution towards electric propulsion aircraft (e.g., electric vertical takeoff-and-landing) brings unique control challenges. These vehicles are typically over-actuated (more effectors than desired control outcomes), may require control strategies for the three phases of flight (hover, transition and cruise), and currently have limited electric power availability. These vehicle challenges bring the need for optimal control allocation to the forefront of research. A leading control allocation algorithm, used in current flight vehicles, is the Cascading Generalized Inverse (CGI). Unfortunately, the Cascading Generalized Inverse algorithm is unable to achieve some desired outcomes, it intermittently provides non-optimal allocations, and it may fail to preserve moment direction near maximal achievable outcomes. In this research, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Rigorous theory is shown that the Modified Cascading Generalized Inverse performs better at obtaining optimal allocations for all attainable outcomes. Numerical case studies for over-actuated vehicles demonstrate resolution to the aforementioned deficiencies.

Control Allocation↗