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NASA NTRS2006

Algorithm for NO2 Vertical Column Retrieval from the Ozone Monitoring Instrument

We describe the operational algorithm for the retrieval of stratospheric, tropospheric, and total column densities of nitrogen dioxide NO2 from earthshine radiances measured by the Ozone Monitoring Instrument (OMI), aboard the EOS-Aura satellite. The algorithm uses the DOAS method for the retrieval of slant column NO densities. Air mass factors (AMFs) calculated from a stratospheric NO2 profile are used to make initial estimates of the vertical column density. Using data collected over a 24-h period, a smooth estimate of the global stratospheric field is constructed. Where the initial vertical column densities exceed the estimated stratospheric field, we infer the presence of tropospheric NO2, and recalculate the vertical column density (VCD) using an AMF calculated from an assumed tropospheric NO2 profile. The parameters that control the operational algorithm were selected with the aid of a set of data assembled from stratospheric and tropospheric chemical transport models. We apply the optimized algorithm to OMI data and present global maps of NO2 VCDs for the first time.

Bucsela, Eric J.↗

NASA NTRS2018

Area Coverage Planning with 3-axis Steerable, 2D Framing Sensors

Existing algorithms for Agile Earth Observing Satellites((Lemaitre et al. 2002)) were largely created for 1D line sensors that acquire images in linear swaths. However, imaging satellites increasingly use 2D framing sensors (cameras) that capture discrete rectangular images. We describe tiling step-stare approaches that are more suited to rectangular image footprints than are 1D swath-based algorithms. Optimal area planning for these 2D framing instruments is an NPcomplete problem and intractable for large areas, so we present four approximation algorithms. Strategies are compared against a prior 2D framing instrument algorithm (Knight 2014) in three computational experiments. The impact of observer agility on schedule makespan is examined. Makespans vary more as observer agility decreases toward a critical point, then vary less after the critical point, suggesting a possible problem phase transition.

Chien, Steve↗

NASA NTRS1990

Optimal probe selection in diagnostic search

Probe selection (PS) in machine diagnosis is viewed as a collection of models that apply under specific conditions. This makes it possible for three polynomial-time optimal algorithms to be developed for simplified PS models that allow different probes to have different costs. The work is compared with the research of Simon and Kadane (1975), who developed a collection of models for optimal problem-solving search. The relationship between these models and the three newly developed algorithms for PS is explored. Two of the algorithms are unlike the ones discussed by Simon and Kadane. The third cannot be related to the problem-solving models.

Bhandari, Inderpal S.↗

DOE OSTI2021

Sequence of polyhedral relaxations for nonlinear univariate functions

Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

42 ENGINEERING↗

NASA NTRS1981

Pilot guidance and display considerations for energy efficient flight profiles

Two computer programs are applied to energy efficient flight operation in order to minimize aircraft operating costs. One algorithm (OPTIM) computes vertical flight profiles which optimize direct operating costs, including fuel and time costs, for an aircraft flying over a fixed range and with a fixed time-of-arrival. The second program (TRAGEN) simulates an aircraft steered to fly along a specified vertical flight trajectory, in order to examine fuel and cost penalties involved in flying nonoptimal trajectories. Constraints such as air traffic control procedures, and atmospheric and weight conditions are considered and supported by graphs and diagrams. The use of the algorithms as preflight planning tools is discussed, emphasizing OPTIM's future application for on-board energy management. Finally, research questions concerning pilot guidance and display considerations for advanced energy/flight management systems are addressed.

Samms, K. H.↗

NASA NTRS1992

The role of under-determined approximations in engineering and science application

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Carpenter, William C.↗

NASA NTRS1993

Structural design utilizing updated, approximate sensitivity derivatives

A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.

Scotti, Stephen J.↗

NASA NTRS1994

Removing cosmic-ray hits from multiorbit HST Wide Field Camera images

We present an optimized algorithm that removes cosmic rays ('CRs') from multiorbit Hubble Space Telescope (HST) Wide Field/Planetary Camera ('WF/PC') images. It computes the image noise in every iteration from the WF/PC CCD equation. This includes all known sources of random and systematic calibration errors. We test this algorithm on WF/PC stacks of 2-12 orbits as a function of the number of available orbits and the formal Poissonian sigma-clipping level. We find that the algorithm needs greater than or equal 4 WF/PC exposures to locate the minimal sky signal (which is noticeably affected by CRs), with an optimal clipping level at 2-2.5 x sigma(sub Poisson). We analyze the CR flux detected on multiorbit 'CR stacks,' which are constructed by subtracting the best CR filtered images from the unfiltered 8-12 orbit average. We use an automated object finder to determine the surface density of CRS as a function of the apparent magnitude (or ADU flux) they would have generated in the images had they not been removed. The power law slope of the CR 'counts' (gamma approximately = 0.6 for N(m) m(exp gamma)) is steeper than that of the faint galaxy counts down to V approximately = 28 mag. The CR counts show a drop off between 28 less than or approximately V less than or approximately 30 mag (the latter is our formal 2 sigma point source sensitivity without spherical aberration). This prevents the CR sky integral from diverging, and is likely due to a real cutoff in the CR energy distribution below approximately 11 ADU per orbit. The integral CR surface density is less than or approximately 10(exp 8)/sq. deg, and their sky signal is V approximately = 25.5-27.0 mag/sq. arcsec, or 3%-13% of our NEP sky background (V = 23.3 mag/sq. arcsec), and well above the EBL integral of the deepest galaxy counts (B(sub J) approximately = 28.0 mag/sq. arcsec). We conclude that faint CRs will always contribute to the sky signal in the deepest WF/PC images. Since WFPC2 has approximately 2.7x lower read noise and a thicker CCD, this will result in more CR detections than in WF/PC, potentially affecting approximately 10%-20% of the pixels in multiorbit WFPC2 data cubes.

Windhorst, Rogier A.↗

NASA NTRS2001

Parallelization of Program to Optimize Simulated Trajectories (POST3D)

This paper describes the parallelization of the Program to Optimize Simulated Trajectories (POST3D). POST3D uses a gradient-based optimization algorithm that reaches an optimum design point by moving from one design point to the next. The gradient calculations required to complete the optimization process, dominate the computational time and have been parallelized using a Single Program Multiple Data (SPMD) on a distributed memory NUMA (non-uniform memory access) architecture. The Origin2000 was used for the tests presented.

Hammond, Dana P.↗

NASA NTRS1995

Performance seeking control excitation mode

Flight testing of the performance seeking control (PSC) excitation mode was successfully completed at NASA Dryden on the F-15 highly integrated digital electronic control (HIDEC) aircraft. Although the excitation mode was not one of the original objectives of the PSC program, it was rapidly prototyped and implemented into the architecture of the PSC algorithm, allowing valuable and timely research data to be gathered. The primary flight test objective was to investigate the feasibility of a future measurement-based performance optimization algorithm. This future algorithm, called AdAPT, which stands for adaptive aircraft performance technology, generates and applies excitation inputs to selected control effectors. Fourier transformations are used to convert measured response and control effector data into frequency domain models which are mapped into state space models using multiterm frequency matching. Formal optimization principles are applied to produce an integrated, performance optimal effector suite. The key technical challenge of the measurement-based approach is the identification of the gradient of the performance index to the selected control effector. This concern was addressed by the excitation mode flight test. The AdAPT feasibility study utilized the PSC excitation mode to apply separate sinusoidal excitation trims to the controls - one aircraft, inlet first ramp (cowl), and one engine, throat area. Aircraft control and response data were recorded using on-board instrumentation and analyzed post-flight. Sensor noise characteristics, axial acceleration performance gradients, and repeatability were determined. Results were compared to pilot comments to assess the ride quality. Flight test results indicate that performance gradients were identified at all flight conditions, sensor noise levels were acceptable at the frequencies of interest, and excitations were generally not sensed by the pilot.

Schkolnik, Gerard↗

DOE OSTI2021

Microhole drilling technology utilizing a golden section search algorithm

A fundamental issue in microhole drilling is that delivering high weight-on-bit (WOB), high torque rotational horsepower to a conventional drill bit does not scale down to the hole sizes necessary to realize the envisioned cost savings An optimization algorithm called a golden section search (GSS) was used to systematically identify the preferred WOB for a given set of conditions. This research focused on implementing and evaluating two low WOB drilling technologies for microhole drilling: - Laser-assisted mechanical drill, which was tested in the laboratory - Lightly modified commercial off-the-shelf (COTS) percussive hammer, which was tested in a limited field test. Data were collected for microhole GSS using WOB optimization via simulation as well as at the Blue Canyon Dome Site in Socorro, NM. Information on the attached files and folders are as follows: - the .tdms files are LabView data files, which can be opened within Excel using a .tdms add-in or using a Matlab .tdms converter - the .tdms_index files are part of the .tdms file structure - sampling rate, column headers, and length data within the .tdms files follow SOP when utilizing Excel and/or Matlab as described above

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Low-depth Clifford circuits approximately solve MaxCut

We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an N -vertex graph by building a depth O ( N ) Clifford circuit. The algorithm has runtime complexity O ( N 2 ) and O ( N 3 ) for sparse and dense graphs, respectively, and space complexity O ( N 2 ) , with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to ∼ 94 % of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW. Published by the American Physical Society 2024

Muñoz-Arias, Manuel H. (ORCID:000000025711029X)↗

DOE OSTI2020

CLUE: A Fast Parallel Clustering Algorithm for High Granularity Calorimeters in High-Energy Physics

One of the challenges of high granularity calorimeters, such as that to be built to cover the endcap region in the CMS Phase-2 Upgrade for HL-LHC, is that the large number of channels causes a surge in the computing load when clustering numerous digitized energy deposits (hits) in the reconstruction stage. In this article, we propose a fast and fully parallelizable density-based clustering algorithm, optimized for high-occupancy scenarios, where the number of clusters is much larger than the average number of hits in a cluster. The algorithm uses a grid spatial index for fast querying of neighbors and its timing scales linearly with the number of hits within the range considered. We also show a comparison of the performance on CPU and GPU implementations, demonstrating the power of algorithmic parallelization in the coming era of heterogeneous computing in high-energy physics.

Rovere, Marco↗

DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗

DOE OSTI2023

Accelerating gradient descent and Adam via fractional gradients

Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

A parameter optimization approach to controller partitioning for integrated flight/propulsion control application

A parameter optimization framework is presented to solve the problem of partitioning a centralized controller into a decentralized hierarchical structure suitable for integrated flight/propulsion control implementation. The controller partitioning problem is briefly discussed and a cost function to be minimized is formulated, such that the resulting 'optimal' partitioned subsystem controllers will closely match the performance (including robustness) properties of the closed-loop system with the centralized controller while maintaining the desired controller partitioning structure. The cost function is written in terms of parameters in a state-space representation of the partitioned sub-controllers. Analytical expressions are obtained for the gradient of this cost function with respect to parameters, and an optimization algorithm is developed using modern computer-aided control design and analysis software. The capabilities of the algorithm are demonstrated by application to partitioned integrated flight/propulsion control design for a modern fighter aircraft in the short approach to landing task. The partitioning optimization is shown to lead to reduced-order subcontrollers that match the closed-loop command tracking and decoupling performance achieved by a high-order centralized controller.

Schmidt, Phillip↗

NASA NTRS1993

A parameter optimization approach to controller partitioning for integrated flight/propulsion control application

Schmidt, Phillip H.↗