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DOE OSTI2022

Real-Time Optimization Workflow Status Update

Economically optimal and safe operation of integrated energy systems (IES) requires optimization at many different time scales. A real-time optimization (RTO) workflow will attempt to maximize revenue and minimize operational costs on a time scale of minutes to hours. Such a workflow requires the use of a digital twin (DT), which is a virtual representation of a physical system. The DT is updated using real-time data from the physical system, and serves as a model in an optimization framework. The optimization results are then sent back to the physical system to complete the loop. This report details the progress made in developing building blocks for a DT/RTO framework. The Risk Analysis Virtual Environment (RAVEN) platform within the Framework for Optimization of Resources and Economics (FORCE) tool suite can perform many of the tasks required for building a DT and performing RTO. The first item of this report details RAVEN enhancements that enable RAVEN workflows to be run in various environments. Data communication between the physical system and its DT is essential for successful RTO. This includes preprocessing real-time data, loading data into a data warehouse, and querying the stored data. The second section of this report describes the progress made in implementing an adapter in Python in order for Deep Lynx to handle the data communication. Typical dispatch optimization frameworks are built on linear programming (LP). The prototype RTO workflow developed in this report uses an LP problem as a part of a receding-horizon- or economic model predictive control (EMPC) based optimization. The third section of this report details the framework of an RTO workflow in which the system consists of a simple electrical storage device. A DT can be built from a reduced-order model (ROM). Integrating a ROM into a typical LP optimization framework has been challenging because most optimization packages require the user to write algebraic expressions for the system model. The final section of this report shows how an externally built RAVEN ROM can be integrated in an RTO framework by using the Python package Pyomo. This demonstrates the RTO workflow capability from a software-only perspective and is an important step in demonstrating the capability to implement an RTO workflow for a physical system.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2002

Initial Mechanical Testing of Superalloy Lattice Block Structures Conducted

The first mechanical tests of superalloy lattice block structures produced promising results for this exciting new lightweight material system. The testing was performed in-house at NASA Glenn Research Center's Structural Benchmark Test Facility, where small subelement-sized compression and beam specimens were loaded to observe elastic and plastic behavior, component strength levels, and fatigue resistance for hundreds of thousands of load cycles. Current lattice block construction produces a flat panel composed of thin ligaments arranged in a three-dimensional triangulated trusslike structure. Investment casting of lattice block panels has been developed and greatly expands opportunities for using this unique architecture in today's high-performance structures. In addition, advances made in NASA's Ultra-Efficient Engine Technology Program have extended the lattice block concept to superalloy materials. After a series of casting iterations, the nickel-based superalloy Inconel 718 (IN 718, Inco Alloys International, Inc., Huntington, WV) was successfully cast into lattice block panels; this combination offers light weight combined with high strength, high stiffness, and elevated-temperature durability. For tests to evaluate casting quality and configuration merit, small structural compression and bend test specimens were machined from the 5- by 12- by 0.5-in. panels. Linear elastic finite element analyses were completed for several specimen layouts to predict material stresses and deflections under proposed test conditions. The structural specimens were then subjected to room-temperature static and cyclic loads in Glenn's Life Prediction Branch's material test machine. Surprisingly, the test results exceeded analytical predictions: plastic strains greater than 5 percent were obtained, and fatigue lives did not depreciate relative to the base material. These assets were due to the formation of plastic hinges and the redundancies inherent in lattice block construction, which were not considered in the simplified computer models. The fatigue testing proved the value of redundancies since specimen strength was maintained even after the fracture of one or two ligaments. This ongoing test program is planned to continue through high-temperature testing. Also scheduled for testing are IN 718 lattice block panels with integral face sheets, as well as specimens cast from a higher temperature alloy. The initial testing suggests the value of this technology for large panels under low and moderate pressure loadings and for high-risk, damage-tolerant structures. Potential aeropropulsion uses for lattice blocks include turbine-engine actuated panels, exhaust nozzle flaps, and side panel structures.

Krause, David L.↗

DOE OSTI2024

4-Clique network minor embedding for quantum annealers

Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1993

Test results from large wing and fuselage panels

This paper presents the first results in an assessment of the strength, stiffness, and damage tolerance of stiffened wing and fuselage subcomponents. Under this NASA funded program, 10 large wing and fuselage panels, variously fabricated by automated tow placement and dry-stitched preform/resin transfer molding, are to be tested. The first test of an automated tow placement six-longeron fuselage panel under shear load was completed successfully. Using NASTRAN finite-element analysis the stiffness of the panel in the linear range prior to buckling was predicted within 3.5 percent. A nonlinear analysis predicted the buckling load within 10 percent and final failure load within 6 percent. The first test of a resin transfer molding six-stringer wing panel under compression was also completed. The panel failed unexpectedly in buckling because of inadequate supporting structure. The average strain was 0.43 percent with a line load of 20.3 kips per inch of width. This strain still exceeds the design allowable strains. Also, the stringers did not debond before failure, which is in contrast to the general behavior of unstitched panels.

Madan, Ram C.↗

NASA NTRS1996

Application of Optimization Techniques to Design of Unconventional Rocket Nozzle Configurations

Several current rocket engine concepts such as the bell-annular tri-propellant engine, and the linear aerospike being proposed for the X-33 require unconventional three dimensional rocket nozzles which must conform to rectangular or sector shaped envelopes to meet integration constraints. These types of nozzles exist outside the current experience database, therefore, the application of efficient design methods for these propulsion concepts is critical to the success of launch vehicle programs. The objective of this work is to optimize several different nozzle configurations, including two- and three-dimensional geometries. Methodology includes coupling computational fluid dynamic (CFD) analysis to genetic algorithms and Taguchi methods as well as implementation of a streamline tracing technique. Results of applications are shown for several geometeries including: three dimensional thruster nozzles with round or super elliptic throats and rectangualar exits, two- and three-dimensional thrusters installed within a bell nozzle, and three dimensional thrusters with round throats and sector shaped exits. Due to the novel designs considered for this study, there is little experience which can be used to guide the effort and limit the design space. With a nearly infinite parameter space to explore, simple parametric design studies cannot possibly search the entire design space within the time frame required to impact the design cycle. For this reason, robust and efficient optimization methods are required to explore and exploit the design space to achieve high performance engine designs. Five case studies which examine the application of various techniques in the engineering environment are presented in this paper.

Follett, W.↗

DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

NASA NTRS1996

Optimization Methodology for Unconventional Rocket Nozzle Design

Several current rocket engine concepts such as the bell-annular tripropellant engine, and the linear aerospike being proposed for the X-33, require unconventional three-dimensional rocket nozzles which must conform to rectangular or sector-shaped envelopes to meet integration constraints. These types of nozzles exist outside the current experience database, therefore, development of efficient design methods for these propulsion concepts is critical to the success of launch vehicle programs. Several approaches for optimizing rocket nozzles, including streamline tracing techniques, and the coupling of CFD analysis to optimization algorithms are described. The relative strengths and weaknesses of four classes of optimization algorithms are discussed: Gradient based methods, genetic algorithms, simplex methods, and surface response methods. Additionally, a streamline tracing technique, which provides a very computationally efficient means of defining a three-dimensional contour, is discussed. The performance of the various optimization methods on thrust optimization problems for tripropellant and aerospike concepts is assessed and recommendations are made for future development efforts.

Follett, W.↗

NASA NTRS1997

Fast Context Switching in Real-Time Propositional Reasoning

The trend to increasingly capable and affordable control processors has generated an explosion of embedded real-time gadgets that serve almost every function imaginable. The daunting task of programming these gadgets is greatly alleviated with real-time deductive engines that perform all execution and monitoring functions from a single core model, Fast response times are achieved using an incremental propositional deductive database (an LTMS). Ideally the cost of an LTMS's incremental update should be linear in the number of labels that change between successive contexts. Unfortunately an LTMS can expend a significant percentage of its time working on labels that remain constant between contexts. This is caused by the LTMS's conservative approach: a context switch first removes all consequences of deleted clauses, whether or not those consequences hold in the new context. This paper presents a more aggressive incremental TMS, called the ITMS, that avoids processing a significant number of these consequences that are unchanged. Our empirical evaluation for spacecraft control shows that the overhead of processing unchanged consequences can be reduced by a factor of seven.

Nayak, P. Pandurang↗

NASA NTRS2007

Generative Representations for Automated Design of Robots

A method of automated design of complex, modular robots involves an evolutionary process in which generative representations of designs are used. The term generative representations as used here signifies, loosely, representations that consist of or include algorithms, computer programs, and the like, wherein encoded designs can reuse elements of their encoding and thereby evolve toward greater complexity. Automated design of robots through synthetic evolutionary processes has already been demonstrated, but it is not clear whether genetically inspired search algorithms can yield designs that are sufficiently complex for practical engineering. The ultimate success of such algorithms as tools for automation of design depends on the scaling properties of representations of designs. A nongenerative representation (one in which each element of the encoded design is used at most once in translating to the design) scales linearly with the number of elements. Search algorithms that use nongenerative representations quickly become intractable (search times vary approximately exponentially with numbers of design elements), and thus are not amenable to scaling to complex designs. Generative representations are compact representations and were devised as means to circumvent the above-mentioned fundamental restriction on scalability. In the present method, a robot is defined by a compact programmatic form (its generative representation) and the evolutionary variation takes place on this form. The evolutionary process is an iterative one, wherein each cycle consists of the following steps: 1. Generative representations are generated in an evolutionary subprocess. 2. Each generative representation is a program that, when compiled, produces an assembly procedure. 3. In a computational simulation, a constructor executes an assembly procedure to generate a robot. 4. A physical-simulation program tests the performance of a simulated constructed robot, evaluating the performance according to a fitness criterion to yield a figure of merit that is fed back into the evolutionary subprocess of the next iteration. In comparison with prior approaches to automated evolutionary design of robots, the use of generative representations offers two advantages: First, a generative representation enables the reuse of components in regular and hierarchical ways and thereby serves a systematic means of creating more complex modules out of simpler ones. Second, the evolved generative representation may capture intrinsic properties of the design problem, so that variations in the representations move through the design space more effectively than do equivalent variations in a nongenerative representation. This method has been demonstrated by using it to design some robots that move, variously, by walking, rolling, or sliding. Some of the robots were built (see figure). Although these robots are very simple, in comparison with robots designed by humans, their structures are more regular, modular, hierarchical, and complex than are those of evolved designs of comparable functionality synthesized by use of nongenerative representations.

Homby, Gregory S.↗

NASA NTRS1977

Some MACSYMA program for solving difference equations

A set of MACSYMA programs are described for finding closed form solutions to linear recurrence relations in equations having either constant or variable coefficients. In the homogenous case, a polymonial equation is obtained and the solution to the recurrence relation can be written as a linear combination of the roots of the polynomial. Exponential generating functions are used to solve variable coefficient relations. Taking successive derivatives and using the recurrence relation, an ordinary differential equation is obtained. Expanding the solution to the differential equation in a Taylor series, shows that the nth term of the series is the solution to the recurrence relation. For second order recurrences, a check is made for those that can be solved in terms of Bessel functions.

Ivie, J.↗

NASA NTRS2005

Integration of an Autopilot for a Micro Air Vehicle

Two autopilots providing autonomous flight capabilities are presented herein. The first is the Pico-Pilot, demonstrated for the 12-inch size class of micro air vehicles. The second is the MicroPilot MP2028(sup g), where its integration into a 36-inch Zagi airframe (tailless, elevons only configuration) is investigated and is the main focus of the report. Analytical methods, which include the use of the Advanced Aircraft Analysis software from DARCorp, were used to determine the stability and control derivatives, which were then validated through wind tunnel experiments. From the aerodynamic data, the linear, perturbed equations of motion from steady-state flight conditions may be cast in terms of these derivatives. Using these linear equations, transfer functions for the control and navigation systems were developed and feedback control laws based on Proportional, Integral, and Derivative (PID) control design were developed to control the aircraft. The PID gains may then be programmed into the autopilot software and uploaded to the microprocessor of the autopilot. The Pico-Pilot system was flight tested and shown to be successful in navigating a 12-inch MAV through a course defined by a number of waypoints with a high degree of accuracy, and in 20 mph winds. The system, though, showed problems with control authority in the roll and pitch motion of the aircraft: causing oscillations in these directions, but the aircraft maintained its heading while following the prescribed course. Flight tests were performed in remote control mode to evaluate handling, adjust trim, and test data logging for the Zagi with integrated MP2028(sup g). Ground testing was performed to test GPS acquisition, data logging, and control response in autonomous mode. Technical difficulties and integration limitations with the autopilot prevented fully autonomous flight from taking place, but the integration methodologies developed for this autopilot are, in general, applicable for unmanned air vehicles within the 36-inch size class or larger that use a PID control based autopilot.

Platanitis, George↗

NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗

NASA NTRS2019

Flat-H Redundant Frangible Joint Design Evolution 2018: Feasibility Study Conclusions

This paper reports results of an investigation into developing a single failure tolerant pyrotechnic linear separation system which features completely redundant explosive trains suitable for human spaceflight. It is a follow up to “Flat-H Redundant Frangible Joint Design Evolution 2017” and “Flat-H Redundant Frangible Joint Evolution”. The paper chronicles the history of the redundant frangible joint development program including testing, analysis, and design improvements from 2014 to the present culminating in a successful proof-of-concept prototype. The paper describes work done to address debris control and containment of combustion products. A performance optimization strategy is presented along with optimization results. Additionally a novel containment manifold design is presented with test results.

Structures↗

NASA NTRS2002

System IDentification Programs for AirCraft (SIDPAC)

A collection of computer programs for aircraft system identification is described and demonstrated. The programs, collectively called System IDentification Programs for AirCraft, or SIDPAC, were developed in MATLAB as m-file functions. SIDPAC has been used successfully at NASA Langley Research Center with data from many different flight test programs and wind tunnel experiments. SIDPAC includes routines for experiment design, data conditioning, data compatibility analysis, model structure determination, equation-error and output-error parameter estimation in both the time and frequency domains, real-time and recursive parameter estimation, low order equivalent system identification, estimated parameter error calculation, linear and nonlinear simulation, plotting, and 3-D visualization. An overview of SIDPAC capabilities is provided, along with a demonstration of the use of SIDPAC with real flight test data from the NASA Glenn Twin Otter aircraft. The SIDPAC software is available without charge to U.S. citizens by request to the author, contingent on the requestor completing a NASA software usage agreement.

Morelli, Eugene A.↗

NASA NTRS1992

Simulation and model reduction for the AFW program

The simulation methodology used in the Active Flexible Wing wind-tunnel test program is described. An overview of the aeroservoelastic modeling used in building the required batch and hot-bench simulations is presented. Successful hot-bench implementation required that the full mathematical model be significantly reduced while assuring that accuracy be maintained for all combinations of 10 inputs and 56 outputs. The reduction was accomplished by using a method based on internally balanced realizations and focussing on the linear, aeroelastic portion of the full mathematical model. The error-bound properties of the internally balanced realization significantly contribute to its utility in the model reduction process. The reduction method and the results achieved are described.

Buttrill, Carey↗

NASA NTRS1997

Applications of Data Assimilation to Analysis of the Ocean on Large Scales

It is commonplace to begin talks on this topic by noting that oceanographic data are too scarce and sparse to provide complete initial and boundary conditions for large-scale ocean models. Even considering the availability of remotely-sensed data such as radar altimetry from the TOPEX and ERS-1 satellites, a glance at a map of available subsurface data should convince most observers that this is still the case. Data are still too sparse for comprehensive treatment of interannual to interdecadal climate change through the use of models, since the new data sets have not been around for very long. In view of the dearth of data, we must note that the overall picture is changing rapidly. Recently, there have been a number of large scale ocean analysis and prediction efforts, some of which now run on an operational or at least quasi-operational basis, most notably the model based analyses of the tropical oceans. These programs are modeled on numerical weather prediction. Aside from the success of the global tide models, assimilation of data in the tropics, in support of prediction and analysis of seasonal to interannual climate change, is probably the area of large scale ocean modeling and data assimilation in which the most progress has been made. Climate change is a problem which is particularly suited to advanced data assimilation methods. Linear models are useful, and the linear theory can be exploited. For the most part, the data are sufficiently sparse that implementation of advanced methods is worthwhile. As an example of a large scale data assimilation experiment with a recent extensive data set, we present results of a tropical ocean experiment in which the Kalman filter was used to assimilate three years of altimetric data from Geosat into a coarsely resolved linearized long wave shallow water model. Since nonlinear processes dominate the local dynamic signal outside the tropics, subsurface dynamical quantities cannot be reliably inferred from surface height anomalies. Because of its potential for large scale synoptic coverage of the deep ocean, acoustic travel time data should be a natural complement to satellite altimetry. Satellite data give us vertical integrals associated with thermodynamic and dynamic processes.

Miller, Robert N.↗

NASA NTRS2010

Incorporating Active Runway Crossings in Airport Departure Scheduling

A mixed integer linear program is presented for deterministically scheduling departure and ar rival aircraft at airport runways. This method addresses different schemes of managing the departure queuing area by treating it as first-in-first-out queues or as a simple par king area where any available aircraft can take-off ir respective of its relative sequence with others. In addition, this method explicitly considers separation criteria between successive aircraft and also incorporates an optional prioritization scheme using time windows. Multiple objectives pertaining to throughput and system delay are used independently. Results indicate improvement over a basic first-come-first-serve rule in both system delay and throughput. Minimizing system delay results in small deviations from optimal throughput, whereas minimizing throughput results in large deviations in system delay. Enhancements for computational efficiency are also presented in the form of reformulating certain constraints and defining additional inequalities for better bounds.

Gupta, Gautam↗

NASA NTRS1961

Methods for Determining Blood Flow Through Intact Vessels of Experimental Animals Under Conditions of Gravitational Stress and in Extraterrestrial Space Capsules

Work during the initial six months of this program has proceeded along three lines: (1) technical development of blood flowmeter instrumentation: (2) surgical considerations related to special problems of chronic implantation of flowmeter probes: (3) study of the relationship between levels of blood flow and organ activity. Principal engineering effort has been focused on the fundamental phenomena operative in the flowmeter probe and on probe design. Two probes have been constructed and a third is nearing completion. A previously unrecognized source of zero drift has been discovered and corrected. has been designed, assembled, tested and successfully employed in work on the several probes. A significant innovation which has been introduced is the use of a transformer coupled input for suppression of unwanted common mode signals. New low noise transistor amplifiers with characteristics suitable for space vehicle packaging are being developed. Linearity of the present apparatus has been found to extend at least into the near turbulent flow region. Attention has been directed to the two vascular beds of physiologic interest that present particular problems with regard to chronic implantation of flowmeter probes, the myocardium and the liver. Surgical techniques have been perfected that will permit myocardial and liver blood flow measurement. Two groups of animals have successfully undergone surgery and await the implantation of probes. Studies of the relationship between organ blood flow and levels of physiologic activity have been initiated. The first organ system studied was the heart, For the first time autoregulatory mechanisms have been demonstrated within the myocardial vascular bed which rapidly and precisely maintain coronary blood flow at a level i n keeping with the magnitude of cardiac work, Following a summary statement of the status of the program, the work performed is described, A financial review of expenditures incurred and a proposal for future funding are appended,

Shaw, R. F.↗