An application of linear programming to minimum fuel optimal control
Application of linear programming to minimum fuel optimal control
OPTIMAL CONTROL↗
SEARCH · Engineering Papers
Results for “program optimizations”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Two-dimensional inverse planning and delivery with a preclinical image guided microirradiator
Purpose: Recent advances in preclinical radiotherapy systems have provided the foundation for scaling many of the elements of clinical radiation therapy practice to the dimensions and energy demanded in small animal studies. Such systems support the technical capabilities to accurately deliver highly complex dose distributions, but methods to optimize and deliver such distributions remain in their infancy. This study developed an optimization method based on empirically measured two-dimensional dose kernel measurements to deliver arbitrary planar dose distributions on a recently developed small animal radiotherapy platform.Methods: A two-dimensional dose kernel was measured with repeated radiochromic film measurements for the circular 1 mm diameter fixed collimator of the small animal radiotherapy system at 1 cm depth in a solid water phantom. This kernel was utilized in a sequential quadratic programming optimization framework to determine optimal beam positions and weights to deliver an arbitrary desired dose distribution. The positions and weights were then translated to a set of stage motions to automatically deliver the optimized dose distribution. End-to-end efficacy of the framework was quantified through five repeated deliveries of two dosimetric challenges: (1) a 5 mm radius bullseye distribution, and (2) a “sock” distribution contained within a 9 × 13 mm bounding box incorporating rectangular, semicircular, and exponentially decaying geometric constructs and a rectangular linear dose gradient region. These two challenges were designed to gauge targeting, geometric, and dosimetric fidelity.Results: Optimization of the bullseye and sock distributions required 2.1 and 5.9 min and utilized 50 and 77 individual beams for delivery, respectively. Automated delivery of the resulting optimized distributions, validated using radiochromic film measurements, revealed an average targeting accuracy of 0.32 mm, and a dosimetric delivery error along four line profiles taken through the sock distribution of 3.9%. Mean absolute delivery error across the 0–1 Gy linear dose gradient over 7.5 mm was 0.01 Gy.Conclusions: The work presented here demonstrates the potential for complex dose distributions to be planned and automatically delivered with millimeter scale heterogeneity at submillimeter accuracy. This capability establishes the technical foundation for preclinical validation of biologically guided radiotherapy investigations and development of unique radiobiological experiments.
61 RADIATION PROTECTION AND DOSIMETRY↗
Feasibility Study for Electrical Discharge Machining of Large DU-Mo Castings
U-10 wt. % Mo (U-10Mo) alloys are being developed as low enrichment monolithic fuel for the CONVERT program. Optimization of processing for the monolithic fuel is being pursued with the use of electrical discharge machining (EDM) under CONVERT HPRR WBS 1.2.4.5 Optimization of Coupon Preparation. The process is applicable to manufacturing experimental fuel plate specimens for the Mini-Plate-1 (MP-1) irradiation campaign. The benefits of EDM are reduced machining costs, ability to achieve higher tolerances, stress-free, burr-free surfaces eliminating the need for milling, and the ability to machine complex shapes. Kerf losses are much smaller with EDM (tenths of mm) compared to conventional machining (mm). Reliable repeatability is achievable with EDM due to its computer-generated machining programs.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Improved method for transonic airfoil design-by-optimization
An improved method for use of optimization techniques in transonic airfoil design is demonstrated. FLO6QNM incorporates a modified quasi-Newton optimization package, and is shown to be more reliable and efficient than the method developed previously at NASA-Ames, which used the COPES/CONMIN optimization program. The design codes are compared on a series of test cases with known solutions, and the effects of problem scaling, proximity of initial point to solution, and objective function precision are studied. In contrast to the older method, well-converged solutions are shown to be attainable in the context of engineering design using computational fluid dynamics tools, a new result. The improvements are due to better performance by the optimization routine and to the use of problem-adaptive finite difference step sizes for gradient evaluation.
Kennelly, R. A., Jr.↗
Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables
Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.
Fenyes, Peter A.↗
An adaptive guidance algorithm for an aerodynamically assisted orbital plane change maneuver
Using analysis results from the post trajectory optimization program, an adaptive guidance algorithm is developed to compensate for density, aerodynamic and thrust perturbations during an atmospheric orbital plane change maneuver. The maneuver offers increased mission flexibility along with potential fuel savings for future reentry vehicles. Although designed to guide a proposed NASA Entry Research Vehicle, the algorithm is sufficiently generic for a range of future entry vehicles. The plane change analysis provides insight suggesting a straight-forward algorithm based on an optimized nominal command profile. Bank angle, angle of attack, and engine thrust level, ignition and cutoff times are modulated to adjust the vehicle's trajectory to achieve the desired end-conditions. A performance evaluation of the scheme demonstrates a capability to guide to within 0.05 degrees of the desired plane change and five nautical miles of the desired apogee altitude while maintaining heating constraints. The algorithm is tested under off-nominal conditions of + or -30% density biases, two density profile models, + or -15% aerodynamic uncertainty, and a 33% thrust loss and for various combinations of these conditions.
Blissit, J. A.↗
Preliminary Sizing Study of Ares-I and Ares-V Liquid Hydrogen Tanks
A preliminary sizing study of two cryogenic propellant tanks was performed using a FORTRAN optimization program to determine weight efficient orthogrid designs for the tank barrels sections only. Various tensile and compressive failure modes were considered, including general buckling of cylinders with a shell buckling knockdown factor. Eight independent combinations of three design requirements were also considered and their effects on the tanks weight. The approach was to investigate each design case with a variable shell buckling knockdown factor, determining the most weight efficient combination of orthogrid design parameters. Numerous optimization analyses were performed, and the results presented herein compare the effects of the different design requirements and shell buckling knockdown factor. Through a series of comparisons between design requirements or shell buckling knockdown factors, the relative change in overall tank barrel weights is shown. The findings indicate that the design requirements can substantually increase the tank weight while a less conservative shell buckling knockdown factor can modestly reduce the tank weight.
Oliver, Stanley T.↗
INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization
It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some NP -hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.
Groër, Christopher S.↗
Combined strength and aeroelastic wing synthesis via constraint approximation
A numerical optimization program using constraint approximations for preliminary sizing of wing structural design parameters to satisfy simultaneous strength and aeroelastic requirements is described. The effects of wing flexibility on loads and flutter are included. The iterative procedure approximates wing internal load distributions and flutter response in generating design constraints. Though a linear Taylor series approximation to the variation of flutter speed is made, constraints in general are formulated as nonlinear and solved in a minimum weight problem using a feasible directions search. The technique is demonstrated for the determination of the optimal ply orientations and for simultaneous sizing for strength and flutter with simple constraint approximations.
Mullen, J., Jr.↗
An integrated approach to the optimum design of actively controlled composite wings
The importance of interactions among the various disciplines in airplane wing design has been recognized for quite some time. With the introduction of high gain, high authority control systems and the design of thin, flexible, lightweight composite wings, the integrated treatment of control systems, flight mechanics and dynamic aeroelasticity became a necessity. A research program is underway now aimed at extending structural synthesis concepts and methods to the integrated synthesis of lifting surfaces, spanning the disciplines of structures, aerodynamics and control for both analysis and design. Mathematical modeling techniques are carefully selected to be accurate enough for preliminary design purposes of the complicated, built-up lifting surfaces of real aircraft with their multiple design criteria and tight constraints. The presentation opens with some observations on the multidisciplinary nature of wing design. A brief review of some available state of the art practical wing optimization programs and a brief review of current research effort in the field serve to illuminate the motivation and support the direction taken in our research. The goals of this research effort are presented, followed by a description of the analysis and behavior sensitivity techniques used. The presentation concludes with a status report and some forecast of upcoming progress.
Livne, E.↗
Optimal partitioning of random programs across two processors
The optimal partitioning of random distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false.
Nicol, D. M.↗
Large scale structural synthesis
A general purpose optimization program is coupled to a large scale finite element program to provide an efficient tool for structural synthesis. The resulting interface program may be used to design structures for minimum weight, subject to constraints on stress, displacement, and vibration frequencies. A variety of state-of-the-art techniques are employed, including design variable linking, constraint deletion, reciprocal variables, and formal approximations. The capability is demonstrated with the design of a gear housing using 30 design variables and over 5000 nonlinear inequality constraints. The finite element model consists of over 1600 elements and 7000 displacement degrees of freedom. The design required six detailed finite element analyses and approximately one hour on a Cray-1s supercomputer. It is concluded that structures of practical size and complexity can be efficiently designed using numerical optimization.
Vanderplaats, G. N.↗
FINAL SCIENTIFIC/TECHNICAL REPORT: Dry Solids Pump - Coal Feed Technologies
Gas Technology Institute (GTI) has concluded the Dry Solids Pump Coal - Feed Technologies (DSP-CFT) program that was initiated on October 1, 2013. The project’s primary objectives have been to gather data to increase the fidelity of the economic benefits of the Dry Solids Pump (DSP) technology for Integrated Gasification Combined Cycle (IGCC) plants, mature the technology to a Technology Readiness Level (TRL) of TRL 6 by continued testing and upgrades to the existing DSP, advance pump configuration knowledge to the point that a commercial pump can be confidently designed for low rank coal feed stocks and develop the next generation design configuration of a 1000 ton per day (tpd) DSP. After initial efforts with the existing DSP, a subscale pump was built to reduce the cost and time required to develop upgrades. The subscale development program evaluated three exit configurations and a host of geometric variations in each configuration concluding a side exit upward discharge configuration offered the greatest improvements. Both configuration and operation focused improvements were implemented on the full scale existing DSP and demonstrated 500 psi operation. An initial Techno-economic Analysis (TEA) and later update that was undertaken by Mr. Chris Higman and associates. The TEA quantifies the dramatic savings in capital and operational expenses achieved by reducing plant height and nitrogen consumption/compression, respectively in a commercial gasifier application. Drawings of the suggested design configuration for a commercial DSP feeder reflect the side exit design and incorporate lighter weight and lower cost fabrication methods. Features used for development testing are removed. A follow-on optimization program to allow the DSP technology to achieve TRL 7 is outlined.
01 COAL, LIGNITE, AND PEAT↗
Future Synchrotron Light Sources Based on Ultimate Storage Rings
The main purpose of this talk is to describe how far one might push the state of the art in storage ring design. The talk will start with an overview of the latest developments and advances in the design of synchrotron light sources based on the concept of an 'ultimate' storage ring. The review will establish how bright a ring based light source might be, where the frontier of technological challenges are, and what the limits of accelerator physics are. Emphasis will be given to possible improvements in accelerator design and developments in technology toward the goal of achieving an ultimate storage ring. An ultimate storage ring (USR), defined as an electron ring-based light source having an emittance in both transverse planes at the diffraction limit for the range of X-ray wavelengths of interest for a scientific community, would provide very high brightness photons having high transverse coherence that would extend the capabilities of X-ray imaging and probe techniques beyond today's performance. It would be a cost-effective, high-coherence 4th generation light source, competitive with one based on energy recovery linac (ERL) technology, serving a large number of users studying material, chemical, and biological sciences. Furthermore, because of the experience accumulated over many decades of ring operation, it would have the great advantage of stability and reliability. In this paper we consider the design of an USR having 10-pm-rad emittance. It is a tremendous challenge to design a storage ring having such an extremely low emittance, a factor of 100 smaller than those in existing light sources, especially such that it has adequate dynamic aperture and beam lifetime. In many ultra-low emittance designs, the injection acceptances are not large enough for accumulation of the electron beam, necessitating on-axis injection where stored electron bunches are completely replaced with newly injected ones. Recently, starting with the MAX-IV 7-bend achromatic cell, we have made significant progress with the design of PEP-X, a USR that would inhabit the decommissioned PEP-II tunnel at SLAC. The enlargement of the dynamic aperture is largely a result of the cancellations of the 4th-order resonances in the 3rd-order achromats and the effective use of lattice optimization programs. In this paper, we will show those cancellations of the 4th-order resonances using an analytical approach based on the exponential Lie operators and the Poisson brackets. Wherever possible, our analytical results will be compared with their numerical counterparts. Using the derived formulae, we will construct 4th-order geometric achromats and use them as modules for the lattice of the PEP-X USR, noting that only geometric terms are canceled to the 4th order.
43 PARTICLE ACCELERATORS↗
Scenario Complexity for Unmanned Aircraft System Traffic
This work introduces an approach to estimate the complexity of a low-altitude air traffic scenario involving multiple UASs using mathematical programming. Given a set of multi-point UAS flight trajectories, vehicle dynamics, and a conflict resolution algorithm, an abstract model is developed such that it can be solved quickly using a mathematical programming optimization software without running high-fidelity simulations that can be computationally expensive and may not suit real-time apA quick and accurate assessment of complexity for a given traffic scenario can help plan and schedule flights to alleviate traffic bottleneck and mitigate operation risks, especially for unmanned aerial system traffic management where high traffic density or complexity is expected. This work introduces a traffic scenario complexity metric that was constructed based on the number of potential conflicts weighted by the conflict resolution cost associated. The cost associated with a conflict is calculated based on the corresponding conflict resolution maneuvers. To obtain the conflict resolution maneuvers, a MILP-based optimization was formulated with the vehicle model and conflict management parameters incorporated. To evaluate the complexity metrics, an approach of using measurements from high-fidelity simulations was proposed. The scenario complexity measurements for 920 random-generated scenarios were obtained through high-fidelity simulations and treated as the ground truth. Two statistics methods: Pearson and Alternative Conditional Expectations were applied for analysis. The results showed that the number of flights has low correlation with the scenario complexity according to the correlation coefficients calculated by both methods. The Alternative Conditional Expectations method shows that the proposed scenario complexity metric has better correlation with the ground truth than the number of potential conflicts.plications. In the abstract model, each vehicle is represented by a time-varied vector associated with position, speed, and heading information. The total extra distance that aircraft need to divert from their original routes to avoid collisions is computed and used to setup a quadratic programming formula. The metrics including the number of conflicts and extra distances travelled by all vehicles are then utilized to estimate the complexity of a given UAS flight scenario. Results and verification against high-fidelity simulations will be provided in the final draft.
traffic complexity↗
Are coupled renewable-battery power plants more valuable than independently sited installations?
Coupled renewable-battery powerplants differ from the traditional concept of independent siting of electricity resources within transmission networks. Prior research on the value proposition and cost savings from coupling did not consider the geographic constraint of co-location. This paper fills the gap by assessing how pricing volatility differences between nodes within electricity markets impact the system value of coupled renewable-battery projects as compared to independent VRE and battery installations. We use wholesale power market prices from 2012–2019 across the seven main U.S. independent system operators (ISOs) with a linear optimization program to compare the electricity market value of coupled projects to the value of the same underlying sub-components, deployed separately. We find that additional value from adding a 4-hour battery sized to 50% of renewable-plant nameplate capacity is $\$$10/MWh across ISOs on average. The highest boost occurs in California ($\$$15/MWh), where the value of adding storage to solar rises over time in tandem with increased solar penetration in the region. If renewables and batteries are deployed independently, we estimate that $\$$12.5/MWh of additional value could be achieved because of more flexibility on battery siting and operation. The $\$$12.5/MWh coupling penalty is reduced to $\$$1.6/MWh when considering alternative approaches to integrating battery storage. This result implies that renewable-battery power plants will play an increasing role in electricity systems if they can be built for $\$$2–$\$$13/MWh less than independent projects of comparable size. However, the wide regional variation in coupling penalties, along with the importance of conditions captured in our sensitivity cases, suggests the tradeoff between coupling penalties and savings will vary by situation. Therefore, roles exist for independent and coupled projects from a system optimization perspective.
14 SOLAR ENERGY↗
Keep it short: Exploring the impacts of configuration choices on the recent economics of solar-plus-battery and wind-plus-battery hybrid energy plants
Coupled renewable-battery powerplants differ from the traditional concept of independent siting of electricity resources within transmission networks. Prior research on the value proposition and cost savings from coupling did not consider the geographic constraint of co-location. This paper fills the gap by assessing how pricing volatility differences between nodes within electricity markets impact the system value of coupled renewable-battery projects as compared to independent VRE and battery installations. We use wholesale power market prices from 2012–2019 across the seven main U.S. independent system operators (ISOs) with a linear optimization program to compare the electricity market value of coupled projects to the value of the same underlying sub-components, deployed separately. We find that additional value from adding a 4-hour battery sized to 50% of renewable-plant nameplate capacity is $\$10$/MWh across ISOs on average. The highest boost occurs in California ($\$15$/MWh), where the value of adding storage to solar rises over time in tandem with increased solar penetration in the region. If renewables and batteries are deployed independently, we estimate that $\$12.5$/MWh of additional value could be achieved because of more flexibility on battery siting and operation. The $\$12.5$/MWh coupling penalty is reduced to $\$1.6$/MWh when considering alternative approaches to integrating battery storage. This result implies that renewable-battery power plants will play an increasing role in electricity systems if they can be built for $\$2$–$\$13$/MWh less than independent projects of comparable size. However, the wide regional variation in coupling penalties, along with the importance of conditions captured in our sensitivity cases, suggests the tradeoff between coupling penalties and savings will vary by situation. Therefore, roles exist for independent and coupled projects from a system optimization perspective.
14 SOLAR ENERGY↗
Analytical Modeling of Cache Behavior for Affine Programs
Modern optimizing compiler design integrates program transformation strategies aimed at reducing data movement to/from main memory by exploiting the data cache hierarchy. But in reality, the effect of these transformations on the actual cache miss count is ignored in compilers due to the lack of precise compile-time models of misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, made possible by focusing on polyhedral programs with static control flow: instead of relying on costly simulation, this paper develops the first closed-form solution for exact modeling of misses in a set-associative cache hierarchy. It enabling simulation-less selection of program transformations at compile-time to optimize cache misses. A push-button tool implementing the approach is developed and used for extensive validation of the complete framework.
affine programs, cache modeling, set associativity↗