Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “global optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Framework for Multi Layer Control in Python (FMLC) v1.0

This package is developed as a backend for multi-layer and multi-time domain controller. One example are controller based on [Model Predictive Control] (MPC) where different modules with different time constants have to be coordinated to allow optimal control. In a simple example, the Weather Forecast must be acquired and processed, the MPC is computed, and finally the control is applied. All these modules typically run on the same time step (Time step: 5 minutes), but are different instances within the framework. The framework allows parallelization using the `multiprocessing` module. However, another real-time controller (Time step: 1 second) must be applied to react on instant system disturbances beyond the MPC time step. Last, a supervisory MPC controller (Time step: 1 hour) might be added to ensure global optimality.

Gehbauer, Christoph↗

Optimal self-healing strategy for microgrid islanding

Renewable resource based microgrids provide reliable and cost-effective electricity with low carbon emissions. The flexibility of operating in grid-connected or islanded modes enables a microgrid to serve loads reliably. In the case of unexpected events happening to the main grid, the microgrid will isolate itself and operate in islanded mode to prevent any adversary impacts. The availability of renewable generation in the microgrid has significant impacts on the islanding strategy and different scenarios need to be considered. This study proposes a comprehensive microgrid self-healing strategy under different circumstances. The proposed strategy encompasses generation re-dispatch, network reconfiguration, and load shedding. The microgrid self-healing problem is formulated as a mixed-integer quadratic programming problem, which provides a globally optimal solution to facilitate smooth islanding of the microgrid. A modified Consortium for Electric Reliability Technology Solutions microgrid is used to conduct simulation under various scenarios. The simulation results demonstrate the efficiency of the proposed self-healing strategy in minimising costs of load shedding and generation with optimal switching actions.

optimal self-healing strategy↗

Optimal Power Flow of Radial Networks and Its Variations: A Sequential Convex Optimization Approach

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.

bi-objective optimization↗

Investigating the solid-liquid phase transition of water nanofilms using the generalized replica exchange method

The generalized Replica Exchange Method (gREM) was applied to study a solid-liquid phase transition in a nanoconfined bilayer water system using the monatomic water (mW) model. Exploiting optimally designed non-Boltzmann sampling weights with replica exchanges, gREM enables an effective sampling of configurations that are metastable or unstable in the canonical ensemble via successive unimodal energy distributions across phase transition regions, often characterized by S-loop or backbending in the statistical temperature. Extensive gREM simulations combined with Statistical Temperature Weighted Histogram Analysis Method (ST-WHAM) for nanoconfined mW water at various densities provide a comprehensive characterization of diverse thermodynamic and structural properties intrinsic to phase transitions. Graph representation of minimized structures of bilayer water systems determined by the basin-hopping global optimization revealed heterogeneous ice structures composed of pentagons, hexagons, and heptagons, consistent with an increasingly ordered solid phase with decreasing density. Apparent crossover from a first-order solid-liquid transition to a continuous one in nanoconfined mW water with increasing density of the system was observed in terms of a diminishing S-loop in the statistical temperature, smooth variation of internal energies and heat capacities, and a characteristic variation of lateral radial distribution functions, and transverse density profiles across transition regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R 2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

54 ENVIRONMENTAL SCIENCES↗

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

ground stations↗

Power Split Supercharging: A Mild Hybrid Approach to Boost Fuel Economy

This work investigates an innovative low-voltage (<60 V) hybrid device that enables engine boosting and downsizing in addition to mild hybrid functionalities such as regenerative braking, start-stop, and torque assist. A planetary gear set and a brake permit the power split supercharger (PSS) to share a 9 kW motor between supercharging the engine and direct torque supply to the crankshaft. In contrast, most e-boosting schemes use two separate motors for these two functionalities. This single motor structure restricts the PSS operation to only one of the supercharging or parallel hybrid modes; therefore, an optimized decision making strategy is necessary to select both the device mode and its power split ratio. An adaptive equivalent consumption minimization strategy (A-ECMS), which uses the battery state of charge (SoC) history to adjust the equivalence factor, is developed for energy management of the PSS. The A-ECMS effectiveness is compared against a dynamic programming (DP) solution with full drive cycle preview through hardware-in-the-loop experiments on an engine dynamometer testbed. The experiments show that the PSS with A-ECMS reduces vehicle fuel consumption by 18.4% over standard FTP75 cycle, compared to a baseline turbocharged engine, while global optimal DP solution decreases the fuel consumption by 22.8% compared to the baseline.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗

Enabling Long-range Exploration in Minimization of Multimodal Functions

We consider the problem of minimizing multi-modal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss’s landscape in black-box optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea of DGS is to conducts 1D long-range exploration with a large smoothing radius along d orthogonal directions in Rd, each of which defines a nonlocal directional derivative as a 1D integral. Such long-range exploration enables the nonlocal gradient to skip small local minima. The d directional derivatives are then assembled to form the nonlocal gradient. We use the Gauss-Hermite quadrature rule to approximate the d 1D integrals to obtain an accurate estimator. The superior performance of our method is demonstrated in three sets of examples, including benchmark functions for global optimization, and two real-world scientific problems.

Zhang, Jiaxin↗

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗

SU-F-T-256: 4D IMRT Planning Using An Early Prototype GPU-Enabled Eclipse Workstation

Purpose: True 4D IMRT planning, based on simultaneous spatiotemporal optimization has been shown to significantly improve plan quality in lung radiotherapy. However, the high computational complexity associated with such planning represents a significant barrier to widespread clinical deployment. We introduce an early prototype GPU-enabled Eclipse workstation for inverse planning. To our knowledge, this is the first GPUintegrated Eclipse system demonstrating the potential for clinical translation of GPU computing on a major commercially-available TPS. Methods: The prototype system comprised of four NVIDIA Tesla K80 GPUs, with a maximum processing capability of 8.5 Tflops per K80 card. The system architecture consisted of three key modules: (i) a GPU-based inverse planning module using a highly-parallelizable, swarm intelligence-based global optimization algorithm, (ii) a GPU-based open-source b-spline deformable image registration module, Elastix, and (iii) a CUDA-based data management module. For evaluation, aperture fluence weights in an IMRT plan were optimized over 9 beams,166 apertures and 10 respiratory phases (14940 variables) for a lung cancer case (GTV = 95 cc, right lower lobe, 15 mm cranio-caudal motion). Sensitivity of the planning time and memory expense to parameter variations was quantified. Results: GPU-based inverse planning was significantly accelerated compared to its CPU counterpart (36 vs 488 min, for 10 phases, 10 search agents and 10 iterations). The optimized IMRT plan significantly improved OAR sparing compared to the original internal target volume (ITV)-based clinical plan, while maintaining prescribed tumor coverage. The dose-sparing improvements were: Esophagus Dmax 50%, Heart Dmax 42% and Spinal cord Dmax 25%. Conclusion: Our early prototype system demonstrates that through massive parallelization, computationally intense tasks such as 4D treatment planning can be accomplished in clinically feasible timeframes. With further optimization, such systems are expected to enable the eventual clinical translation of higher-dimensional and complex treatment planning strategies to significantly improve plan quality. This work was partially supported through research funding from National Institutes of Health (R01CA169102) and Varian Medical Systems, Palo Alto, CA, USA.

60 APPLIED LIFE SCIENCES↗

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗

Feeding Ten Billion People Is Possible Within Four Terrestrial Planetary Boundaries

Global agriculture puts heavy pressure on planetary boundaries, posing the challenge to achieve future food security without compromising Earth system resilience. On the basis of process-detailed, spatially explicit representation of four interlinked planetary boundaries (biosphere integrity, land-system change, freshwater use, nitrogen flows) and agricultural systems in an internally consistent model framework, we here show that almost half of current global food production depends on planetary boundary transgressions. Hotspot regions, mainly in Asia, even face simultaneous transgression of multiple underlying local boundaries. If these boundaries were strictly respected, the present food system could provide a balanced diet (2,355 kcal per capita per day) for 3.4 billion people only. However, as we also demonstrate, transformation towards more sustainable production and consumption patterns could support 10.2 billion people within the planetary boundaries analysed. Key prerequisites are spatially redistributed cropland, improved water–nutrient management, food waste reduction and dietary changes. Adoption of the Sustainable Development Goals by all nations in 2015 is the first ever commitment to a world development path that safeguards the stability of the Earth system as a prerequisite for meeting universal human standards1. The longstanding challenge of achieving food security through sustainable agriculture is particularly acute in this context as world agriculture is a leading cause for the current transgressions of multiple planetary boundaries (PBs) globally and regionally2–5. The PB framework is a comprehensive scientific attempt to synoptically define our planet’s biogeophysical limits to anthropogenic interference. It suggests bounds to nine interacting processes that together delineate a Holocene-like Earth system state. The Holocene is chosen as the reference state as it is the only period known to provide a safe operating space for a world population of several billion people, and according to a precautionary principle, the PBs are set in sufficient distance from processes that may critically undermine Earth system resilience and global sustainability. A challenging question, thus, is whether human development goals such as food security can be met while maintaining multiple PBs along with their subglobal manifestations. Further PB transgressions could jeopardize the chances of providing sufficient food for a world population projected to be wealthier and reach >9 billion by 2050. This conundrum portrays a tradeoff between Earth’s biophysical carrying capacity and humankind’s rising food demand, calling in response for radical rethinking of food production and consumption patterns6–9. Yield gap closures, avoidance of excessive input use, shifts towards less resource-demanding diets, food waste reductions and efficient international trade are crucial options for sustainably increasing the food supply10–15. For example, enhancing water-use efficiency on irrigated and rain-fed farms can triple or quadruple crop yields in low-performing systems, suggesting possible global gains of >20% (ref. 16). Even higher gains appear feasible through globally optimized configurations of the land-use pattern17, and cutting food losses by half could generate food for another billion people18. Thus, collective large-scale implementation of such options could sustain food for a further growing world population19. Yet achieving this within a safe operating space as defined by PBs requires not only a halt to but actually a reversal of existing PB transgressions. Previous studies suggest that such a reconciliation might be possible, but these were based on aggregate representations of PBs (not accounting for the spatial patterns of limits, transgressions and interactions) or considered only one boundary in isolation17,20–23. Here, we systematically quantify to what extent current food production depends on local to global transgressions of the PBs for biosphere integrity, land-system change, freshwater use and nitrogen (N) flows, along with the potential of a range of solutions to avoid these transgressions and still increase food supply (Table 1). To this end, we configured an internally consistent process-based model of the terrestrial biosphere including agriculture (LPJmL) with multiple spatially distributed PBs and their interactions. LPJmL is among the longest-established and best-evaluated biosphere models, showing robust performance regarding simulation of, for example, carbon, water and crop yield dynamics (Supplementary Figs. 1 and 2 and Supplementary Table 1; see ref. 24 for a comprehensive benchmarking and Supplementary Methods for more detail on model evaluations). In principle following established definitions4, we refine the computation of some PBs with respect to their regional patterns and interactions (Methods), providing globally gridded precautionary limits to human interference with the Earth system at a level of great detail. In particular, we account for the evidence that many PBs need to be represented spatially explicitly4 to cover their

Gerten, Dieter↗

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Zwack, Matthew R.↗

A Machine Learning-Genetic Algorithm (ML-GA) Approach for Rapid Optimization Using High-Performance Computing

A Machine Learning-Genetic Algorithm (ML-GA) approach was developed to virtually discover optimum designs using training data generated from multi-dimensional simulations. Machine learning (ML) presents a pathway to transform complex physical processes that occur in a combustion engine into compact informational processes. In the present work, a total of over 2000 sector-mesh computational fluid dynamics (CFD) simulations of a heavy-duty engine were performed. These were run concurrently on a supercomputer to reduce overall turnaround time. The engine being optimized was run on a low-octane (RON70) gasoline fuel under partially premixed compression ignition (PPCI) mode. A total of nine input parameters were varied, and the CFD simulation cases were generated by randomly sampling points from this nine-dimensional input space. These input parameters included fuel injection strategy, injector design, and various in-cylinder flow and thermodynamic conditions at intake valve closure (IVC). The outputs (targets) of interest from these simulations included five metrics related to engine performance and emissions. Over 2000 samples generated from CFD were then used to train an ML model that could predict these five targets based on the nine input features. A robust super learner approach was employed to build the ML model, where results from a collection of different ML algorithms were pooled together. Thereafter, a stochastic global optimization genetic algorithm (GA) was used, with the ML model as the objective function, to optimize the input parameters based on a merit function so as to minimize fuel consumption while satisfying CO and NOx emissions constraints. The optimized configuration from ML-GA was found to be very close to that obtained from a sequentially performed CFD-GA approach, where a CFD simulation served as the objective function. In addition, the overall turnaround time was (at least) 75% lower with the ML-GA approach, as the training data was generated from concurrent CFD simulations and employing the ML model as the objective function significantly accelerated the GA optimization. Finally, this study demonstrates the potential of ML-GA and high-performance computing (HPC) to reduce the number of CFD simulations to be performed for optimization problems without loss in accuracy, thereby providing significant cost savings compared to traditional approaches.

97 MATHEMATICS AND COMPUTING↗

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Low Thrust↗

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.↗

The Global Geodetic Observing System: Space Geodesy Networks for the Future

Ground-based networks of co-located space geodetic techniques (VLBI, SLR, GNSS. and DORIS) are the basis for the development and maintenance of the International Terrestrial Reference frame (ITRF), which is our metric of reference for measurements of global change, The Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG) has established a task to develop a strategy to design, integrate and maintain the fundamental geodetic network and supporting infrastructure in a sustainable way to satisfy the long-term requirements for the reference frame. The GGOS goal is an origin definition at 1 mm or better and a temporal stability on the order of 0.1 mm/y, with similar numbers for the scale and orientation components. These goals are based on scientific requirements to address sea level rise with confidence, but other applications are not far behind. Recent studies including one by the US National Research Council has strongly stated the need and the urgency for the fundamental space geodesy network. Simulations are underway to examining accuracies for origin, scale and orientation of the resulting ITRF based on various network designs and system performance to determine the optimal global network to achieve this goal. To date these simulations indicate that 24 - 32 co-located stations are adequate to define the reference frame and a more dense GNSS and DORIS network will be required to distribute the reference frame to users anywhere on Earth. Stations in the new global network will require geologically stable sites with good weather, established infrastructure, and local support and personnel. GGOS wil seek groups that are interested in participation. GGOS intends to issues a Call for Participation of groups that would like to contribute in the network implementation and operation. Some examples of integrated stations currently in operation or under development will be presented. We will examine necessary conditions and challenges in designing a co-location station.

Pearlman, Michael↗