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At least 19 records

Structural optimization by methods of feasible directions.

A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

Vanderplaats, G. N.

Automated Derivation of Complex System Constraints from User Requirements

International Space Station (ISS) payload developers submit their payload science requirements for the development of on-board execution timelines. The ISS systems required to execute the payload science operations must be represented as constraints for the execution timeline. Payload developers use a software application, User Requirements Collection (URC), to submit their requirements by selecting a simplified representation of ISS system constraints. To fully represent the complex ISS systems, the constraints require a level of detail that is beyond the insight of the payload developer. To provide the complex representation of the ISS system constraints, HOSC operations personnel, specifically the Payload Activity Requirements Coordinators (PARC), manually translate the payload developers simplified constraints into detailed ISS system constraints used for scheduling the payload activities in the Consolidated Planning System (CPS). This paper describes the implementation for a software application, User Requirements Integration (URI), developed to automate the manual ISS constraint translation process.

Muery, Kim

Automated Derivation of Complex System Constraints from User Requirements

The Payload Operations Integration Center (POIC) located at the Marshall Space Flight Center has the responsibility of integrating US payload science requirements for the International Space Station (ISS). All payload operations must request ISS system resources so that the resource usage will be included in the ISS on-board execution timelines. The scheduling of resources and building of the timeline is performed using the Consolidated Planning System (CPS). The ISS resources are quite complex due to the large number of components that must be accounted for. The planners at the POIC simplify the process for Payload Developers (PD) by providing the PDs with a application that has the basic functionality PDs need as well as list of simplified resources in the User Requirements Collection (URC) application. The planners maintained a mapping of the URC resources to the CPS resources. The process of manually converting PD's science requirements from a simplified representation to a more complex CPS representation is a time-consuming and tedious process. The goal is to provide a software solution to allow the planners to build a mapping of the complex CPS constraints to the basic URC constraints and automatically convert the PD's requirements into systems requirements during export to CPS.

Foshee, Mark

Informed total-error-minimizing priors: Interpretable cosmological parameter constraints despite complex nuisance effects

While Bayesian inference techniques are standard in cosmological analyses, it is common to interpret resulting parameter constraints with a frequentist intuition. This intuition can fail, for example, when marginalizing high-dimensional parameter spaces onto subsets of parameters, because of what has come to be known as projection effects or prior volume effects. We present the method of informed total-error-minimizing (ITEM) priors to address this problem. An ITEM prior is a prior distribution on a set of nuisance parameters, such as those describing astrophysical or calibration systematics, intended to enforce the validity of a frequentist interpretation of the posterior constraints derived for a set of target parameters (e.g., cosmological parameters). Our method works as follows. For a set of plausible nuisance realizations, we generate target parameter posteriors using several different candidate priors for the nuisance parameters. We reject candidate priors that do not accomplish the minimum requirements of bias (of point estimates) and coverage (of confidence regions among a set of noisy realizations of the data) for the target parameters on one or more of the plausible nuisance realizations. Of the priors that survive this cut, we select the ITEM prior as the one that minimizes the total error of the marginalized posteriors of the target parameters. As a proof of concept, we applied our method to the density split statistics measured in Dark Energy Survey Year 1 data. We demonstrate that the ITEM priors substantially reduce prior volume effects that otherwise arise and that they allow for sharpened yet robust constraints on the parameters of interest.

79 ASTRONOMY AND ASTROPHYSICS

Coupled Riccati equations for complex plane constraint

A new Linear Quadratic Gaussian design method is presented which provides prescribed imaginary axis pole placement for optimal control and estimation systems. This procedure contributes another degree of design freedom to flexible spacecraft control. Current design methods which interject modal damping into the system tend to have little affect on modal frequencies, i.e., they predictably shift open plant poles horizontally in the complex plane to form the closed loop controller or estimator pole constellation, but make little provision for vertical (imaginary axis) pole shifts. Imaginary axis shifts which reduce the closed loop model frequencies (the bandwidths) are desirable since they reduce the sensitivity of the system to noise disturbances. The new method drives the closed loop modal frequencies to predictable (specified) levels, frequencies as low as zero rad/sec (real axis pole placement) can be achieved. The design procedure works through rotational and translational destabilizations of the plant, and a coupling of two independently solved algebraic Riccati equations through a structured state weighting matrix. Two new concepts, gain transference and Q equivalency, are introduced and their use shown.

Strong, Kristin M.

SOFIA's Choice: Automating the Scheduling of Airborne Observations

This paper describes the problem of scheduling observations for an airborne telescope. Given a set of prioritized observations to choose from, and a wide range of complex constraints governing legitimate choices and orderings, how can we efficiently and effectively create a valid flight plan which supports high priority observations? This problem is quite different from scheduling problems which are routinely solved automatically in industry. For instance, the problem requires making choices which lead to other choices later, and contains many interacting complex constraints over both discrete and continuous variables. Furthermore, new types of constraints may be added as the fundamental problem changes. As a result of these features, this problem cannot be solved by traditional scheduling techniques. The problem resembles other problems in NASA and industry, from observation scheduling for rovers and other science instruments to vehicle routing. The remainder of the paper is organized as follows. In 2 we describe the observatory in order to provide some background. In 3 we describe the problem of scheduling a single flight. In 4 we compare flight planning and other scheduling problems and argue that traditional techniques are not sufficient to solve this problem. We also mention similar complex scheduling problems which may benefit from efforts to solve this problem. In 5 we describe an approach for solving this problem based on research into a similar problem, that of scheduling observations for a space-borne probe. In 6 we discuss extensions of the flight planning problem as well as other problems which are similar to flight planning. In 7 we conclude and discuss future work.

Frank, Jeremy

Implementation of a Six Degree of Freedom Precision Lunar Landing Algorithm Using Dual Quaternion Representation

In this study, a powered descent guidance algorithm using a unit dual quaternion represen- tation of the vehicle dynamics is implemented in a high-fidelity simulation and on representative flight hardware. This Dual-Quaternion Guidance (DQG) algorithm is applied to the precision lunar landing problem which levies complex constraints upon the trajectory, including state triggered attitude constraints to enable terrain-relative navigation and hazard detection as well as real-time requirements for landing site re-designation. The investigation explores DQG’s usefulness as a mission design tool as well as a real-time guidance algorithm and defines real-time performance requirements for the hazard detection and avoidance (HDA) re-targeting phase of precision lunar landing. The experiment is presented in two parts. First, DQG is implemented within a high-fidelity Monte Carlo simulation to tune the algorithm’s parameters for the simulated vehicle, to refine the mission design, and to develop guidance update timing requirements to perform the HDA maneuver. DQG generates trajectories online for the divert which are tracked by the vehicle’s inner-loop controllers to the targeted landing site. Second, DQG is run on representative hardware to demonstrate real-time operation through a divert maneuver. These results allow for rapid, flexible, optimal mission design satisfying complex constraints, and for the definition of real-time performance requirements for the HDA operations inherent in precision lunar landing. The HDA divert maneuver is found to require guidance trajectory updates in less than three seconds. DQG is found to be too slow to meet this update timing on the descent and landing computer (DLC) in its current implementation. DQG running on alternative hardware can meet the update rate requirement. Algorithm implementation improvements are also recommended which are expected to speed up computation sufficiently to meet requirements on the DLC.

GN&C

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.

Design

Compositional Solution Space Quantification for Probabilistic Software Analysis

Probabilistic software analysis aims at quantifying how likely a target event is to occur during program execution. Current approaches rely on symbolic execution to identify the conditions to reach the target event and try to quantify the fraction of the input domain satisfying these conditions. Precise quantification is usually limited to linear constraints, while only approximate solutions can be provided in general through statistical approaches. However, statistical approaches may fail to converge to an acceptable accuracy within a reasonable time. We present a compositional statistical approach for the efficient quantification of solution spaces for arbitrarily complex constraints over bounded floating-point domains. The approach leverages interval constraint propagation to improve the accuracy of the estimation by focusing the sampling on the regions of the input domain containing the sought solutions. Preliminary experiments show significant improvement on previous approaches both in results accuracy and analysis time.

Monte Carlo Methods

Human Performance of Novice Schedulers for Complex Spaceflight Operations Timelines

Objective: Investigate the effects on human performance as a function of scheduling task complexity for novice schedulers creating spaceflight timelines. Background: Future astronauts will be expected to self-schedule, yet will not be experts in creating timelines that meet complex constraints inherent to spaceflight operations. Method: Conducted a within-subject experiment to measure scheduling efficiency, effectiveness, workload and situation awareness while varying scheduling task complexity factors, namely number of constraints and types of constraints. Results: Fifteen participants completed various scheduling problems. Performance differences were identified between the independent variables. There was a main effect due to the number of constraints and type of constraint for efficiency, effectiveness, and workload. Significant interactions were observed in situation awareness and workload for certain types of constraints. Results also suggest that a lower number of constraints may be manageable by novice schedulers when compared to scheduling activities without constraints. Conclusion: Results suggest that novice schedulers performance decreases with high number of constraints and future scheduling aids may have to be targeted to type of constraint. Application: Knowledge on the effect of scheduling task complexity will help design scheduling systems that will enable self-scheduling for future astronauts. It will also inform other domains that conduct complex scheduling, such as nursing and manufacturing.

scheduling

EUROPA2: Plan Database Services for Planning and Scheduling Applications

NASA missions require solving a wide variety of planning and scheduling problems with temporal constraints; simple resources such as robotic arms, communications antennae and cameras; complex replenishable resources such as memory, power and fuel; and complex constraints on geometry, heat and lighting angles. Planners and schedulers that solve these problems are used in ground tools as well as onboard systems. The diversity of planning problems and applications of planners and schedulers precludes a one-size fits all solution. However, many of the underlying technologies are common across planning domains and applications. We describe CAPR, a formalism for planning that is general enough to cover a wide variety of planning and scheduling domains of interest to NASA. We then describe EUROPA(sub 2), a software framework implementing CAPR. EUROPA(sub 2) provides efficient, customizable Plan Database Services that enable the integration of CAPR into a wide variety of applications. We describe the design of EUROPA(sub 2) from the perspective of both modeling, customization and application integration to different classes of NASA missions.

Bedrax-Weiss, Tania

Observation Scheduling System

Software has been designed to schedule remote sensing with the Earth Observing One spacecraft. The software attempts to satisfy as many observation requests as possible considering each against spacecraft operation constraints such as data volume, thermal, pointing maneuvers, and others. More complex constraints such as temperature are approximated to enable efficient reasoning while keeping the spacecraft within safe limits. Other constraints are checked using an external software library. For example, an attitude control library is used to determine the feasibility of maneuvering between pairs of observations. This innovation can deal with a wide range of spacecraft constraints and solve large scale scheduling problems like hundreds of observations and thousands of combinations of observation sequences.

Chien, Steve A.

Structure Constraints in a Constraint-Based Planner

In this paper we report our work on a new constraint domain, where variables can take structured values. Earth-science data processing (ESDP) is a planning domain that requires the ability to represent and reason about complex constraints over structured data, such as satellite images. This paper reports on a constraint-based planner for ESDP and similar domains. We discuss our approach for translating a planning problem into a constraint satisfaction problem (CSP) and for representing and reasoning about structured objects and constraints over structures.

Pang, Wan-Lin

Machine Learning for Fairness-Aware Load Shedding: A Real-Time Solution via Identifying Binding Constraints: Preprint

Timely and effective load shedding in power systems is critical for maintaining supply-demand balance and preventing cascading blackouts. To eliminate load shedding bias against specific regions in the system, optimization-based methods are uniquely positioned to help balance between economic and fairness considerations. However, the resulting optimization problem involves complex constraints, which can be time-consuming to solve and thus cannot meet the real-time requirements of load shedding. To tackle this challenge, in this paper we present an efficient machine learning algorithm to enable millisecond-level computation for the optimization-based load shedding problem. Numerical studies on both a 3-bus toy example and a realistic RTS-GMLC system have demonstrated the validity and efficiency of the proposed algorithm for delivering fairness-aware and real-time load shedding decisions.

97 MATHEMATICS AND COMPUTING

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints

Techniques for generating highly reliable redundant systems.

A simple heuristic algorithm for designing highly reliable modularly redundant computer systems under complexity constraints is presented. The technique, which produces near optimal solutions, is intuitively appealing and easy to apply. The algorithms performance is shown to compare very well with the optimal solution obtained via a computerized model for dynamic programming.

White, J. B.

Parallel dynamic programming for on-line flight path optimization

Parallel systolic algorithms for dynamic programming(DP) and their respective hardware implementations are presented for a problem in on-line trajectory optimization. The method is applied to a model for helicopter flight path optimization through a complex constraint region. This problem has application to an air traffic control problem and also to a terrain following/threat avoidance problem.

Slater, G. L.