Results for “objective function” — Page 43

NASA NTRS2023

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

NASA NTRS2023

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

NASA NTRSDate not supplied

Implementation of Combinatorial Optimization Techniques for Automated Fiber Placement Through Thickness Defect Stack-Up Minimization

The Computer Aided Process Planning (CAPP) module was developed to facilitate and accelerate the process planning workflow for Automated Fiber Placement (AFP). CAPP assists process planners in identifying optimal starting point locations and layup strategies for each ply of a laminate. Ply optimization operates on measurement and scoring of geometry-based defects such as gaps, overlaps, angle deviation, and steering. This paper expands on the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: (1) genetic algorithm, (2) differential evolution, (3) particle swarm, and (4) greedy search. The algorithms identify the optimal combination of ply-level layup strategies, by scoring potential laminates on defect stacking, using two different objective functions. A final optimization approach is also presented which trades some performance for a large gain in efficiency. These approaches are compared to a randomized combination using a complex tool surface in a virtual case study. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack up.

CAPP↗

NASA NTRSDate not supplied

Influence of the Perception Constraint, Observer Position, and Broadband Self-Noise on Low-Fidelity UAM Vehicle Perception-Influenced-Design (PID) Optimization

This paper will present an approach in design optimization of a proprotor in a forward flight condition with several acoustic objective functions that simulate community response. An adjoint-capable blade element momentum theory (BEMT), implemented in CCBlade.jl, will be used to compute the blade forces and inflow properties required to compute tonal and broadband noise using the second-generation Aircraft NOise Prediction Program (ANOPP2). The influence of broadband noise, observer location, and choice of perception constraint on optimized values of rotation rate, chord distribution, and twist angle will be shown. It is determined that broadband self-noise is an influential source noise mechanism in the design optimization when frequency weighting is used to predict the noise at an out-of-plane observer position.

acoustics↗

NASA NTRSDate not supplied

Influence of the Perception Constraint, Observer Position, and Broadband Self-Noise on Low-Fidelity UAM Vehicle Perception-Influenced-Design (PID) Optimization

This paper will present an approach in design optimization of a proprotor in a forward flight condition with several acoustic objective functions that simulate community response. An adjoint-capable blade element momentum theory (BEMT), implemented in CCBlade.jl, will be used to compute the blade forces and inflow properties required to compute tonal and broadband noise using the second-generation Aircraft NOise Prediction Program (ANOPP2). The influence of broadband noise, observer location, and choice of perception constraint on optimized values of rotation rate, chord distribution, and twist angle will be shown. It is determined that broadband self-noise is an influential source noise mechanism in the design optimization when frequency weighting is used to predict the noise at an out-of-plane observer position.

acoustics↗

NASA NTRSDate not supplied

Towards Low-Noise Design of a Proprotor with the Vortex Lattice Method and Gradient-Based Optimization

This work aims to combine an aerodynamic model based on the unsteady vortex lattice method with an acoustic model provided by Farassat's formulation 1A to perform gradient-based optimizations of a proprotor with aerodynamic and acoustic constraints. The resulting combination of tools is applied to the problem of designing a single proprotor operating at a cruise condition, with and without an acoustic constraint and wing placed downstream of the proprotor rotation plane. Results are compared to a baseline design studied previously, and to similar optimizations performed with a simpler blade element momentum theory aerodynamic model. Each optimization case achieved feasibility and made significant improvements in the objective function, but the optimality criterion was not satisfied. Overall the designs the optimizer found roughly comported with our previous experience with similar problems, with some discrepancies that are discussed.

Aerodynamics↗

NASA NTRSDate not supplied

Framework for National Airspace System (NAS) Level Sustainability Assessment of New Aircraft

This paper introduces a framework for investigating the future sustainability benefits of conceptual vehicles. The framework considers the complex interactions between such vehicles and how it can be flown in the National Airspace System. Aggregate benefits for reduction in fuel use and emissions need to consider fleet wide operations, demand distributions, NAS Infrastructure, and differing business models. To extract true system level benefits multi-objective function optimization for operational energy use, acoustics, emissions and NAS Wide efficiency and interoperability incorporating physic-based system-wide flight simulations in the National Airspace system is required. The framework marries traditional vehicle synthesis processes with a NAS Simulation environment to simulate how a new synthesized vehicle will behave in the NAS.

Sustainability↗

NASA NTRSDate not supplied

Towards Low-Noise Design of a Proprotor with the Vortex Lattice Method and Gradient-Based Optimization

This work aims to combine an aerodynamic model based on the unsteady vortex lattice method with an acoustic model provided by Farassat's formulation 1A to perform gradient-based optimizations of a proprotor with aerodynamic and acoustic constraints. The resulting combination of tools is applied to the problem of designing a single proprotor operating at a cruise condition, with and without an acoustic constraint and wing placed downstream of the proprotor rotation plane. Results are compared to a baseline design studied previously, and to similar optimizations performed with a simpler blade element momentum theory aerodynamic model. Each optimization case achieved feasibility and made significant improvements in the objective function, but the optimality criterion was not satisfied. Overall the designs the optimizer found roughly comported with our previous experience with similar problems, with some discrepancies that are discussed.

Aerodynamics↗

NASA NTRSDate not supplied

Electric Sail Design Sensitivities

Electric Sails (E-Sails) are a promising propulsion technology that seek to enable high characteristic propellentless acceleration for spacecraft to reach distant and/or difficult to reach orbits such as rapid transit to heliopause. The E-Sail system exchanges momentum by using positively charged electrostatic tethers to repel solar wind photons to push it through space. This concept was first theorized by Pekka Janhunen in 2004 with further developments occurring including a NASA Innovative Advanced Concepts Phase 1 and Phase 2 hosted out of NASA’s Marshall Space Flight Center (MSFC). These developments led to further maturation of the overall system, and this paper is designed to help identify different design sensitivities of an integrated Electric Sail system. To approach this, a small team at MSFC took an in-house developed three degrees of freedom (3DoF) simulation tool and a trajectory modelling tool to look at different design parameters and to determine a potential ideal E-Sail configuration. An E-Sail system has different design architectures including a barbell design, hub and spoke design, and a potential hybrid solution. The barbell design features two equally massed satellites that spin around a central point in the tether system. The hub and spoke design features a large central spacecraft with small end spacecraft to aid in formation control of the overall E-Sail system. Leveraging elements from both the hub and spoke, and barbell design, a hybrid option exists where one could have a larger central mass and one or two tethers extended to a smaller end mass [2]. In summary, the hub and spoke design is the ideal configuration for E-Sail with tethers spanning kilometers to achieve the designed design characteristic acceleration of at least one mm/s2 with this architecture being the focus of this study. Different key design parameters were varied as part of this study. These parameters include the total number of tethers, the length of the tethers, spin rate, relative spacecraft mass, tether voltage, inertia per tether, and impact of slew rate changes. These results started from an internal MSFC technology demonstration mission design and then the parameters were varied with engineering judgement to ensure that the results were consistent with expected results. These were varied in the MSFC 3DoF tool and compared to baseline results to generate a candidate ideal E-Sail design system. These results were then used to help inform the mission analysis design for the system. The 3DoF trajectory optimization was performed in the Astrodynamics and Space Science Enabling Toolbox (ASSET) and utilized collocation optimization of control vector pointing with the objective function being transfer duration. A representative model of the E-Sail force was derived as a function of the Sun-pointing vector direction. This model was initialized with a zero Sun Incidence Angle (SIA) trajectory for the initial guess generation, then with a portion of the mission optimized SIA time history for fast outbound transfers. After the trajectory is hyperbolic relative to a heliocentric frame, the SIA is maintained at 0 degrees except for any needed trajectory correction maneuvers. This trajectory optimization looked at different characteristic acceleration values to analyze the impact it had on mission performance. As a result of this study, the team can best inform mission designers and technology development efforts to mature the E-Sail system. This study will allow mission designers to have defined rules-of-thumb to design an E-Sail system to meet desired mission needs as well as providing several sample mission profiles. These design drivers will inform maturation efforts on which design requirements to consider for an integrated E-Sail design.

E-Sail↗

NASA NTRSDate not supplied

Aerothermal Shape Optimization of Actively-Cooled Battery Packs using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

thermal management↗

NASA NTRSDate not supplied

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization↗

NASA NTRSDate not supplied

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. The transient finite-element analysis is done using TACS, and the cell-discharge battery model uses OpenMDAO and dymos. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization↗

NASA NTRSDate not supplied

Aerothermal Shape Optimization of Actively-Cooled Battery Packs Using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

heat transfer↗

NASA NTRS2024

Harnessing Collaborative Learning Automata to Guide Multi-objective Optimization based Inverse Analysis for Structural Damage Identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

Yang Zhang↗

NASA NTRS2026

A Modular Conjugate Heat Transfer Optimization Framework for Thermal Management of Electric Aircraft

Conjugate heat transfer (CHT) analysis and optimization is a powerful method for improving thermal management, as it simultaneously resolves the temperature distribution in both fluid and solid domains. This paper presents a modular, discrete adjoint-based CHT optimization capability integrated within the OpenMDAO/MPhys framework. A unique feature of the proposed framework is its flexibility to extend to multidisciplinary optimization, including aero-structural-thermal applications. The fluid domain is modeled using a finite-volume Computational Fluid Dynamics (CFD) solver, and the solid domain with a conduction heat transfer solver. A mixed Neumann-Dirichlet boundary condition is developed to enable full submersion of the solid geometry within the fluid domain, while ensuring consistent temperature and heat flux coupling at the CHT interface. Gradient-based optimization is performed; the gradients are efficiently computed using the discrete adjoint solvers implemented in DAFoam. To demonstrate the method, this paper considers two cases related to electric aircraft thermal management: a U-bend heat exchanger and an actively cooled battery pack. The U-bend case aims to minimize pressure loss while maximizing heat flux by changing the pipe geometry. The optimized design reduces pressure loss by 52.7% and increases total heat flux by 2.3%. In the battery pack case, a 3-by-3 cell configuration is cooled by ambient airflow, with constant heat generation prescribed in the cells. The battery casing shape serves as the design variable, and the objective function is a weighted sum of pressure loss and pack weight, subject to a maximum temperature constraint. The optimized design achieves a 44.6% reduction in pressure loss and a 1.5% reduction in weight, while satisfying the thermal constraint. To ensure the reliability of the optimized designs, this study validates coarse-mesh, steady-state predictions against fine-mesh unsteady simulations, demonstrating consistency within acceptable errors. This work demonstrates the potential of the developed framework to enable rapid, high-fidelity design of thermal management systems for electric aircraft.

heat transfer↗

DOE OSTI2020

Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning

We assume that we are given a time series of data from a dynamical system and our task is to learn the flow map of the dynamical system. We present a collection of results on how to enforce constraints coming from the dynamical system in order to accelerate the training of deep neural networks to represent the flow map of the system as well as increase their predictive ability. In particular, we provide ways to enforce constraints during training for all three major modes of learning, namely supervised, unsupervised and reinforcement learning. In general, the dynamic constraints need to include terms which are analogous to memory terms in model reduction formalisms. Such memory terms act as a restoring force which corrects the errors committed by the learned flow map during prediction. For supervised learning, the constraints are added to the objective function. For the case of unsupervised learning, in particular generative adversarial networks, the constraints are introduced by augmenting the input of the discriminator. Finally, for the case of reinforcement learning and in particular actor-critic methods, the constraints are added to the reward function. In addition, for the reinforcement learning case, we present a novel approach based on homotopy of the action-value function in order to stabilize and accelerate training. We use numerical results for the Lorenz system to illustrate the various constructions.

Stinis, Panagiotis↗

DOE OSTI2020

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow: Preprint

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2020

PREEMPT: Scalable Epidemic Interventions Using Submodular Optimization on Multi-GPU Systems

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we make several contributions: First, we present a new approach for intervention via maximizing the influence of vaccinated nodes on the network. We call this method \preempt. Next, we prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for \preempt, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that \preempt{} is able to achieve a significant reduction (up to 6.75$\times$) in the percentage of people infected on a city-scale network. We also show strong scaling results of \preempt{} on 128 nodes of the Summit supercomputer. Our parallel implementation is able to significantly reduce time to solution, from hours to minutes on large networks. This work represents a first-of-its-kind effort in parallelizing greedy hill climbing and applying it toward devising effective interventions for epidemics.

Minutoli, Marco↗