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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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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Using the Flow-3D General Moving Object Model to Simulate Coupled Liquid Slosh - Container Dynamics on the SPHERES Slosh Experiment: Aboard the International Space Station

The SPHERES Slosh Experiment (SSE) is a free floating experimental platform developed for the acquisition of long duration liquid slosh data aboard the International Space Station (ISS). The data sets collected will be used to benchmark numerical models to aid in the design of rocket and spacecraft propulsion systems. Utilizing two SPHERES Satellites, the experiment will be moved through different maneuvers designed to induce liquid slosh in the experiment's internal tank. The SSE has a total of twenty-four thrusters to move the experiment. In order to design slosh generating maneuvers, a parametric study with three maneuvers types was conducted using the General Moving Object (GMO) model in Flow-30. The three types of maneuvers are a translation maneuver, a rotation maneuver and a combined rotation translation maneuver. The effectiveness of each maneuver to generate slosh is determined by the deviation of the experiment's trajectory as compared to a dry mass trajectory. To fully capture the effect of liquid re-distribution on experiment trajectory, each thruster is modeled as an independent force point in the Flow-3D simulation. This is accomplished by modifying the total number of independent forces in the GMO model from the standard five to twenty-four. Results demonstrate that the most effective slosh generating maneuvers for all motions occurs when SSE thrusters are producing the highest changes in SSE acceleration. The results also demonstrate that several centimeters of trajectory deviation between the dry and slosh cases occur during the maneuvers; while these deviations seem small, they are measureable by SSE instrumentation.

Schulman, Richard↗
NASA NTRS2019

Real-Time UAV Trajectory Prediction for Safety Monitoring in Low-Altitude Airspace

The rising number of small unmanned aerial vehicles (UAVs) expected in the next decade will enable a new series of commercial, service, and military operations in low altitude airspace as well as above densely populated areas. These operations may include on-demand delivery, medical transportation services, law enforcement operations, traffic surveillance and many more. Such unprecedented scenarios create the need for robust, efficient ways to monitor the UAV state in time to guarantee safety and mitigate contingencies throughout the operations. This work proposes a generalized monitoring and prediction methodology that utilizes realtime measurements of an autonomous UAV following a series of way-points. Two different methods, based on sinusoidal acceleration profiles and high-order splines, are utilized to generate the predicted path. The monitoring approach includes dynamic trajectory re-planning in the event of unexpected detour or hovering of the UAV during flight. It can be further extended to different vehicle types, to quantify uncertainty affecting the state variables, e.g., aerodynamic and other environmental effects, and can also be implemented to prognosticate safety-critical metrics which depend on the estimated flight path and required thrust. The proposed framework is implemented on a simplified, scalable UAV modeling and control system traversing 3D trajectories. Results presented include examples of real-time predictions of the UAV trajectories during flight and a critical analysis of the proposed scenarios under uncertainty constraints.

UAV trajectory prognosis↗
NASA NTRS1973

An evaluation of some special techniques for nuclear waste disposal in space

A preliminary examination is reported of several special ways for space disposal of nuclear waste material which utilize the radioactive heat in the waste to assist in the propulsion for deep space trajectories. These include use of the wastes in a thermoelectric generator (RTG) which operates an electric propulsion device and a radioisotope - thermal thruster which uses hydrogen or ammonia as the propellant. These propulsive devices are compared to the space tug and the space tug/solar electric propulsion combination for disposal of waste on a solar system escape trajectory. Such comparisons indicate that the waste-RTG approach has considerable potential provided the combined specific mass of the waste container - RTG system does not exceed approximately 150 kg/kw sub e. Several exploratory numerical calculations have been made for high earth orbit and Earth escape destinations.

Mackay, J. S.↗
NASA NTRS1995

Motor adaptation to Coriolis force perturbations of reaching movements: endpoint but not trajectory adaptation transfers to the nonexposed arm

1. Reaching movements made in a rotating room generate Coriolis forces that are directly proportional to the cross product of the room's angular velocity and the arm's linear velocity. Such Coriolis forces are inertial forces not involving mechanical contact with the arm. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished at the onset of each reach. Prerotation subjects pointed with both the right and left arms in alternating sets of eight movements. During rotation at 10 rpm, the subjects reached only with the right arm. Postrotation, the subjects pointed with the left and right arms, starting with the left, in alternating sets of eight movements. 3. The initial perrotary reaching movements of the right arm were highly deviated both in movement path and endpoint relative to the prerotation reaches of the right arm. With additional movements, subjects rapidly regained straight movement paths and accurate endpoints despite the absence of visual or tactile feedback about reaching accuracy. The initial postrotation reaches of the left arm followed straight paths to the wrong endpoint. The initial postrotation reaches of the right arm had paths with mirror image curvature to the initial perrotation reaches of the right arm but went to the correct endpoint. 4. These observations are inconsistent with current equilibrium point models of movement control. Such theories predict accurate reaches under our experimental conditions. Our observations further show independent implementation of movement and posture, as evidenced by transfer of endpoint adaptation to the nonexposed arm without transfer of path adaptation. Endpoint control may occur at a relatively central stage that represents general constraints such as gravitoinertial force background or egocentric direction relative to both arms, and control of path may occur at a more peripheral stage that represents moments of inertia and muscle dynamics unique to each limb. 5. Endpoint and path adaptation occur despite the absence both of mechanical contact cues about the perturbing force and visual or tactile cues about movement accuracy. These findings point to the importance of muscle spindle signals, monitoring of motor commands, and possibly joint and tendon receptors in a detailed trajectory monitoring process. Muscle spindle primary and secondary afferent signals may differentially influence adaptation of movement shape and endpoint, respectively.

Non-NASA Center↗
NASA NTRS2014

Thermal Model Predictions of Advanced Stirling Radioisotope Generator Performance

This paper presents recent thermal model results of the Advanced Stirling Radioisotope Generator (ASRG). The three-dimensional (3D) ASRG thermal power model was built using the Thermal Desktop(trademark) thermal analyzer. The model was correlated with ASRG engineering unit test data and ASRG flight unit predictions from Lockheed Martin's (LM's) I-deas(trademark) TMG thermal model. The auxiliary cooling system (ACS) of the ASRG is also included in the ASRG thermal model. The ACS is designed to remove waste heat from the ASRG so that it can be used to heat spacecraft components. The performance of the ACS is reported under nominal conditions and during a Venus flyby scenario. The results for the nominal case are validated with data from Lockheed Martin. Transient thermal analysis results of ASRG for a Venus flyby with a representative trajectory are also presented. In addition, model results of an ASRG mounted on a Cassini-like spacecraft with a sunshade are presented to show a way to mitigate the high temperatures of a Venus flyby. It was predicted that the sunshade can lower the temperature of the ASRG alternator by 20 C for the representative Venus flyby trajectory. The 3D model also was modified to predict generator performance after a single Advanced Stirling Convertor failure. The geometry of the Microtherm HT insulation block on the outboard side was modified to match deformation and shrinkage observed during testing of a prototypic ASRG test fixture by LM. Test conditions and test data were used to correlate the model by adjusting the thermal conductivity of the deformed insulation to match the post-heat-dump steady state temperatures. Results for these conditions showed that the performance of the still-functioning inboard ACS was unaffected.

radioisotope power system↗
DOE OSTI2025

Adaptive Dynamic Digital Twin for Test Scenario Generation

Vehicle testing has been an important part in the development of both highly automated vehicles (HAV) and advanced driving assistant systems (ADAS). Obtaining a good representation of the Vehicle Under Test (VUT) is crucial for test scenario library generation (TSLG). Current vehicle testing methods often involve calibrating car-following models using vehicle trajectory data to create static representations that cannot be dynamically updated. For instance, when multiple vehicle trajectories are collected, it is difficult to automatically determine whether a new trajectory improves the model's representativeness or degrades its accuracy. In this paper, we introduce a dynamically updated digital twin modeling framework featuring an adaptive mechanism that evaluates new trajectory data. This mechanism can decide whether to incorporate newly collected data into the current model or create a separate digital twin model when the trajectory significantly differs from prior data. Vehicle location, speed, and acceleration extracted from the newly collected trajectory data are used to support the dynamic update decision. By integrating this digital twin model into the test library generation process, we demonstrate its ability to assist in generating test libraries while effectively handling newly collected data.

Chen, Hanlin [ORNL] (ORCID:0000000165087715)↗
NASA NTRS1999

Lunar Prospector Extended Mission

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector as one of the discovery missions to conduct solar system exploration science investigations. The mission is NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control focused on the use of innovative and proven trajectory analysis programs. As part of this effort, the Ames Research Center and the Goddard Space Flight Center have become partners in the Lunar Prospector trajectory team to provide the trajectory analysis, maneuver planning, orbit determination support, and product generation. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100 km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered the extended mission phase. Initially the mission orbit was lowered from 100 km to a mean altitude of 40 km. The altitude of Lunar Prospector varied between 25 and 55 km above the mean lunar geode due to lunar potential effects. After one month, the lunar potential model was updated based upon the new tracking data at 40 km. On January 29, 1999, the altitude was lowered again to a mean altitude of 30 km. This altitude varies between 12 and 48 km above the mean lunar geode. Since the minimum altitude is very close to the mean geode, various approaches were employed to get accurate lunar surface elevation including Clementine altimetry and line of sight analysis. Based upon the best available terrain maps, Lunar Prospector will reach altitudes of 8 km above lunar mountains in the southern polar and far side regions. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. This paper details the trajectory design and orbit determination planning, and actual results of the the Lunar Prospector extended mission including maneuver design, eccentricity & argument of perigee evolution, and lunar potential modeling.

Folta, David↗
NASA NTRS1999

Lunar Prospector Extended Mission

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector (LP) as one of the discovery missions to conduct solar system exploration science investigations. The mission is NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control focused on the use of innovative and proven trajectory analysis programs. As part of this effort, the Ames Research Center and the Goddard Space Flight Center have become partners in the Lunar Prospector trajectory team to provide the trajectory analysis, maneuver planning, orbit determination support, and product generation. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100 km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered the extended mission phase. Initially the mission orbit was lowered from 100 km to a mean altitude of 40 km. The altitude of Lunar Prospector varied between 25 and 55 km above the mean lunar geode due to lunar potential effects. After one month, the lunar potential model was updated based upon the new tracking data at 40 km. On January 29, 1999, the altitude was lowered again to a mean altitude of 30 km. This altitude varies between 12 and 48 km above the mean lunar geode. Since the minimum altitude is very close to the mean geode, various approaches were employed to get accurate lunar surface elevation including Clementine altimetry and line of sight analysis. Based upon the best available terrain maps, Lunar Prospector will reach altitudes of 8 km above lunar mountains in the southern polar and far side regions. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. This paper details the trajectory design and orbit determination planning and actual results of the Lunar Prospector extended mission including maneuver design, eccentricity & argument of perigee evolution, and lunar potential modeling.

Folta, David↗
NASA NTRSDate not supplied

Power Measurements to Excavate Lunar Soil Simulant GRC-3B Using Arc Backhoe Trajectories

Understanding, mitigating, and minimizing power and mass requirements are crucial to developing the next generation excavation technologies for lunar and planetary in-situ resource utilization (ISRU). Towards this end, electrical power to the Advanced Planetary Excavator (APEX) was measured while excavating granular lunar soil simulant GRC-3B. Using a 21.6-cm wide bucket having a 30° leading edge, arc-shaped backhoe trajectories were dug to depths of 5, 10, and 20 cm with rake angles of 10, 20, and 30 degrees. Maximum net power, net energy, net energy per mass excavated, rate of mass excavated, horizontal distance from soil entry to exit (at bucket tip), and the trajectory to bucket volume percentage are presented to inform the scientific community as trajectories and designs are planned for future missions. Using APEX’s capability to evaluate power and energy consumption of excavation tools and processes gives guidance to developing power requirements and efficient methods for lunar excavation.

Excavation↗
NASA NTRS2025

Single Integrated Flux Files to Account for Spacecraft Attitude Motion in Meteoroid Risk Assessments Using the NASA MEM3 and Bumper Codes

Spacecraft meteoroid risk assessments can be performed using NASA’s Meteoroid Engineering Model 3 (MEM3) and the Bumper risk assessment code. The MEM3 meteoroid flux is highly directional in heliocentric space. To represent the directionality, MEM3 outputs the flux in commonly used coordinate frames. For example, if a spacecraft attitude is fixed in the orbital tangential frame, a single Bumper run using the MEM3 flux file in the body-fixed frame can be performed. Cases exist in which the spacecraft does not remain fixed in one of these frames during a mission. This could be handled by performing a series of Bumper runs at points along the trajectory. For each trajectory point, the spacecraft has to be rotated into the frame in which the MEM3 flux file is defined. Another option presented here is to generate a single integrated flux (SIF) file. A SIF file is an average over a trajectory of the time varying MEM3 flux files rotated from their native frame into the spacecraft bus frame. A SIF file enables accounting for spacecraft rotation (coupled with flux variation over the trajectory) in a single Bumper run. An example of an application of SIF files is the meteoroid risk assessment for the Mars Sample Return (MSR) campaign Capture Containment and Return System (CCRS). This report discusses how SIF files were generated for the CCRS risk assessment and presents metrics on the accuracy of the impinging fluence that is generated when using the files. The results show a maximum difference per element in a finite element model within 1 percent for seven of the eight examined cases, with the outlier being less than 2 percent. The results also show that the maximum standard deviation of differences across all elements is within 0.275 percent. The maximum difference in the total fluence across all the elements is 0.0463 percent. The maximum difference in the mean fluence across all the elements is 0.0407 percent.

Meteoroids↗
NASA NTRS2022

Trajectory Specification Applied to Terminal Airspace

Despite major efforts to automate air traffic control (ATC), it is still performed by humans today. The complexity and safety-criticality of ATC makes it very difficult to safely automate, but it must be automated to increase airspace capacity (the density of traffic that can be safely managed) and airport throughput (the number of arrivals and departures that an airport can safely handle in a given period of time) beyond what is possible with human controllers. This paper presents the Trajectory Specification (TS) concept, which can help to safely automate ATC. TS is a method of specifying aircraft trajectories such that the position at any given time in flight is restricted to a precisely defined bounding space, removing all ambiguity as to where the flight is allowed to be. The bounding space or volume is determined by tolerances relative to a reference trajectory (position as a function of time). The tolerances are dynamic and are based on the aircraft navigation capabilities and the traffic situation. The tolerances can be a piecewise linear function of time or distance along the route, allowing the tolerances to vary as needed, typically increasing with time for departures and decreasing for arrivals. A Trajectory Specification Language (TSL) is proposed for communicating trajectories from aircraft to ATC as requests and from ATC to aircraft as assignments. The TS concept requires a new generation of airborne Flight Management Systems (FMS) that understand the TSL and can fly the assigned trajectories, but this paper focuses on the ATC functions and the prototype ATC algorithms and software that were developed to test the TS concept. Assuming conformance, TS can guarantee safe separation for an arbitrary length of time even in the event of an ATC system or communication outage. It can help to achieve the high level of safety and reliability needed for ATC automation, and it can also reduce the reliance on ATC backup systems for tactical conflict detection and resolution during normal operation. TS can be applied to any controlled airspace, including enroute, terminal, and urban airspace, but this paper presents algorithms and software for arrival spacing and conflict detection and resolution in the terminal airspace serving a major airport. In a fast-time simulation of a full day of traffic in a major terminal airspace, all conflicts were resolved in near real time, demonstrating the computational feasibility and the preliminary operational feasibility of the TS concept. This paper is a compilation of previous papers, and it adds significant information that was omitted from those papers due to length limitations. It also updates some of the results of those earlier papers due to algorithm refinements and corrections of minor software errors.

air traffic control, trajectory↗
NASA NTRS1994

Compatibility of TOPEX/Poseidon trajectory propagation with JPL and GSFC/FDF operational software

Two independent trajectory software systems are used to perform the TOPEX/Poseidon operational orbit determination and propagation: the Goddard Trajectory Determination System (GTDS) at the GSF/FDF and the Double Precision Trajectory System (DPTRAJ) at JPL. GTDS is used for operational tracking and TDRS-based orbit determination. DPTRAJ is used for ephemeris generation necessary to conduct day-to-day mission operations. This paper describes the DPTRAJ/GTDS trajectory comparison analysis conducted jointly by JPL and GSFC to ensure the compatibility of these two independent trajectory software systems.

Salama, Ahmed↗
NASA NTRS2010

Orion Entry Display Feeder and Interactions with the Entry Monitor System

The Orion spacecraft is designed to return astronauts to a landing within 10 km of the intended landing target from low Earth orbit, lunar direct-entry, and lunar skip-entry trajectories. Al pile the landing is nominally controlled autonomously, the crew can fly precision entries manually in the event of an anomaly. The onboard entry displays will be used by the crew to monitor and manually fly the entry, descent, and landing, while the Entry Monitor System (EMS) will be used to monitor the health and status of the onboard guidance and the trajectory. The entry displays are driven by the entry display feeder, part of the Entry Monitor System (EMS). The entry re-targeting module, also part of the EMS, provides all the data required to generate the capability footprint of the vehicle at any point in the trajectory, which is shown on the Primary Flight Display (PFD). It also provides caution and warning data and recommends the safest possible re-designated landing site when the nominal landing site is no longer within the capability of the vehicle. The PFD and the EMS allow the crew to manually fly an entry trajectory profile from entry interface until parachute deploy having the flexibility to manually steer the vehicle to a selected landing site that best satisfies the priorities of the crew. The entry display feeder provides data from the ENIS and other components of the GNC flight software to the displays at the proper rate and in the proper units. It also performs calculations that are specific to the entry displays and which are not made in any other component of the flight software. In some instances, it performs calculations identical to those performed by the onboard primary guidance algorithm to protect against a guidance system failure. These functions and the interactions between the entry display feeder and the other components of the EMS are described.

Baird, Darren↗
NASA NTRS1983

Trajectory analysis of radiative heating for planetary missions with aerobraking of spacecraft

The aerodynamic drag generated during a grazing pass through a planetary atmosphere can be used to expend energy which a spacecraft has in excess of that required to achieve a closed orbit. The propulsion fuel mass saved by eliminating retropropulsive braking maneuvers makes possible missions which are otherwise impossible or impractical. The present investigation has the objective to examine the influence of atmospheric entry trajectory parameters on the magnitude of the radiative heating rates for both the Titan aerocapture and near-earth orbital transfer missions. Calculations are performed for a wide range of entry conditions encompassing those of many conceptual mission scenarios for both Titan and earth. It is found that the nonequilibrium radiative heating is enhanced over that for equilibrium and generally exceeds that for convection for most mission profiles. Nonequilibrium radiation heating is, therefore, an important factor in the design of the corresponding thermal protection systems.

Menees, G. P.↗
DOE OSTI2022

Autonomous Aerial Power Plant Inspection in GPS-denied Environments

Inspection of coal-fired power plants is frequently dangerous, includes difficult places to reach, and can turn expensive due to the downtimes and cost of inspection crew. Robotic systems have shown capabilities to address some of these issues, but most of the current robotic inspection technology in power plants is designed for specific components. Conversely, recent advances in machine vision have empowered aerial platforms for long-range, remotely-controlled, GPS-based inspections of industrial plants. This capability has led to wide spread utilization of aerial robots (commonly termed Drones, UVS or UAS) platforms for inspection in less challenging environments where both collision avoidance, and GPS reception are not significant issues. The challenge in adapting airborne technology for power plant inspection lies in internal structures and the complex network of piping, and distribution systems, which impose significant risks for collision and can hinder the reception and transmission of GPS signals. The current state of the art in aerial inspection technology within the energy sector is controlled via radio control, and utilizes GPS-based navigation, for inspection of large-scale plants such as offshore platforms and wind turbine parks. Nevertheless, close-range and autonomous inspection in the GPS-denied environments of power plants has not yet been achieved, as it requires precise guidance and navigation with real-time situational awareness and obstacle avoidance capabilities. This endeavor introduced the use of rotary wing flying robots, due to their station keeping and vertical take-off capabilities for power plant components inspection. To enable close quarter inspection two methods were used. One method uses the 3D CAD (Three-dimensional Computer-Aided Design) model of the asset to inspect to generate the UAV’s inspection path. To acquire, analyze and process the 3D model, first, the STL file is produced to obtain surface points and vectors normal to the surface. Later, by introducing other variables such as wall offset and a controlled trajectory between each outline and each subsequent layer, the flight path is generated. The proposed framework will generate a path that will pass as close as desired from the surface and navigate in intricate environments. A second method, use advanced manufacturing techniques such as CNC (Computer Numerical Control) and additive manufacturing. Once the inspection flight path is obtained, vision-based navigation systems are employed to have the UAV autonomously tracking the provided trajectory. Finally, Artificial Intelligence-enabled developments are in charge of detecting cracks and corrosion in structural components of power plants. The proposed methods are validated in simulations, laboratory and industrial setups, where it is shown that the developed systems acting together enable close-quarter autonomous aerial inspection and mapping in power plant assets. The system can be further improved by adding more sensors to navigate in different GPS-denied environments, with non-homogeneous lighting conditions, dust and in general situations where vision-based systems may fail.

01 COAL, LIGNITE, AND PEAT↗
NASA NTRS2020

Aircraft Engine Run-To-Failure Data Set Under Real Flight Conditions

The generation of data-driven prognostics models requires the availability of datasets with run-to-failure trajectories. In order to contribute to the development of these methods, the dataset provides a new realistic dataset of run-to-failure trajectories for a small fleet of aircraft engines under realistic flight conditions. The damage propagation modelling used for the generation of this synthetic dataset builds on the modelling strategy from previous work [1] and incorporates two new levels of fidelity. First, it considers real flight conditions as recorded on board of a commercial jet [2]. Secondly, it extends the degradation modelling by relating the degradation process to the operation history. The dataset was generated with the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dynamical model [3]. More details about the generation process can be found in [4].

CMAPSS↗
NASA NTRS2011

Ares I-X Range Safety Trajectory Analyses Overview and Independent Validation and Verification

All Flight Analysis data products were successfully generated and delivered to the 45SW in time to support the launch. The IV&V effort allowed data generators to work through issues early. Data consistency proved through the IV&V process provided confidence that the delivered data was of high quality. Flight plan approval was granted for the launch. The test flight was successful and had no safety related issues. The flight occurred within the predicted flight envelopes. Post flight reconstruction results verified the simulations accurately predicted the FTV trajectory.

Tarpley, Ashley F.↗
DOE OSTI2020

A Tchebycheff-based multi-objective combined with a PSO–SQP dynamic real-time optimization framework for cycling energy systems

The aim in this work is to develop an optimization framework to address cycling of baseload energy systems due to the penetration of renewables into the grid. The developed strategy corresponds to a multi-objective and dynamic real-time optimization (MOO-DRTO) framework applied to a postcombustion MEA-based CO 2 capture process from a baseload coal-fired power plant under cycling conditions. A Tchebycheff-based method is used for the multi-objective optimization (MOO) component. Also, a hybrid approach consisting of Particle Swarm Optimization (PSO) and Sequential Quadratic Programming (SQP) is implemented for the first time in process systems engineering to solve the dynamic real-time optimization (DRTO) component. The objectives considered in the MOO-DRTO framework are economic and environmental. The proposed MOO-DRTO strategy is successfully implemented and 24-h optimal output trajectories for the carbon capture system under cycling are generated. Also, the optimal compromise is chosen from the Pareto front according to a set of selected weights for the objectives with minimal interaction between the framework and decision maker. The results indicated that the developed framework has potential to be extended to plant-wide optimization applications under cycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗