Results for “simultaneous optimization” — Page 21

NASA NTRS2004

New Acoustic Arena Qualified at NASA Glenn's Aero-Acoustic Propulsion Laboratory

A new acoustic arena has been qualified in the Aero-Acoustic Propulsion Laboratory (AAPL) at the NASA Glenn Research Center. This arena is outfitted specifically for conducting fan noise research with the Advanced Noise Control Fan (ANCF) test rig. It features moveable walls with large acoustic wedges (2 by 2 by 1 ft) that create an acoustic environment usable at frequencies as low as 250 Hz. The arena currently uses two dedicated microphone arrays to acquire fan inlet and exhaust far-field acoustic data. It was used successfully in fiscal year 2003 to complete three ANCF tests. It also allowed Glenn to improve the operational efficiency of the four test rigs at AAPL and provided greater flexibility to schedule testing. There were a number of technical challenges to overcome in bringing the new arena to fruition. The foremost challenge was conflicting acoustic requirements of four different rigs. It was simply impossible to construct a static arena anywhere in the facility without intolerably compromising the acoustic test environment of at least one of the test rigs. This problem was overcome by making the wall sections of the new arena movable. Thus, the arena can be reconfigured to meet the operational requirements of any particular rig under test. Other design challenges that were encountered and overcome included structural loads of the large wedges, personnel access requirements, equipment maintenance requirements, and typical time and budget constraints. The new acoustic arena improves operations at the AAPL facility in several significant ways. First, it improves productivity by allowing multiple rigs to operate simultaneously. Second, it improves research data quality by providing a unique test area within the facility that is optimal for conducting fan noise research. Lastly, it reduces labor and equipment costs by eliminating the periodic need to transport the ANCF into and out of the primary AAPL acoustic arena. The investment to design, fabricate, and install the new compact arena in fiscal year 2002 has paid dividends in fiscal year 2003 and will for many years to come. It has provided a dedicated, high-quality acoustic arena to support low-speed fan testing for ANCF while minimizing scheduling impacts and improving operational productivity in the AAPL facility.

Wnuk, Stephen P.↗

NASA NTRS2016

The Atacama Cosmology Telescope: The Polarization-Sensitive ACTPol Instrument

The Atacama Cosmology Telescope (ACT) makes high angular resolution measurements of anisotropies in the Cosmic Microwave Background (CMB) at millimeter wavelengths. We describe ACTPol, an upgraded receiver for ACT, which uses feedhorn-coupled, polarization-sensitive detector arrays, a 3deg field of view, 100 mK cryogenics with continuous cooling, and meta material antireflection coatings. ACTPol comprises three arrays with separate cryogenic optics: two arrays at a central frequency of 148 GHz and one array operating simultaneously at both 97 GHz and 148 GHz. The combined instrument sensitivity, angular resolution, and sky coverage are optimized for measuring angular power spectra, clusters via the thermal Sunyaev-Zel'dovich (SZ) and kinetic SZ signals, and CMB lensing due to large-scale structure. The receiver was commissioned with its first 148 GHz array in 2013, observed with both 148 GHz arrays in 2014, and has recently completed its first full season of operations with the full suite of three arrays. This paper provides an overview of the design and initial performance of the receiver and related systems.

Telescope↗

NASA NTRS2008

Optimizing Requirements Decisions with KEYS

Recent work with NASA's Jet Propulsion Laboratory has allowed for external access to five of JPL's real-world requirements models, anonymized to conceal proprietary information, but retaining their computational nature. Experimentation with these models, reported herein, demonstrates a dramatic speedup in the computations performed on them. These models have a well defined goal: select mitigations that retire risks which, in turn, increases the number of attainable requirements. Such a non-linear optimization is a well-studied problem. However identification of not only (a) the optimal solution(s) but also (b) the key factors leading to them is less well studied. Our technique, called KEYS, shows a rapid way of simultaneously identifying the solutions and their key factors. KEYS improves on prior work by several orders of magnitude. Prior experiments with simulated annealing or treatment learning took tens of minutes to hours to terminate. KEYS runs much faster than that; e.g for one model, KEYS ran 13,000 times faster than treatment learning (40 minutes versus 0.18 seconds). Processing these JPL models is a non-linear optimization problem: the fewest mitigations must be selected while achieving the most requirements. Non-linear optimization is a well studied problem. With this paper, we challenge other members of the PROMISE community to improve on our results with other techniques.

requirements↗

NASA NTRS2019

Using Wind Observations from Nearby Aircraft to Update the Optimal Descent Trajectory in Real-Time

The ability to meet a controlled time of arrival during a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. However, if the wind forecast used to compute the initial trajectory plan is not accurate enough, the guidance system will need to correct time deviations from the plan during the execution of the descent. Previous work proposed an on-board guidance strategy based on model predictive control, which repeatedly updates the trajectory plan in real-time from the current aircraft state and for the remainder of the descent. However, the wind conditions downstream, at altitudes not explored yet, were difficult to predict due to the lack of data. This paper shows the potential benefits of using wind observations, broadcast by nearby aircraft, to reconstruct the wind profile downstream. The wind profile in the trajectory optimization problem is modeled as a spline, which control points are updated to fit the observations before re-planning the trajectory. Results from simulations using realistic wind data show that the performance of model predictive control significantly improves when including up-to-date wind observations, in terms of time and energy errors at the metering fix and fuel consumption.

Dalmau, Ramon↗

NASA NTRS1986

Near-optimal strategies for sub-decimeter satellite tracking with GPS

Decimeter tracking of low Earth orbiters using differential Global Positioning System (GPS) techniques is discussed. A precisely known global network of GPS ground receivers and a receiver aboard the user satellite are needed, and all techniques simultaneously estimate the user and GPS satellite orbits. Strategies include a purely geometric, a fully dynamic, and a hybrid strategy. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the hybrid strategy show the most promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a gravity adjustment method to exploit data from repeat ground tracks. These techniques promise to deliver subdecimeter accuracy down to the lowest satellite altitudes.

Yunck, Thomas P.↗

NASA NTRS1988

Telepresence and telerobotics

The capability for a single operator to simultaneously control complex remote multi degree of freedom robotic arms and associated dextrous end effectors is being developed. An optimal solution within the realm of current technology, can be achieved by recognizing that: (1) machines/computer systems are more effective than humans when the task is routine and specified, and (2) humans process complex data sets and deal with the unpredictable better than machines. These observations lead naturally to a philosophy in which the human's role becomes a higher level function associated with planning, teaching, initiating, monitoring, and intervening when the machine gets into trouble, while the machine performs the codifiable tasks with deliberate efficiency. This concept forms the basis for the integration of man and telerobotics, i.e., robotics with the operator in the control loop. The concept of integration of the human in the loop and maximizing the feed-forward and feed-back data flow is referred to as telepresence.

Garin, John↗

NASA NTRS1992

Multifunction tests of a frequency domain based flutter suppression system

The process is described of analysis, design, digital implementation, and subsonic testing of an active control flutter suppression system for a full span, free-to-roll wind tunnel model of an advanced fighter concept. The design technique uses a frequency domain representation of the plant and used optimization techniques to generate a robust multi input/multi output controller. During testing in a fixed-in-roll configuration, simultaneous suppression of both symmetric and antisymmetric flutter was successfully shown. For a free-to-roll configuration, symmetric flutter was suppressed to the limit of the tunnel test envelope. During aggressive rolling maneuvers above the open-loop flutter boundary, simultaneous flutter suppression and maneuver load control were demonstrated. Finally, the flutter damping controller was reoptimized overnight during the test using combined experimental and analytical frequency domain data, resulting in improved stability robustness.

Christhilf, David M.↗

NASA NTRS1998

Stellar Occultation Studies of the Solar System

Earth-based observations of stellar occultations provide extremely high spatial resolution for bodies in the outer solar system, about 10,000 times better than that of traditional imaging observations. Stellar occultation data can be used to establish the structure of atmospheres and rings of solar system bodies at high spatial resolution. Airborne occultation observations are particularly effective, since the controlled mobility of the observing platform allows the observer to fly within the optimum part of the occultation shadow for most events that are visible from Earth. Airborne observations are carried out above any clouds and are nearly free of scintillation noise from the Earth's atmosphere. KAO occultation observations resulted in the first detection of gravity waves in the Martian atmosphere, discovery of the Uranian rings, the first detection of Pluto's atmosphere, the first Earth-based investigations of Triton's atmosphere, and the discovery of narrow jets from Chiron's nucleus. The first SOFIA occultation opportunity will be an investigation of Pluto's atmospheric structure in November, 2002, and will resolve a problem that has lingered since the KAO discovery observation fourteen years earlier. We plan to continue our successful airborne occultation program with the greatly enhanced capability provided by SOFIA. We propose here to replace our KAO occultation photometer with one having twice the throughput, half the noise, a somewhat wider wavelength range, four times the field of view, and ten times the frame rate to optimize its performance and to capitalize on the larger collecting area offered by SOFIA. It will also allow for simultaneous visible and IR occultation observations, greatly enriching the results that we can obtain from occultations. We call this new imaging occultation photometer HOPI (High-speed Occultation Photometer and Imager). HOPI will provide a signal-to-noise ratio two to four times that of our present photometer for a given event, will permit useful observations of the more numerous events involving fainter stars, and will allow higher time resolution observations to be made. HOPI's characteristics also make it an ideal instrument for initial and ongoing evaluations of the SOFIA telescope's performance.

Elliot, James L.↗

NASA NTRS1998

Stellar Occultation Studies of the Solar System

Earth-based observations of stellar occultations provide extremely high spatial resolution for bodies in the outer solar system, about 10,000 times better than that of traditional imaging observations. Stellar occultation data can be used to establish the structure of atmospheres and rings of solar system bodies at high spatial resolution. Airborne occultation observations are particularly effective, since the controlled mobility of the observing platform allows the observer to fly within the optimum part of the occultation shadow for most events that are visible from Earth. Airborne observations are carried out above any clouds and are nearly free of scintillation noise from the Earth's atmosphere. KAO occultation observations resulted in the first detection of gravity waves in the Martian atmosphere, discovery of the Uranian rings, the first detection of Pluto's atmosphere, the first Earth-based investigations of Triton's atmosphere, and the discovery of narrow jets from Chiron's nucleus. The first SOFIA occultation opportunity will be an investigation of Pluto's atmospheric structure in November, 2002, and will resolve a problem that has lingered since the KAO discovery observation fourteen years earlier. We plan to continue our successful airborne occultation program with the greatly enhanced capability provided by SOFIA. We propose here to replace our KAO occultation photometer with one having twice the throughput, half the noise, a somewhat wider wavelength range, four times the field of view, and ten times the frame rate to optimize its performance and to capitalize on the larger collecting area offered by SOFIA. It will also allow for simultaneous visible and IR occultation observations, greatly enriching the results that we can obtain from occultations. We call this new imaging occultation photometer HOPI (High-speed Occultation Photometer and Imager). HOPI will provide a signal-to-noise ratio two to four times that of our present photometer for a given event, will permit useful observations of the more numerous events involving fainter stars, and will allow higher time resolution observations to be made. HOPI's characteristics also make it an ideal instrument for initial and ongoing evaluations of the SOFIA telescope's performance.

Elliot, James L.↗

NASA NTRS2011

Developing a Prototype ALHAT Human System Interface for Landing

The goal of the Autonomous Landing and Hazard Avoidance Technology (ALHAT) project is to safely execute a precision landing anytime/anywhere on the moon. This means the system must operate in any lighting conditions, operate in the presence of any thruster generated regolith clouds, and operate without the help of redeployed navigational aids or prepared landing site at the landing site. In order to reach this ambitious goal, computer aided technologies such as ALHAT will be needed in order to permit these landings to be done safely. Although there will be advanced autonomous capabilities onboard future landers, humans will still be involved (either onboard as astronauts or remotely from mission control) in any mission to the moon or other planetary body. Because many time critical decisions must be made quickly and effectively during the landing sequence, the Descent and Landing displays need to be designed to be as effective as possible at presenting the pertinent information to the operator, and allow the operators decisions to be implemented as quickly as possible. The ALHAT project has established the Human System Interface (HSI) team to lead in the development of these displays and to study the best way to provide operators enhanced situational awareness during landing activities. These displays are prototypes that were developed based on multiple design and feedback sessions with the astronaut office at NASA/ Johnson Space Center. By working with the astronauts in a series of plan/build/evaluate cycles, the HSI team has obtained astronaut feedback from the very beginning of the design process. In addition to developing prototype displays, the HSI team has also worked to provide realistic lunar terrain (and shading) to simulate a "out the window" view that can be adjusted to various lighting conditions (based on a desired date/time) to allow the same terrain to be viewed under varying lighting terrain. This capability will be critical to determining the effect of terrain/lighting on the human pilot, and how they use windows and displays during landing activities. The Apollo missions were limited to about 28 possible launch days a year due to lighting and orbital constraints. In order to take advantage of more landing opportunities and venture to more challenging landing locations, future landers will need to utilize sensors besides human eyes for scanning the surface. The ALHAT HSI system must effectively convey ALHAT produced information to the operator, so that landings can occur during less "optimal" conditions (lighting, surface terrain, slopes, etc) than was possible during Apollo missions. By proving this capability, ALHAT will simultaneously provide more flexible access to the moon, and greater safety margins for future landers. This paper will specifically focus on the development of prototype displays (the Trajectory Profile Display (TPD), Landing Point Designation (LPD), and Crew Camera View (CCV) ), implementation of realistic planetary terrain, human modeling, and future HSI plans.

Hirsh, Robert L.↗

NASA NTRSDate not supplied

Langley Automated Sensor Inter-calibration System (LASICS): Open Access Tools for Satellite Imager Inter- Calibration

Satellite imager calibration teams are tasked with maintaining stable measurement records to facilitate reliable monitoring of geophysical parameters and ensure dependable input for forecast models. Satellite imagers are neither uniformly calibrated nor radiometrically scaled to a common reference standard. Consistent inter-calibration between various earth-orbiting satellite imager pairs is a critical step in the creation of seamless earth-scene reflectance data records over time for input to higher level algorithms that retrieve earth system climate-sensitive properties. Each imager inherently by virtue of its optics (and associated properties like spectral response etc.) and orbit will have a unique measurement of the same earth-scene reflected signal. A key part of this is the computationally efficient and optimal identification and prediction of science opportunities where the imager pairs from the irrespective earth-orbits near-simultaneously view the same stable terrestrial targets with nearly identical viewing and solar geometry.

Arun Gopalan↗

NASA NTRSDate not supplied

Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs

A novel approach for modeling the aero-propulsive characteristics of an electric vertical takeoff and landing (eVTOL) aircraft was developed and demonstrated in wind tunnel testing. The approach was applied to the NASA LA-8 tandem tilt-wing eVTOL aircraft, using an efficient, hybrid experiment design composed of a static I-optimal response surface design for slowly-varying test variables, and dynamic orthogonal phase-optimized multisine excitations for the control surfaces and electric propulsors. Both the static and dynamic experiment designs were executed simultaneously to collect informative data for model identification. Statistically-weighted multivariate orthogonal function modeling was used to combine local modeling results computed in the frequency domain using data collected with dynamic excitations operating on the control effectors to form an aggregate aero-propulsive model. The final identified model exhibited good predictive capability when compared to validation data acquired separately from the data used to develop the model. The required test time using these new techniques was reduced by at least a factor of five compared to previous static wind tunnel testing for the LA-8 aircraft, while providing more informative data, greater parameterization flexibility, and high-quality models.

system identification↗

NASA NTRSDate not supplied

Deep Reinforcement Learning based Routing in an Air-to-Air Ad-hoc Network

This paper studies the Multiple Sources and Multiple Destinations (MSMD) routing problem in a dynamic Air-to-Air Ad-hoc Network (AAAN). We consider a spectrum limited scenario where multiple links have to share the same frequency channel so that co-channel interference becomes inevitable. As a result, routing decisions and spectrum access are coupled and must be jointly considered. This paper proposes a deep Q-learning based algorithm to find an optimal routing and channel selection strategy that minimizes the end-to-end communication delay. Specifically, under the assumption that only local information is available to every node, the Deep Q-Network (DQN) is trained offline to learn the optimal routing and channel selection strategy. After the trained DQN is implemented in every node, multiple relay nodes can simultaneously determine their next-hop relay and channel selections in real-time. Simulation results demonstrate the efficacy of our proposed algorithm.

AAAN↗

NASA NTRSDate not supplied

Deep Reinforcement Learning based Routing in an Air-to-Air Ad-hoc Network

This paper studies the Multiple Sources and Multiple Destinations (MSMD) routing problem in a dynamic Air-to-Air Ad-hoc Network (AAAN). We consider a spectrum limited scenario where multiple links have to share the same frequency channel so that co-channel interference becomes inevitable. As a result, routing decisions and spectrum access are coupled and must be jointly considered. This paper proposes a deep Q-learning based algorithm to find an optimal routing and channel selection strategy that minimizes the end-to-end communication delay. Specifically, under the assumption that only local information is available to every node, the Deep Q-Network (DQN) is trained offline to learn the optimal routing and channel selection strategy. After the trained DQN is implemented in every node, multiple relay nodes can simultaneously determine their next-hop relay and channel selections in real-time. Simulation results demonstrate the efficacy of our proposed algorithm.

AAAN↗

NASA NTRS2023

Mineralogical, Elemental, and Tomographic Reconnaissance Investigation for CLPS (METRIC)

METRIC is a robotic science laboratory that can determine the mineralogy, elemental chemistry, micromorphology, and thermophysical properties of planetary regolith. The METRIC suite comprises METRIC XRD/F, an X-ray diffraction/X-ray fluorescence instrument that can determine the mineralogy and elemental chemistry of regolith samples; METRIC XCT, a micro X-ray computed tomography instrument that can be used to evaluate grain/crystallite sizes and textures; METRIC IRS, an imaging spectrometer mounted on a rover that can determine mineralogy and thermophysical properties at the landing site; and a pneumatic sample collection, processing, distribution system developed by Honeybee Robotics. The payload elements could be deployed on a static lander or a rover. Data returned from the METRIC payload would inform origin, formation, and evolution of rocky planetary bodies. METRIC XRD/F draws on heritage from the CheMin instrument on the Mars Science Laboratory (MSL) Curiosity rover [1], with a few important improvements. Like CheMin, METRIC XRD/F operates in transmission geometry and uses piezoelectric actuators on sample cells in a tuning fork geometry to induce convective grain motion of the regolith to create a randomly oriented powder. MSL CheMin uses an energy-sensitive CCD to collect XRD patterns and XRF spectra simultaneously from the same sample cell, resulting in qualitative XRF data. METRIC XRD/F uses two different sample cells, one optimized for XRD and one optimized for XRF, and a silicon drift detector to detect fluoresced X-rays. This improvement to the XRF capabilities provides quantitative geochemical data of major elements down to Z = 11 and allows for the detection of minor and trace elements that are critical for evaluating geologic evolution of the Moon (e.g., P and Th). Modest improvements to the XRD geometry and hardware allow for better angular resolution and the ability to distinguish between members of the pyroxene group. METRIC XCT uses the same geometry and much of the same hardware as METRIC XRD/F, where a CCD would capture images of a regolith sample in a 3 mm diameter sample tube that is rotated 360° in steps <1°. Image brightness can be used to infer compositional data, where brighter materials indicate a higher Z, much like scanning electron microscopy. Data from METRIC XCT complement those from METRIC XRD/F. Particle size, shape, and texture can provide petrologic and provenance information, whereas vesicle size and morphology in volcanic or impact melt lithologies can inform cooling rates. METRIC IRS is a hyperspectral thermal imager that can be mounted to a lander or rover to provide mineralogical data from the broader landing site and help determine whether the samples analyzed by METRIC XRD/F and XCT are representative. The METRIC IRS spectral range (8–14 μm) and resolution (10.8 cm-1) allow for quantitative mineralogy from modelling Reststrahlen bands of major rock-forming minerals (e.g., silicates, phosphates). Radiance cubes can be processed and modelled with an onboard high-performance computer to determine mineral abundances of plagioclase, high-Ca pyroxene, pigeonite, orthopyroxene, olivine, and glass. Regolith samples can be acquired, processed, and delivered to the X-ray instruments via multiple sample handling systems, but the pneumatic sampling systems developed by Honeybee Robotics [e.g., 2] are best suited for relatively low-cost missions that are being competed for the Moon (e.g., NASA’s Payloads and Research Investigations for the Surface of the Moon program). There are pneumatic sampling systems that collect surface material and other systems that pneumatically drill up to ~1 m below the surface, providing material that has not been space weathered and has not been affected by the lander’s exhaust. [1] Blake, D. F., Vaniman, D., Achilles, C., Anderson, R., Bish, D., et al. (2012). Space Sci. Rev. 170, 341-478. https://doi.org/10.1007/s11214-012-9905-1. [2] Zacny, K., Betts, B., Hedlund, M., Long, P., Gramlich, M., Tura, K., Chu, P., Jacob, A., Garcia, A. (2014). IEEE Aerospace Conference, 3-7 March 2014, Big Sky, MT, U.S.A.

X-ray diffraction↗

NASA NTRS1998

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Majumdar, Alok↗

NASA NTRS2005

High Frequency QRS ECG Accurately Detects Cardiomyopathy

High frequency (HF, 150-250 Hz) analysis over the entire QRS interval of the ECG is more sensitive than conventional ECG for detecting myocardial ischemia. However, the accuracy of HF QRS ECG for detecting cardiomyopathy is unknown. We obtained simultaneous resting conventional and HF QRS 12-lead ECGs in 66 patients with cardiomyopathy (EF = 23.2 plus or minus 6.l%, mean plus or minus SD) and in 66 age- and gender-matched healthy controls using PC-based ECG software recently developed at NASA. The single most accurate ECG parameter for detecting cardiomyopathy was an HF QRS morphological score that takes into consideration the total number and severity of reduced amplitude zones (RAZs) present plus the clustering of RAZs together in contiguous leads. This RAZ score had an area under the receiver operator curve (ROC) of 0.91, and was 88% sensitive, 82% specific and 85% accurate for identifying cardiomyopathy at optimum score cut-off of 140 points. Although conventional ECG parameters such as the QRS and QTc intervals were also significantly longer in patients than controls (P less than 0.001, BBBs excluded), these conventional parameters were less accurate (area under the ROC = 0.77 and 0.77, respectively) than HF QRS morphological parameters for identifying underlying cardiomyopathy. The total amplitude of the HF QRS complexes, as measured by summed root mean square voltages (RMSVs), also differed between patients and controls (33.8 plus or minus 11.5 vs. 41.5 plus or minus 13.6 mV, respectively, P less than 0.003), but this parameter was even less accurate in distinguishing the two groups (area under ROC = 0.67) than the HF QRS morphologic and conventional ECG parameters. Diagnostic accuracy was optimal (86%) when the RAZ score from the HF QRS ECG and the QTc interval from the conventional ECG were used simultaneously with cut-offs of greater than or equal to 40 points and greater than or equal to 445 ms, respectively. In conclusion 12-lead HF QRS ECG employing RAZ scoring is a simple, accurate and inexpensive screening technique for cardiomyopathy. Although HF QRS ECG is highly sensitive for cardiomyopathy, its specificity may be compromised in patients with cardiac pathologies other than cardiomyopathy, such as uncomplicated coronary artery disease or multiple coronary disease risk factors. Further studies are required to determine whether HF QRS might be useful for monitoring cardiomyopathy severity or the efficacy of therapy in a longitudinal fashion.

Schlegel, Todd T.↗

NASA NTRS1973

DOPEX-1D2C: A one-dimensional, two-constraint radiation shield optimization code

A one-dimensional, two-constraint radiation sheild weight optimization procedure and a computer program, DOPEX-1D2C, is described. The DOPEX-1D2C uses the steepest descent method to alter a set of initial (input) thicknesses of a spherical shield configuration to achieve a minimum weight while simultaneously satisfying two dose-rate constraints. The code assumes an exponential dose-shield thickness relation with parameters specified by the user. Code input instruction, a FORTRAN-4 listing, and a sample problem are given. Typical computer time required to optimize a seven-layer shield is less than 1/2 minute on an IBM 7094.

Lahti, G. P.↗