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At least 613 records · Page 34

Analysis of Coupled Seals, Secondary and Powerstream Flow Fields in Aircraft and Aerospace Turbomachines

Higher power, high efficiency gas turbine engines require optimization of the seals and secondary flow systems as well as their impact on the powerstream. This work focuses on two aspects: 1. To apply the present day CFD tools (SCISEAL) to different real-life secondary flow applications from different original equipment manufacturers (OEM s) to provide feedback data and 2. Develop a computational methodology for coupled time-accurate simulation of the powerstream and secondary flow with emphasis on the interaction between the disk-cavity and rim seals flows with the powerstream (SCISEAL-MS-TURBO). One OEM simulation was of the Allison Engine Company T-56 turbine drum cavities including conjugate heat transfer with good agreement with data and provided design feedback information. Another was the GE aspirating seal where the 3-D CFD simulations played a major role in analysis and modification of that seal configuration. The second major objective, development of a coupled flow simulation capability was achieved by using two codes MS-TURBO for the powerstream and SCISEAL for the secondary flows with an interface coupling algorithm. The coupled code was tested against data from three differed configurations: 1. bladeless-rotor-stator-cavity turbine test rig, 2. UTRC high pressure turbine test rig, and, 3. the NASA Low-Speed-Air Compressor rig (LSAC) with results and limitations discussed herein.

Athavale, M. M.↗

Central-Monitor Software Module

One of the software modules of the emergency-vehicle traffic-light-preemption system of the two preceding articles performs numerous functions for the central monitoring subsystem. This module monitors the states of all units (vehicle transponders and intersection controllers): It provides real-time access to the phases of traffic and pedestrian lights, and maps the positions and states of all emergency vehicles. Most of this module is used for installation and configuration of units as they are added to the system. The module logs all activity in the system, thereby providing information that can be analyzed to minimize response times and optimize response strategies. The module can be used from any location within communication range of the system; with proper configuration, it can also be used via the Internet. It can be integrated into call-response centers, where it can be used for alerting emergency vehicles and managing their responses to specific incidents. A variety of utility subprograms provide access to any or all units for purposes of monitoring, testing, and modification. Included are "sniffer" utility subprograms that monitor incoming and outgoing data for accuracy and timeliness, and that quickly and autonomously shut off malfunctioning vehicle or intersection units.

Bachelder, Aaron↗

Extraction and Separation Modeling of Orion Test Vehicles with ADAMS Simulation

The Capsule Parachute Assembly System (CPAS) project has increased efforts to demonstrate the performance of fully integrated parachute systems at both higher dynamic pressures and in the presence of wake fields using a Parachute Compartment Drop Test Vehicle (PCDTV) and a Parachute Test Vehicle (PTV), respectively. Modeling the extraction and separation events has proven challenging and an understanding of the physics is required to reduce the risk of separation malfunctions. The need for extraction and separation modeling is critical to a successful CPAS test campaign. Current PTV-alone simulations, such as Decelerator System Simulation (DSS), require accurate initial conditions (ICs) drawn from a separation model. Automatic Dynamic Analysis of Mechanical Systems (ADAMS), a Commercial off the Shelf (COTS) tool, was employed to provide insight into the multi-body six degree of freedom (DOF) interaction between parachute test hardware and external and internal forces. Components of the model include a composite extraction parachute, primary vehicle (PTV or PCDTV), platform cradle, a release mechanism, aircraft ramp, and a programmer parachute with attach points. Independent aerodynamic forces were applied to the mated test vehicle/platform cradle and the separated test vehicle and platform cradle. The aero coefficients were determined from real time lookup tables which were functions of both angle of attack ( ) and sideslip ( ). The atmospheric properties were also determined from a real time lookup table characteristic of the Yuma Proving Grounds (YPG) atmosphere relative to the planned test month. Representative geometries were constructed in ADAMS with measured mass properties generated for each independent vehicle. Derived smart separation parameters were included in ADAMS as sensors with defined pitch and pitch rate criteria used to refine inputs to analogous avionics systems for optimal separation conditions. Key design variables were dispersed in a Monte Carlo analysis to provide the maximum expected range of the state variables at programmer deployment to be used as ICs in DSS. Extensive comparisons were made with Decelerator System Simulation Application (DSSA) to validate the mated portion of the ADAMS extraction trajectory. Results of the comparisons improved the fidelity of ADAMS with a ramp pitch profile update from DSSA. Post-test reconstructions resulted in improvements to extraction parachute drag area knock-down factors, extraction line modeling, and the inclusion of ball-to-socket attachments used as a release mechanism on the PTV. Modeling of two Extraction parachutes was based on United States Air Force (USAF) tow test data and integrated into ADAMS for nominal and Monte Carlo trajectory assessments. Video overlay of ADAMS animations and actual C-12 chase plane test videos supported analysis and observation efforts of extraction and separation events. The COTS ADAMS simulation has been integrated with NASA based simulations to provide complete end to end trajectories with a focus on the extraction, separation, and programmer deployment sequence. The flexibility of modifying ADAMS inputs has proven useful for sensitivity studies and extraction/separation modeling efforts. 1

Fraire, Usbaldo, Jr.↗

Improving the Fidelity of Capability & Resource Weighting in A Probalistic Risk Assessment Model for Spaceflight

INTRODUCTION NASA’s Informing Mission Planning via Analysis of Complex Tradespaces (IMPACT) tool uses Probabilistic Risk Assessment (PRA) to provide an evidence-based, data-driven estimate of how medical system capabilities affect mission outcomes. IMPACT maps condition incidence to available resources thereby facilitating the calculation of outcome metrics that allow the estimation of mission medical risk. Conditions can be nominally categorized as either treated or untreated depending on the availability of necessary diagnostic and therapeutic capabilities. This categorization enables IMPACT to estimate the effect of various medical system configurations on mission outcomes such as crew mortality, disability, crew member down-time, return to duty/recovery, and need for evacuation. IMPACT currently employs an equal weighting, “partial credit” approach to define treatment in which each of the capabilities associated with a given condition contributes an equal amount to management of the condition. This feature enables IMPACT to report values in between “fully untreated” and “fully treated” based on the proportion of capabilities available within the model. However, as is normal in medical/clinical practice, not all individual capabilities contribute equally to medical care. For example, the ability to provide intramuscular epinephrine during an anaphylactic episode contributes more likelihood of overall management success than does the administration of oral diphenhydramine. We hypothesize that weighting the relative contribution of each capability to each specific condition will improve outcome prediction and therefore will better provide mission planners with more nuanced and accurate options when designing space medical systems. METHODS Using a five-point Fibonacci scaling sequence (1, 2, 3, 5, 8) subject matter experts from NASA’s Exploration Medical Capabilities (ExMC) element assigned relative contribution weighting values to each identified capability within IMPACT. Since the relative importance of each capability varies depending on the specific condition, the resulting “partial” weighting was completed for more than 1,600 individual weighting assignments for 666 capabilities across 121 conditions. Each assignment required three-physician concurrence based on the overall importance of the capability to the diagnosis and management of the condition being considered and the difficulty with which it could be improvised by the crew. Once complete, 100,000 IMPACT simulations were run for a 6-month Lunar mission with a 30-day surface stay to evaluate the effect of this modification of the model. RESULTS Partial weighting significantly decreased predicted task time loss (TTL), evacuation, and loss of crew life without causing significant changes to the recommended medical system design. CONCLUSIONS The paucity of real-world referent data to support long-duration space missions of this type limits the ability to judge one predictive analytics method as superior to another. However, since the proposed method significantly reduces and optimizes outcome risks—without changing the medical system design—incorporating a partial weighting methodology is likely to provide a more accurate and operationally-relevant representation of medical risk without compromising IMPACTs ability to inform overarching medical system requirements.

Steller JG↗

CODEX Optical Design and Alignment

The COronal Diagnostic EXperiment (CODEX) is a Heliophysics mission to measure the density, temperature, and velocity of the electrons in the solar corona with the primary goal of improving our understanding of the physical conditions of the solar wind in the acceleration region. The temperature and velocity measurement requires much higher signal-to-noise ratio than the density measurements. In solar coronagraphs, the diffraction of the solar disk light due to the occulting element is the dominant source of noise. Therefore, to further suppress the diffracted sun light with respect to the existing coronagraphs is a critical element of the CODEX design. To minimize the stray light due to diffraction, the selected optical design is a two-stage standard coronagraph with an external occulter, an internal occulter, and a Lyot stop. What is unique for this design is that a focal mask was inserted at the telescope focal plane. It works together with the field lens suppressing the stray light down by ~ another order of magnitude as compared to a traditional three-stage approach. During the optical design, a Fourier Transform based beam propagation software, i.e., GLAD, was used to model the beam path through the full coronagraph, from the external occulter to the detector array. All diffraction sensitive elements: external occulter, internal occulter, focal mask, and Lyot stop were carefully modeled and optimized. As a result, the requirement of achieving a stray light level which is one order of magnitude lower than F-corona was satisfied. On the other hand, to achieve the final suppression, a precision optical alignment is another must. This paper also presents our creative alignment procedure: using the combination of metrology, precision alignment equipment, and real time diffraction ring monitoring to minimize the diffraction. The final test results show that the suppression ratio (B/B 0 ) reaches 10 -11 level, which is equivalent to one order of magnitude lower than F-corona.

CODEX optical design and alignment↗

Real-time neuromorphic algorithms for inverse kinematics of redundant manipulators

The paper presents an efficient neuromorphic formulation to accurately solve the inverse kinematics problem for redundant manipulators. The approach involves a dynamical learning procedure based on a novel formalism in neural network theory: the concept of 'terminal' attractors. Topographically mapped terminal attractors are used to define a neural network whose synaptic elements can rapidly encapture the inverse kinematics transformations, and, subsequently generalize to compute joint-space coordinates required to achieve arbitrary end-effector configurations. Unlike prior neuromorphic implementations, this technique can also systematically exploit redundancy to optimize kinematic criteria, e.g., torque optimization. Simulations on 3-DOF and 7-DOF redundant manipulators, are used to validate the theoretical framework and illustrate its computational efficacy.

Barhen, Jacob↗

Considerations for Isochronous Data Services over the Proximity-1 Space Link

Future mission concepts for robotic and human explorations will involve a high level of real time control/monitoring operations such as tele-operation for spacecraft rendezvous and surface mobile platforms carrying life-support equipments. The timely dissemination of voice, command, and real-time telemetry for monitoring and coordination purposes is critical for mission success. It is envisioned that future missions will require a network infrastructure capable of supporting isochronous data services. The CCSDS Proximity-1 Space Link Protocol1 could be used to provide isochronous service over the surface-to-Earth relay as well as "beyond-the-horizon" communications between distant Lunar or Mars surface elements. This paper will analyze the latency, jitter, and throughput performance of the Proximity-1 protocol for isochronous applications. In particular we will focus on constrained scenarios where the protocol operates in full-duplex mode, carrying isochronous traffic in one direction and error-controlled traffic in the other direction. We analyze the impact of the strict priority scheme in Proximity-1 on delay jitter and the impact of the isochronous traffic on the efficiency of the reliable data transfer in the other direction, and discuss methods for performance optimization. In general, jitter performance is driving by relative loading of isochronous traffic on the forward link compared to the acknowledgement traffic. Under light loading condition, the upper-bound of the delay jitter is the transmission duration of an acknowledgement frame on the forward link; for higher loading scenarios, the maximum jitter is scaled up by the inverse of the residual bandwidth, i.e., the spare capacity available in the forward link to carry isochronous traffic.

isochronous communications↗

Bandwidth limitations on noiseless optical channel capacity

The channel capacity of an optical communications link utilizing direct photon detection can be substantially larger than the heterodyne detection quantum limit. In the limit of a noiseless channel the capacity per received photon can even be infinite. In most communications systems the real constraint is to deliver a certain throughput capacity measured in nats/second. The current investigation has the objective to show that due to physical limitations on the minimum time resolution which can be achieved, and for any given throughput capacity in nats/second, there exists an optimum PPM word size which maximizes the 'power efficiency capacity' expressed in nats/photon. Such an optimization will allow the system-designer to minimize the amount of power needed to achieve the desired throughput without violating his bandwidth constraint.

Butman, S. A.↗

Containerless processing technologies at the Jet Propulsion Laboratory

Acoustic and electrostatic levitation (EL) techniques for maintaining sample-wall distance in order to ensure contamination-free conditions during microgravity materials science experiments on board the Shuttle are examined. A laboratory model for acoustic containerless (AC) processing is described, noting the use of three commercially available drivers for sample levitation. The arrangement of the speakers results in a point node to which a liquid drop sample migrates. Varying the field through manipulation of the dB levels and phase of the drivers' outputs permits control of sample position and movement. Rotation of a styrofoam ball at 2000 rpm has been achieved. Oscillations can also be induced. An advanced version of the AC system is analytically defined, with further studies mentioned for stable levitation modes using a cylindrical chamber and optimizing acoustic power transfer between hot and cold regions. A tetrahedral EL system has proven to work in a reduced gravity environment. El involves imparting an electrical charge to an object and then positioning and maintaining it through use of EM fields. The presence of human operators to perform the processing on the Shuttle is mentioned as offering real-time capability of altering the experimental conditions.

Wang, T. G.↗

STS-53 Space Shuttle mission report

The STS-53 Space Shuttle Program Mission Report provides a summary of the Orbiter, External Tank (ET), Solid Rocket Booster/Redesigned Solid Rocket Motor (SRB/RSRM), and the Space Shuttle Main Engine (SSME) subsystems performance during the fifty-second flight of the Space Shuttle Program, and the fifteenth flight of the Orbiter vehicle Discovery (OV-103). In addition to the Orbiter, the flight vehicle consisted of an ET, which was designated as ET-49/LWT-42; three SSME's, which were serial numbers 2024, 2012, and 2017 in positions 1, 2, and 3, respectively; and two SRB's, which were designated BI-055. The lightweight RSRM's that were installed in each SRB were designated 360L028A for the left SRB, and 360L028B for the right SRB. The primary objective of this flight was to successfully deploy the Department of Defense 1 (DOD-1) payload. The secondary objectives of this flight were to perform the operations required by the Glow Experiment/Cryogenic Heat Pipe Experiment Payload (GCP); the Hand-Held, Earth-Oriented, Real-Time, Cooperative, User-Friendly, Location-Targeting and Environmental System (HERCULES); the Space Tissue Loss (STL); the Battlefield Laser Acquisition Sensor Test (BLAST); the Radiation Monitoring Equipment-III (RME-III); the Microcapsules in Space-1 (MIS-1); the Visual Function Tester-2 (VFT-2); the Cosmic Radiation Effects and Activation Monitor (CREAM); the Clouds Logic to Optimize Use of Defense Systems-1A (CLOUDS-1A); the Fluids Acquisition and Resupply Experiment (FARE); and the Orbital Debris Radar Calibration Spheres (ODERACS). In addition to presenting a summary of subsystem performance, this report also discusses each Orbiter, ET, SSME, SRB, and RSRM in-flight anomaly in the applicable section of the report. Listed in the discussion of each anomaly is the officially assigned tracking number as published by each Project Office in their respective Problem Tracking List. All times given in this report are in Greenwich mean time (G.m.t.) as well as mission elapsed time (MET).

Fricke, Robert W., Jr.↗

Developing Mars-Based Clinical Scenarios for an Earth Independent Medical Operations (EIMO) – Based Decision Support Service

As crewed missions move beyond Low-Earth Orbit, pre-mission planning cannot fully buy down the medical risks of exploration-class missions. Martian missions, where increased hazards exist, (such as long-duration spaceflight, surface-level EVA operations, and communications delays) will require a paradigm shift in the structure of a medical system. An Earth-Independent Medical Operations-based Medical System (EIMO-MS) will need to optimize four critical domains to help provide medical care: utilization of Pre-Mission Planning, augmentation of Acute and Prolonged Medical Decision Making, automated tracking of Resource Management, and assistance in Task Load Balance. The ideal EIMO-MS will be able to accomplish this goal by having an interactive, adaptable interface that will be able to provide real-time medical services. It must respond based on the level of crewmember training, medical situation, and available medical and non-medical resources. To showcase the capabilities and requirements of such a sophisticated automated MS, a series of clinical scenarios of escalating complexity were developed with clinical and systems engineering input. These scenarios describe in clinical detail what a theoretical future medical system, enhanced with multiple information streams (such as a medical database, an AI-based Decision Support System, real-time monitoring, enhanced in-situ laboratory imaging, etc.) can achieve in conjunction with a trained and experienced crew. Scenarios are comprised of: a context section including objectives and applicable spaceflight environment, a highlighted assumptions section, a clinical narrative section, and a systems engineering activity diagram demonstrating the integrated Medical System (MS). The “swim lanes” of the activity diagram act as the logistical core of each scenario and show how the MS will interact with the crew, ground support, and other in-flight systems. The Design Reference Mission that is used for the scenarios is based on existing reference mission profiles [1] with a projected 30-sol stay on the Martian surface. Scenarios span the spectrum from planned evaluations, minor medical care, urgent care, surgical guidance, critical and expectant management, and behavioral health care. Mission complexity will exponentially increase during deep space and Mars exploration-class missions, and medical support for these missions will likewise need to increase in autonomy and adaptability. The integrated system that will support these missions will need to provide assistance in a variety of anticipated and unforeseen scenarios. These medical scenarios, guided by clinician input, are initial steps in crafting the requirements for an EIMO-based medical system. By working in a systems engineering framework, requirements and capabilities can be extracted and mapped while maintaining a clinical core.

Prashant Parmar↗

A System Trade Study of Remote Infrared Imaging for Space Shuttle Reentry

A trade study reviewing the primary operational parameters concerning the deployment of imaging assets in support of the Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) project was undertaken. The objective was to determine key variables and constraints for obtaining thermal images of the Space Shuttle orbiter during reentry. The trade study investigated the performance characteristics and operating environment of optical instrumentation that may be deployed during a HYTHIRM data collection mission, and specified contributions to the Point Spread Function. It also investigated the constraints that have to be considered in order to optimize deployment through the use of mission planning tools. These tools simulate the radiance modeling of the vehicle as well as the expected spatial resolution based on the Orbiter trajectory and placement of land based or airborne optical sensors for given Mach numbers. Lastly, this report focused on the tools and methodology that have to be in place for real-time mission planning in order to handle the myriad of variables such as trajectory ground track, weather, and instrumentation availability that may only be known in the hours prior to landing.

Schwartz, Richard J.↗

Data-Analysis System for Entry, Descent, and Landing

A report describes the Entry Descent Landing Data Analysis (EDA), which is a system of signal-processing software and computer hardware for acquiring status data conveyed by multiple-frequency-shift-keying tone signals transmitted by a spacecraft during descent to the surface of a remote planet. The design of the EDA meets the challenge of processing weak, fluctuating signals that are Doppler-shifted by amounts that are only partly predictable. The software supports both real-time and post processing. The software performs fast-Fourier-transform integration, parallel frequency tracking with prediction, and mapping of detected tones to specific events. The use of backtrack and refinement parallel-processing threads helps to minimize data gaps. The design affords flexibility to enable division of a descent track into segments, within each of which the EDA is configured optimally for processing in the face of signal conditions and uncertainties. A dynamic-lock-state feature enables the detection of signals using minimum required computing power less when signals are steadily detected, more when signals fluctuate. At present, the hardware comprises eight dual-processor personal-computer modules and a server. The hardware is modular, making it possible to increase computing power by adding computers.

Pham, Timothy↗

Virtual Exercise Training Software System

The purpose of this study was to develop and evaluate a virtual exercise training software system (VETSS) capable of providing real-time instruction and exercise feedback during exploration missions. A resistive exercise instructional system was developed using a Microsoft Kinect depth-camera device, which provides markerless 3-D whole-body motion capture at a small form factor and minimal setup effort. It was hypothesized that subjects using the newly developed instructional software tool would perform the deadlift exercise with more optimal kinematics and consistent technique than those without the instructional software. Following a comprehensive evaluation in the laboratory, the system was deployed for testing and refinement in the NASA Extreme Environment Mission Operations (NEEMO) analog.

Vu, L.↗

Climate drives modeled forest carbon cycling resistance and resilience in the Upper Great Lakes Region, USA

Forests dominate the global terrestrial carbon budget, but their ability to continue doing so in the face of a changing climate is uncertain. A key uncertainty is how forests will respond to (resistance) and recover from (resilience) rising levels of disturbance of varying intensities. This knowledge gap can optimally be addressed by integrating manipulative field experiments with ecophysiological modeling. We used the Ecosystem Demography-2.2 (ED-2.2) model to project carbon fluxes for a northern temperate deciduous forest subjected to a real-world disturbance severity manipulation experiment. ED-2.2 was run for 150 years, starting from near bare ground in 1900 (approximating the clear-cut conditions at the time), and subjected to three disturbance treatments under an ensemble of climate conditions. Both disturbance severity and climate strongly affected carbon fluxes such as gross primary production (GPP), and interacted with one another. We then calculated resistance and resilience, two dimensions of ecosystem stability. Modeled GPP exhibited a two-fold decrease in mean resistance across disturbance severities of 45%, 65%, and 85% mortality; conversely, resilience increased by a factor of two with increasing disturbance severity. This pattern held for net primary production and net ecosystem production, indicating a trade-off in which greater initial declines were followed by faster recovery. Notably, however, heterotrophic respiration responded more slowly to disturbance, and its highly variable response was affected by different drivers. This work provides insight into how future conditions might affect the functional stability of mature forests in this region under ongoing climate change and changing disturbance regimes.

Kalyn Dorheim↗

Climate drives modeled forest carbon cycling resistance and resilience in the Upper Great Lakes Region, USA

Forests dominate the global terrestrial carbon budget, but their ability to continue doing so in the face of a changing climate is uncertain. A key uncertainty is how forests will respond to (resistance) and recover from (resilience) rising levels of disturbance of varying intensities. This knowledge gap can optimally be addressed by integrating manipulative field experiments with ecophysiological modeling. We used the Ecosystem Demography-2.2 (ED-2.2)model to project carbon fluxes for a northern temperate deciduous forest subjected to a real-world disturbance severity manipulation experiment. ED-2.2 was run for 150 years, starting from near bare ground in 1900(approximating the clear-cut conditions at the time),and subjected to three disturbance treatments under an ensemble of climate conditions. Both disturbance severity and climate strongly affected carbon fluxes such as gross primary production (GPP),and interacted with one another. We then calculated resistance and resilience, two dimensions of ecosystem stability. Modeled GPP exhibited a two-fold decrease in mean resistance across disturbance severities of 45%, 65%, and 85% mortality; conversely, resilience increased by a factor of two with increasing disturbance severity. This pattern held for net primary production and net ecosystem production, indicating a trade-off in which greater initial declines were followed by faster recovery. Notably, however, heterotrophic respiration responded more slowly to disturbance, and its highly variable response was affected by different drivers. This work provides insight into how future conditions might affect the functional stability of mature forests in this region under ongoing climate change and changing disturbance regimes.

Kalyn Dorheim↗

The Future of in-Situ Sequencing-Based Microbial Monitoring: Development of a Shelf-Stable Method for Artemis and Beyond

Microbial monitoring onboard the International Space Station (ISS) is essential for assessing the efficiency of the Environmental Control and Life Support Systems (ECLSS) and providing insight into potential risk to both crew and spacecraft. Historically, this monitoring required the need to culture organisms onboard, return these cultures to Earth, and then complete the identifications, a process that would take months. Over the past decade, and through numerous payloads, advances in molecular biology have enabled in-flight microbial identifications using nanopore sequencing. The swab-to-sequencer method resulting from these efforts was transitioned from research to operations for microbial monitoring under the Crew Health Care Systems (CHeCS) BioMole. Collectively, these accomplishments have propelled the swab-to-sequencer method to be selected as the Microbial Surface Monitor (MSM) for Gateway, as well as a payload on Artemis IV. However, the lack of cold stowage availability for Artemis requires modifications to the entire method due to the thermal instability of the reagents required for sample preparation. To achieve this, new development, optimization, and validations were undertaken. Key considerations included enzyme concentration, buffer compatibility, and equal or enhanced sensitivity and specificity. At each step, thorough side-by-side comparisons with the current ISS method were performed. The development of a robust shelf-stable method will ensure continued sequencing-based microbial monitoring for Artemis and beyond, providing data in near real-time, enhancing risk response time, and yielding clear insight into the microbiome of spacecraft.

Christian G Mena↗

A PC program to optimize system configuration for desired reliability at minimum cost

High reliability is desired in all engineered systems. One way to improve system reliability is to use redundant components. When redundant components are used, the problem becomes one of allocating them to achieve the best reliability without exceeding other design constraints such as cost, weight, or volume. Systems with few components can be optimized by simply examining every possible combination but the number of combinations for most systems is prohibitive. A computerized iteration of the process is possible but anything short of a super computer requires too much time to be practical. Many researchers have derived mathematical formulations for calculating the optimum configuration directly. However, most of the derivations are based on continuous functions whereas the real system is composed of discrete entities. Therefore, these techniques are approximations of the true optimum solution. This paper describes a computer program that will determine the optimum configuration of a system of multiple redundancy of both standard and optional components. The algorithm is a pair-wise comparative progression technique which can derive the true optimum by calculating only a small fraction of the total number of combinations. A designer can quickly analyze a system with this program on a personal computer.

Hills, Steven W.↗