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At least 343 records · Page 19

The Attraction Indian Buffet Distribution

We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.

97 MATHEMATICS AND COMPUTING↗

Coal gasification systems engineering and analysis, volume 2

The major design related features of each generic plant system were characterized in a catalog. Based on the catalog and requirements data, approximately 17 designs and cost estimates were developed for MBG and alternate products. A series of generic trade studies was conducted to support all of the design studies. A set of cost and programmatic analyses were conducted to supplement the designs. The cost methodology employed for the design and sensitivity studies was documented and implemented in a computer program. Plant design and construction schedules were developed for the K-T, Texaco, and B&W MBG plant designs. A generic work breakdown structure was prepared, based on the K-T design, to coincide with TVA's planned management approach. An extensive set of cost sensitivity analyses was completed for K-T, Texaco, and B&W design. Product price competitiveness was evaluated for MBG and the alternate products. A draft management policy and procedures manual was evaluated. A supporting technology development plan was developed to address high technology risk issues. The issues were identified and ranked in terms of importance and tractability, and a plan developed for obtaining data or developing technology required to mitigate the risk.

Source record↗

A Framework for Robust Multivariable Optimization of Integrated Circuits in Space Applications

Application Specific Integrated Circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way which facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as framework of software modules, templates and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation. Templates provide a starting point for both while toolbox functions minimize the code required. Once a test bench has been coded to optimize a particular circuit, it is also used to verify the final design. The combination of test bench and cost function can then serve as a template for similar circuits or be re-used to migrate the design to different processes by re-running it with the new process specific device models. The system has been used in the design of time to digital converters for laser ranging and time-of-flight mass spectrometry to optimize analog, mixed signal and digital circuits such as charge sensitive amplifiers, comparators, delay elements, radiation tolerant dual interlocked (DICE) flip-flops and two of three voter gates.

DuMonthier, Jeffrey↗

LPV Modeling of a Flexible Wing Aircraft Using Modal Alignment and Adaptive Gridding Methods

One of the earliest approaches in gain-scheduling control is the gridding based approach, in which a set of local linear time-invariant models are obtained at various gridded points corresponding to the varying parameters within the flight envelop. In order to ensure smooth and effective Linear Parameter-Varying control, aligning all the flexible modes within each local model and maintaining small number of representative local models over the gridded parameter space are crucial. In addition, since the flexible structural models tend to have large dimensions, a tractable model reduction process is necessary. In this paper, the notion of s-shifted H2- and H Infinity-norm are introduced and used as a metric to measure the model mismatch. A new modal alignment algorithm is developed which utilizes the defined metric for aligning all the local models over the entire gridded parameter space. Furthermore, an Adaptive Grid Step Size Determination algorithm is developed to minimize the number of local models required to represent the gridded parameter space. For model reduction, we propose to utilize the concept of Composite Modal Cost Analysis, through which the collective contribution of each flexible mode is computed and ranked. Therefore, a reduced-order model is constructed by retaining only those modes with significant contribution. The NASA Generic Transport Model operating at various flight speeds is studied for verification purpose, and the analysis and simulation results demonstrate the effectiveness of the proposed modeling approach.

LPV Modeling↗

Robust Multivariable Optimization and Performance Simulation for ASIC Design

Application-specific-integrated-circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power, and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem, which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques, which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable, are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way that facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as a framework of software modules, templates, and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation.

DuMonthier, Jeffrey↗

Star counts and galactic structure

Star counts are discussed as an aid in studies of galactic structure. Iterative computations using a method-of-color-bins to match numerical models with observational data are described. The star counts provide bounds for the luminosity function and the color-magnitude diagram and allow spheroid normalization in a copycat Galaxy model which posits a galaxy with a Population I disk and a Population II spheroid. Good agreement has been obtained between star counts predicted by the model and observed distributions, including color and magnitude ranges and direction. Modifications being considered for the model include consideration of the halo, a galactic bulge and a thick disk. Several galactic structural features which have yet to be modeled and which may be tractable to the copycat model corrected with star counts are identified.

Bahcall, John N.↗

Geometric Modeling of Inclusions as Ellipsoids

Nonmetallic inclusions in gas turbine disk alloys can have a significant detrimental impact on fatigue life. Because large inclusions that lead to anomalously low lives occur infrequently, probabilistic approaches can be utilized to avoid the excessively conservative assumption of lifing to a large inclusion in a high stress location. A prerequisite to modeling the impact of inclusions on the fatigue life distribution is a characterization of the inclusion occurrence rate and size distribution. To help facilitate this process, a geometric simulation of the inclusions was devised. To make the simulation problem tractable, the irregularly sized and shaped inclusions were modeled as arbitrarily oriented, three independent dimensioned, ellipsoids. Random orientation of the ellipsoid is accomplished through a series of three orthogonal rotations of axes. In this report, a set of mathematical models for the following parameters are described: the intercepted area of a randomly sectioned ellipsoid, the dimensions and orientation of the intercepted ellipse, the area of a randomly oriented sectioned ellipse, the depth and width of a randomly oriented sectioned ellipse, and the projected area of a randomly oriented ellipsoid. These parameters are necessary to determine an inclusion s potential to develop a propagating fatigue crack. Without these mathematical models, computationally expensive search algorithms would be required to compute these parameters.

Bonacuse, Peter J.↗

Validation of Image-Based Neural Network Controllersthrough Adaptive Stress Testing

Neural networks have become state-of-the-art for computer vision problems because of their ability to efficiently model complex functions from large amounts of data. While neural networks can be shown to perform well empirically fora variety of tasks, their performance is difficult to guarantee.Neural network verification tools have been developed that can certify robustness with respect to a given input image; however,for neural network systems used in closed-loop controllers,robustness with respect to individual images does not address multi-step properties of the neural network controller and itsenvironment. Furthermore, neural network systems interacting in the physical world and using natural images are operating in a black-box environment, making formal verification in-tractable. This work combines the adaptive stress testing (AST)framework with neural network verification tools to search for the most likely sequence of image disturbances that cause the neural network controlled system to reach a failure. Anautonomous aircraft taxi application is presented, and results show that the AST method finds failures with more likely image disturbances than baseline methods. Further analysis of AST results revealed an explainable cause of the failure, giving insight into the problematic scenarios that should be addressed.

Adaptive Stress Testing, Marabou, Deep Neural Netw↗

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than \building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) confirm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results analysis methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exemplified through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of the Monte Carlo N-Particle radiation transport simulation tool, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) confirm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results assessment methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exemplified through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of the Monte Carlo N-Particle radiation transport simulation tool, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) con firm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results assessment methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exempli fied through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reveal, A General Reverse Engineering Algorithm for Inference of Genetic Network Architectures

Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/output patterns of its variables? We investigated this possibility using binary models of genetic networks. Trajectories, or state transition tables of Boolean nets, resemble time series of gene expression. By systematically analyzing the mutual information between input states and output states, one is able to infer the sets of input elements controlling each element or gene in the network. This process is unequivocal and exact for complete state transition tables. We implemented this REVerse Engineering ALgorithm (REVEAL) in a C program, and found the problem to be tractable within the conditions tested so far. For n = 50 (elements) and k = 3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10(exp 15)) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean networks, the algorithm is generalizable to include multi-state models, essentially allowing direct application to realistic biological data sets. The ability to adequately solve the inverse problem may enable in-depth analysis of complex dynamic systems in biology and other fields.

Liang, Shoudan↗

SPECTER: efficient evaluation of the spectral EMD

The Energy Mover’s Distance (EMD) has seen use in collider physics as a metric between events and as a geometric method of defining infrared and collinear safe observables. Recently, the Spectral Energy Mover’s Distance (SEMD) has been proposed as a more analytically tractable alternative to the EMD. In this work, we obtain a closed-form expression for the Riemannian-like p = 2 SEMD metric between events, eliminating the need to numerically solve an optimal transport problem. Additionally, we show how the SEMD can be used to define event and jet shape observables by minimizing the distance between events and parameterized energy flows (similar to the EMD), and we obtain closed-form expressions for several of these observables. We also present the Specter framework, an efficient and highly parallelized implementation of the SEMD metric and SEMD-derived shape observables as an analogue of the previously-introduced Shaper for EMD-based computations. We demonstrate that computing the SEMD with Specter can be up to a thousand times faster than computing the EMD with standard optimal transport libraries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fast and accurate simulations of calorimeter showers with normalizing flows

In this study, we introduce caloflow, a fast detector simulation framework based on normalizing flows. For the first time, we demonstrate that normalizing flows can reproduce many-channel calorimeter showers with extremely high fidelity, providing a fresh alternative to computationally expensive geant4 simulations, as well as other state-of-the-art fast simulation frameworks based on generative adversarial networks (GANs) or variational autoencoders (VAEs). In addition to the usual histograms of physical features and images of calorimeter showers, we introduce a new metric for judging the quality of generative modeling: the performance of a classifier trained to differentiate real from generated images. We show that GAN-generated images can be identified by the classifier with nearly 100% accuracy, while images generated from caloflow are better able to fool the classifier. More broadly, normalizing flows offer several advantages compared to other state-of-the-art approaches (GANs and VAEs), including tractable likelihoods, stable and convergent training, and principled model selection. Normalizing flows also provide a bijective mapping between data and the latent space, which could have other applications beyond simulation, for example, to detector unfolding.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Monatomic ions influence substrate permeation across bacterial microcompartment shells

Abstract Bacterial microcompartments (BMCs) are protein organelles consisting of an inner enzymatic core encased within a selectively permeable shell. BMC shells are modular, tractable architectures that can be repurposed with new interior enzymes for biomanufacturing purposes. The permeability of BMC shells is function-specific and regulated by biophysical properties of the shell subunits, especially its pores. We hypothesized that ions may interact with pore residues in a manner that influences the substrate permeation process. In vitro activity comparisons between native and broken BMCs demonstrated that increasing NaCl negatively affects permeation rates. Molecular dynamics simulations of the dominant shell protein (BMC-H) revealed that chloride ions preferentially occupy the positive pore, hindering substrate permeation, while sodium cations remain excluded. Overall, these results demonstrate that shell properties influence ion permeability and leverages the integration of experimental and computational techniques to improve our understanding of BMC shells towards their repurposing for biotechnological applications.

59 BASIC BIOLOGICAL SCIENCES↗

Challenges for density functional theory: calculation of CO adsorption on electrocatalytically relevant metals

Density Functional Theory (DFT) is currently the most tractable choice of theoretical model used to understand the mechanistic pathways for electrocatalytic processes such as CO 2 or CO reduction. In this work, we assess the performance of two DFT functionals designed specifically to describe surface interactions, RTPSS and RPBE, as well as two popular meta-GGA functionals, SCAN and B97M-rV, that have not been a priori optimized for better interfacial properties. We assess all four functionals against available experimental data for prediction of bulk and bare surface properties on four electrocatalytically relevant metals, Au, Ag, Cu, and Pt, and for binding CO to surfaces of these metals. To partially mitigate issues such as thermal and anharmonic corrections associated with comparing computations with experiments, molecular benchmarks against high level quantum chemistry are reported for CO complexes with Au, Ag, Cu and Pt atoms, as well as the CO–water complex and the water dimer. Overall, we find that the surface modified RPBE functional performs reliably for many of the benchmarks examined here, and the meta-GGA functionals also show promising results. Specifically B97M-rV predicts the correct site preference for CO binding on Ag and Au (the only functional tested here to do so), while RTPSS performs well for surface relaxations and binding of CO on Pt and Cu.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hierarchical Modeling and Robust Synthesis for the Preliminary Design of Large Scale Complex Systems

Large-scale complex systems are characterized by multiple interacting subsystems and the analysis of multiple disciplines. The design and development of such systems inevitably requires the resolution of multiple conflicting objectives. The size of complex systems, however, prohibits the development of comprehensive system models, and thus these systems must be partitioned into their constituent parts. Because simultaneous solution of individual subsystem models is often not manageable iteration is inevitable and often excessive. In this dissertation these issues are addressed through the development of a method for hierarchical robust preliminary design exploration to facilitate concurrent system and subsystem design exploration, for the concurrent generation of robust system and subsystem specifications for the preliminary design of multi-level, multi-objective, large-scale complex systems. This method is developed through the integration and expansion of current design techniques: Hierarchical partitioning and modeling techniques for partitioning large-scale complex systems into more tractable parts, and allowing integration of subproblems for system synthesis; Statistical experimentation and approximation techniques for increasing both the efficiency and the comprehensiveness of preliminary design exploration; and Noise modeling techniques for implementing robust preliminary design when approximate models are employed. Hierarchical partitioning and modeling techniques including intermediate responses, linking variables, and compatibility constraints are incorporated within a hierarchical compromise decision support problem formulation for synthesizing subproblem solutions for a partitioned system. Experimentation and approximation techniques are employed for concurrent investigations and modeling of partitioned subproblems. A modified composite experiment is introduced for fitting better predictive models across the ranges of the factors, and an approach for constructing partitioned response surfaces is developed to reduce the computational expense of experimentation for fitting models in a large number of factors. Noise modeling techniques are compared and recommendations are offered for the implementation of robust design when approximate models are sought. These techniques, approaches, and recommendations are incorporated within the method developed for hierarchical robust preliminary design exploration. This method as well as the associated approaches are illustrated through their application to the preliminary design of a commercial turbofan turbine propulsion system. The case study is developed in collaboration with Allison Engine Company, Rolls Royce Aerospace, and is based on the Allison AE3007 existing engine designed for midsize commercial, regional business jets. For this case study, the turbofan system-level problem is partitioned into engine cycle design and configuration design and a compressor modules integrated for more detailed subsystem-level design exploration, improving system evaluation. The fan and low pressure turbine subsystems are also modeled, but in less detail. Given the defined partitioning, these subproblems are investigated independently and concurrently, and response surface models are constructed to approximate the responses of each. These response models are then incorporated within a commercial turbofan hierarchical compromise decision support problem formulation. Five design scenarios are investigated, and robust solutions are identified. The method and solutions identified are verified by comparison with the AE3007 engine. The solutions obtained are similar to the AE3007 cycle and configuration, but are better with respect to many of the requirements.

Koch, Patrick N.↗