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NASA NTRS1996

Cascade Optimization Strategy for Aircraft and Air-Breathing Propulsion System Concepts

Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the respective merit functions. Because of the diversity of constraint types and the overall distortion of the design space, the most reliable single optimization algorithm available in COMETBOARDS could not produce a satisfactory feasible optimum solution. Some of COMETBOARDS' unique features, which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications, successfully optimized the performance of both aircraft and engines. The cascade method has two principal steps: In the first, the solution initiates from a user-specified design and optimizer, in the second, the optimum design obtained in the first step with some random perturbation is used to begin the next specified optimizer. The second step is repeated for a specified sequence of optimizers or until a successful solution of the problem is achieved. A successful solution should satisfy the specified convergence criteria and have several active constraints but no violated constraints. The cascade strategy available in the combined COMETBOARDS, FLOPS, and NEPP design tool converges to the same global optimum solution even when it starts from different design points. This reliable and robust design tool eliminates manual intervention in the design of aircraft and of air-breathing propulsion engines where it eases the cycle analysis procedures. The combined code is also much easier to use, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capability of the combined design tool through the optimization of a subsonic aircraft and a high-bypass-turbofan wave-rotor-topped engine.

Patnaik, Surya N.↗

NASA NTRS1996

Optimization of Air-Breathing Engine Concept

The design optimization of air-breathing propulsion engine concepts has been accomplished by soft-coupling the NASA Engine Performance Program (NEPP) analyzer with the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Engine problems, with their associated design variables and constraints, were cast as nonlinear optimization problems with thrust as the merit function. Because of the large number of mission points in the flight envelope, the diversity of constraint types, and the overall distortion of the design space; the most reliable optimization algorithm available in COMETBOARDS, when used by itself, could not produce satisfactory, feasible, optimum solutions. However, COMETBOARDS' unique features-which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications-successfully optimized the performance of subsonic and supersonic engine concepts. Even when started from different design points, the combined COMETBOARDS and NEPP results converged to the same global optimum solution. This reliable and robust design tool eliminates manual intervention in the design of air-breathing propulsion engines and eases the cycle analysis procedures. It is also much easier to use than other codes, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capabilities of the combined design tool through the optimization of a high-bypass- turbofan wave-rotor-topped subsonic engine and a mixed-flow-turbofan supersonic engine.

Patnaik, Surya N.↗

NASA NTRS1998

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Patniak, Surya N.↗

NASA NTRS1997

GOME wavelength calibration using solar and atmospheric spectra

Spectral information in the global ozone monitoring experiment (GOME) solar irradiance spectra and GOME earth radiance spectra are used in conjunction with the GOME solar reference spectrum to provide absolute vacuum internal wavelength calibration for GOME. Two methods for wavelength calibration of GOME data are investigated. The first employs chi-square minimization of a merit function involving wavelength and the GOME slit function. It is quite robust and requires little GOME data in the processing (calibration window regions from 15 to 40 pixels). The second employs cross correlation of GOME data and the solar reference spectrum in the Fourier transform domain, using a procedure in the image reduction and analysis facility (IRAF) software system developed for the determination of galaxy redshifts. It also requires small amounts of GOME data (calibration window regions with from 10 to 15 pixels). Both methods provide absolute wavelength calibration accurate to a small fraction of a GOME pixel across the entire GOME spectrum, and to 0.001 nm over much of the range.

Caspar, C.↗

NASA NTRS2004

Measurements With a Split-Fiber Probe in Complex Unsteady Flows

A split-fiber probe was used to acquire unsteady data in a research compressor. A calibration method was devised for a split-fiber probe, and a new algorithm was developed to decompose split-fiber probe signals into velocity magnitude and direction. The algorithm is based on the minimum value of a merit function that is built over the entire range of flow velocities for which the probe was calibrated. The split-fiber probe performance and signal decomposition was first verified in a free-jet facility by comparing the data from three thermo-anemometric probes, namely a single-wire, a single-fiber, and the split-fiber probe. All three probes performed extremely well as far as the velocity magnitude was concerned. However, there are differences in the peak values of measured velocity unsteadiness in the jet shear layer. The single-wire probe indicates the highest unsteadiness level, followed closely by the split-fiber probe. The single-fiber probe indicates a noticeably lower level of velocity unsteadiness. Experiments in the NASA Low Speed Axial Compressor facility revealed similar results. The mean velocities agreed well, and differences in the velocity unsteadiness are similar to the case of a free jet. A reason for these discrepancies is in the different frequency response characteristics of probes used. It follows that the single-fiber probe has the slowest frequency response. In summary, the split-fiber probe worked reliably during the entire program. The acquired data averaged in time followed closely data acquired by conventional pneumatic probes.

Lepicovsky, Jan↗

NASA NTRS1995

Cascade Optimization Strategy Maximizes Thrust for High-Speed Civil Transport Propulsion System Concept

The design of a High-Speed Civil Transport (HSCT) air-breathing propulsion system for multimission, variable-cycle operations was successfully optimized through a soft coupling of the engine performance analyzer NASA Engine Performance Program (NEPP) to a multidisciplinary optimization tool COMETBOARDS that was developed at the NASA Lewis Research Center. The design optimization of this engine was cast as a nonlinear optimization problem, with engine thrust as the merit function and the bypass ratios, r-values of fans, fuel flow, and other factors as important active design variables. Constraints were specified on factors including the maximum speed of the compressors, the positive surge margins for the compressors with specified safety factors, the discharge temperature, the pressure ratios, and the mixer extreme Mach number. Solving the problem by using the most reliable optimization algorithm available in COMETBOARDS would provide feasible optimum results only for a portion of the aircraft flight regime because of the large number of mission points (defined by altitudes, Mach numbers, flow rates, and other factors), diverse constraint types, and overall poor conditioning of the design space. Only the cascade optimization strategy of COMETBOARDS, which was devised especially for difficult multidisciplinary applications, could successfully solve a number of engine design problems for their flight regimes. Furthermore, the cascade strategy converged to the same global optimum solution even when it was initiated from different design points. Multiple optimizers in a specified sequence, pseudorandom damping, and reduction of the design space distortion via a global scaling scheme are some of the key features of the cascade strategy. HSCT engine concept, optimized solution for HSCT engine concept. A COMETBOARDS solution for an HSCT engine (Mach-2.4 mixed-flow turbofan) along with its configuration is shown. The optimum thrust is normalized with respect to NEPP results. COMETBOARDS added value in the design optimization of the HSCT engine.

Source record↗

NASA NTRS1997

COMETBOARDS Can Optimize the Performance of a Wave-Rotor-Topped Gas Turbine Engine

A wave rotor, which acts as a high-technology topping spool in gas turbine engines, can increase the effective pressure ratio as well as the turbine inlet temperature in such engines. The wave rotor topping, in other words, may significantly enhance engine performance by increasing shaft horse power while reducing specific fuel consumption. This performance enhancement requires optimum selection of the wave rotor's adjustable parameters for speed, surge margin, and temperature constraints specified on different engine components. To examine the benefit of the wave rotor concept in engine design, researchers soft coupled NASA Lewis Research Center's multidisciplinary optimization tool COMETBOARDS and the NASA Engine Performance Program (NEPP) analyzer. The COMETBOARDS-NEPP combined design tool has been successfully used to optimize wave-rotor-topped engines. For illustration, the design of a subsonic gas turbine wave-rotor-enhanced engine with four ports for 47 mission points (which are specified by Mach number, altitude, and power-setting combinations) is considered. The engine performance analysis, constraints, and objective formulations were carried out through NEPP, and COMETBOARDS was used for the design optimization. So that the benefits that accrue from wave rotor enhancement could be examined, most baseline variables and constraints were declared to be passive, whereas important parameters directly associated with the wave rotor were considered to be active for the design optimization. The engine thrust was considered as the merit function. The wave rotor engine design, which became a sequence of 47 optimization subproblems, was solved successfully by using a cascade strategy available in COMETBOARDS. The graph depicts the optimum COMETBOARDS solutions for the 47 mission points, which were normalized with respect to standard results. As shown, the combined tool produced higher thrust for all mission points than did the other solution, with maximum benefits around mission points 11, 25, and 31. Such improvements can become critical, especially when engines are sized for these specific mission points.

Patnaik, Surya N.↗

NASA NTRS2009

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗

NASA NTRS2010

Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya N.↗

NASA NTRS2010

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗

NASA NTRS2013

Issues and Strategies in Solving Multidisciplinary Optimization Problems

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya↗

NASA NTRS1993

NTP comparison process

The systems engineering process for the concept definition phase of the program involves requirements definition, system definition, and consistent concept definition. The requirements definition process involves obtaining a complete understanding of the system requirements based on customer needs, mission scenarios, and nuclear thermal propulsion (NTP) operating characteristics. A system functional analysis is performed to provide a comprehensive traceability and verification of top-level requirements down to detailed system specifications and provides significant insight into the measures of system effectiveness to be utilized in system evaluation. The second key element in the process is the definition of system concepts to meet the requirements. This part of the process involves engine system and reactor contractor teams to develop alternative NTP system concepts that can be evaluated against specific attributes, as well as a reference configuration against which to compare system benefits and merits. Quality function deployment (QFD), as an excellent tool within Total Quality Management (TQM) techniques, can provide the required structure and provide a link to the voice of the customer in establishing critical system qualities and their relationships. The third element of the process is the consistent performance comparison. The comparison process involves validating developed concept data and quantifying system merits through analysis, computer modeling, simulation, and rapid prototyping of the proposed high risk NTP subsystems. The maximum amount possible of quantitative data will be developed and/or validated to be utilized in the QFD evaluation matrix. If upon evaluation of a new concept or its associated subsystems determine to have substantial merit, those features will be incorporated into the reference configuration for subsequent system definition and comparison efforts.

Corban, Robert↗

NASA NTRS1990

Random search optimization based on genetic algorithm and discriminant function

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

Kiciman, M. O.↗

DOE OSTI2022

Punzi-loss: a non-differentiable metric approximation for sensitivity optimisation in the search for new particles

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling, based on the minimisation of a figure-of-merit related function typical of particle physics, a Punzi-loss function, and the neural network that utilises this loss function a Punzi-net. We show that the Punzi-net outperforms standard multivariate analysis techniques and generalises well to mass hypotheses for which it was not trained. This is achieved by training a single classifier that provides a coherent and optimal classification of all signal hypotheses over the whole search space. Our result constitutes a complementary approach to fully differentiable analyses in particle physics. We implemented this work using PyTorch and provide users full access to a public repository containing all the codes and a training example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2002

Quadratic Optimization in the Problems of Active Control of Sound

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Loncaric, J.↗

NASA NTRS1992

Aircraft concept optimization using the global sensitivity approach and parametric multiobjective figures of merit

An extension of our parametric multidisciplinary optimization method to include design results connecting multiple objective functions is presented. New insight into the effect of the figure of merit (objective function) on aircraft configuration size and shape is demonstrated using this technique. An aircraft concept, subject to performance and aerodynamic constraints, is optimized using the global sensitivity equation method for a wide range of objective functions. These figures of merit are described parametrically such that a series of multiobjective optimal solutions can be obtained. Computational speed is facilitated by use of algebraic representations of the system technologies. Using this method, the evolution of an optimum design from one objective function to another is demonstrated. Specifically, combinations of minimum takeoff gross weight, fuel weight, and maximum cruise performance and productivity parameters are used as objective functions.

Malone, Brett↗

NASA NTRS2012

Systematic Sensor Selection Strategy (S4) User Guide

This paper describes a User Guide for the Systematic Sensor Selection Strategy (S4). S4 was developed to optimally select a sensor suite from a larger pool of candidate sensors based on their performance in a diagnostic system. For aerospace systems, selecting the proper sensors is important for ensuring adequate measurement coverage to satisfy operational, maintenance, performance, and system diagnostic criteria. S4 optimizes the selection of sensors based on the system fault diagnostic approach while taking conflicting objectives such as cost, weight and reliability into consideration. S4 can be described as a general architecture structured to accommodate application-specific components and requirements. It performs combinational optimization with a user defined merit or cost function to identify optimum or near-optimum sensor suite solutions. The S4 User Guide describes the sensor selection procedure and presents an example problem using an open source turbofan engine simulation to demonstrate its application.

Sowers, T. Shane↗

NASA NTRS2013

Software Tools to Support the Assessment of System Health

This presentation provides an overview of three software tools that were developed by the NASA Glenn Research Center to support the assessment of system health: the Propulsion Diagnostic Method Evaluation Strategy (ProDIMES), the Systematic Sensor Selection Strategy (S4), and the Extended Testability Analysis (ETA) tool. Originally developed to support specific NASA projects in aeronautics and space, these software tools are currently available to U.S. citizens through the NASA Glenn Software Catalog. The ProDiMES software tool was developed to support a uniform comparison of propulsion gas path diagnostic methods. Methods published in the open literature are typically applied to dissimilar platforms with different levels of complexity. They often address different diagnostic problems and use inconsistent metrics for evaluating performance. As a result, it is difficult to perform a one ]to ]one comparison of the various diagnostic methods. ProDIMES solves this problem by serving as a theme problem to aid in propulsion gas path diagnostic technology development and evaluation. The overall goal is to provide a tool that will serve as an industry standard, and will truly facilitate the development and evaluation of significant Engine Health Management (EHM) capabilities. ProDiMES has been developed under a collaborative project of The Technical Cooperation Program (TTCP) based on feedback provided by individuals within the aircraft engine health management community. The S4 software tool provides a framework that supports the optimal selection of sensors for health management assessments. S4 is structured to accommodate user ]defined applications, diagnostic systems, search techniques, and system requirements/constraints. One or more sensor suites that maximize this performance while meeting other user ]defined system requirements that are presumed to exist. S4 provides a systematic approach for evaluating combinations of sensors to determine the set or sets of sensors that optimally meet the performance goals and the constraints. It identifies optimal sensor suite solutions by utilizing a merit (i.e., cost) function with one of several available optimization approaches. As part of its analysis, S4 can expose fault conditions that are difficult to diagnose due to an incomplete diagnostic philosophy and/or a lack of sensors. S4 was originally developed and applied to liquid rocket engines. It was subsequently used to study the optimized selection of sensors for a simulation ]based aircraft engine diagnostic system. The ETA Tool is a software ]based analysis tool that augments the testability analysis and reporting capabilities of a commercial ]off ]the ]shelf (COTS) package. An initial diagnostic assessment is performed by the COTS software using a user ]developed, qualitative, directed ]graph model of the system being analyzed. The ETA Tool accesses system design information captured within the model and the associated testability analysis output to create a series of six reports for various system engineering needs. These reports are highlighted in the presentation. The ETA Tool was developed by NASA to support the verification of fault management requirements early in the Launch Vehicle process. Due to their early development during the design process, the TEAMS ]based diagnostic model and the ETA Tool were able to positively influence the system design by highlighting gaps in failure detection, fault isolation, and failure recovery.

Melcher, Kevin J.↗