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Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.
The goal of this work was to analyze the potential of neural networks and fuzzy logic methods to develop approximate response surfaces as process modeling, that is for mapping of input into output. Structural response was chosen as an example. Each of the many methods surveyed are explained and the results are presented. Future research directions are also discussed.
An injector optimization methodology, method i, is used to investigate optimal design points for a gaseous oxygen/gaseous hydrogen (GO2/GH2) swirl coaxial injector element. The element is optimized in terms of design variables such as fuel pressure drop, DELTA P(sub f), oxidizer pressure drop, DELTA P(sub 0) combustor length, L(sub comb), and full cone swirl angle, theta, for a given mixture ratio and chamber pressure. Dependent variables such as energy release efficiency, ERE, wall heat flux, Q(sub w) injector heat flux, Q(sub inj), relative combustor weight, W(sub rel), and relative injector cost, C(sub rel), are calculated and then correlated with the design variables. An empirical design methodology is used to generate these responses for 180 combinations of input variables. Method i is then used to generate response surfaces for each dependent variable. Desirability functions based on dependent variable constraints are created and used to facilitate development of composite response surfaces representing some, or all, of the five dependent variables in terms of the input variables. Two examples illustrating the utility and flexibility of method i are discussed in detail. First, joint response surfaces are constructed by sequentially adding dependent variables. Optimum designs are identified after addition of each variable and the effect each variable has on the design is shown. This stepwise demonstration also highlights the importance of including variables such as weight and cost early in the design process. Secondly, using the composite response surface that includes all five dependent variables, unequal weights are assigned to emphasize certain variables relative to others. Here, method i is used to enable objective trade studies on design issues such as component life and thrust to weight ratio.
An injector optimization methodology, method i, is used to investigate optimal design points for a gaseous oxygen/gaseous hydrogen (GO2/GH2) impinging injector element. The unlike impinging element, a fuel-oxidizer- fuel (F-O-F) triplet, is optimized in terms of design variables such as fuel pressure drop, (Delta)P(sub f), oxidizer pressure drop, (Delta)P(sub o), combustor length, L(sub comb), and impingement half-angle, alpha, for a given mixture ratio and chamber pressure. Dependent variables such as energy release efficiency, ERE, wall heat flux, Q(sub w), injector heat flux, Q(sub inj), relative combustor weight, W(sub rel), and relative injector cost, C(sub rel), are calculated and then correlated with the design variables. An empirical design methodology is used to generate these responses for 163 combinations of input variables. Method i is then used to generate response surfaces for each dependent variable. Desirability functions based on dependent variable constraints are created and used to facilitate development of composite response surfaces representing some, or all, of the five dependent variables in terms of the input variables. Three examples illustrating the utility and flexibility of method i are discussed in detail. First, joint response surfaces are constructed by sequentially adding dependent variables. Optimum designs are identified after addition of each variable and the effect each variable has on the design is shown. This stepwise demonstration also highlights the importance of including variables such as weight and cost early in the design process. Secondly, using the composite response surface which includes all five dependent variables, unequal weights are assigned to emphasize certain variables relative to others. Here, method i is used to enable objective trade studies on design issues such as component life and thrust to weight ratio. Finally, specific variable weights are further increased to illustrate the high marginal cost of realizing the last increment of injector performance and thruster weight.
An injector optimization methodology, method i, is used to investigate optimal design points for gaseous oxygen/gaseous hydrogen (GO2/GH2) injector elements. A swirl coaxial element and an unlike impinging element (a fuel-oxidizer-fuel triplet) are used to facilitate the study. The elements are optimized in terms of design variables such as fuel pressure drop, APf, oxidizer pressure drop, deltaP(sub f), combustor length, L(sub comb), and full cone swirl angle, theta, (for the swirl element) or impingement half-angle, alpha, (for the impinging element) at a given mixture ratio and chamber pressure. Dependent variables such as energy release efficiency, ERE, wall heat flux, Q(sub w), injector heat flux, Q(sub inj), relative combustor weight, W(sub rel), and relative injector cost, C(sub rel), are calculated and then correlated with the design variables. An empirical design methodology is used to generate these responses for both element types. Method i is then used to generate response surfaces for each dependent variable for both types of elements. Desirability functions based on dependent variable constraints are created and used to facilitate development of composite response surfaces representing the five dependent variables in terms of the input variables. Three examples illustrating the utility and flexibility of method i are discussed in detail for each element type. First, joint response surfaces are constructed by sequentially adding dependent variables. Optimum designs are identified after addition of each variable and the effect each variable has on the element design is illustrated. This stepwise demonstration also highlights the importance of including variables such as weight and cost early in the design process. Secondly, using the composite response surface that includes all five dependent variables, unequal weights are assigned to emphasize certain variables relative to others. Here, method i is used to enable objective trade studies on design issues such as component life and thrust to weight ratio. Finally, combining results from both elements to simulate a trade study, thrust-to-weight trends are illustrated and examined in detail.
The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric surface imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method models. Data collection methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps on how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the pre-processing methods and results from Py_TIGIRS are provided and compared for Composite Test Article (CTA) 8.2B. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future development of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.
This method uses a magnetic-field- response contact sensor that is designed to identify surface contact and motion between contact locations. The sensor has three components: (1) a capacitor-inductor circuit with two sets of electrical contact pads, (2) a capacitor with a set of electrical contact pads, and (3) an inductor with a set of electrical contact pads. A unique feature of this sensor is that it is inherently multifunctional. Information can be derived from analyzing such sensor response attributes as amplitude, frequency, and bandwidth. A change in one attribute can be due to a change in a physical property of a system. A change in another attribute can be due to another physical property, which has no relationship to the first one.
Impact damage in thin carbon fiber reinforced polymer composites often results in a relatively small region of damage at the front surface, with increasing damage near the back surface. Conventional methods for reducing the pulsed thermographic responses of the composite tend to underestimate the size of the back surface damage, since the smaller near surface damage gives the largest thermographic indication. A method is presented for reducing the thermographic data to produce an estimated size for the impact damage that is much closer to the size of the damage estimated from other NDE techniques such as microfocus x-ray computed tomography and pulse echo ultrasonics. Examples of the application of the technique to experimental data acquired on specimens with impact damage are presented. The method is also applied to the results of thermographic simulations to investigate the limitations of the technique.
To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.
Nuclear detection methods are being used to understand the radiation environment at Mars. JPL (Jet Propulsion Laboratory) assets on Mars include: Orbiter -2001 Mars Odyssey [High Energy Neutron Detector (HEND)]; Mars Science Laboratory Rover -Curiosity [(Radiation Assessment Detector (RAD); Dynamic Albedo Neutron (DAN))]. Spacecraft have instruments able to detect ionizing and non-ionizing radiation. Instrument response on orbit and on the surface of Mars to space weather and local conditions [is discussed] - Data available at NASA-PDS (Planetary Data System).
Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are ones that are built up progressively as global information is added from new sample points in the parameter space. As the response surfaces are globally upgraded based on new information, heuristic indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured fashion, or in an unstructured fashion. Whatever the approach, at least in early stages of sampling it is usually desirable to sample the entire parameter space uniformly. At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly over the entire parameter space (Progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in early stages of sampling (Adaptive response surfaces). Here we consider Progressive response surfaces where a balanced indication of global response over the parameter space is desired.We use a variant of Moving Least Squares to fit and interpolate structured and unstructured point sets over the parameter space. On a 2-D test problem we compare response surface accuracy for three incremental sampling methods: Progressive Lattice Sampling; Simple-Random Monte Carlo; and Halton Quasi-Monte-Carlo sequences. We are ultimately after a system for constructing efficiently upgradable response surface approximations with reliable error estimates.
We can determine distances between objects and points of interest in 3-D space to a useful degree of accuracy from a set of camera images by using multiple camera views and reference targets in the camera s field of view (FOV). The core of the software processing is based on the previously developed foreign-object debris vision trajectory software (see KSC Research and Technology 2004 Annual Report, pp. 2 5). The current version of this photogrammetry software includes the ability to calculate distances between any specified point pairs, the ability to process any number of reference targets and any number of camera images, user-friendly editing features, including zoom in/out, translate, and load/unload, routines to help mark reference points with a Find function, while comparing them with the reference point database file, and a comprehensive output report in HTML format. In this system, scene reference targets are replaced by a photogrammetry cube whose exterior surface contains multiple predetermined precision 2-D targets. Precise measurement of the cube s 2-D targets during the fabrication phase eliminates the need for measuring 3-D coordinates of reference target positions in the camera's FOV, using for example a survey theodolite or a Faroarm. Placing the 2-D targets on the cube s surface required the development of precise machining methods. In response, 2-D targets were embedded into the surface of the cube and then painted black for high contrast. A 12-inch collapsible cube was developed for room-size scenes. A 3-inch, solid, stainless-steel photogrammetry cube was also fabricated for photogrammetry analysis of small objects.
Small unmanned aircraft and electric vertical takeoff and landing (eVTOL) aircraft have recently emerged as vehicles able to perform new missions and stimulate future air transportation methods. This dissertation presents several system identification research advancements for these modern aircraft configurations enabling accurate mathematical model development for flight dynamics simulations based on wind-tunnel and flight-test data. The first part of the dissertation focuses on advances in flight-test system identification methods using small, fixed-wing, remotely-piloted, electric, propeller-driven aircraft. A generalized approach for flight dynamics model development for small fixed-wing aircraft from flight data is described and is followed by presentation of novel flight-test system identification applications, including: aero-propulsive model development for propeller aircraft and nonlinear dynamic model identification without mass properties. The second part of the dissertation builds on established fixed-wing and rotary-wing aircraft system identification methods to develop modeling strategies for transitioning, distributed propulsion, eVTOL aircraft. Novel wind-tunnel experiment designs and aero-propulsive modeling approaches are developed using a subscale, tandem tilt-wing, eVTOL aircraft, leveraging design of experiments and response surface methodology techniques. Additionally, a method applying orthogonal phase-optimized multisine input excitations to aircraft control effectors in wind-tunnel testing is developed to improve test efficiency and identified model utility. Finally, the culmination of this dissertation is synthesis of the techniques described throughout the document to form a flight-test system identification approach for eVTOL aircraft that is demonstrated using a high-fidelity flight dynamics simulation. The research findings highlighted throughout the dissertation constitute substantial progress in efficient empirical aircraft modeling strategies that are applicable to many current and future aeronautical vehicles enabling accurate flight simulation development, which can subsequently be used to foster advancement in many other pertinent technology areas.
The Scientifically Calibrated In-Flight Imagery (SCIFLI) team captured high-resolution, calibrated, near-infrared imagery of the Orion capsule during atmospheric reentry of the EFT-1 mission. A US Navy NP-3D aircraft equipped with a multi-band optical sensor package, referred to as Cast Glance, acquired imagery of the Orion capsule's heatshield during a period when Orion was slowing from approximately Mach 10 to Mach 7. The line-of-sight distance ranged from approximately 65 to 40 nmi. Global surface temperatures of the capsule's thermal heatshield derived from the near-infrared intensity measurements complemented the in-depth (embedded) thermocouple measurements. Moreover, these derived surface temperatures are essential to the assessment of the thermocouples' reliance on inverse heat transfer methods and material response codes to infer the surface temperature from the in-depth measurements. The paper describes the image processing challenges associated with a manually-tracked, high-angular rate air-to-air observation. Issues included management of significant frame-to-frame motions due to both tracking jerk and jitter as well as distortions due to atmospheric effects. Corrections for changing sky backgrounds (including some cirrus clouds), atmospheric attenuation, and target orientations and ranges also had to be made. The image processing goal is to reduce the detrimental effects due to motion (both sensor and capsule), vibration (jitter), and atmospherics for image quality improvement, without compromising the quantitative integrity of the data, especially local intensity (temperature) variations. The paper will detail the approach of selecting and utilizing only the highest quality images, registering several co-temporal image frames to a single image frame to the extent frame-to-frame distortions would allow, and then co-adding the registered frames to improve image quality and reduce noise. Using preflight calibration data, the registered and averaged infrared intensity images were converted to surface temperatures on the Orion capsule's heatshield. Temperature uncertainties will be discussed relative to uncertainties of surface emissivity and atmospheric transmission loss. Comparison of limited onboard surface thermocouple data to the image derived surface temperature will be presented.
Double-parameter expansions, leading to an instantaneous multiscale analysis, are used to obtain time-frequency graphs from time-series data for interpretation of scatterometer response to sea surface geometry. This method is used to define, as well as possible, one-dimensional signal input (elevation and slope). However, some important fundamental parameters, such as the asymmetric development of short scales in crests and troughs, the long-wave amplitude modulation, the different zero-crossings, and so forth, are easily extracted from the wavelet images.
One of NASA's primary missions is to reduce the cost of access to space while simultaneously increasing safety. A key component, and one of the least understood, is the recurring operations and support cost for reusable launch systems. In order to predict these costs, NASA, under the leadership of the Independent Program Assessment Office (IPAO), has commissioned the development of a Launch Systems Operations Cost Model (LSOCM). LSOCM is a tool to predict the operations & support (O&S) cost of new and modified reusable (and partially reusable) launch systems. The requirements are to predict the non-recurring cost for the ground infrastructure and the recurring cost of maintaining that infrastructure, performing vehicle logistics, and performing the O&S actions to return the vehicle to flight. In addition, the model must estimate the time required to cycle the vehicle through all of the ground processing activities. The current version of LSOCM is an amalgamation of existing tools, leveraging our understanding of shuttle operations cost with a means of predicting how the maintenance burden will change as the vehicle becomes more aircraft like. The use of the Conceptual Operations Manpower Estimating Tool/Operations Cost Model (COMET/OCM) provides a solid point of departure based on shuttle and expendable launch vehicle (ELV) experience. The incorporation of the Reliability and Maintainability Analysis Tool (RMAT) as expressed by a set of response surface model equations gives a method for estimating how changing launch system characteristics affects cost and cycle time as compared to today's shuttle system. Plans are being made to improve the model. The development team will be spending the next few months devising a structured methodology that will enable verified and validated algorithms to give accurate cost estimates. To assist in this endeavor the LSOCM team is part of an Agency wide effort to combine resources with other cost and operations professionals to support models, databases, and operations assessments.
This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resulting in new (posterior) knowledge that combines information from both sources. A logical merger of Bayesian methods and certain aspects of Response Surface Modeling is explored. Specific applications to wind tunnel testing, computational code validation, and instrumentation calibration are discussed.
Hybrid flow control, a combination of micro-ramps and steady micro-jets, was experimentally investigated in the 15x15 cm Supersonic Wind Tunnel at the NASA Glenn Research Center. A central composite design of experiments method, was used to develop response surfaces for boundary-layer thickness and reversed-flow thickness, with factor variables of inter-ramp spacing, ramp height and chord length, and flow injection ratio. Boundary-layer measurements and wall static pressure data were used to understand flow separation characteristics. A limited number of profiles were measured in the corners of the tunnel to aid in understanding the three-dimensional characteristics of the flowfield.