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NASA NTRS2019

Optimal Control within the Context of Multidisciplinary Design, Analysis, and Optimization

Multidisciplinary design, analysis and optimization involves modeling the interactions of complex systems across a variety of disciplines. The optimization of such systems can be a computationally expensive exercise with multiple levels of nested nonlinear solvers running under an optimizer.The application of optimal control in project development often involves performing trajectory optimization for fixed vehicle designs or parametric sweeps across some key vehicle properties.This information is then relayed to the subsystem design teams who update their designs and relay some bulk characteristics back to the trajectory optimization procedure.This iteration is then repeated until the design closes.However, with increasing interest in more tightly coupled systems, such as electric and hybrid-electric aircraft propulsion and boundary layer ingestion, this process is prone to ignore subtle coupling between vehicle subsystem designs and vehicle operation on a given mission.Integrating trajectory optimization into a tightly coupled multidisciplinary design procedure can be computationally prohibitive, depending on the complexity of the subsystem analyses and the optimal control technique applied.To address these issues a new optimal control software tool, Dymos, has been developed.Dymos is built upon NASA's OpenMDAO software and can leverage its capabilities to efficiently compute gradients for the optimization and optimize complex models in parallel on distributed memory systems.This report provides some explanation into the numerical methods employed in Dymos and provides several use cases that demonstrate its performance on traditional optimal control problems and improvements ino techniques have been used extensively in recent decades to solve a variety of optimal control problems, typically in the form of aerospace vehicle trajectory optimization.

pseudospectral↗

NASA NTRS1993

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example.

Felippa, Carlos A.↗

NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗

NASA NTRS1994

Hypersonic vehicle model and control law development using H(infinity) and micron synthesis

The control system design for a Single Stage To Orbit (SSTO) air breathing vehicle will be central to a successful mission because a precise ascent trajectory will preserve narrow payload margins. The air breathing propulsion system requires the vehicle to fly roughly halfway around the Earth through atmospheric turbulence. The turbulence, the high sensitivity of the propulsion system to inlet flow conditions, the relatively large uncertainty of the parameters characterizing the vehicle, and continuous acceleration make the problem especially challenging. Adequate stability margins must be provided without sacrificing payload mass since payload margins are critical. Therefore, a multivariable control theory capable of explicitly including both uncertainty and performance is needed. The H(infinity) controller in general provides good robustness but can result in conservative solutions for practical problems involving structured uncertainty. Structured singular value mu framework for analysis and synthesis is potentially much less conservative and hence more appropriate for problems with tight margins. An SSTO control system requires: highly accurate tracking of velocity and altitude commands while limiting angle-of-attack oscillations, minimized control power usage, and a stabilized vehicle when atmospheric turbulence and system uncertainty are present. The controller designs using H(infinity) and mu-synthesis procedures were compared. An integrated flight/propulsion dynamic mathematical model of a conical accelerator vehicle was linearized as the vehicle accelerated through Mach 8. Vehicle acceleration through the selected flight condition gives rise to parametric variation that was modeled as a structured uncertainty. The mu-analysis approach was used in the frequency domain to conduct controller analysis and was confirmed by time history plots. Results demonstrate the inherent advantages of the mu framework for this class of problems.

Gregory, Irene M.↗

NASA NTRS2000

Parametric Cost Modeling of Space Missions Using the Develop New Projects (DMP) Implementation Process

This paper presents an overview of a parametric cost model that has been built at JPL to estimate costs of future, deep space, robotic science missions. Due to the recent dramatic changes in JPL business practices brought about by an internal reengineering effort known as develop new products (DNP), high-level historic cost data is no longer considered analogous to future missions. Therefore, the historic data is of little value in forecasting costs for projects developed using the DNP process. This has lead to the development of an approach for obtaining expert opinion and also for combining actual data with expert opinion to provide a cost database for future missions. In addition, the DNP cost model has a maximum of objective cost drivers which reduces the likelihood of model input error. Version 2 is now under development which expands the model capabilities, links it more tightly with key design technical parameters, and is grounded in more rigorous statistical techniques. The challenges faced in building this model will be discussed, as well as it's background, development approach, status, validation, and future plans.

Rosenberg, Leigh↗

NASA NTRSDate not supplied

Lunar Water Extraction Via Lunar Auger Dryer ISRU (LADI)

In 2009, the Lunar Reconnaissance Orbiter (LRO) and Lunar Crater Observation and Sensing Satellite (LCROSS) provided definitive proof of water in the Lunar’s southern permanently shadowed region (PSR)1. Both the 2020 NASA Technology Taxonomy2 and the Lunar Surface Innovation Initiative (LSII) team identified capability gaps in icy regolith transfer and reactor processing in Permanently Shadowed Region (PSR) environmental conditions. A water processing plant operating inside the PSR can continuously process water (and volatiles) for both breathable air and propellant. NASA’s Johnson Space Center (JSC) fabricated a unique breadboard test stand for validating the feasibility of this concept,developed a lunar auger dryer sizing tool, and identified the physical flow and thermal models required to design an Engineering Development Unit (EDU) for environmental testing. Over the two years this project was active, models were developed including: a) a sizing tool that scales the auger parameters based on production targets, b) accurate thermal models in both lab and lunar conditions, c) a Discreet Element Model (DEM) for observing particle effects in low-g, and d) incorporated these subsystem models into a MATLAB parametric Modular Open System Approach (MOSA) system model. These models were validated by testing the auger in both a mechanical and thermal system configuration. The results of this testing increased the Technology Readiness Level (TRL) of the Lunar Auger Dryer ISRU (LADI) system to TRL 4.

Lunar↗

NASA NTRSDate not supplied

Loci/STREAM Sharp Interface Model Validation of Cryogenic Propellant Tank Self-Pressurization

This paper documents a model validation effort for the prediction of cryogenic propellant tank selfpressurization physics using the Loci/STREAM sharp interface CFD model developed at NASA MSFC. Cryogenic fluid management (CFM) applications for long duration spaceflight missions require accurate modeling of heat transfer and thermodynamics. Therefore, detailed validation of those physics is important to ensure simulation accuracy. In the past, the MSFC Propulsion Fluid Dynamics Branch has validated and used the Loci/STREAM Volume of Fluid (VOF) module extensively for propellant slosh applications, which are dominated by fluid motion. For cases where the interface gas/liquid interface is essentially static, the Loci/STREAM sharp interface was developed for more rapid and efficient CFM analysis. In the present study, Loci/STREAM sharp interface simulations were compared with the NASA K-site self-pressurization experiment of a flight weight, partially full, LH2 tank in normal gravity. This study investigated several parametric effects and made a number of important observations on the performance of the Loci/STREAM sharp interface method: - First, a homogeneous model was derived to verify the CFD model. The homogeneous model assumes both gas and liquid phases are uniform and are at saturation temperature. The predicted pressure rise rates at 3.5 W/m2 and 2.0 W/m2 with a 49% fill level are all lower than the experimental measurement. This is expected due to the observed temperature stratification near the gas-liquid interface during testing. - The k-w and k-e turbulence models predict comparable pressurization rates, which are much lower than the experiment measurement. On the other hand, the pressure values and pressurization rates from both models are almost the same as those of the homogeneous model. The current turbulence model is too diffusive and is not capable of capturing the thermal stratification in the liquid and ullage. - When using the laminar flow model, the pressurization rate is found to be very close to the experimental value when a quasi-steady flow field is allowed to develop by continuously venting the tank prior to pressurization as was done during testing. On the other hand, without initial venting, the rate is not constant. Additionally, the development time to reach a quasi-steady flow field differed from the experiment due to the lack of turbulent mixing away from the gas-liquid interface that is expected in reality. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 15% of the experimental value for 49% fill level at 3.5 W/m 2 and is within 18% for 2.0 W/m 2 heat loading. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 18% of the experimental value for a 29% fill level and within 15% for an 83% fill level.

H. Q. Yang↗

NASA NTRS2009

Stress Analysis of Bolted, Segmented Cylindrical Shells Exhibiting Flange Mating-Surface Waviness

Bolted, segmented cylindrical shells are a common structural component in many engineering systems especially for aerospace launch vehicles. Segmented shells are often needed due to limitations of manufacturing capabilities or transportation issues related to very long, large-diameter cylindrical shells. These cylindrical shells typically have a flange or ring welded to opposite ends so that shell segments can be mated together and bolted to form a larger structural system. As the diameter of these shells increases, maintaining strict fabrication tolerances for the flanges to be flat and parallel on a welded structure is an extreme challenge. Local fit-up stresses develop in the structure due to flange mating-surface mismatch (flange waviness). These local stresses need to be considered when predicting a critical initial flaw size. Flange waviness is one contributor to the fit-up stress state. The present paper describes the modeling and analysis effort to simulate fit-up stresses due to flange waviness in a typical bolted, segmented cylindrical shell. Results from parametric studies are presented for various flange mating-surface waviness distributions and amplitudes.

Knight, Norman F., Jr.↗

NASA NTRS2002

Process Cost Modeling for Multi-Disciplinary Design Optimization

For early design concepts, the conventional approach to cost is normally some kind of parametric weight-based cost model. There is now ample evidence that this approach can be misleading and inaccurate. By the nature of its development, a parametric cost model requires historical data and is valid only if the new design is analogous to those for which the model was derived. Advanced aerospace vehicles have no historical production data and are nowhere near the vehicles of the past. Using an existing weight-based cost model would only lead to errors and distortions of the true production cost. This report outlines the development of a process-based cost model in which the physical elements of the vehicle are costed according to a first-order dynamics model. This theoretical cost model, first advocated by early work at MIT, has been expanded to cover the basic structures of an advanced aerospace vehicle. Elemental costs based on the geometry of the design can be summed up to provide an overall estimation of the total production cost for a design configuration. This capability to directly link any design configuration to realistic cost estimation is a key requirement for high payoff MDO problems. Another important consideration in this report is the handling of part or product complexity. Here the concept of cost modulus is introduced to take into account variability due to different materials, sizes, shapes, precision of fabrication, and equipment requirements. The most important implication of the development of the proposed process-based cost model is that different design configurations can now be quickly related to their cost estimates in a seamless calculation process easily implemented on any spreadsheet tool. In successive sections, the report addresses the issues of cost modeling as follows. First, an introduction is presented to provide the background for the research work. Next, a quick review of cost estimation techniques is made with the intention to highlight their inappropriateness for what is really needed at the conceptual phase of the design process. The First-Order Process Velocity Cost Model (FOPV) is discussed at length in the next section. This is followed by an application of the FOPV cost model to a generic wing. For designs that have no precedence as far as acquisition costs are concerned, cost data derived from the FOPV cost model may not be accurate enough because of new requirements for shape complexity, material, equipment and precision/tolerance. The concept of Cost Modulus is introduced at this point to compensate for these new burdens on the basic processes. This is treated in section 5. The cost of a design must be conveniently linked to its CAD representation. The interfacing of CAD models and spreadsheets containing the cost equations is the subject of the next section, section 6. The last section of the report is a summary of the progress made so far, and the anticipated research work to be achieved in the future.

Bao, Han P.↗

NASA NTRS2002

Predicting Production Costs for Advanced Aerospace Vehicles

Bao, Han P.↗

NASA NTRS2020

First-Order Runtime Verification using BDDs

Runtime Verification (RV) expedites the analyses of execution traces for detecting system errors and for statistical and quality analysis. Having started modestly, with checking temporal properties that are based on propositional (yes/no) values, the current practice of RV often involves properties that are parametrized by the data observed in the input trace. The specifications are based on various formalisms, such as automata, temporal logics, rule systems, and stream processing. Checking execution traces that are data intensive against a specification that imposes strong dependencies between the data, poses a nontrivial challenges; in particular if runtime verification has to be performed online, while many events that carry data appear within small time proximities. Towards achieving this goal, it was recently suggested to represent relations over the observed data values, based on BDDs, where data elements are enumerated and then converted into bit vectors. This representation provided a very simple and natural extension of an RV algorithm from propositional to first-order LTL, but more importantly, was shown to contribute to the memory compactness and to the speed, as was demonstrated using a corresponding implementation. We extend here the capabilities of BDD-based RV with the ability to express timing constraints, where the monitored events include (integer) clock values. We show how to efficiently operate on BDDs that represent both relations on (enumerations of) values and time dependencies, as required by the addition of the time constraints. We demonstrate our algorithm with an efficient implementation and provide experimental results.

Peled, Doron↗

NASA NTRS1992

Ground clutter measurements using the NASA airborne doppler radar: Description of clutter at the Denver and Philadelphia airports

Detection of hazardous wind shears from an airborne platform, using commercial sized radar hardware, has been debated and researched for several years. The primary concern has been the requirement for 'look-down' capability in a Doppler radar during the approach and landing phases of flight. During 'look-down' operation, the received signal (weather signature) will be corrupted by ground clutter returns. Ground clutter at and around urban airports can have large values of Normalized Radar Cross Section (NRCS) producing clutter returns which could saturate the radar's receiver, thus disabling the radar entirely, or at least from its intended function. The purpose of this research was to investigate the NRCS levels in an airport environment (scene), and to characterize the NRCS distribution across a variety of radar parameters. These results are also compared to results of a similar study using Synthetic Aperture Radar (SAR) images of the same scenes. This was necessary in order to quantify and characterize the differences and similarities between results derived from the real-aperature system flown on the NASA 737 aircraft and parametric studies which have previously been performed using the NASA airborne radar simulation program.

Harrah, Steven D.↗

NASA NTRS2013

On-Orbit Lunar Modulation Transfer Function Measurements for the Moderate Resolution Imaging Spectroradiometer

Spatial quality of an imaging sensor can be estimated by evaluating its modulation transfer function (MTF) from many different sources such as a sharp edge, a pulse target, or bar patterns with different spatial frequencies. These well-defined targets are frequently used for prelaunch laboratory tests, providing very reliable and accurate MTF measurements. A laboratory-quality edge input source was included in the spatial-mode operation of the Spectroradiometric Calibration Assembly (SRCA), which is one of the onboard calibrators of the Moderate Resolution Imaging Spectroradiometer (MODIS). Since not all imaging satellites have such an instrument, SRCA MTF estimations can be used as a reference for an on-orbit lunar MTF algorithm and results. In this paper, the prelaunch spatial quality characterization process from the Integrated Alignment Collimator and SRCA is briefly discussed. Based on prelaunch MTF calibration using the SRCA, a lunar MTF algorithm is developed and applied to the lifetime on-orbit Terra and Aqua MODIS lunar collections. In each lunar collection, multiple scan-directionMoon-to-background transition profiles are aligned by the subpixel edge locations from a parametric Fermi function fit. Corresponding accumulated edge profiles are filtered and interpolated to obtain the edge spread function (ESF). The MTF is calculated by applying a Fourier transformation on the line spread function through a simple differentiation of the ESF. The lifetime lunar MTF results are analyzed and filtered by a relationship with the Sun-Earth-MODIS angle. Finally, the filtered lunarMTF values are compared to the SRCA MTF results. This comparison provides the level of accuracy for on-orbit MTF estimations validated through prelaunch SRCA measurements. The lunar MTF values had larger uncertainty than the SRCA MTF results; however, the ratio mean of lunarMTF fit and SRCA MTF values is within 2% in the 250- and 500-m bands. Based on the MTF measurement uncertainty range, the suggested lunar MTF algorithm can be applied to any on-orbit imaging sensor with lunar calibration capability.

Choi, Taeyong↗

NASA NTRSDate not supplied

Guiding Integration of Formal Verification in Assurance Cases

Assurance cases are being increasingly acknowledged as away to build trust in complex systems with autonomous capabilities. An assurance case is a comprehensive, defensible, and valid justification that a system will function as intended for a specific mission and operating environment. Formal verification is often reserved for the most critical components of such systems. However, formal verification tools are often complex, and their usage is subject to many constraints and contextual dependencies. This can raise challenges both for performing the verification as well as reflecting the verification results appropriately in the assurance case, especially for non-expert users of the verification tool. To address these challenges, we present a tool-supported methodology for integrating formal verification results in an assurance case by capturing key verification method information in a rigorously constructed assurance case. In particular, we capture the tool specification in terms of its inputs, outputs, and assurance constraints as assumptions over inputs and guarantees provided over its outputs. The tool specification is parametrized over the inputs and outputs to both guide the intended application of the tool, as well as to check that the tool has been applied following the stated assumptions and that the guarantees hold. We define a generic tool assurance argument pattern that enables integration of the verification results in the assurance case by allowing custom refinement and automated instantiation for each tool use. We demonstrate our methodology on two formal verification tools and their applications to the verification of neural network properties for the aircraft domain.

Assurance Cases↗

NASA NTRS1993

Blasim: A computational tool to assess ice impact damage on engine blades

A portable computer called BLASIM was developed at NASA LeRC to assess ice impact damage on aircraft engine blades. In addition to ice impact analyses, the code also contains static, dynamic, resonance margin, and supersonic flutter analysis capabilities. Solid, hollow, superhybrid, and composite blades are supported. An optional preprocessor (input generator) was also developed to interactively generate input for BLASIM. The blade geometry can be defined using a series of airfoils at discrete input stations or by a finite element grid. The code employs a coarse, fixed finite element mesh containing triangular plate finite elements to minimize program execution time. Ice piece is modeled using an equivalent spherical objective that has a high velocity opposite that of the aircraft and parallel to the engine axis. For local impact damage assessment, the impact load is considered as a distributed force acting over a region around the impact point. The average radial strain of the finite elements along the leading edge is used as a measure of the local damage. To estimate damage at the blade root, the impact is treated as an impulse and a combined stress failure criteria is employed. Parametric studies of local and root ice impact damage, and post-impact dynamics are discussed for solid and composite blades.

Reddy, E. S.↗

NASA NTRS2002

Application of the generalized vertical coordinate ocean model for better representing satellite data

It is found that two adaptive parametric functions can be introduced into the basic ocean equations for utilizing the optimal or hybrid features of commonly used z-level, terrain- following, isopycnal, and pressure coordinates in numerical ocean models. The two parametric functions are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara (1 974), the Jacobian pressure gradient formulation of Song (1 998), and a newly developed metric factor that permits both compressible (non-Boussinesq) and incompressible (Boussinesq) approximations. Based on the new formulation, an adaptive modeling strategy is proposed and a staggered finite volume method is designed to ensure conservation of important physical properties and numerical accuracy. Implementation of the combined techniques to SCRUM (Song and Haidvogel1994) shows that the adaptive modeling strategy can be applied to any existing ocean model without incurring computational expense or altering the original numerical schemes. Such a generalized coordinate model is expected to benefit diverse ocean modelers for easily choosing optimal vertical structures and sharing modeling resources based on a common model platform. Several representing oceanographic problems with different scales and characteristics, such as coastal canyons, basin-scale circulation, and global ocean circulation, are used to demonstrate the model's capability for multiple applications. New results show that the model is capable of simultaneously resolving both Boussinesq and non-Boussinesq, and both small- and large-scale processes well. This talk will focus on its applications of multiple satellite sensing data in eddy-resolving simulations of Asian Marginal Sea and Kurosio. Attention will be given to how Topex/Poseidon SSH, TRMM SST; and GRACE ocean bottom pressure can be correctly represented in a non- Boussinesq model.

numerical ocean model generalized coordinate syste↗

NASA NTRS2024

Harnessing Collaborative Learning Automata to Guide Multi-objective Optimization based Inverse Analysis for Structural Damage Identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

Yang Zhang↗

NASA NTRS2004

Intelligent Control for the BEES Flyer

This paper describes the effort to provide a preliminary capability analysis and a neural network based adaptive flight control system for the JPL-led BEES aircraft project. The BEES flyer was envisioned to be a small, autonomous platform with sensing and control systems mimicking those of biological systems for the purpose of scientific exploration on the surface of Mars. The platform is physically tightly constrained by the necessity of efficient packing within rockets for the trip to Mars. Given the physical constraints, the system is not an ideal configuration for aerodynamics or stability and control. The objectives of this effort are to evaluate the aerodynamics characteristics of the existing design, to make recommendaaons as to potential improvements and to provide a control system that stabilizes the existing aircraft for nominal flight and damaged conditions. Towards this several questions are raised and analyses are presented to arrive at answers to some of the questions raised. CART3D, a high-fidelity inviscid analysis package for conceptual and preliminary aerodynamic design, was used to compute a parametric set of solutions over the expected flight domain. Stability and control derivatives were extracted from the database and integrated with the neural flight control system. The Integrated Vehicle Modeling Environment (IVME) was also used for estimating aircraft geometric, inertial, and aerodynamic characteristics. A generic neural flight control system is used to provide adaptive control without the requirement for extensive gain scheduling or explicit system identification. The neural flight control system uses reference models to specify desired handling qualities in the roll, pitch, and yaw axes, and incorporates both pre-trained and on-line learning neural networks in the inverse model portion of the controller. Results are presented for the BEES aircraft in the subsonic regime for terrestrial and Martian environments.

Krishnakumar, K.↗