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The Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements (INTEGRATE) project is developing a new inverse-design capability for wind turbine rotors using invertible neural networks. This artificial intelligence (AI)-based technology can capture complex nonlinear aerodynamic effects 100 times faster than alternative design approaches.
Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.
High Mountain Asia has long been known as a hotspot for landslide risk, and studies have suggested that landslide hazard is likely to increase in this region over the coming decades. Extreme precipitation may become more frequent, with a nonlinear response relative to increasing global temperatures. However, these changes are geographically varied. This article maps probable changes to landslide hazard, as shown by a landslide hazard indicator (LHI) derived from downscaled precipitation and temperature. In order to capture the nonlinear response of slopes to extreme precipitation, a simple machine-learning model was trained on a database of landslides across High Mountain Asia to develop a regional LHI. This model was applied to statistically downscaled data from the 30 members of the Seamless System for Prediction and Earth System Research large ensembles to produce a range of possible outcomes under the Shared Socioeconomic Pathways 2-4.5 and 5-8.5. The LHI reveals that landslide hazard will increase in most parts of High Mountain Asia. Absolute increases will be highest in already hazardous areas such as the Central Himalaya, but relative change is greatest on the Tibetan Plateau. Even in regions where landslide hazard declines by year 2100, it will increase prior to the mid-century mark. However, the seasonal cycle of landslide occurrence will not change greatly across High Mountain Asia. Although substantial uncertainty remains in these projections, the overall direction of change seems reliable. These findings highlight the importance of continued analysis to inform disaster risk reduction strategies for stakeholders across High Mountain Asia.
Providing advance warning of East African rainfall variations is a particular focus of several groups including those participating in the Famine Early Warming Systems Network. Both seasonal and long-term model projections of climate variability are being used to examine the societal impacts of hydrometeorological variability on seasonal to interannual and longer time scales. The NASA / USAID SERVIR project, which leverages satellite and modeling-based resources for environmental decision making in developing nations, is focusing on the evaluation of both seasonal and climate model projections to develop downscaled scenarios for using in impact modeling. The utility of these projections is reliant on the ability of current models to capture the embedded relationships between East African rainfall and evolving forcing within the coupled ocean-atmosphere-land climate system. Previous studies have posited relationships between variations in El Niño, the Walker circulation, Pacific decadal variability (PDV), and anthropogenic forcing. This study applies machine learning methods (e.g. clustering, probabilistic graphical model, nonlinear PCA) to observational datasets in an attempt to expose the importance of local and remote forcing mechanisms of East African rainfall variability. The ability of the NASA Goddard Earth Observing System (GEOS5) coupled model to capture the associated relationships will be evaluated using Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations.
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.
The need for a predictive budget/funging model is obvious. The current models used by the Resource Analysis Office (RAO) are used to predict the total costs of satellite projects. An effort to extend the modeling capabilities from total budget analysis to total budget and budget outlays over time analysis was conducted. A statistical based and data driven methodology was used to derive and develop the model. Th budget data for the last 18 GSFC-sponsored satellite projects were analyzed and used to build a funding model which would describe the historical spending patterns. This raw data consisted of dollars spent in that specific year and their 1989 dollar equivalent. This data was converted to the standard format used by the RAO group and placed in a database. A simple statistical analysis was performed to calculate the gross statistics associated with project length and project cost ant the conditional statistics on project length and project cost. The modeling approach used is derived form the theory of embedded statistics which states that properly analyzed data will produce the underlying generating function. The process of funding large scale projects over extended periods of time is described by Life Cycle Cost Models (LCCM). The data was analyzed to find a model in the generic form of a LCCM. The model developed is based on a Weibull function whose parameters are found by both nonlinear optimization and nonlinear regression. In order to use this model it is necessary to transform the problem from a dollar/time space to a percentage of total budget/time space. This transformation is equivalent to moving to a probability space. By using the basic rules of probability, the validity of both the optimization and the regression steps are insured. This statistically significant model is then integrated and inverted. The resulting output represents a project schedule which relates the amount of money spent to the percentage of project completion.
Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.
This paper presents the tests and analytical approach used on the development of a steel riser cutter for the CEV Parachute Assembly System (CPAS) used on the Orion crew module. Figure 1 shows the riser cutter and the steel riser bundle which consists of six individual cables. Due to the highly compressed schedule, initial unavailability of the riser material and the Orion Forward Bay mechanical constraints, JSC primarily relied on a combination of internal ballistics analysis and LS-DYNA simulation for this project. Various one dimensional internal ballistics codes that use standard equation of state and conservation of energy have commonly used in the development of CAD devices for initial first order estimates and as an enhancement to the test program. While these codes are very accurate for propellant performance prediction, they usually lack a fully defined kinematic model for dynamic predictions. A simple piston device can easily and accurately be modeled using an equation of motion. However, the accuracy of analytical models is greatly reduced on more complicated devices with complex external loads, nonlinear trajectories or unique unlocking features. A 3D finite element model of CAD device with all critical features included can vastly improve the analytical ballistic predictions when it is used as a supplement to the ballistic code. During this project, LS-DYNA structural 3D model was used to predict the riser resisting load that was needed for the ballistic code. A Lagrangian model with eroding elements shown in Figure 2 was used for the blade, steel riser and the anvil. The riser material failure strain was fine tuned by matching the dent depth on the anvil with the actual test data. LS-DYNA model was also utilized to optimize the blade tip design for the most efficient cut. In parallel, the propellant type and the amount were determined by using CADPROG internal ballistics code. Initial test results showed a good match with LS-DYNA and CADPROG simulations. Final paper will present a detailed roadmap from initial ballistic modeling and LS-DYNA simulation to the performance testing. Blade shape optimization study will also be presented.
Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a non-autoregressive time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. Further, we evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the principal component directions obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover-and critical for many applications of these surrogates-inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.
This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.
The goal of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project is to detect and study astrophysical gravitational waves and use data from them for research in physics and astronomy. LIGO will support studies concerning the nature and nonlinear dynamics for gravity, the structures of black holes, and the equation of state of nuclear matter. It will also measure the masses, birth rates, collisions, and distributions of black holes and neutron stars in the universe and probe the cores of supernovae and the very early universe. The technology for LIGO has been developed during the past 20 years. Construction will begin in 1992, and under the present schedule, LIGO's gravitational-wave searches will begin in 1998.
Current projects include loading adhesive bond in shear in MTS machine, ultrasonic tests with shear waves, shear-fatigue adhesive bonding, and use of ultrasound to detect onset of nonlinearity.
This document reports on the progress in developing hybrid sensors for the simultaneous measurement of pressure and shear stress. The key feature for the success of the proposed hybrid sensor array is the ability to deposit Cu-Ni alloy with proper composition (55 - 45) on a silicon wafer to form a strain gage. This alloy strain gage replaces the normally used Si strain gages in MEMS, which are highly nonlinear and temperature dependent. The copper nickel, with proper composition (55 - 45), was successfully deposited on a silicon wafer with a few trials during this period of the project. Pictures of the Cu-Ni alloy strain gage and the x-ray spectra indicating the composition are shown. The planned tests are also reviewed.
Continued studies have been undertaken to investigate and develop aerodynamic models that predict aircraft response in nonlinear unsteady flight regimes for transport configurations. The models retain conventional static and dynamic terms but replace conventional acceleration terms with indicial functions. In the Subsonic Fixed Wing Project of the NASA Fundamental Aeronautics Program and the Integrated Resilient Aircraft Controls project of the NASA Aviation Safety Program one aspect of the research is to apply these current developments to transport configurations to facilitate development of advanced simulation and control design technology. This paper continues development and application of a more general modeling methodology to the NASA Langley Generic Transport Model, a sub-scale flight test vehicle. In the present study models for the lateral-directional aerodynamics are developed.
The AeroServoElasticity task under the NASA Supersonics Project is developing dynamic models of the propulsion system and the vehicle in order to conduct research for integrated vehicle dynamic performance. As part of this effort, a nonlinear quasi 1-dimensional model of the 2-dimensional bifurcated mixed compression supersonic inlet is being developed. The model utilizes computational fluid dynamics for both the supersonic and subsonic diffusers. The oblique shocks are modeled utilizing compressible flow equations. This model also implements variable geometry required to control the normal shock position. The model is flexible and can also be utilized to simulate other mixed compression supersonic inlet designs. The model was validated both in time and in the frequency domain against the legacy LArge Perturbation INlet code, which has been previously verified using test data. This legacy code written in FORTRAN is quite extensive and complex in terms of the amount of software and number of subroutines. Further, the legacy code is not suitable for closed loop feedback controls design, and the simulation environment is not amenable to systems integration. Therefore, a solution is to develop an innovative, more simplified, mixed compression inlet model with the same steady state and dynamic performance as the legacy code that also can be used for controls design. The new nonlinear dynamic model is implemented in MATLAB Simulink. This environment allows easier development of linear models for controls design for shock positioning. The new model is also well suited for integration with a propulsion system model to study inlet/propulsion system performance, and integration with an aero-servo-elastic system model to study integrated vehicle ride quality, vehicle stability, and efficiency.
The AeroServoElasticity task under the NASA Supersonics Project is developing dynamic models of the propulsion system and the vehicle in order to conduct research for integrated vehicle dynamic performance. As part of this effort, a nonlinear quasi 1-dimensional model of an axisymmetric external compression supersonic inlet is being developed. The model utilizes compressible flow computational fluid dynamics to model the internal inlet segment as well as the external inlet portion between the cowl lip and normal shock, and compressible flow relations with flow propagation delay to model the oblique shocks upstream of the normal shock. The external compression portion between the cowl-lip and the normal shock is also modeled with leaking fluxes crossing the sonic boundary, with a moving CFD domain at the normal shock boundary. This model has been verified in steady state against tunnel inlet test data and it s a first attempt towards developing a more comprehensive model for inlet dynamics.
The inverted pendulum system, a canonical example of an unstable mechanical system, is often used to model the control problems encountered in the flight of rockets in the initial stages of launch, when the airspeed is too small for aerodynamic stability. A system with a flexible pendulum is a variant that more accurately simulates rocket flight nonlinearities (particularly, the flex modes of the rocket). To increase NASA capability of modeling dynamical systems for which closed form solutions are not clear or easily developed, this project aims to provide a machine learning approach that produces a learned dynamical model of the PENNY robot (a rover with a flexible inverted pendulum) from operational data. The developed approach can then be generalized to other complex dynamical systems, including but not limited to rockets and other robotic systems.
The buckling response of geometrically perfect and imperfect cylindrical sandwich shells can be investigated using nonlinear finite element analyses with two-dimensional general-purpose shell elements. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of sandwich composite cylindrical structures under uniaxial compressive load. As such, finite element models of sandwich composite cylinders were developed and analyses were performed to predict the buckling responses of geometrically perfect and imperfect sandwich composite cylinders. The development of the selected finite-element modeling approach for a sandwich composite cylinder is discussed. Buckling-response sensitivity of geometrically imperfect sandwich cylinders for various shell element types were investigated as part of this study. Preliminary results of geometric imperfections influence on buckling response of sandwich cylinders are also presented.