Parametrically-defined Approximate Control Variates
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GF Bomarito↗
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Multi-Output Approximate Control Variate Estimation for Enhanced Variance Reduction
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Thomas Dixon↗
Multi Model Monte Carlo with Python (MXMCPy)
Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.
Geoffrey F Bomarito↗
Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control
We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.
a posteriori error estimate↗
Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning
Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
uncertainty quantification↗
Singular perturbations for a Mayer variational problem
Optimal trajectory and control approximate solution by asymptotic expansion, considering Mayer variational problem solution
Kelley, H. J.↗
Measurements in Flight of the Flying Qualities of a Chance Vought F4U-4 Airplane: TED No. NACA 2388
The results of flight tests to determine flying qualities of a Chance Vought F4U-4 airplane are presented and discussed herein. In addition to comprehensive measurements at low altitude (about 8000 ft), tests of limited scope were made at high altitude (about 25,000 ft). The more important characteristics, based on a comparison of the test results and opinions of the pilots with the Navy requirements, can be summarized as follows: 1. The short-period control-free oscillations of the elevator angle and the normal acceleration were satisfactorily damped. 2. The most rearward center-of-gravity locations for satisfactory static longitudinal stability with power on, as determined by the control-force variations, were approximately 30 and 27 percent M.A.C. with flaps and gear up and down, respectively. 3. In maneuvering flight the conditions for which control-force gradients of satisfactory magnitude were obtained were seriously limited by sizable changes in the gradient with center-of-gravity location, airspeed, altitude, acceleration factor, and direction of turn. 4. The elevator and rudder controls were satisfactory for landings and take-offs. 5. The trim tabs were sufficiently effective for all controls. 6. The directional and lateral dynamic stability was positive, but the rudder oscillation did not damp within one cycle. The airplane oscillation damped sufficiently at low altitude but not at high altitude. 7. Both rudder-fixed and rudder-free static directional stability were positive over a sideslip range of +/-15 deg. However, the rudder force tended to reverse at high angles of right sideslip with flaps and gear up, power on, at low speeds. 8. The stick-fixed static lateral stability (dihedral effect) was positive in all conditions, but the stick-free dihedral effect was neutral at low speeds with flap and gear down, power on. 9. The yaw due to abrupt full aileron deflection at low speed was mot excessive, and the rudder control was adequate to hold trim sideslip. 10. In abrupt rudder-fixed aileron rolls in the clean configuration the maximum pb/2V for full aileron deflection at low and normal speeds was only 0.064. 11. The stalling characteristics were considered unsatisfactory in all configurations in both straight and turning flight due to inadequate stall warning. The motions in the stalls were not unduly severe, and recovery could be effected promptly by normal use of the controls.
Liddell, Charles J., Jr.↗
Effect of Control Mode and Load Rate on Fracture Toughness of Brittle Ceramics
The effects of control mode and rate on the fracture toughness of ceramics were measured by using chevron-notched flexure specimen in accordance with ASTM C1421. The use of stroke control gave consistent results with about 2% variation in measured fracture toughness for a very wide range of rates (0.005 to 0.5 mm/min). Use of strain or CMOD control gave an approximately 5% variation over a very wide range of rates, with the measurements being a function of rate. However, the effect was eliminated by use of dry nitrogen, implying a stress corrosion effect rather than a stability effect. With the use of nitrogen for strain control, fracture toughness values were within about 1% over a wide range of rates (1 to 80 micro-epsilon/sec.). CMOD or strain control did allow stable crack extension well past maximum load, and thus is preferred for energy calculations. The effort is being used to confirm recommendations in ASTM International standard C1421 on fracture toughness measurement.
control mode↗
Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems
In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.
Bayesian approximation error↗
Design of dominant-type control systems with large parameter variations
Optimum design of dominant type adaptive control systems with large parameter variations, using fourth order approximation
Horowitz, I. M.↗
An Online Reinforcement Learning Controller Design For Mars Ascent Vehicle
This paper presents a neural network (NN) approximator-based online reinforcement learning (ORL) controller design for Mars Ascent Vehicle (MAV) under parametric variation and significant external disturbances. The ORL controller, which does not require any offline training, involves two NNs where an action NN produces optimal short-term control performance while a critic NN evaluates the performance of the action NN using an approximated cost function. The simulation example with comparisons against baseline Proportional-Integral-Derivative (PID) and gain scheduled pole-placement PID (GS-PP-PID) controllers show the proposed controller’s effectiveness and robustness under parametric variation and high external disturbances.
Han Woong Bae↗
Robust Control Methodology Via Loop Shaping, Root Locus, and Model Reference Control
The paper describes the development of a robust control methodology that can tolerate large uncertainties in plant dynamics in terms of proportional gain variations as well as frequencies and damping. For this to be accomplished, the methodology starts by designing a feedback controller based on a loop shaping technique. The design is then improved by employing a root locus control design approach. Finally, the response of the feedback system is further improved by augmenting the control design using model reference control. The design approach also takes into consideration the speed of the process actuator for a fast response and for high disturbance rejection. Results from two control design examples covered in the paper show that this control approach can tolerate plant proportional gain uncertainty of approximately ± two orders of magnitude with relatively large variations in plant frequencies and damping.
Control Systems↗
Control methods for aiding a pilot during STOL engine failure transients
Candidate autopilot control laws that control the engine failure transient sink rates by demonstrating the engineering application of modern state variable control theory were defined. The results of approximate modal analysis were compared to those derived from full state analyses provided from computer design solutions. The aircraft was described, and a state variable model of its longitudinal dynamic motion due to engine and control variations was defined. The classical fast and slow modes were assumed to be sufficiently different to define reduced order approximations of the aircraft motion amendable to hand analysis control definition methods. The original state equations of motion were also applied to a large scale state variable control design program, in particular OPTSYS. The resulting control laws were compared with respect to their relative responses, ease of application, and meeting the desired performance objectives.
Nelson, E. R.↗
Control system development for an organic Ranking cycle engine
An organic Rankine cycle engine is used as part of a solar thermal power conversion assembly (PCA). The PCA, including a direct-heated cavity receiver and a shaft-mounted alternator, is mounted at the focal point of a parabolic dish concentrator. The engine controls are required to maintain approximately constant values of turbine inlet temperature and shaft speed, despite variation in the concentrated solar power input to the receiver. The controls design approach, system models, and initial stability and performance analysis results are presented herein.
Bergthold, F. M., Jr.↗
Time-varying Weights in Multi-Objective Optimal Control for Flexible Wing Aircraft
A multi-objective optimal control technique is modified to accommodate changing cost function weights and is used to control a flexible wing aircraft model. Variation of the weights is used to adjust the relative importance of each objective according to either a prescribed function of time or of the state. Several techniques for obtaining a practical approximation to the optimal control solution are presented, and stability of a specific weight structure with the optimal controller is demonstrated. Functionality of the multi-objective control design with weight variation is demonstrated in simulation of a flexible wing transport aircraft and is shown to improve performance over the fixed weight version both at a constant flight condition and across changing flight conditions.
Hashemi, Kelley E.↗
Meteorological control of lower stratospheric minor species variations - An observational example
Lower stratospheric air trajectories entering the region over Alaska at the approximately 125 mb level during late May, 1975 indicate a substantial shift in the geographical source regions for the air masses present during that time. This shift coincides with an approximately 25% decrease in the observed halocarbon mixing ratios at the 125 mb level as determined from a daily sequence of halocarbon profiles. Since the halocarbon species measured are essentially chemically inactive at this level, the observed variation is linked to the changing meteorological pattern.
Alyea, F. N.↗
Design of flight control systems via robust decoupled servomechanism theory
Decoupling theory and robust servomechanism theory are applied to the design of linear multivariable systems with large parameter variations. In addition to being approximately decoupled in the transient period, the over-all system achieves tracking and disturbance rejection robustly in the steady state. An example in flight control system is given.
Wang, S.-H.↗
Breakdown of the Static Dielectric Screening Approximation of Coulomb Interactions in Atomically Thin Semiconductors
Coulomb interactions in atomically thin materials are remarkably sensitive to variations in the dielectric screening of the environment, which can be used to control exotic quantum many-body phases and engineer exciton potential landscapes. For decades, static or frequency-independent approximations of the dielectric response, where increased dielectric screening is predicted to cause an energy redshift of the exciton resonance, have been sufficient. These approximations were first applied to quantum wells and were more recently extended with initial success to layered transition metal dichalcogenides (TMDs). Here, we use charge-tunable exciton resonances to investigate screening effects in TMD monolayers embedded in materials with low-frequency dielectric constants ranging from 4 to more than 1000, a range of 2 orders of magnitude larger than in previous studies. In contrast to the redshift predicted by static models, we observe a blueshift of the exciton resonance exceeding 30 meV in higher dielectric constant environments. We explain our observations by introducing a dynamical screening model based on a solution to the Bethe-Salpeter equation (BSE). When dynamical effects are strong, we find that the exciton binding energy remains mostly controlled by the low-frequency dielectric response, while the exciton self-energy is dominated by the high-frequency one. Our results supplant the understanding of screening in layered materials and their heterostructures, introduce a knob to tune selected many-body effects, and reshape the framework for detecting and controlling correlated quantum many-body states and designing optoelectronic and quantum devices.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗