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At least 289 records · Page 16

Adaptive Control of a Utility-Scale Wind Turbine Operating in Region 3

Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. The turbulent and unpredictable conditions in which wind turbines operate create many challenges for their operation. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility scale, variable-speed horizontal axis wind turbine. The objective of the adaptive pitch controller in Region 3 is to regulate generator speed and reject step disturbances. The control objective is accomplished by collectively pitching the turbine blades. We use an extension of the Direct Model Reference Adaptive Control (DMRAC) approach to track a reference point and to reject persistent disturbances. The turbine simulation models the Controls Advanced Research Turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility-scale wind turbine which has a well-developed and extensively verified simulator. The adaptive collective pitch controller for Region 3 was compared in simulations with a bas celliansesical Proportional Integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the baseline PI pitch controller and it demonstrated robustness to modeling errors.

Frost, Susan A.↗

Stability and Performance Metrics for Adaptive Flight Control

This paper addresses the problem of verifying adaptive control techniques for enabling safe flight in the presence of adverse conditions. Since the adaptive systems are non-linear by design, the existing control verification metrics are not applicable to adaptive controllers. Moreover, these systems are in general highly uncertain. Hence, the system's characteristics cannot be evaluated by relying on the available dynamical models. This necessitates the development of control verification metrics based on the system's input-output information. For this point of view, a set of metrics is introduced that compares the uncertain aircraft's input-output behavior under the action of an adaptive controller to that of a closed-loop linear reference model to be followed by the aircraft. This reference model is constructed for each specific maneuver using the exact aerodynamic and mass properties of the aircraft to meet the stability and performance requirements commonly accepted in flight control. The proposed metrics are unified in the sense that they are model independent and not restricted to any specific adaptive control methods. As an example, we present simulation results for a wing damaged generic transport aircraft with several existing adaptive controllers.

Stepanyan, Vahram↗

Flight Test Results from the NF-15B Intelligent Flight Control System (IFCS) Project with Adaptation to a Simulated Stabilator Failure

Adaptive flight control systems have the potential to be more resilient to extreme changes in airplane behavior. Extreme changes could be a result of a system failure or of damage to the airplane. A direct adaptive neural-network-based flight control system was developed for the National Aeronautics and Space Administration NF-15B Intelligent Flight Control System airplane and subjected to an inflight simulation of a failed (frozen) (unmovable) stabilator. Formation flight handling qualities evaluations were performed with and without neural network adaptation. The results of these flight tests are presented. Comparison with simulation predictions and analysis of the performance of the adaptation system are discussed. The performance of the adaptation system is assessed in terms of its ability to decouple the roll and pitch response and reestablish good onboard model tracking. Flight evaluation with the simulated stabilator failure and adaptation engaged showed that there was generally improvement in the pitch response; however, a tendency for roll pilot-induced oscillation was experienced. A detailed discussion of the cause of the mixed results is presented.

Bosworth, John T.↗

Verification and Tuning of an Adaptive Controller for an Unmanned Air Vehicle

This paper focuses on the analysis and tuning of a controller based on the Adaptive Control Technology for Safe Flight (ACTS) architecture. The ACTS architecture consists of a nominal, non-adaptive controller that provides satisfactory performance under nominal flying conditions, and an adaptive controller that provides robustness under off-nominal ones. A framework unifying control verification and gain tuning is used to make the controller s ability to satisfy the closed-loop requirements more robust to uncertainty. In this paper we tune the gains of both controllers using this approach. Some advantages and drawbacks of adaptation are identified by performing a global robustness assessment of both the adaptive controller and its non-adaptive counterpart. The analyses used to determine these characteristics are based on evaluating the degradation in closed-loop performance resulting from uncertainties having increasing levels of severity. The specific adverse conditions considered can be grouped into three categories: aerodynamic uncertainties, structural damage, and actuator failures. These failures include partial and total loss of control effectiveness, locked-in-place control surface deflections, and engine out conditions. The requirements considered are the peak structural loading, the ability of the controller to track pilot commands, the ability of the controller to keep the aircraft s state within the reliable flight envelope, and the handling/riding qualities of the aircraft. The nominal controller resulting from these tuning strategies was successfully validated using the NASA GTM Flight Test Vehicle.

Crespo, Luis G.↗

Performance Benefits Associated with Context-Dependent Arm Pointing Adaptation

Our previous work has demonstrated that head orientation can be used as a contextual cue to switch between mUltiple adaptive states. Subjects were assigned to one of three groups: the head orientation group tilted the head towards the right shoulder when drawing under a 0.5 gain of display and towards the left shoulder when drawing under a 1.5 gain of display; the target orientation group had the home & target positions rotated counterclockwise when drawing under the 0.5 gain and clockwise for the l.5 gain; the arm posture group changed the elbow angle of the arm they were not drawing with from full flexion to full extension with 0.5 and l.5 gain display changes. The head orientation cue was effectively associated with the multiple gains, in comparison to the control conditions. The purpose of the current investigation was to determine whether this context-dependent adaptation results in any savings in terms of performance measures such as movement duration and movement smoothness when subjects switch between multiple adaptive states. Subjects in the head adaptation group demonstrated reduced movement duration and increased movement smoothness (measured via normalized j erk scores) in comparison to the two control groups when switching between the 0.5 and 1.5 gain. of display. This work has demonstrated not only that subjects can acquire context-dependent adaptation, but also that it results in a significant savings of performance upon transfer between adaptive states

Seidler, R. D.↗

Adaptive Control Allocation in the Presence of Actuator Failures

In this paper, a novel adaptive control allocation framework is proposed. In the adaptive control allocation structure, cooperative actuators are grouped and treated as an equivalent control effector. A state feedback adaptive control signal is designed for the equivalent effector and allocated to the member actuators adaptively. Two adaptive control allocation algorithms are proposed, which guarantee closed-loop stability and asymptotic state tracking in the presence of uncertain loss of effectiveness and constant-magnitude actuator failures. The proposed algorithms can be shown to reduce the controller complexity with proper grouping of the actuators. The proposed adaptive control allocation schemes are applied to two linearized aircraft models, and the simulation results demonstrate the performance of the proposed algorithms.

Liu, Yu↗

Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation

An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.

Buning, Pieter G.↗

Full-Scaled Advanced Systems Testbed: Ensuring Success of Adaptive Control Research Through Project Lifecycle Risk Mitigation

The National Aeronautics and Space Administration's Dryden Flight Research Center completed flight testing of adaptive controls research on the Full-Scale Advance Systems Testbed (FAST) in January of 2011. The research addressed technical challenges involved with reducing risk in an increasingly complex and dynamic national airspace. Specific challenges lie with the development of validated, multidisciplinary, integrated aircraft control design tools and techniques to enable safe flight in the presence of adverse conditions such as structural damage, control surface failures, or aerodynamic upsets. The testbed is an F-18 aircraft serving as a full-scale vehicle to test and validate adaptive flight control research and lends a significant confidence to the development, maturation, and acceptance process of incorporating adaptive control laws into follow-on research and the operational environment. The experimental systems integrated into FAST were designed to allow for flexible yet safe flight test evaluation and validation of modern adaptive control technologies and revolve around two major hardware upgrades: the modification of Production Support Flight Control Computers (PSFCC) and integration of two, fourth-generation Airborne Research Test Systems (ARTS). Post-hardware integration verification and validation provided the foundation for safe flight test of Nonlinear Dynamic Inversion and Model Reference Aircraft Control adaptive control law experiments. To ensure success of flight in terms of cost, schedule, and test results, emphasis on risk management was incorporated into early stages of design and flight test planning and continued through the execution of each flight test mission. Specific consideration was made to incorporate safety features within the hardware and software to alleviate user demands as well as into test processes and training to reduce human factor impacts to safe and successful flight test. This paper describes the research configuration, experiment functionality, overall risk mitigation, flight test approach and results, and lessons learned of adaptive controls research of the Full-Scale Advanced Systems Testbed.

Pavlock, Kate M.↗

Design of Low Complexity Model Reference Adaptive Controllers

Flight research experiments have demonstrated that adaptive flight controls can be an effective technology for improving aircraft safety in the event of failures or damage. However, the nonlinear, timevarying nature of adaptive algorithms continues to challenge traditional methods for the verification and validation testing of safety-critical flight control systems. Increasingly complex adaptive control theories and designs are emerging, but only make testing challenges more difficult. A potential first step toward the acceptance of adaptive flight controllers by aircraft manufacturers, operators, and certification authorities is a very simple design that operates as an augmentation to a non-adaptive baseline controller. Three such controllers were developed as part of a National Aeronautics and Space Administration flight research experiment to determine the appropriate level of complexity required to restore acceptable handling qualities to an aircraft that has suffered failures or damage. The controllers consist of the same basic design, but incorporate incrementally-increasing levels of complexity. Derivations of the controllers and their adaptive parameter update laws are presented along with details of the controllers implementations.

Hanson, Curt↗

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

Nguyen, Nhan T.↗

Improving Early Adaptation Following Long Duration Spaceflight by Enhancing Vestibular Information

Crewmember adapted to the microgravity state may need to egress the vehicle within a few minutes for safety and operational reasons after g-transitions. The transition from one sensorimotor state to another consists of two main mechanisms: strategic and plastic-adaptive and have been demonstrated in astronauts returning after long duration space flight. Strategic modifications represent "early adaptation" -immediate and transitory changes in control that are employed to deal with short-term changes in the environment. If these modifications are prolonged then plastic-adaptive changes are evoked that modify central nervous system function, automating new behavioral responses. More importantly, this longer term adaptive recovery mechanism was significantly associated with their strategic ability to recover on the first day after return to Earth G. We are developing a method based on stochastic resonance (SR) to enhance information transfer by improving the brain's ability to detect vestibular signals especially when combined with balance training exercises for rapid improvement in functional skill, for standing and mobility. The countermeasure to improve post-flight balance and locomotor disturbances is a stimulus delivery system that is wearable/portable providing low imperceptible levels of white noise based binaural bipolar electrical stimulation of the vestibular system (stochastic vestibular stimulation, SVS). The techniques for improving signal detection using SVS may thus provide additional information to improve such strategic abilities and thus help in significantly reducing the number of days required to recover functional performance to preflight levels after long duration space flight. We have conducted a series of studies to document the efficacy of SVS stimulation on balance/locomotion tasks on unstable surfaces and motion tracking tasks during intra-vestibular system conflicts. In an initial study, we showed that SVS improved overall balance performance while standing on an unstable surface indicating that SVS may be sufficient to provide a comprehensive countermeasure approach for improving postural stability. In a second study, we showed that SVS improved locomotor performance on a treadmill mounted on an oscillating platform indicating that SVS may also be used to maximize locomotor performance during walking in unstable environments. In a third study, SVS was evaluated during an otolith-canal conflict scenario in a variable radius centrifuge at low frequency of oscillation (0.1 Hz) on both eye movements and perceptual responses (using a joystick) to track imposed oscillations. The variable radius centrifuge provides a selective tilting sensation that is detectable only by the otolith organs providing conflicting information from the canal organs of the vestibular system (intra-vestibular conflict). Results show that SVS significantly reduced the timing difference between both the eye movement responses as well as the perceptual tracking responses with respect to the imposed tilt sensations. These results indicate that SVS can improve performance in sensory conflict scenarios like that experienced during space flight. Such a SR countermeasure will act synergistically along with the pre-and in-flight adaptability training protocols providing an integrated, multi-disciplinary countermeasure capable of fulfilling multiple requirements making it a comprehensive and cost effective countermeasure approach to enhance sensorimotor capabilities following long-duration space flight.

Mulavara, Ajitkumar↗

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

VanZwieten, Tannen↗

Comparing Anisotropic Output-Based Grid Adaptation Methods by Decomposition

Anisotropic grid adaptation is examined by decomposing the steps of flow solution, ad- joint solution, error estimation, metric construction, and simplex grid adaptation. Multiple implementations of each of these steps are evaluated by comparison to each other and expected analytic results when available. For example, grids are adapted to analytic metric fields and grid measures are computed to illustrate the properties of multiple independent implementations of grid adaptation mechanics. Different implementations of each step in the adaptation process can be evaluated in a system where the other components of the adaptive cycle are fixed. Detailed examination of these properties allows comparison of different methods to identify the current state of the art and where further development should be targeted.

Park, Michael A.↗

Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Toward CFD Vision 2030

Unstructured grid adaptation is a powerful tool to control discretization error for Computational Fluid Dynamics (CFD). It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provides a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity continue to be significant bottlenecks in the CFD work flow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to diffuse grid adaptation technology into production CFD work flows.

Park, Michael A.↗

Adjoint-Based Mesh Adaptation for the Sonic Boom Signature Loudness

The mesh adaptation functionality of FUN3D is utilized to obtain a mesh optimized to calculate sonic boom ground signature loudness. During this process, the coupling between the discrete-adjoints of the computational fluid dynamics tool FUN3D and the atmospheric propagation tool sBOOM is exploited to form the error estimate. This new mesh adaptation methodology will allow generation of suitable meshes adapted to reduce the estimated errors in the ground loudness, which is an optimization metric employed in supersonic aircraft design. This new output-based adaptation could allow new insights into meshing for sonic boom analysis and design, and complements existing output-based adaptation techniques such as adaptation to reduce estimated errors in off-body pressure functional. This effort could also have implications for other coupled multidisciplinary adjoint capabilities (e.g., aeroelasticity) as well as inclusion of propagation specific parameters such as prevailing winds or non-standard atmospheric conditions. Results are discussed in the context of existing methods and appropriate conclusions are drawn as to the efficacy and efficiency of the developed capability.

Rallabhandi, Sriram K.↗

The Benefits of Incorporating Shipping Containers into the Climate Change Adaption Plans at NASA Wallops Flight Facility

The National Aeronautics and Space Administration has several centers and facilities located near the coast that are undoubtedly susceptible to climate change. One of those facilities is Wallops Flight Facility on the Eastern Shore of Virginia which is separated into three areas: Main Base, Mainland, and the Island. Wallops Island has numerous buildings and assets that are vulnerable to flood inundation, intense storms, and storm surge. The shoreline of Wallops Island is prone to beach erosion and is slated for another beach replenishment project in 2019. In addition, current climate projections for NASAs centers and facilities, conducted by the Climate Adaptation Science Investigators, warn of inevitable increases in annual temperature, precipitation, sea level rise, and extreme events such as heat waves. The aforementioned vulnerabilities Wallops Island faces in addition to the projections of future climate change reveal an urgency for NASA to adjust how new buildings at its centers and facilities near the coast are built to adapt to the inevitable effects of climate change. Although the agency has made strides to mitigate the effects of climate change by incorporating L.E.E.D. into new buildings that produce less greenhouse gas, the strides for the agency to institute clear climate adaptation policies for the buildings at its centers and facilities near the coast seem to lag behind. As NASA continues to formulate formidable climate change adaptation plans for its centers and facilities, an architectural trend that should be examined for its potential to replace several old buildings at Wallops Island is shipping containers buildings. Shipping containers or Intermodal Steel Building Units offer an array of benefits such as strength, durability, versatility, modular, and since they can be upcycled, they are also eco-friendly. Some disadvantages of shipping containers are they contain harmful chemicals, insulation must be added, fossil fuels must be used to transport them to the site, and multiple ISBUs are needed. However, the benefits of shipping container buildings could be utilized at NASA centers or facilities near the coast such as Wallops Island on new buildings that are designed to adapt to the impending effects of climate change. Thus, this Masters Research Project will explore how those benefits can be incorporated into the climate change adaptation plans at Wallops Island and make recommendations for policy guidelines and shipping container buildings specific to Wallops Island.

Sustainable Design↗

Neo – Mars Adaptive Training Integrative Knowledge System (MATRIKS) to Improve Operational Performance and its Neural Basis for Spaceflight

With prolonged mission durations, spaceflight crews will become increasingly dependent on onboard technologies for knowledge acquisition and maintenance. It is expected that not all skills and knowledge required for these missions can be retained and retrieved based on pre-mission training alone. Limited and delayed communication will significantly constrain support from Mission Control and crews will increasingly rely on autonomous onboard technologies to successfully perform post-landing operations. With the present project we will target NASA’s particular interest in developing and assessing an adaptive, just-in-time countermeasure that will consolidate and improve skills that are most relevant to space flight operations. To achieve this aim, NASA established a Virtual NASA Specialized Center of Research (VNSCOR)referred to as “Mars Adaptive Training Integrative Knowledge System (MATRIKS)”, comprising the following three projects: (1) “Trinity–Multi-Environment Virtual Training for Long Duration Exploration Missions”, PI: A. Anderson (UC Boulder); (2) “Morpheus–A Haptic Sensory Supplement to Optimize In-Flight Adaptive Training for Human Control of Spacecraft Robotic Arms”, PI: S. Robinson, UC Davis); and the present project “Neo–Adaptive Training integrative knowledge System to Improve Operational Performance and its Neural Basis for Spaceflight” (UPenn, PI: A.C. Stahn). Neo leverages a validated workstation called 6DF that simulates a rendezvous and docking maneuver using real spacecraft flight dynamics. It is designed to (1) train and improve sensorimotor skills relevant for inflight and post-landing operational tasks; (2) feature an autonomous and adaptive training approach that does not rely on feedback from flight operations on the ground; (3) maximize the transfer of mission-relevant motor skills; (4) allow the assessment of the neural circuitry underlying the task; and (5) deliver the training in a motivating and meaningful way to astronauts. Neocomprises two overarching aims: First, we will identify the neural circuitry underlying spaceflight relevant tasks by performing a subset of the 6DFtaskduring functional magnetic resonance imaging (MRI)in a total of up to N=30 subjects with varying levels of 6DF training experience. Second, as part of the above-mentioned VNSCOR MATRIKS the proposed 6DF autonomous intelligent tutor system will be integrated in an additive manner with a haptic feedback intervention (Morpheus), and a multi-environment virtual trainer(Trinity).It is expected that Neo, Morpheus and Trinity mutually complement each other to facilitate an effective countermeasure tool to acquire and retain operational skills that are critical for exploration class missions. To assess the efficacy of this combined effort, the VNSCOR MATRIKS will collect data inN=16 crew members in one HERA campaign of 45 days duration with N=16 crew members(four missions with N=4 crew member seach).The primary goal is to identify changes in operational performance as assessed by NASA’s simulator of Canadarm2 operations, i.e., Robotic On-board Trainer (ROBoT-r) in response to MATRIKS. As part of Neo we will also identify if, and to what extent MATRIKS will promote transfer to general cognitive performance (Cognition battery), distinctive visuo-spatial tasks critical for telerobotic tasks (Spatial Cognition battery), and affect brain structural changes and the neural circuitry of key brain networks expected to be relevant for spaceflight-related performance. At the conclusion of the research, we will have defined and demonstrated the use of a neuroscience-based, adaptive training integrative knowledge system to potentially mitigate visuo-spatial and sensorimotor brain changes associated with prolonged isolation and confinement to reduce the likelihood or impact of potential decrements in human performance capabilities during long-duration space missions. The expected significance of this 4-year project relates to its relevance for facilitating effective countermeasure tools to acquire and retain operational skills that are critical for exploration class missions. This will support the development of necessary countermeasures and technologies in support of human space exploration, focusing on mitigating operational performance risks.

A C Stahn↗

Domain Adaptation for Measurements of Strong Gravitational Lenses

Upcoming surveys are predicted to discover galaxy-scale strong lenses on the order of $10^5$, making deep learning methods necessary in lensing data analysis. Currently, there is insufficient real lensing data to train deep learning algorithms, but the alternative of training only on simulated data results in poor performance on real data. Domain Adaptation may be able to bridge the gap between simulated and real datasets. We utilize domain adaptation for the estimation of Einstein radius ($\Theta_E$) in simulated galaxy-scale gravitational lensing images with different levels of observational realism. We evaluate two domain adaptation techniques - Domain Adversarial Neural Networks (DANN) and Maximum Mean Discrepancy (MMD). We train on a source domain of simulated lenses and apply it to a target domain of lenses simulated to emulate noise conditions in the Dark Energy Survey (DES). We show that both domain adaptation techniques can significantly improve the model performance on the more complex target domain dataset. This work is the first application of domain adaptation for a regression task in strong lensing imaging analysis. Our results show the potential of using domain adaptation to perform analysis of future survey data with a deep neural network trained on simulated data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗