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At least 199 records · Page 11

Generalized Predictive Control for Active Stability Augmentation and Vibration Reduction on an Aeroelastic Tiltrotor Model

Tiltrotor aircraft are defining the state-of-the-art in vertical lift technology as they have the potential to greatly expand rotary-wing operational boundaries. However, they are often limited in forward flight speed due to complex coupled rotor and wing dynamic instabilities. The U.S. Army and NASA have been developing a new wind tunnel model, the TiltRotor Aeroelastic Stability Testbed(TRAST), to test proprotors in the NASA Langley Research Center Transonic Dynamics Tunnel (TDT) to investigate aeroelastic stability in cruise. The test is intended to provide high-quality research data for analytical tool development and validation. In addition, the TRAST model will support, develop, and mature new technologies for the design of advanced proprotor aircraft. Stability augmentation and vibration reduction during testing is planned with the use of an active control methodology known as Generalized Predictive Control(GPC). GPC is an autoregressive control law that experimentally acquires a system identification to derive the input-output relation of controls and corresponding sensors. This type of control law is especially useful for complex dynamic interactions that are difficult to explicitly model such as proprotor pylon instability, often referred to as whirl flutter. GPC has been successfully employed on other tiltrotor vehicles to suppress whirl flutter instabilities and vibrations. To aid in the characterization of the wind-tunnel model and in tool development, an analytical representation of the wind-tunnel model was developed using the rotorcraft comprehensive analysis system (RCAS) that simulates structural dynamics and aerodynamics. RCAS was used to derive state-space estimates of the physical plant at various flight conditions to test control law effectiveness. This paper will present an overview of the test article development, a description of RCAS, an explanation of the GPC methodology, and results of GPC being applied to state-space plant estimates of the TRAST model. In these simulations, GPC was effective at stabilizing the aircraft beyond the whirl-flutter boundary while simultaneously reducing vibrations across the flight regime. Additionally, a modern advancement to GPC, termed advanced GPC (AGPC), is introduced that enables a self-adapting system identification. Preliminary results show that AGPC is successful at self-correction as the plant changes from what was used for system identification.

tiltrotor↗

Using Energy Storage-Based Grid Forming Inverters for Operational Reserve in Hybrid Diesel Microgrids

In remote arctic communities, where access to a bulk electrical grid interconnection is not available, the implementation of islanded microgrids has been the most viable way to produce and distribute electricity services to their inhabitants. Historically, these islanded grids have relied primarily on diesel generators or hydropower resources to supply the baseload. However, this practice can result in increased expense due to the high costs associated with fuel transportation and the significant amounts of on-site storage necessary when fuel transportation is unavailable during winter months. In order to mitigate this problem, arctic microgrids have started to transition to a hybrid-source operational mode by incorporating renewable energy sources that are inherently variable in nature, such as wind or solar. Due to their highly stochastic behavior, these hybrid-source islanded microgrids can pose potential issues related to power quality due to introduction of rapid net load fluctuations and inability of diesel generators to respond rapidly. In addition, non-firm stochastic sources can require significant idling diesel generator resources to serve as spinning reserves, which is inefficient and wasteful. This work studies the problems that may arise in the transient dynamics of a real-world hybrid diesel microgrid when subjected to a loss of wind generation. Moreover, this work proposes a transition from a diesel spinning reserve to a battery energy-storage system (BESS) operating reserve scheme. The study of the proposed transition is important in establishing the fundamental implication of transient dynamics and the potential benefits of integrating a BESS as a spinning reserve in terms of stability, frequency nadir, and transient voltage deviation. The methods to investigate and validate the transient dynamics relied on both electromagnetic simulation models of GFMIs and a commercially available GFMI in an experimental power hardware-in-the-loop setup. The simulation results showed that the proposed operating reserve scheme improves the power quality of the system in terms of voltage deviation and frequency nadir when the microgrid is subjected to a loss of wind generation scenario. Depending on the simulation cases, adding a GFMI reduced the frequency nadir between 65.3% and 86.7%. Moreover, the reductions in the voltage deviations improved between 3.6% and 23.0%. From these results it can be concluded that the integration of a GFMI can reduce the frequency nadir in a hybrid diesel microgrid, and in turn, reduce diesel consumption, which improves system reliability while reducing fuel expenses. Furthermore, the novelty of this work relies on the fact that the offline simulation results were validated using a power hardware-in-the-loop platform that incorporated a 100 kVA commercially available GFMI as the device under test.

Hernandez-Alvidrez, Javier↗

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Dynamics and Adaptive Control for Stability Recovery of Damaged Aircraft

This paper presents a recent study of a damaged generic transport model as part of a NASA research project to investigate adaptive control methods for stability recovery of damaged aircraft operating in off-nominal flight conditions under damage and or failures. Aerodynamic modeling of damage effects is performed using an aerodynamic code to assess changes in the stability and control derivatives of a generic transport aircraft. Certain types of damage such as damage to one of the wings or horizontal stabilizers can cause the aircraft to become asymmetric, thus resulting in a coupling between the longitudinal and lateral motions. Flight dynamics for a general asymmetric aircraft is derived to account for changes in the center of gravity that can compromise the stability of the damaged aircraft. An iterative trim analysis for the translational motion is developed to refine the trim procedure by accounting for the effects of the control surface deflection. A hybrid direct-indirect neural network, adaptive flight control is proposed as an adaptive law for stabilizing the rotational motion of the damaged aircraft. The indirect adaptation is designed to estimate the plant dynamics of the damaged aircraft in conjunction with the direct adaptation that computes the control augmentation. Two approaches are presented 1) an adaptive law derived from the Lyapunov stability theory to ensure that the signals are bounded, and 2) a recursive least-square method for parameter identification. A hardware-in-the-loop simulation is conducted and demonstrates the effectiveness of the direct neural network adaptive flight control in the stability recovery of the damaged aircraft. A preliminary simulation of the hybrid adaptive flight control has been performed and initial data have shown the effectiveness of the proposed hybrid approach. Future work will include further investigations and high-fidelity simulations of the proposed hybrid adaptive Bight control approach.

Nguyen, Nhan↗

Fully Coupled Aeroelastic Stability Analysis of Adaptive Shape Memory Alloy Structural Technologies for Airframe Noise Reduction

This final report documents work performed by ATA Engineering, Inc., (ATA) to develop computational models and analyze the coupled fluid-structure response of two types of noise treatments applied to the leading-edge-slat component of a high-lift system typical of modern transport aircraft. The first treatment is a slat-gap filler (SGF), which closes the gap between the suction surfaces of a deployed slat and an aircraft main wing, and the second treatment is a slat-cove filler (SCF), which replaces the recirculating flow on the slat cove with a surface that promotes flow attachment. The representative airframe chosen for this work was NASA’s High-Lift Common Research Model (CRM-HL) in a baseline high-lift configuration. Superelastic shape memory alloys (SMAs) have been identified as enabling materials for these structural treatments. Since the technology elements rely upon having a highly reconfigurable structure, designs were assessed for their static aeroelastic deflection as well as their dynamic aeroelastic stability using coupled computational fluid dynamics (CFD) and nonlinear computational structural dynamics (NL-CSD) tools. Specifically, fluid-structure interaction (FSI) problems were solved computationally using the CFD solver Loci/CHEM and the NL-CSD solver Abaqus. As a part of the overall project, a similar capability was implemented using the CFD solver FUN3D coupled to Abaqus, although that work is documented in a separate report and that FSI framework was not used to analyze any of NASA’s SGF and SCF configurations. The technical approach consisted of solving for the flow field around the entire vehicle using a global CFD model, followed by extraction of relevant local subdomain data for CFD and NL-CSD co-simulations. The SGF design was analyzed using both 2D and 3D co-simulations to predict quasi-static aeroelastic deformations and to assess dynamic aeroelastic stability, whereas the SCF was analyzed in 2D only. SGF static aeroelastic response predictions focused on characterizing the deformed shape, with maximum displacements predicted to be on the order of magnitude of the technology element panel thickness. SGF dynamic aeroelastic response predictions used Partial Floquet analysis of the temporal evolution of selected nodal displacements to quantify the sign and magnitude of aeroelastic damping. Results suggest that the CRM-HL operating conditions would result in a dynamically stable response. The simulated dynamic pressure was also increased up to a factor of about four, and resulting responses suggest that predicted dynamic stability would be achieved with some margin.

Fluid Structure Interaction↗

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stability boundary and optimal operating parameter identification in milling using Bayesian learning

Here, this paper describes a novel Bayesian learning approach for stability boundary and optimal parameter identification in milling without the knowledge of the underlying tool dynamics or material cutting force coefficients. The paper is divided into two parts. First, a Bayesian learning method for stability lobe identification using test results is described. Each axial depth and spindle speed combination is characterized by a probability of stability which is updated using Bayes’ rule when a test result (stable or unstable) is made available. A novel likelihood function is defined which incorporates knowledge of the stability behavior. Numerical results show convergence to the analytical stability lobe diagram. Second, an adaptive experimental strategy to identify optimal operating parameters that maximize material removal rate is described. Numerical evaluation shows convergence to the optimal operating point with error less than 15 % within ten tests on average. The approach is validated using experimental results. Results show that the proposed method is an efficient and robust learning method to identify the stability lobe diagram and optimal operating parameters with a limited number of tests/data points.

Bayesian machine learning↗

Development and test of photon-counting microchannel plate detector arrays for use on space telescopes

The full sensitivity, dynamic range, and photometric stability of microchannel array plates(MCP) are incorporated into a photon-counting detection system for space operations. Components of the system include feedback-free MCP's for high gain and saturated output pulse-height distribution with a stable response; multi-anode readout arrays mounted in proximity focus with the output face of the MCP; and multi-layer ceramic headers to provide electrical interface between the anode array in a sealed detector tube and the associated electronics.

Timothy, J. G.↗

Analytic investigation of the AEM-A/HCMM attitude control system performance

The Heat Capacity Mapping Mission (HCMM), scheduled for launch in 1978, will be three-axis stabilized relative to the earth in a 600-kilometer altitude, polar orbit. The autonomous attitude control system consists of three torquing coils and a momentum wheel driven in response to error signals computed from data received from an infrared horizon sensor and a magnetometer. This paper presents a simple model of the attitude dynamics and derives the equations that determine the stability of the system during both attitude acquisition (acquisition-mode) and mission operations (mission-mode). Modifications to the proposed mission-mode control laws which speed the system's response to transient attitude errors and reduce the steady-state attitude errors are suggested. Numerical simulations are performed to validate the results obtained with the simple model.

Lerner, G. M.↗

An efficient approximate factorization implicit scheme for the equations of gasdynamics

An efficient implicit finite-difference algorithm for the gas dynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved while maintaining the same favorable stability characteristics and generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows about a NACA 0012 airfoil. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations. It is shown that the method offers advantages over the conventional Beam and Warming scheme and can retrofit existing Beam and Warming codes with minimal effort.

Barth, T. J.↗

NASA rotor systems research aircraft: Fixed-wing configuration flight-test results

The fixed-wing, airplane configuration flight-test results of the Rotor System Research Aircraft (RSRA), NASA 740, at Ames/Dryden Flight Research Center are documented. Fourteen taxi and flight tests were performed from December 1983 to October 1984. This was the first time the RSRA was flown with the main rotor removed; the tail rotor was installed. These tests confirmed that the RSRA is operable as a fixed-wing aircraft. Data were obtained for various takeoff and landing distances, control sensitivity, trim and dynamics stability characteristics, performance rotor-hub drag, and acoustics signature. Stability data were obtained with the rotor hub both installed and removed. The speed envelope was developed to 261 knots true airspeed (KTAS), 226 knots calibrated airspeed (KCAS) at 10,000 ft density altitude. The airplane was configured at 5 deg. wing incidence with 5 deg. wing flaps as a normal configuration. Level-flight data were acquired at 167 KCAS for wing incidence from 0 to 10 deg. Step inputs and doublet inputs of various magnitudes were utilized to acquire dynamic stability and control sensitivity data. Sine-wave inputs of constantly increasing frequency were used to generate parameter identification data. The maximum load factor attained was 2.34 g at 206 KCAS.

Erickson, R. E.↗

Dynamic Characteristics and Stability Analysis of Space Shuttle Main Engine Oxygen Pump

The dynamic characteristics of the Space Shuttle high pressure oxygen pump are presented. Experimental data is presented to show the vibration spectrum and response under actual engine operation and also in spin pit testing for balancing. The oxygen pump appears to be operating near a second critical speed and is sensitive to self excited aerodynamic cross coupling forces in the turbine and pump. An analysis is presented to show the improvement in pump stability by the application of turbulent flow seals, preburner seals, and pump shaft cross sectional modifications.

Gunter, Edgar J.↗

Laboratory demonstrations of superconducting gravity and inertial sensors for space and airborne gravity measurements

The paper describes the superconducting gravity gradiometers (SGGs) and superconducting accelerometers being developed at the University of Maryland, which take advantage of many exotic properties of superconductivity to obtain the required low noise, high stability, and large dynamic range. Results of laboratory demonstrations of some of these instruments are presented together with the design and operating principles. Particular attention is given to the three-axis Model II SGG and a six-axis superconducting accelerometer model (Model I SSA). Model II SGG, after a residual common-mode balance, exhibited a noise level of 0.05/sq rt Hz above 0.1 Hz and a 1/f-squared noise below 0.1 Hz. All six channels of Model I SSA operated simultaneously with linear and angular acceleration noise levels of 3 x 10 exp -10 g(E)/sq rt Hz and 5 x 10 exp -8 rad/sec per sec per sq rt Hz, respectively.

Paik, Ho J.↗

Flight Dynamics Performances of the MetOp A Satellite during the First Months of Operations

The 19th of October 2006 at 16:28 UTC the first MetOp satellite (MetOp A) was successfully launched from the Baykonur cosmodrome by a Soyuz/Fregat launcher. After only three days of LEOP operations, performed by ESOC, the satellite was handed over to EUMETSAT, who is since then taking care of all satellite operations. MetOp A is the first European operational satellite for meteorology flying in a Low Earth Orbit (LEO), all previous satellites operated by EUMETSAT, belonging to the METEOSAT family, being located in the Geo-stationary orbit. To ensure safe operations for a LEO satellite accurate and continuous commanding from ground of the on-board AOCS is required. That makes the operational transition at the end of the LEOP quite challenging, as the continuity of the Flight Dynamics operations is to be maintained. That means that the main functions of the Flight Dynamics have to be fully validated on-flight during the LEOP, before taking over the operational responsibility on the spacecraft, and continuously monitored during the entire mission. Due to the nature of a meteorological operational mission, very stringent requirements in terms of overall service availability (99 % of the collected data), timeliness of processing of the observation data (3 hours after sensing) and accuracy of the geo-location of the meteorological products (1 km) are to be fulfilled. That translates in tight requirements imposed to the Flight Dynamics facility (FDF) in terms of accuracy, timeliness and availability of the generated orbit and clock solutions; a detailed monitoring of the quality of these products is thus mandatory. Besides, being the accuracy of the image geo-location strongly related with the pointing performance of the platform and with the on-board timing stability, monitoring from ground of the behaviour of the on-board sensors and clock is needed. This paper presents an overview of the Flight Dynamics operations performed during the different phases of the MetOp A mission up to routine. The activities performed to validate all the Flight Dynamics functions, characterize the behaviour of the satellite and monitor the performances of the Flight Dynamics facility will be highlighted. The MetOp Flight Dynamics Operations team is led by Anders Meier Soerensen and composed by Pier Luigi Righetti, Francisco Sancho, Antimo Damiano and David Lazaro. The team is supported by Hilda Meixner, responsible for all Flight Dynamics validation activities.

Righetti, Pier Luigi↗

Test Outline for Flutter Analysis of Rectangular Panels in Rarefied Flow Conditions

Jet plume impingement forces acting on large flexible space structures may precipitate dynamically unstable behavior during space flights. Typical operating conditions in space involve rarefied gas flow regimes which are intrinsically distinct from continuum gas flow and are normally modeled using the kinetic theory of gas flow. Docking and undocking operations of the Space Shuttle with the Russian Mir space laboratory represent a scenario in which the stability boundaries of solar panels may be of interest. Extensive literature review of research work on the dynamic stability of rectangular panels in rarefied gas flow conditions indicated the lack of published reports dealing with this phenomenon. A recently completed preliminary study for NASA JSC dealing with the mathematical analysis of the stability of two-degree-of-freedom elastically supported rigid panels under the effect of rarefied gas flow was reviewed. A test plan outline is prepared for the purpose of conducting a series of experiments on four rectangular rigid test articles in a vacuum chamber under the effect of continuous and pulsating Nitrogen jet plumes. The purpose of the test plan is to gather enough data related to a number of key parameters to allow the validation of the two-degree-of-freedom mathematical model. The hardware required careful design to select a very lightweight material while satisfying rigidity and frequency requirements within the constraints of the test environment. The data to be obtained from the vacuum chamber tests can be compared with the predicted behavior of the theoretical two-degree-of-freedom model. Using the data obtained in this study, further research can identify the limitations of the mathematical model. In addition modifications to the mathematical model can be made, if warranted, to accurately predict the behavior of rigid panels under rarefied gas flow regimes.

Akl, Fred A.↗

Magnetically oriented nanosheet interlayer for dynamic regeneration in lithium metal batteries

Lithium (Li) metal has been recognized as a promising anode to advance the energy density of current Li-based batteries. However, the growth of the solid–electrolyte interphase (SEI) layer and dendritic Li microstructure pose significant challenges for the long-term operation of Li metal batteries (LMBs). Herein, we propose the utilization of a suspension electrolyte with dispersed magnetically responsive nanosheets whose orientation can be manipulated by an external magnetic field during cell operation for realizing in situ regeneration in LMBs. The regeneration mechanism arises from the redistribution of the ion flux and the formation of an inorganic-rich SEI for uniform and compact Li deposition. With the magnetic-field-induced regeneration process, we show that a Li||Li symmetric cell stably operates for 350 h at 2 mA cm −2 and 2 mA h cm −2 , ~5 times that of the cell with the pristine electrolyte. Furthermore, the cycling stability can be significantly extended in the Li||NMC full cell of 3 mA h cm −2 , showing a capacity retention of 67% after 500 cycles at 1C. The dynamic Li metal regeneration demonstrated here could bring useful design considerations for reviving the operating cells for achieving high-energy, long-duration battery systems.

Ju, Zhengyu↗