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At least 1,081 records · Page 60

Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling

Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrator's focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.

buckling↗

Analytic Ballistic Performance Model of Whipple Shields

The dual-wall, Whipple shield is the shield of choice for lightweight, long-duration flight. The shield uses an initial sacrificial wall to initiate fragmentation and melt an impacting threat that expands over a void before hitting a subsequent shield wall of a critical component. The key parameters to this type of shield are the rear wall and its mass which stops the debris, as well as the minimum shock wave strength generated by the threat particle impact of the sacrificial wall and the amount of room that is available for expansion. Ensuring the shock wave strength is sufficiently high to achieve large scale fragmentation/melt of the threat particle enables the expansion of the threat and reduces the momentum flux of the debris on the rear wall. Three key factors in the shock wave strength achieved are the thickness of the sacrificial wall relative to the characteristic dimension of the impacting particle, the density and material cohesion contrast of the sacrificial wall relative to the threat particle and the impact speed. The mass of the rear wall and the sacrificial wall are desirable to minimize for launch costs making it important to have an understanding of the effects of density contrast and impact speed. An analytic model is developed here, to describe the influence of these three key factors. In addition this paper develops a description of a fourth key parameter related to fragmentation and its role in establishing the onset of projectile expansion.

Miller, J. E.↗

Mixed-Strategy Chance Constrained Optimal Control

This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

Ono, Masahiro↗

Options for Staging Orbits in Cis-Lunar Space

NASA has been studying options to conduct missions beyond Low Earth Orbit, but within the Earth‐Moon system, in preparation for deep space exploration including human missions to Mars. Referred to as the Proving Ground, this arena of exploration activities will enable the development of human spaceflight systems and operations to satisfy future exploration objectives beyond the cis‐lunar environment. One option being considered includes the deployment of a habitable element or elements, which could be used as a central location for aggregation of supplies and resources for human missions in cis‐lunar space and beyond. Characterizing candidate orbit locations for this asset and the impacts on system design and mission operations is important in the overall assessment of the options being considered. The orbits described in this paper were initially selected by taking advantage of previous studies conducted by NASA and the work of other authors. In this paper orbits are assessed for their relative attractiveness based on various factors. A set of constraints related to the capability of the combined Orion and SLS system to deliver humans and cargo to and from the orbit are evaluated. Deployed assets intended to spend multiple years in the Proving Ground would ideally require minimal station keeping costs to reduce the mass budget allocated to this function. Additional mission design drivers include eclipse frequency, potential for uninterrupted communication with deployed assets, thermal, attitude control, communications, and other operational implications. Also the ability to support potential lunar surface activities and excursion missions beyond Earth‐Moon space is considered. The results of the characterization and evaluation of the selected orbits indicate a Near Rectilinear Orbit (NRO) is an attractive candidate as an aggregation point or staging location for operations. In this paper, the NRO is further described in terms which balance a number of key attributes that favor a variety of mission classes to meet multiple, sometimes competing, constraints.

Martinez, Roland↗

Options for Staging Orbits in Cis-Lunar Space

NASA has been studying options to conduct missions beyond Low Earth Orbit, but within the Earth-Moon system, in preparation for deep space exploration including human missions to Mars. Referred to as the Proving Ground, this arena of exploration activities will enable the development of human spaceflight systems and operations to satisfy future exploration objectives beyond the cis-lunar environment. One option being considered includes the deployment of a habitable element or elements, which could be used as a central location for aggregation of supplies and resources for human missions in cis-lunar space and beyond. Characterizing candidate orbit locations for this asset and the impacts on system design and mission operations is important in the overall assessment of the options being considered. The orbits described in this paper were initially selected by taking advantage of previous studies conducted by NASA and the work of other authors. In this paper orbits are assessed for their relative attractiveness based on various factors. First, a set of constraints related to the capability of the combined Orion and SLS system to deliver humans and cargo to and from the orbit are evaluated. Second, the ability to support potential lunar surface activities is considered. Finally, deployed assets intended to spend multiple years in the Proving Ground would ideally require minimal station keeping costs to reduce the mass budget allocated to this function. Additional mission design drivers include potential for uninterrupted communication with deployed assets, thermal, communications, and other operational implications. The results of the characterization and evaluation of the selected orbits indicate a Near Rectilinear Orbit (NRO) is an attractive candidate as an aggregation point or staging location for operations. In this paper, the NRO is further described in terms which balance a number of key attributes that favor a variety of mission classes to meet multiple, sometimes competing, constraints.

Whitley, Ryan↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

Integrated Demand Management: Minimizing Unanticipated Excessive Departure Delay while Ensuring Fairness from a Traffic Management Initiative

This paper introduces NASA's Integrated Demand Management (IDM) concept and presents the results from an early proof-of-concept evaluation and an exploratory experiment. An initial development of the concept was focused on integrating two systems - i.e. the FAA's newly deployed Traffic Flow Management System (TFMS) tool called the Collaborative Trajectory Options Program (CTOP) and the Time-Based Flow Management (TBFM) system with Extended Metering (XM) capabilities to manage projected heavy traffic demand into a capacity-constrained airport. A human-in-the-loop (HITL) simulation experiment was conducted to demonstrate the feasibility of the initial development of the concept by adapting it to an arrival traffic problem at Newark Liberty International Airport (EWR) during clear weather conditions. In this study, the CTOP was utilized to strategically plan the arrival traffic demand by controlling take-off times of both short- and long-haul flights (long-hauls specify aircraft outside TBFM regions and short-hauls specify aircraft within TBFM regions) in a way that results in equitable delays among the groups. Such strategic planning allows less airborne delay to occur within TBFM by feeding manageable long-haul traffic demand while reserving sufficient slots in the overhead streams for the short-haul departures. The manageable traffic demand indicates the TBFM scheduler assigns no more airborne delay than its assigned airspace is capable of absorbing. TBFM then uses its time-based metering capabilities to deliver the desirable throughput by tactically rescheduling the TBFM entered long-haul flights and short-haul departures. Additional research was also performed to explore use of Required Time of Arrival (RTA) capabilities as a potential control mechanism for the airborne flights to improve arrival traffic delivery accuracy of scheduled long-haul traffic demand. The study results show that both short- and long-haul flights received similar ground delays. In addition, there was a noticeable reduction in the total amount of excessive unanticipated last-minute ground delays, i.e. delays that are frequently imposed on the short-haul flight in current day operations due to saturation in the overhead stream, commonly referred to as 'double penalty'. Furthermore, the concept achieved the target throughput while minimizing the expected cost associated with overall delays in arrival traffic. Assessment of the RTA capabilities showed that there was indeed improvement of the scheduled entry times into TBFM regions by using RTA capabilities. However, with respect to reduction in delays incurred within TBFM, there was no observable benefit of improving the precision of long-haul flights entry times.

Collaborative Trajectory Options Program (CTOP)↗

Using Virtual Reality and Motion Capture as Tools for Human Factors Engineering at Nasa Marshall Space Flight Center

MSFC’s Human Factors Engineering (HFE) team is responsible for all worksite analyses performed for the SLS pre-launch integration activities at Kennedy Space Center (KSC). There is a wide variety of tasks associated with pre-launch integration activities and it is important to verify that vehicle integration will be successful early in the design process. The VR work performed by the HFE team at MSFC has allowed fast changing layouts to be analyzed by various departments with minimal impact to cost or schedule. Implementing these methods for SLS allows for VR use in early design cycles, saving time and budget. Utilizing the resulting HFE analyses improves usability and safety. Ultimately, the goal is to provide a safe environment for the technicians assembling the vehicle and the astronaut crew at launch.

Andrews, Tanya↗

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral instruments produce high-resolution and information-dense radiance spectra, thus offering the opportunity to reduce uncertainties in retrieval products. An optimal estimation-based cirrus cloud optical and microphysical product retrieval is under development for the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and the Earth Surface Mineral Dust Source Investigation (EMIT) instruments, and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder). The spectral coverage of all three instruments includes the ultraviolet, visible, and near-infrared. In this study a very fast radiative transfer model, the Principal Component-based Radiative Transfer Model in the solar spectral region (PCRTM-Solar), is used for forward modeling computations. This will reduce the computational burden in the forward radiance and Jacobian calculations as the cost function is minimized, enabling the entire AVIRIS, EMIT, and CLARREO-Pathfinder spectral range to be used in the optimal estimation framework. Using the entire spectrum will maximize the information content, resulting in a more robust and more accurate retrieval. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water. Preliminary results will be shown.

Jeffrey Mast↗

Enhancing Cargo Transportation by Reducing Airship Operating Costs

The cargo sector, contributing 8% of global greenhouse gas emissions, requires immediate action as the transportation industry gradually shifts towards greener energy solutions. In place of conventional cargo transportation, airships provide both an emission-free and cost-effective alternative. However, the cost of helium is increasing with time, making helium unsustainable to use for current state-of-the-art airships in the long term. This report explores and examines a variety of strategies and methods to make the transition to airships smoother, addressing cost concerns to ensure a beneficial shift for both aviation and cargo sectors. The main methods that have been explored and proposed are the conservation of helium through the usage of superheated steam, recycling helium using a cryogenic distillation system, ensuring the use of an efficient propulsion system, ensuring the use of an efficient electrical system—a hydrogen fuel system, and a path-finding algorithm (A* algorithm) to navigate through hazardous weather. By implementing these systems, sustainable airships can be achievable due to the concern of high-costs being greatly minimized.

Ahana Mitra↗

Full circle mechanical dynamic characterization including experimental modal analysis and finite element analysis

During operation, it was observed that a specific mechanical system experienced undesirable vibration and it became necessary to understand and mitigate this phenomenon. This document investigates the tools, methodology, and results of the dynamic characterization of the system. The characterization makes use of the experimental modal analysis (EMA) methods of single input multiple output (SIMO) and single input single output (SISO). The validity of the theory of reciprocity is confirmed to minimize measurement error, cost, and time of repeat testing. Finite element analysis (FEA) is used in choosing transducer and modal impact locations to adequately characterize the system. Single degree of freedom (SDOF) and multiple degree of freedom (MDOF) curve fitting is used to fully characterize the system’s mode shapes and natural frequencies. The EMA characterization results are used to modify and validate the FEA model so that FEA can be used to model potential structural modifications to the system to mitigate the undesirable vibration. Structural modifications are chosen, implemented, and their effectiveness is quantified using EMA. Finally, a qualitative evaluation of the methodology of FEA validation by EMA and tuning of the model to match the experimental results is discussed.

42 ENGINEERING↗

Optimizing HVAC Operations in Multi-unit Buildings for Grid Demand Response

The thermal inertia of buildings, along with the flexibility associated with thermostatically controlled loads (TCL) allows heating ventilation and cooling (HVAC) systems to be used for grid demand response (DR). In this work, we consider an HVAC system that serves multiple units in a residential building to meet their space heating requirements. We aim to determine the optimal power flow to each unit that minimizes the power costs incurred by the building's occupants while keeping in consideration their thermal comfort. The DR program is assumed to allow the building temperatures to deviate from the set-points up to a maximum limit. Despite the complex, non-linear structure of the problem, we show how the optimal solutions can be obtained efficiently using quadratic programming. Since HVAC systems can run on either electricity or natural gas, we study the efficacy of the DR regime for both hourly electricity prices and flat gas prices over the course of 24 hours. Finally, we run simulations to determine the optimal thermal power and the evolution of unit temperatures for various energy pricing schemes.

Naqvi, Syed A.↗

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗

Miniature sensors with probe insertable into and for obtaining measurements from plants and a variety of other mediums

Apparatus, methods, and systems for transducing measurements from a medium of interest. One non-limiting example is in planta monitoring of plants. In one aspect, a micro- or nano-scale probe body includes one or more microprobes (e.g. microneedles or waveguides) to access desired plant tissue, and one or more microsensors on the probe body. A microcircuit on or in the probe body transduces relevant measurements from the microsensor(s). An output interface allows storage, communication, or transfer of the transduced measurement for further use. Non-limiting examples are processing into estimations of chemical concentrations or the like for biochemical sensing. As such, if used as in planta sensors, they can be minimally invasive and cost effective for both single use and use in sets for plural plants with one central station.

Dong, Liang↗

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗

Demand-adaptive Transit Design for Urban Transportation Hubs

In this study, we proposed a novel three-stage framework for planning the optimal demand-adaptive transit (DAT) at urban transportation hubs. Given the potential trip demand and road traffic condition, the proposed framework sequentially generates the optimal set of candidate routes, combines the outgoing routes and incoming routes at the hub, and derives the optimal fleet size and corresponding route frequency under the fixed budget. In particular, we build the route generation algorithm which maximizes passenger demand coverage with travel time deviation constraint. And a heuristic algorithm is further developed which yields near-optimal operation routes for real-time demand. The fleet optimization problem is formulated to minimize the weighted cost of energy savings, operation cost and trip revenue. We conduct comprehensive numerical experiments for planning DAT with electric buses at JFK airport in NYC using NYC taxi and for-hire vehicle trip data and GoogleMap speed data. The results show the superior performance of the proposed route generation algorithm which is able to cover citywide passenger demand with only 61 DAT routes. The results also suggest that the proposed DAT planning framework may serve over 47% of existing taxi and FHV demand by operating 18 routes using the fleet of 62 electric buses.

demand adaptive↗

Model Predictive Control for a Grid-interactive Efficient Thermal Storage-integrated Heat Pump System

Building heating and cooling systems can be used to overcome the mismatch between the intermittent supply of renewable power and the fluctuating demand for electricity. A novel underground thermal energy storage integrated with a dual-source heat pump has been proposed to mitigate the mismatch while meeting the thermal demand of buildings efficiently. Conventional thermostat control with heuristic rules cannot provide intelligent decisions to maximize the thermal efficiency and flexibility of the proposed system. Advanced control strategies like model predictive control (MPC) have provided a new paradigm for grid-interactive efficient building operation with the advancement of computation and sensing. This study developed an MPC for the proposed system to provide grid service for Demand Side Management and minimize the operating cost of building owners. A control-oriented dynamic model of the proposed system has been developed. Given an objective function and proper constraints, an optimization problem is formulated to determine the optimal control strategy of the system. Dynamic Programming is adopted to solve the optimization problem. A rule-based control (RBC) is also developed to achieve similar goals. Short-term simulations are conducted to compare the system performance resulting from the two controls. The simulation results indicate that the MPC performs more intelligently than the RBC in charging thermal energy storage and selecting heat pump sources by taking advantage of the predicted cooling demands of the building and the performance of the integrated system. As a result, the MPC could save energy and reduce operating costs compared with the RBC. A case study shows that, for a 3-day operation, the MPC saves 36.9% energy and reduces 38.5% operating cost compared with the RBC.

Shi, Liang↗

Hybrid Heat Pump Controls: Conventional Dual Fuel versus Seamlessly Fuel Flexible Heat Pump

This paper compares the performance of a novel seamlessly fuel flexible heat pump (SFFHP) and conventional dual fuel heat pump (DFHP) for space heating. The conventional dual fuel systems either run on the gas furnace or electric heat pump at any given moment, as a comparison, the proposed seamlessly fuel flexible heat pump simultaneously consumes gas and electricity by continuously optimizing the proportion of each. The process air flows across the heat pump condenser first and then flows across the furnace coil, therefore, the heat pump temperature lift is reduced. SFFHP delivers energy savings by allowing each subsystem, i.e., gas furnace and electric heat pump, to operate where it performs best.For DFHP, two operation control strategies, i.e., non-restricted control and restricted control, are available on market. For the non-restricted mode, the thermostat has a switching temperature-programmed according to the balancing point of heating load and capacity curve. Heat pump operates above the switching temperature, while the furnace takes over under the switching temperature. For the restricted control, the compressor of a heat pump is disabled below a predefined lockout outdoor temperature to let the furnace take over. For SFFHP, a model predictive control strategy is developed to continuously adjust the capacities of the electric heat pump and gas furnace based on the foreseen weather data, utility price signals, and marginal grid emission signals with the goal of minimizing the utility cost and CO2 emission while guaranteeing comfort requirements.In this paper, DFHP and SFFHP are simulated using high-fidelity heat pump performance curves generated from DOE/ORNL heat pump design model. Performance comparison of DFHP and SFFHP during 2019-2020 heating season in Los Angeles shows that SFFHP with model predictive control achieves 23% utility cost reduction and 17 % CO2 emission reduction. Case studies demonstrate that SFFHP can deliver significant reductions in peak demand, utility cost, and CO2 emission. As a result, SFFHP can deliver superior benefits for utility cost reduction and CO2 emission reduction over conventional dual fuel heat pump.

Li, Zhenning↗