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Accuracy of Center of Pressure Determination via Motion Capture

BACKGROUND: This study was conducted to support the stability assessment for tasks in lunar gravity and exercises on a Vibration Isolation and Stabilization (VIS) system in microgravity based on the dynamic feasibility criterion of whether the calculated position of the center of pressure (COP) falls within the base of support (BOS) which outlines the subject’s feet. Motion capture data combined with biomechanical modeling and simulation allows the forces and moments between the human and the VIS platform to be computed and the position of the COP as well as the location and shape of the BOS to be determined. The goal of this study was to assess the accuracy of the COP trajectory calculated using motion capture-based data. METHODS AND RESULTS: To obtain the dynamic quantities from which COP is calculated, motion capture data is first collected in the 1g lab environment by recording the trajectories of passive retroreflective markers placed on a subject during exercise or performance of a given task. The OpenSim [1] inverse kinematics (IK) tool is used to fit a scaled subject model to recorded marker trajectories while minimizing marker error to obtain joint angles. Then, a custom OpenSim plugin [2] is used to determine the subject’s time-varying moment of inertia and its time derivative, center of mass (CM) position, velocity, and acceleration, as well as the angular momentum and its time derivative relative to the subject’s CM. Some of these quantities are not needed for modeling tasks performed on a stationary lunar surface but, due to the moving exercise platform, are needed to model VIS response to the subject’s motion. Hand positions, used in calculating a cable force if present, are recorded as well. These quantities are used to calculate the total force (F ⃗^((plate) )) and moment (M ⃗^((plate) )) exerted by the lunar surface or the VIS plate on the subject’s shoe soles. COP is then calculated from the following equations: r_x^((cop) )= M_z^((plate) )/F_y^((plate) ) and r_z^((cop) )= 〖-M〗_x^((plate) )/F_y^((plate) ), where the y axis is normal to the surface. COP accuracy for feasibility assessments is then determined by whether it falls within the BOS, which is also computed by the plugin. To study the accuracy of COP calculated from motion capture, we first investigated whether COP remained within the BOS, as it must, for exercises performed in the 1g lab environment. Standard exercises such as back squat and deadlift were analyzed, as well as more explosive exercises including hang clean and press. Cases in which the COP exited the BOS indicated that COP accuracy required further investigation. In this study, an exercise device with cables was used, so cable force modeling accuracy should also be considered. In a separate study, we collected motion capture and force plate data for twenty-seven motions not involving an exercise device. About a third were genuine countermeasures exercises (e.g., hang clean and press), some were relevant for lunar tasks (e.g., object pick up), and the rest were of a “unit test” nature (e.g., swaying back and forth or side to side). Motion capture-based COP positions were compared with force plate measured COP. We found that while force plate measured COP remained within the BOS, motion capture-based COP was observed to briefly exit the BOS on occasion. Techniques to mitigate IK artifacts and filtering of calculated data could be used to improve the agreement of calculated and measured results, resolving excursions from the BOS within this dataset. The mean error between calculated and measured COP was found to be less than 6 mm. Additionally, we derived and investigated equations for the COP in terms of the cable force, cable location, as well as the human CM position, acceleration, and angular momentum with respect to the CM, and analyzed them for sensitivity to errors in individual quantities. Several were found, but the most significant one was that when the vertical force on the feet approaches zero, indicating a near-detachment or ‘jump off’ condition, errors are amplified. This is consistent with the observation that in the absence of pressure, the concept of the center of pressure would become meaningless.

C A Bell↗

DOE OSTI2021

The EGS Collab Project: Status and Accomplishments

The EGS Collab project, supported by the US Department of Energy, is addressing challenges in implementing enhanced geothermal systems (EGS). This includes improving understanding of the stimulation of crystalline rock to create appropriate flow pathways, and the ability to effectively simulate both the stimulation and the flow and transport processes in the resulting fracture network. The project is performing intensively monitored rock stimulation and flow tests at the 10-m scale in an underground research laboratory. Data and observations from the field test are compared to simulations to understand processes and to build confidence in numerical modeling of the processes. In Experiment 1, we examined hydraulic fracturing an underground test bed at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, at a depth of approximately 1.5 km. We drilled eight sub-horizontal boreholes in a well-characterized phyllite. Six of the boreholes were instrumented with many sensor types to allow careful monitoring of stimulation events and flow tests, and the other two boreholes were used for water injection and production. We performed a number of stimulations and flow tests in the testbed. Our monitoring systems allowed detailed observations and collection of numerous data sets of processes occurring during stimulation and during dynamic flow tests. Long-term ambient temperature and chilled water flow tests were performed in addition to many tracer tests to examine system behavior. Data were rapidly analyzed, allowing adaptive control of the tests. Numerical simulation was used to answer key experimental design questions, to forecast fracture propagation trajectories and extents, and to analyze and evaluate results. Many simulations were performed in near-real-time in conjunction with the field experiments, with more detailed process study simulations performed on a longer timeframe. Experiment 2 will examine hydraulic shearing in a test bed being built at the SURF at a depth of about 1.25 km in amphibolite under a different set of stress and fracture conditions than Experiment 1. Five sets of fracture orientations were considered in design, and three orientations seem to be consistently observed.

EGS Collab↗

NASA NTRS2018

Extraction of Doppler Observables from Open-Loop Recordings for the Juno Radio Science Investigation

The goal of the Juno Gravity Science investigation is to estimate the gravitational field of Jupiter by measurement of the spacecraft velocity during periods of closest approach. Velocity is measured by the Doppler shift of dual X- and Ka-band radio links between the Juno spacecraft, in orbit around Jupiter, and the DSS-25 antenna of the Deep Space Network (DSN). During times of closest-approach, Juno experiences large dynamic ranges caused by the orbital dynamics and spin signatures caused by the spin-stabilized spacecraft that are detectable by the receivers at DSS-25. Open-loop recordings of received voltages are processed to compute Doppler observables utilized in the estimation of the gravity field. Presented is a method to process open-loop data collected by the DSN to compensate for the spin signature of the spacecraft, removal of artifacts from Doppler observables caused by the high dynamic environment, and improve performance of the digital phase-locked loop utilized in the data processing.

Buccino, Dustin R.↗

DOE OSTI2023

OPEN leaf : an open‐source cloud‐based phenotyping system for tracking dynamic changes at leaf‐specific resolution in Arabidopsis

SUMMARY The first draft of the Arabidopsis genome was released more than 20 years ago and despite intensive molecular research, more than 30% of Arabidopsis genes remained uncharacterized or without an assigned function. This is in part due to gene redundancy within gene families or the essential nature of genes, where their deletion results in lethality (i.e., thedark genome). High‐throughput plant phenotyping (HTPP) offers an automated and unbiased approach to characterize subtle or transient phenotypes resulting from gene redundancy or inducible gene silencing; however, access to commercial HTPP platforms remains limited. Here we describe the design and implementation ofOPEN leaf, an open‐source phenotyping system with cloud connectivity and remote bilateral communication to facilitate data collection, sharing and processing.OPEN leaf, coupled with our SMART imaging processing pipeline was able to consistently document and quantify dynamic changes at the whole rosette level and leaf‐specific resolution when plants experienced changes in nutrient availability. Our data also demonstrate that VIS sensors remain underutilized and can be used in high‐throughput screens to identify and characterize previously unidentified phenotypes in a leaf‐specific time‐dependent manner. Moreover, the modular and open‐source design ofOPEN leafallows seamless integration of additional sensors based on users and experimental needs.

Plant Sciences↗

NASA NTRS2010

Acquisition of a Biomedical Database of Acute Responses to Space Flight during Commercial Personal Suborbital Flights

There is currently too little reproducible data for a scientifically valid understanding of the initial responses of a diverse human population to weightlessness and other space flight factors. Astronauts on orbital space flights to date have been extremely healthy and fit, unlike the general human population. Data collection opportunities during the earliest phases of space flights to date, when the most dynamic responses may occur in response to abrupt transitions in acceleration loads, have been limited by operational restrictions on our ability to encumber the astronauts with even minimal monitoring instrumentation. The era of commercial personal suborbital space flights promises the availability of a large (perhaps hundreds per year), diverse population of potential participants with a vested interest in their own responses to space flight factors, and a number of flight providers interested in documenting and demonstrating the attractiveness and safety of the experience they are offering. Voluntary participation by even a fraction of the flying population in a uniform set of unobtrusive biomedical data collections would provide a database enabling statistical analyses of a variety of acute responses to a standardized space flight environment. This will benefit both the space life sciences discipline and the general state of human knowledge.

Charles, John B.↗

NASA NTRS2016

Rotary Balance Wind Tunnel Testing for the FASER Flight Research Aircraft

Flight dynamics research was conducted to collect and analyze rotary balance wind tunnel test data in order to improve the aerodynamic simulation and modeling of a low-cost small unmanned aircraft called FASER (Free-flying Aircraft for Sub-scale Experimental Research). The impetus for using FASER was to provide risk and cost reduction for flight testing of more expensive aircraft and assist in the improvement of wind tunnel and flight test techniques, and control laws. The FASER research aircraft has the benefit of allowing wind tunnel and flight tests to be conducted on the same model, improving correlation between wind tunnel, flight, and simulation data. Prior wind tunnel tests include a static force and moment test, including power effects, and a roll and yaw damping forced oscillation test. Rotary balance testing allows for the calculation of aircraft rotary derivatives and the prediction of steady-state spins. The rotary balance wind tunnel test was conducted in the NASA Langley Research Center (LaRC) 20-Foot Vertical Spin Tunnel (VST). Rotary balance testing includes runs for a set of given angular rotation rates at a range of angles of attack and sideslip angles in order to fully characterize the aircraft rotary dynamics. Tests were performed at angles of attack from 0 to 50 degrees, sideslip angles of -5 to 10 degrees, and non-dimensional spin rates from -0.5 to 0.5. The effects of pro-spin elevator and rudder deflection and pro- and anti-spin elevator, rudder, and aileron deflection were examined. The data are presented to illustrate the functional dependence of the forces and moments on angle of attack, sideslip angle, and angular rate for the rotary contributions to the forces and moments. Further investigation is necessary to fully characterize the control effectors. The data were also used with a steady state spin prediction tool that did not predict an equilibrium spin mode.

Denham, Casey↗

NASA NTRS2017

Predicting the Operational Acceptability of Route Advisories

NASA envisions a future Air Traffic Management system that allows safe, efficient growth in global operations, enabled by increasing levels of automation and autonomy. In a safety-critical system, the introduction of increasing automation and autonomy has to be done in stages, making human-system integrated concepts critical in the foreseeable future. One example where this is relevant is for tools that generate more efficient flight routings or reroute advisories. If these routes are not operationally acceptable, they will be rejected by human operators, and the associated benefits will not be realized. Operational acceptance is therefore required to enable the increased efficiency and reduced workload benefits associated with these tools. In this paper, the authors develop a predictor of operational acceptability for reroute advisories. Such a capability has applications in tools that identify more efficient routings around weather and congestion and that better meet airline preferences. The capability is based on applying data mining techniques to flight plan amendment data reported by the Federal Aviation Administration and data on requested reroutes collected from a field trial of the NASA developed Dynamic Weather Routes tool, which advised efficient route changes to American Airlines dispatchers in 2014. 10-Fold cross validation was used for feature, model and parameter selection, while nested cross validation was used to validate the model. The model performed well in predicting controller acceptance or rejection of a route change as indicated by chosen performance metrics. Features identified as relevant to controller acceptance included the historical usage of the advised route, the location of the maneuver start point relative to the boundaries of the airspace sector containing the maneuver start (the maneuver start sector), the reroute deviation from the original flight plan, and the demand level in the maneuver start sector. A random forest with forty trees was the best performing of the five models evaluated in this paper.

route advisories↗

NASA NTRS2017

Predicting the Operational Acceptability of Route Advisories

operational acceptability↗

DOE OSTI2015

Enhanced resting-state dynamics of the hemoglobin signal as a novel biomarker for detection of breast cancer

Purpose: The work presented here demonstrates an application of diffuse optical tomography (DOT) to the problem of breast-cancer diagnosis. The potential for using spatial and temporal variability measures of the hemoglobin signal to identify useful biomarkers was studied. Methods: DOT imaging data were collected using two instrumentation platforms the authors developed, which were suitable for exploring tissue dynamics while performing a simultaneous bilateral exam. For each component of the hemoglobin signal (e.g., total, oxygenated), the image time series was reduced to eight scalar metrics that were affected by one or more dynamic properties of the breast microvasculature (e.g., average amplitude, amplitude heterogeneity, strength of spatial coordination). Receiver-operator characteristic (ROC) analyses, comparing groups of subjects with breast cancer to various control groups (i.e., all noncancer subjects, only those with diagnosed benign breast pathology, and only those with no known breast pathology), were performed to evaluate the effect of cancer on the magnitudes of the metrics and of their interbreast differences and ratios. Results: For women with known breast cancer, simultaneous bilateral DOT breast measures reveal a marked increase in the resting-state amplitude of the vasomotor response in the hemoglobin signal for the affected breast, compared to the contralateral, noncancer breast. Reconstructed 3D spatial maps of observed dynamics also show that this behavior extends well beyond the tumor border. In an effort to identify biomarkers that have the potential to support clinical aims, a group of scalar quantities extracted from the time series measures was systematically examined. This analysis showed that many of the quantities obtained by computing paired responses from the bilateral scans (e.g., interbreast differences, ratios) reveal statistically significant differences between the cancer-positive and -negative subject groups, while the corresponding measures derived from individual breast scans do not. ROC analyses yield area-under-curve values in the 77%–87% range, depending on the metric, with sensitivity and specificity values ranging from 66% to 91%. An interesting result is the initially unexpected finding that the hemodynamic-image metrics are only weakly dependent on the tumor burden, implying that the DOT technique employed is sensitive to tumor-induced changes in the vascular dynamics of the surrounding breast tissue as well. Computational modeling studies serve to identify which properties of the vasomotor response (e.g., average amplitude, amplitude heterogeneity, and phase heterogeneity) principally determine the values of the metrics and their codependences. Findings from the modeling studies also serve to clarify the influence of spatial-response heterogeneity and of system-design limitations, and they reveal the impact that a complex dependence of metric values on the modeled behaviors has on the success in distinguishing between cancer-positive and -negative subjects. Conclusions: The authors identified promising hemoglobin-based biomarkers for breast cancer from measures of the resting-state dynamics of the vascular bed. A notable feature of these biomarkers is that their spatial extent encompasses a large fraction of the breast volume, which is mainly independent of tumor size. Tumor-induced induction of nitric oxide synthesis, a well-established concomitant of many breast cancers, is offered as a plausible biological causal factor for the reported findings.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Utilizing Geo-located Sensors and Social Media for Studying Population Dynamics and Land Classification

The ability to understand where, when, and why humans move across space and time has always been essential to research areas such as urban planning, transportation, population dynamics, and emergency preparedness and response. The increasing sources of activity data is generating novel opportunities to understand human dynamics that previously was not possible; Geo-located user generated content from mobile devices and sensors allow a level of spatial and temporal granularity that could possibly answer the reasons for human movement at a high-resolution. This work discusses a broad array of research agenda in human dynamics and land use by proposing an explicit model that assists in delineating and articulating the opportunities, challenges, and limitations of using new forms of unauthoritated data, such as social media in main-stream GIS research. We study mobile phone call volume and GPS locations to characterize human activity patterns and provide inference on land use. Later, we demonstrate the ability of geo-located social media posts to provide insight on population density estimates for special events and Points of Interest detection. The chapter underpins the need to utilize new forms of data collection mechanism as well as their use to augment our understanding of human dynamics research and future application of geographical information systems.

Thakur, Gautam Malviya↗

DOE OSTI2019

Simple analytical model for fitting QENS data from liquids

The advent of new generation of neutron spectrometers for quasielastic scattering measurements has demonstrated the need for multi-component (at least two-component) fitting of data collected from liquids. The narrowest component is associated with long-range translational diffusion, whereas the broader component originates from localized center-of-mass motions in the transient cage of the nearest neighbors. Intra-particle dynamics (e.g., of molecular side groups) may give rise to additional components besides the center-of-mass motions. We present a simple analytical model for two-component fits of quasielastic neutron scattering data collected from liquids. Here, the use of such models is optional (albeit helpful) in the traditional approach, where fits are performed sequentially and independently for the data collected at separate Q values, but imperative in the global fitting, where the data are fitted simultaneously at all Q values, which may be necessary to rationalize the data from increasingly complex systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Ab initio structure determination of nanocrystals of organic pharmaceutical compounds by electron diffraction at room temperature using a Timepix quantum area direct electron detector

A specialized quantum area detector for electron diffraction studies makes it possible to solve the structure of small organic compound nanocrystals in non-cryo conditions by direct methods. Until recently, structure determination by transmission electron microscopy of beam-sensitive three-dimensional nanocrystals required electron diffraction tomography data collection at liquid-nitrogen temperature, in order to reduce radiation damage. Here it is shown that the novel Timepix detector combines a high dynamic range with a very high signal-to-noise ratio and single-electron sensitivity, enabling ab initio phasing of beam-sensitive organic compounds. Low-dose electron diffraction data (∼0.013 e{sup −} Å{sup −2} s{sup −1}) were collected at room temperature with the rotation method. It was ascertained that the data were of sufficient quality for structure solution using direct methods using software developed for X-ray crystallography (XDS, SHELX) and for electron crystallography (ADT3D/PETS, SIR2014)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Experimental and Computational Characterization of a Modified Sioutas Cascade Impactor for Respirable Radioactive Aerosols

Oak Ridge National Laboratory is collecting and characterizing aerosols released when spent nuclear fuel (SNF) rods are fractured in bending. An aerosol collection system was designed and tested to collect respirable sized (<10 μm aerodynamic diameter [AED]) particulates inside a hot cell facility. The setup is a modified version of the commercially available Sioutas cascade impactor, to which additional stages were added to expand the aerosol collection range from 2.5 to ~15 μm AED. To accommodate the additional stages and specific test conditions, the operating flow rate for aerosol collection was reduced, and testing was conducted by using pressure drop measurements, surrogate dust collection, and particle size characterization. The fluid flow distribution within the cascade and its stages was simulated in STAR-CCM+, and the stage-wise pressure drops obtained using the computational fluid dynamics model were then compared to experimental data. Lagrangian particle simulations were also performed, and stage-wise collection statistics were obtained from the simulation for comparison with the experimental data obtained using SNF-surrogate dust particles. The results provide valuable insights into the stage-wise particle collection characteristics of the modified cascade impactor and can also be used to improve the prediction accuracy of the manufacturer-determined analytical correlations.

aerosol modeling↗

DOE OSTI2014

Prony Ringdown GUI (CERTS Prony Ringdown, part of the DSI Tool Box)

The PNNL Prony Ringdown graphical user interface is one analysis tool included in the Dynamic System Identification toolbox (DSI Toolbox). The Dynamic System Identification toolbox is a MATLAB-based collection of tools for parsing and analyzing phasor measurement unit data, especially in regards to small signal stability. It includes tools to read the data, preprocess it, and perform small signal analysis. 5. Method of Solution: The Dynamic System Identification Toolbox (DSI Toolbox) is designed to provide a research environment for examining phasor measurement unit data and performing small signal stability analysis. The software uses a series of text-driven menus to help guide users and organize the toolbox features. Methods for reading in populate phasor measurement unit data are provided, with appropriate preprocessing options for small-signal-stability analysis. The toolbox includes the Prony Ringdown GUI and basic algorithms to estimate information on oscillatory modes of the system, such as modal frequency and damping ratio.

Tuffner, Francis↗

NASA NTRS1999

An EVA Suit Fatigue, Strength, and Reach Model

The number of Extra-Vehicular Activities (EVAs) performed will increase dramatically with the upcoming Space Station assembly missions. It is estimated that up to 900 EVA hours may be required to assemble the Space Station with an additional 200 hours per year for maintenance requirements. Efficient modeling tools will be essential to assist in planning these EVAS. Important components include strength and fatigue parameters, multi-body dynamics and kinematics. This project is focused on building a model of the EVA crew member encompassing all these capabilities. Phase 1, which is currently underway, involves collecting EMU suited and unsuited fatigue, strength and range of motion data, for all major joints of the body. Phase 2 involves processing the data for model input, formulating comparisons between the EMU suits and deriving generalized relationships between suited and unsuited data. Phase 3 will be formulation of a multi-body dynamics model of the EMU capable of predicting mass handling properties and integration of empirical data into the model. Phase 4 will be validation of the model with collected EMU data from the Neutral Buoyancy Laboratory at NASA/JSC. Engineers and designers will use tie EVA suit database to better understand the capabilities of the suited individuals. This knowledge will lead to better design of tools and planned operations. Mission planners can use the modeling system and view the animations and the visualizations of the various parameters, such as overall fatigue, motion, timelines, reach, and strength to streamline the timing, duration, task arrangement, personnel and overall efficiency of the EVA tasks. Suit designers can use quantifiable data at common biomechanical structure points to better analyze and compare suit performance.

Maida, James C.↗

NASA NTRS1993

Loading, electromyograph, and motion during exercise

A system is being developed to gather kineto-dynamic data for a study to determine the load vectors applied to bone during exercise on equipment similar to that used in space. This information will quantify bone loading for exercise countermeasures development. Decreased muscle loading and external loading of bone during weightlessness results in cancellous bone loss of 1 percent per month in the lower extremities and 2 percent per month in the calcaneous. It is hypothesized that loading bone appropriately during exercise may prevent the bone loss. The system consists of an ergometer instrumented to provide position of the pedal (foot), pedaling forces on the foot (on the sagittal plane), and force on the seat. Accelerometers attached to the limbs will provide acceleration. These data will be used as input to an analytical model of the limb to determine forces on the bones and on groups of muscles. EMG signals from activity in the muscles will also be used in conjunction with the equations of mechanics of motion to be able to discern forces exerted by specific muscles. The tasks to be carried out include: design of various mechanical components to mount transducers, specification of mechanical components, specification of position transducers, development of a scheme to control the data acquisition instruments (TEAC recorder and optical encoder board), development of a dynamic model of the limbs in motion, and development of an overall scheme for data collection analysis and presentation. At the present time, all the hardware components of the system are operational, except for a computer board to gather position data from the pedals and crank. This board, however, may be put to use by anyone with background in computer based instrumentation. The software components are not all done. Software to transfer data recorded from the EMG measurements is operational, software to drive the optical encoder card is mostly done. The equations to model the kinematics and dynamics of motion of the limbs have been developed, but they have not yet been implemented in software. Aside from the development of the hardware and software components of the system, the methodology to use accelerometers and encoders and the formulation of the appropriate equations are an important contribution to the area of biomechanics, particularly in space applications.

Figueroa, Fernando↗

DOE OSTI2021

A rapid heating and high magnetic field thermal analysis technique

Abstract A new thermal analysis technique is described that allows measurements to be performed on bulk samples at extreme heating and cooling rates and in high magnetic fields. High heating rates, up to 1000 °C min −1 , are achieved through electromagnetic induction heating of a custom-built apparatus fitted with commercial thermal analysis heads and sensor. Rapid cooling rates, up to 100 °C min −1 , are enabled by gas quenching and the small thermal mass of the induction furnace. The custom apparatus is designed to fit inside a superconducting magnet capable of fields up to 9 Tesla. This study demonstrates that the instrument is capable of collecting accurate thermal analysis data in high magnetic fields and rapidly acquiring data for dynamic processes. While the full potential of the technique is still unrealized, currently, it can provide insight into phenomena at time scales relevant to heat treatment in many industrial processes and into little understood effects of high magnetic field processing.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Dynamic signal recovery in distribution grids using compressive lossy measurements

Distribution system state estimation requires reliable aggregation of the measured data. However, the large volume of the measured data imposes a significant stress on the underlying communication infrastructure. With the challenges associated with measurement availability, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. In this paper, we evaluate the robustness of an updated Kalman filtered modified compressive sensing (KF-ModCS) technique that dynamically estimates the grid states using a small fraction of measured data. In practice, measurements used for sparsity based state estimation may also be intermittent due to communication network induced losses. Further, to understand the effect of packet losses on KF-ModCS, we provide an upper bound for the expected variances of the state estimation error for a given rate of information loss. This upper bound is further improved if the support set of the sparse signal that characterizes the state dynamics does not change over time and/or the reduced model is observable. Simulations based on two practical data sets collected from actual customers in a distribution grid validate the theoretical results.

24 POWER TRANSMISSION AND DISTRIBUTION↗