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DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Computational discovery of ultra-strong, stable, and lightweight refractory multi-principal element alloys. Part II: comprehensive ternary design and validation

Abstract Here the discovery of refractory multi-principal element alloys (MPEAs) with high-temperature strength and stability is pursued within a constrained and application-relevant design space. A comprehensive approach is developed and applied to explore all 165 ternary systems in the Al-Ce-Fe-Hf-Mo-Nb-Ta-Ti-V-W-Zr family. A subset of ternary systems that contain large areas in composition–temperature space with high strength and robust BCC phase stability is found. Twelve sets of high-performing alloys are identified, each set optimized for one combination of phase constraint, optimization target, and temperature range. Preliminary mechanical tests support the viability of the method. This work highlights the importance of considering phase stability, exploring non-equiatomic regions of composition space, and applying application-relevant constraints. Parts I and II provide three down-selection techniques for identifying high-performing BCC refractory MPEAs, design guidelines, and many candidates predicted to have BCC phase stability and strengths 2–3 times higher than any reported to date.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion

Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. In this work, we build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors’ data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Reinforcement Learning-Based Approach for EMT Automation of Large-Scale PV Plants

In the pursuit of efficient and precise modeling of large-scale power systems, particularly utility-scale photovoltaic (PV) plants, Electromagnetic Transient (EMT) simulations play a crucial role. As utility-scale PV plants increase in size and complexity, traditional computational methods become inadequate, necessitating more advanced techniques. This paper highlights the progressive efforts made to accelerate EMT simulations. A novel continuous reinforcement learning (RL) strategy is explored to automate the differentiation and categorization of stiff and non-stiff differential algebraic equations (DAEs). The use of stiff and non-stiff integration methods applied to relevant parts of the DAEs assists with the speed-up of the simulations. The paper details the data acquisition, development and offline training of the RL model, leading to its validation that demonstrates a high precision in optimizing simulation methods. The proposed RL promises to significantly enhance the efficacy of EMT simulations, offering a robust framework for the future of power system analysis.

Xia, Qianxue↗

DOE OSTI2024

Design, Modeling, and Control of a Hardware-in-the-Loop Testbed for Off-Road Vehicles

This paper presents the design, modeling, and control of a hardware-in-the-loop (HIL) testbed for off-road vehicles. The proposed HIL testbed employs a transient hydrostatic dynamometer to load a diesel engine to emulate any loading cycles of a wheel loader, which is a representative off-road vehicle. A fully validated wheel loader model is used to calculate the engine load, including both the drive and work functions. Besides, iterative learning control (ILC) has been designed for the loading torque tracking of the hydrostatic dynamometer to ensure accurate emulation of real-world operation scenarios. The developed HIL testbed is used to demonstrate more than 26% energy benefits of automated wheel loaders through systematic optimization compared with human-operated wheel loaders. As a result, this HIL testbed serves as a robust platform for advancing research and development across various off-road vehicles, including excavators, tractors, and harvesters.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

First-Principles Studies of Tritium Species Diffusivity Across the Interface of Nickel-Plated Zircaloy-4

α-Zr and its alloys are known as best 3 H getters due to their excellent corrosion resistance under chemically corrosive environment, low thermal neutron absorption cross-section and robust mechanical strength at high temperature. In this work, we conducted a systematic study on constructing and optimizing Ni and Zr surfaces, interfacing the stable Ni and Zr surfaces to create an optimal Ni-Zr interface, and an understanding the diffusion mechanisms for 3 H across Ni(111)-Zr(0001) interface with and without vacancies and impurities such as Sn and O.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Higher Efficiency, Demand Flexible Refrigerator with On-Demand Micro-Vibrational De-icing Technology

Refrigerator technology has advanced significantly over the last couple of decades. Today’s refrigerators use only about 25% of the energy that was required to power models built in 1975. Even as they continually improve efficiency to meet standards, refrigerators have increased in size by almost 20%, added energy-consuming features such as through-the-door ice, and provide more benefits than ever before. However, a few challenges and technology gaps are preventing further improvement of the demand responsiveness and efficiency of the refrigerators. One of the major technology gaps in existing refrigerators is their outdated de-icing process. When the evaporator generates frost, an old-fashioned resistive heating element melts the ice. Most refrigerators have a timed defrost cycle, rather than an active system that could monitor the state of the frost. In these systems, not only is the precious electricity used at its least efficient form of conversion (direct conversion of electricity to heat), but also all the latent heat associated with the ice is wasted during the melting process. On top of that, the refrigerator needs to work harder to pull the temperature down after defrosting, and, last but not least, the food quality is severely impacted by the temperature swings during the defrost cycle. According to a study, the EU alone wastes 89 million tons of food in the supply chain every year. Any temperature swing during defrosting (about 6F according to Emerson for low-temperature cases) can negatively impact the shelf life of meat and other products for multiple days. All these issues can happen during the peak demand time of the electric grid. Unlike the conventional systems, the proposed novel advanced micro-vibrational deicing process uses no heat for defrosting. Instead, it uses the micro vibrations generated by a piezoelectric or vibration-generating module to mechanically break ice from the heat exchanger almost instantaneously. The project titled “Higher Efficiency, Demand Flexible Refrigerator with On-Demand Micro-Vibrational De-icing Technology, performed by Ultrasonic Technology Solutions, LLC (UTS) of Knoxville, TN, in collaboration with Emerson (now Copeland), represents the final phase of a multi-year effort funded under the U.S. Department of Energy’s Building Technologies Office (BTO) BENEFIT FOA 2020. Initiated on October 1, 2021, and completed after a nine-month no-cost extension ending September 30, 2025, this project aimed to develop and validate a novel micro-vibrational mechanical defrosting system, achieving more than 25% improvement in defrosting energy efficiency over conventional baseline defrosting technologies. Over sixteen quarters, the project advanced from fundamental ice-mechanical characterization and prototype development to full-scale system integration and validation. Initial efforts established project management infrastructure and characterized ice adhesion properties, followed by the design and fabrication of early aluminum-based prototypes for resonance frequency testing. Subsequent quarters saw rapid technical progression, including the identification of optimal piezoelectric and motor-based vibration mechanisms, the demonstration of effective de-icing over 6x6-inch aluminum surfaces. The team achieved its Go/No-Go milestone by exceeding the 25% energy-efficiency improvement target—reaching up to 3,340% under optimized conditions—and later confirmed that motor-driven systems offered superior performance and energy efficiency compared to piezoelectric alternatives. Continued refinement led to the development of amplifier systems on printed circuit boards, improved control and instrumentation hardware, and integration into full-scale heat exchanger (HX) prototypes at both UTS and Copeland facilities. Multiple vibration-mounting studies and frost-growth experiments guided mechanical optimization and noise-mitigation strategies, achieving a 17.5 dB reduction in sound pressure level and verifying robust mechanical performance. Advanced analyses, including modal and harmonic simulations, established a quantitative understanding of vibrational behavior and de-icing efficiency across >1000 cm² systems. The final project phase successfully demonstrated scalable integration within reach-in and chest freezer prototypes, confirmed >25% efficiency improvements in large-area systems, and completed a comprehensive business model and scale-up strategy identifying electric defrost systems as the primary beachhead market. The culmination of this DOE-supported effort establishes micro-vibrational defrosting as a viable, high-efficiency, low-noise, and demand-flexible de-icing technology, paving the way for commercial deployment and broader application in next-generation refrigeration systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Geometric remapping of particle distributions in the Discrete Element Model for Sea Ice (DEMSI v0.0)

Abstract. A new sea ice dynamical core, the Discrete Element Model for Sea Ice (DEMSI), is under development for use in coupled Earth system models. DEMSI is based on the discrete element method, which models collections of ice floes as interacting Lagrangian particles. In basin-scale sea ice simulations the Lagrangian motion results in significant convergence and ridging, which requires periodic remapping of sea ice variables from a deformed particle configuration back to an undeformed initial distribution. At the resolution required for Earth system models we cannot resolve individual sea ice floes, so we adopt the sub-grid-scale thickness distribution used in continuum sea ice models. This choice leads to a series of hierarchical tracers depending on ice fractional area or concentration that must be remapped consistently. The circular discrete elements employed in DEMSI help improve the computational efficiency at the cost of increased complexity in the effective element area definitions for sea ice cover that are required for the accurate enforcement of conservation. An additional challenge is the accurate remapping of element values along the ice edge, the location of which varies due to the Lagrangian motion of the particles. In this paper we describe a particle-to-particle remapping approach based on well-established geometric remapping ideas that enforces conservation, bounds preservation, and compatibility between associated tracer quantities, while also robustly managing remapping at the ice edge. One element of the remapping algorithm is a novel optimization-based flux correction that enforces concentration bounds in the case of nonuniform motion. We demonstrate the accuracy and utility of the algorithm in a series of numerical test cases.

58 GEOSCIENCES↗

NASA NTRS1987

Spillover stabilization and decentralized modal control of large space structures

The stabilization of the neglected dynamics of the higher modes of vibration in large space structures is studied, and the influence of the structure of the plant noise intensity matrix of the Kalman-Bucy filter on the stability margin of the residual modes is shown. An optimization procedure uses information on the residual modes to minimize spillover of known residual modes while preserving robustness with respect to the unknown dynamics, and the optimum plant noise intensity matrix is selected to maximize the stability margins of the residual modes and to properly place the observer poles. Examples for both centralized and decentralized control are considered.

Czajkowski, Eva A.↗

NASA NTRS1989

A multiloop, digital flutter suppression control law synthesis case study

A methodology for obtaining a digital low-order, multiloop, robust control law for aeroelastic application from a full-state Linear Quadratic Gaussian design is presented. As part of the design methodology, the multivariable system robustness at the plant input and output is evaluated using singular value properties and improved using constrained optimization procedures. To validate the methodology, a digital flutter suppression system has been designed for the full-span Active Flexible Wing (AFW) wind-tunnel model as part of a collaborative effort between the NASA Langley Research Center and Rockwell International. Preliminary results for a low-order discrete, symmetric flutter suppression system design that significantly improved the AFW model stability are provided and the experiences gained during the design process are discussed.

Mukhopadhyay, Vivek↗

NASA NTRS1989

Autonomous spacecraft attitude control using magnetic torquing only

Magnetic torquing of spacecraft has been an important mechanism for attitude control since the earliest satellites were launched. Typically a magnetic control system has been used for precession/nutation damping for gravity-gradient stabilized satellites, momentum dumping for systems equipped with reaction wheels, or momentum-axis pointing for spinning and momentum-biased spacecraft. Although within the small satellite community there has always been interest in expensive, light-weight, and low-power attitude control systems, completely magnetic control systems have not been used for autonomous three-axis stabilized spacecraft due to the large computational requirements involved. As increasingly more powerful microprocessors have become available, this has become less of an impediment. These facts have motivated consideration of the all-magnetic attitude control system presented here. The problem of controlling spacecraft attitude using only magnetic torquing is cast into the form of the Linear Quadratic Regulator (LQR), resulting in a linear feedback control law. Since the geomagnetic field along a satellite trajectory is not constant, the system equations are time varying. As a result, the optimal feedback gains are time-varying. Orbit geometry is exploited to treat feedback gains as a function of position rather than time, making feasible the onboard solution of the optimal control problem. In simulations performed to date, the control laws have shown themselves to be fairly robust and a good candidate for an onboard attitude control system.

Musser, Keith L.↗

NASA NTRS1993

Parallel algorithm for dominant points correspondences in robot binocular stereo vision

This paper presents an algorithm to find the correspondences of points representing dominant feature in robot stereo vision. The algorithm consists of two main steps: dominant point extraction and dominant point matching. In the feature extraction phase, the algorithm utilizes the widely used Moravec Interest Operator and two other operators: the Prewitt Operator and a new operator called Gradient Angle Variance Operator. The Interest Operator in the Moravec algorithm was used to exclude featureless areas and simple edges which are oriented in the vertical, horizontal, and two diagonals. It was incorrectly detecting points on edges which are not on the four main directions (vertical, horizontal, and two diagonals). The new algorithm uses the Prewitt operator to exclude featureless areas, so that the Interest Operator is applied only on the edges to exclude simple edges and to leave interesting points. This modification speeds-up the extraction process by approximately 5 times. The Gradient Angle Variance (GAV), an operator which calculates the variance of the gradient angle in a window around the point under concern, is then applied on the interesting points to exclude the redundant ones and leave the actual dominant ones. The matching phase is performed after the extraction of the dominant points in both stereo images. The matching starts with dominant points in the left image and does a local search, looking for corresponding dominant points in the right image. The search is geometrically constrained the epipolar line of the parallel-axes stereo geometry and the maximum disparity of the application environment. If one dominant point in the right image lies in the search areas, then it is the corresponding point of the reference dominant point in the left image. A parameter provided by the GAV is thresholded and used as a rough similarity measure to select the corresponding dominant point if there is more than one point the search area. The correlation is used as a final decision tool when there is still more than one point in the search area. If there is no dominant point in the search area of if the points in the search area are below a correlation threshold, then the dominant point in the reference image is occluded and can not be corresponded. The algorithm has been modeled, implemented and shown to be fast, robust and parallel. The parallelism is created from three main features: locality of the operators; a memory optimization scheme; and the ability to fully parallelize the extraction phase which is the most computational intensive task in the algorithm. The last feature is achieved by performing the extraction phase on the two images simultaneously.

Al-Tammami, A.↗

NASA NTRS2011

Base Flow Investigation of the Apollo AS-202 Command Module

In recent years, both Europe and the US are developing hypersonic research and operational vehicles. These include (re)entry capsules (both ballistic and lifting) and lifting bodies such as ExoMars, EXPERT, ARV, CEV and IXV. The research programs are meant to enable technology and engineering capabilities to support during the next decade the development of affordable (possibly reusable) space transportation systems as well as hypersonic weapons systems for time critical targets. These programs have a broad range of goals, ranging from the qualification of thermal protection systems, the assessment of RCS performances, the development of GNC algorithms, to the full demonstration of the performance and operability of the integrated vehicles. Since the aerothermodynamic characteristics influence nearly all elements of the vehicle design, the accurate prediction of the aerothermal environment is a prerequisite for the design of efficient hypersonic systems. Significant uncertainties in the prediction of the hypersonic aerodynamic and the aerothermal loads can lead to conservative margins in the design of the vehicle including its Outer Mould Line (OML), thermal protection system, structure, and required control system robustness. The current level of aerothermal prediction uncertainties results therefore in reduced vehicle performances (e.g., sub-optimal payload to mass ratio, increased operational constraints). On the other hand, present computational capabilities enable the simulation of three dimensional flow fields with complex thermo-chemical models over complete trajectories and ease the validation of these tools by, e.g., reconstruction of detailed wind tunnel tests performed under identified and controlled conditions (flow properties and vehicle attitude in particular). These controlled conditions are typically difficult to achieve when performing in flight measurements which in turn results in large associated measurement uncertainties. Similar problems arise when attempting to rebuild measurements performed in "hot" ground facilities, where the difficulty level is increased by the addition of the free-flow characterization itself. The implementation of ever more sophisticated thermochemical models is no obvious cure to the aforementioned problems since their effect is often overwhelmed by the large measurement uncertainties incurred in both flight and ground high enthalpy facilities. Concurrent to the previous considerations, a major contributor to the overall vehicle mass of re-entry vehicles is the afterbody thermal protection system. This is due to the large acreage (equal or bigger than that of the forebody) to be protected. The present predictive capabilities for base flows are comparatively lower than those for windward flowfields and offer therefore a substantial potential for improving the design of future re-entry vehicles. To that end, it is essential to address the accuracy of high fidelity CFD tools exercised in the US and EU, which motivates a thorough investigation of the present status of hypersonic flight afterbody heating. This paper addresses the predictive capabilities of after body flow fields of re-entry vehicles investigated in the frame of the NATO/RTO - RTG-043 Task Group and is structured as follows: First, the verification of base flow topologies on the basis of available wind-tunnel results performed under controlled supersonic conditions (i.e., cold flows devoid of reactive effects) is performed. Such tests address the detailed characterization of the base flow with particular emphasis on separation/reattachment and their relation to Mach number effects. The tests have been performed on an Apollo-like re-entry capsule configuration. Second, the tools validated in the frame of the previous effort are exercised and appraised against flight-test data collected during the Apollo AS-202 re-entry.

Walpot, Louis M. G.↗

NASA NTRSDate not supplied

A Microphone Phased Array for Launch Acoustics Application

A new, portable, phased array of microphones is built at NASA Ames Research Center specifically for the harsh environment encountered in launch acoustics applications. It uses 70 rugged, piezo-electric, dynamic pressure sensors optimally distributed on a 10.5ft diameter open frame dome structure. The open frame is light yet robust to sustain the high wind load of typical seaside launch pads, and the blast and acoustic loads from the launch. A 200-ft long cable bundle carries the microphone signals to a weather-protected electronic cabinet containing the data acquisition system, computers, and other equipment. The array is equipped with an infra-red camera and a visible wavelength camera for imaging the launch site. The beamformed noise maps will be superimposed on the video footages collected by the cameras for correct identification of the noise sources. The array is tested with very loud noise sources to determine the beamforming ability. Multiple mathematical models, such as the conventional beamforming, functional beamforming, spectral element method etc. are used to determine the minimum spatial resolution of the sound sources that can be measured at different frequencies. Additionally, the array hardware is being tested for different environmental conditions and electro-magnetic compliance. The immediate goal is to use the array for NASA’s Artemis/SLS vehicle that will be launched from a newly built Mobile Launch platform and a modified launch pad.

microphone phased-array↗

NASA NTRSDate not supplied

A Microphone Phased Array for Launch Acoustics Application

A new, portable, phased array of microphones is built at NASA Ames Research Center specifically for the harsh environment encountered in launch pads of rocket vehicles. It uses 70 rugged, piezo-electric, dynamic pressure sensors optimally distributed on a 10.5ft diameter open frame dome structure. The open frame is light yet robust to sustain the high wind load of typical seaside launch pads, and the blast and acoustic loads from the launch. A 200-ft long cable bundle carries the microphone signals to a weather-protected electronic cabinet containing the data acquisition system, computers, and other equipment. The array is equipped with an infra-red camera and a visible wavelength camera for imaging the launch site. The beamformed noise maps will be superimposed on the video footages collected by the cameras for correct identification of the noise sources. The array is tested with very loud noise sources to determine the beamforming ability. Multiple mathematical models, such as the conventional beamforming, orthogonal-functional beamforming, spectral element method etc. are used to determine the minimum spatial resolution of the sound sources that can be measured at different frequencies. Additionally, the array hardware is being tested for different environmental conditions and electro-magnetic compliance. The goal is to use the array for NASA’s Artemis/SLS vehicle that will be launched from a newly built Mobile Launch platform and a modified launch pad. Data from a couple of validation tests will be presented in this paper. The first test involves an outdoor setup where the array was placed on a crane at several different heights and distances from a pair of very loud noise sources. The second test from the static firing of the RS25 engines in an outdoor test stand.

Acoustics↗

NASA NTRSDate not supplied

A Microphone Phased Array for Launch Acoustics Application

A new, portable, phased array of microphones is built at NASA Ames Research Center specifically for the harsh environment encountered in launch pads of rocket vehicles. It uses 70 piezoresistive, dynamic pressure sensors, optimally distributed on a 10.5ft diameter open frame dome structure. The open frame is light yet robust to sustain the high wind load of typical seaside launch pads, and the blast and acoustic loads from the launch. A 200-ft long cable bundle carries the microphone signals to a weather-protected cabinet containing the data systems, and allows for the placement of the array tall structures. The array is equipped with an infra-red camera and a visible wavelength camera for imaging the launch pad. The beamformed noise maps will be superimposed on the video footages collected by the cameras for correct identification of the noise sources. The array is tested with very loud speaker sources to determine the beamforming ability using different schemes, such as the conventional beamforming, orthogonal-functional beamforming, and spectral element methods. A comparative study was conducted to determine the minimum attainable spatial resolution. Data from a validation test in an outdoor setup, where the array was placed on a Telehandler at several different heights and distances from either a single or a pair of speakers, is presented in this paper. The final goal is to use the array during NASA’s Artemis-II launch to determine the distribution of noise sources on the Mobile Launcher.

Acoustics↗

DOE OSTI2020

Examining the Net Revenue and Downstream Flow Impact Trade-Offs for a Network of Cascading, Small-Scale Hydropower Facilities: Preprint

In this work, we used a price-taker model to investigate the trade-offs between net revenue and downstream flow impacts for a network of small, cascading hydro facilities. The network consisted of 36 facilities, each with a small amount of local storage (between 2 and 45 minutes). Generator sizes ranged between 0.5 and 1 MW, nominal, and the total capacity of the network was 33.5 MW. We used a multi-integer linear programing model to maximize the net revenue of the combined network subject to operating and environmental constraints. Net revenue optimizations relied on historic price data, and dry, typical, and wet years were studied to help ensure robustness. Energy and ancillary service sales were included in the net revenue calculations, and both unit commitment and dispatch simulations were performed. We found that limiting the downstream flows to ±50% of the river’s natural flows had a negligible impact on net revenues (<1% reduction), irrespective of hydrologic conditions, and even when downstream flows were limited to ±5%, net revenues were only impacted by 4%. These outcomes are significant because they demonstrate how an array of small-scale hydropower facilities can be operated to have minimal impact on natural stream flows—addressing a critical environmental concern.

downstream flow↗

DOE OSTI2023

Measurement of the muon anomalous precession frequency in runs 2 \& 3 of the Muon $g-2$ Experiment at Fermilab

This dissertation presents a measurement of the muon anomalous precession frequency for the Runs 2 \& 3 data of the E989 Muon $g-2$ Experiment at Fermilab. The muon anomalous precession frequency is one of two key inputs, the other being the magnetic field, used to precisely determine the muon magnetic anomaly, $a_{\mu}$. In April 2021, the E989 collaboration reported its first measurement of $a_{\mu}$ to an unprecedented precision of 460 parts-per-billion (ppb). This result is in agreement with the previous measurement performed by the E821 collaboration at Brookhaven National Laboratory, and the combined experimental value is in tension with the Standard Model prediction at 4.2$\sigma$, a possible hint of new physics. The first result from E989 was based on the Run-1 data, which was collected in 2018 and comprises 6\% of the experiment’s target statistics; the Run-1 result was statistics-limited. The Runs 2 \& 3 data were collected in 2019-2020 and constitute a four-fold increase i n statistics compared to Run-1 and consequently, a factor of two reduction in the measurement’s statistical uncertainty. This reduced statistical uncertainty, as well as continued understanding of systematic effects, will result in an even more precise measurement of $a_{\mu}$ and will help clarify the observed tension between theory and experiment. The precession frequency analysis presented in this dissertation includes a number of improvements compared to Boston University's Run-1 analysis: the implementation of a more robust pileup-subtraction procedure, the implementation of a kernel ratio method, the adoption of the statistically optimal asymmetry-weighted method, and investigations that led to an improved understanding of an outstanding residual slow effect. This dissertation motivates a measurement of the muon magnetic anomaly, describes the experimental principle, gives an overview of the E989 experiment, and presents a precession frequency analysis with full systematic unc ertainty evaluation for the Runs 2 \& 3 data. The combined precession frequency measurement, using the ratio asymmetry-weighted method, has a statistical uncertainty of 201 ppb and a systematic uncertainty of 25 ppb, constituting the most precise determination of the muon anomalous precision frequency to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗