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NASA NTRSDate not supplied

Adaptive Optimization for System Performance and Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

The emerging urban air mobility (UAM) sector in aerospace is driving development of unconventional multi-modal vehicle configurations and autonomous flight. The combination of multi-modal vehicle dynamics, complex environment, requirements to deal with flight contingencies in an efficient and safe manner, as well as necessity for precise trajectory following and performance, are the driving influence behind adaptive optimization for system performance. We are interested in trajectory optimization algorithm that would system parameter estimation and identifying the optimal switching time between modes of hybrid dynamical systems. This presentation discusses a parameterized optimal control trajectory optimization algorithm that is an extended and generalized version of Differential Dynamic Programming (DDP), titled Parameterized Differential Dynamic Programming (PDDP). DDP is an efficient trajectory optimization algorithm relying on second order approximations of a system’s dynamics and cost function and has recently been applied to optimize systems with time invariant parameters. Experiments are presented applying PDDP to solve model predictive control (MPC) and moving horizon estimation (MHE) tasks simultaneously. In particular, PDDP is used to determine the optimal transition point between flight regimes of a complex urban air mobility (UAM) class vehicle exhibiting multiple phases of flight and to identify and compensate for actuation faults.

optimization↗
NASA NTRS1995

Methodologies to determine forces on bones and muscles of body segments during exercise, employing compact sensors suitable for use in crowded space vehicles

Work under this grant was carried out by the author and by a graduate research assistant. An instrumented bicycle ergometer was implemented focusing on the stated objective: to estimate the forces exerted by each muscle of the feet, calf, and thigh of an individual while bicycling. The sensors used were light and compact. These were probes to measure muscle EMG activity, miniature accelerometers, miniature load sensors, and small encoders to measure angular positions of the pedal. A methodology was developed and implemented to completely describe the kinematics of the limbs using data from the sensors. This work has been published as a Master's Thesis by the Graduate student supported by the grant. The instrumented ergometer along with the sensors and instrumentation were tested during a KC-135 Zero-Gravity flight in July, 1994. A complete description of the system and the tests performed have been published as a report submitted to NASA Johnson Space Center. The data collected during the KC-135 flight is currently being processed so that a kinematic description of the bicycling experiment will be soon determined. A methodology to estimate the muscle forces has been formulated based on previous work. The methodology involves the use of optimization concepts so that the individual muscle forces that represent variables in dynamic equations of motion may be estimated. Optimization of a criteria (goal) function such as minimization of energy will be used along with constraint equations defined by rigid body equations of motion. Use of optimization principles is necessary, because the equations of motion alone constitute an indeterminate system of equations with respect to the large amount of muscle forces which constitute the variables in these equations. The number of variables is reduced somewhat by using forces measured by the load cells installed on the pedal. These load cells measure pressure and shear forces on the foot. The author and his collaborators at NASA and at the University of Alabama, Tuscaloosa, are continuing the work of reducing the experimental data from the KC-135 flight, and the implementation of the optimization methods to estimate muscle forces. As soon as results from these efforts are available, they will be published in reputable journals. Results of this work will impact studies addressing bone density loss and development of countermeasures to minimize bone loss in zero gravity conditions. By analyzing muscle forces on Earth and in Space during exercise, scientists could eventually formulate new exercises and machines to help maintain bone density. On Earth, this work will impact studies concerning arthritis, and will provide the means to study possible exercise countermeasures to minimize arthritis problems.

Figueroa, Fernando↗
NASA NTRS2021

Thermal Conductivity Estimation from Transient Test Data with Embedded Thermocouples using Genetic Algorithm Optimization

Inverse heat transfer methodology previously developed to estimate thermal properties of high temperature fibrous insulation from embedded thermocouples was applied to the thermoplastic polymer, polyether-ether-ketone (PEEK). A small experimental setup was utilized to test the PEEK sample between temperatures of 300 K and 525 K at atmospheric pressure. Cylindrical plugs of PEEK with three thermocouples embedded at various depths were incorporated in the test sample. The experimental PEEK thermocouple data were used as the boundary and initial conditions of a one-dimensional numerical thermal model to predict the internal temperatures of the material. The thermal conductivity of PEEK was estimated with the Continuous Genetic Algorithm optimization technique by searching for the coefficients of a functional form of thermal conductivity that minimized the difference between the experimentally measured and model predicted internal temperature values. The thermal testing, one-dimensional numerical thermal model, optimization algorithm, analysis, and results are presented.

Thermal Properties↗
DOE OSTI2020

Planck 2018 results

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E -mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f NL local = -0.9 ± 5.1; f NL equil = -26 ± 47; and f NL ortho = -38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 σ . Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g NL local = (-5.8 ± 6.5) × 10 4 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases.1 Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission.2 Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an Advanced Design Methods (ADM) based approach. This approach applies the concepts of Design of Experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development e ort. In order to t a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of Ground Rules and Assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated \what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are t to the outputs of each environment and are integrated via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any \what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will have the potential to lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗
NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases. Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission. Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an advanced design methods (ADM) based approach. This approach applies the concepts of design of experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development effort. In order to fit a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of ground rules and assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated "what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are fit to the outputs of each environment and are "integrated" via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any ''what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will help ensure lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗
NASA NTRS1979

Formulations and applications of large structure actuator and sensor placements

A new approach based on the steady-state solutions of the optimal control and estimation problems is presented to study respectively the actuator and sensor locations for large flexible structures. A simple and computer-implementable formulation for minimizing the steady state optimal cost function and the state estimation error inherent in the estimation process is given. In conjunction with the new approach, two criteria are established relating the actuator and the sensor placement optimalities respectively to the minimums of the optimal cost function and the state estimation error. To illustrate the concepts of this paper, we present the results of some numerical and analytical studies on the actuator and the sensor locations of several simple flexible beam modes.

Juang, J.-N.↗
DOE OSTI2023

Optimal adjustment sets for causal query estimation in partially observed biomolecular networks

Abstract Causal query estimation in biomolecular networks commonly selects a ‘valid adjustment set’, i.e. a subset of network variables that eliminates the bias of the estimator. A same query may have multiple valid adjustment sets, each with a different variance. When networks are partially observed, current methods use graph-based criteria to find an adjustment set that minimizes asymptotic variance. Unfortunately, many models that share the same graph topology, and therefore same functional dependencies, may differ in the processes that generate the observational data. In these cases, the topology-based criteria fail to distinguish the variances of the adjustment sets. This deficiency can lead to sub-optimal adjustment sets, and to miss-characterization of the effect of the intervention. We propose an approach for deriving ‘optimal adjustment sets’ that takes into account the nature of the data, bias and finite-sample variance of the estimator, and cost. It empirically learns the data generating processes from historical experimental data, and characterizes the properties of the estimators by simulation. We demonstrate the utility of the proposed approach in four biomolecular Case studies with different topologies and different data generation processes. The implementation and reproducible Case studies are at https://github.com/srtaheri/OptimalAdjustmentSet.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2001

Fast Quaternion Attitude Estimation from Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.

Markley, F. Landis↗
NASA NTRS2012

Constructing a Database from Multiple 2D Images for Camera Pose Estimation and Robot Localization

The LMDB (Landmark Database) Builder software identifies persistent image features (landmarks) in a scene viewed multiple times and precisely estimates the landmarks 3D world positions. The software receives as input multiple 2D images of approximately the same scene, along with an initial guess of the camera poses for each image, and a table of features matched pair-wise in each frame. LMDB Builder aggregates landmarks across an arbitrarily large collection of frames with matched features. Range data from stereo vision processing can also be passed to improve the initial guess of the 3D point estimates. The LMDB Builder aggregates feature lists across all frames, manages the process to promote selected features to landmarks, and iteratively calculates the 3D landmark positions using the current camera pose estimations (via an optimal ray projection method), and then improves the camera pose estimates using the 3D landmark positions. Finally, it extracts image patches for each landmark from auto-selected key frames and constructs the landmark database. The landmark database can then be used to estimate future camera poses (and therefore localize a robotic vehicle that may be carrying the cameras) by matching current imagery to landmark database image patches and using the known 3D landmark positions to estimate the current pose.

Wolf, Michael↗
DOE OSTI2021

Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Here, we perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg 2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be ${A}_{\phi }=0.949\,\pm \,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening" or linear bias correction, and reducing the systematic uncertainty on A Φ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A Φ along with A L , the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A Φ and seven times lower effective lensing reconstruction noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Automatic Calibration and Health Monitoring of Infrastructure Sensors

Smart transportation infrastructure relies on networks of heterogeneous sensors - cameras, radars, and lidars - continuously monitoring traffic conditions. However, executing the initial spatial calibration of multiple sensors and the subsequent health monitoring presents significant operational challenges. Environmental factors, mechanical vibrations, and gradual drift cause spatial misalignment, degrading fusion performance and tracking accuracy. Traditional calibration approaches require manual intervention with specialized targets or survey equipment, resulting in service interruptions and high maintenance costs. This work presents an automated framework for initial calibration and continuous health monitoring without human intervention or service disruption. Our approach addresses two critical problems: (1) detecting when sensors become miscalibrated during operation, and (2) automatically re-establishing spatial alignment using only operational traffic data. The health monitoring component analyzes measurement innovations - differences between sensor observations and predicted object states - to detect systematic biases indicative of calibration drift. By computing bias magnitude, directional consistency, and rejection rates, the system identifies miscalibrations as small as 0.5 meters. Unlike traditional methods requiring known calibration targets, our diagnostic operates continuously on live traffic observations, enabling early detection before fusion quality degrades. The automatic recalibration algorithm leverages overlapping sensor fields-of-view and temporal correlation of vehicle observations. Using graph-based optimization, the system automatically discovers which sensor pairs observe common regions, estimates pairwise spatial transformations using RANSAC-based robust estimation, and jointly optimizes all sensor poses through bundle adjustment. The framework handles practical deployment challenges, including different sensor sampling rates (1-10 Hz), varying installation positions, unknown orientations, and limited overlap regions (>10%). When approximate sensor positions are available from installation surveys (+/-1m accuracy), the algorithm additionally estimates sensor orientations, refining both position and rotation to sub-meter and sub-degree accuracy. We validate the framework on multi-hour traffic datasets from six heterogeneous sensors with sampling rates ranging from 1 Hz to 10 Hz. Results demonstrate successful calibration even with sparse overlap (<20%) and automatic detection of miscalibrations exceeding 0.8 meters. This work enables a "deploy-and-forget" sensor infrastructure that maintains calibration autonomously, reducing maintenance costs while improving tracking accuracy. The techniques generalize beyond transportation to any multi-sensor monitoring application requiring robust spatial alignment, including smart cities, industrial monitoring, and surveillance systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Introducing the GeoRePORT Resource Size Tool: Reporting on Geothermal Resource Size Estimations Using the Geothermal Resource Portfolio Optimization and Reporting Technique (GeoRePORT): Preprint

The Geothermal Resource Portfolio Optimization and Reporting Technique (GeoRePORT) was developed with funding from the U.S. Department of Energy Geothermal Technologies Office to assist in identifying and pursuing long-term investment strategies through the development of a resource reporting protocol. The assessment protocols used in GeoRePORT allow for comparison of project attributes across locations and geological settings to understand the feasibility of geothermal development. This work introduces the Resource Size Tool, a new feature within the GeoRePORT package that compiles two independent methods for estimating geothermal resource size in terms of energy capacity in MW. Energy production potential for twenty-three case studies was estimated with the Resource Size Tool in order to 1) generate a reasonable range of resource size estimates for a particular geothermal field; 2) illustrate the advantages and limitations of each methodology (such as data input requirements, estimate accuracy and precision, and the appropriate circumstances of use); and 3) test the ability of the resource size tool to provide useful and accurate information for geothermal stakeholders. The tool employs two methods widely used in the geothermal industry: (1) USGS Volumetric and (2) Power Density. Results from our case studies show general overlap between these two methods in terms of resource size estimates; however, they also reveal key differences between the two approaches that should be considered when using such estimates to drive development. First, the two methods rely on different input parameters and therefore one method may be more appropriate and/or accurate for a given project than the other. Second, the Power Density method was found to generate wider ranges of resource size predictions, more consistently aligning with actual power production of the field but with larger scales of error; whereas the USGS Volumetric method predicts narrower ranges but tends to overestimate when compared to current MW production. Future work will refine variables used in the methods with input data from other sections of GeoRePORT and modify uncertainty levels based on the particular datasets used for a given project.

geological↗
NASA NTRS1989

Real-Time Optimization Of Receiver Bandwidth

Estimates of signal and noise spectra enhance reception of weak signals. Carrier-tracking phase-locked loop represented by linear mathematical model at small rms phase errors. Loop continuously generates estimates of received phase. Bandwidth (in effect, scale of complex-frequency variable p) optimized to minimize rms phase error. Minimum signals tracked 5 to 15 dB below those tracked by current receivers. Improvement accomplished by use of bandwidths of 0.1 to 1.0 Hz, in contrast with 3-Hz bandwidth in current use. Principle of real-time optimization of bandwidth adapted to other situations to enhance reception of weak signals otherwise "buried" in noise.

Vilnrotter, V. A.↗
NASA NTRS2000

A Multidisciplinary Performance Analysis of a Lifting-Body Single-Stage-to-Orbit Vehicle

Lockheed Martin Skunk Works (LMSW) is currently developing a single-stage-to-orbit reusable launch vehicle called VentureStar(TM) A team at NASA Langley Research Center participated with LMSW in the screening and evaluation of a number of early VentureStar(TM) configurations. The performance analyses that supported these initial studies were conducted to assess the effect of a lifting body shape, linear aerospike engine and metallic thermal protection system (TPS) on the weight and performance of the vehicle. These performance studies were performed in a multidisciplinary fashion that indirectly linked the trajectory optimization with weight estimation and aerothermal analysis tools. This approach was necessary to develop optimized ascent and entry trajectories that met all vehicle design constraints. Significant improvements in ascent performance were achieved when the vehicle flew a lifting trajectory and varied the engine mixture ratio during flight. Also, a considerable reduction in empty weight was possible by adjusting the total oxidizer-to-fuel and liftoff thrust-to-weight ratios. However, the optimal ascent flight profile had to be altered to ensure that the vehicle could be trimmed in pitch using only the flow diverting capability of the aerospike engine. Likewise, the optimal entry trajectory had to be tailored to meet TPS heating rate and transition constraints while satisfying a crossrange requirement.

Tartabini, Paul V.↗
DOE OSTI2020

Joint Estimation of Behind-the-Meter Solar Generation in a Community

Distribution grid planning, control, and optimization require accurate estimation of solar photovoltaic (PV) generation and electric load in the system. Most of the small residential solar PV systems are installed behind-the-meter making only the net load readings available to the utilities. This paper presents an unsupervised framework for joint disaggregation of the net load readings of a group of customers into the solar PV generation and electric load. Our algorithm synergistically combines a physical PV system performance model for individual solar PV generation estimation with a statistical model for joint load estimation. The electric loads for a group of customers are estimated jointly by a mixed hidden Markov model (MHMM) which enables modeling the general load consumption behavior present in all customers while acknowledging the individual differences. At the same time, the model can capture the change in load patterns over a time period by the hidden Markov states. The proposed algorithm is also capable of estimating the key technical parameters of the solar PV systems. Our proposed method is evaluated using the net load, electric load, and solar PV generation data gathered from residential customers located in Austin, Texas. Testing results show that our proposed method reduces the mean squared error of state-of-the-art net-load disaggregation algorithms by 67%.

behind-the-meter solar generation↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

H ∞ Control for Energy Dispatch in Autonomous Nanogrid With Communication Delays

This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H$ ∞ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H$ ∞ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗