Results for “Sensor placement”

DOE OSTI2024

Leveraging Optimal Sparse Sensor Placement to Aggregate a Network of Digital Twins for Nuclear Subsystems

Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.

42 ENGINEERING↗

DOE OSTI2024

A data-driven sensor placement approach for detecting voltage violations in distribution systems

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

DOE OSTI2025

Sensor Placement Optimization Study for the Built Environment: Operational Use Cases

Systems of fixed-position radiation sensors can provide information that assists emergency responders following nuclear and radiological incidents. State, local, tribal, and territorial (SLTT) government agencies that implement systems of fixed-position sensors are faced with numerous decisions regarding sensor selection, quantity, and placement. To develop guidance on implementation of radiation detection systems, we simulated the release of radioactive material in an urban environment using a combination of three models: the Weather Research Forecasting (WRF), Quick Urban and Industrial Complex (QUIC), and Monte Carlo N-Particle (MCNP) models. We then evaluated the performance of several hypothetical sensor systems. The small number of simulations we conducted are not sufficient to generate definitive design guidance for radiation sensor systems, but we did identify trends that would be of interest to emergency planners. For a scenario that releases 1000 curies of Cs-137, radiation detectors were needed at 500-meter intervals to have a high likelihood of event detection and to estimate source location and plume detection. We also noted that optimal detector altitude varied with distance to the source. We recommend additional research in this area be conducted to support developing sensor placement guidelines that expand on a range of locations, isotopes, activity levels, and different weather conditions. Original simulation strategies included a range of environments, additional radioisotopes (Am241 and AmBe), and a larger selection of sensor types. These types of expansions would support SLTT guidance on sensor system recommendations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Sensor Placement Optimization Study for the Built Environment: Next Steps Report

Systems of fixed-position radiation sensors can provide information that assists emergency responders following nuclear incidents. First responder organizations that implement systems of fixed-position sensors face numerous decisions regarding sensor selection, quantity, and placement. Researchers at Pacific Northwest National Laboratory (PNNL) have evaluated the performance of several hypothetical sensor systems during a simulated activation of a radiological dispersal device. Due to technical limitations, PNNL’s analysis was limited to a single location and number of scenarios. This document describes additional research and analysis that would result in improved guidance to first responder organizations considering installation of radiation monitoring systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Journey over Destination: Dynamic Sensor Placement Enhances Generalization

Reconstructing complex, high-dimensional global fields from limited data points is a challenge across various scientific and industrial domains. This is particularly important for recovering spatio-temporal fields using sensor data from, for example, laboratory-based scientific experiments, weather forecasting, or drone surveys. Given the prohibitive costs of specialized sensors and the inaccessibility ofcertain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of machine learning algorithms trained to reconstruct fields given a limited dataset is of critical importance. In this study, we introduce a generalapproach that employs moving sensors to enhance data exploitation during the training of an attention based neural network, thereby improving field reconstruction. The training of sensor locations is accomplished using an end-to-end workflow, ensuringdifferentiability in the interpolation of field values associated to the sensors, and is simple to implement using differentiable programming. Additionally, we have incorporated a correction mechanism to prevent sensors from entering invalid regions within the domain. We evaluated our method using two distinct datasets; the results show that our approach enhances learning, as evidenced by improved test scores.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Optimizing Point-in-Space Continuous Monitoring System Sensor Placement on Oil and Gas Sites

Not Available

Jia, Meng [Department of Applied Mathematics and S↗

DOE OSTI2026

Demonstration of Algorithm for Sensor Placement Optimization using Simulation Data

This deliverable reports FY26 progress in advancing a neural-network-based Green’s-function framework for reconstructing neutron-flux distributions from ex-core measurements and for translating reconstruction requirements into a practical detector-layout strategy. Building on the FY25 formulation, the present work had two main objectives: (1) refine and re-evaluate the reconstruction methodology on an updated Purdue University Reactor Number One (PUR-1) model, and (2) develop a systematic, Green’s-function-guided procedure for boundary detector placement.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Assessing the design of integrated methane sensing networks

Abstract While methane is the second largest contributor to global warming after carbon dioxide, it has a larger warming effect over a much shorter lifetime. Despite accelerated technological efforts to radically reduce global carbon dioxide emissions, rapid reductions in methane emissions are needed to limit near-term warming. Being primarily emitted as a byproduct from agricultural activities and energy extraction, methane is currently monitored via bottom–up (i.e. activity level) or top–down (via airborne or satellite retrievals) approaches. However, significant methane leaks remain undetected and emission rates are challenging to characterize with current monitoring frameworks. In this paper, we study the design of a layered monitoring approach that combines bottom–up and top–down approaches as an integrated sensing network. By recognizing that varying meteorological conditions and emission rates impact the efficacy of bottom–up monitoring, we develop a probabilistic approach to optimal sensor placement in its bottom–up network. Subsequently, we derive an inverse Bayesian framework to quantify the improvement that a design-optimized integrated framework has on emission-rate quantifications and their uncertainties. We find that under realistic meteorological conditions, the overall error in estimating the true emission rates is approximately 1.3 times higher, with their uncertainties being approximately 2.4 times higher, when using a randomized network over an optimized network, highlighting the importance of optimizing the design of integrated methane sensing networks. Further, we find that optimized networks can improve scenario coverage fractions by more than a factor of 2 over experimentally-studied networks, and identify a budget threshold beyond which the rate of optimized-network coverage improvement exhibits diminishing returns, suggesting that strategic sensor placement is also crucial for maximizing network efficiency.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design

SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.

58 GEOSCIENCES↗

DOE OSTI2026

The NREL Sensor Laboratory Detection of Hydrogen Emissions

The development of a functional hydrogen detection system is a multifaceted process that integrates hardware, deployments strategies, and analytics which can be supported by the NREL Sensor Laboratory: 1. Support of the design, validation and optimization of sensing prototypes; 2. Guide optimized sensing element development, including control electronics; 3. Laboratory testing to validate/optimize metrological performance (measurement range, detection limit, etc.); 4. Provide test sites for field deployments representative of real-world scenarios with controlled hydrogen releases; 5. Develop sensor placement and operation guidance; 6. Provide guidance on electronics to accommodate facility integration; 7. Electrical safety designs to allow for operation within restricted zones; 8. Integration into facility monitoring and control systems; 9. Guide incorporation of cyber security elements to protect facilities from malicious attacks; 10. Modeling and application of advanced analytics to detect and quantify emissions; 11. Higher Order dispersion models to guide sensor placement for reliable detection; 12. Advanced analytics for improved metrological performances, and to inform inverse modeling; 13. Market support and commercialization (national and international markets); 14. Commercial deployments in H2@SCALE markets (e.g., HUBs and other large-scale hydrogen markets); and 15. Leverage off international collaborations/partnerships (e.g., NREL is on the advisory board for the European initiative "pre-Normative Research on Hydrogen Releases Assessment"-NHyRA).

08 HYDROGEN↗

DOE OSTI2026

Soil and groundwater environmental sensor data, Wax Lake Delta, Louisiana, March 2023 - March 2024

This study evaluates how environmental parameters that integrate biogeochemical processes vary with water table fluctuations in the freshwater Wax Lake Delta (WLD) in Louisiana, U.S.A. This data package contains seven *.csv files and one Excel file that compiles all the data from the individual .csv files. This dataset reports high frequency (15-min) observations of water level, soil redox potential, specific conductance, and pH made for one year along elevation transects located on the older, proximal (OT) and younger, distal (YT) ends of a deltaic island. Water depth relative to the ground surface (cm; HOBO U20L-04; error ± 0.4 cm), water pH and temperature (HOBO MX2501), and specific conductance and temperature (HOBO U24-001) sensors were installed in March 2023. Water depth was corrected for barometric pressure recorded by a separate logger secured to a platform above the highest water level. Soil redox probes (SWAP ORP-40-4-B) were also installed in March 2023. Each probe had four Pt sensors (2 mm width) placed at 10 cm, 20 cm, 30 cm, and 40 cm below the ground surface. Redox data were referenced to an external Ag0/AgCl (3M KCl) reference probe placed in saturated ground and recorded on CR1000X dataloggers (Campbell Scientific) powered by solar panels. A second reference probe was positioned near the primary reference probe for backup and data correction. The tops of the soil redox probes and soil moisture probes were flush with the soil surface so that sensors are reported at their indicated depths below ground surface. Here, we report data collected between 15 March 2023 to 15 March 2024 for all sensors, with some differences due to exact dates of sensor placement or data gaps associated with sensor malfunction. For example, water depth at OT4 was not recorded between March to November 2023. Data flags indicate whether a value is valid (1) or was excluded from data analysis in the associated manuscript (-1).

EARTH SCIENCE > LAND SURFACE > SOILS↗

DOE OSTI2026

Hydrogen Dispersion Modeling for Development of Smart Distributed Monitoring

Studying hydrogen dispersion is crucial for ensuring the safe and effective deployment of hydrogen as an energy carrier. This study presents a comprehensive CFD modeling framework for simulating hydrogen dispersion at a real-world hydrogen production, storage, and utilization facility. Utilizing the Hydrogen Research Facility under the Advanced Research on Integrated Energy Systems (ARIES) at the National Renewable Energy Laboratory's (NREL) Flatirons campus, controlled hydrogen releases at 27 kg-H2/hr were simulated. The model incorporated site-specific atmospheric conditions, including hourly wind speeds and temperatures recorded between 8 AM and 8 PM from October to December 2023. To reduce computational demands, a statistical reduction technique was applied to condense the dataset to 100 representative scenarios, validated by statistical tests for wind speeds and power law coefficients. Simulations were conducted using the Reynolds-Averaged Navier-Stokes equations. Results demonstrated that wind speed substantially influences hydrogen dispersion, with low wind conditions forming concentrated clouds and higher wind speeds stretching the plume. Additionally, clustering analysis informed optimal sensor placement at various elevations with up to 10 sensor locations on each elevation. This framework offers a robust approach for understanding hydrogen behavior in ambient conditions and informing detection strategies.

08 HYDROGEN↗

DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Conceptual Design of Neutron Sensor Qualification Device

The Advanced Sensors and Instrumentation Program at Idaho National Laboratory has been formulating strategies to qualify sensors for use in nuclear environments, particularly in irradiation experiments and advanced reactors. When qualifying neutron sensors for use in high-temperature environments, the wide range of neutron flux levels and representative energy spectra presents significant challenges. This paper discusses the development of the Neutron Sensor Qualification Device (NQD), which is designed to test neutron sensors in high temperature controlled environments with known neutron spectra, addressing the spatial and spectral complexities of neutron fluxes in reactor cores. The proposed NQD will be situated in the exposure room at the Armed Forces Radiobiology Research Institute, thus affording a unique capability to expose sensors to high neutron and gamma fluxes. To achieve thermal control, the device will utilize a radiation-hardened tube furnace, accommodating multiple sensors and neutron activation dosimetry wires. Titanium, iron, and cobalt dosimeter wires are chosen from the American Society for Testing and Materials and International Reactor Dosimetry and Fusion File libraries as references for providing energy-dependent fluence measurements. The design ensures precise sensor positioning to minimize mutual shielding and flux perturbation, which are evaluated via Monte Carlo N particle Transport Code (MCNP) simulations. These simulations have informed the development of guidelines on sensor placement within the NQD. The NQD is essential to the qualification of neutron sensors for advanced reactor technologies. It enables controlled testing of a statistically significant number of sensors, thereby supporting assessments of sensor performance across various neutron flux levels and temperatures. This paper highlights the detailed planning for the NQD prototype, along with its inaugural irradiation (scheduled for fiscal year [FY] 2025). The results from this initial testing will be fundamental in evaluating the device’s performance and establishing measurement uncertainty for in-pile neutron sensor measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗