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Copula based Damage Detection for Structural Health Monitoring

This project utilizes copulas for damage detection in a Structural Health Monitoring (SHM) application. A copula-based system was chosen for the benefit of multivariate joint distribution with a goal to detect damage based on how the system as a whole reacts rather than one or two sensors by themselves. Copulas are commonly used in the field of finance for risk modeling based on two or more random inputs. A few applications in the field of SHM and Non-Destructive Evaluation (NDE) have been researched mostly on risk or reliability of the structure. The goal of this project is to determine if a copula-based approach can be used for damage detection. An unsupervised learning method was desired to reduce the dimensionality, minimal training, and be a faster evaluation method than other unsupervised methods. If a copula method can be used to detect damage what additional information on the damage can be interpreted. The remainder of this report will go over the background needed, SHM methodology, SHM applications, conclusions, and future developments.

47 OTHER INSTRUMENTATION

Enhanced Design of Radiation Tolerant High-Temperature Structural Health Monitoring Sensors

Acoustic emission sensors are vital in the nuclear industry for real-time structural health monitoring and early detection of material degradation. By capturing high-frequency stress waves emitted from defects like cracks, corrosion, or fatigue, acoustic emission sensors enable non-invasive monitoring of critical components such as reactor vessels, piping, and containment structures. This technology supports predictive maintenance, enhances safety, and ensures regulatory compliance by providing early warnings of potential failures. It is also instrumental in research, particularly in material testing reactors, where it is used to monitor the behavior of fuels and materials under irradiation, by allowing the detection of cracking or other acoustic signals in real time. This enables the evaluation of performance and accident behavior of advanced fuel concepts.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN

The Past, Present and Future of Structural Health Monitoring: An Overview of Three Ages

This paper presents an overview of the discipline of structural health monitoring (SHM), organised in terms of three proposed ages. The first age is delineated by the prehistory of SHM and the period where nondestructing testing methods evolved into an organised set of principles built upon physics-based models; this age ended when the model-based approaches reached an impasse in terms of their ability to properly deal with real-world problems. The second age of SHM began with a transition to data-based methods based on statistical pattern recognition, which provided a holistic approach to SHM problems for the first time. This age arguably ended when the methods foundered in situations where the necessary training data were scarce. It is argued here that the third age began with the development of population-based SHM, which has been designed to overcome the problem of data scarcity. As there is very limited space in a single article to provide a comprehensive overview, an appendix has been provided here that gives a very systematic bibliography of SHM reviews—a meta-bibliography.

60 APPLIED LIFE SCIENCES

Embedded Sensing in Additive Manufacturing Metal and Polymer Parts: A Comparative Study of Integration Techniques and Structural Health Monitoring Performance

This study presents a comparative evaluation of post-process sensor integration in additively manufactured (AM) metal and the in-situ process for polymer structures for structural health monitoring (SHM), with an emphasis on embedded sensors. Geometrically identical specimens were fabricated using copper via metal fused filament fabrication (FFF) and PLA via polymer FFF, with piezoelectric transducers (PZTs) inserted into internal cavities to assess the influence of material and placement on sensing fidelity. Mechanical testing under compressive and point loads generated signals that were transformed into time–frequency spectrograms using a Short-Time Fourier Transform (STFT) framework. An engineered RGB representation was developed, combining global amplitude scaling with an amplitude-envelope encoding to enhance contrast and highlight subtle wave features. These spectrograms served as inputs to convolutional neural networks (CNNs) for classification of load conditions and detection of damage-related features. Results showed reliable recognition in both copper and PLA specimens, with CNN classification accuracies exceeding 95%. Embedded PZTs were especially effective in PLA, where signal damping and environmental sensitivity often hinder surface-mounted sensors. This work demonstrates the advantages of embedded sensing in AM structures, particularly when paired with spectrogram-based feature engineering and CNN modeling, advancing real-time SHM for aerospace, energy, and defense applications.

additive manufacturing

Machine Learning Analysis of Temperature-Strain Relationships for Structural Health Monitoring of Pipes: Self-powered wireless sensor system for health monitoring of liquid-sodium cooled fast reactors

This report presents machine learning (ML) analysis of temperature-strain relationships for structural health monitoring of nuclear reactor stainless steel (SS) pipes with the strain gauge sensor directly printed on the pipe with a 3D conformal aerosol jet printer. We investigate correlations for two sensor pairs installed on the same SS304 pipe: commercial K-type thermocouple with a printed gold strain gauge (TC3-SG3), and commercial K-type thermocouple with commercial Kyowa strain gauge (TC0-SG0). The temperature ranges for the sensor pairs TC0-SG0 and TC3-SG3 are 20.00°C to 266.37°C and 39.95°C to 219.28°C respectively. ML algorithms in this study include Linear Regression (baseline method), Ridge Regression, Lasso Regression, and Gradient Boosting. Performance evaluation metrics include Root Mean Square Error (RMSE), Mean Square Error (MSE), Mean Absolute Error (MAE), R 2 Score, and Explained Variance. Using advanced feature engineering techniques, we extracted 27 temperature-based features and 30 strategic inclusion features. The best performance was obtained with the Gradient Boosting method, which achieves prediction accuracy of R 2 = 0.9999 and RMSE = 7.69 μStrain for TC0-SG0, and R 2 = 0.9998 and RMSE = 18.03 μStrain for TC3-SG3. While the temperature-strain correlations are weaker for the gauge directly printed on the pipe than for the commercial strain gauge, deployment-ready performance exceeding industry standards is achieved for both sensor pairs.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Self-Sensing Composites via an Embedded 3D-Printed PVDF-MoS 2 Nanosensor for Structural Health Monitoring

Carbon fiber (CF)-reinforced epoxy composites are widely used in vehicle applications, where early damage detection is crucial for reliability and safety. To address this need, we developed a self-sensing epoxy/CF composite by embedding a PVDF-MoS 2 nanosensor via an embedded 3D printing method. By harnessing the intrinsic curing kinetics of epoxy, we tailored its rheological properties to optimize the embedded printing process, enabling precise and reliable support for sensor filaments without compromising the composite’s structural and functional integrity. Through comprehensive rheological and kinetic analysis, we established a quantitative relationship among curing temperature, conversion rate, and resulting yield modulus─defining a narrow processing window essential for successful sensor integration. Specifically, we identified that an epoxy yield modulus range of 180–294 Pa and a conversion rate below 10% are critical to support the PVDF-MoS 2 filament architecture. Here, this embedded 3D printing method produces complex and multimaterial PVDF-MoS 2 sensors within an epoxy matrix with minimal deformation and reduced postprocessing, which is scalable and adaptable for industrial applications. Under cyclic loading, the embedded sensors exhibited stable signals under constant loads and increased voltage signals in response to crack formation (17–35% higher) and catastrophic failure (1 order of magnitude higher), effectively capturing structural changes in real time. This study demonstrates the potential of PVDF-MoS 2 nanocomposite sensor materials for real-time structural health monitoring in epoxy–CF composite systems, enabling early detection of defects and stress anomalies, significantly reducing the risk of unexpected failures, and enhancing structural reliability.

PVDF-MoS2 sensor

Embedding Fiber Optic Sensors in Stainless Steel using Spark Plasma Sintering for Structural Health Monitoring in Harsh Environments

Embedded fiber optic sensors such as fiber Bragg gratings (FBGs) offer a unique route for distributed real-time in-situ imaging of various engineering parameters for numerous purposes. This study advanced the current sensor embedding approaches by exploring a spark plasma sintering (SPS)-assisted technology to embed FBGs in high-temperature structural materials and demonstrated the capability of temperature measurement. In this approach, single-mode FBGs were integrated into stainless steel (SS) 316L components using SPS, followed by the evaluation of the bonding quality between the FBGs and matrix, the optical attenuation of the fibers induced by embedding, and the sensing characters of the FBGs under temperature stimuli. The results demonstrated that superior bonding was achieved between the FBGs and highly-densified SS316L. Examination of the behavior of Bragg gratings validated signal fidelity after embedding. Real-time thermal imaging under temperature cycling using the FBGs demonstrated the effectiveness of the technique for smart materials manufacturing.

36 - MATERIALS SCIENCE

Feasibility of an Accelerometer-Based Structural Health Monitoring System for the LANL Blast Tube

A modeling- and simulation-based study was conducted on the feasibility of implementing an accelerometer-based SHM system on the Los Alamos National Laboratory blast tube. A blast tube experiment was modeled using the Abaqus explicit finite element solver. A custom user subroutine was written to apply test-like pressure loading to the inside surface of the blast tube. The subroutine applies analytically defined pressure loads derived from tracer output taken from a Compressible Flow Computational Fluid Dynamics Solver model of the blast tube. Five unique versions of the model were created: an undamaged reference model at 65°F was used as the baseline and compared to equivalent models at 10°F and 100°F. These three models were compared to models with small damage at the reference temperature. The two types of damage considered were a radial (circumferential) crack in the main tube body and a longitudinal crack in the supports. Acceleration outputs were extracted from accelerometer bodies included in the model and were post processed using a variety of standard SHM techniques. Different potential features signaling failure were extracted and compared using statistical methods in the time and frequency domains. A method was identified that clearly shows that differences in structural response resulting from the modeled damage can be differentiated from the structural response resulting from changing environmental conditions. However, the amount of damage applied to create observable differences in the accelerometer data was so large that simpler methods of damage detection would be more cost effective in locating damage.

42 ENGINEERING

Image-Driven Hybrid Structural Analysis Based on Continuum Point Cloud Method with Boundary Capturing Technique

Conventional approaches for the structural health monitoring of infrastructures often rely on physical sensors or targets attached to structural members, which require considerable preparation, maintenance, and operational effort, including continuous on-site adjustments. This paper presents an image-driven hybrid structural analysis technique that combines digital image processing (DIP) and regression analysis with a continuum point cloud method (CPCM) built on a particle-based strong formulation. Polynomial regressions capture the boundary shape change due to the structural loading and precisely identify the edge and corner coordinates of the deformed structure. The captured edge profiles are transformed into essential boundary conditions. This allows the construction of a strongly formulated boundary value problem (BVP), classified as the Dirichlet problem. Capturing boundary conditions from the digital image is novel, although a similar approach was applied to the point cloud data. It was shown that the CPCM is more efficient in this hybrid simulation framework than the weak-form-based numerical schemes. Unlike the finite element method (FEM), it can avoid aligning boundary nodes with regression points. A three-point bending test of a rubber beam was simulated to validate the developed technique. The simulation results were benchmarked against numerical results by ANSYS and various relevant numerical schemes. The technique can effectively solve the Dirichlet-type BVP, yielding accurate deformation, stress, and strain values across the entire problem domain when employing a linear strain model and increasing the number of CPCM nodes. In addition, comparative analysis with conventional displacement tracking techniques verifies the developed technique’s robustness. The proposed technique effectively circumvents the inherent limitations of traditional monitoring methods resulting from the reliance on physical gauges or target markers so that a robust and non-contact solution for remote structural health monitoring in real-scale infrastructures can be provided, even in unfavorable experimental environments.

Chemistry

Development of High-Temperature Bonding Techniques to Enable High-Temperature Static or Dynamic Strain Measurements

Current light-water nuclear reactors rely on a variety of different sensors and sensor applications to meet their structural health monitoring needs throughout the entirety of the reactor primary, secondary, and containment systems. Optical fiber–based sensor technologies could provide solutions to reduce the sensor system footprint while enhancing the measurement fidelity and spatial resolution by leveraging distributed monitoring techniques. Moreover, advanced reactors may require optical fiber–based sensors for structural health monitoring because their operating temperatures will exceed the limits of conventional transducers used to acquire dynamic strain or acoustic data in nuclear power plants. Therefore, this report describes experiments targeting the development of high-temperature bonding techniques that would allow for potentially long lengths of fibers to be bonded to metallic reactor components in advanced reactor systems. The high temperatures experienced within target application, next-generation nuclear reactors, necessitate a high-temperature resistant bond to limit the amount of tension on the fiber at the target application temperature. The primary bonding method investigated in this work is brazing; hot-rolling has also been investigated to a lesser extent. Both techniques are well-suited to bonding optical fibers to large reactor components such as primary coolant piping, pressure vessels, or heat exchangers. Optical frequency domain reflectometry was used to monitor the strain in metal-coated optical fibers before, during, and after the high-temperature bonding process. On select optical fibers that were successfully bonded, additional thermal cycling was performed to assess the extent to which the fiber remained bonded based on the expected thermal expansion of the test specimen material. The results of the various experiments yielded the following general conclusions: (1) brazing is a viable technique for bonding and allows significant compressive strain to be applied to the fiber at room temperature; (2) hot-rolling is a viable technique as well, which has been more optimized than the brazing technique for bonding, but less residual compressive strain has been observed with this technique; and (3) both techniques will need further development and optimization to demonstrate bonding of a long length of fiber that can provably operate at relevant temperatures for an advanced nuclear reactor application.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Non-destructive structural characterization of graphite components using mechanical resonance and deep learning

As compared to conventional nuclear reactors, microreactors have the potential to significantly reduce construction timelines and capital costs, decreasing the barriers for advanced nuclear reactor technologies. However, the lower power output of these microreactors (typically < 20 MWe) creates challenging economics if operation and maintenance costs cannot be sufficiently reduced. The compact size of these designs presents an opportunity for comprehensive in-situ structural health monitoring to provide real-time feedback in order to reduce operational costs associated with maintenance and downtime. Many microreactor concepts use graphite for both in-core neutron moderation and as a structural material, which has typically required some form of periodic and laborious inspection. This report provides a description and assessment of recent work with graphite to couple acoustic-based experimental measurements and characterization with machine learning models to mature structural health monitoring capabilities and generate benefits for the nuclear microreactor industry. With resilient embedded sensors in development in other programs funded by the US Department of Energy’s Office of Nuclear Energy and elsewhere, the work described herein builds upon previously funded efforts to mature non-destructive testing technology that relates measured vibrational signatures to structural changes, using a combination of new experimental measurements and machine learning processing. Building on past successful demonstrations of predictive workflows to identify structural changes in a hexagonal stainless steel test article with excellent acoustic propagation, we first performed baseline characterization on graphite samples with canonical geometries to ensure compatibility and confidence in the applied techniques for a material with distinctly different mechanical properties. In contrast to efforts in previous years, we worked exclusively with unidirectional vibration data that is more comparable to those expected from the existing embedded sensor technologies which are suitable for deployment in a reactor setting. Established acoustic and modern machine-learning-based characterization approaches were applied to the resulting datasets from these simple geometries. Both approaches were found to be highly capable of detecting even small geometric irregularities amongst nominally identical samples. As such, we then moved to testing these approaches for detection of artificial local stress perturbations introduced into a more complex geometry: a hexagonal block with drilled holes. A main outcome of this work is that a generalizable ML workflow can be used to detect and predict the characteristics of small artificial anomalies in a graphite component with a relevant geometry. While this work was performed using surficial vibration data, we expect the approach to be flexible and viable for other monitoring scenarios, such as those with different arrangements or types of sensor arrays. As compared to previously funded efforts, an existing ML workflow based on neural networks was enhanced through the addition of recently developed Fourier neural operators. As applied to previously collected and new vibration datasets, prediction accuracies of anomaly characterizations were greatly improved with minimal added computational cost. As trained on small durations of vibration data (tens of seconds) collected over a realistic number of locations, the model was able to reliably determine the presence of a subtle stress anomaly and begin to provide location estimates. Such an approach is likely to be viable for more relevant reactor damage scenarios for graphite components, such as progressive crack growth or creep.

36 MATERIALS SCIENCE

A Miniaturized, High-Bandwidth Optical Fiber Fabry–Perot Cavity Vibration Sensor Demonstrated up to 800 °C

A typical structural health monitoring technique involves measuring the vibrational characteristics of components or systems to detect signs of degradation or damage. Many industrial applications require engineered systems to safely operate under extreme, high-temperature environments that pose challenges not only to materials but also to sensors that would be used for structural health monitoring. Here, in this study, miniaturized optical Fabry-Perot cavities (FPCs) were developed and tested as a means of measuring the resonant frequencies of metal components that are most relevant to extreme-environment applications. Two of the three candidate FPC designs tested up to 800 ° C provided accurate measurements (validated by theoretical models and laser Doppler vibrometry) of the fundamental vibrational mode of the specimen to which each was bonded, although both sensors failed during thermal cycling. An analysis of the reflected optical spectrum from the FPC and X-ray computed tomography revealed two opportunities to improve the sensor reliability. First, the Cu optical fiber coating that was used could either be replaced with a more oxidation-resistant material or protected with commercially available films. Second, the adhesives used to bond the fibers to metal capillaries and establish the FPC could be replaced with a more robust solution, although the Resbond 907TS adhesive appeared to outperform Resbond 907.

Birri, Anthony [Oak Ridge National Laboratory (ORN

A Probabilistic Reasoner Based on Bayes Risk for Damage Detection in Structural Systems

Structural health monitoring (SHM) systems are used to inform operation of structural systems subject to loads and environments that may affect their integrity. SHM systems rely on continuous monitoring of the structure to determine its health state. These systems are often coupled with a model of the deployed structure to determine the consequences of changes in the system by forecasting the response to future states. These models, which may be thought of as digital twins, need to be updated to reflect the latest state of the structural system. This work makes use of an uncertainty-aware machine learning model that enforces distance preservation of the original input space to determine deviations from the training data input space distributions. This workflow enables domain shift detection to determine whether damage is present in the structure. The uncertainty metrics generated by this network are then used in a Bayes risk framework to design an optimal damage detector given cost and risk considerations. The approach is demonstrated on a computational example with simulated damage.

Najera-Flores, David [ATA Engineering, Inc.]

Monitoring the Structural Health of the Stage-Four Gibbs Resistor In Order to Maintain a Functioning Pulse-Forming Network

The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility at Los Alamos National Laboratory (LANL) is a critical facility used for nuclear weapons research and development (Los Alamos National Laboratory). Its primary function is to provide high-resolution, real-time images of the behavior of materials under extreme conditions, specifically during the hydrodynamic testing of nuclear weapons surrogates. The facility uses advanced radiographic techniques, such as dual-axis X-ray imaging, to capture detailed snapshots of these materials as they react to high-pressure environments. DARHT plays a key role in maintaining the safety, security, and reliability of the U.S. nuclear arsenal, supporting the Stockpile Stewardship Program. The facility helps ensure that nuclear weapons perform as designed without the need for nuclear tests. Its dual-axis radiography provides more precise data than traditional single-axis imaging, offering a comprehensive view of the internal dynamics of a weapon's primary stage.

42 ENGINEERING