Temperature sensing is one of the most common measurements of a nuclear reactor monitoring system. The coolant fluid flow in a reactor core depends on the reactor power state. We investigated the monitoring and estimation of the thermocouple time series using machine learning for a range of flow regimes. Measurement data were obtained, in two separate experiments, in a flow loop filled with water and with liquid metal Galinstan. We developed long short-term memory (LSTM) recurrent neural networks (RNNs) for sensor predictions by training on the sensor's own prior history, and transfer learning LSTM (TL-LSTM) by training on a correlated sensor's prior history. Sensor cross-correlations were identified by calculating the Pearson correlation coefficient of the time series. The accuracy of LSTM and TL-LSTM predictions of temperature was studied as a function of Reynolds number (Re). The root-mean-square error (RMSE) for the test segment of time series of each sensor was shown to linearly increase with Re for both water and Galinstan fluids. Using linear correlations, we estimated the range of values of Re for which RMSE is smaller than the thermocouple measurement uncertainty. For both water and Galinstan fluids, we showed that both LSTM and TL-LSTM provide reliable estimations of temperature for typical flow regimes in a nuclear reactor. The LSTM runtime was shown to be substantially smaller than the data acquisition rate, which allows for performing estimation and validation of sensor measurements in real time.

Thermal tomography (TT) is a computational method for the reconstruction of depth profile of the internal material defects from Pulsed Infrared Thermography (PIT) nondestructive evaluation. The PIT method consists of recording material surface temperature transients with a fast frame infrared camera, following thermal pulse deposition on the material surface with a flashlamp and heat diffusion into material bulk. TT algorithm obtains depth reconstructions of thermal effusivity, which has been shown to provide visualization of the subsurface internal defects in metals. In many applications, one needs to determine the defect shape and orientation from reconstructed effusivity images. Interpretation of TT images is non-trivial because of blurring, which increases with depth due to the heat diffusion-based nature of image formation. We have developed a deep learning convolutional neural network (CNN) to classify the size and orientation of subsurface material defects in TT images. CNN was trained with TT images produced with computer simulations of 2D metallic structures (thin plates) containing elliptical subsurface voids. The performance of CNN was investigated using test TT images developed with computer simulations of plates containing elliptical defects, and defects with shapes imported from scanning electron microscopy images. CNN demonstrated the ability to classify radii and angular orientation of elliptical defects in previously unseen test TT images. We have also demonstrated that CNN trained on the TT images of elliptical defects is capable of classifying the shape and orientation of irregular defects.

Laser powder bed fusion (LPBF) is a method of additive manufacturing (AM) that selectively melts and fuses together microscopic metallic powder. LPBF offers the benefit of producing custom structures out of high strength metals that can be difficult to fabricate with conventional methods. The challenge of LPBF is that 3D printed structures often have internal pores due to process flaws. Pulsed thermal tomography (PTT) is a method for reconstructing the depth profile of materials, allowing the visualization internal voids in solids. In prior work, we developed a convolutional neural network (CNN) which, having been trained on simulated 2D PTT images of subsurface elliptical defects, was able to classify the semi-major radii, semi-minor radii, and angular orientation of the best-fit ellipses in previously unseen PTT images. The unseen PTT images contained subsurface irregular defect shapes imported from scanning electron microscopy (SEM) images of metallic LPBF-printed specimens. Training the CNN on irregular defect shapes instead of on elliptical shapes would make the resulting classifications more descriptive of actual defect shapes. However, this requires a much higher volume of SEM images of material defects, which are difficult to obtain because of random occurrence of defects in LPBF. To address this challenge, we developed a generative adversarial network (GAN) to augment the existing dataset of SEM defect images. The GAN model is demonstrated to create novel yet realistic defect shapes that can be used as input for simulated PTT images to train CNN.

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of complex topology nuclear reactor parts from high-strength corrosion resistance alloys, such as stainless steel and Inconel. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process. Some of the challenges with using LPBF method for nuclear manufacturing include the possibility of introducing pores into metallic structures. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures in high temperature nuclear reactor environment. Currently, there exist limited capabilities to evaluate actual AM structures non-destructively. Pulsed Thermal Tomography Imaging (PTT) provides a capability for non-destructive evaluation (NDE) of subsurface defects in arbitrary size structures. The PTT method is based on recording material surface temperature transients with infrared (IR) camera following thermal pulse delivered on material surface with flash light. The PTT method has advantages for NDE of actual AM structures because the method involves one-sided non-contact measurements and fast processing of large sample areas captured in one image. Following initial qualification of an AM component for deployment in a nuclear reactor, a PTT system can also be used for in-service nondestructive evaluation (NDE) applications. In this report, we describe recent progress in enhancing PTT capabilities in detecting and visualizing microscopic defects in metallic specimens. The thermal tomography (TT) algorithm obtains depth reconstructions of spatial effusivity from the data cube of sequentially recorded surface temperatures. However, interpretation of TT images is non-trivial because of blurring of images with increasing depth. To address this challenge, we have developed a deep learning convolutional neural network (CNN) to classify size and orientation subsurface defects in simulated TT images. CNN is trained on a database of TT images created for a set of simulated metallic structures with elliptical subsurface voids. Test of CNN performance demonstrate the ability to classify radii and angular orientation of subsurface defects in TT images. In addition, we have shown that CNN trained on elliptical defects is capable of classifying irregular-shaped defects obtained from scanning electron microscopy (SEM) of stainless steel sections printed with LPBF.

High-temperature advanced reactors under development, such as sodium fast reactors (SFR) and molten salt cooled reactors (MSCR), are expected to offer lower levelized cost of energy (LCOE) compared to existing light water reactor (LWR’s). In the existing light water reactors (LWR’s), operation and maintenance (O&M) expenses constitute the largest fraction of the total operating cost. Some of the O&M costs are related maintenance of sensors which can fail due to exposure to harsh environment in a reactor. The O&M costs of Advanced Reactor (AR)’s are expected to constitute a significant fraction of the total cost as well, because of high temperature and radiation level in AR are likely to cause material fatigue and premature failure of sensors and components. The O&M costs in AR’s could be reduced through integration of advanced informatics of performance-related sensors into a digital twin designed for reactor monitoring. For example, machine learning (ML) could be employed for real-time validation and correction of performance-related sensors, and reducing the number of performance-related physical sensor units through virtual sensing. As part of the effort, we investigate real-time validation of thermal hydraulic sensors through one-step ahead forecasting of sensor values using long short-term memory (LSTM) recurrent neural networks (RNN). The sensors are installed in a flow loop containing a thermal mixing tee, which is a common experimental model to study thermal fatigue in a thermal hydraulic loop. In addition, nonlinear transients generated in a thermal mixing tee constitute a good challenge data set for training and validation of ML algorithms. Sensors in this study include thermocouples, flow meters, and optical fibers for distributed temperature sensing. In one experiment, measurement data sets were obtained for a loop was filled with water, and in another experiment, measurements were performed on a loop filled with liquid metal Galinstan. We have also conducted preliminary investigation of one-step ahead prediction of fiber optics-based distributed temperature sensing with LSTM networks. In predicting fiber-based temperature measurements, we treated each gauge pitch of the fiber as an independent sensor. Accuracy of one-step ahead forecasting was estimated by calculating root mean square error (RMSE) for the test segment of time series of each sensor. RMSE’s for temperature sensors in water loop were, for the most part, lower than for the same sensors in Galinstan loop. The RMSE’s for flow meters were similar for both loops. The RMSE’s for distributed temperature measured with the fiber optic sensor were similar to those of the point sensors. Results of this study demonstrated the capability of LSTM one-step ahead forecasting with RMSE comparable to uncertainty in sensor measurements.

The future of quickly, economically produced metallic nuclear reactor parts with minimal supply-chain dependence lies in Laser Powder Bed Fusion (LPBF) Additive Manufacturing (AM): a 3D printing method involving laser melting and net shaping stainless steel and Inconel metallic powder into a solid structure. However, intrinsic features in LPBF frequently leads to the formation of materials defects, such as pores, within 3D printed structures. As safe long-term use in energy applications requires knowledge of all relevant defects before deployment in a reactor, we must develop methods for nondestructive detection of these defects. We are investigating Pulsed Thermal Tomography (PTT), which is a non-contact nondestructive imaging method scalable to arbitrary structure size. Thermal tomography (TT) is a computational method for 3D spatial reconstruction of material thermal effusivity from flash or pulsed thermography temperature data cube. Thermography data cube consists of 2D surface temperature measurements at different times. The objective of the present work is to investigate limits on defect detection in AM metallic structures with PTT. To this effect, we modeled PTT with COMSOL heat transfer computer simulations. We developed a layered media COMSOL simulation consisting of a Stainless Steel 316 (SS316) plate with an internal layer of un-sintered SS316 powder. Thermophysical properties of the powder layer were modeled with equivalent volume mixing model. To account for partial sintering at the boundary of the defect, the transition between solid and powder layers was modeled as a Gaussian. Using data from COMSOL simulations, we reconstructed depth-dependent thermal effusivity, which allowed defect visibility estimation. A series of parametric studies determined that at 1mm depth, 50µm is the smallest detectable defect. In addition, classification of the defects which can lead to early fatigue of the metallic structure in a reactor is briefly discussed.