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DOE OSTI2023

Frequency Domain Reflectometry (FDR) Simulation Techniques for Digital Twin Representation of an Electrical Cable

Simulation of cable system response to frequency domain reflectometry (FDR) tests can be instrumental to understanding these tests and the nature and influence of various cable anomalies on test signatures. Reflectometry simulations are based upon a finite element representation of cable conductors and insulation to produce an S-parameter at each evaluated frequency. The aggregate collection of cable model S-parameters can simulate the influence on a test signal injected into a physical cable. Such an approach was undertaken in this work to produce a digital twin simulation of a low-voltage electrical cable. The electrical cable digital twin examined the influence of test simulation parameters and the relative influence of cable anomalies, including thermal aging, water or moisture exposure, water or moisture ingress, and other anomalies. The digital twin in this work included modeling of the conductors, insulation, jacket, and surrounding environment (air, water, etc.). The digital twin could be expanded to include cable bends, junctions and splices, branch or T systems, and termination impedances of motors or instruments. Observations and conclusions of this work include: 1. Fully 3D digital twin simulation of an electrical cable using an FDR approach is possible. However, there are tradeoffs between simulation fidelity and solution time, which must be balanced to ensure the simulation solves in an adequate amount of time (e.g., less than 20 minutes). Simulation parameters to balance include frequency bandwidth, number of frequencies, mesh density, connection impedance, and permittivity tolerance. 2. The digital twin simulation can explain FDR sensitivity to various cable anomalies, including entry and exit from an oven or water bath. 3. The digital twin simulation FDR response attenuates with distance along the cable and is further affected by the frequency bandwidth, which is similar to that observed with physical measurements. 4. The resolution of the digital twin FDR peaks increased with increasing bandwidth and with increasing number of frequencies, again similar to physical measurements. 5. The presence of multiple anomalies in the digital twin does not substantially attenuate the FDR response to anomalies located beyond the first encountered anomaly and impedance mismatch. 6. Spectral variation of the permittivity did not have a significant effect on the FDR response compared to a fixed nominal value. 7. Extension of the digital twin to 1000 ft still allowed for detection of distal anomalies near the far end of the electrical cable from the instrument connection point. 8. The ARENA test bed facilitates efficient NDE evaluations of well understood cable anomalies with various NDE methods without risking actual plant damage.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗

DOE OSTI2024

The Uranium-Containing and Thorium-Containing Anions Studied by Photoelectron Spectroscopy

An in-depth knowledge of actinide chemistry is fundamental to many aspects of nuclear science and technology, including the synthesis and processing of materials and the remediation of waste disposal sites. Among the actinides, the chemical bonding behaviors of actinium and thorium resemble those of the transition metals; the 5f-electrons of protactinium, uranium, neptunium, and plutonium often play important roles in their bonding; and among the still heavier elements, their bonding tends to mimic the lanthanide elements in terms of electron shielding and their f-electron contributions. Bonding that involves 5f-electrons, however, is especially important, in part because of the significance of uranium and plutonium, but also because these elements are among the few where f-electron participation in bonding is relatively common. This work focused on studying uranium-containing and thorium-containing anions in the gas phase using negative ion photoelectron spectroscopy. Since this technique directly probed valence electrons, it was uniquely positioned to address open questions regarding molecular bonding and electron configurations. A particularly important issue concerned how bonding in actinide-containing molecules was affected by modifications to their actinide atoms’ environment, i.e., due to their interaction with ligands. A closely related question was how actinide atoms’ suborbitals were qualitatively reordered and their energies quantitatively shifted as a result of their ligated environments. These were especially relevant issues in regard to uranium due to it having multiple possible oxidation states (OS) and the potential for 5f electron participation in bonding. The effects of ligands on oxidation states and 5f-orbital energies in uranium bonding was expected to be pronounced. Both ligands and excess electrons were seen as probes of actinide atoms within actinide-containing molecules. Our strategy for advancing knowledge of chemical bonding in the actinide-containing species utilized the synergy between experiments and theory, where in some cases experimental results validated theory and where in others computational results assisted in interpreting experiments. Calculations on actinide systems are terrifically challenging due to large spin-orbit interactions, relativistic effects, and just the sheer number of electrons involved. Even in the simplest species, e.g., U and U2, the most sophisticated, modern calculations carried out by the most experienced theorists often only approximate experimentally-measured values, such as electron affinities. For theory to provide confident predictions that can be used to solve real problems it needed an iterative and ultimately corrective mechanism by which its methods can develop further. Experiments can be used to identify when theory has failed; whereupon the subsequent process of using the experiment-theory interplay can be used to find the cause of the failure. Upon fixing it in one case, different test species can be proposed and studied by the experiment-theory combination to determine whether the problem has been corrected. Thus, experiments not only measure the values of molecular properties, they also provide navigational 3 beacons that keep computations off the reefs in an otherwise dark sea with few reference points. Experimental measurements in the actinide field are not only important, they are in actuality essential to computational progress. While it was not always possible to compare the theoreticallydetermined quantity of interest directly with the same experimentally-measured observable, it was usually possible to compare consequential properties that are both calculable and measurable. In the work completed here electron affinities and electronic state spacings were often sensitive consequential parameters. Reasonable agreement between measured and computational values signaled that a calculation that was very likely to be on-track. We had established collaborative relationships with five computational groups, all of which have expertise in computational actinide chemistry. Their PI’s are L. Cheng, D. Dixon, L. Gagliardi, K. Peterson, and B. Vlaisavljevich. Our close interaction with our theory partners led to us suggesting systems to them and them to us. This reciprocal interaction between our experimental and their computational results was among the most important strengths of this work and was a thread woven throughout. Even though anion photoelectron spectroscopic studies are conducted on anions, much of the information that they provide, pertains to the electronic structure of the neutral counterparts of those anions; among these are electron affinities and electronically excited state spacings. Our experimental tools included several specialized ion sources for forming the anionic species of interest, a mass spectrometer for identifying and mass-selecting them, and an anion photoelectron spectrometer for determining their electron affinities (EA) and characterizing the electronic states of the selected anions’ neutral counterparts. Anion photoelectron spectroscopy is conducted by crossing a mass-selected beam of anions with a fixed-frequency laser beam and energy-analyzing the resultant photodetached electrons. The photodetachment process is governed by the energyconserving relationship: hν = EBE + EKE, where hν is the photon’s energy, EBE is the electron binding (photodetachment transition) energy, and EKE is the electron’s kinetic energy. In our apparatus mass-selection is accomplished via time-of-flight mass spectrometry (TOF-MS), electron energy analysis is achieved with either a magnetic bottle or by velocity mapped imaging. Photodetachment of electrons from anions is implemented via either Nd:YAG or excimer lasers. The photodetachment transition energy, i.e., the EBE, between the ground vibrational and electronic state of an anion and the ground vibrational and electronic state of that anion’s neutral counterpart is the adiabatic electron affinity (EA) of that neutral molecule. Likewise, photodetachment transitions between the ground vibrational and electronic state of an anion and the various electronically-excited states of that anion’s corresponding neutral map the electronic spectrum of that neutral species, i.e., the spectral spacings in the photoelectron spectrum are a mirror image of the neutral’s electronic spectrum. It was, of course, crucial to be able to form the anionic species of interest. There, we had a particularly broad field of anion sources from which to choose. These included several variants of pulsed laser vaporization (LV), laser photoemission, infrared desorption plus photoemission, pulsed arc discharge (PACIS), electrospray ionization (ESI), and Rydberg electron transfer (RET). Each of these anion sources were readily combined with, i.e., connected to, the anion photoelectron spectroscopic portion of our apparatus as described above. Among the sources that utilize lasers, visible light for LV sources as well as IR for desorption sources are provided by Nd:YAG lasers. Ultraviolet photons are provided by both Nd:YAG and excimer lasers, whereas the excitation wavelengths for RET experiments come from two Nd:YAG-pumped dye lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗