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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics

This article synthesizes a filtering adaptive output feedback controller for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The unmodeled dynamics are bounded-input bounded-output stable. By adopting an estimation/cancellation strategy, a piecewise constant adaptive law drives the estimation error to zero at every time instant, which yields the adaptive parameters; a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, while a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. A feedforward control law is designed to track a given command. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed filtering adaptive output feedback control architecture, comparisons with the model reference adaptive control demonstrates the superiority of the proposed control method.

filtering adaptive control, mismatched uncertainit↗
DOE OSTI2023

Fault isolation and fault-tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

Here, in this paper, a fault isolation, diagnosis and fault tolerant control algorithm is proposed for nonlinear multiple multiplicative faults stochastic distribution control systems employing Takagi–Sugeno fuzzy system. To obtain the detailed fault information, a fault detection algorithm is introduced to discover the fault occurrence time. Then a fault isolation observer is built to produce the residual, and the error system is separated to subsystems affected only by disturbance and multiplicative faults. Moreover, a fault estimation scheme is presented to obtain the fault magnitude information. When faults occur, the system output probability density function will deviate from the desired distribution. So the model predictive control fault tolerant control scheme is needed to minimize the impact of faults as much as possible to make sure that the post fault output probability density function track the desired probability density function. The validity of the designed algorithm is demonstrated through a simulation example, where the fault tolerant control algorithm ensures that the system output probability density function still track the given output probability density function despite the complex case of multiple multiplicative faults occurring simultaneously.

42 ENGINEERING↗
DOE OSTI2017

A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∊ [10, 700],Mo ∊ [1 x 10 -6 , 5 x 10 3 , and θ ∊ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R 2 = 0.97 and other available experimental data with 13.0% absolute average relative error and R 2 = 0.84 outperforming existing correlations and models.

Mechanics↗
DOE OSTI2026

LDRD FY25 Program Overview

As Lawrence Livermore National Laboratory’s (LLNL’s) Laboratory Directed Research and Development (LDRD) program enters its fifth decade of leading-edge research and development, its impact and importance have never been stronger. The program continues to advance strategic investments in pioneering science, technology, and engineering, ensuring LLNL will be ready to deliver on our mission as it evolves over the coming decades. Investing in LDRD research, and the people who perform this critical work, gives LLNL the ability to sustain our role as a leader in the Department of Energy and National Nuclear Security Administration enterprise. The LDRD program enables high-risk, high-payoff research that anticipates emerging threats and future mission needs. By nurturing the ingenuity of the Lab’s greatest asset, its people, LDRD funding advances not only our research but also grows and nurtures our workforce: engaging future innovators with student mentoring, challenging postdoctoral researchers to apply their skills to support national security, and strengthening the leadership skills of early career staff. This annual report documents how LDRD investments advance LLNL’s science, technology, and engineering across our mission space. To assess LDRD’s impact we track both short and long-term metrics such as peer-reviewed publications, number of students, or professional fellows. In addition to reviewing these metrics, I encourage you to delve deeper into the breadth of science and technology that illustrate the strategic value of this research portfolio. For instance, a recent exploratory research project used advanced manufacturing to construct miniaturized three-dimensional ion traps for a quantum computer with reduced quantum error rates to enable applications that address national security missions and support basic science. Another project has delved into studying detonation by examining deflagration to enhance the safety and security of the nuclear weapons stockpile. LDRD researchers are also deploying AI agents on two of the world’s most powerful supercomputers to automate and accelerate inertial confinement fusion experiments. Other teams are delivering more accurate optical constants to enable improved validation for aluminum to advance atomic and molecular physics models. LDRD-driven discoveries of how metals deform under extreme conditions strengthen our ability to model and design materials for demanding national security environments. National security challenges are increasingly complex and continuously evolving. LDRD focuses our most innovative science and technology on these challenges, ensuring the Laboratory is developing creative, forward-leaning solutions for our nation and the world. The following pages feature highlights of published scientific advances, patents, and honors that stem from LDRD investments. As you read this report, I hope you will understand how these investments position the Laboratory, and our partners, to meet the demands of the decades ahead.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Impacts on cloud radiative effects induced by coexisting aerosols converted from international shipping and maritime DMS emissions

International shipping emissions (ISE), particularly sulfur dioxide, can influence the global radiation budget by interacting with clouds and radiation after being oxidized into sulfate aerosols. A better understanding of the uncertainties in estimating the cloud radiative effects (CREs) of ISE is of great importance in climate science. Many international shipping tracks cover oceans with substantial natural dimethyl sulfide (DMS) emissions. The interplay between these two major aerosol sources on CREs over vast oceanic regions with a relatively low aerosol concentration is an intriguing yet poorly addressed issue confounding estimation of the CREs of ISE. Using an Earth system model including two aerosol modules with different aerosol mixing configurations, we derive a significant global net CRE of ISE (-0.153 W m -2 with a standard error of ±0.004 W m -2 ) when using emissions consistent with current ship emission regulations. This global net CRE would become much weaker and actually insignificant (-0.001 W m -2 standard error of ±0.007 W m -2 ) if a more stringent regulation were adopted. We then reveal that the ISE-induced CRE would achieve a significant enhancement when a lower DMS emission is prescribed in the simulations, owing to the sublinear relationship between aerosol concentration and cloud response. In addition, this study also demonstrates that the representation of certain aerosol processes, such as mixing states, can influence the magnitude and pattern of the ISE-induced CRE. These findings suggest a reevaluation of the ISE-induced CRE with consideration of DMS variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

SU-F-J-55: Feasibility of Supraclavicular Field Treatment by Investigating Variation of Junction Position Between Breast Tangential and Supraclavicular Fields for Deep Inspiration Breath Hold (DIBH) Left Breast Radiation

Purpose: To explore the feasibility of supraclavicular field treatment by investigating the variation of junction position between tangential and supraclavicular fields during left breast radiation using DIBH technique. Methods: Six patients with left breast cancer treated using DIBH technique were included in this study. AlignRT system was used to track patient’s breast surface. During daily treatment, when the patient’s DIBH reached preset AlignRT tolerance of ±3mm for all principle directions (vertical, longitudinal, and lateral), the remaining longitudinal offset was recorded. The average with standard-deviation and the range of daily longitudinal offset for the entire treatment course were calculated for all six patients (93 fractions totally). The ranges of average ± 1σ and 2σ were calculated, and they represent longitudinal field edge error with the confidence level of 68% and 95%. Based on these longitudinal errors, dose at junction between breast tangential and supraclavicular fields with variable gap/overlap sizes was calculated as a percentage of prescription (on a representative patient treatment plan). Results: The average of longitudinal offset for all patients is 0.16±1.32mm, and the range of longitudinal offset is −2.6 to 2.6mm. The range of longitudinal field edge error at 68% confidence level is −1.48 to 1.16mm, and at 95% confidence level is −2.80 to 2.48mm. With a 5mm and 1mm gap, the junction dose could be as low as 37.5% and 84.9% of prescription dose; with a 5mm and 1mm overlap, the junction dose could be as high as 169.3% and 117.6%. Conclusion: We observed longitudinal field edge error at 95% confidence level is about ±2.5mm, and the junction dose could reach 70% hot/cold between different DIBH. However, over the entire course of treatment, the average junction variation for all patients is within 0.2mm. The results from our study shows it is potentially feasible to treat supraclavicular field with breast tangents.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

A Data-Driven Framework for Direct Local Tensile Property Prediction of Laser Powder Bed Fusion Parts

This article proposes a generalizable, data-driven framework for qualifying laser powder bed fusion additively manufactured parts using part-specific in situ data, including powder bed imaging, machine health sensors, and laser scan paths. To achieve part qualification without relying solely on statistical processes or feedstock control, a sequence of machine learning models was trained on 6299 tensile specimens to locally predict the tensile properties of stainless-steel parts based on fused multi-modal in situ sensor data and a priori information. A cyberphysical infrastructure enabled the robust spatial tracking of individual specimens, and computer vision techniques registered the ground truth tensile measurements to the in situ data. The co-registered 230 GB dataset used in this work has been publicly released and is available as a set of HDF5 files. The extensive training data requirements and wide range of size scales were addressed by combining deep learning, machine learning, and feature engineering algorithms in a relay. The trained models demonstrated a 61% error reduction in ultimate tensile strength predictions relative to estimates made without any in situ information. Lessons learned and potential improvements to the sensors and mechanical testing procedure are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The Road to Useful Quantum Computers

Building a useful quantum computer is a grand science and engineering challenge, currently pursued intensely by teams around the world. In the 1980s, Richard Feynman and Yuri Manin observed independently that computers based on quantum mechanics might enable better simulations of quantum phenomena. Their vision remained an intellectual curiosity until Peter Shor published his famous quantum algorithm for integer factoring, and shortly thereafter a proof that errors in quantum computations can be corrected. Since then, quantum computing R&D has progressed rapidly, from small-scale experiments in university physics laboratories to well-funded industrial efforts and prototypes. Hype notwithstanding, quantum computers have yet to solve scientifically or practically important problems -- a target often called quantum utility. In this article, we describe the capabilities of contemporary quantum computers, compare them to the requirements of quantum utility, and illustrate how to track progress from today to utility. We highlight key science and engineering challenges on the road to quantum utility, touching on relevant aspects of our own research.

Emerging Technologies (cs.ET)↗
DOE OSTI2019

On the Convergence of the Inexact Running Krasnosel'skii-Mann Method

This letter leverages a framework based on averaged operators to tackle the problem of tracking fixed points associated with maps that evolve over time. In particular, this letter considers the Krasnosel'skii-Mann (KM) method in a settings where: 1) the underlying map may change at each step of the algorithm, thus leading to a 'running' implementation of the KM method, and 2) an imperfect information of the map may be available. An imperfect knowledge of the maps can capture cases where processors feature a finite precision or quantization errors, or the case where (part of) the map is obtained from measurements. The analytical results are applicable to inexact running algorithms for solving optimization problems, whenever the algorithmic steps can be written in the form of (a composition of) averaged operators; examples are provided for inexact running gradient methods and the forward-backward splitting method. Convergence of the average fixed-point residual is investigated for the non-expansive case; linear convergence to a unique fixed-point trajectory is showen in the case of inexact running algorithms emerging from contractive operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-J-58: Comparison of Conformal Tracking Methods Using Initial, Adaptive and Preceding Image Frames for Image Registration

Purpose: Accounting for tumor motion during radiation therapy is important to ensure that the tumor receives the prescribed dose. Increasing the field size to account for this motion exposes the surrounding healthy tissues to unnecessary radiation. In contrast to using motion-encompassing techniques to treat moving tumors, conformal radiation therapy (RT) uses a smaller field to track the tumor and adapts the beam aperture according to the motion detected. This work investigates and compares the performance of three markerless, EPID based, optical flow methods to track tumor motion with conformal RT. Methods: Three techniques were used to track the motions of a 3D printed lung tumor programmed to move according to the tumor of seven lung cancer patients. These techniques utilized a multi-resolution optical flow algorithm as the core computation for image registration. The first method (DIR) registers the incoming images with an initial reference frame, while the second method (RFSF) uses an adaptive reference frame and the third method (CU) uses preceding image frames for registration. The patient traces and errors were evaluated for the seven patients. Results: The average position errors for all patient traces were 0.12 ± 0.33 mm, −0.05 ± 0.04 mm and −0.28 ± 0.44 mm for CU, DIR and RFSF method respectively. The position errors distributed within 1 standard deviation are 0.74 mm, 0.37 mm and 0.96 mm respectively. The CU and RFSF algorithms are sensitive to the characteristics of the patient trace and produce a wider distribution of errors amongst patients. Although the mean error for the DIR method is negatively biased (−0.05 mm) for all patients, it has the narrowest distribution of position error, which can be corrected using an offset calibration. Conclusion: Three techniques of image registration and position update were studied. Using direct comparison with an initial frame yields the best performance. The authors would like to thank Dr.YeLin Suh for making the Cyberknife dataset available to us. Scholarship funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) and CancerCare Manitoba Foundation is acknowledged.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Estimation of Tropical Cyclone Intensity in the North Atlantic and Northeastern Pacific Basins Using TRMM Satellite Passive Microwave Observations

Here, a statistical passive microwave intensity estimation (PMW-IE) algorithm for estimating the intensity of tropical cyclones (TCs) in the North Atlantic and northeastern and central Pacific basins is developed and tested. The algorithm is derived from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) 85-GHz brightness temperatures and near-surface rain-rate retrievals to provide objective estimates of current maximum sustained surface winds (Vmax) and 6-h future Vmax of TCs. The full record of TRMM data (1998–2013) including 2326 TMI overpasses of 503 TCs is separated into dependent samples (1998–2010) for model development and independent samples (2011–13) for model verification. The best track intensities are used as dependent variables in a stepwise multiple-regression approach. Separately for each basin, three regression models are derived using selected 1) 85-GHz-only variables, 2) rain-rate-only variables, and 3) combined 85-GHz and rain variables. The algorithms are assessed using independent samples and those with contemporaneous aircraft-reconnaissance measurements. Rain-only and combined models perform better than the 85-GHz-only model. Lower errors are found for estimating the 6-h future Vmax than estimating the current Vmax using all three models. This implies that it is optimal to use passive-microwave-retrieved rain variables observed a few hours earlier to estimate TC intensity. The MAE (RMSE) of 6-h future Vmax is 9 (12) kt (1 kt ≈ 0.51 m s -1 ) when testing the combined models with ATL and EPA independent samples. Aircraft-reconnaissance-based independent samples yields a MAE of 9.6 kt and RMSE of 12.6 kt for estimating 6-h future Vmax.

58 GEOSCIENCES↗
DOE OSTI2022

Magnetostrictive Ultrasonic Waveguide Transducer for In-Pile Thermometry

Real-time and reliable temperature measurement on nuclear fuels is crucial for the safe operation of existing pressurized-water reactors and future advanced nuclear reactors. Magnetostrictive materials deform when subjected to a magnetic field or exhibit magnetization variation when stressed. Here, based on these properties, this study prototyped an ultrasonic thermometer (UT) consisting of a magnetostrictive waveguide, a dc coil providing appropriate magnetic biasing, and an ac coil generating an acoustic impulse and detecting the resulting acoustic echoes. By tracking the time of flight between the excitation pulse and the echoes, the UT can potentially detect nuclear fuel cladding temperature from a long distance. In this study, magnetostrictive iron–gallium alloys, or Galfenol, were selected as the waveguide due to their large magnetostriction, superior temperature survivability, excellent radiation resilience, and high mechanical robustness. A multiphysics finite-element model considering electrical, magnetic, and mechanical dynamics in the magnetostrictive UT was then developed. The model exhibited an error of 0.24% in time-of-flight simulation and, therefore, enabled computer-aided design and guided signal processing. Between room temperature and 120 °C, the new Galfenol-based UT exhibits a linear sensitivity of 162.8×10 ₋6 °C ₋1 , which is 51.7% higher than a previous magnetostrictive UT based on iron–cobalt–vanadium alloys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

MO-F-CAMPUS-I-03: GPU Accelerated Monte Carlo Technique for Fast Concurrent Image and Dose Simulation

Purpose: To develop an accurate and fast Monte Carlo (MC) method of simulating CT that is capable of correlating dose with image quality using voxelized phantoms. Methods: A realistic voxelized phantom based on patient CT data, XCAT, was used with a GPU accelerated MC code for helical MDCT. Simulations were done with both uniform density organs and with textured organs. The organ doses were validated using previous experimentally validated simulations of the same phantom under the same conditions. Images acquired by tracking photons through the phantom with MC require lengthy computation times due to the large number of photon histories necessary for accurate representation of noise. A substantial speed up of the process was attained by using a low number of photon histories with kernel denoising of the projections from the scattered photons. These FBP reconstructed images were validated against those that were acquired in simulations using many photon histories by ensuring a minimal normalized root mean square error. Results: Organ doses simulated in the XCAT phantom are within 10% of the reference values. Corresponding images attained using projection kernel smoothing were attained with 3 orders of magnitude less computation time compared to a reference simulation using many photon histories. Conclusion: Combining GPU acceleration with kernel denoising of scattered photon projections in MC simulations allows organ dose and corresponding image quality to be attained with reasonable accuracy and substantially reduced computation time than is possible with standard simulation approaches.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Patterns of Precipitation Change and Climatological Uncertainty among CMIP5 Models, with a Focus on the Midlatitude Pacific Storm Track

Projections of modeled precipitation ( P ) change in global warming scenarios demonstrate marked intermodel disagreement at regional scales. Empirical orthogonal functions (EOFs) and maximum covariance analysis (MCA) are used to diagnose spatial patterns of disagreement in the simulated climatology and end-of-century P changes in phase 5 of the Coupled Model Intercomparison Project (CMIP5) archive. The term principal uncertainty pattern (PUP) is used for any robust mode calculated when applying these techniques to a multimodel ensemble. For selected domains in the tropics, leading PUPs highlight features at the margins of convection zones and in the Pacific cold tongue. The midlatitude Pacific storm track is emphasized given its relevance to wintertime P projections over western North America. The first storm-track PUP identifies a sensitive region of disagreement in P increases over the eastern midlatitude Pacific where the storm track terminates, related to uncertainty in an eastward extension of the climatological jet. The second PUP portrays uncertainty in a zonally asymmetric meridional shift of storm-track P , related to uncertainty in the extent of a poleward jet shift in the western Pacific. Both of these modes appear to arise primarily from intermodel differences in the response to radiative forcing, distinct from sampling of internal variability. The leading storm-track PUPs for P and zonal wind change exhibit similarities to the leading uncertainty patterns for the historical climatology, indicating important and parallel sensitivities in the eastern Pacific storm-track terminus region. However, expansion coefficients for climatological uncertainties tend to be weakly correlated with those for end-of-century change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

On Effect of Information Loss on Fuser Quality and Utility

We abstract the accuracy performance of any fuser into a fusion quality measure that is within the range [0; 1] and monotonically decreases with increasing errors. Although there are many possible ways to map the actual error to this quality measure, we adopt a mapping function consisting of both concave and convex regions and its parameters can be tuned based on system design requirements. The effect of communication loss over the links from the sensors, where estimates are generated, to the fuser is then considered, and based on the variations of the quality measure with loss, we define the overall fuser utility that characterizes the resilience of a fuser with increasingly adverse communication constraints. Tracking examples are shown to demonstrate the comparative quality and utility performances of several closed-form fusers.

Rao, Nageswara↗
DOE OSTI2017

Utilizing the SACADA system to collect simulator training data to inform human reliability analyses - 169

Lack of appropriate human performance data for the development of human reliability analysis (HRA) methods has been identified as a key issue contributing to the method-to-method variability among the HRA methods. The United States Nuclear Regulatory Commission (NRC) worked with domain experts to develop the Scenario Authoring, Characterization, and Debriefing Application (SACADA) system to collect nuclear power plants' licensed operator simulator training and examination data to inform HRA. In the past two decades, significant improvements in understanding and modelling human performance in HRA have affected the perspectives of the types of data to be collected for HRA. A significant change is that human performance is strongly dependent on the context of the tasks to be performed. To incorporate this understanding, the SACADA data taxonomy collects the context and actual performance information of the training objective elements (TOEs) in nuclear plant operator simulator training. This provides a framework consistent with HRA to use context to estimate human error probabilities. It is recognized that measuring crew performance is equally important as improving operator training. SACADA is designed to support the nuclear trainers in capturing this important information that is used to identify training weaknesses and drive continuous improvement. This paper discusses the SACADA taxonomy, the SACADA system's functions, and the supporting software design to enable the SACADA system to be practically implemented in the nuclear power plants' operator simulator training program to collect data for tracking operator performance and HRA analysis. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Understanding and quantifying the systematic effects of clutter within a radiation detection scene

Because of low signal-to-noise ratios, the main difficultly in real-world detection scenarios is distinguishing between benign sources and potentially-threatening radioactive materials. The variability in observed signal during a radiation detection search operation can be contributed to the stochastic nature of the underlying physics and the systematic errors inherent to the detection systems employed. This variability is compounded for dynamic detection scenarios, where objects, referred to as clutter, traverse through the primary detection scene, introducing potential suppressions in the observed signal due to the attenuation of background radiation. This study examines the impact that clutter, namely automobiles such as small utility vehicles, sedans, and trucks, produces on the observed signal in a 2 in. × 4 in. × 16 in. NaI(Tl) detector. The clutter is identified and tracked in the detection scene using a time-synced video camera and a 2-D light distance and ranging contextual sensors. Two experiments were performed on the Oak Ridge National Laboratory reservation: one using a distributed source within the scene to understand the systematics of detecting and analyzing the clutter, and the second experiment mimicking an urban environment with large buildings positioned on either side of a roadway. The experiments exhibited unique results in the amount of signal suppression and variability of the cluttered signal, both demonstrating an observable suppression from the clutter-free background. These results reveal a new potential category of signal noise intrinsic to real-world detection scenarios that should be considered when establishing detection thresholds based on expected values.

Stewart, Ian R.↗
DOE OSTI2022

Direct Measurement of the Nickel Spectrum in Cosmic Rays in the Energy Range from 8.8 GeV/$\mathcal{n}$ to 240 GeV/$\mathcal{n}$ with CALET on the International Space Station

The relative abundance of cosmic ray nickel nuclei with respect to iron is by far larger than for all other transiron elements; therefore it provides a favorable opportunity for a low background measurement of its spectrum. Since nickel, as well as iron, is one of the most stable nuclei, the nickel energy spectrum and its relative abundance with respect to iron provide important information to estimate the abundances at the cosmic ray source and to model the Galactic propagation of heavy nuclei. However, only a few direct measurements of cosmic-ray nickel at energy larger than ~ 3 GeV/n are available at present in the literature, and they are affected by strong limitations in both energy reach and statistics. In this Letter, we present a measurement of the differential energy spectrum of nickel in the energy range from 8.8 to 240 GeV/n , carried out with unprecedented precision by the Calorimetric Electron Telescope (CALET) in operation on the International Space Station since 2015. The CALET instrument can identify individual nuclear species via a measurement of their electric charge with a dynamic range extending far beyond iron (up to atomic number Z = 40 ). The particle’s energy is measured by a homogeneous calorimeter (1.2 proton interaction lengths, 27 radiation lengths) preceded by a thin imaging section (3 radiation lengths) providing tracking and energy sampling. This Letter follows our previous measurement of the iron spectrum [O. Adriani et al. (CALET Collaboration), Phys. Rev. Lett. 126, 241101 (2021).], and it extends our investigation on the energy dependence of the spectral index of heavy elements. It reports the analysis of nickel data collected from November 2015 to May 2021 and a detailed assessment of the systematic uncertainties. In the region from 20 to 240 GeV/n our present data are compatible within the errors with a single power law with spectral index -2.51 ± 0.07 .

79 ASTRONOMY AND ASTROPHYSICS↗