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At least 793 records · Page 44

Profiles of upcoming HPC Applications and their Impact on Reservation Strategies

With the expected convergence between HPC, BigData and AI, new applications with different profiles are coming to HPC infrastructures. Here, we aim at better understanding the features and needs of these applications in order to be able to run them efficiently on HPC platforms. The approach followed is bottom-up: we study thoroughly an emerging application from the neuroscience community (SLANT) to understand its behavior. Based on these observations, we derive a generic, yet simple, application model (namely, a linear sequence of stochastic jobs). We expect this model to be representative for a large set of upcoming applications that require the computational power of HPC clusters without fitting the typical behavior of large-scale traditional applications. In a second step, we show how one can manipulate this generic model in a scheduling framework. Specifically we consider the problem of making reservations (both time and memory) for an execution on an HPC platform. We derive solutions using the model of the first step of this work. We experimentally show the robustness of the model, even with very few data or with another application, to generate the model, and provide performance gains with regards to standard and more recent approaches used in the neuroscience community.

97 MATHEMATICS AND COMPUTING↗

The Role of Theory and Modeling in the International Living with a Star Program

Today, theory and modeling play a critical role in our quest to understand the connection between solar eruptive phenomena, and their impacts in interplanetary space and in the near-Earth space environment. This new role is based on two developments, one related to the goal of basic physical understanding, and the other to space weather-related applications. When targeting physical our focus is shifting away from investigations aiming at basic discoveries, to missions and studies that address our basic understanding of processes we know to be important. For these studies, theory and models provide physical explanations that need to be verified or falsified by empirical evidence. Within this paradigm, a much more tight integration between theory modeling, and space flight mission design and execution is not only beneficial, but essential. One of the prime objectives of space weather research, on the other hand, is the prediction of space environmental conditions for the benefit of humans and their assets in near-Earth space and on the ground, as well as on solar system bodies like Mars that are of interest to exploration by humans. By its very nature, prediction requires modeling, which, in turn, requires understanding. We will present an overview of the role of theory and modeling within the International Living With a Star program. Specifically, we will focus on an assessment of present-day and future capabilities, as well as on strategies for tight integration of theory and modeling in space science investigations.

Hesse, M.↗

Program to Optimize Simulated Trajectories II (POST2) Surrogate Models for Mars Ascent Vehicle (MAV) Performance Assessment

The primary purpose of the multiPOST tool is to enable the execution of much larger sets of vehicle cases to allow for broader trade space exploration. However, this exploration is not achieved solely with the increased case throughput. The multiPOST tool is applied to carry out a Design of Experiments (DOE), which is a set of cases that have been structured to capture a maximum amount of information about the design space with minimal computational effort. The results of the DOE are then used to fit a surrogate model, ultimately enabling parametric design space exploration. The approach used for the MAV study includes both DOE and surrogate modeling. First, the primary design considerations for the vehicle were used to develop the variables and ranges for the multiPOST DOE. The final set of DOE variables were carefully selected in order to capture the desired vehicle trades and take into account any special considerations for surrogate modeling. Next, the DOE sets were executed through multiPOST. Following successful completion of the DOE cases, a manual verification trial was performed. The trial involved randomly selecting cases from the DOE set and running them by hand. The results from the human analyst's run and multiPOST were then compared to ensure that the automated runs were being executed properly. Completion of the verification trials was then followed by surrogate model fitting. After fits to the multiPOST data were successfully created, the surrogate models were used as a stand-in for POST2 to carry out the desired MAV trades. Using the surrogate models in lieu of POST2 allowed for visualization of vehicle sensitivities to the input variables as well as rapid evaluation of vehicle performance. Although the models introduce some error into the output of the trade study, they were very effective at identifying areas of interest within the trade space for further refinement by human analysts. The next section will cover all of the ground rules and assumptions associated with DOE setup and multiPOST execution. Section 3.1 gives the final DOE variables and ranges, while section 3.2 addresses the POST2 specific assumptions. The results of the verification trials are given in section 4. Section 5 gives the surrogate model fitting results, including the goodness-of-fit metrics for each fit. Finally, the MAV specific results are discussed in section 6.

Zwack, M. R.↗

Analyzing Contents of a Computer Cache

The Cache Contents Estimator (CCE) is a computer program that provides information on the contents of level-1 cache of a PowerPC computer. The CCE is configurable to enable simulation of any processor in the PowerPC family. The need for CCE arises because the contents of level-1 caches are not available to either hardware or software readout mechanisms, yet information on the contents is crucial in the development of fault-tolerant or highly available computing systems and for realistic modeling and prediction of computing- system performance. The CCE comprises two independent subprograms: (1) the Dynamic Application Address eXtractor (DAAX), which extracts the stream of address references from an application program undergoing execution and (2) the Cache Simulator (CacheSim), which models the level-1 cache of the processor to be analyzed, by mimicking what the cache controller would do, in response to the address stream from DAAX. CacheSim generates a running estimate of the contents of the data and the instruction subcaches of the level-1 cache, hit/miss ratios, the percentage of cache that contains valid or active data, and time-stamped histograms of the cache content.

Beahan, John↗

Energy Performance Assessment of Radiant Cooling System through Modeling and Calibration at Component Level

The paper describes a case study of an information technology office building with a radiant cooling system and a conventional variable air volume (VAV) system installed side by side so that performancecan be compared. First, a 3D model of the building involving architecture, occupancy, and HVAC operation was developed in EnergyPlus, a simulation tool. Second, a different calibration methodology was applied to develop the base case for assessing the energy saving potential. This paper details the calibration of the whole building energy model to the component level, including lighting, equipment, and HVAC components such as chillers, pumps, cooling towers, fans, etc. Also a new methodology for the systematic selection of influence parameter has been developed for the calibration of a simulated model which requires large time for the execution. The error at the whole building level [measured in mean bias error (MBE)] is 0.2%, and the coefficient of variation of root mean square error (CvRMSE) is 3.2%. The total errors in HVAC at the hourly are MBE = 8.7% and CvRMSE = 23.9%, which meet the criteria of ASHRAE 14 (2002) for hourly calibration. Different suggestions have been pointed out to generalize the energy saving of radiant cooling system through the existing building system. So a base case model was developed by using the calibrated model for quantifying the energy saving potential of the radiant cooling system. It was found that a base case radiant cooling system integrated with DOAS can save 28% energy compared with the conventional VAV system.

Building Energy Simulation↗

Simulation of Malfunctions for the ISS Double-Gimbal Control Moment Gyroscope

This paper presents a simplified approach to simulation of malfunctions of the Control Moment Gyroscope (CMG) on board the International Space Station (ISS). These malfunctions will be used as part of flight training of CMG failure scenarios in the guidance navigation control (GNC) subsystem of the Training Systems for 21st Century (TS21) simulator. The CMG malfunctions are grouped under mechanical, thermal and electrical categories. A malfunction can be as simple as one which only affects the telemetry or a complex one that changes the state and behavior of the CMG model. In both cases, the ISS GNC flight software will read the telemetry and respond accordingly. The user executes these malfunctions by supplying conditional data which modify internal model states and then elicit a response as seen on the user displays. Ground operators and crew on board the ISS use CMG malfunction procedures to better understand and respond to anomalies observed within the CMG subsystem.

Inampudi, Ravi↗

Critical Role of the Public Theory & Modeling Program for Commercial Fusion Energy

This white paper contributes input from the Executive Committee of the Theory Coordinating Committee to the 2024 FESAC Decadal Plan Subcommittee. It is argued that the public Theory and Modeling program plays a critical role in the pursuit of commercial fusion energy. A new mechanism for fostering engagement between the fusion industry and the public Theory and Modeling program could provide better alignment between the goals of the public program and the needs of private industry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Supporting Simulation Families in Nuclear Reactor Workflows SBIR Phase I. Final Scientific/Technical Report

The US Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) Toolkit has accelerated both the solutions to existing problems and deployment of new designs for current and advanced reactors. Within the toolkit, there exist various families of simulation tools that target specific aspects of a multi-physics simulation for a nuclear reactor. Tools within a specific family vary in both complexity and fidelity as well as the types of resources they require. To complement the NEAMS effort, the Computational Model Builder (CMB) has been designed to provide a graphical user interface to design and execute nuclear reactor workflows. Previously, we had designed a workflow in CMB to design and prepare for execution a neutronics simulation using DIF3D, a diffusion and transport solver developed at Argonne National Laboratory. For this Phase I effort, we extended CMB’s reactor modeling tools to design and execute a workflow using Proteus-SN, a higher-fidelity transport solver developed at Argonne with more preparatory requirements from the workflow. Furthermore, this workflow was designed to maximize the common features of the two workflows, describing the analogous tasks between the workflows as belonging to a “simulation family”. This perspective facilitates the abstraction of the neutronics simulations to a single bifurcated workflow, allowing the engineer to design a reactor and then choose the appropriate simulation according to his or her needs for fidelity and computational cost.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MBSE Execution of Scalable Autonomous Operations for a High Density Vertiplex

The High Density Vertiplex (HDV) subproject of NASA’s Advanced Air Mobility (AAM) project adopted Model-Based Systems Engineering (MBSE) and NASA SE processes were executed via MBSE using MagicDraw. Since the adoption of MBSE and utilization of MagicDraw, the systems engineering team has made tremendous strides in each pillar of MBSE including, requirements, behavior, and structure. Scalable Autonomous Operations (SAO) was a stage in the development of the High Density Vertiplex focusing on the autonomous terminal operations of a vertiport with sUAS aircraft. MBSE served the systems engineering team to document and verify the physical architecture and capture a logical architecture of SAO for distribution to the AAM community. This paper will detail methodologies that were created to successfully execute NASA SE processes via MBSE in the SAO stage as well as highlight challenges and lessons learned.

Demetrios Katsaduros↗

DE-NE0000724 - Research Performance Final Report - Investigation of Thermal Aging Effects on the Evolution of Microstructure and Mechanical Properties of Cast Duplex Stainless Steels

This report details the research activities carried out under DOE-NEUP award number DE-NE0000724 concerning the evolution of structural and mechanical properties during thermal aging of CF–3 and CF–8 cast duplex stainless steels (CDSS). The overall objective of this project was to use state-of-the-art characterization techniques to elucidate trends and phenomena in the mechanical and structural evolution of cast duplex stainless steels (CDSS) during thermal aging. These steels are commonly used as structural materials in commercial light water nuclear power plants, undergoing aging for decades in operation as cooling water pipes, pump casings, valve bodies, etc. During extended exposure to these conditions, CDSS are known to undergo a change in mechanical properties resulting in a loss of ductility, i.e. embrittlement. While it is generally accepted that structural changes within the ferrite phase, such as decomposition into iron (Fe)-rich and chromium (Cr)-rich domains, lead to the bulk embrittlement of the steels, many questions remain as to the mechanisms of embrittlement at multiple length scales. This work is intended to shed insight into the atomic level composition changes, associated kinetic mechanisms, and effects of changing phase structure on micro- and nano-scale deformation that lead to loss of impact toughness and tensile ductility in these steels. In general, this project provides a route to answer some of these major questions using techniques such as 3-dimensional (3-D) atom probe tomography (APT) and real-microstructure finite element method (FEM) modeling, which were not readily available when these steels were originally selected for service in light water reactors. Mechanical properties evaluated by Charpy V-notch impact testing (CVN), tensile testing, and microhardness and nanohardness measurements were obtained for each condition and compared with the initial baseline properties to view trends in deformation behavior during aging. Concurrent analysis of the microstructure and nanostructure by atom probe tomography (APT) and transmission electron microscopy (TEM) provide mechanistic insight into the kinetic and mechanical behavior occurring on the nano-scale. The presence and morphology of the ferrite, austenite, and carbide phases have been characterized, and formation of new phases during aging, including spinodal decomposition products (α- and α'-ferrite) and G-phase, have been observed. The mechanical and structural characterization have been used to create accurate FEM models based on the real micro- and nano-structures of the systems. These models provide new insight into the local deformation behavior of these steels and the effects of each individual phase (including ferrite, austenite, carbides, and spinodal decomposition products) on the evolving bulk mechanical behavior of the system. The project was divided into three major tasks: 1. Initial Microstructure and Mechanical Property Survey and Initiate Heat Treatment; 2. Microstructural Characterization and Mechanical Property Testing During Aging; and 3. Microstructure-based Finite Element Modeling. Each of these tasks was successfully executed, resulting in reliable data and analysis that add to the overall body of work on the CDSS materials. Baseline properties and aging trends in mechanical data confirm prior observations and add new insights into the mechanical behavior of the steels. Structural characterization on multiple length scales provides new information on phase changes occurring during aging and sheds light on the kinetic processes occurring at the atomic scale. Furthermore, a combination of mechanical testing and microstructural characterization techniques was utilized to design FEM models of local deformation behavior of the ferrite and austenite phases, providing valuable new information regarding the effects of each of the microstructural components on the hardening and embrittlement processes. The data and analysis presented in this report and the publication associated with this project (§V) increase the understanding of aging and deformation in CF–3 and CF–8 steels. These results provide valuable information that can be utilized to aid in making informed decisions regarding the ongoing use of these steels in commercial nuclear infrastructure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs

A novel approach for modeling the aero-propulsive characteristics of an electric vertical takeoff and landing (eVTOL) aircraft was developed and demonstrated in wind tunnel testing. The approach was applied to the NASA LA-8 tandem tilt-wing eVTOL aircraft, using an efficient, hybrid experiment design composed of a static I-optimal response surface design for slowly-varying test variables, and dynamic orthogonal phase-optimized multisine excitations for the control surfaces and electric propulsors. Both the static and dynamic experiment designs were executed simultaneously to collect informative data for model identification. Statistically-weighted multivariate orthogonal function modeling was used to combine local modeling results computed in the frequency domain using data collected with dynamic excitations operating on the control effectors to form an aggregate aero-propulsive model. The final identified model exhibited good predictive capability when compared to validation data acquired separately from the data used to develop the model. The required test time using these new techniques was reduced by at least a factor of five compared to previous static wind tunnel testing for the LA-8 aircraft, while providing more informative data, greater parameterization flexibility, and high-quality models.

system identification↗

Wave climate and energy resources in American Samoa from a 42-year high-resolution hindcast

Here, this paper presents an analysis of the wave climate and a characterization of the wave energy resources in American Samoa, a U.S. territory covering seven south central Pacific islands and atolls. A numerical wave model based on WAVEWATCH III® and unstructured SWAN was developed, validated, and executed for 1979–2020 to generate a hindcast dataset suitable for resource characterization. Model-data comparisons were performed with measurements collected in situ and from satellite-based altimeters. The model was found to perform well with a bias in significant wave height of -0.14 m and -0.06 m against buoy and altimeters, respectively. The multimodal sea state of American Samoa is investigated by identifying the sources of energy reaching the islands and partitioning the wave spectrum accordingly. The wave resources characterization follows the International Electrotechnical Commission Technical Specifications to be compatible with studies performed for other U.S. regions. The average omnidirectional wave power at 2 km from shore around Tutuila, the main island of American Samoa, is 14 kW/m. Locations east and west of the islands have a more consistent resource throughout the year because the northwest and southwest swells that are dominant during different seasons complement each other.

16 TIDAL AND WAVE POWER↗

A theoretical basis for the analysis of redundant software subject to coincident errors

Fundamental to the development of redundant software techniques fault-tolerant software, is an understanding of the impact of multiple-joint occurrences of coincident errors. A theoretical basis for the study of redundant software is developed which provides a probabilistic framework for empirically evaluating the effectiveness of the general (N-Version) strategy when component versions are subject to coincident errors, and permits an analytical study of the effects of these errors. The basic assumptions of the model are: (1) independently designed software components are chosen in a random sample; and (2) in the user environment, the system is required to execute on a stationary input series. The intensity of coincident errors, has a central role in the model. This function describes the propensity to introduce design faults in such a way that software components fail together when executing in the user environment. The model is used to give conditions under which an N-Version system is a better strategy for reducing system failure probability than relying on a single version of software. A condition which limits the effectiveness of a fault-tolerant strategy is studied, and it is posted whether system failure probability varies monotonically with increasing N or whether an optimal choice of N exists.

Eckhardt, D. E., Jr.↗

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗

Multi-Formalism Modeling for Disaster Resilience, Forecasting, and Response

Disaster response preparedness, risk mitigation, and effective post-event response are critical for national security, public health, and economic integrity. For areas impacted by extreme events, timely and accurate impact assessments of lifeline infrastructures are critical. Traditional disaster management and situational awareness platforms are not capable of handling the massive influx of available information from traditional and non-traditional sources. Next-generation analytic assessment approaches, where use of dynamically sourced, heterogeneous data with near real-time availability are integrated into a continually-updated analytics framework. The objective of this research was to develop a foundational multi-formalism modeling platform to integrate novel data sources for use in improving situational awareness after a disaster event. Specifically, to 1) provide an architecture for machine-learning based data fusion various multi-sensor datasets; 2) classify, geolocate, and temporally bin novel data sources for use in spatially-enabled machine-learning based data fusion; and 3) derive confidence-based observation data with machine-learning based prediction to fill spatial and temporal observation gaps. This project developed a reusable cloud-based pipeline architecture for ingesting, storing, and analyzing relevant data, executing a range of deep-learning models, and visualize the information geographically. The pipeline development was informed by previous PNNL investments (StreamKit) and built upon leading-edge technologies consisting of: 1) a raw datastore; 2) a data enrichment pipeline with custom and third-party analytics; 3) enriched data storage; and 4) a custom UI to display the enriched data. Machine learning/deep learning models were selected and tested to classify social media images for relevancy and presence of flood waters. Our custom trained relevance models were run on a validation dataset and the overall accuracy of the relevance classifiers ranged from 65% to 90%. We found that convolutional neural network (CNN) models were both faster and more accurate than more traditional machine learning models. We applied the relevance classifier to remove non-relevant images and then undertook a limited training of CNN models to detect flood on ~1,800 labeled images. The testing accuracy of the flood detection models were ~88%. To improve the geographic location of both social media and oblique aerial images we tested a multi-step workflow built on a pre-trained deep-learning model. To identify similarity features from test and reference scenes, we applied the Xception and Faiss models to a set of test images with inaccurate spatial locations, as well and precisely-located reference scenes from the general area. Matching reference scenes to the test scenes with the closest similarity index had limited success in improving the precision of test scene location and additional methods have been identified for testing. Data fusion between authoritative geographic data (satellite imaging) and non-authoritative crowdsourced data is an underlying theme throughout this research and methods are tested bring these data to a common geographic form through feature matching and transformations. The automated extraction of supporting information for disaster response from oblique aerial images or ground-level social media images is accomplished through semantic image segmentation and transformation. The non-authoritative data are used to validate the authoritative data collections and processing and optionally, t+0 flood models. In addition, the common form geographic data are combined with other static landscape features to develop spatially-explicit training vectors used in deep generative statistical inference models to develop complex non-linear relationships in static and dynamic data and ultimately derive a spatially continuous and probabilistic assessment of flood damage with the event domain.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A direct-execution parallel architecture for the Advanced Continuous Simulation Language (ACSL)

A direct-execution parallel architecture for the Advanced Continuous Simulation Language (ACSL) is presented which overcomes the traditional disadvantages of simulations executed on a digital computer. The incorporation of parallel processing allows the mapping of simulations into a digital computer to be done in the same inherently parallel manner as they are currently mapped onto an analog computer. The direct-execution format maximizes the efficiency of the executed code since the need for a high level language compiler is eliminated. Resolution is greatly increased over that which is available with an analog computer without the sacrifice in execution speed normally expected with digitial computer simulations. Although this report covers all aspects of the new architecture, key emphasis is placed on the processing element configuration and the microprogramming of the ACLS constructs. The execution times for all ACLS constructs are computed using a model of a processing element based on the AMD 29000 CPU and the AMD 29027 FPU. The increase in execution speed provided by parallel processing is exemplified by comparing the derived execution times of two ACSL programs with the execution times for the same programs executed on a similar sequential architecture.

Carroll, Chester C.↗

A Prototype System for Ground Control Space Telerobotics

A telerobotics system is described which provides supervised autonomous control capability for time-delayed ground-remote control applications. The system includes a local site operator interface for interactive task description and a remote site task execution system. Interactive stereo graphics overlay on video is provided at the local site to update the remote environmental model. The remote site system is capable of nominal task execution as well as monitoring and reflex action. Execution utilizes multiple control modules which execute based upon command parameterization.

robotics autonomous control telerobotics manipulat↗

Serious Gaming for Building a Basis of Certification via Trust and Trustworthiness of Autonomous Systems

Autonomous systems governed by a variety of adaptive and nondeterministic algorithms are being planned for inclusion into safety-critical environments, such as unmanned aircraft and space systems in both civilian and military applications. However, until autonomous systems are proven and perceived to be capable and resilient in the face of unanticipated conditions, humans will be reluctant or unable to delegate authority, remaining in control aided by machine-based information and decision support. Proving capability, or trustworthiness, is a necessary component of certification. Perceived capability is a component of trust. Trustworthiness is an attribute of a cyber-physical system that requires context-driven metrics to prove and certify. Trust is an attribute of the agents participating in the system and is gained over time and multiple interactions through trustworthy behavior and transparency. Historically, artificial intelligence and machine learning systems provide answers without explanation - without a rationale or insight into the machine “thinking”. In order to function as trusted teammates, machines must be able to explain their decisions and actions. This transparency is a product of both content and communication. NASA’s Autonomy Teaming & TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR) project seeks to build a basis for certification of autonomous systems via establishing metrics for trustworthiness and trust in multi-agent team interactions, using AI (Artificial Intelligence) explainability and persistent modeling and simulation, in the context of mission planning and execution, with analyzable trajectories. Inspired by Massively Multiplayer Online Role Playing Games (MMORPG) and Serious Gaming, the proposed ATTRACTOR modeling and simulation environment is similar to online gaming environments in which player (aka agent) participants interact with each other, affect their environment, and expect the simulation to persist and change regardless of any individual agent’s active participation. This persistent simulation environment will accommodate individual agents, groups of self-organizing agents, and large-scale infrastructure behavior. The effects of the emerging adaptation and coevolution can be observed and measured to building a basis of measurable trustworthiness and trust, toward certification of safety-critical autonomous systems.

Allen, B. Danette↗