Results for “Digital command system”

DOE OSTI2025

Implementation and Demonstration of the Digital Twin Certification System Remote Operations Framework

Microreactors are one promising advanced-reactor concept being pursued by the nuclear industry. They are distinguished by a relatively low power output of 20 MWth or less. These microreactors are intended for deployment in applications where conventional small-capacity power solutions, such as diesel generators, are either economically unfeasible or logistically challenging. Such applications include providing electric power and/or heat for remote communities, mining sites, defense installations, and humanitarian and disaster-relief missions. An important feature for the successful deployment of microreactors is their capability to be operated remotely. This capability can significantly reduce staffing costs by eliminating the need for licensed operators to be physically present at each reactor site. Instead, operators can be centralized in a single remote operations center placed in an economically advantageous location, thereby optimizing resources by consolidating expertise and enhancing operational efficiency. However, the implementation of a remote operation system for nuclear reactors raises new concerns regarding the security, reliability, and resilience of such a system. One way in which remote operations can be supported in a manner that maintains system security, reliability, and resilience is through the use of digital twins in a novel framework designed to verify and validate sensor data and commands communicated between the remote operations center and reactor. This framework, known as the Digital Twin Certification System (DTCS), has previously been proposed as an operations architecture that can bring security and resiliency levels of remote nuclear-reactor operations to a level acceptable for commercial deployment. This paper moves the proposed DTCS architecture from concept to reality by presenting the implementation and testing of the system. The rationale and implementation of the DTCS using tools such as DeepLynx and Apache Airflow, is covered in-depth. This is followed by a demonstration of the DTCS by applying the implemented system architecture to the Single Primary Heat Extraction and Removal Emulator, a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The demonstration includes both normal and abnormal operating scenarios to highlight how the DTCS can increase the security, reliability, and resilience of a remote operations system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Implementation and Demonstration of the Digital Twin Certification System Remote Operations Framework

Microreactors are one promising advanced-reactor concept being pursued by the nuclear industry. They are distinguished by a relatively low power output of 20 MWth or less. These microreactors are intended for deployment in applications where conventional small-capacity power solutions, such as diesel generators, are either economically unfeasible or logistically challenging. Such applications include providing electric power and/or heat for remote communities, mining sites, defense installations, and humanitarian and disaster-relief missions. An important feature for the successful deployment of microreactors is their capability to be operated remotely. This capability can significantly reduce staffing costs by eliminating the need for licensed operators to be physically present at each reactor site. Instead, operators can be centralized in a single remote operations center placed in an economically advantageous location, thereby optimizing resources by consolidating expertise and enhancing operational efficiency. However, the implementation of a remote operation system for nuclear reactors raises new concerns regarding the security, reliability, and resilience of such a system. One way in which remote operations can be supported in a manner that maintains system security, reliability, and resilience is through the use of digital twins in a novel framework designed to verify and validate sensor data and commands communicated between the remote operations center and reactor. This framework, known as the Digital Twin Certification System (DTCS), has previously been proposed as an operations architecture that can bring security and resiliency levels of remote nuclear-reactor operations to a level acceptable for commercial deployment. This paper moves the proposed DTCS architecture from concept to reality by presenting the implementation and testing of the system. The rationale and implementation of the DTCS using tools such as DeepLynx and Apache Airflow, is covered in-depth. This is followed by a demonstration of the DTCS by applying the implemented system architecture to the Single Primary Heat Extraction and Removal Emulator, a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The demonstration includes both normal and abnormal operating scenarios to highlight how the DTCS can increase the security, reliability, and resilience of a remote operations system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Preliminary proof-of-concept of real-time divertor heat flux control from infrared cameras with nitrogen injection in the DIII-D tokamak

In future tokamak reactors like ITER and the Fusion Pilot Plant (FPP), real-time feedback control of heat flux to the plasma-facing components (PFC) will be critical for steady-state operation. This work presents the first experimental demonstration of real-time divertor heat flux estimation with infrared thermography and feedback control with impurity seeding on the DIII-D tokamak. The flexible infrastructure of the Plasma Control System (PCS) on DIII-D makes this new capability possible. The PCS software runs on a gateway computer system, and five real-time compute nodes. An array of low latency streaming digitizers from D-TACQ Solutions connects to these real-time computers to collect and process data, and send commands to actuators during plasma discharges. This system handles the signal IO from the tokamak and allows the PCS to utilize the diagnostic data necessary to perform control in real-time. Feedback control on heat flux was accomplished by feeding infrared camera data from the “Infrared TV” (IRTV) camera to a custom-developed User Datagram Protocol (UDP) server. This server transmits infrared data to a newly developed PCS algorithm that estimates the heat flux to PFC. Here, a proportional integral derivative (PID) controller minimizes the error between a heat flux reference and the real-time estimate by injecting nitrogen gas into the divertor.

Algorithm development↗

DOE OSTI2025

Employing a Hardware-in-the-Loop Approach to Realize a Fully Homomorphic Controller for a Small Modular Advanced High Temperature Reactor

This paper addresses the cybersecurity challenges of advanced nuclear reactors by integrating fully homomorphic encryption (FHE) into their control systems, enabling encrypted processing of control signals without compromising functionality. Advanced nuclear reactors, including Small Modular Reactors (SMRs) and microreactors, aim to achieve autonomous and remote operations, reducing costs and enhancing competitiveness. However, these advancements expand the attack surface for cyberattacks, particularly in autonomous and remote operation scenarios. Cyberattacks can exploit vulnerabilities to manipulate physical processes, causing shutdowns, asset damage, or public harm. Such attacks begin with passive reconnaissance, where adversaries intercept communications or observe behaviors to gather information, which is then leveraged to execute cyber-physical attacks by injecting malicious commands. Nuclear power must adopt cybersecurity protection measures to secure the integrity and availability of their digital control systems. This paper demonstrates the application of FHE to secure operations by enabling encrypted processing of sensitive signals and parameters -- ensuring privacy without exposing data. FHE supports secure mathematical operations on encrypted data without requiring decryption. Using a hardware-in-the-loop (HIL) approach, this paper implements an FHE-integrated controller on a BeagleBone Black (BBB) controlling a simulation of the Small Modular Advanced High Temperature Reactor (SmAHTR). By doing so, the encrypted controller protects the integrity of critical set points and control signals during transmission and processing. Thus, FHE-integrated controllers enhance secure operations of advanced nuclear reactors while maintaining functionality.

control systems↗

DOE OSTI2021

A Self-Synchronizing Underwater Acoustic Network for Mooring Load Monitoring of a Wave Energy Converter

This paper reports on the development of a self-synchronizing underwater acoustic network developed for remote monitoring of mooring loads in Wave Energy Converters (WECs). This network uses Time Division Multiple Access and operates self-contained with the ability for users to remotely transmit commands to the network as needed. Each node is a self-contained unit, consisting of a protocol adaptor board, an FAU-DPAM underwater acoustic modem and a battery pack. A node can be connected to a load cell, to a topside user or to the WEC. Every node is swapable. The protocol adaptor board, named Protocol Adaptor for Digital LOad Cell (PADLOC) supports a variety of digital load cell message formats (CAN, MODBUS, custom ASCII) and underwater acoustic modem serial formats. PADLOC enables topside users to connect to separate load cells through a user-specific command. This is especially important if the user is monitoring multiple load cells during deployment or maintenance, when the primary data system may be offline. Each PADLOC board handles formatting, buffering and has a one-on-one serial connection with each pair (node) of a digital load cell and acoustic modem. In addition, each PADLOC board handles the timekeeping and power saving features for each node. The only limitation is the data bit rate and delay limitations associated with the underwater acoustic modem. A four node self-synchronizing network has been developed to demonstrate the load cell monitoring capability using the PADLOC technology on the CalWave WEC.

acoustic↗

DOE OSTI2026

Graphical User Interface for a Biasing Board for the PSEC6

The PSEC6 is an application-specific integrated circuit (ASIC) designed for a readout system for a large area picosecond photodetector (LAPPD). The PSEC6 is currently in fabrication and pending testing. The testing system for the PSEC5, the previous iteration of the ASIC, required expensive and non-portable equipment, because the ASIC needs twelve adjustable reference voltages. The new testing system consists of an low-cost, open-source, cross-platform graphical user interface (GUI), a digital system, and a biasing board. The digital system is the interface between the GUI and biasing board, and can be implemented on a microcontroller or field-programmable gate array (FPGA). The biasing board contains twelve digital-to-analog converters (DACs) that are configurable via the GUI, which gives users the ability to write voltage values to all or specific DACs. The GUI was developed in C on Linux using the widget library GTK4 and cross-compiled for Windows compatibility. I2C and SPI protocols were implemented on an Adafruit Feather ESP32-S3 microcontroller to write commands to the DACs and PSEC6. A hardware implementation of the I2C protocol is in development on an FPGA. Since LAPPDs will be used by the Accelerator Neutrino Neutron Interaction Experiment (ANNIE) at Fermilab, the PSEC6 testing system in this internship project can potentially benefit future neutrino research. The project is relevant to the Department of Energy’s microelectronics mission, because the PSEC6 is an ASIC that will handle fast time signals arriving from the detector for readout. It also provided experience with building a cross-platform user interface, practicing digital design and implementation in hardware description language (HDL), and using simulations to inform new design iterations.

Guerrero, Sasha Camila [North Central Coll.]↗

DOE OSTI2026

Graphical User Interface for a Biasing Board for the PSEC6

The PSEC6 is an application-specific integrated circuit (ASIC) designed for a readout system for a large area picosecond photodetector (LAPPD). The PSEC6 is currently in fabrication and pending testing. The testing system for the PSEC5, the previous iteration of the ASIC, required expensive and non-portable equipment, because the ASIC needs twelve adjustable reference voltages. The new testing system consists of an low-cost, open-source, cross-platform graphical user interface (GUI), a digital system, and a biasing board. The digital system is the interface between the GUI and biasing board, and can be implemented on a microcontroller or field-programmable gate array (FPGA). The biasing board contains twelve digital-to-analog converters (DACs) that are configurable via the GUI, which gives users the ability to write voltage values to all or specific DACs. The GUI was developed in C on Linux using the widget library GTK4 and cross-compiled for Windows compatibility. I2C and SPI protocols were implemented on an Adafruit Feather ESP32-S3 microcontroller to write commands to the DACs and PSEC6. A hardware implementation of the I2C protocol is in development on an FPGA. Since LAPPDs will be used by the Accelerator Neutrino Neutron Interaction Experiment (ANNIE) at Fermilab, the PSEC6 testing system in this internship project can potentially benefit future neutrino research. The project is relevant to the Department of Energy’s microelectronics mission, because the PSEC6 is an ASIC that will handle fast time signals arriving from the detector for readout. It also provided experience with building a cross-platform user interface, practicing digital design and implementation in hardware description language (HDL), and using simulations to inform new design iterations.

Guerrero, Sasha Camila [North Central Coll.]↗

DOE OSTI2020

Evaluating software defined networking solutions to reduce the digital attack surface of nuclear security systems

Most nuclear security systems used today were not designed for today’s threat environment. Systems that were intended to be stand alone are now interconnected. Devices that have a single purpose are built on multi-purpose platforms and communication protocols that, while effective, have no ability to authenticate authorized versus unauthorized commands. These attributes provide an attacker significant ability to affect the system, pivot throughout the interconnected networks, and remain undetected if he/she is able to compromise a single node. Software defined networking (SDN) has been used for years by information technology (IT) cloud service providers to quickly provision or remove servers or other systems to meet changing demand. The same concept has recently been applied to operational technology (OT) systems to enable very fast failover on critical systems that have stringent and deterministic (<5ms) transmit/receive times. By carefully engineering the communication flows through a network using preplanned routes and specific pathways it is possible to achieve deterministic and extremely reliable message delivery even when components fail. This engineering approach to network design has added security benefits including securing the networking control plane, eliminating network scanning and mapping, inhibiting ARP spoofing and host masquerading, eliminating unauthorized network pivoting and enabling greater situational awareness on the network. SDN in OT environments is new but early testing in electrical power and other critical infrastructure has shown it to be a very powerful tool for building reliable networks and reducing the digital attack surface of the network. The authors tested a software defined network switch on a simple physical protection system with components commonly found in nuclear security systems and found improved mitigations to denial of service attacks, lateral movement and network reconnaissance. The paper details the tests and their results.

Cyber security, Nuclear security, software defined↗

DOE OSTI2025

Real-Time Testbed for Studying Cyberattacks and Defense in DER-integrated Smart Inverter Systems

In this paper, we propose a Hardware-in-the-Loop (HIL) simulation testbed suitable for the implementation and testing of realistic cyberattacks on grid-tied smart inverter systems integrated with Distributed Energy Resources (DER) that use the Distributed Network Protocol-3 (DNP3) protocol for communications between grid components. Specifically, our testbed combines a Real-Time Digital Simulator (RTDS) NovaCor device, outfitted with GNETx2 network interface cards, a gridtied DER topology implemented via the RTDS software package RSCAD, and a custom virtual network that emulates a man in the middle attacker. The Man-in-the-Middle (MITM) attacker captures DNP3 traffic and falsifies telemetry data in DNP3 packets to trigger unwarranted commands from a DNP3 controller that exploit smart inverter grid support functions. We choose DNP3 and implement grid support functions according to the IEEE Std. 1547-2018 mandated for the interconnection and interoperability of DER power systems with associated power components. Furthermore, we develop a protocol payload agnostic attack detection framework that leverages the round-trip time (RTT) anomalies between DNP3 requests and responses and can detect the presence of attacks without having to analyze the payload’s contents, while balancing trade-offs between false alarm counts, missed detections, and time to detection. To facilitate further research, we publicly release benign and attack network traffic exchanged between various sensors, controllers, and actuators in our grid-tied inverter testbed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Securing Smart Manufacturing: Detection of Cyber-Physical Attacks in CNC-Based Systems

As Industry 4.0 advances, the integration of computer numerical control (CNC) machines and advanced manufacturing technologies is transforming production into smart manufacturing systems that blend physical and digital processes as cyber-physical systems. However, this increased cyber-physical connectivity exposes manufacturing systems to cyber threats that can cause severe operational and financial disruptions. This paper presents a comparative study on cyber attacks and anomaly detection techniques in manufacturing, focusing on network traffic from CNC machines. The data extracted from network packets includes machine commands and control signals exchanged between the machine's interface and control system, crucial for maintaining operational integrity. We explore two types of cyber attacks, design modification and command injection, which pose substantial risks to CNC machine productivity and system integrity. Our investigation involves experiments on a real CNC system, highlighting the urgent need for effective detection mechanisms. To address these threats, we evaluate three anomaly detection methods: dynamic time warping (DTW), rolling average, and a deep learning, long short-term memory (LSTM) time-series-based autoencoder. Each is assessed for its effectiveness in identifying anomalous behaviors caused by the attacks. Our findings demonstrate the unique strengths and limitations of each detection technique, providing a deeper understanding of their applicability in realworld manufacturing environments. The comparative analysis indicates that while certain methods are highly effective against specific attack types, others offer broader applicability across different attacks. This study contributes to the accurate detection of anomalies in CNC machining processes, thereby enhancing the reliability and security of smart manufacturing systems against diverse cyber threats.

Williams, Bethanie [Tennessee Technological Univer↗

DOE OSTI2023

Creating a Simulation Platform for Research and Development of Advanced Control Methods

Advanced nuclear reactors are essential to meet the changing energy requirements throughout both the United States and the rest of world. In addition to other features, they are designed to enable deployment in remote locations and operate in a fully (or near-fully) autonomous manner, which will require a new control paradigm. To realize autonomously operating reactors, the U.S. Department of Energy’s Nuclear Energy Enabling Technologies Advanced Sensors and Instrumentation (NEET ASI) program conducts research and development into the enabling technologies and methods needed, including digital twins, machine learning, and risk modeling, in addition to various types of control methods. These technologies and methods are the key foundations needed to achieve fully autonomous systems. To develop and evaluate the technologies and methods necessary for achieving autonomous operations, it is critical to identify a software tool capable of integrating all the required elements. In surveying the available solutions, no software platforms were identified that could accomplish what was needed without introducing drawbacks. This challenge was the motivation for the current effort: to develop a software platform that can seamlessly integrate autonomouscontrol-enabling technologies and methods, allowing for accelerated research and development and transfer of ideas. The resulting platform, known as the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND), is Python-based, and leverages open-source tools to provide flexibility and facilitate building upon prior research. It is designed to enable advanced reactor developers to deploy and test advanced control technologies and methods coupled with their own models, solutions, and hardware. Given the substantial undertaking of developing such a platform, the current effort focused on laying down scalable, flexible software foundations and infrastructure, then demonstrating the platform via a use case. These foundations included developing generic modules, which contain the base variable and system blocks (the information and functional building blocks, respectively, that can be used to design a simulation) and the data handling and storage blocks needed to exchange information between the various blocks; as well as enablingtechnology-specific modules. This platform was evaluated via a use case, which was to simulate and control a process for the Microreactor Automated Control System (MACS) test bed. While MACS is not currently directly coupled to any specific microreactor physics, it was initially developed in concert with the Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor, and so the MARVEL physics are used here. As part of this use case, several enabling-technology-specific blocks within COMMAND were integrated, including a proportional integral derivative (PID) control block, a Reactor Excursion and Leak Analysis Program (RELAP5-3D) block, and an anomaly detection block. The COMMAND software platform was successfully demonstrated to achieve the scalability and flexibility objectives of this effort and will be leveraged by the program’s research efforts to advance state of the art control methodologies towards autonomous operations of advanced reactors. As new use cases are created and implemented, it is anticipated that COMMAND will continue to grow and evolve to meet new requirements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Development of a Hardware-in-The-Loop Testbed for a Decentralized, Data-Driven Electric Vehicle Charging Control Algorithm

This study presents the design of an electric vehicle (EV)-grid integration (EVGI) hardware test-bed to implement smart EV charging algorithms. Here, the proposed test-bed also allows to create different grid events via flexible integration of other power hardware (e.g., controllable loads and battery energy storage systems) and test their impacts on EV charging. The design uses a real-time digital simulator to realize a complex distribution grid model with primary and secondary networks. A grid simulator physically realizes the selected nodes of the simulated grid to power an actual EV, forming a hardware-in-the-loop (HIL) test setup. The EV-grid integration is demonstrated based on the custom hardware and software implementation of the J1772 charging protocol using dSPACE MicroLabBox, operating as a custom EV Supply Equipment (EVSE). The HIL test-bed features a novel testing platform for accurate implementation and analysis of scalable charging algorithms. To this end, a data-driven, decentralized, model-free charging controller based on the Additive Increase and Multiplicative Decrease (AIMD) algorithm is presented and validated on an EV using the HIL test-bed. We tested the proposed algorithm under various case studies, and presented a comparison study with an existing droop-based, decentralized charging solution. The results showed that the EV successfully performed charging commands generated by the EVSE and regulated its charging power to effectively reduce the system loading caused by high EV penetration.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Science Federation Emulation Testbed: Demonstration of VFSIE Functionalities

The Virtual Federated Science Instrument Environment (VFSIE) is a digital twin of a federated infrastructure of multiple sites with science instruments and computing systems that are geographically dispersed. It emulates the federation using containers and virtual hosts (vhosts) connected over local and wide-area networks for the main purpose of supporting the development and testing of science workflows and software stacks, which will subsequently transition to the physical infrastructure. In this demo, we present VFSIE of a four sites scenario and illustrate the following use cases: (i) execution of federation stack components that expose resources to enable a science user to execute workflows, (ii) execution of remote control commands of beam-line instruments to collect measurements and position the sensor, and (iii) remote execution and access of Jupyter Notebook for tomographic image computations

Al Najjar, Anees↗

DOE OSTI2024

Achieving Cyber-Resilience for Power Systems using a Learning, Model-Assisted Blockchain Framework

The secure integration and management of distributed energy resources (DER) and power aggregators in the electric grid requires secure communications and a physics-aware Command and Control (C2) strategy. A Blockchain (BC)-based overlay network was developed to provide a security layer for the existing power grid network that mitigates risks in current and legacy network and C2 protocols. By integrating a Model-Assisted Machine Learning (MAML) framework with a Secure Blockchain Overlay Network (SBON) a defense-in-depth strategy was achieved. In our approach, the MAML framework leveraged a smart contract framework to gather network data and learn the dynamics of DER to develop detection strategies for attacks targeting sensors and actuators used by DER. The MAML framework learned dynamical systems models for individual DERs to detect sensor attacks. For DER we utilized a Digital Twin (DT) to accelerate the learning process for a model resistant to stealthy attacks. The project created DT for PV inverters and BESS. The DTs were coupled with a model-assisted, data-driven learning of DER behavior. Specifically, we evaluated architectures for model-based learning with model-free fine-tuning. Additionally, differential privacy techniques were used to obfuscate data, while still allowing the computation of attack detection results based on obfuscated data. The SBON developed leverages a private permissioned blockchain network orchestrated with the Hyperledger Fabric framework. To connect the cyber world, which orchestrates the blockchain fabric, and the physical world where the power network resides, we developed a system implementation to enable the secure interaction of the physical world and the abstracted blockchain.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Opportunities, Challenges, and Research Needs for Remote Microreactor Operations

As the nuclear industry develops new advanced reactor technologies, many companies are embracing this advancement by pursuing the development of microreactors. The term microreactor generally refers to a nuclear reactor with an operating power of 20 MW(thermal) or less. The power range of microreactors makes them appealing for many use cases, such as powering remote communities, mining sites, and military bases. Most of the microreactor designs being pursued are expected to incorporate remote facility operations into the final product. However, no framework has yet been developed to determine what remote operations systems require for reliable, resilient, and secure operation of a microreactor. Here, this work identifies the research needs for challenges that are unique to remote operations and monitoring for microreactors, specifically regarding instrumentation and control, communication methods, regulatory requirements, and operational policies. The types of commands and sensor measurements that must be transmitted between the facilities, as well as methods for verifying the trustworthiness of these signals, are assessed. This work evaluates the security, reliability, and performance requirements that must be met when considering the selection of communication hardware and protocols for use in remote operations. Also, an assessment was performed to study how remote operations fit within current regulatory requirements and what may need to be updated in regulatory policy to allow for remote operation. Finally, the operational contingencies unique to remote operations that must be in place for responses to abnormal events are identified. This paper identifies the challenges and research opportunities within the areas of importance for the design of remote operation systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

A Real-Time Testbed for Smart Inverter Cyber Security Studies

Distributed energy resources (DER) have become a popular solution to modern-day issues surrounding the efficiency and reliability of power generation, as well as climate change concerns. Energy centers are shifting towards incorporating smart inverters with embedded functionalities such as high voltage ride through (HVRT), low voltage ride through (LVRT), active and reactive power compensation. However, the integration of smart inverters leave DER systems highly vulnerable to cybersecurity threats. The distributed network protocol 3 (DNP3) is a common method of communication between grid-tied hardware. Despite its popularity, the level of security leaves all hardware connected to the grid at risk of severe cyber-attacks. Thus, it is important to study any potential cybersecurity threats towards grid-tied smart inverters to mitigate cybersecurity vulnerabilities and refine existing cyber-security protections. This report describes the proposed testbed design to study cybersecurity threats to smart inverters. The testbed utilizes a real-time simulation case in RSCAD that includes a grid-tied wind turbine (WT) topology featuring two back-to-back two-level voltage source converters (BTB,2L-VSCs) and a permanent magnet synchronous machine (PMSM). The simulated case runs within the NovaCor real time digital simulator (RTDS). This report focuses on the design and implementation of a single module of the GTNETx2 card as a distributed network protocol and the configuration of an IEEE 1518 DNP database file that includes input and output variables mapped to different connection points in the grid that transmit and receive discrete, analog, and binary signals on command. This allows realistic emulation of the communication between the smart inverter and the grid for cybersecurity studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗