Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical software”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Parachute Models Used in the Mars Science Laboratory Entry, Descent, and Landing Simulation

An end-to-end simulation of the Mars Science Laboratory (MSL) entry, descent, and landing (EDL) sequence was created at the NASA Langley Research Center using the Program to Optimize Simulated Trajectories II (POST2). This simulation is capable of providing numerous MSL system and flight software responses, including Monte Carlo-derived statistics of these responses. The MSL POST2 simulation includes models of EDL system elements, including those related to the parachute system. Among these there are models for the parachute geometry, mass properties, deployment, inflation, opening force, area oscillations, aerodynamic coefficients, apparent mass, interaction with the main landing engines, and off-loading. These models were kept as simple as possible, considering the overall objectives of the simulation. The main purpose of this paper is to describe these parachute system models to the extent necessary to understand how they work and some of their limitations. A list of lessons learned during the development of the models and simulation is provided. Future improvements to the parachute system models are proposed.

Cruz, Juan R.↗

Spinoff 2013

Topics covered include: Innovative Software Tools Measure Behavioral Alertness; Miniaturized, Portable Sensors Monitor Metabolic Health; Patient Simulators Train Emergency Caregivers; Solar Refrigerators Store Life-Saving Vaccines; Monitors Enable Medication Management in Patients' Homes; Handheld Diagnostic Device Delivers Quick Medical Readings; Experiments Result in Safer, Spin-Resistant Aircraft; Interfaces Visualize Data for Airline Safety, Efficiency; Data Mining Tools Make Flights Safer, More Efficient; NASA Standards Inform Comfortable Car Seats; Heat Shield Paves the Way for Commercial Space; Air Systems Provide Life Support to Miners; Coatings Preserve Metal, Stone, Tile, and Concrete; Robots Spur Software That Lends a Hand; Cloud-Based Data Sharing Connects Emergency Managers; Catalytic Converters Maintain Air Quality in Mines; NASA-Enhanced Water Bottles Filter Water on the Go; Brainwave Monitoring Software Improves Distracted Minds; Thermal Materials Protect Priceless, Personal Keepsakes; Home Air Purifiers Eradicate Harmful Pathogens; Thermal Materials Drive Professional Apparel Line; Radiant Barriers Save Energy in Buildings; Open Source Initiative Powers Real-Time Data Streams; Shuttle Engine Designs Revolutionize Solar Power; Procedure-Authoring Tool Improves Safety on Oil Rigs; Satellite Data Aid Monitoring of Nation's Forests; Mars Technologies Spawn Durable Wind Turbines; Programs Visualize Earth and Space for Interactive Education; Processor Units Reduce Satellite Construction Costs; Software Accelerates Computing Time for Complex Math; Simulation Tools Prevent Signal Interference on Spacecraft; Software Simplifies the Sharing of Numerical Models; Virtual Machine Language Controls Remote Devices; Micro-Accelerometers Monitor Equipment Health; Reactors Save Energy, Costs for Hydrogen Production; Cameras Monitor Spacecraft Integrity to Prevent Failures; Testing Devices Garner Data on Insulation Performance; Smart Sensors Gather Information for Machine Diagnostics; Oxygen Sensors Monitor Bioreactors and Ensure Health and Safety; Vision Algorithms Catch Defects in Screen Displays; and Deformable Mirrors Capture Exoplanet Data, Reflect Lasers.

Source record↗

Voyager Interstellar Mission: Challenges of Flying a Very Old Spacecraft on a Very Long Mission

Two Voyager spacecraft were launched in 1977. After the successful flybys of Jupiter and Saturn by both Voyagers and Uranus and Neptune by Voyager 2, the mission has been extended for another 30 years in search of the transition region between the dominance of the solar energy and interstellar energy. The Voyager Interstellar Mission (VIM) started on January 1, 1990. It can be characterized by several factors including extremely long communication distances, aging hardware, reduced staffing levels and difficulty in obtaining Deep Space Network (DSN) resources necessitated by the increasing distance between the spacecraft and Earth. The mission was redesigned to compensate for such factors while maximizing the science return. After 25 years of VIM and several significant science discoveries, both Voyager spacecraft are still functioning well and the Voyager flight team is preparing for an even longer mission - until the year 2025 and beyond. In order to work around the challenges and to continue the mission even further, the team has been implementing numerous changes, mainly through flight software modifications and hardware reconfiguration. The major drivers for the changes are two-fold: resource constraints (such as decreasing power output and difficulty in obtaining the necessary DSN coverage) and anomalies due to the aging hardware. The majority of changes occur through flight software modifications so the state of the on-board responses is appropriate for the changing space environment and mission phase, and the flight software is compatible in allowing the maximum data gathering. The on-board flight software routines such as baseline sequence, fault protection routines, the High Gain Antenna POINTing to Earth (HPOINT) table, and long-term events table need to be maintained through flight software updates. The changes also occur through hardware reconfiguration such as selecting the backup Hybrid Buffer Interface Circuits (HYBIC) or attitude propulsion thrusters. This paper will describe the challenges of VIM and what has been done to overcome or mitigate those challenges. The primary focus will be the major flight software changes made during VIM and the changes that are in store for the near future in preparation for continuing the extended mission, from the originally projected year of 2020 out to the year 2025 and possibly beyond.

Matsumoto, Sun Kang↗

Electrical Power System Sizing Within the Numerical Propulsion System Simulation

Electrified aircraft propulsion seeks to address ambitious goals in the commercial airline industry, including significant decreases in fuel burn, emissions, noise, and takeoff field length. In order to move these electrified propulsion concepts forward, analysis tools are needed that can model propulsion systems containing both gas turbine and power system components. This work presents the definition of an electric port, a set of electrical power systems tools, and simulation examples for the Numerical Propulsion System Simulation (NPSS) software. NPSS is the industry standard modeling and simulation package for aircraft propulsion systems, and the ability to design, size, integrate, and analyze electric power systems will enable industry efforts towards the development of electrified aircraft propulsion.

aircraft electrification↗

Fusing Symbolic and Numerical Diagnostic Computations

X-2000 Anomaly Detection Language denotes a developmental computing language, and the software that establishes and utilizes the language, for fusing two diagnostic computer programs, one implementing a numerical analysis method, the other implementing a symbolic analysis method into a unified event-based decision analysis software system for realtime detection of events (e.g., failures) in a spacecraft, aircraft, or other complex engineering system. The numerical analysis method is performed by beacon-based exception analysis for multi-missions (BEAMs), which has been discussed in several previous NASA Tech Briefs articles. The symbolic analysis method is, more specifically, an artificial-intelligence method of the knowledge-based, inference engine type, and its implementation is exemplified by the Spacecraft Health Inference Engine (SHINE) software. The goal in developing the capability to fuse numerical and symbolic diagnostic components is to increase the depth of analysis beyond that previously attainable, thereby increasing the degree of confidence in the computed results. In practical terms, the sought improvement is to enable detection of all or most events, with no or few false alarms.

James, Mark↗

Electromagnetic Field Effects in Semiconductor Crystal Growth

This proposed two-year research project was to involve development of an analytical model, a numerical algorithm for its integration, and a software for the analysis of a solidification process under the influence of electric and magnetic fields in microgravity. Due to the complexity of the analytical model that was developed and its boundary conditions, only a preliminary version of the numerical algorithm was developed while the development of the software package was not completed.

Dulikravich, George S.↗

Challenges and Demands on Automated Software Revision

In the past three decades, automated program verification has undoubtedly been one of the most successful contributions of formal methods to software development. However, when verification of a program against a logical specification discovers bugs in the program, manual manipulation of the program is needed in order to repair it. Thus, in the face of existence of numerous unverified and un- certified legacy software in virtually any organization, tools that enable engineers to automatically verify and subsequently fix existing programs are highly desirable. In addition, since requirements of software systems often evolve during the software life cycle, the issue of incomplete specification has become a customary fact in many design and development teams. Thus, automated techniques that revise existing programs according to new specifications are of great assistance to designers, developers, and maintenance engineers. As a result, incorporating program synthesis techniques where an algorithm generates a program, that is correct-by-construction, seems to be a necessity. The notion of manual program repair described above turns out to be even more complex when programs are integrated with large collections of sensors and actuators in hostile physical environments in the so-called cyber-physical systems. When such systems are safety/mission- critical (e.g., in avionics systems), it is essential that the system reacts to physical events such as faults, delays, signals, attacks, etc, so that the system specification is not violated. In fact, since it is impossible to anticipate all possible such physical events at design time, it is highly desirable to have automated techniques that revise programs with respect to newly identified physical events according to the system specification.

Bonakdarpour, Borzoo↗

Dense Feature Tracking of Atmospheric Winds with Deep Optical Flow

Atmospheric winds are a key physical phenomenon impacting natural hazards, energy transport, ocean currents, large-scale circulation, and ecosystem fluxes. Observing winds is a complex process and presents a large gap in NASA’s Earth Observation System. Atmospheric motion vectors (AMVs) aim to fill this gap by making numerical estimates of cloud movement between sequences of multi-spectral satellite images, tracking clouds and water vapor. Recent imaging hardware and software advancements have enabled the use of numerical optical flow techniques to produce accurate and dense vector fields outperforming traditional methods. This work presents WindFlow as the first machine learning based system for feature tracking atmospheric motion using optical flow. Due to the lack of large-scale satellite-based observations, we leverage high-resolution numerical simulations from NASA's GEOS-5 Nature Run to perform supervised learning and transfer to satellite images. We demonstrate that our approach using deep learning based optical flow scales to ultra-high-resolution images of size 2881x5760 with less than 1 m/s bias and 2.5 m/s average error. Four network and learning architectures are compared and it is found that recurrent all-pairs field transforms (RAFT) produces the lowest errors on all metrics for wind speed and direction. Results on held out numerical outputs shows RAFT's good performance in each of the spatial, temporal, and physical dimensions. A comparison between WindFlow and an operational AMV product against rawinsonde observations show that RAFT transfers across simulations and thermal infrared satellite observations. This work shows that machine learning based optical flow is an efficient approach to generating robust feature tracking for AMVs consistently over large regions.

Atmospheric winds↗

Methodology for Designing Fault-Protection Software

A document describes a methodology for designing fault-protection (FP) software for autonomous spacecraft. The methodology embodies and extends established engineering practices in the technical discipline of Fault Detection, Diagnosis, Mitigation, and Recovery; and has been successfully implemented in the Deep Impact Spacecraft, a NASA Discovery mission. Based on established concepts of Fault Monitors and Responses, this FP methodology extends the notion of Opinion, Symptom, Alarm (aka Fault), and Response with numerous new notions, sub-notions, software constructs, and logic and timing gates. For example, Monitor generates a RawOpinion, which graduates into Opinion, categorized into no-opinion, acceptable, or unacceptable opinion. RaiseSymptom, ForceSymptom, and ClearSymptom govern the establishment and then mapping to an Alarm (aka Fault). Local Response is distinguished from FP System Response. A 1-to-n and n-to- 1 mapping is established among Monitors, Symptoms, and Responses. Responses are categorized by device versus by function. Responses operate in tiers, where the early tiers attempt to resolve the Fault in a localized step-by-step fashion, relegating more system-level response to later tier(s). Recovery actions are gated by epoch recovery timing, enabling strategy, urgency, MaxRetry gate, hardware availability, hazardous versus ordinary fault, and many other priority gates. This methodology is systematic, logical, and uses multiple linked tables, parameter files, and recovery command sequences. The credibility of the FP design is proven via a fault-tree analysis "top-down" approach, and a functional fault-mode-effects-and-analysis via "bottoms-up" approach. Via this process, the mitigation and recovery strategy(s) per Fault Containment Region scope (width versus depth) the FP architecture.

Barltrop, Kevin↗

Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PHILMS) (Technical Report)

The research work at University of California Santa Barbara (UCSB) resulted in several new developments in the areas of scientific machine learning, numerical analysis, and practical methods for data-driven modeling, prediction, reductions, and simulation. Many of the projects were carried out in collaboration with members of the national laboratories at Sandia National Laboratories (SNL), Pacific Northwestern National Laboratories (PNNL), and other institutions. Results included developing new scientific machine learning methods, related theory and mathematical frameworks for analysis and training, data-driven numerical solvers, and related tools and software for scientific computation. During the support period, over 16+ papers were submitted for publication, and 4 open-source software packages were developed and released (available at http://atzberger.org/). In addition, 7+ students and 2 post-docs were mentored in collaboration with the laboratory staff for future careers in academia, government labs, and industry.

97 MATHEMATICS AND COMPUTING↗

Proceedings of the First NASA Formal Methods Symposium

Topics covered include: Model Checking - My 27-Year Quest to Overcome the State Explosion Problem; Applying Formal Methods to NASA Projects: Transition from Research to Practice; TLA+: Whence, Wherefore, and Whither; Formal Methods Applications in Air Transportation; Theorem Proving in Intel Hardware Design; Building a Formal Model of a Human-Interactive System: Insights into the Integration of Formal Methods and Human Factors Engineering; Model Checking for Autonomic Systems Specified with ASSL; A Game-Theoretic Approach to Branching Time Abstract-Check-Refine Process; Software Model Checking Without Source Code; Generalized Abstract Symbolic Summaries; A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing; Component-Oriented Behavior Extraction for Autonomic System Design; Automated Verification of Design Patterns with LePUS3; A Module Language for Typing by Contracts; From Goal-Oriented Requirements to Event-B Specifications; Introduction of Virtualization Technology to Multi-Process Model Checking; Comparing Techniques for Certified Static Analysis; Towards a Framework for Generating Tests to Satisfy Complex Code Coverage in Java Pathfinder; jFuzz: A Concolic Whitebox Fuzzer for Java; Machine-Checkable Timed CSP; Stochastic Formal Correctness of Numerical Algorithms; Deductive Verification of Cryptographic Software; Coloured Petri Net Refinement Specification and Correctness Proof with Coq; Modeling Guidelines for Code Generation in the Railway Signaling Context; Tactical Synthesis Of Efficient Global Search Algorithms; Towards Co-Engineering Communicating Autonomous Cyber-Physical Systems; and Formal Methods for Automated Diagnosis of Autosub 6000.

Denney, Ewen↗

Numerical Simulations For the F-16XL Aircraft Configuration

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the kε turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Elmiligui, Alaa A.↗

Benchmark study of a new simplified DFN model for shearing of intersecting fractures and faults

It is challenging to quantitatively predict shearing of intersecting fractures/faults because of dynamic frictional contacts accompanied by possible nonlinear rock deformation. To address such challenges, a new conceptual model—the simplified DFN model—was proposed and validated by Hu et al. 46 to use major paths (MPs) to represent complicated DFNs for calculation of shearing. In this work, we conducted a benchmark study for three examples that involve different levels of complexity of intersecting fractures, and correspondingly different numbers of MPs. The codes and software that were used in the benchmark cover a range of continuum, discontinuum and hybrid numerical methods: NMM (LBNL), FLAC3D (LBNL), GBDEM (KIGAM), FRACOD (DynaFrax), and CASRock (CAS). The general consistency between DFN and MP cases as predicted by all the codes/software demonstrates that major paths can be used to simplify the geometry of DFNs in a wide range of software. Disagreement in results made by some software and potential future improvements are discussed. We show that (1) shearing of one or multiple major fractures can be reduced if there are multiple smaller intersecting fractures in that area, which is a useful basis for understanding and controlling induced seismicity and merits further analysis, and (2) the agreement achieved in the benchmark examples provide confidence that the simplified DFN model is a promising conceptual model that can be used for different types of numerical approaches and software for simplifying the analysis of the shearing of intersecting fractures and faults.

58 GEOSCIENCES↗

Democratizing uncertainty quantification

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.

Benchmarks↗

Using Bond Graphs for Articulated, Flexible Multi-bodies, Sensors, Actuators, and Controllers with Application to the International Space Station

Conceptually, modeling of flexible, multi-body systems involves a formulation as a set of time-dependent partial differential equations. However, for practical, engineering purposes, this modeling is usually done using the method of Finite Elements, which approximates the set of partial differential equations, thus generalizing the approach to all continuous media. This research investigates the links between the Bond Graph method and the classical methods used to develop system models and advocates the Bond Graph Methodology and current bond graph tools as alternate approaches that will lead to a quick and precise understanding of a flexible multi-body system under automatic control. For long endurance, complex spacecraft, because of articulation and mission evolution the model of the physical system may change frequently. So a method of automatic generation and regeneration of system models that does not lead to implicit equations, as does the Lagrange equation approach, is desirable. The bond graph method has been shown to be amenable to automatic generation of equations with appropriate consideration of causality. Indeed human-interactive software now exists that automatically generates both symbolic and numeric system models and evaluates causality as the user develops the model, e.g. the CAMP-G software package. In this paper the CAMP-G package is used to generate a bond graph model of the International Space Station (ISS) at an early stage in its assembly, Zvezda. The ISS is an ideal example because it is a collection of bodies that are articulated, many of which are highly flexible. Also many reaction jets are used to control translation and attitude, and many electric motors are used to articulate appendages, which consist of photovoltaic arrays and composite assemblies. The Zvezda bond graph model is compared to an existing model, which was generated by the NASA Johnson Space Center during the Verification and Analysis Cycle of Zvezda.

Montgomery, Raymond C.↗

NCAP: Noncanonical Amino Acid Parameterization Software for CHARMM Potentials

Noncanonical Amino Acids (NCAAs) provide numerous avenues for introduction of novel functionality to peptides and proteins. NCAAs can be incorporated through solid phase synthesis or genetic code expansion in conjugation with heterologous expression of the encoded protein modification. Due to the difficulty of synthesis, wide chemical space and lack of empirically resolved structures modeling the effects of NCAA mutation is critical for rational protein design. To evaluate the structural and functional perturbations NCAAs introduce we utilize molecular potentials that describe the forces in protein structure. Most potentials such as CHARMM are designed to model canonical residues but can be parameterized in include novel NCAAs. Here, in this work, we introduce NCAP a software package to generate CHARMM compatible parameters from quantum chemical calculation. Unlike currently available tools NCAP is designed to recognize NCAA structure and automatically bridge the gap between DFT calculations and potential parameters. For our software we discuss workflow, validation against canonical parameter sets and comparison to published NCAA-protein structures.

59 BASIC BIOLOGICAL SCIENCES↗

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

Abstract In a manufacturing system, production control‐related decision‐making activities occur at different levels. At the process level, one of the main control activities is to tune the parameters of individual manufacturing equipment. At the system level, the main activity is to coordinate production resources and to route parts to appropriate workstations based on their processing requirement, priority indices, and control policy. At the factory level, the goal is to plan and schedule the processing of parts at different operations for the entire system in order to optimize certain objectives. Note that the results of such activities at different levels are closely coupled and affect the overall performance of the manufacturing system as a whole. Therefore, it is important to systematically integrate these control and optimization activities into one unified platform to ensure the goal of each individual activity is aligned with the overall performance of the system. In this paper, we develop a simulation‐based virtual testbed that implements dynamic optimization, automatic information exchange, and decision‐making from the process‐level, system‐level, and factory‐level of a manufacturing system into an integrated computation environment. This is demonstrated by connecting a Python‐based numerical computation program, discrete‐event simulation software (Simul8), and an optimization solver (CPLEX) via a third‐party master program. The application of this simulation‐based virtual testbed is illustrated by a case study in a machining shop.

Sun, Yuting↗