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Application Table: A Bridge Connecting the Designing “With-The-Material” and “The-Material” Paradigms

Over the last few decades, advances in high-performance computing, new material characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. In 2016 NASA sponsored a 2040 Vision study (which appeared in 2018) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. The study envisions a cyber-physical-social ecosystem comprised of experimentally verified and validated (V & V) computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of “fit-for-purpose” materials, components, and systems. Consequently, the development of a robust information management system that incorporates (across the full life cycle) both experimental (real data) and virtual data resulting from the application of various simulation tools (at single or multiple length scales), therefore enabling the virtual design and optimization of materials throughout their processing – internal structure – property – performance envelope, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality, and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. This is particularly true when attempting to merge ICME practices with recent additive manufacturing technology which will enable production of the resulting 2040 Vision material and structural designs. At NASA Glenn Research Center we are exploring the future of material science through the use of novel characterization methodologies, high performance computing, and recently an emphasis on integrated computational materials engineering (ICME). Herein, recent efforts to incorporate an Application Table within NASA Glenn Research Center’s ICME Granta MI database is presented. The goal is to provide a place where material and structural application information/requirements can be linked so as to marry the “design the-material” and the “design-with-material” paradigms and thereby enable application-driven design and optimization of materials and structures by providing a central location that links material processing at various length scales to the application’s performance requirements. This paper discusses the specifics of this Application Table as well as best practices and key principles for the development of a robust materials information management system to enable the 2040 Vision integrated materials and structures ecosystem. Furthermore, it presents the intended role of the Application Table in the future of ICME design of “fit-for-purpose” materials, showing the need for a well-established framework that can successfully bridge the gap between the design “the material” and design “with-the-material” paradigms.

Materials↗

Application Table: A Bridge Connecting the Designing “With-the-Material” and “the-Material”

Over the last few decades, advances in high-performance computing, new material characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. In 2016 NASA sponsored a 2040 Vision study (which appeared in 2018) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. The study envisions a cyber-physical-social ecosystem comprised of experimentally verified and validated (V & V) computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of “fit-for-purpose” materials, components, and systems. Consequently, the development of a robust information management system that incorporates (across the full life cycle) both experimental (real data) and virtual data resulting from the application of various simulation tools (at single or multiple length scales), therefore enabling the virtual design and optimization of materials throughout their processing – internal structure – property – performance envelope, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality, and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. This is particularly true when attempting to merge ICME practices with recent additive manufacturing technology which will enable production of the resulting 2040 Vision material and structural designs. At NASA Glenn Research Center we are exploring the future of material science through the use of novel characterization methodologies, high performance computing, and recently an emphasis on integrated computational materials engineering (ICME). Herein, recent efforts to incorporate an Application Table within NASA Glenn Research Center’s ICME Granta MI database is presented. The goal is to provide a place where material and structural application information/requirements can be linked so as to marry the “design the-material” and the “design-with-material” paradigms and thereby enable application-driven design and optimization of materials and structures by providing a central location that links material processing at various length scales to the application’s performance requirements. This paper discusses the specifics of this Application Table as well as best practices and key principles for the development of a robust materials information management system to enable the 2040 Vision integrated materials and structures ecosystem. Furthermore, it presents the intended role of the Application Table in the future of ICME design of “fit-for-purpose” materials, showing the need for a well-established framework that can successfully bridge the gap between the design “the material” and design “with-the-material” paradigms.

Materials↗

US Department of Energy, Office of Science High Performance Computing Facility Operational Assessment 2019 Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory's (ORNL's) Leadership Computing Facility (OLCF) continues to surpass its operational target goals: supporting users; delivering fast, reliable computational ecosystems; creating innovative solutions for high performance computing (HPC) needs; and managing risks, safety, and security associated with operating some of the most powerful computers in the world. The results can be seen in the cutting-edge science conducted by users and the praise from the research community. Calendar year (CY) 2019 was a big year as OLCF staff ran five world-class resources (the leadershipclass computers Titan and Summit, the large analysis cluster called Eos, and the massive parallel filesystems called Atlas and Alpine)) and also began power and cooling upgrades for a 2021 exascale system called Frontier. While continuing exceptional operation of Titan, Eos, and Rhea, the OLCF released the Summit supercomputer for production on January 1, 2019. Summit debuted as the most capable and efficient system in its class and has been recognized as the most powerful system in the world for its performance on both the high performance linpack (HPL) and conjugate gradient (HPCG) benchmark applications since June 2018 according to TOP500. Summit represents the culmination of a multiyear effort between the OLCF, IBM, NVIDIA, and Mellanox to deliver a system that is unmatched for modeling, simulation, data analysis, and learning. To hit the ground running with science-ready applications on day one, application teams worked closely with the OLCF through the Center for Accelerated Application Readiness (CAAR) program for years in advance of the Summit deployment. CY 2019 was filled with outstanding results and accomplishments: a very high rating from users on overall satisfaction for the sixth year in a row; a tremendous amount of core-hours delivered to researchers from two leadership-class systems; and success in delivering on the allocation split of roughly 60%, 30%, and 10% of core-hours offered for the Innovative and Novel Computational Impact on Theory and Experiment (INCITE), Advanced Scientific Computing Research Leadership Computing Challenge (ALCC), and Director's Discretionary (DD) programs, respectively (see Operational Performance section). These accomplishments, coupled with the high utilization rates (overall and capability usage), represent the fulfillment of the promise of both leadership-class machines: efficient facilitation of leadership-class computational applications. Table ES.1 presents a summary of the 2019 OLCF metric targets and the associated results. More information can be found in the Operational Performance section for each OLCF resource. The scientific accomplishments of OLCF users are a strong indication of long-term operational success, with publications this year in such notable journals and publications as Nature, Nature Physics, Nature Plants, Physical Review X, Journal of the American Physical Society, Cell, Nano Letters, and Trends in Biotechnology. Crucial domain-specific discoveries facilitated by resources at the OLCF are described in the High Performance Computing Facility Operational Assessment 2019 Oak Ridge Leadership Computing Facility (OAR) Strategic Results section. For example, researchers used Summit to pinpoint and understand the production of proteins from genetic information, including mutations and the functional expression of disease (Section 8.2).

97 MATHEMATICS AND COMPUTING↗

Combustion of hydrogen in a two-dimensional duct with step fuel injectors

An investigation of the combustion of hydrogen perpendicularly injected from step fuel injectors into a Mach 2.72, 2100 K vitiated test gas was conducted. The model simulated the flow between the center and side struts of an integrated scramjet module at Mach 7 flight and an altitude of 29 km. Parametric variation included equivalence ratio, fuel dynamic pressure ratio, and area distribution of the model. The overall area ratio of the model was held constant at 2.87. The data analysis indicated that no measurable improvement in mixing or combustion efficiency was obtained by varying the fuel dynamic pressure ratio from 0.79 to 2.45. Computations indicated approximately 80 percent of the fuel was mixed so that it could react; however, only approximately 50 percent of the mixed fuel actually reacted in two test configurations, and 74 percent in later tests where less area expansion of the flow occurred.

Eggers, J. M.↗

A Ground Systems Architecture Transition for A Distributed Operations System

The Marshall Space Flight Center (MSFC) Ground Systems Department (GSD) recently undertook an architecture change in the product line that serves the ISS program. As a result, the architecture tradeoffs between data system product lines that serve remote users versus those that serve control center flight control teams were explored extensively. This paper describes the resulting architecture that will be used in the ISS payloads program, and the resulting functional breakdown of the products that support that architecture. It also describes the lessons learned from the path that was followed, as a migration of products cause the need to reevaluate the allocation of functions across the architecture. The result is a set of innovative ground system solutions that is scalable so it can support facilities of wide-ranging sizes, from a small site up to large control centers. Effective use of system automation, custom components, design optimization for data management, data storage, data transmissions, and advanced local and wide area networking architectures, plus the effective use of Commercial-Off-The-Shelf (COTS) products, provides flexible Remote Ground System options that can be tailored to the needs of each user. This paper offers a description of the efficiency and effectiveness of the Ground Systems architectural options that have been implemented, and includes successful implementation examples and lessons learned.

Sellers, Donna↗

A Ground Systems Architecture Transition for a Distributed Operations System

The Marshall Space Flight Center (MSFC) Ground Systems Department (GSD) recently undertook an architecture change in the product line that serves the ISS program. As a result, the architecture tradeoffs between data system product lines that serve remote users versus those that serve control center flight control teams were explored extensively. This paper describes the resulting architecture that will be used in the International Space Station (ISS) payloads program, and the resulting functional breakdown of the products that support this architecture. It also describes the lessons learned from the path that was followed, as a migration of products cause the need to reevaluate the allocation of functions across the architecture. The result is a set of innovative ground system solutions that is scalable so it can support facilities of wide-ranging sizes, from a small site up to large control centers. Effective use of system automation, custom components, design optimization for data management, data storage, data transmissions, and advanced local and wide area networking architectures, plus the effective use of Commercial-Off-The-Shelf (COTS) products, provides flexible Remote Ground System options that can be tailored to the needs of each user. This paper offers a description of the efficiency and effectiveness of the Ground Systems architectural options that have been implemented, and includes successful implementation examples and lessons learned.

Sellers, Donna↗

Testing of an Amine-Based Pressure-Swing System for Carbon Dioxide and Humidity Control

In a crewed spacecraft environment, atmospheric carbon dioxide (CO2) and moisture control is crucial. Hamilton Sundstrand has developed a stable and efficient amine-based CO2 and water vapor sorbent, SA9T, that is well-suited for use in a spacecraft environment. The sorbent is efficiently packaged in pressure-swing regenerable beds that are thermally linked to improve removal efficiency and minimize vehicle thermal loads. Flows are all controlled with a single spool valve. This technology has been baselined for the new Orion spacecraft. However, more data was needed on the operational characteristics of the package in a simulated spacecraft environment. A unit was therefore tested with simulated metabolic loads in a closed chamber at Johnson Space Center during the last third of 2006. Tests were run at a variety of cabin temperatures and with a range of operating conditions varying cycle time, vacuum pressure, air flow rate, and crew activity levels. Results of this testing are presented and potential flight operational strategies discussed.

Lin, Amy↗

Further Testing of an Amine-based Pressure-Swing System for Carbon Dioxide and Humidity Control

In a crewed spacecraft environment, atmospheric carbon dioxide (CO2) and moisture control are crucial. Hamilton Sundstrand has developed a stable and efficient amine-based CO2 and water vapor sorbent, SA9T, that is well suited for use in a spacecraft environment. The sorbent is efficiently packaged in pressure-swing regenerable beds that are thermally linked to improve removal efficiency and minimize vehicle thermal loads. Flows are all controlled with a single spool valve. This technology has been baselined for the new Orion spacecraft. However, more data was needed on the operational characteristics of the package in a simulated spacecraft environment. A unit was therefore tested with simulated metabolic loads in a closed chamber at Johnson Space Center during the last third of 2006. Those test results were reported in a 2007 ICES paper. A second test article was incorporated for a third phase of testing, and that test article was modified to allow pressurized gas purge regeneration on the launch pad in addition to the standard vacuum regeneration in space. Metabolic rates and chamber volumes were also adjusted to reflect current programmatic standards. The third phase of tests was performed during the spring and summer of 2007. Tests were run with a range of operating conditions, varying: cycle time, vacuum pressure (or purge gas flow rate), air flow rate, and crew activity levels. Results of this testing are presented and potential flight operational strategies discussed.

Lin, Amy↗

Benefits of Delay Tolerant Networking for Earth Science Missions

To date there has been much discussion about the value of Delay Tolerant Networking (DTN) for space missions. Claims of various benefits, based on paper analysis, are good; however a benefits statement with empirical evidence to support is even better. This paper presents potential and actual advantages of using DTN for Earth science missions based on results from multiple demonstrations, conducted by the Communications, Standards, and Technology Laboratory (CSTL) at NASA Goddard Space Flight Center (GSFC). Demonstrations included two flight demonstrations using the Earth Observing Mission 1 (EO-1) and the Near Earth Network (NEN), a ground based demonstration over satellite links to the Internet Router in Space (IRIS) payload on Intelsat-14, and others using the NASA Tracking Data Relay Satellite System (TDRSS). Real and potential findings include increased flexibility and efficiency in science campaigns, reduced latency in a collaborative science scenario, and improved scientist-instrument communication and control.

Davis, Faith↗

Effects of Unsteady Flow Interactions on the Performance of a Highly-Loaded Transonic Compressor Stage

The primary focus of this paper is to investigate the loss sources in an advanced GE transonic compressor design with high reaction and high stage loading. This advanced compressor has been investigated both experimentally and analytically in the past. The measured compressor efficiency is significantly lower than the efficiency calculated with various existing tools based on RANS and URANS. The general understanding is that some important flow physics in this modern compressor design are not represented in the current tools. To pinpoint the source of the efficiency miss, an advanced test with detailed flow traverse was performed for the front one and a half stage at the NASA Glenn Research Center. In the present paper, a Large Eddy Simulation (LES) is employed to determine whether a higher-fidelity simulation can pick up any additional flow physics that can explain past efficiency miss with RANS and URANS. The results from the Large Eddy Simulation were compared with the NASA test results and the GE interpretation of the test data. LES calculates lower total pressure and higher total temperature on the pressure side of the stator, resulting in large loss generation on the pressure side of the stator. On the other hand, existing tools based on the RANS and URANS do not calculate this high total temperature and low total pressure on the pressure side of the stator. The calculated loss through the stator from LES seems to match the measured data and the GE data interpretation. Detailed examination of the unsteady flow field from LES indicates that the accumulation of high loss near the pressure side of the stator is due to the interaction of the rotor wake with the stator blade. The strong rotor wake interacts quite differently with the pressure side of the stator than with the suction side of the stator blade. The concave curvature on the pressure side of the stator blade increases the mixing of the rotor wake with the pressure side boundary layer significantly. On the other hand, the convex curvature on the suction side of the stator blade decreases the mixing and the suction side blade boundary layer remains thin. The jet velocity in the rotor wake in the stator frame seems to magnify the curvature effect in addition to inviscid redistribution of wake fluid toward the pressure side of the blade.

LES↗

Transforming Energy Through Sustainable Mobility: Expanding Low-Carbon Transportation R&D Solutions

As the nation's premier laboratory for cutting-edge transportation decarbonization research and development solutions, the National Renewable Energy Laboratory (NREL) pioneers the creation and deployment of sustainable mobility technologies and strategies, with a focus on slashing transportation sector greenhouse gas emissions and combatting climate change. Trucks, planes, cargo ships, and other difficult-to-decarbonize vehicles are part of this essential transition for the transportation sector, which is currently the nation's largest source of the greenhouse gas emissions. NREL provides the scientific building blocks needed to spur innovation through multifaceted analysis, research, and engineering. This work acts as a catalyst to help industry bring affordable, high-performance, energy-efficient, and low-emission modes of transport and related infrastructure to market sooner. Our researchers collaborate closely with academic, government, and industry partners to design better batteries, drivetrains, and engines. They develop technologies for high-power charging, thermal management, energy storage, and power electronics. They are also reimagining fuels and combustion while creating sustainable lightweight materials. Unbiased expert guidance - backed by credible data and analysis, tools, and scientific rigor - empowers partners to make informed decisions about sustainable transportation. NREL recognizes that communities with limited mobility options face reduced access to employment opportunities, health care, and education, lowering overall quality of life. Alongside partners, NREL experts are creating transportation solutions that meet community-identified needs and increase mobility equity in historically underserved and overburdened communities. Rather than providing a one-size-fits-all solution, we take an interdisciplinary approach to mobility equity that considers the needs and challenges of diverse groups, maximizing benefits at the individual, community, and societal levels.

ADVANCED PROPULSION SYSTEMS↗

Operational processing and cloud boundary detection from micro pulse lidar data

Micro Pulse Lidar (MPL) was developed at NASA Goddard Space Flight Center (GSFC) as the result of research on space-borne lidar techniques. It was designed to provide continuous, unattended observations of all significant atmospheric cloud and aerosol structure with a rugged, compact system design and the benefit of eye safety (Spinhirne 1993). The significant eye safety feature is achieved by using low pulse energies and high pulse repetition rates compared to standard lidar systems. MPL systems use a diode pumped 10 microj, 2500 Hz doubled Nd:YLF laser. In addition, a solid state Geiger mode avalanche photo diode (GAPD) photon counting detector is used allowing for quantum efficiencies approaching 70%. Other design features have previously been noted by Spinhirne (1995). Though a commercially available instrument, with nearly 20 systems operating around the world, the most extensive MPL work has come from those operated by the Atmospheric Radiation Measurement (ARM) (Stokes and Schwartz 1994) program. The diverse ability of the instrument relating to the measurement of basic cloud macrophysical structure and both cloud and aerosol radiative properties well suits the ARM research philosophy. MPL data can be used to yield many parameters including cloud boundary heights to the limit of signal attenuation, cloud scattering cross sections and optical thicknesses, planetary boundary layer heights and aerosol scattering profiles, including those into the stratosphere in nighttime cases (Hlavka et al 1996). System vertical resolution ranges from 30 m to 300 m (i.e. high and low resolution respectively) depending on system design. The lidar research group at GSFC plays an advisory role in the operation, calibration and maintenance of NASA and ARM owned MPL systems. Over the past three years, processing software and system correction techniques have been developed in anticipation of the increasing population of systems amongst the community. Datasets produced by three ARM-owned systems have served as the basis for this development. With two operating at the southern Great Plains Cloud and Radiation Testbed Site (SGP CART) since December 1993 and another at the Manus Island Atmospheric Radiation and Cloud Station (TWP ARCS) location in the tropical western Pacific since February 1997, the ARM archive contains over 4 years of observations. In addition, high resolution systems planning to come on-line at the North Slope, AK CART shortly with another scheduled to follow at the TWP ARCS-II will diversify this archive with more extensive observations.

Campbell, James R.↗

Model-based data center cooling controls comparative co-design

This article presents a comparative simulation-based control logic design process. It uses the Control Description Language (CDL) and the ASHRAE Guideline 36 high-performing building control sequences with the Modelica Buildings Library (MBL) to demonstrate a comparative analysis of two control designs for a data center chilled water plant. Details include a description of the closed-loop plant and control design methodology, including sizing and parameterization, base and alternative (Guideline 36) control logic with software implementation structure, and outline of the simulation experimentation process. The selected control designs are paired with comparable chilled water plant configurations. The models include a chiller, a water-side economizer, and an evaporative cooling tower. The plant provides cooling at 27ºC zone supply air temperature to a data center in Sacramento, CA. The comparative simulation results examined the impacts of a selected control logic detail, and present an example model-based design application. Overall, the simulation results showed a 25% annual and a 18% summer energy use reduction for alternative controls. This shows that simulation-based control logic design performance evaluation can improve energy efficiency and resilience aspects of system controls at large.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Enhancing Discoverability and Management of Atmospheric Data at Scale: Solutions from the ARM Data Center

The Atmospheric Radiation Measurement (ARM) is a multi-laboratory and multi-institutional U.S. Department of Energy (DOE) Office of Science National User Facility. The ARM Data Center (ADC), located at Oak Ridge National Laboratory, collects, archives, and shares vast atmospheric data crucial for climate research. The ADC manages over 7 PB of data from 460 instruments worldwide, processing it into more than 11,000 diverse data products using the Network Common Data Form (NetCDF) for machine-independent accessibility. The primary challenge addressed in this paper is the efficient management and distribution of vast and diverse datasets essential for the climate research community, enhancing accessibility through advanced tools like Data Discovery. The ADC has developed advanced infrastructure and software architecture to handle the continuous influx of heterogeneous data to enhance data discoverability, resulting in increased scientific collaboration. In 2023, users from over 34 countries downloaded and utilized ARM data, resulting in 1,455 publications. The ADC’s efforts have significantly improved the discoverability and usability of atmospheric data, fostering extensive scientific research and collaboration. This paper details the solutions implemented by the ADC team for efficient data discovery and distribution, and it demonstrates ARM’s capability of staging processed data for scientific analysis.

Shah, Chirag [ORNL] (ORCID:0000000203145737)↗

An application of machine learning to the organization of institutional software repositories

Software reuse has become a major goal in the development of space systems, as a recent NASA-wide workshop on the subject made clear. The Data Systems Technology Division of Goddard Space Flight Center has been working on tools and techniques for promoting reuse, in particular in the development of satellite ground support software. One of these tools is the Experiment in Libraries via Incremental Schemata and Cobweb (ElvisC). ElvisC applies machine learning to the problem of organizing a reusable software component library for efficient and reliable retrieval. In this paper we describe the background factors that have motivated this work, present the design of the system, and evaluate the results of its application.

Bailin, Sidney↗

Conceptual Design of the Space Station Fluids Module

The purpose of this paper is to describe the conceptual design of the Fluids Module for the International Space Station Alpha (ISSA). This module is part of the Space Station Fluids/Combustion Facility (SS FCF) under development at the NASA Lewis Research Center. The Fluids/Combustion Facility is one of several science facilities which are being developed to support microgravity science investigations in the US Laboratory Module of the ISSA. The SS FCF will support a multitude of fluids and combustion science investigations over the lifetime of the ISSA and return state-of-the-art science data in a timely and efficient manner to the scientific communities. This will be accomplished through modularization of hardware, with planned, periodic upgrades; modularization of like scientific investigations that make use of common facility functions; and use of orbital replacement units (ORU's) for incorporation of new technology and new functionality. Portions of the SS FCF are scheduled to become operational on-orbit in 1999. The Fluids Module is presently scheduled for launch to orbit and integration with the Fluids/Combustion Facility in 2001. The objectives of this paper are to describe the history of the Fluids Module concept, the types of fluids science investigations which will be accommodated by the module, the hardware design heritage, the hardware concept, and the hardware breadboarding efforts currently underway.

Rohn, Dennis W.↗

Conceptual design of the Space Station combustion module

The purpose of this paper is to describe the conceptual design of the Combustion Module for the International Space Station Alpha (ISSA). This module is part of the Space Station Fluids/Combustion Facility (SS FCF) under development at the NASA Lewis Research Center. The Fluids/Combustion Facility is one of several science facilities which are being developed to support microgravity science investigations in the US Laboratory Module of the ISSA. The SS FCF will support a multitude of fluids and combustion science investigations over the lifetime of the ISSA and return state-of-the-art science data in a timely and efficient manner to the scientific communities. This will be accomplished through modularization of hardware, with planned, periodic upgrades; modularization of like scientific investigations that make use of common facility functions; and through the use of orbital replacement units (ORU's) for incorporation of new technology and new functionality. The SS FCF is scheduled to become operational on-orbit in 1999. The Combustion Module is presently scheduled for launch to orbit and integration with the Fluids/Combustion Facility in 1999. The objectives of this paper are to describe the history of the Combustion Module concept, the types of combustion science investigations which will be accommodated by the module, the hardware design heritage, the hardware concept, and the hardware breadboarding efforts currently underway.

Morilak, Daniel P.↗

Fundamental Mistuning Model for Probabilistic Analysis Studied Experimentally

The Fundamental Mistuning Model (FMM) is a reduced-order model for efficiently calculating the forced response of a mistuned bladed disk. FMM ID is a companion program that determines the mistuning in a particular rotor. Together, these methods provide a way to acquire mistuning data in a population of bladed disks and then simulate the forced response of the fleet. This process was tested experimentally at the NASA Glenn Research Center, and the simulated results were compared with laboratory measurements of a "fleet" of test rotors. The method was shown to work quite well. It was found that the accuracy of the results depends on two factors: (1) the quality of the statistical model used to characterize mistuning and (2) how sensitive the system is to errors in the statistical modeling.

Griffin, Jerry H.↗