Search NASA⌕ Search

SEARCH · Search NASA

Results for “Vector Processing”

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 487 records · Page 27

An Approach to Identifying Aspects of Positive Pilot Behavior within the Aviation Safety Reporting System

The National Airspace System (NAS) is constantly evolving as air traffic continues to ramp up to pre-pandemic numbers and projected to grow to unprecedented levels in the coming years. As well as increasing demand to the current system, emerging operations such as Unmanned Autonomous Systems are also expected to add to complexity in the airspace. To address these issues, the industry and government agencies supporting the NAS will need to rely upon additional automation and new technologies to address future operational requirements, while continuing to be a world-leading safe transportation system. As these new technologies are implemented, the system continues to rely on human pilots and controllers in the loop to monitor the system and intervene in situations the automation cannot handle. The goal of proactively addressing safety is of foremost concern to ensure passenger confidence. The industry has implemented various Safety Monitoring Systems to identify safety risks and proactively address them before they result in a serious incident or accident. One such program is the Aviation Safety Reporting System (ASRS). ASRS is a long-established system where pilots and controllers voluntarily and anonymously report safety incidents they experienced and observed during line operations by providing rich text narratives describing the events, the environment, and conditions leading to the safety event of concern. These narratives provide insight and context around events of interest and can be used to identify emerging problems. They can trigger investigations within Flight Operational Quality Assurance or Flight Data Monitoring programs. However, this process typically focuses on the adverse events and the unsafe aspects of the operations surrounding the reported or detected events. This perspective of investigating factors that went wrong around an adverse event is commonly referred to as Safety I. Alternatively, characterizing successful actions that operators perform every day under varying conditions that keep the system within safe operating bounds is a concept referred to as Safety II. The benefit of the Safety II view is that the scope is much larger than that of Safety I since a vast majority of the operations result in successful flights. Many of the successful techniques used to manage operational threats are not documented in standard operating procedures or taught during training. They are typically acquired over time by working with experienced pilots during line operations or in many cases after experiencing a problem for the first time and reacting to it in situ, drawing from years of experience to manage the threat. In an attempt to quantify these positive actions, we are proposing an approach to extracting key behaviors within ASRS reports that can support the Safety II concept. Our analysis assumes that ASRS reports contain some descriptions of corrective actions that operators performed to prevent a situation from leading to an accident. Leveraging recent advances in Natural Language Process modeling, we have developed an approach to extract positive sentiment from reports, embed these positive statements in a vector space where they can be numerically analyzed, and clustering these statements into similar contextual categories. From these contextualized categories we can attempt to summarized and distilled aspects of the positive behavior. The goal is to identify categories of behavior that describe consistent operator techniques that supports the Safety II concept. With this information, airlines may enable learning from these positive actions, or address procedures that need to be changed to avoid having pilots implement a workaround. These insights can provide a lens into what is “going right” in the operations that may otherwise not be known widely within the community. It is envisioned that this approach can be extended to other narrative programs such as Line Operation Safety Audit or Learning Improvement Team reports where similar observed behavior can be analyzed to extract positive actions and inform the overall operations.

NLP↗

An Approach to Identifying Aspects of Positive Pilot Behavior within the Aviation Safety Reporting System

The National Airspace System (NAS) is constantly evolving as air traffic continues to ramp up to pre-pandemic numbers and projected to grow to unprecedented levels in the coming years. As well as increasing demand to the current system, emerging operations such as Unmanned Autonomous Systems are also expected to add to complexity in the airspace. To address these issues, the industry and government agencies supporting the NAS will need to rely upon additional automation and new technologies to address future operational requirements, while continuing to be a world-leading safe transportation system. As these new technologies are implemented, the system continues to rely on human pilots and controllers in the loop to monitor the system and intervene in situations the automation cannot handle. The goal of proactively addressing safety is of foremost concern to ensure passenger confidence. The industry has implemented various Safety Monitoring Systems to identify safety risks and proactively address them before they result in a serious incident or accident. One such program is the Aviation Safety Reporting System (ASRS). ASRS is a long-established system where pilots and controllers voluntarily and anonymously report safety incidents they experienced and observed during line operations by providing rich text narratives describing the events, the environment, and conditions leading to the safety event of concern. These narratives provide insight and context around events of interest and can be used to identify emerging problems. They can trigger investigations within Flight Operational Quality Assurance or Flight Data Monitoring programs. However, this process typically focuses on the adverse events and the unsafe aspects of the operations surrounding the reported or detected events. This perspective of investigating factors that went wrong around an adverse event is commonly referred to as Safety I. Alternatively, characterizing successful actions that operators perform every day under varying conditions that keep the system within safe operating bounds is a concept referred to as Safety II. The benefit of the Safety II view is that the scope is much larger than that of Safety I since a vast majority of the operations result in successful flights. Many of the successful techniques used to manage operational threats are not documented in standard operating procedures or taught during training. They are typically acquired over time by working with experienced pilots during line operations or in many cases after experiencing a problem for the first time and reacting to it in situ, drawing from years of experience to manage the threat. In an attempt to quantify these positive actions, we are proposing an approach to extracting key behaviors within ASRS reports that can support the Safety II concept. Our analysis assumes that ASRS reports contain some descriptions of corrective actions that operators performed to prevent a situation from leading to an accident. Leveraging recent advances in Natural Language Process modeling, we have developed an approach to extract positive sentiment from reports, embed these positive statements in a vector space where they can be numerically analyzed, and clustering these statements into similar contextual categories. From these contextualized categories we can attempt to summarized and distilled aspects of the positive behavior. The goal is to identify categories of behavior that describe consistent operator techniques that supports the Safety II concept. With this information, airlines may enable learning from these positive actions, or address procedures that need to be changed to avoid having pilots implement a workaround. These insights can provide a lens into what is “going right” in the operations that may otherwise not be known widely within the community. It is envisioned that this approach can be extended to other narrative programs such as Line Operation Safety Audit or Learning Improvement Team reports where similar observed behavior can be analyzed to extract positive actions and inform the overall operations.

NLP↗

Utilization of Machine Learning Techniques for Managing the Tracking and Data Relay Satellite Constellation

National Aeronautics and Space Administration’s (NASA) Goddard Space Flight Center (GSFC) operates a constellation of ten geosynchronous Tracking and Data Relay Satellites (TDRS). The TDRS constellation consists of multiple geosynchronous communication relay satellites located around the equator so they can provide continual coverage of any mission in low earth orbit. The TDRS are located primarily in three oceanic regions around the earth. NASA’s White Sands Complex provides the ground communication support for TDRS located over the Atlantic and Pacific Oceans. Another TDRS ground station in Guam supports the TDRS over the Indian Ocean. With these satellites the TDRS network can provide continuous coverage of satellites in low-earth orbit. The NASA Space Network (SN) project office at GSFC manages the constellation of spacecraft. Major customers of the TDRS constellation include, but are not limited to, the International Space Station and the Hubble Space Telescope. The TDRS constellation has three generations of satellites and has been active for over 30 years providing reliable communication links between customer satellites and corresponding ground stations. However, one of the major concerns for TDRS, and in any space mission, is to ensure the health and safety of the spacecraft. Generally, engineers use telemetry data to monitor and analyze the performance and state of health of the spacecraft. Telemetry data contains hundreds of parameters that monitor each important component in the spacecraft, which can be utilized to recognize and characterize the behavior of the spacecraft. Each parameter contains considerable information to represent time-dependent properties of each spacecraft subsystem and component. During the entire life of a TDRS spacecraft, thousands of gigabytes of telemetry data are transmitted in real-time from the spacecraft to the ground station at the White Sands Complex in Las Cruces, New Mexico, and recorded as historical data sets for engineers to process and analyze the events that occurred on-orbit. These parameters contain the function of multiple spacecraft subsystems, such as the attitude control system (ACS), Thermal, Electrical Power Subsystem (EPS), etc. . The first and second generations have exceeded their required lifetime and NASA is keen to manage these spacecrafts carefully in order to maximize the remaining life using the spacecraft telemetry. The challenge is to know when the risk of losing a spacecraft in geosynchronous orbit exceeds the benefit of continued operations for customer support. In the TDRS fleet, the EPS is the most critical subsystem related to spacecraft operations. Failure of the EPS would strand a spacecraft in geosynchronous orbit. Since EPS provides power to the spacecraft, component failures ultimately lead to the inability to support the spacecraft loads and the communications payload. For instance, TDRS-8 has several anomalies in EPS including the Bus Voltage Limiter (BVL) shunt current, solar array loss of circuits, and failed battery cells. Any of these anomalies can cause critical issues to the spacecraft. Therefore, developing a system to analyze and perform early detection of a potential anomaly is an important issue in telemetry data analysis. In recent years, Telemetry Mining (TM) has been proposed to process telemetry data by using Data Mining (DM) techniques such as classification, clustering, regression and anomaly detection. Anomaly detection, also known as outlier detection, has been widely used in many data mining areas such as remote sensing, medical data processing and digital image processing. The goal of anomaly detection is to detect abnormal data, which contains a relatively low probability of occurrence among the entire data set. Early detection of anomalies is one of the most significant issues in managing the spacecraft configuration. If anomalies can be detected early enough, then the redundant resources can be used to extend the life of the operational spacecraft. We present an unsupervised anomaly detection method to process the EPS data extracted from TDRS-8. This is different from traditional analytical methods, which use telemetry data to illustrate behavior and physical meaning of each spacecraft component. TM connects multiple parameters as a vector and then conducts data analysis on this high dimension telemetry vector. This method is looking at the properties of a high dimensional vector that is able to consider the relationship between different parameters in the anomaly detection problem. This kind of method performs much better than the traditional limit checking method. In addition, we propose a new approach of real-time anomaly detection to process telemetry data in real-time, which can then be applied to spacecraft monitoring with high reliability, low cost and high accuracy.

Machine Learning (ML)↗

Calibration Test Set for a Phase-Comparison Digital Tracker

An apparatus that generates four signals at a frequency of 7.1 GHz having precisely controlled relative phases and equal amplitudes has been designed and built. This apparatus is intended mainly for use in computer-controlled automated calibration and testing of a phase-comparison digital tracker (PCDT) that measures the relative phases of replicas of the same X-band signal received by four antenna elements in an array. (The relative direction of incidence of the signal on the array is then computed from the relative phases.) The present apparatus can also be used to generate precisely phased signals for steering a beam transmitted from a phased antenna array. The apparatus (see figure) includes a 7.1-GHz signal generator, the output of which is fed to a four-way splitter. Each of the four splitter outputs is attenuated by 10 dB and fed as input to a vector modulator, wherein DC bias voltages are used to control the in-phase (I) and quadrature (Q) signal components. The bias voltages are generated by digital-to-analog- converter circuits on a control board that receives its digital control input from a computer running a LabVIEW program. The outputs of the vector modulators are further attenuated by 10 dB, then presented at high-grade radio-frequency connectors. The attenuation reduces the effects of changing mismatch and reflections. The apparatus was calibrated in a process in which the bias voltages were first stepped through all possible IQ settings. Then in a reverse interpolation performed by use of MATLAB software, a lookup table containing 3,600 IQ settings, representing equal amplitude and phase increments of 0.1 , was created for each vector modulator. During operation of the apparatus, these lookup tables are used in calibrating the PCDT.

Boas, Amy↗

Multi-Objective Multi-User Scheduling for Space Science Missions

We have developed an architecture called MUSE (Multi-User Scheduling Environment) to enable the integration of multi-objective evolutionary algorithms with existing domain planning and scheduling tools. Our approach is intended to make it possible to re-use existing software, while obtaining the advantages of multi-objective optimization algorithms. This approach enables multiple participants to actively engage in the optimization process, each representing one or more objectives in the optimization problem. As initial applications, we apply our approach to scheduling the James Webb Space Telescope, where three objectives are modeled: minimizing wasted time, minimizing the number of observations that miss their last planning opportunity in a year, and minimizing the (vector) build up of angular momentum that would necessitate the use of mission critical propellant to dump the momentum. As a second application area, we model aspects of the Cassini science planning process, including the trade-off between collecting data (subject to onboard recorder capacity) and transmitting saved data to Earth. A third mission application is that of scheduling the Cluster 4-spacecraft constellation plasma experiment. In this paper we describe our overall architecture and our adaptations for these different application domains. We also describe our plans for applying this approach to other science mission planning and scheduling problems in the future.

science planning↗

Relative Navigation for Formation Flying of Spacecraft

This paper presents a robust and efficient approach for relative navigation and attitude estimation of spacecraft flying in formation. This approach uses measurements from a new optical sensor that provides a line of sight vector from the master spacecraft to the secondary satellite. The overall system provides a novel, reliable, and autonomous relative navigation and attitude determination system, employing relatively simple electronic circuits with modest digital signal processing requirements and is fully independent of any external systems. Experimental calibration results are presented, which are used to achieve accurate line of sight measurements. State estimation for formation flying is achieved through an optimal observer design. Also, because the rotational and translational motions are coupled through the observation vectors, three approaches are suggested to separate both signals just for stability analysis. Simulation and experimental results indicate that the combined sensor/estimator approach provides accurate relative position and attitude estimates.

Alonso, Roberto↗

Hydrogen as an energy vector

The feasibility of utilizing hydrogen as an energy vector is considered, with special attention given to means of hydrogen production. The state-of-the-art in thermochemical processes is reviewed, and criteria for the technical and economic feasibility of large-scale thermochemical water splitting processes are presented. The production of hydrogen from coal and from photolysis of water is discussed.

Powers, W. D.↗

Direction-Sensitive Latch

Mechanism eliminates clearance and applies positive load latched to member. Simpler and lighter than previous direction-sensitive latches (also called "vector-sensitive latches"). New mechanism well suited to operation by automatic control or by remote controlled manipulator. Stages of latching process begin with application of downward force to secondary member, causing it to displace roller. After secondary member has passed roller and joined primary member, actuator removes clearance between roller and secondary member.

Acres, W. R.↗

Microwave absorption by a lossy dielectric sphere in a rectangular cavity

A new theory of absorption of microwave power by a lossy dielectric sphere in a resonant rectangular chamber is developed here. In this treatment, resonant modes of the cavity are resolved into traveling plane-wave fields, and Mie's theory of scattering and absorption of a plane electromagnetic wave by a sphere is utilized. The fields in the cavity containing the sphere are found by superposition of results for the individual scattering problem for each traveling plane wave. Absorbed power is then calculated by evaluating the time-averaged Poynting vector and integrating over the surface of the sphere. Applications of microwave power absorption are discussed, with particular emphasis on processing of materials. Numerical studies based on the newly derived formulas are presented. The results exhibit the manner in which microwave absorption is influenced by a number of different experimentally controllable parameters. The examples considered were chosen with a view toward designing experiments and apparatus for containerless processing of materials in the microgravity environment of space.

Jackson, H. W.↗

Determination of the stability and control derivatives of the NASA F/A-18 HARV using flight data

This report documents the research conducted for the NASA-Ames Cooperative Agreement No. NCC 2-759 with West Virginia University. A complete set of the stability and control derivatives for varying angles of attack from 10 deg to 60 deg were estimated from flight data of the NASA F/A-18 HARV. The data were analyzed with the use of the pEst software which implements the output-error method of parameter estimation. Discussions of the aircraft equations of motion, parameter estimation process, design of flight test maneuvers, and formulation of the mathematical model are presented. The added effects of the thrust vectoring and single surface excitation systems are also addressed. The results of the longitudinal and lateral directional derivative estimates at varying angles of attack are presented and compared to results from previous analyses. The results indicate a significant improvement due to the independent control surface deflections induced by the single surface excitation system, and at the same time, a need for additional flight data especially at higher angles of attack.

Napolitano, Marcello R.↗

Performance evaluation of the Engineering Analysis and Data Systems (EADS) 2

The Engineering Analysis and Data System (EADS)II (1) was installed in March 1993 to provide high performance computing for science and engineering at Marshall Space Flight Center (MSFC). EADS II increased the computing capabilities over the existing EADS facility in the areas of throughput and mass storage. EADS II includes a Vector Processor Compute System (VPCS), a Virtual Memory Compute System (CFS), a Common Output System (COS), as well as Image Processing Station, Mini Super Computers, and Intelligent Workstations. These facilities are interconnected by a sophisticated network system. This work considers only the performance of the VPCS and the CFS. The VPCS is a Cray YMP. The CFS is implemented on an RS 6000 using the UniTree Mass Storage System. To better meet the science and engineering computing requirements, EADS II must be monitored, its performance analyzed, and appropriate modifications for performance improvement made. Implementing this approach requires tool(s) to assist in performance monitoring and analysis. In Spring 1994, PerfStat 2.0 was purchased to meet these needs for the VPCS and the CFS. PerfStat(2) is a set of tools that can be used to analyze both historical and real-time performance data. Its flexible design allows significant user customization. The user identifies what data is collected, how it is classified, and how it is displayed for evaluation. Both graphical and tabular displays are supported. The capability of the PerfStat tool was evaluated, appropriate modifications to EADS II to optimize throughput and enhance productivity were suggested and implemented, and the effects of these modifications on the systems performance were observed. In this paper, the PerfStat tool is described, then its use with EADS II is outlined briefly. Next, the evaluation of the VPCS, as well as the modifications made to the system are described. Finally, conclusions are drawn and recommendations for future worked are outlined.

Debrunner, Linda S.↗

BOREAS HYD-8 DEM Data Over the NSA-MSA and SSA-MSA in the UTM Projection

The BOREAS HYD-8 team focused on describing the scaling behavior of water and carbon flux processes at local and regional scales. These DEMs were produced from digitized contours at a cell resolution of 100 meters. Vector contours of the area were used as input to a software package that interpolates between contours to create a DEM representing the terrain surface. The vector contours had a contour interval of 25 feet. The data cover the BOREAS MSAs of the SSA and NSA and are given in a UTM map projection. Most of the elevation data from which the DEM was produced were collected in the 1970s or 1980s. The data are stored in binary, image format files. The data files are available on a CD-ROM (see document number 20010000884) or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

Wang, Xue-Wen↗

Development of Numerical Tools for the Investigation of Plasma Detachment from Magnetic Nozzles

A multidimensional numerical simulation framework aimed at investigating the process of plasma detachment from a magnetic nozzle is introduced. An existing numerical code based on a magnetohydrodynamic formulation of the plasma flow equations that accounts for various dispersive and dissipative processes in plasmas was significantly enhanced to allow for the modeling of axisymmetric domains containing three.dimensiunai momentum and magnetic flux vectors. A separate magnetostatic solver was used to simulate the applied magnetic field topologies found in various nozzle experiments. Numerical results from a magnetic diffusion test problem in which all three components of the magnetic field were present exhibit excellent quantitative agreement with the analytical solution, and the lack of numerical instabilities due to fluctuations in the value of del(raised dot)B indicate that the conservative MHD framework with dissipative effects is well-suited for multi-dimensional analysis of magnetic nozzles. Further studies will focus on modeling literature experiments both for the purpose of code validation and to extract physical insight regarding the mechanisms driving detachment.

Sankaran, Kamesh↗

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations↗

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗

Fortran for the nineties

Fortran has largely enjoyed prominence for the past few decades as the computer programming language of choice for numerically intensive scientific, engineering, and process control applications. Fortran's well understood static language syntax has allowed resulting parsers and compiler optimizing technologies to often generate among the most efficient and fastest run-time executables, particularly on high-end scalar and vector supercomputers. Computing architectures and paradigms have changed considerably since the last ANSI/ISO Fortran release in 1978, and while FORTRAN 77 has more than survived, it's aged features provide only partial functionality for today's demanding computing environments. The simple block procedural languages have been necessarily evolving, or giving way, to specialized supercomputing, network resource, and object-oriented paradigms. To address these new computing demands, ANSI has worked for the last 12-years with three international public reviews to deliver Fortran 90. Fortran 90 has superseded and replaced ISO FORTRAN 77 internationally as the sole Fortran standard; while in the US, Fortran 90 is expected to be adopted as the ANSI standard this summer, coexisting with ANSI FORTRAN 77 until at least 1996. The development path and current state of Fortran will be briefly described highlighting the many new Fortran 90 syntactic and semantic additions which support (among others): free form source; array syntax; new control structures; modules and interfaces; pointers; derived data types; dynamic memory; enhanced I/O; operator overloading; data abstraction; user optional arguments; new intrinsics for array, bit manipulation, and system inquiry; and enhanced portability through better generic control of underlying system arithmetic models. Examples from dynamical astronomy, signal and image processing will attempt to illustrate Fortran 90's applicability to today's general scalar, vector, and parallel scientific and engineering requirements and object oriented programming paradigms. Time permitting, current work proceeding on the future development of Fortran 2000 and collateral standards will be introduced.

Himer, J. T.↗

Realistic Covariance Prediction For the Earth Science Constellations

Routine satellite operations for the Earth Science Constellations (ESC) include collision risk assessment between members of the constellations and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed via Monte Carlo techniques as well as numerically integrating relative probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by NASA Goddard's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the ESC satellites: Aqua, Aura, and Terra

Duncan, Matthew↗

A Coupled Approach for Structural Damage Detection with Incomplete Measurements

This historical work couples model order reduction, damage detection, dynamic residual/mode shape expansion, and damage extent estimation to overcome the incomplete measurements problem by using an appropriate undamaged structural model. A contribution of this work is the development of a process to estimate the full dynamic residuals using the columns of a spring connectivity matrix obtained by disassembling the structural stiffness matrix. Another contribution is the extension of an eigenvector filtering procedure to produce full-order mode shapes that more closely match the measured active partition of the mode shapes using a set of modified Ritz vectors. The full dynamic residuals and full mode shapes are used as inputs to the minimum rank perturbation theory to provide an estimate of damage location and extent. The issues associated with this process are also discussed as drivers of near-term development activities to understand and improve this approach.

James, George↗