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Stability margins for multilinear interval systems by way of phase conditions: A unified approach

A simple way of checking the stability with respect to an arbitrary stability region of a family of polynomials containing a vector of parameters varying within prescribed intervals is discussed. It is assumed that the parameters appear affine multilinearly in the characteristic polynomial coefficients. The condition proposed is simply to check the phase difference of the vertex polynomials. This test based on the mapping theorem significantly reduces computational complexity. Mathematical proofs are omitted. The results can be used to determine various stability margins of control systems containing interconnected interval subsystems. These include the gain, phase, time-delay, H(sup infinity), and nonlinear sector bounded stability margins of multilinear interval systems.

Keel, L. H.

Interval estimates for closure-phase and closure-amplitude imaging in radio astronomy

Interval estimates for closure-phase and closure-amplitude imaging that enable the reconstruction of a radioimage from results of approximate measurements are presented. If the intervals for the measured values are known, the precision of the result of the reconstruction cannot be solved by standard interval methods, because the phase value is based on a circle but not on a real line. If the phase theta (x bar) is measured with precision epsilon, so that the closure phase theta (x bar) + theta (y bar) - theta (x bar + y bar) is known with precision 3 epsilon, then from these measurements theta can be reconstructed with precision 6 epsilon. Similar estimates are given for closure amplitude.

Kreinovich, Vladik

Precision Interval Estimation of the Response Surface by Means of an Integrated Algorithm of Neural Network and Linear Regression

The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.

Lo, Ching F.

Contributions of tidal lung inflation to human R-R interval and arterial pressure fluctuations

We studied the effects of mechanical lung inflation on respiratory frequency R-R interval and arterial pressure fluctuations in nine healthy young adults undergoing elective orthopedic surgery. We conducted this research to define the contribution of pulmonary and thoracic stretch receptor input to respiratory sinus arrhythmia. We compared fast Fourier transform spectral power during three modes of ventilation: (1) spontaneous, frequency-controlled (0.25 Hz) breathing, (2) intermittent positive pressure ventilation (0.25 Hz, with a tidal volume of 8 ml/kg) and (3) high frequency jet ventilation (5.0 Hz, 2.5 kg/cm2), after sedation and vecuronium paralysis. Mean R-R intervals, arterial pressures and arterial blood gas levels were comparable during all three breathing conditions. Respiratory frequency systolic pressure spectral power was comparable during spontaneous breathing and conventional mechanical ventilation, but was significantly reduced during high frequency jet ventilation (P < 0.05). Respiratory frequency R-R interval spectral power (used as an index of respiratory sinus arrhythmia) declined dramatically with sedation and muscle paralysis (P < 0.05), but was greater during conventional mechanical, than high frequency jet ventilation (P < 0.05). These results suggest that although phasic inputs from pulmonary and thoracic stretch receptors make a statistically significant contribution to respiratory sinus arrhythmia, that contribution is small.

Clinical Trial

Power law behavior of RR-interval variability in healthy middle-aged persons, patients with recent acute myocardial infarction, and patients with heart transplants

BACKGROUND. The purposes of the present study were (1) to establish normal values for the regression of log(power) on log(frequency) for, RR-interval fluctuations in healthy middle-aged persons, (2) to determine the effects of myocardial infarction on the regression of log(power) on log(frequency), (3) to determine the effect of cardiac denervation on the regression of log(power) on log(frequency), and (4) to assess the ability of power law regression parameters to predict death after myocardial infarction. METHODS AND RESULTS. We studied three groups: (1) 715 patients with recent myocardial infarction; (2) 274 healthy persons age and sex matched to the infarct sample; and (3) 19 patients with heart transplants. Twenty-four-hour RR-interval power spectra were computed using fast Fourier transforms and log(power) was regressed on log(frequency) between 10(-4) and 10(-2) Hz. There was a power law relation between log(power) and log(frequency). That is, the function described a descending straight line that had a slope of approximately -1 in healthy subjects. For the myocardial infarction group, the regression line for log(power) on log(frequency) was shifted downward and had a steeper negative slope (-1.15). The transplant (denervated) group showed a larger downward shift in the regression line and a much steeper negative slope (-2.08). The correlation between traditional power spectral bands and slope was weak, and that with log(power) at 10(-4) Hz was only moderate. Slope and log(power) at 10(-4) Hz were used to predict mortality and were compared with the predictive value of traditional power spectral bands. Slope and log(power) at 10(-4) Hz were excellent predictors of all-cause mortality or arrhythmic death. To optimize the prediction of death, we calculated a log(power) intercept that was uncorrelated with the slope of the power law regression line. We found that the combination of slope and zero-correlation log(power) was an outstanding predictor, with a relative risk of > 10, and was better than any combination of the traditional power spectral bands. The combination of slope and log(power) at 10(-4) Hz also was an excellent predictor of death after myocardial infarction. CONCLUSIONS. Myocardial infarction or denervation of the heart causes a steeper slope and decreased height of the power law regression relation between log(power) and log(frequency) of RR-interval fluctuations. Individually and, especially, combined, the power law regression parameters are excellent predictors of death of any cause or arrhythmic death and predict these outcomes better than the traditional power spectral bands.

Non-NASA Center

Use of Data Comm by Flight Crew to Conduct Interval Management Operations to Parallel Dependent Runways

The Interval Management (IM) concept is being developed as a method to maintain or increase high traffic density airport arrival throughput while allowing aircraft to conduct near idle thrust descents. The Interval Management with Spacing to Parallel Dependent Runways (IMSPiDR1) experiment at NASA Langley Research Center used 24 commercial pilots to examine IM procedures to conduct parallel dependent runway arrival operations while maintaining safe but efficient intervals behind the preceding aircraft. The use of IM procedures during these operations requires a lengthy and complex clearance from Air Traffic Control (ATC) to the participating aircraft, thereby making the use of Controller Pilot Data Link Communications (CPDLC) highly desirable as the communication method. The use of CPDLC reduces the need for voice transmissions between controllers and flight crew, and enables automated transfer of IM clearance elements into flight management systems or other aircraft avionics. The result is reduced crew workload and an increase in the efficiency of crew procedures. This paper focuses on the subset of data collected related to the use of CPDLC for IM operations into a busy airport. Overall, the experiment and results were very successful, with the mean time under 43 seconds for the flight crew to load the clearance into the IM spacing tool, review the calculated speed, and respond to ATC. An overall mean rating of Moderately Agree was given when the crews were asked if the use of CPDLC was operationally acceptable as simulated in this experiment. Approximately half of the flight crew reported the use of CPDLC below 10,000 for IM operations was unacceptable, with 83% reporting below 5000 was unacceptable. Also described are proposed modifications to the IM operations that may reduce CPDLC Respond time to less than 30 seconds and should significantly reduce the complexity of crew procedures, as well as follow-on research issues for operational use of CPDLC during IM operations.

Baxley, Brian T.

Experiment Description and Results for Arrival Operations Using Interval Management with Spacing to Parallel Dependent Runways (IMSPiDR)

The predicted increase in the number of commercial aircraft operations creates a need for improved operational efficiency. Two areas believed to offer increases in aircraft efficiency are optimized profile descents and dependent parallel runway operations. Using Flight deck Interval Management (FIM) software and procedures during these operations, flight crews can achieve by the runway threshold an interval assigned by air traffic control (ATC) behind the preceding aircraft that maximizes runway throughput while minimizing additional fuel consumption and pilot workload. This document describes an experiment where 24 pilots flew arrivals into the Dallas Fort-Worth terminal environment using one of three simulators at NASA?s Langley Research Center. Results indicate that pilots delivered their aircraft to the runway threshold within +/- 3.5 seconds of their assigned time interval, and reported low workload levels. In general, pilots found the FIM concept, procedures, speeds, and interface acceptable. Analysis of the time error and FIM speed changes as a function of arrival stream position suggest the spacing algorithm generates stable behavior while in the presence of continuous (wind) or impulse (offset) error. Concerns reported included multiple speed changes within a short time period, and an airspeed increase followed shortly by an airspeed decrease.

Baxley, Brian T.

Acceptability of Flight Deck-Based Interval Management Crew Procedures

The Interval Management for Near-term Operations Validation of Acceptability (IM-NOVA) experiment was conducted at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) in support of the NASA Next Generation Air Transportation System (NextGen) Airspace Systems Program's Air Traffic Management Technology Demonstration - 1 (ATD-1). ATD-1 is intended to showcase an integrated set of technologies that provide an efficient arrival solution for managing aircraft using NextGen surveillance, navigation, procedures, and automation for both airborne and ground-based systems. The goal of the IM-NOVA experiment was to assess if procedures outlined by the ATD-1 Concept of Operations, when used with a minimum set of Flight deck-based Interval Management (FIM) equipment and a prototype crew interface, were acceptable to and feasible for use by flight crews in a voice communications environment. To investigate an integrated arrival solution using ground-based air traffic control tools and aircraft automatic dependent surveillance broadcast (ADS-B) tools, the LaRC FIM system and the Traffic Management Advisor with Terminal Metering and Controller Managed Spacing tools developed at the NASA Ames Research Center (ARC) were integrated in LaRC's Air Traffic Operations Laboratory. Data were collected from 10 crews of current, qualified 757/767 pilots asked to fly a high-fidelity, fixed based simulator during scenarios conducted within an airspace environment modeled on the Dallas-Fort Worth (DFW) Terminal Radar Approach Control area. The aircraft simulator was equipped with the Airborne Spacing for Terminal Area Routes algorithm and a FIM crew interface consisting of electronic flight bags and ADS-B guidance displays. Researchers used "pseudo-pilot" stations to control 24 simulated aircraft that provided multiple air traffic flows into DFW, and recently retired DFW air traffic controllers served as confederate Center, Feeder, Final, and Tower controllers. Pilot participant feedback indicated that the procedures used by flight crews to receive and execute interval management (IM) clearances in a voice communications environment were logical, easy to follow, did not contain any missing or extraneous steps, and required the use of an acceptable level of workload. The majority of the pilot participants found the IM concept, in addition to the proposed FIM crew procedures, to be acceptable and indicated that the ATD-1 procedures can be successfully executed in a near-term NextGen environment.

Murdock, Jennifer L.

Prediction Interval Development for Wind-Tunnel Balance Check-Loading

Results from the Facility Analysis Verification and Operational Reliability project revealed a critical gap in capability in ground-based aeronautics research applications. Without a standardized process for check-loading the wind-tunnel balance or the model system, the quality of the aerodynamic force data collected varied significantly between facilities. A prediction interval is required in order to confirm a check-loading. The prediction interval provides an expected upper and lower bound on balance load prediction at a given confidence level. A method has been developed which accounts for sources of variability due to calibration and check-load application. The prediction interval method of calculation and a case study demonstrating its use is provided. Validation of the methods is demonstrated for the case study based on the probability of capture of confirmation points.

Landman, Drew

Feasibility Criteria for Interval Management Operations as Part of Arrival Management Operations

Interval Management (IM) is a future airborne spacing concept that aims to provide more precise inter-aircraft spacing to yield throughput improvements and greater use of fuel efficient trajectories for arrival and approach operations. To participate in an IM operation, an aircraft must be equipped with avionics that provide speeds to achieve and maintain an assigned spacing interval relative to another aircraft. It is not expected that all aircraft will be equipped with the necessary avionics, but rather that IM fits into a larger arrival management concept developed to support the broader mixed-equipage environment. Arrival management concepts are comprised of three parts: a ground-based sequencing and scheduling function to develop an overall arrival strategy, ground-based tools to support the management of aircraft to that schedule, and the IM tools necessary for the IM operation (i.e., ground-based set-up, initiation, and monitoring, and the flight-deck tools to conduct the IM operation). The Federal Aviation Administration is deploying a near-term ground-automation system to support metering operations in the National Airspace System, which falls within the first two components of the arrival management concept. This paper develops a methodology for determining the required delivery precision at controlled meter points for aircraft that are being managed to a schedule and aircraft being managed to a relative spacing interval in order to achieve desired flow rates and adequate separation at the meter points.

Levitt, Ian M.

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.

Crespo, Luis G.

Air Traffic Management Technology Demostration Phase 1 (ATD) Interval Management for Near-Term Operations Validation of Acceptability (IM-NOVA) Experiment

The Interval Management for Near-term Operations Validation of Acceptability (IM-NOVA) experiment was conducted at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) in support of the NASA Airspace Systems Program's Air Traffic Management Technology Demonstration-1 (ATD-1). ATD-1 is intended to showcase an integrated set of technologies that provide an efficient arrival solution for managing aircraft using Next Generation Air Transportation System (NextGen) surveillance, navigation, procedures, and automation for both airborne and ground-based systems. The goal of the IMNOVA experiment was to assess if procedures outlined by the ATD-1 Concept of Operations were acceptable to and feasible for use by flight crews in a voice communications environment when used with a minimum set of Flight Deck-based Interval Management (FIM) equipment and a prototype crew interface. To investigate an integrated arrival solution using ground-based air traffic control tools and aircraft Automatic Dependent Surveillance-Broadcast (ADS-B) tools, the LaRC FIM system and the Traffic Management Advisor with Terminal Metering and Controller Managed Spacing tools developed at the NASA Ames Research Center (ARC) were integrated into LaRC's Air Traffic Operations Laboratory (ATOL). Data were collected from 10 crews of current 757/767 pilots asked to fly a high-fidelity, fixed-based simulator during scenarios conducted within an airspace environment modeled on the Dallas-Fort Worth (DFW) Terminal Radar Approach Control area. The aircraft simulator was equipped with the Airborne Spacing for Terminal Area Routes (ASTAR) algorithm and a FIM crew interface consisting of electronic flight bags and ADS-B guidance displays. Researchers used "pseudo-pilot" stations to control 24 simulated aircraft that provided multiple air traffic flows into the DFW International Airport, and recently retired DFW air traffic controllers served as confederate Center, Feeder, Final, and Tower controllers. Analyses of qualitative data revealed that the procedures used by flight crews to receive and execute interval management (IM) clearances in a voice communications environment were logical, easy to follow, did not contain any missing or extraneous steps, and required the use of an acceptable workload level. The majority of the pilot participants found the IM concept, in addition to the proposed FIM crew procedures, to be acceptable and indicated that the ATD-1 procedures could be successfully executed in a nearterm NextGen environment. Analyses of quantitative data revealed that the proposed procedures were feasible for use by flight crews in a voice communications environment. The delivery accuracy at the achieve-by point was within +/-5 sec, and the delivery precision was less than 5 sec. Furthermore, FIM speed commands occurred at a rate of less than one per minute, and pilots found the frequency of the speed commands to be acceptable at all times throughout the experiment scenarios.

Kibler, Jennifer L.

Wind Information Uplink to Aircraft Performing Interval Management Operations

Interval Management (IM) is an ADS-B-enabled suite of applications that use ground and flight deck capabilities and procedures designed to support the relative spacing of aircraft (Barmore et al., 2004, Murdoch et al. 2009, Barmore 2009, Swieringa et al. 2011; Weitz et al. 2012). Relative spacing refers to managing the position of one aircraft to a time or distance relative to another aircraft, as opposed to a static reference point such as a point over the ground or clock time. This results in improved inter-aircraft spacing precision and is expected to allow aircraft to be spaced closer to the applicable separation standard than current operations. Consequently, if the reduced spacing is used in scheduling, IM can reduce the time interval between the first and last aircraft in an overall arrival flow, resulting in increased throughput. Because IM relies on speed changes to achieve precise spacing, it can reduce costly, low-altitude, vectoring, which increases both efficiency and throughput in capacity-constrained airspace without negatively impacting controller workload and task complexity. This is expected to increase overall system efficiency. The Flight Deck Interval Management (FIM) equipment provides speeds to the flight crew that will deliver them to the achieve-by point at the controller-specified time, i.e., assigned spacing goal, after the target aircraft crosses the achieve-by point (Figure 1.1). Since the IM and target aircraft may not be on the same arrival procedure, the FIM equipment predicts the estimated times of arrival (ETA) for both the IM and target aircraft to the achieve-by point. This involves generating an approximate four-dimensional trajectory for each aircraft. The accuracy of the wind data used to generate those trajectories is critical to the success of the IM operation. There are two main forms of uncertainty in the wind information used by the FIM equipment. The first is the accuracy of the forecast modeling done by the weather provider. This is generally a global environmental prediction obtained from a weather model such as the Rapid Refresh (RAP) from the National Centers for Environmental Prediction (NCEP). The weather forecast data will have errors relative to the actual, or truth, winds that the aircraft will encounter. The second source of uncertainty is that only a small subset of the forecast data can be uplinked to the aircraft for use by the FIM equipment. This results in loss of additional information. The Federal Aviation Administration (FAA) and RTCA are currently developing standards for the communication of wind and atmospheric data to the aircraft for use in NextGen operations. This study examines the impact of various wind forecast sampling methods on IM performance metrics to inform the standards development.

Ahmad, Nashat N.

Development of an Interval Management Algorithm Using Ground Speed Feedback for Delayed Traffic

One of the goals of NextGen is to enable frequent use of Optimized Profile Descents (OPD) for aircraft, even during periods of peak traffic demand. NASA is currently testing three new technologies that enable air traffic controllers to use speed adjustments to space aircraft during arrival and approach operations. This will allow an aircraft to remain close to their OPD. During the integration of these technologies, it was discovered that, due to a lack of accurate trajectory information for the leading aircraft, Interval Management aircraft were exhibiting poor behavior. NASA's Interval Management algorithm was modified to address the impact of inaccurate trajectory information and a series of studies were performed to assess the impact of this modification. These studies show that the modification provided some improvement when the Interval Management system lacked accurate trajectory information for the leading aircraft.

Barmore, Bryan E.

Concept of Operations for Interval Management Arrivals and Approach

This paper presents the concept of operations for interval management operations to be deployed in the US National Airspace System (NAS) by the Federal Aviation Administration (FAA) after 2020. The use of interval management operations is described that begin in en route airspace and continue to a termination point inside the arrival terminal area, in a terminal environment that includes other arrival management tools such as arrival metering, Ground-based Interval Management - Spacing (GIM-S), and Terminal Sequencing and Spacing (TSAS). The roles of Air Traffic Controllers and Flight Crews and the ground automation tools that are used by Air Traffic Controllers to enable the primary operation and variations are described.

Hicok, Daniel S.

Advanced Interval Management: A Benefit Analysis

This document is the final report for the NASA Langley Research Center (LaRC)- sponsored task order 'Possible Benefits for Advanced Interval Management Operations.' Under this research project, Architecture Technology Corporation performed an analysis to determine the maximum potential benefit to be gained if specific Advanced Interval Management (AIM) operations were implemented in the National Airspace System (NAS). The motivation for this research is to guide NASA decision-making on which Interval Management (IM) applications offer the most potential benefit and warrant further research.

Timer, Sebastian

Air Traffic Management Technology Demonstration-1 (ATD-1) Avionics Phase 2 Flight Test Training for Interval Management

Prior to the successful flight test validation of a new avionics prototype, participants from Boeing, Honeywell, and United Airlines underwent group training at NASA Langley Research Center. New prototype software for an algorithm which enables greater efficiency in high-density airspace, called Interval Management, was to be incorporated into Electronic Flight Bags and placed in the cockpit for pilot usage. The goals of the training were to teach the flight test pilots how to operate the new software, establish techniques to simultaneously position three aircraft prior to each test scenario, and ensure a common communication protocol among team members when coordinating the position of aircraft for the next scenario. The multi-tiered interactive training regimen consisted of a process that continually built upon previous foundational material. The primary learning elements were 1) a portable computer-based trainer that was provided to the pilots prior to classroom training sessions, 2) classroom learning, 3) full mock-up simulator training, and 4) refresher training just prior to the flight test. Each part of the regimen was designed to repeat and build upon the previous element. The purpose of this Technical Memorandum is to inform the aviation industry how flight training for Interval Management was conducted at Langley Research Center in order to reduce overall development costs of future Interval Management training programs. Secondly, the paper provides insight regarding the decision-making process when attempting to conduct a flight test.

Roper, Roy D.

PMSM Parameter Estimation using a Linear Unknown Input Interval Observer

In this paper, the problem of permanent magnet synchronous motor (PMSM) speed and unknown load torque estimation is addressed. For this purpose, a interval unknown input observer (UIO) for linear time-invariant (LTI) systems is used. First, the PMSM model is linearized in order to make it in a suitable form for the linear interval UIO. Then, the interval UIO is applied to allow the joint estimation of the motor speed and the unknown load torque disturbance. The main advantages of this approach is that it not only allows the joint state and unknown input estimation, but also to take the different uncertainty sources into account. Indeed, taking model and measurement uncertainty into account is crucial. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state (motor speed) and then for the unknown input (load torque). The proposed approach and its limitations are demonstrated with the nonlinear PMSM model derived from its equivalent electrical circuit.

Elinirina I Robinson