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DOE OSTI2023

Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for \({\boldsymbol{\mathcal{H}_2}}\) Model Reduction

This paper presents an extension of the Adaptive-Antoulas-Anderson (AAA) algorithm for rational modelling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing stability constraints on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published RKFIT algorithm. Vector Fitting and RKFIT both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must re-start Vector Fitting or RKFIT with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by AAA is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. In conclusion, the examples presented demonstrate that smiAAA can efficiently produce approximations of similar or better accuracy than Vector Fitting and RKFIT while requiring less input from the user.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗

NASA NTRS1978

AAA gunnermodel based on observer theory

The Luenberger observer theory is used to develop a predictive model of a gunner's tracking response in antiaircraft artillery systems. This model is composed of an observer, a feedback controller and a remnant element. An important feature of the model is that the structure is simple, hence a computer simulation requires only a short execution time. A parameter identification program based on the least squares curve fitting method and the Gauss Newton gradient algorithm is developed to determine the parameter values of the gunner model. Thus, a systematic procedure exists for identifying model parameters for a given antiaircraft tracking task. Model predictions of tracking errors are compared with human tracking data obtained from manned simulation experiments. Model predictions are in excellent agreement with the empirical data for several flyby and maneuvering target trajectories.

Kou, R. S.↗

NASA NTRS2015

Avionics Configuration Assessment for Flightdeck Interval Management: A Comparison of Avionics and Notification Methods

Flightdeck Interval Management is one of the NextGen operational concepts that FAA is sponsoring to realize requisite National Airspace System (NAS) efficiencies. Interval Management will reduce variability in temporal deviations at a position, and thereby reduce buffers typically applied by controllers - resulting in higher arrival rates, and more efficient operations. Ground software generates a strategic schedule of aircraft pairs. Air Traffic Control (ATC) provides an IM clearance with the IM spacing objective (i.e., the TTF, and at which point to achieve the appropriate spacing from this aircraft) to the IM aircraft. Pilots must dial FIM speeds into the speed window on the Mode Control Panel in a timely manner, and attend to deviations between actual speed and the instantaneous FIM profile speed. Here, the crew is assumed to be operating the aircraft with autothrottles on, with autopilot engaged, and the autoflight system in Vertical Navigation (VNAV) and Lateral Navigation (LNAV); and is responsible for safely flying the aircraft while maintaining situation awareness of their ability to follow FIM speed commands and to achieve the FIM spacing goal. The objective of this study is to examine whether three Notification Methods and four Avionics Conditions affect pilots' performance, ratings on constructs associated with performance (workload, situation awareness), or opinions on acceptability. Three Notification Methods (alternate visual and aural alerts that notified pilots to the onset of a speed target, conformance deviation from the required speed profile, and reminded them if they failed to enter the speed within 10 seconds) were examined. These Notification Methods were: VVV (visuals for all three events), VAV (visuals for all three events, plus an aural for speed conformance deviations), and AAA (visual indications and the same aural to indicate all three of these events). Avionics Conditions were defined by the instrumentation (and location) used to present IM information to crews: (1) Integrated (IM information is embedded in extant PFD (Primary Flight Display), ND (Navigation Display), EICAS (Engine Indicating and Crew Alerting System) displays); (2) EFB_Aft (IM information is only supplied in an EFB and mounted in location similar to that for MITRE's UPS work); (3) EFB_Fore (IM information is only supplied in an EFB which is mounted more forward, under the side window), and (4) EFB_Aft plus use of an AGD (the same IM information is supplied in an EFB and on an AGD, both mounted in locations similar to that in MITRE's UPS work ). Twelve commercial pilot crews flew descent scenarios (VNAV Speed with the mode control panel (MCP) speed window open until flaps extended, then VNAV Path) in a commercial transport flight simulator with realistic visual scene and communications. The results of this study serve three practical aims: (1) contribute to the down-select of avionics configuration for future assessment of the ASTAR spacing algorithm at NASA; (2) provide information useful to the FAA Human Factors Division (ANG-C1)'s mission to identify issues pertinent to flight certification of, and flight standards; (3) identify methodological considerations in support of future FIM human-in-the-loop (HITL) investigations.

Latorella, Kara A.↗