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Parameter and Structure Inference for Nonlinear Dynamical Systems

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Morris, Robin D.↗

Narrow band noise as a model of time-dependent accelerations - Study of the stability of a fluid surface in a microgravity environment

We introduce a stochastic model to analyze in quantitative detail the effect of the high frequency components of the residual accelerations onboard spacecraft (often called g-jitter) on fluid motion. The residual acceleration field is modeled as a narrow band noise characterized by three independent parameters: its intensity G squared, a dominant frequency Omega, and a characteristic spectral width tau exp -1. The white noise limit corresponds to Omega tau goes to O, with G squared tau finite, and the limit of a periodic g-jitter (or deterministic limit) can be recovered for Omega tau goes to infinity, G squared finite. The analysis of the response of a fluid surface subjected to a fluctuating gravitational field leads to the stochastic Mathieu equation driven by both additive and multiplicative noise. We discuss the stability of the solutions of this equation in the two limits of white noise and deterministic forcing, and in the general case of narrow band noise. The results are then applied to typical microgravity conditions.

Casademunt, Jaume↗

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of the tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiements were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiements. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. With few exceptions the error estimated generated by the Kalman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter ouput and the actual observations were drawn from a population with statistics given by the Kalman filter estimaes. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Miller, Robert N.↗

Landing Gear Noise Prediction and Analysis for Tube-and-Wing and Hybrid-Wing-Body Aircraft

Improvements and extensions to landing gear noise prediction methods are developed. New features include installation effects such as reflection from the aircraft, gear truck angle effect, local flow calculation at the landing gear locations, gear size effect, and directivity for various gear designs. These new features have not only significantly improved the accuracy and robustness of the prediction tools, but also have enabled applications to unconventional aircraft designs and installations. Systematic validations of the improved prediction capability are then presented, including parametric validations in functional trends as well as validations in absolute amplitudes, covering a wide variety of landing gear designs, sizes, and testing conditions. The new method is then applied to selected concept aircraft configurations in the portfolio of the NASA Environmentally Responsible Aviation Project envisioned for the timeframe of 2025. The landing gear noise levels are on the order of 2 to 4 dB higher than previously reported predictions due to increased fidelity in accounting for installation effects and gear design details. With the new method, it is now possible to reveal and assess the unique noise characteristics of landing gear systems for each type of aircraft. To address the inevitable uncertainties in predictions of landing gear noise models for future aircraft, an uncertainty analysis is given, using the method of Monte Carlo simulation. The standard deviation of the uncertainty in predicting the absolute level of landing gear noise is quantified and determined to be 1.4 EPNL dB.

Guo, Yueping↗

Readout Noise of Digital Frequency Multiplexed TES Detectors for CUPID

The superconducting transition-edge sensor (TES) detectors have been the standard in cosmic microwave background (CMB) experiments for almost two decades and are now being adapted for use in nuclear physics, such as neutrinoless double beta decay searches. In this article, we focus on a new high-bandwidth frequency multiplexed TES readout system developed for CUPID, a neutrinoless double beta decay experiment that will replace CUORE. In order to achieve the high energy resolution requirements for CUPID, the readout noise of the system must be kept to a minimum. Low TES operating resistance and long wiring between the readout SQUID and the warm electronics are needed for CUPID, prompting a careful consideration of the design parameters of this application of frequency multiplexing. In this work, we characterize the readout noise of the newly designed frequency multiplexed TES readout system for CUPID and construct a noise model to understand it. Here, we find that current sharing between the SQUID coil impedance and other branches of the circuit, as well as the long output wiring, worsen the readout noise of the system. To meet noise requirements, a SQUID with a low input inductance, high transimpedance, and/or low dynamic impedance is needed, and the wiring capacitance should be kept as small as possible. Alternatively, the option of adding a cryogenic low-noise amplifier at the output of the SQUID should be explored.

CUPID↗

Spatially random models, estimation theory, and robot arm dynamics

Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

Rodriguez, G.↗

Forced response sound radiation from acoustically or mechanically excited small plates

Sound radiation from an acoustically excited, clamped aluminum plate is measured and expressed in terms of noise reduction to take into account the incident acoustic excitation field. Its mode shapes and modal frequencies are measured and show good agreement with the predictions from a finite element MSC/NASTRAN model. Noise reduction is measured at 15 points behind the plate and demonstrate good agreement with predictions employing the SYSNOISE numerical analysis system for acoustic-structure interaction.

Grosveld, Ferdinand W.↗

The Effect of Bypass Nozzle Exit Area on Fan Aerodynamic Performance and Noise in a Model Turbofan Simulator

The design of effective new technologies to reduce aircraft propulsion noise is dependent on identifying and understanding the noise sources and noise generation mechanisms in the modern turbofan engine, as well as determining their contribution to the overall aircraft noise signature. Therefore, a comprehensive aeroacoustic wind tunnel test program was conducted called the Fan Broadband Source Diagnostic Test as part of the NASA Quiet Aircraft Technology program. The test was performed in the anechoic NASA Glenn 9- by 15-Foot Low Speed Wind Tunnel using a 1/5 scale model turbofan simulator which represented a current generation, medium pressure ratio, high bypass turbofan aircraft engine. The investigation focused on simulating in model scale only the bypass section of the turbofan engine. The test objectives were to: identify the noise sources within the model and determine their noise level; investigate several component design technologies by determining their impact on the aerodynamic and acoustic performance of the fan stage; and conduct detailed flow diagnostics within the fan flow field to characterize the physics of the noise generation mechanisms in a turbofan model. This report discusses results obtained for one aspect of the Source Diagnostic Test that investigated the effect of the bypass or fan nozzle exit area on the bypass stage aerodynamic performance, specifically the fan and outlet guide vanes or stators, as well as the farfield acoustic noise level. The aerodynamic performance, farfield acoustics, and Laser Doppler Velocimeter flow diagnostic results are presented for the fan and four different fixed-area bypass nozzle configurations. The nozzles simulated fixed engine operating lines and encompassed the fan stage operating envelope from near stall to cruise. One nozzle was selected as a baseline reference, representing the nozzle area which would achieve the design point operating conditions and fan stage performance. The total area change from the smallest to the largest nozzle was 12.9 percent of the baseline nozzle area. The results will show that there are significant changes in aerodynamic performance and farfield acoustics as the fan nozzle area is increased. The weight flow through the fan model increased between 7 and 9 percent, the fan and stage pressure dropped between 8 and 10 percent, and the adiabatic efficiency increased between 2 and 3 percent--the magnitude of the change dependent on the fan speed. Results from force balance measurements of fan and outlet guide vane thrust will show that as the nozzle exit area is increased the combined thrust of the fan and outlet guide vanes together also increases, between 2 and 3.5 percent, mainly due to the increase in lift from the outlet guide vanes. In terms of farfield acoustics, the overall sound power level produced by the fan stage dropped nearly linearly between 1 dB at takeoff condition and 3.5 dB at approach condition, mainly due to a decrease in the broadband noise levels. Finally, fan swirl angle survey and Laser Doppler Velocimeter mean velocity and turbulence data obtained in the fan wake will show that the swirl angles and turbulence levels within the wake decrease as the fan nozzle area increases, which helps to explain the drop in the fan broadband noise at all fan speeds.

Hughes, Christopher E.↗

Empirical modeling for intelligent, real-time manufacture control

Artificial neural systems (ANS), also known as neural networks, are an attempt to develop computer systems that emulate the neural reasoning behavior of biological neural systems (e.g. the human brain). As such, they are loosely based on biological neural networks. The ANS consists of a series of nodes (neurons) and weighted connections (axons) that, when presented with a specific input pattern, can associate specific output patterns. It is essentially a highly complex, nonlinear, mathematical relationship or transform. These constructs have two significant properties that have proven useful to the authors in signal processing and process modeling: noise tolerance and complex pattern recognition. Specifically, the authors have developed a new network learning algorithm that has resulted in the successful application of ANS's to high speed signal processing and to developing models of highly complex processes. Two of the applications, the Weld Bead Geometry Control System and the Welding Penetration Monitoring System, are discussed in the body of this paper.

Xu, Xiaoshu↗

A broad-band low-noise SIS receiver for submillimeter astronomy

A quasi-optical heterodyne receiver using a Pb-alloy superconductor-insulator-superconductor (SIS) tunnel junction as the detector and a planar logarithmic spiral antenna for the RF coupling is described, and its performance is compared with a the predicted performance of a theoretical model. Noise measurements were made in the laboratory at frequencies between 115 GHz and 761 GHz, yielding double-sideband noise temperatures ranging from 33 K to 1100 K. The receiver has also been used for astronomical spectroscopy on the Caltech Submillimeter Observatory (Mauna Kea, Hawaii) at 115, 230, 345, and 492 GHz.

Buttgenbach, Thomas H.↗

Terrain Relative Navigation for Guided Descent on Titan

Titan’s dense atmosphere, low gravity, and high winds at high altitudes create descent times of >90 minutes with standard entry/descent/landing (EDL) architectures and result in large unguided landing ellipses, with 99% values of 110x110 km and 149x72 km in recent Titan lander proposals. Enabling precision landing on Titan could increase science return for the types of missions proposed to date and make additional types of landing sites accessible, opening up new possibilities for science investigations. Precision landing on Titan has unique challenges, because the hazy atmosphere makes it difficult to see the surface and because it requires guided descent with divert ranges that are one to two orders of magnitude larger than needed for other target bodies, i.e. up to on the order of 100 km. It is conceivable that such a divert capability could be provided economically by a parafoil or other steerable aerodynamic decelerator deployed several 10s of km above the surface. The long descent times lead to large inertial navigation errors, hence a need for terrain relative navigation (TRN). This would require a TRN capability that can operate at such altitudes, despite challenges of seeing the surface sufficiently clearly and of depending on map products that are two orders of magnitude lower in spatial resolution than those for Mars and airless bodies. We then develop algorithms for map matching and feature tracking with descent images and test these with synthetic images created from Cassini/Huygens data sets and our radiative transfer model. We also introduce new possibilities for TRN based on the potential to discriminate some specific types of terrain onboard in descent imagery, such as lake vs adjacent ground and dune vs interdune. We use sensor measurement noise models in simulations of state estimation with an extended Kalman filter that includes coordinates of a set of tracked features in the state vector. Case studies were done for two notional landing sites, one in a site with only dry ground and one in a Titan lake district. In both cases, the filter error model shows 3 position error at touchdown on the order of 2 km. More work is needed to validate these results with higher fidelity camera models and larger data sets, but this is very promising.

Matthies, Larry↗

Signal-to-noise ratios in IUE SWP-LO spectra of chromospheric emission-line sources

The short-wavelength-prime (SWP) detector of the International Ultraviolet Explorer should operate near the photon-counting limit, but the noise levels in flat-field images are several times higher. The exaggerated noise can be traced to the incomplete removal of the pixel-to-pixel granularity of the television frames by the prevailing spectral image processing system. An empirical noise model for the current-epoch photometric linearization strategy and one for a hypothetical processing system that achieves complete flat fielding of the raw images are derived. A formula is then proposed to predict the signal-to-noise ratio in the measured flux of an emission line (possibly superimposed on a smooth continuum) in an IUE low-dispersion (5 A resolution) far-ultraviolet (1150 A-1950 A) spectrum as recorded with the SWP camera. For illustration, the formula is specialized to the important C IV 1549 A feature of F-K stars. The S/N relation permits one to determine sensitivity limits, upper limits in faint exposures, and optimum exposure times.

Ayres, Thomas R.↗

Short-term time variability of Cygnus X-1. III

Data from a SAS 3 observation of Cygnus X-1 have been analyzed, assuming a simple shot-noise model for the time variability. The results confirm the suggestion of Sutherland, Weisskopf, and Kahn that the shot parameters are constant when the source is in its low state. The first significant measurement of the time sense of the shot-noise pulses was performed, with the result that the average pulse shape is time-symmetric, not asymmetric as has been previously assumed.

Weisskopf, M. C.↗

Supersonics Project - Airport Noise Tech Challenge

The Airport Noise Tech Challenge research effort under the Supersonics Project is reviewed. While the goal of "Improved supersonic jet noise models validated on innovative nozzle concepts" remains the same, the success of the research effort has caused the thrust of the research to be modified going forward in time. The main activities from FY06-10 focused on development and validation of jet noise prediction codes. This required innovative diagnostic techniques to be developed and deployed, extensive jet noise and flow databases to be created, and computational tools to be developed and validated. Furthermore, in FY09-10 systems studies commissioned by the Supersonics Project showed that viable supersonic aircraft were within reach using variable cycle engine architectures if exhaust nozzle technology could provide 3-5dB of suppression. The Project then began to focus on integrating the technologies being developed in its Tech Challenge areas to bring about successful system designs. Consequently, the Airport Noise Tech Challenge area has shifted efforts from developing jet noise prediction codes to using them to develop low-noise nozzle concepts for integration into supersonic aircraft. The new plan of research is briefly presented by technology and timelines.

Bridges, James↗

NASA Jet Noise Research

The presentation highlights NASA's jet noise research for 2016. Jet-noise modeling efforts, jet-surface interactions results, acoustic characteristics of multi-stream jets, and N+2 Supersonic Aircraft system studies are presented.

reduction↗

Four-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: On-sky Receiver Performance at 40, 90, 150, and 220 GHz Frequency Bands

The Cosmology Large Angular Scale Surveyor (CLASS) observes the polarized cosmic microwave background (CMB) over the angular scales of 1° ≲ θ ≤ 90° with the aim of characterizing primordial gravitational waves and cosmic reionization. We report on the on-sky performance of the CLASS Q-band (40 GHz), W-band (90 GHz), and dichroic G-band (150/220 GHz) receivers that have been operational at the CLASS site in the Atacama desert since 2016 June, 2018 May, and 2019 September, respectively. We show that the noise-equivalent power measured by the detectors matches the expected noise model based on on-sky optical loading and lab-measured detector parameters. Using Moon, Venus, and Jupiter observations, we obtain power to antenna temperature calibrations and optical efficiencies for the telescopes. From the CMB survey data, we compute instantaneous array noise-equivalent-temperature sensitivities of 22, 19, 23, and 71 $\mu {{\rm{K}}}_{\mathrm{cmb}}\sqrt{{\rm{s}}}$ for the 40, 90, 150, and 220 GHz frequency bands, respectively. These noise temperatures refer to white noise amplitudes, which contribute to sky maps at all angular scales. Future papers will assess additional noise sources impacting larger angular scales.

Observational cosmology↗

Characterizing and Mitigating Intraday Variability: Reconstructing Source Structure in Accreting Black Holes with mm-VLBI

The extraordinary physical resolution afforded by the Event Horizon Telescope has opened a window onto the astrophysical phenomena unfolding on horizon scales in two known black holes, M87* and Sgr A*. However, with this leap in resolution has come a new set of practical complications. Sgr A* exhibits intraday variability that violates the assumptions underlying Earth aperture synthesis, limiting traditional image reconstruction methods to short timescales and data sets with very sparse (u, v) coverage. We present a new set of tools to detect and mitigate this variability. We develop a data-driven, model-agnostic procedure to detect and characterize the spatial structure of intraday variability. This method is calibrated against a large set of mock data sets, producing an empirical estimator of the spatial power spectrum of the brightness fluctuations. We present a novel Bayesian noise modeling algorithm that simultaneously reconstructs an average image and statistical measure of the fluctuations about it using a parameterized form for the excess variance in the complex visibilities not otherwise explained by the statistical errors. These methods are validated using a variety of simulated data, including general relativistic magnetohydrodynamic simulations appropriate for Sgr A* and M87*. We find that the reconstructed source structure and variability are robust to changes in the underlying image model. We apply these methods to the 2017 EHT observations of M87*, finding evidence for variability across the EHT observing campaign. The variability mitigation strategies presented are widely applicable to very long baseline interferometry observations of variable sources generally, for which they provide a data-informed averaging procedure and natural characterization of inter-epoch image consistency.

79 ASTRONOMY AND ASTROPHYSICS↗