Signal power distributions for simulated outdoor sound propagation in varying refractive conditions.

Probability distributions of acoustic signals propagating through the near-ground atmosphere are simulated by the parabolic equation method. The simulations involve propagation at four angles relative to the mean wind, with frequencies of 100, 200, 400, and 800 Hz. The environmental representation includes realistic atmospheric refractive profiles, turbulence, and ground interactions; cases are considered with and without parametric uncertainties in the wind velocity and surface heat flux. The simulated signals are found to span a broad range of scintillation indices, from near zero to exceeding ten. In the absence of uncertainties, the signal power (or intensity) is fit well by a two-parameter gamma distribution, regardless of the frequency and refractive conditions. When the uncertainties are included, three-parameter distributions, namely, the compound gamma or generalized gamma, are needed for a good fit to the simulation data. The compound gamma distribution appears preferable because its parameters have a straight forward interpretation related to the saturation and modulation of the signal by uncertainties.

Comprehensive compartmental model and calibration algorithm for the study of clinical implications of the population-level spread of COVID-19: a study protocol.

INTRODUCTION: The complex dynamics of the coronavirus disease 2019 (COVID-19) pandemic has made obtaining reliable long-term forecasts of the disease progression difficult. Simple mechanistic models with deterministic parameters are useful for short-term predictions but have ultimately been unsuccessful in extrapolating the trajectory of the pandemic because of unmodelled dynamics and the unrealistic level of certainty that is assumed in the predictions. METHODS AND ANALYSIS: We propose a 22-compartment epidemiological model that includes compartments not previously considered concurrently, to account for the effects of vaccination, asymptomatic individuals, inadequate access to hospital care, post-acute COVID-19 and recovery with long-term health complications. Additionally, new connections between compartments introduce new dynamics to the system and provide a framework to study the sensitivity of model outputs to several concurrent effects, including temporary immunity, vaccination rate and vaccine effectiveness. Subject to data availability for a given region, we discuss a means by which population demographics (age, comorbidity, socioeconomic status, sex and geographical location) and clinically relevant information (different variants, different vaccines) can be incorporated within the 22-compartment framework. Considering a probabilistic interpretation of the parameters allows the model's predictions to reflect the current state of uncertainty about the model parameters and model states. We propose the use of a sparse Bayesian learning algorithm for parameter calibration and model selection. This methodology considers a combination of prescribed parameter prior distributions for parameters that are known to be essential to the modelled dynamics and automatic relevance determination priors for parameters whose relevance is questionable. This is useful as it helps prevent overfitting the available epidemiological data when calibrating the parameters of the proposed model. Population-level administrative health data will serve as partial observations of the model states. ETHICS AND DISSEMINATION: Approved by Carleton University's Research Ethics Board-B (clearance ID: 114596). Results will be made available through future publication.

Machine-learning of long-range sound propagation through simulated atmospheric turbulence.

Conventional numerical methods can capture the inherent variability of long-range outdoor sound propagation. However, computational memory and time requirements are high. In contrast, machine-learning models provide very fast predictions. This comes by learning from experimental observations or surrogate data. Yet, it is unknown what type of surrogate data is most suitable for machine-learning. This study used a Crank-Nicholson parabolic equation (CNPE) for generating the surrogate data. The CNPE input data were sampled by the Latin hypercube technique. Two separate datasets comprised 5000 samples of model input. The first dataset consisted of transmission loss (TL) fields for single realizations of turbulence. The second dataset consisted of average TL fields for 64 realizations of turbulence. Three machine-learning algorithms were applied to each dataset, namely, ensemble decision trees, neural networks, and cluster-weighted models. Observational data come from a long-range (out to 8 km) sound propagation experiment. In comparison to the experimental observations, regression predictions have 5-7 dB in median absolute error. Surrogate data quality depends on an accurate characterization of refractive and scattering conditions. Predictions obtained through a single realization of turbulence agree better with the experimental observations.

Distribution of the two-point product of complex amplitudes in the fully saturated scattering regime.

This Letter considers probability density functions (pdfs) involving products of the complex amplitudes observed at two points (which may, in general, involve separations in space, time, or frequency) in conditions of fully saturated scattering. First, the pdf is derived for the product of the complex amplitude at one point with the conjugate of the complex amplitude at another point. It is shown that the real and imaginary parts of this product each have a variance gamma pdf. Second, expressions are derived for several joint pdfs involving complex amplitude products and powers at two points.

Multilevel modeling and regression of community annoyance to transportation noise.

A multilevel (hierarchical) model is devised that separates noise tolerance into variations occurring at the levels of individual listeners and communities. This approach successfully describes the characteristics of real community transportation noise surveys, with the individual- and community-level variations producing distinct statistical signatures, both of which are evident in the surveys. Predictions are provided for quantities such as the probability of annoyance based on the observed noise level and statistical parameters characterizing the community tolerance. Regression analyses are performed using a multilevel, generalized linear model, which provides an appropriate generalization encompassing both no pooling (separate community-by-community analysis) and full pooling (all communities together) of survey data, and enables noise tolerances and their variations at the individual and community levels to be distinguished and quantified. Variations in individual tolerance and sound exposure within communities are found to be larger than variations in tolerance between communities; however, the variations between communities are still significant and observable. Analysis of multiple types of transportation noise with the multilevel model indicates that tolerance is highest for railway noise with low vibrations, followed by roadway noise, airport noise, and railway noise with high vibrations, as consistent with previous studies.

Comparisons between physics-based, engineering, and statistical learning models for outdoor sound propagation.

Many outdoor sound propagation models exist, ranging from highly complex physics-based simulations to simplified engineering calculations, and more recently, highly flexible statistical learning methods. Several engineering and statistical learning models are evaluated by using a particular physics-based model, namely, a Crank-Nicholson parabolic equation (CNPE), as a benchmark. Narrowband transmission loss values predicted with the CNPE, based upon a simulated data set of meteorological, boundary, and source conditions, act as simulated observations. In the simulated data set sound propagation conditions span from downward refracting to upward refracting, for acoustically hard and soft boundaries, and low frequencies. Engineering models used in the comparisons include the ISO 9613-2 method, Harmonoise, and Nord2000 propagation models. Statistical learning methods used in the comparisons include bagged decision tree regression, random forest regression, boosting regression, and artificial neural network models. Computed skill scores are relative to sound propagation in a homogeneous atmosphere over a rigid ground. Overall skill scores for the engineering noise models are 0.6%, -7.1%, and 83.8% for the ISO 9613-2, Harmonoise, and Nord2000 models, respectively. Overall skill scores for the statistical learning models are 99.5%, 99.5%, 99.6%, and 99.6% for bagged decision tree, random forest, boosting, and artificial neural network regression models, respectively.

Description and quantification of uncertainty in outdoor sound propagation calculations.

The accuracy of outdoor sound propagation predictions is often limited by imperfect knowledge of the atmospheric and ground properties, and random environmental variations such as turbulence. This article describes the impact of such uncertainties, and how they can be efficiently addressed and quantified with stochastic sampling techniques such as Monte Carlo and Latin hypercube sampling (LHS). Extensions to these techniques, such as importance sampling based on simpler, more efficient propagation models, and adaptive importance sampling, are described. A relatively simple example problem involving the Lloyd's mirror effect for an elevated sound source in a homogeneous atmosphere is considered first, followed by a more complicated example involving near-ground sound propagation with refraction and scattering by turbulence. When uncertainties in the atmospheric and ground properties dominate, LHS with importance sampling is found to converge to an accurate estimate with the fewest samples. When random turbulent scattering dominates, the sampling method has little impact. A comprehensive computational approach is demonstrated that is both efficient and accurate, while simultaneously incorporating broadband sources, turbulent scattering, and uncertainty in the environmental properties.

Information-criterion based selection of models for community noise annoyance.

Statistical evidence for various models relating day-night sound level (DNL) to community noise annoyance is assessed with the Akaike information criterion. In particular, community-specific adjustments such as the community tolerance level (CTL, the DNL at which 50% of survey respondents are highly annoyed) and community tolerance spread (CTS, the difference between the DNL at which 90% and 10% are highly annoyed) are considered. The results strongly support models characterizing annoyance on a community-by-community basis, rather than with complete pooling and analysis of all available surveys. The most likely model was found to be a 2-parameter logistic model, with CTL and CTS fit independently to survey data from each community.

Proper orthogonal decomposition and cluster weighted modeling for sensitivity analysis of sound propagation in the atmospheric surface layer.

Outdoor sound propagation predictions are compromised by uncertainty and error in the atmosphere and terrain representations, and sometimes also by simplified or incorrect physics. A model's predictive power, i.e., its accurate representation of the sound propagation, cannot be assessed without first quantifying the ensemble sound pressure variability and sensitivity to uncertainties in the model's governing parameters. This paper describes fundamental steps toward this goal for a single-frequency point source. The atmospheric surface layer is represented through Monin-Obukhov similarity theory and the acoustic ground properties with a relaxation model. Sound propagation is predicted with the parabolic equation method. Governing parameters are modeled as independent random variables across physically reasonable ranges. Latin hypercube sampling and proper orthogonal decomposition (POD) are employed in conjunction with cluster-weighted models to develop compact representations of the sound pressure random field. Full-field sensitivity of the sound pressure field is computed via the sensitivities of the POD mode coefficients to the system parameters. Ensemble statistics of the full-field sensitivities are computed to illustrate their relative importance at every down range location. The central role of sensitivity analysis in uncertainty quantification of outdoor sound propagation is discussed and pitfalls of sampling-based sensitivity analysis for outdoor sound propagation are described.

Characterization of uncertainty in outdoor sound propagation predictions.

Predictive skill for outdoor sound propagation is assessed using high-resolution atmospheric fields from large-eddy simulations (LES). Propagation calculations through the full LES fields are compared to calculations through subsets of the LES fields that have been processed in typical ways, such as mean vertical profiles and instantaneous vertical profiles synchronized to the sound propagation. It is found that mean sound pressure levels can be predicted with low errors from the mean profiles, except in refractive shadow regions. Prediction of sound pressure levels for short-duration events is much less accurate, with errors of 8 -10 dB for near-ground propagation being typical.