Developmental design, fabrication, and test of acoustic suppressors for fans of high bypass turbofan engines

An analysis procedure was developed for design of acoustically treated nacelles for high bypass turbofan engines. The plan was applied to the conceptual design of a nacelle for the quiet engine typical of a 707/DC-8 airplane installation. The resultant design was modified to a test nacelle design for the NASA Lewis quiet fan. The acoustic design goal was a 10 db reduction in effective perceived fan noise levels during takoff and approach. Detailed nacelle designs were subsequently developed for both the quiet engine and the quiet fan. The acoustic design goal for each nacelle was 15 db reductions in perceived fan noise levels from the inlet and fan duct. Acoustically treated nacelles were fabricated for the quiet engine and quiet fan for testing. Performance of selected inlet and fan duct lining configurations was experimentally evaluated in a flow duct. Results of the tests show that the linings perform as designed

Statistical Communication Theory

Contains reports on two research projects.National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-04),National Aeronautics and Space Administration (Grant NsG-496

Sediment-Induced Amplification in the Northeastern United States: a Case Study in Providence, Rhode Island

We employed ambient-noise measurements to assess the potential for seismic site response in sediment-filled valleys that intersect beneath downtown Providence, Rhode Island. At eight valley stations and at two sites on an adjacent bedrock highland, we recorded ground motion from two types of sources: pile drivers at a local construction site and ambient microtremors. At all valley sites where sediment thicknesses exceed 10 m, spectral ratios contain amplitude peaks at frequencies of 1.5 to 3.0 Hz. In contrast, spectral ratios from the two sites on the bedrock highland where sediment cover is less than 4-m thick are relatively flat within this frequency range. A variety of borehole logs identified two fundamental sediment types (soft sediment and a consolidated glacial till) and were used to map layer thicknesses over the entire study region. Refraction data constrained P-wave velocity in the bedrock to be 3680 ± 160 m/sec and indicated two soft-sediment layers with P-wave velocities of 300 ± 50 and 1580 ± 120 m/sec. Using a one-dimensional reflection matrix technique, we matched the spectral-ratio peak observed at each valley site with the frequency of fundamental resonance predicted for local layer thicknesses and velocities. A positive correlation between the best-fitting soft-sediment velocities and bedrock depth may reflect greater compaction in the deepest sediments or a locally two-dimensional sediment resonance at the deepest sediment sites. We conclude that unconsolidated sediment layers under downtown Providence have the potential to amplify earthquake ground motion at frequencies damaging to engineered structures

Multivariate Copula Analysis Toolbox (MvCAT): Describing Dependence and Underlying Uncertainty Using a Bayesian Framework

We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual-based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid-evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis

Signal Processing

Contains reports on three research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

An information theoretic approach to statistical dependence: copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Statistical Communication Theory

Contains reports on eleven completed research projects and four on-going research projects.Joint Services Electronics Program (Contract DA36-039-AMC-03200(E))National Science Foundation (Grant GP-2495)National Aeronautics and Space Administration (Grant NsG-334)National Aeronautics and Space Administration (Grant NsG-496

Signal Processing

Contains research objectives and reports on work completed and one research project.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Statistical Communication Theory

Contains reports on five research projects.National Science Foundation (Grant GP- 2495)National Institutes of Health (Grant MH-04737-05)National Aeronautics and Space Administration (Grant NsG-496