Model and parameter uncertainty in IDF relationships under climate change

Quantifying distributional behavior of extreme events is crucial in hydrologic designs. Intensity Duration Frequency (IDF) relationships are used extensively in engineering especially in urban hydrology, to obtain return level of extreme rainfall event for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty due to the distribution fitted to the data and uncertainty as a result of using multiple GCMs. It is important to study these uncertainties and propagate them to future for accurate assessment of return levels for future. The objective of this study is to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using Bayesian approach. Posterior distribution of parameters is obtained from Bayes rule and the parameters are transformed to obtain return levels for a specified return period. Markov Chain Monte Carlo (MCMC) method using Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Twenty six CMIP5 GCMs along with four RCP scenarios are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore city in India. GCM uncertainty due to the use of multiple GCMs is treated using Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty. (C) 2015 Elsevier Ltd. All rights reserved.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation.

Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

Uncertainty Quantification in Ultrasonic Wave Based Detection of Delamination in Composite Structures

In this paper we consider the problem of guided wave scattering from delamination in laminated composite and further the problem of estimating delamination size and layer-wise location from the guided wave measurement. Damage location and region/size can be estimated from time of flight and wave packet spread, whereas depth information can be obtained from wavenumber modulation in the carrier packet. The key challenge is that these information are highly sensitive to various uncertainties. Variation in reflected and transmitted wave amplitude in a bar due to boundary/interface uncertainty is studied to illustrate such effect. Effect of uncertainty in material parameters on the time of flight are estimated for longitudinal wave propagation. To evaluate the effect of uncertainty in delamination detection, we employ a time domain spectral finite element (tSFEM) scheme where wave propagation is modeled using higher-order interpolation with shape function have spectral convergence properties. A laminated composite beam with layer-wise placement of delamination is considered in the simulation. Scattering due to the presence of delamination is analyzed. For a single delamination, two identical waveforms are created at the two fronts of the delamination, whereas waves in the two sub-laminates create two independent waveforms with different wavelengths. Scattering due to multiple delaminations in composite beam is studied.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Damage assessment of composite plate structures with material and measurement uncertainty

Composite materials are very useful in structural engineering particularly in weight sensitive applications. Two different test models of the same structure made from composite materials can display very different dynamic behavior due to large uncertainties associated with composite material properties. Also, composite structures can suffer from pre-existing imperfections like delaminations, voids or cracks during fabrication. In this paper, we show that modeling and material uncertainties in composite structures can cause considerable problein in damage assessment. A recently developed C-0 shear deformable locking free refined composite plate element is employed in the numerical simulations to alleviate modeling uncertainty. A qualitative estimate of the impact of modeling uncertainty on the damage detection problem is made. A robust Fuzzy Logic System (FLS) with sliding window defuzzifier is used for delamination damage detection in composite plate type structures. The FLS is designed using variations in modal frequencies due to randomness in material properties. Probabilistic analysis is performed using Monte Carlo Simulation (MCS) on a composite plate finite element model. It is demonstrated that the FLS shows excellent robustness in delamination detection at very high levels of randomness in input data. (C) 2016 Elsevier Ltd. All rights reserved.