Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.

Late Quaternary vegetational and climatic changes from tropical peats in southern India - An extended record up to 40,000 years BP

Stable carbon isotope ratios of peats dated (by C-14) back to 40 kyr BP from the montane region (> 1800 m asl) of the Nilgiris, southern India, reflect changes in the relative proportions of C3 and C4 plant types, which are influenced by soil moisture (and hence monsoonal precipitation), From prior to 40 kyr BP until 28 kyr BP, a general decline in delta(13)C values from about - 14 per mil to - 19 per mil suggests increased dominance of C3 plants concurrent with increasingly moist conditions, During 28-18 kyr BP there seems relatively little change with delta(13) C of - 19 to - 18 per mil, At about 16 kyr BP a sharp reversal in delta(13)C to a peak of - 14.7 per mil indicates a clear predominance of C4 vegetation associated with arid conditions, possibly during or just after the Last Glacial Maximum, A moist phase at about 9 kyr BP (the Holocene Optimum) with dominance of C3 vegetation type is observed, while arid conditions are re-established during 5-2 kyr BP with an overall dominance of C4 vegetation, New data do not support the occurrence of a moist phase coinciding with the Mediaeval Warm Period (at 0.6 kyr BP) as suggested earlier, Overall, the climate and vegetation in the high altitude regions of the southern Indian tropics seem to have responded to past global climatic changes, and this is consistent with other evidences from India and other tropical regions.

Rapid quenching and glass formation in chalcogenide glasses: Preparation and properties of Ge-As-Te glasses over an extended composition ranges

In Ge-As-Te system, the glass forming region determined by normal melt quenching method has two regions (GFR I and GFR II) separated by few compositions gap. With a simple laboratory built twin roller apparatus, we have succeeded in preparing Ge7.5AsxTe92.5-x glasses over extended composition ranges. A distinct change in T-g is observed at x = 40, exactly at which the separation of the glass forming regions occur indicating the changes in the connectivity and the rigidity of the structural network. The maximum observed in glass transition (T-g) at x = 55 corresponding to the average coordination number (Z(av)) = 2.70 is an evidence for the shift of the rigidity percolation threshold (RPT) from Z(av) = 2.40 as predicted by the recent theories. The glass forming tendency (K-gl) and Delta T (=T-c-T-g) is low for the glasses in the GFR I and high for the glasses in the GFR II.

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Compact fiber Bragg grating dynamic strain sensor cum broadband thermometer for thermally unstable ambience

An instrument for simultaneous measurement of dynamic strain and temperature in a thermally unstable ambience has been proposed, based on fiber Bragg grating technology. The instrument can function as a compact and stand-alone broadband thermometer and a dynamic strain gauge. It employs a source wavelength tracking procedure for linear dependence of the output on the measurand, offering high dynamic range. Two schemes have been demonstrated with their relative merits. As a thermometer, the present instrumental configuration can offer a linear response in excess of 500 degrees C that can be easily extended by adding a suitable grating and source without any alteration in the procedure. Temperature sensitivity is about 0.06 degrees C for a bandwidth of 1 Hz. For the current grating, the upper limit of strain measurement is about 150 mu epsilon with a sensitivity of about 80 n epsilon Hz(-1/2). The major source of uncertainty associated with dynamic strain measurement is the laser source intensity noise, which is of broad spectral band. A low noise source device or the use of optical power regulators can offer improved performance. The total harmonic distortion is less than 0.5% up to about 50 mu epsilon, 1.2% at 100 mu epsilon and about 2.3% at 150 mu epsilon. Calibrated results of temperature and strain measurement with the instrument have been presented. Traces of ultrasound signals recorded by the system at 200 kHz, in an ambience of 100-200 degrees C temperature fluctuation, have been included. Also, the vibration spectrum and engine temperature of a running internal combustion engine has been recorded as a realistic application of the system.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

Reservoir performance under uncertainty in hydrologic impacts of climate change

Relatively few studies have addressed water management and adaptation measures in the face of changing water balances due to climate change. The current work studies climate change impact on a multipurpose reservoir performance and derives adaptive policies for possible futurescenarios. The method developed in this work is illustrated with a case study of Hirakud reservoir on the Mahanadi river in Orissa, India,which is a multipurpose reservoir serving flood control, irrigation and power generation. Climate change effects on annual hydropower generation and four performance indices (reliability with respect to three reservoir functions, viz. hydropower, irrigation and flood control, resiliency, vulnerability and deficit ratio with respect to hydropower) are studied. Outputs from three general circulation models (GCMs) for three scenarios each are downscaled to monsoon streamflow in the Mahanadi river for two future time slices, 2045-65 and 2075-95. Increased irrigation demands, rule curves dictated by increased need for flood storage and downscaled projections of streamflow from the ensemble of GCMs and scenarios are used for projecting future hydrologic scenarios. It is seen that hydropower generation and reliability with respect to hydropower and irrigation are likely to show a decrease in future in most scenarios, whereas the deficit ratio and vulnerability are likely to increase as a result of climate change if the standard operating policy (SOP) using current rule curves for flood protection is employed. An optimal monthly operating policy is then derived using stochastic dynamic programming (SDP) as an adaptive policy for mitigating impacts of climate change on reservoir operation. The objective of this policy is to maximize reliabilities with respect to multiple reservoir functions of hydropower, irrigation and flood control. In variations to this adaptive policy, increasingly more weightage is given to the purpose of maximizing reliability with respect to hydropower for two extreme scenarios. It is seen that by marginally sacrificing reliability with respect to irrigation and flood control, hydropower reliability and generation can be increased for future scenarios. This suggests that reservoir rules for flood control may have to be revised in basins where climate change projects an increasing probability of droughts. However, it is also seen that power generation is unable to be restored to current levels, due in part to the large projected increases in irrigation demand. This suggests that future water balance deficits may limit the success of adaptive policy options. (C) 2010 Elsevier Ltd. All rights reserved.

A combined extended and helical backbone for Boc-(Ala-Leu-Ac(7)c-)(2)-OMe

The structure of the peptide Boc-Ala-Leu-Ac(7)c-Ala-Leu-Ac(7)c-OMe (Ac(7)c,1-aminocycloheptane-1-carboxylic acid) is described in crystals. The presence of two Ac(7)c residues was expected to stabilize a 3(10)-helical fold. Contrary to expectation the structural analysis revealed an unfolded amino terminus, with Ala(1) adopting an extended beta-conformation (phi = -93degrees,psi = 112degrees). Residues 2-5 form a 3(10)-helix, stabilized by three successive intramolecular hydrogen bonds. Notably, two NH groups Ala(1) and Ac(7)c(3) do not form any hydrogen bonds in the crystal. Peptide assembly appears to be dominated by packing of the cycloheptane rings that stack against one another within the molecule and also throughout the crystal in columns.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Extended self-similarity works for the Burgers equation and why

Extended self-similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier-Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the IR and UV end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.