Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.

Nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives

This paper presents nonlinear finite element analysis of adhesively bonded joints considering the elastoviscoplastic constitutive model of the adhesive material and the finite rotation of the joint. Though the adherends have been assumed to be linearly elastic, the yielding of the adhesive is represented by a pressure sensitive modified von Mises yield function. The stress-strain relation of the adhesive is represented by the Ramberg-Osgood relation. Geometric nonlinearity due to finite rotation in the joint is accounted for using the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in a total Lagrangian formulation. Critical time steps have been calculated based on the eigenvalues of the transition matrices of the viscoplastic model of the adhesive. Stability of the viscoplastic solution and time dependent behaviour of the joints are examined. A parametric study has been carried out with particular reference to peel and shear stress along the interface. Critical zones for failure of joints have been identified. The study is of significance in the design of lap joints as well as on the characterization of adhesive strength. (C) 1999 Elsevier Science Ltd. All rights reserved.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.

Estimating specific yield and transmissivity with magnetic resonance sounding in an unconfined sandstone aquifer (Niger)

The unconfined aquifer of the Continental Terminal in Niger was investigated by magnetic resonance sounding (MRS) and by 14 pumping tests in order to improve calibration of MRS outputs at field scale. The reliability of the standard relationship used for estimating aquifer transmissivity by MRS was checked; it was found that the parametric factor can be estimated with an uncertainty a parts per thousand currency sign150% by a single point of calibration. The MRS water content (theta (MRS)) was shown to be positively correlated with the specific yield (Sy), and theta (MRS) always displayed higher values than Sy. A conceptual model was subsequently developed, based on estimated changes of the total porosity, Sy, and the specific retention Sr as a function of the median grain size. The resulting relationship between theta (MRS) and Sy showed a reasonably good fit with the experimental dataset, considering the inherent heterogeneity of the aquifer matrix (residual error is similar to 60%). Interpreted in terms of aquifer parameters, MRS data suggest a log-normal distribution of the permeability and a one-sided Gaussian distribution of Sy. These results demonstrate the efficiency of the MRS method for fast and low-cost prospection of hydraulic parameters for large unconfined aquifers.

Multi-Tone Testing of Linear and Nonlinear Analog Circuits using Polynomial Coefficients

A method of testing for parametric faults of analog circuits based on a polynomial representation of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies in addition to DC. Classification or Cur is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. This testing method requires no design for test hardware as might be added to the circuit fly some other methods. The proposed method is illustrated for a benchmark elliptic filter. It is shown to uncover several parametric faults causing deviations as small as 5% from the nominal values.

Approximate methods for step function response of undamped non-linear spring mass systems with arbitrary hardening type spring characteristic

The possibility of applying two approximate methods for determining the salient features of response of undamped non-linear spring mass systems subjected to a step input, is examined. The results obtained on the basis of these approximate methods are compared with the exact results that are available for some particular types of spring characteristics. The extension of the approximate methods for non-linear systems with general polynomial restoring force characteristics is indicated.

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications. (C) 2005 Elsevier B. V. All rights reserved.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Polynomial Coefficient Based Multi-Tone Testing of Analog Circuits

Abstract—A method of testing for parametric faults of analog circuits based on a polynomial representaion of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies apart from DC. Classification of CUT is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. The method needs very little augmentation of circuit to make it testable as only output parameters are used for classification. This procedure is shown to uncover several parametric faults causing smaller than 5 % deviations the nominal values. Fault diagnosis based upon sensitivity of polynomial coefficients at relevant frequencies is also proposed.

V-Transform: “An Enhanced Polynomial Coefficient Based DC Test for Non-linear Analog Circuits

Abstract—DC testing of parametric faults in non-linear analog circuits based on a new transformation, entitled, V-Transform acting on polynomial coefficient expansion of the circuit function is presented. V-Transform serves the dual purpose of monotonizing polynomial coefficients of circuit function expansion and increasing the sensitivity of these coefficients to circuit parameters. The sensitivity of V-Transform Coefficients (VTC) to circuit parameters is up to 3x-5x more than sensitivity of polynomial coefficients. As a case study, we consider a benchmark elliptic filter to validate our method. The technique is shown to uncover hitherto untestable parametric faults whose sizes are smaller than 10 % of the nominal values. I.

Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Yield stress, thixotropy and shear banding in a dilute aqueous suspension of few layer graphene oxide platelets

We demonstrate a rigidity percolation transition and the onset of yield stress in a dilute aqueous dispersion of graphene oxide platelets (aspect ratio similar to 5000) above a critical volume fraction of 3.75 x 10(-4) with a percolation exponent of 2.4 +/- 0.1. The viscoelastic moduli of the gel at rest measured as a function of time indicate the absence of structural evolution of the 3D percolated network of disks. However a shear-induced aging giving rise to a compact jammed state and shear rejuvenation indicating a homogenous flow is observed when a steady shear stress (sigma) is imposed in creep experiments. We construct a shear diagram (sigma vs. volume fraction phi) and the critical stress above which shear rejuvenation occurs is identified as the yield stress sigma(y) of the gel. The minimum steady state shear rate (gamma) over dot(m) obtained from creep experiments agrees well with the end of the plateau region in a controlled shear rate flow curve, indicating a shear localization below (gamma) over dot(m). A steady state shear banding in the plateau region of the flow curve observed in particle velocimetry measurements in a Couette geometry confirms that the dilute suspensions of GO platelets form a thixotropic yield stress fluid.

Effect of choice of basis functions in neural network for capturing unknown function for dynamic inversion control

The basic requirement for an autopilot is fast response and minimum steady state error for better guidance performance. The highly nonlinear nature of the missile dynamics due to the severe kinematic and inertial coupling of the missile airframe as well as the aerodynamics has been a challenge for an autopilot that is required to have satisfactory performance for all flight conditions in probable engagements. Dynamic inversion is very popular nonlinear controller for this kind of scenario. But the drawback of this controller is that it is sensitive to parameter perturbation. To overcome this problem, neural network has been used to capture the parameter uncertainty on line. The choice of basis function plays the major role in capturing the unknown dynamics. Here in this paper, many basis function has been studied for approximation of unknown dynamics. Cosine basis function has yield the best response compared to any other basis function for capturing the unknown dynamics. Neural network with Cosine basis function has improved the autopilot performance as well as robustness compared to Dynamic inversion without Neural network.