Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

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.

Two Dimensional Principal Component Analysis for Online Tamil Character Recognition

This paper presents a new application of two dimensional Principal Component Analysis (2DPCA) to the problem of online character recognition in Tamil Script. A novel set of features employing polynomial fits and quartiles in combination with conventional features are derived for each sample point of the Tamil character obtained after smoothing and resampling. These are stacked to form a matrix, using which a covariance matrix is constructed. A subset of the eigenvectors of the covariance matrix is employed to get the features in the reduced sub space. Each character is modeled as a separate subspace and a modified form of the Mahalanobis distance is derived to classify a given test character. Results indicate that the recognition accuracy using the 2DPCA scheme shows an approximate 3% improvement over the conventional PCA technique.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

Carnatic music analysis: Shadja, swara identification and rAga verification in AlApana using stochastic models

We analyze the AlApana of a Carnatic music piece without the prior knowledge of the singer or the rAga. AlApana is ameans to communicate to the audience, the flavor or the bhAva of the rAga through the permitted notes and its phrases. The input to our analysis is a recording of the vocal AlApana along with the accompanying instrument. The AdhAra shadja(base note) of the singer for that AlApana is estimated through a stochastic model of note frequencies. Based on the shadja, we identify the notes (swaras) used in the AlApana using a semi-continuous GMM. Using the probabilities of each note interval, we recognize swaras of the AlApana. For sampurNa rAgas, we can identify the possible rAga, based on the swaras. We have been able to achieve correct shadja identification, which is crucial to all further steps, in 88.8% of 55 AlApanas. Among them (48 AlApanas of 7 rAgas), we get 91.5% correct swara identification and 62.13% correct R (rAga) accuracy.

Computer-aided analysis of high-speed protective relays

Most of the modern distance relays are designed to avoid overreaching due to the transient d.c. component of the fault current, whereas a more likely source of transients in e.h.v. systems is the oscillatory discharge of the system charging current into the fault. Until now attempts have not been made to reproduce these transients in the laboratory. This paper describes an analogue and an accurate digital simulation of these harmonic transients. The dynamic behaviour of a typical polarised mho-type relay is analysed, and results are presented. The paper also advocates the use of active filters for filtering the harmonics associated with e.h.v. system, and hence, to improve the speed of response and accuracy of the protective relays.

Null Dereference Verification via Over-approximated Weakest Pre-conditions Analysis

Null dereferences are a bane of programming in languages such as Java. In this paper we propose a sound, demand-driven, inter-procedurally context-sensitive dataflow analysis technique to verify a given dereference as safe or potentially unsafe. Our analysis uses an abstract lattice of formulas to find a pre-condition at the entry of the program such that a null-dereference can occur only if the initial state of the program satisfies this pre-condition. We use a simplified domain of formulas, abstracting out integer arithmetic, as well as unbounded access paths due to recursive data structures. For the sake of precision we model aliasing relationships explicitly in our abstract lattice, enable strong updates, and use a limited notion of path sensitivity. For the sake of scalability we prune formulas continually as they get propagated, reducing to true conjuncts that are less likely to be useful in validating or invalidating the formula. We have implemented our approach, and present an evaluation of it on a set of ten real Java programs. Our results show that the set of design features we have incorporated enable the analysis to (a) explore long, inter-procedural paths to verify each dereference, with (b) reasonable accuracy, and (c) very quick response time per dereference, making it suitable for use in desktop development environments.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

Multi-Port Network Approach for the Analysis of Dual Band Fractal Microstrip Antennas

The multiport network approach is extended to analyze the behavior of microstrip fractal antennas. The capacitively fedmicrostrip square ring antenna has the side opposite to the feed arm replaced with a fractal Minkowski geometry. Dual frequency operation is achieved by suitably choosing the indentation of this fractal geometry. The width of the two sides adjacent to this is increased to further control the resonant characteristics and the ratio of the two resonance frequencies of this antenna. The impedance matrix for the multiport network model of this antenna is simplified exploiting self-similarity of the geometry with greater accuracy and reduced analysis time. Experimentally validated results confirm utility of the approach in analyzing the input characteristics of similar multi-frequency fractal microstrip antennas with other fractal geometries.

Implications of program phase behavior on timing analysis

Knowledge about program worst case execution time (WCET) is essential in validating real-time systems and helps in effective scheduling. One popular approach used in industry is to measure execution time of program components on the target architecture and combine them using static analysis of the program. Measurements need to be taken in the least intrusive way in order to avoid affecting accuracy of estimated WCET. Several programs exhibit phase behavior, wherein program dynamic execution is observed to be composed of phases. Each phase being distinct from the other, exhibits homogeneous behavior with respect to cycles per instruction (CPI), data cache misses etc. In this paper, we show that phase behavior has important implications on timing analysis. We make use of the homogeneity of a phase to reduce instrumentation overhead at the same time ensuring that accuracy of WCET is not largely affected. We propose a model for estimating WCET using static worst case instruction counts of individual phases and a function of measured average CPI. We describe a WCET analyzer built on this model which targets two different architectures. The WCET analyzer is observed to give safe estimates for most benchmarks considered in this paper. The tightness of the WCET estimates are observed to be improved for most benchmarks compared to Chronos, a well known static WCET analyzer.

Analysis of multi-conductor coupled microstrip lines with an aperture in the ground plane for the design of a broadband filter

Closed-form expressions for the propagation characteristics of coupled microstrip lines with a symmetrical aperture in the ground plane are derived. Expressions for the regular microstrip coupled lines have been modified using physical insights to incorporate the effect of the aperture. The accuracy of these expressions has been verified by full-wave simulations and compared with conformal mapping analysis. These expressions are accurate within 5% for a substrate whose thickness varies from 0.2 to 1.6mm and permittivity in the range of 210. Designing a broadband filter based on planar multi-conductor coupled lines with aperture in the ground plane is demonstrated in this paper using the proposed expressions for its practical use.

Analysis of Bandwidth-Unit-Vector-Distortion Tradeoff in PLL During Abnormal Grid Conditions

Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the unit vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the unit vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the unit vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of unit vector THD. The tuning method for SRF-PLL is also validated experimentally.