Automated inspection of aircraft parts using a modified ICP algorithm

The application of computer-aided inspection integrated with the coordinate measuring machine and laser scanners to inspect manufactured aircraft parts using robust registration of two-point datasets is a subject of active research in computational metrology. This paper presents a novel approach to automated inspection by matching shapes based on the modified iterative closest point (ICP) method to define a criterion for the acceptance or rejection of a part. This procedure improves upon existing methods by doing away with the following, viz., the need for constructing either a tessellated or smooth representation of the inspected part and requirements for an a priori knowledge of approximate registration and correspondence between the points representing the computer-aided design datasets and the part to be inspected. In addition, this procedure establishes a better measure for error between the two matched datasets. The use of localized region-based triangulation is proposed for tracking the error. The approach described improves the convergence of the ICP technique with a dramatic decrease in computational effort. Experimental results obtained by implementing this proposed approach using both synthetic and practical data show that the present method is efficient and robust. This method thereby validates the algorithm, and the examples demonstrate its potential to be used in engineering applications.

Adsorption of Nitrogen on Activated Carbon-Refit of Experimental Data and Derivation of Properties Required for Design of Equipment

Volumetric method based adsorption measurements of nitrogen on two specimens of activated carbon (Fluka and Sarabhai) reported by us are refitted to two popular isotherms, namely, Dubunin−Astakhov (D−A) and Toth, in light of improved fitting methods derived recently. Those isotherms have been used to derive other data of relevance in design of engineering equipment such as the concentration dependence of heat of adsorption and Henry’s law coefficients. The present fits provide a better representation of experimental measurements than before because the temperature dependence of adsorbed phase volume and structural heterogeneity of micropore distribution have been accounted for in the D−A equation. A new correlation to the Toth equation is a further contribution. The heat of adsorption in the limiting uptake condition is correlated with the Henry’s law coefficients at the near zero uptake condition.

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

A unit cube in k dimensions (k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k where R-i (for 1 <= i <= k) is a closed interval of the form [a(i), a(i) + 1] on the real line. A graph G on n nodes is said to be representable as the intersection of k-cubes (cube representation in k dimensions) if each vertex of C can be mapped to a k-cube such that two vertices are adjacent in G if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G denoted as cub(G) is the minimum k for which G can be represented as the intersection of k-cubes. An interesting aspect about cubicity is that many problems known to be NP-complete for general graphs have polynomial time deterministic algorithms or have good approximation ratios in graphs of low cubicity. In most of these algorithms, computing a low dimensional cube representation of the given graph is usually the first step. We give an O(bw . n) algorithm to compute the cube representation of a general graph G in bw + 1 dimensions given a bandwidth ordering of the vertices of G, where bw is the bandwidth of G. As a consequence, we get O(Delta) upper bounds on the cubicity of many well-known graph classes such as AT-free graphs, circular-arc graphs and cocomparability graphs which have O(Delta) bandwidth. Thus we have: 1. cub(G) <= 3 Delta - 1, if G is an AT-free graph. 2. cub(G) <= 2 Delta + 1, if G is a circular-arc graph. 3. cub(G) <= 2 Delta, if G is a cocomparability graph. Also for these graph classes, there axe constant factor approximation algorithms for bandwidth computation that generate orderings of vertices with O(Delta) width. We can thus generate the cube representation of such graphs in O(Delta) dimensions in polynomial time.

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.

Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.

An alternate form of the ramberg-osgood formula for matrix displacement analysis

A new stress-strain law, which is a three parameter representation of stress in terms of strain has been proposed for the matrix displacement analysis of structures made of non-hookean materials. This formula has been utilized to study three typical problems. These studies brought out the effectiveness and suitability of this law for matrix displacement analysis.

Hardness of approximation results for the problem of finding the stopping distance in Tanner graphs

Tanner Graph representation of linear block codes is widely used by iterative decoding algorithms for recovering data transmitted across a noisy communication channel from errors and erasures introduced by the channel. The stopping distance of a Tanner graph T for a binary linear block code C determines the number of erasures correctable using iterative decoding on the Tanner graph T when data is transmitted across a binary erasure channel using the code C. We show that the problem of finding the stopping distance of a Tanner graph is hard to approximate within any positive constant approximation ratio in polynomial time unless P = NP. It is also shown as a consequence that there can be no approximation algorithm for the problem achieving an approximation ratio of 2(log n)(1-epsilon) for any epsilon > 0 unless NP subset of DTIME(n(poly(log n))).

Robust prediction of residual velocities and ballistic limits of projectiles for impact on thin aluminium plates

This paper deals with the simulation-driven study of the impact of hardened steel projectiles on thin aluminium target plates using explicit finite element analysis as implemented in LS-DYNA. The evaluation of finite element modelling includes a comprehensive mesh convergence study using shell elements for representing target plates and the solid element-based representation of ogivalnosed projectiles. A user-friendly automatic contact detection algorithm is used for capturing interaction between the projectile and the target plate. It is shown that the proper choice of mesh density and strain rate-dependent material properties is crucial as these parameters significantly affect the computed residual velocity. The efficacy of correlation with experimental data is adjudged in terms of a 'correlation index' defined in the present study for which values close to unity are desirable.By simulating laboratory impact tests on thin aluminium plates carried out by earlier investigators, extremely good prediction of experimental ballistic limits has been observed with correlation indices approaching unity. Additional simulation-based parametric studies have been carried out and results consistent with test data have been obtained. The simulation procedures followed in the present study can be applied with confidence in designing thin aluminium armour plates for protection against low calibre projectiles.

Memory-based reasoning approach for pattern recognition of binary images

Template matching is concerned with measuring the similarity between patterns of two objects. This paper proposes a memory-based reasoning approach for pattern recognition of binary images with a large template set. It seems that memory-based reasoning intrinsically requires a large database. Moreover, some binary image recognition problems inherently need large template sets, such as the recognition of Chinese characters which needs thousands of templates. The proposed algorithm is based on the Connection Machine, which is the most massively parallel machine to date, using a multiresolution method to search for the matching template. The approach uses the pyramid data structure for the multiresolution representation of templates and the input image pattern. For a given binary image it scans the template pyramid searching the match. A binary image of N × N pixels can be matched in O(log N) time complexity by our algorithm and is independent of the number of templates. Implementation of the proposed scheme is described in detail.

Belief Propagation Based Decoding of Large Non-Orthogonal STBCs

In this paper,we present a belief propagation (BP) based algorithm for decoding non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approachinvolves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode non-orthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BP-based decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves near-capacity turbo coded BER performance; for e.g., with BP decoding of 24 x 24 STBC from CDA using BPSK (i.e.,n576 real dimensions) and rate-1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved.

Extension of Darken's Quadratic Formalism to Dilute Multicomponent Solutions

Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.

A self-consistent formulation for analysis and generation of non-uniform DNA structure

A fully self-consistent formulation is described here for the analysis and generation of base-pairs in non-uniform DNA structures, in terms of various local parameters. It is shown that the internal "wedge parameters" are mathematically related to the parameters describing the base-pair orientation with respect to an external helix axis. Hence any one set of three translation and three rotation parameters are necessary and sufficient to completely describe the relative orientation of the base-pairs comprising a step (or doublet). A general procedure is outlined for obtaining an average or global helix axis from the local helix axes for each step. A graphical representation of the local helix axes in the form of a polar plot is also shown and its application for estimating the curvature of oligonucleotide structures is illustrated, with examples of both A and B type structures.

Study Of The Hvdc-Torsional Interactions Through Digital Dynamic Simulation

This paper presents the detailed dynamic digital simulation for the study of phenomenon of torsional interaction between HVDC-Turbine generator shaft, dynamics using the novel converter model presented in [ 1 ] The system model includes detailed representation of the synchronous generator and the shaft dynamics, the ac and dc network transients. The results of a case study indicate the various factors that influence the torsional interaction.

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

A numerical study of projectile impact on mild steel armour plates

The present article deals with the development of a finite element modelling approach for the prediction of residual velocities of hard core ogival-nose projectiles following normal impact on mild steel target plates causing perforation. The impact velocities for the cases analysed are in the range 818–866.3 m/s. Assessment of finite element modelling and analysis includes a comprehensive mesh convergence study using shell elements for representing target plates and solid elements for jacketed projectiles with a copper sheath and a rigid core. Dynamic analyses were carried out with the explicit contact-impact LS-DYNA 970 solver. It has been shown that proper choice of element size and strain rate-based material modelling of target plate are crucial for obtaining test-based residual velocity.The present modelling procedure also leads to realistic representation of target plate failure and projectile sheath erosion during perforation, and confirms earlier observations that thermal effects are not significant for impact problems within the ordnance range. To the best of our knowledge, any aspect of projectile failure or degradation obtained in simulation has not been reported earlier in the literature. The validated simulation approach was applied to compute the ballistic limits and to study the effects of plate thickness and projectile diameter on residual velocity, and trends consistent with experimental data for similar situations were obtained.