Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using l(1)-norm-based linear image reconstruction method

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ l(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of l(1)-norm based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional l(2)-based techniques. Moreover, it is shown that the proposed l(1)-based technique is computationally efficient compared to its counterpart (l(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

Development of moving magnet type linear motor for dual piston compressor for pulse tube cryocooler

This paper describes the design, fabrication and testing of a moving magnet type linear motor of dual piston configuration for a pulse tube cryocooler for ground applications. Eight radially magnetized segmented magnets were used to form one set of a magnet ring. Four magnet rings of such type were constructed, in which one pair of rings has north-pole on its outer diameter and south-pole on inner diameter, while the other pair is it's complementary. The magnets were mounted with opposite poles together on the magnet holder with an axial moving shaft having a piston mounted on both ends of the shaft. The shaft movement was restricted to the axial direction by using C-clamp type flexures, mounted on both sides of the shaft. The force requirement for driving the compressor was calculated based on which the electrical circuit of motor is designed by proper selection of wire gauge and Ampere-turns. The flexure spring force estimation was done through simulation using ANSYS 11.0 and was verified experimentally; while the magnet spring force was determined experimentally. The motor with mounted piston was tested using a variable voltage and variable frequency power supply capable of driving 140 watts of load.

Evaluation of mechanical losses in a linear motor pressure wave generator

A moving magnet linear motor compressor or pressure wave generator (PWG) of 2 cc swept volume with dual opposed piston configuration has been developed to operate miniature pulse tube coolers. Prelimnary experiments yielded only a no-load cold end temperature of 180 K. Auxiliary tests and the interpretation of detailed modeling of a PWG suggest that much of the PV power has been lost in the form of blow-by at piston seals due to large and non-optimum clearance seal gap between piston and cylinder. The results of experimental parameters simulated using Sage provide the optimum seal gap value for maximizing the delivered PV power.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Efficient Algorithms for Linear Summed Error Structural SVMs

Structural Support Vector Machines (SSVMs) have become a popular tool in machine learning for predicting structured objects like parse trees, Part-of-Speech (POS) label sequences and image segments. Various efficient algorithmic techniques have been proposed for training SSVMs for large datasets. The typical SSVM formulation contains a regularizer term and a composite loss term. The loss term is usually composed of the Linear Maximum Error (LME) associated with the training examples. Other alternatives for the loss term are yet to be explored for SSVMs. We formulate a new SSVM with Linear Summed Error (LSE) loss term and propose efficient algorithms to train the new SSVM formulation using primal cutting-plane method and sequential dual coordinate descent method. Numerical experiments on benchmark datasets demonstrate that the sequential dual coordinate descent method is faster than the cutting-plane method and reaches the steady-state generalization performance faster. It is thus a useful alternative for training SSVMs when linear summed error is used.

Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Flowfield Analysis of Linear Plug Nozzle

Full-length and truncated linear plug nozzle flowfields have been analyzed, using both experimental and computational tools, for pressure ratios ranging from 5 to 72, which include the transition of an open base wake to a closed base wake. A good agreement has been found between computational and experimental results on the plug surface. Considering the deficiencies of the computational tools in predicting base flows associated with truncated plug nozzles, an engineering model to predict the wake structure transition in such flows is proposed. The utility of this model in conjunction with empirical tools for the closed-wake base pressure prediction is established. The model is validated against the experimental results available in open literature.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

A nested linear codes approach to distributed function computation over subspaces

In this paper, we consider a distributed function computation setting, where there are m distributed but correlated sources X1,...,Xm and a receiver interested in computing an s-dimensional subspace generated by [X1,...,Xm]Γ for some (m × s) matrix Γ of rank s. We construct a scheme based on nested linear codes and characterize the achievable rates obtained using the scheme. The proposed nested-linear-code approach performs at least as well as the Slepian-Wolf scheme in terms of sum-rate performance for all subspaces and source distributions. In addition, for a large class of distributions and subspaces, the scheme improves upon the Slepian-Wolf approach. The nested-linear-code scheme may be viewed as uniting under a common framework, both the Korner-Marton approach of using a common linear encoder as well as the Slepian-Wolf approach of employing different encoders at each source. Along the way, we prove an interesting and fundamental structural result on the nature of subspaces of an m-dimensional vector space V with respect to a normalized measure of entropy. Here, each element in V corresponds to a distinct linear combination of a set {Xi}im=1 of m random variables whose joint probability distribution function is given.

Information dissemination in socially aware networks under the linear threshold model

We provide new analytical results concerning the spread of information or influence under the linear threshold social network model introduced by Kempe et al. in, in the information dissemination context. The seeder starts by providing the message to a set of initial nodes and is interested in maximizing the number of nodes that will receive the message ultimately. A node's decision to forward the message depends on the set of nodes from which it has received the message. Under the linear threshold model, the decision to forward the information depends on the comparison of the total influence of the nodes from which a node has received the packet with its own threshold of influence. We derive analytical expressions for the expected number of nodes that receive the message ultimately, as a function of the initial set of nodes, for a generic network. We show that the problem can be recast in the framework of Markov chains. We then use the analytical expression to gain insights into information dissemination in some simple network topologies such as the star, ring, mesh and on acyclic graphs. We also derive the optimal initial set in the above networks, and also hint at general heuristics for picking a good initial set.

Linear programming approach for state estimation incorporating phasor measurements

This paper presents methodologies for incorporating phasor measurements into conventional state estimator. The angle measurements obtained from Phasor Measurement Units are handled as angle difference measurements rather than incorporating the angle measurements directly. Handling in such a manner overcomes the problems arising due to the choice of reference bus. Current measurements obtained from Phasor Measurement Units are treated as equivalent pseudo-voltage measurements at the neighboring buses. Two solution approaches namely normal equations approach and linear programming approach are presented to show how the Phasor Measurement Unit measurements can be handled. Comparative evaluation of both the approaches is also presented. Test results on IEEE 14 bus system are presented to validate both the approaches.

Optimal MSE solution for a decision feedback equalizer

Due to the inherent feedback in a decision feedback equalizer (DFE) the minimum mean square error (MMSE) or Wiener solution is not known exactly. The main difficulty in such analysis is due to the propagation of the decision errors, which occur because of the feedback. Thus in literature, these errors are neglected while designing and/or analyzing the DFEs. Then a closed form expression is obtained for Wiener solution and we refer this as ideal DFE (IDFE). DFE has also been designed using an iterative and computationally efficient alternative called least mean square (LMS) algorithm. However, again due to the feedback involved, the analysis of an LMS-DFE is not known so far. In this paper we theoretically analyze a DFE taking into account the decision errors. We study its performance at steady state. We then study an LMS-DFE and show the proximity of LMS-DFE attractors to that of the optimal DFE Wiener filter (obtained after considering the decision errors) at high signal to noise ratios (SNR). Further, via simulations we demonstrate that, even at moderate SNRs, an LMS-DFE is close to the MSE optimal DFE. Finally, we compare the LMS DFE attractors with IDFE via simulations. We show that an LMS equalizer outperforms the IDFE. In fact, the performance improvement is very significant even at high SNRs (up to 33%), where an IDFE is believed to be closer to the optimal one. Towards the end, we briefly discuss the tracking properties of the LMS-DFE.