928 resultados para Parametric Linear System
Resumo:
The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and an infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.
Resumo:
Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.
Resumo:
This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.
Resumo:
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.
Resumo:
Dodecagonal (12-sided) space vector pulsewidth modulation (PWM) schemes are characterized by the complete absence of (6n +/- 1)th-order harmonics (for odd n) in the phase voltages, within the linear modulation range and beyond, including over-modulation. This paper presents a new topology suitable for the realization of such multilevel inverter schemes for induction motor (IM) drives, by cascading two-level inverters with flying-capacitor-inverter fed floating H-bridge cells. Now, any standard IM may be used to get the dodecagonal operation which hitherto was possible only with open-end winding IM. To minimize the current total harmonic distortion (THD), a strategy for synchronous PWM is also proposed. It is shown that the proposed method is capable of obtaining better THD figures, compared to conventional dodecagonal schemes. The topology and the PWM strategy are validated through analysis and subsequently verified experimentally.
Resumo:
The paper identified and characterized a special multi-degree of freedom toggle behavior, called double toggle, observed in a typical MCCB switching mechanism. For an idealized system, the condition of toggle sequence is derived geometrically. The existing tools available in a multi-body dynamics package are used for exploring the dynamic behavior of such systems parametrically. The double toggle mechanism is found to make the system insensitive to the operator's behavior; however, the system is vulnerable under extreme usage. The linkage kinematics and stopper locations are found to have dominant role on the behavior of the system. It is revealed that the operating time is immune to the inertial property of the input link and sensitive to that of the output link. Novel designs exploiting this observation, in terms of spring and toggle placements, to enhance switching performance have also been reported in the paper. Detailed study revealed that strategic placement of the spring helps in selective alteration of system performance. Thus, the study establishes the critical importance of the kinematic design of MCCB over the dynamic parameters. (C) 2013 Elsevier Ltd. All rights reserved.
Resumo:
In this paper, a method for the tuning the membership functions of a Mamdani type Fuzzy Logic Controller (FLC) using the Clonal Selection Algorithm(CSA) a model of the Artificial Immune System(AIS) paradigm is examined. FLC's are designed for two problems, firstly the linear cart centering problem and secondly the highly nonlinear inverted pendulum problem. The FLC tuned by AIS is compared with FLC tuned by GA. In order to check the robustness of the designed PLC's white noise was added to the system, further, the masses of the cart and the length and mass of the pendulum are changed. The PLC's were also tested in the presence of faulty rules. Finally, Kruskal Wallis test was performed to compare the performance of the GA and AIS. An insight into the algorithms are also given by studying the effect of the important parameters of GA and AIS.
Resumo:
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.
Resumo:
State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.
Resumo:
Measurement of in-plane motion with high resolution and large bandwidth enables model-identification and real-time control of motion-stages. This paper presents an optical beam deflection based system for measurement of in-plane motion of both macro- and micro-scale motion stages. A curved reflector is integrated with the motion stage to achieve sensitivity to in-plane translational motion along two axes. Under optimal settings, the measurement system is shown to theoretically achieve sub-angstrom measurement resolution over a bandwidth in excess of 1 kHz and negligible cross-sensitivity to linear motion. Subsequently, the proposed technique is experimentally demonstrated by measuring the in-plane motion of a piezo flexure stage and a scanning probe microcantilever. For the former case, reflective spherical balls of different radii are employed to measure the in-plane motion and the measured sensitivities are shown to agree with theoretical values, on average, to within 8.3%. For the latter case, a prototype polydimethylsiloxane micro-reflector is integrated with the microcantilever. The measured in-plane motion of the microcantilever probe is used to identify nonlinearities and the transient dynamics of the piezo-stage upon which the probe is mounted. These are subsequently compensated by means of feedback control. (C) 2013 AIP Publishing LLC.
Resumo:
Visual search in real life involves complex displays with a target among multiple types of distracters, but in the laboratory, it is often tested using simple displays with identical distracters. Can complex search be understood in terms of simple searches? This link may not be straightforward if complex search has emergent properties. One such property is linear separability, whereby search is hard when a target cannot be separated from its distracters using a single linear boundary. However, evidence in favor of linear separability is based on testing stimulus configurations in an external parametric space that need not be related to their true perceptual representation. We therefore set out to assess whether linear separability influences complex search at all. Our null hypothesis was that complex search performance depends only on classical factors such as target-distracter similarity and distracter homogeneity, which we measured using simple searches. Across three experiments involving a variety of artificial and natural objects, differences between linearly separable and nonseparable searches were explained using target-distracter similarity and distracter heterogeneity. Further, simple searches accurately predicted complex search regardless of linear separability (r = 0.91). Our results show that complex search is explained by simple search, refuting the widely held belief that linear separability influences visual search.
Resumo:
In this article, we obtain explicit solutions of a system of forced Burgers equation subject to some classes of bounded and compactly supported initial data and also subject to certain unbounded initial data. In a series of papers, Rao and Yadav (2010) 1-3] obtained explicit solutions of a nonhomogeneous Burgers equation in one dimension subject to certain classes of bounded and unbounded initial data. Earlier Kloosterziel (1990) 4] represented the solution of an initial value problem for the heat equation, with initial data in L-2 (R-n, e(vertical bar x vertical bar 2/2)), as a series of self-similar solutions of the heat equation in R-n. Here we express the solutions of certain classes of Cauchy problems for a system of forced Burgers equation in terms of self-similar solutions of some linear partial differential equations. (C) 2013 Elsevier Inc. All rights reserved.
Resumo:
Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains. (C) 2013 AIP Publishing LLC.
Resumo:
The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.
Resumo:
Multiple input multiple output (MIMO) systems with large number of antennas have been gaining wide attention as they enable very high throughputs. A major impediment is the complexity at the receiver needed to detect the transmitted data. To this end we propose a new receiver, called LRR (Linear Regression of MMSE Residual), which improves the MMSE receiver by learning a linear regression model for the error of the MMSE receiver. The LRR receiver uses pilot data to estimate the channel, and then uses locally generated training data (not transmitted over the channel), to find the linear regression parameters. The proposed receiver is suitable for applications where the channel remains constant for a long period (slow-fading channels) and performs quite well: at a bit error rate (BER) of 10(-3), the SNR gain over MMSE receiver is about 7 dB for a 16 x 16 system; for a 64 x 64 system the gain is about 8.5 dB. For large coherence time, the complexity order of the LRR receiver is the same as that of the MMSE receiver, and in simulations we find that it needs about 4 times as many floating point operations. We also show that further gain of about 4 dB is obtained by local search around the estimate given by the LRR receiver.