Browsing by Subject "Nonlinear theories"
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Item A fault diagnosis algorithm for nonlinear analog circuits and systems(Texas Tech University, 1980-08) Hsieh, Ming-chengA fault detection algorithm for nonlinear analog circuits is developed on the basis of the unique characteristics of the solid stage nonlinear device. A large-scale system can be decomposed into subsystems by driving the nonlinear devices into their cut-off regions. The reversed bias applied to the nonlinear devices wi11 reveal the failures caused by the shorted or leaky devices. The resultant decoupled linear subsystems are of much smaller simension. Test signals can be applied to each subsystem as long as it is decoupled from the other. A diagnosis scheme is developed for testing linear subsystems. The test results are used to construct the test signature table to indicate the failed linear components in each subsystem. The overall system which, is free of shorted or leaky devices and/or failed linear components, is then put back to the normal operating condition. The static operating point and the dynamic performance of each nonlinear device will give the indication of failures caused by opened or deteriorated devices. The fault diagnosis for the large-scale system is thus completed. Several numerical examples are given to illustrate the test scheme and the possible implementation of the automatic test system.Item Integration methods in system analysis(Texas Tech University, 1976-12) Pan, Ching-TsaiNot availableItem Multiscale basis optimization for Darcy flow(2007-05) Rath, James Michael, 1975-; Arbogast, Todd James, 1957-Simulation of flow through a heterogeneous porous medium with fine-scale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives a faster approximation of the flow but loses some detail. We propose an algorithm that obtains the fully resolved approximation but only iterates on a sequence of coarsened problems. The sequence is chosen by optimizing the shapes of the coarse finite element basis functions. As a stand-alone method, the algorithm converges globally and monotonically with a quadratic asymptotic rate. Computational experience indicates the number of iterations needed is independent of the resolution and heterogeneity of the medium. However, an externally provided error estimate is required; the algorithm could be combined as an accelerator with another iterative algorithm. A single "inner" iteration of the other algorithm would yield an error estimate; following it with an "outer" iteration of our algorithm would give a viable method.Item Non-linear stochastic flutter of aeroelastic structural systems(Texas Tech University, 1985-12) Heo, HunThe main objective of t h i s investigation is to examine the linear and non-linear modal interactions of a two-degree-of-freedom aero-elastic structure subjected to a wide band random excitation. The linear analysis involves linear dynamic coupling and parametric random coupling. In terms of normal coordinates the response mean squares are obtained as functions of the system frequency ratio. The analysis shows that for modest values of mass ratio the first mode is suppressed when the natural frequencies of the two beams are identical. Furthermore, the system mean square responses are governed mainly by the external forced excitation, while the influence of the random parametric component is almost negligible. The non-linear modal analysis involves quadratic non-linearity referred to as autoparametric coupling. This type of coupling gives rise to a new type of instability when the relationship between normal mode frequencies is linear. In the neighborhood of the internal resonance condition w2/w1=0.5 (where w1 and w2 are the normal mode frequencies of the system), a general differential equation of the response moments is derived and found to constitute an infinite hierarchy set. Two different closure schemes, based on a cumulant-neglect concept, are used to truncate the moment differential equations. The first is the Gaussian closure, which leads to fourteen coupled differential equations, while the second, known as the non- Gaussian closure, gives 69 coupled differential equations. These two sets of equations are solved numerically for the response moments. The Gaussian closure solution results in a quasi-stationary response, while the non-Gaussian closure solution gives a strict stationary response. The two solutions exhibit an exchange of energy between the two modes in such a manner that one mode acts as a vibration absorber of the second mode in the neighborhood of internal resonance condition w2/w1=0.5±0(e)f where e is a small parameter. The influence of ranc3cam variation of the system parameters such as damping and stiffness is investigated. It is found that the damping variation has less effect on the random response of the structure than the stiffness variation. Numerical solutions for different initial conditions are obtained to find out if the system possesses more than one limit cycle. It is found that the initial conditions affect only the transition response, while the steady state response does not change by changing the initial conditions.Item Nonlinear analysis of rectangular glass plates by Galerkin method(Texas Tech University, 1983-05) Ku, Fu-yuNot availableItem Item Numerical methods for solving nonlinear equations.(Texas Tech University, 1974-08) Liu, Dan-KaiNot availableItem Numerical methods for the control of chaos(Texas Tech University, 1993-12) Stubbendieck, Gregg T.The study of chaos is a relatively recent phenomenon. There is little doubt that the modem computer has played an important role in the growth of interest in chaos. High speed computers and sophisticated grzphical displays make it possible to explore aspects of chaos that have not previously been accessible. Chaos is a type of nonlinear behavior that appears to be random although it is driven by deterministic processes. A defining aspect of chaotic behavior is its sensitivity to perturbations. SmaU changes in a chaotic system lead to large differences in behavior later on. Although chaos seems to be random when first encotmtered, there is an underlying structure to chaos that can be exploited. A method was developed by E. Ott, C. Grebogi and J. A. Yorke (OGY) to exploit the underlying stmcture of chaos and its sensitivity to perturbations to induce chaotic d5'namical systems into periodic behavior. The method has been successfully tested in a number of experimental situations. We have developed a reconfigurable Online ControUer that integrates several of the elements related to the OGY control method with the OGY control method itself. The control method is thus expanded to include the related elements, previously treated as offline procedures, as part of its definition. The OGY method requires certain properties of a chaotic system to be controUed. The Online ControUer does not add to the required properties. The specialized data structures and algorithms developed in the course of this research to implement the related elements in an online situation are described. Alternate methods for calculating the stability information required by the OGY method that take advantage of the properties of the Online ControUer are described. The alternate methods address inadequacies in the methods suggested by Ott et al. A number of experiments Ulustrating various features of the Online Controller are described, and their results are discussed. The Online ControUer provides a stable platform upon which the remaining methods required to fully automate the control of chaos can be developed.Item On approximation structures for nonlinear systems(2006) Story, Mark Allan; Sandberg, Irwin W.Item Real-time estimation and control of large-scale nonlinear DAE systems(2005) Hedengren, John David; Edgar, Thomas F.Item Simulation of linear and nonlinear systems with orthogonal functionals(Texas Tech University, 1970-08) Kuhler, Ronald JamesNot availableItem The approximation of improper integrals using the generalized G transformation(Texas Tech University, 1972-05) Williams, Marshall ParkerNot availableItem The evolution of one higher education consortium on NK fitness landscapes: a case study(Texas Tech University, 1998-05) Workman, Mark E.The focus of this research was on the adaptive evolution of a singie higher education consortium--the Higher Education Consortium of Texas, Oklahoma, and Kansas. The major purpose of this in-depth case study was to apply Kauffman's NK model of rugged fitness landscapes, a model grounded in nonlinear dynamical systems theory, as a viable conceptual framework for studying the structure of an evolving higher education consortium. This research addressed two questions in order to provide a more complete understanding of higher education consortia: (1) How does the structure of a higher education consortium evolve over time? and (2) What factors affect the adaptive evolution of a higher education consortium on NK fitness landscapes? A case study approach using qualitative research methods was chosen as the most appropriate design for investigating the organization and evolution of the Consortium. Data collection methods utiiized include document gathering, participant observation, and informant interviews; field notes, reflexive journai entries, and audio recordings were three data coiiection techniques used. Data analysis was accomplished with a modified constant comparative method using analytic techniques of coding, theoretical sampling, and comparative analysis.Item Two-dimensional nonlinear controllability with numerical examples(Texas Tech University, 1980-12) Stangeland, Ronald DeanNot available