Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

An account of chronological developments in control of distributed parameter systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum.Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

Electric-field-dependent average resistance and the resistance fluctuation in one-dimensional disordered systems

Following an invariant-imbedding approach, we obtain analytical expressions for the ensemble-averaged resistance (ρ) and its Sinai’s fluctuations for a one-dimensional disordered conductor in the presence of a finite electric field F. The mean resistance shows a crossover from the exponential to the power-law length dependence with increasing field strength in agreement with known numerical results. More importantly, unlike the zero-field case the resistance distribution saturates to a Poissonian-limiting form proportional to A‖F‖exp(-A‖F‖ρ) for large sample lengths, where A is constant.

Modeling Finite Buffer Effects on TCP Traffic over an IEEE 802.11 Infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is known (see, for example, (3), [9]) that because of packet loss due to finite buffers at the Ap, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno.

Performance of slotted ALOHA satellite channels with finite buffer

The behaviour of the slotted ALOHA satellite channel with a finite buffer at each of the user terminals is studied. Approximate relationships between the queuing delay, overflow probabilities and buffer size are derived as functions of the system input parameters (i.e. the number of users, the traffic intensity, the transmission and the retransmission probabilities) for two cases found in the literature: the symmetric case (same transmission and retransmission probabilities), and the asymmetric case (transmission probability far greater than the retransmission probability). For comparison, the channel performance with an infinite buffer is also derived. Additionally, the stability condition for the system is defined in the latter case. The analysis carried out in the paper reveals that the queuing delays are quite significant, especially under high traffic conditions.

Realization of first order optical systems using thin lensest

A first order optical system is investigated in full generality within the context of wave optics. The problem is reduced to a study of the ray transfer matrices. The simplest such systems correspond to axially symmetric propagation. Realization of such systems by centrally located lenses separated by finite distances is studied. It is shown that, contrary to the commonly held view, the set of first order systems that can be realized using axially symmetric thin lenses exhausts the entire SL(2, R) group; at most three lenses are needed to realize any element of this group. In particular, the inverse of free propagation can be so realized. Among anisotropic systems it is again shown that every element of the lens group Sp(4, R) can be realized using a finite number of thin lenses.

Performance of slotted ALOHA satellite channels with finite buffer

The behaviour of the slotted ALOHA satellite channel with a finite buffer at each of the user terminals is studied. Approximate relationships between the queuing delay, overflow probabilities and buffer size are derived as functions of the system input parameters (i.e. the number of users, the traffic intensity, the transmission and the retransmission probabilities) for two cases found in the literature: the symmetric case (same transmission and retransmission probabilities), and the asymmetric case (transmission probability far greater than the retransmission probability). For comparison, the channel performance with an infinite buffer is also derived. Additionally, the stability condition for the system is defined in the latter case. The analysis carried out in the paper reveals that the queuing delays are quite significant, especially under high traffic conditions.

Hybrid Simulation of Queuing-System Dynamics

This paper presents a simple hybrid computer technique to study the transient behaviour of queueing systems. This method is superior to stand-alone analog or digital solution because the hardware requirement is excessive for analog technique whereas computation time is appreciable in the latter case. By using a hybrid computer one can share the analog hardware thus requiring fewer integrators. The digital processor can store the values, play them back at required time instants and change the coefficients of differential equations. By speeding up the integration on the analog computer it is feasible to solve a large number of these equations very fast. Hybrid simulation is even superior to the analytic technique because in the latter case it is difficult to solve time-varying differential equations.

Queuing Models for Estimating Aircraft Fleet Availability

The availability of a small fleet of aircraft in a flying-base, repair-depot combination is modeled and studied. First, a deterministic flow model relates parameters of interest and represents the state-of-the art in the planning of such systems. Second, a cyclic queue model shows the effect of the principal uncertainties in operation and repair and shows the consequent decrease in the availability of aircraft at the flying-base. Several options such as increasing fleet size, investments in additional repair facilities, or building reliability and maintainability into the individual aircraft during its life-cycle are open for increasing the availability. A life-cycle cost criterion brings out some of these features. Numerical results confirm Rose's prediction that there exists a minimal cost combination of end products and repair-depot capability to achieve a prescribed operational availability.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

A Finite Variable Difference Relaxation Scheme for hyperbolic-parabolic equations

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.

An FETI-preconditioned conjuerate gradient method for large-scale stochastic finite element problems

In the spectral stochastic finite element method for analyzing an uncertain system. the uncertainty is represented by a set of random variables, and a quantity of Interest such as the system response is considered as a function of these random variables Consequently, the underlying Galerkin projection yields a block system of deterministic equations where the blocks are sparse but coupled. The solution of this algebraic system of equations becomes rapidly challenging when the size of the physical system and/or the level of uncertainty is increased This paper addresses this challenge by presenting a preconditioned conjugate gradient method for such block systems where the preconditioning step is based on the dual-primal finite element tearing and interconnecting method equipped with a Krylov subspace reusage technique for accelerating the iterative solution of systems with multiple and repeated right-hand sides. Preliminary performance results on a Linux Cluster suggest that the proposed Solution method is numerically scalable and demonstrate its potential for making the uncertainty quantification Of realistic systems tractable.

Grids with multiple batch systems for performance enhancement of multi-component and parameter sweep parallel applications

In this work, we evaluate the benefits of using Grids with multiple batch systems to improve the performance of multi-component and parameter sweep parallel applications by reduction in queue waiting times. Using different job traces of different loads, job distributions and queue waiting times corresponding to three different queuing policies(FCFS, conservative and EASY backfilling), we conducted a large number of experiments using simulators of two important classes of applications. The first simulator models Community Climate System Model (CCSM), a prominent multi-component application and the second simulator models parameter sweep applications. We compare the performance of the applications when executed on multiple batch systems and on a single batch system for different system and application configurations. We show that there are a large number of configurations for which application execution using multiple batch systems can give improved performance over execution on a single system.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.