Mathematical Problems in Engineering

https://www.hindawi.com/journals/mpe/

List of Papers (Total 7,788)

A Method for Multicriteria Group Decision Making with Different Evaluation Criterion Sets

Multicriteria group decision making (MCGDM) with different evaluation criterion sets is a special kind of MCGDM problem, where criterion sets considered by multiple experts may be different, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method for MCGDM with different evaluation criterion sets. In the method...

Study of a least-squares-based algorithm for autoregressive signals subject to white noise

A simple algorithm is developed for unbiased parameter identification of autoregressive (AR) signals subject to white measurement noise. It is shown that the corrupting noise variance, which determines the bias in the standard least-squares (LS) parameter estimator, can be estimated by simply using the expected LS errors when the ratio between the driving noise variance and the...

Parameter Estimation Method of Mixture Distribution for Construction Machinery

Due to the harsh working environment of the construction machinery, a simple distribution cannot be used to approximate the shape of the rainflow matrix. In this paper, the Weibull-normal (W-n) mixture distribution is used. The lowest Akaike information criterion (AIC) value is employed to determine the components number of the mixture. A parameter estimation method based on the...

Nonlinear singularly perturbed systems of differential equations: A survey

In this paper a survey of the most effective methods in singular perturbations is presented. Many applied problems can be modeled by nonlinear singularly perturbed systems, as, for example, problems in kinetics, biochemistry, semiconductors theory, theory of electrical chains, economics, and so on. In this survey we consider averaging and constructive methods that are very useful...

A data-based damping modeling technique

Damping mechanisms exist in all vibration systems, but their nature is little understood and there is no systematic method for modeling general damping. This paper describes a novel damping modeling method (the Method of Energy Approximation, or MEA). This method is novel because it is a unique damping modeling method without assumed damping linearity; it is based on experimental...

Torsional and longitudinal vibration of suspension bridge subject to aerodynamic forces

In this paper we consider a dynamic model of suspension bridge governed by a pair of coupled partial differential equations which describe both torsional and longitudinal vibration of the road bed. The vertical and torsional motions are coupled through a nonlinear operation with the nonlinearity arising from loss of tension in the vertical cables supporting the decks. We study...

A problem related to the hall effect in a semiconductor with an electrode of an arbitrary shape

A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the...

Forced vibration of a ball attached to a cable

This work describes an analytic solution to predict the forced oscillation of a suspended cable and an attached ball. The oscillations are driven by a sinusoidal movement at the fixed end of the cable. This problem may be used in the verification of numerical software which is commonly used to design systems with suspended cables.

Passivation and control of partially known SISO nonlinear systems via dynamic neural networks

In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN), containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both...

Synthesis of fixed-architecture, robust H2 and H∞ controllers

This paper discusses and compares the synthesis of fixed-architecture controllers that guarantee either robust H2 or H∞ performance. The synthesis is accomplished by solving a Riccati equation feasibility problem resulting from mixed structured singular value theory with Popov multipliers. Whereas the algorithm for robust H2 performance had been previously implemented, a major...

Robustness with respect to disturbance model uncertainty: Theory and application to autopilot performance analysis

This paper deals with the notion of disturbance model uncertainty. The disturbance is modeled as the output of a first-order filter which is driven by white noise and whose bandwidth and gain are uncertain. An analytical expression for the steady-state output variance as a function of the uncertain bandwidth and gain is derived, and several properties of this variance function...

Escape probability and mean residence time in random flows with unsteady drift

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial...

Effect of rotation on wave propagation in a transversely isotropic medium

Wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry is studied. For propagation at high frequencies, effects of rotation are negligible but for a frequency which is much smaller than the frequency of rotation, there is a fast wave and two very slow waves. When the two frequencies are equal, the speed of a wave becomes unbounded.

Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems

The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis of trajectories, the Maximum Principle also is a sufficient condition for time-optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems.

A hybrid domain analysis for systems with delays in state and control

The solution of time-delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block-pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of...

Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems

In this paper, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems. Such a collection of dynamical systems may or may not have well defined ensemble averages as the existence of ensemble averages is predicated on the specification of appropriate initial conditions. A meaningful “average“ dynamical system can...

Transient analysis of a queue where potential customers are discouraged by queue length

The transient solution is obtained analytically using continued fractions for a state-dependent birth-death queue in which potential customers are discouraged by the queue length. This queueing system is then compared with the well-known infinite server queueing system which has the same steady state solution as the model under consideration, whereas their transient solutions are...

Fundamental problems for infinite plate with a curvilinear hole having finite poles

In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of...

An upper and lower solution approach for a generalized Thomas–Fermi theory of neutral atoms

This paper presents an upper and lower solution theory for boundary value problems modelled from the Thomas–Fermi equation subject to a boundary condition corresponding to the neutral atom with Bohr radius.

New filtering technique for the impulsive noise reduction in color images

We present a novel approach to the problem of impulsive noise reduction for colorimages. The new image-filtering technique is based on the maximization of the similarities between pixels in the filtering window. Themethod is able to remove the noise component, while adapting itself to the local image structure. In this way, the proposed algorithm eliminates impulsive noise while...

The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate

An analytic solution of the flow of a third-grade fluid on a porous plate is constructed. The porous plate is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous plate is also examined. It is also shown that in case of third-grade fluid, a combination of suction/injection and...

Peristaltic transport of an Oldroyd-B fluid in a planar channel

The effects of an Oldroyd-B fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effects of the various parameters of interest on the flow are shown and discussed.

Long-run availability of a priority system: a numerical approach

We consider a two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we...

A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations

The basic idea of this new method resides in the fact that the major part of the relative information to the solution to calculate is contained in the small modes of a development of Fourier series; the raised modes of which the coefficients associated being small, being negligible to every instant, however, the effect of these modes on a long interval of time is not negligible...

Realization problem for positive linear systems with time delay

The realization problem for positive single-input single-output discrete-time systems with one time delay is formulated and solved. Necessary and sufficient conditions for the solvability of the realization problem are established. A procedure for computation of a minimal positive realization of a proper rational function is presented and illustrated by an example.