Showing papers in "Mathematical Problems in Engineering in 2001"
TL;DR: In this paper, a method for identifying the bottleneck of a production line with Markovian machines having different cycle times is proposed. But it is only applied to a camshaft production line at an automotive engine plant.
Abstract: The bottleneck of a production line is a machine that impedes the system performance in the strongest manner. In production lines with the so-called Markovian model of machine reliability, bottlenecks with respect to the downtime, uptime, and the cycle time of the machines can be introduced. The two former have been addressed in recent publications [1] and [2]. The latter is investigated in this paper. Specifically, using a novel aggregation procedure for performance analysis of production lines with Markovian machines having different cycle time, we develop a method for c-bottleneck identification and apply it in a case study to a camshaft production line at an automotive engine plant.
109 citations
TL;DR: In this paper, a unified dynamical system framework for a general class of systems possessing left-continuous flows was developed, which includes hybrid, impulsive, and switching dynamical systems as special cases.
Abstract: In this paper we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems.
47 citations
TL;DR: In this article, a numerical approach based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness is proposed.
Abstract: A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost.
36 citations
TL;DR: 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.
Abstract: 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 different. A natural measure of speed of convergence of the mean number in the system to its stationarity is also computed.
34 citations
TL;DR: A relaxation of Tanaka's stability condition is proposed: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them, so that the coefficients of this sums depend on the membership functions.
Abstract: This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS) fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC). An application to the inverted pendulum is proposed here.
34 citations
TL;DR: Rationalized Haar functions are developed to approximate the solutions of the nonlinear Volterra-Hammerstein integral equations in this paper, and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations to some algebraic equations.
Abstract: Rationalized Haar functions are developed to approximate the solutions of the nonlinear Volterra-Hammerstein integral equations. Properties of Rationalized Haar functions are first presented, and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations to into some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.
32 citations
TL;DR: In this article, the boundary value problem for the Laplace equation outside several cuts in a plane is studied and the jump of the solution of the equation and its normal derivative are specified on the cuts.
Abstract: The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the jump of its normal derivative are specified on the cuts. The problem is studied under different conditions at infinity, which lead to different uniqueness and existence theorems. The solution of this problem is constructed in the explicit form by means of single layer and angular potentials. The singularities at the ends of the cuts are investigated.
27 citations
TL;DR: In this paper, the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems were investigated in the modelling effort of studying water quality constituents in fresh stream.
Abstract: In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.
25 citations
TL;DR: In this article, a manpower planning problem is studied in which includes scheduling different types of workers over different tasks, employing and terminating different type of workers, and assigning different types to various trainning programs, while keeping the time-varying demand for minimum number of workers working on each different tasks satisfied.
Abstract: A manpower planning problem is studied in this paper. The model includes scheduling different types of workers over different tasks, employing and terminating different types of workers, and assigning different types of workers to various trainning programmes. The aim is to find an optimal way to do all these while keeping the time-varying demand for minimum number of workers working on each different tasks satisfied. The problem is posed as an optimal discrete-valued control problem in discrete time. A novel numerical scheme is proposed to solve the problem, and an illustrative example is provided.
16 citations
TL;DR: In this paper, the authors proposed a hybrid time-delay solution using block-pulse functions and Chebyshev polynomials, which is based upon expanding various time functions in the system as their truncated hybrid functions.
Abstract: 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 integration and delay are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
13 citations
TL;DR: In this article, the authors investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay.
Abstract: In this paper, we investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ∞-performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.
TL;DR: In this article, the authors investigated fluid transport in random velocity fields with unsteady drift and developed numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations.
Abstract: 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 differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.
TL;DR: In this paper, the authors studied wave propagation in a transversely isotropic unbounded medium rotating about its axis of symmetry and showed that the speed of a wave becomes unbounded when the two frequencies are equal.
Abstract: 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.
TL;DR: In this article, the problem of control by the initial conditions of the heat equation with an integral boundary condition is studied and a non-local control problem is given. But the problem is ill-posed.
Abstract: In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
TL;DR: In this article, a sufficient condition for admissibility of the control operator B, under which operator B can be acceptable in order to work with controllability and stabilizability, is given.
Abstract: In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B, conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N(μ). Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N(μ) in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.
TL;DR: In this article, Muskhelishvili's complex variable method 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 general rational mapping function.
Abstract: 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 general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.
TL;DR: In this paper, a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied and the theory of interacting continua or mixture theory is used.
Abstract: The flow of a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied. The theory of interacting continua or mixture theory is used. Constitutive relations for the stress tensor of the granular materials and the interaction force are presented and discussed. The flow of interest is an ideal one where we assume the flow to be steady and fully developed; the mixture is flowing between two long vertical plates. The non-linear boundary value problem is solved numerically, and the results are presented for the dimensionless velocity profiles and the volume fraction as functions of various dimensionless numbers.
TL;DR: In this article, a diffeomorphic state space transformation is proposed to put the initial mutivariable nonlinear model into an appropriate regular form, which constitutes a guidance for a natural choice of the sliding surface.
Abstract: The paper shows how to compute a diffeomorphic state space transformation in order to put the initial mutivariable nonlinear model into an appropriate regular form. This form is an extension of the one proposed by Lukyanov and Utkin [9], and constitutes a guidance for a “natural” choice of the sliding surface. Then stabilization is achieved via a sliding mode strategy. In order to overcome the chattering phenomenon, a new nonlinear gain is introduced.
TL;DR: In this paper, two simplified methods for the evaluation of magnetisation loops in laminated SiFe alloys, using the Preisach theory and the statistical loss theory, are investigated in detail as a practical alternative for a very accurate, but much involved numerical approach.
Abstract: In this paper we present 2 simplified methods for the evaluation of magnetisation loops in laminated SiFe alloys, using the Preisach theory and the statistical loss theory. These methods are investigated in detail as a practical alternative for a very accurate, but much involved numerical approach, viz a combined lamination model – dynamic Preisach model earlier developed by the authors. Particularly, one of the 2 methods provides accurate results inspite of a dramatic reduction of the CPU-time in comparison with the earlier developed combined model. For the other simplified method, the reduction of CPU-time is less pronounced but still considerable and the results are fairly good.
TL;DR: In this paper, two different finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered, and the results of numerical experiments are presented, and accuracy and the Central Processor (CPU) times needed for each of the methods are discussed.
Abstract: Two different finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the (3,3) alternating direction implicit (ADI) finite difference scheme and the (3,9) alternating direction implicit formula. These schemes are unconditionally stable. The basis of analysis of the finite difference equation considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyett [17]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. These schemes use less central processor times than the fully implicit schemes for two-dimensional diffusion with temperature overspecification. The alternating direction implicit schemes developed in this report use more CPU times than the fully explicit finite difference schemes, but their unconditional stability is significant. The results of numerical experiments are presented, and accuracy and the Central Processor (CPU) times needed for each of the methods are discussed. We also give error estimates in the maximum norm for each of these methods.
TL;DR: In this paper, a general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign, and this theory is applied to the case where the dependent variable has a change sign.
Abstract: A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign.
TL;DR: In this paper, the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed, and sometimes the unknown coefficients can be estimated from the realization with the required accuracy.
Abstract: Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.
TL;DR: In this article, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems, which can represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average.
Abstract: 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 represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average. They
can also prove to be very attractive from a computational perspective. An advantage to the construction of the meaningful average is that it involves integrating a nonlinear differential equation, of the same order as that of any member in the collection. An average dynamical system can be used in the analysis and design of hierarchical systems, and will allow one to capture approximately the response of any member of the collection.
TL;DR: In this paper, the authors generalize this result for Lagrange, Mayer, and Bolza optimization problems and show that if there exists regular synthesis of trajectories, the maximum principle also is a sufficient condition for time-optimality.
Abstract: 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.
TL;DR: In this paper, the design of full order linear dynamic output feedback controllers for flexible structures is addressed, where a controller is designed in order to minimize a given H2 performance function while keeping the maximum supported H∞ perturbation below some appropriate level.
Abstract: This paper addresses the design of full order linear dynamic output feedback controllers for flexible structures. Unstructured H∞ uncertainty models are introduced for systems in modal coordinates and in reduced order form. Then a controller is designed in order to minimize a given H2 performance function while keeping the maximum supported H∞ perturbation below some appropriate level. To solve this problem we develop an algorithm able to provide local optimal solutions to optimization problems with convex constraints and non-convex but differentiable objective functions. A controller design procedure based on a trade-off curve is proposed and a simple example is solved, providing a comparison between the proposed method and the usual minimization of an upper bound H2 to the norm. The method is applied to two different flexible structure theoretical models and the properties of the resulting controllers are shown in several simulations.
TL;DR: In this paper, a new form of the strong law of large numbers for dependent vector sequences using the double averaged correlation function is presented, which generalizes the well-known Cramer-Lidbetter's theorem.
Abstract: A new form of the strong law of large numbers for dependent vector sequences using the “double averaged” correlation function is presented. The suggested theorem generalizes the well-known Cramer–Lidbetter's theorem and states more general conditions for fulfilling the strong law of large numbers within the class of vector random processes generated by a non stationary stable forming filters with an absolutely integrable impulse function.
TL;DR: In this article, the absolute stability of nonlinear systems with time delays is investigated and sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities, and applications of those results to cellular neural networks are presented.
Abstract: In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
TL;DR: In this article, a nonlinear ordinary differential equation obtained by means of self-similar reduction of the generalized Burgers equation with the nonlinear damping term was investigated, and the existence of positive bounded solutions with exponential and algebraic types of decay to zero at infinity was proved for special ranges of parameters.
Abstract: The object of investigation in this paper is a nonlinear ordinary differential equation obtained by means of self-similar reduction of the generalized Burgers equation $u_t+u^\beta u_x+\lambda u^\alpha=\delta u_{xx}$ with the nonlinear damping term $\lambda u^\alpha$. More exactly, the authors study the initial value problem $g"+2\eta g'+2\beta^{-1}g-2^{3/2}g^\beta g'-4\lambda g^\alpha=0$, $g(0)=
u$, $g'(0)=0$ by using both numerical and analytical methods. Here $\alpha>0$, $\beta=(\alpha-1)/2>0$, $\lambda$, $\delta>0$ and $
u >0$ are constants. Existence of positive bounded solutions with exponential and algebraic types of decay to zero at infinity is proved for special ranges of parameters.
TL;DR: The design of exPLOre is described: a modular, object-oriented, production line optimization software architecture that combines the output of a throughput evaluator with the business model.
Abstract: The general design problem in serial production lines concerns the allocation of resources such as the number of servers, their service rates, and buffers given production-specific constraints, associated costs, and revenue projections. We describe the design of exPLOre: a modular, object-oriented, production line optimization software architecture. An abstract optimization module can be instantiated using a variety of stochastic optimization methods such as simulated annealing and genetic algorithms. Its search space is constrained by a constraint checker while its search direction is guided by a cost analyser which combines the output of a throughput evaluator with the business model. The throughput evaluator can be instantiated using Markovian, generalised queueing network methods, a decomposition, or an expansion method algorithm.
TL;DR: In this paper, an indirect adaptive control scheme for continuous-time systems is presented, where the estimated plant model is controllable while the estimation model is free from singularities.
Abstract: This paper presents an indirect adaptive control scheme for continuous-time systems. The estimated plant model is controllable while the estimation model is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. This property is achieved by ensuring that the absolute value of its determinant does not lie below a prescribed positive threshold. A switching rule is used in the estimates modification algorithm to ensure the controllability of the modified estimated model while avoiding possible chattering. For that purpose, the switching rule takes values at two possible distinct prefixed thresholds. In the event when the Sylvester determinant takes the current value of the switching function then that one switches to
the alternative threshold. The convergence of both the unmodified and modified
estimates to finite limits guarantees that switching ends in finite time. Thus, the solution to the controlled plant exist so that all the signals within the loop are well-posed.