Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1993"
TL;DR: In this article, an integrated technique based on the vibration theory to nondestructively identify multiple discrete cracks in a structure is presented, where two damage modeling techniques, one involving the use of massless, infinitesimal springs to represent discrete cracks and the other one employing the continuum damage concept, are integrated to provide a crack-detection technique that utilizes the global vibration characteristics of a structure but offers local information on each individual crack, including location and extent of the cracks.
Abstract: An integrated technique based on the vibration theory to nondestructively identify multiple discrete cracks in a structure is presented. Two damage modeling techniques, one involving the use of massless, infinitesimal springs to represent discrete cracks and the other one employing the continuum damage concept, are integrated to provide a crack-detection technique that utilizes the global vibration characteristics of a structure but offers local information on each individual crack, including location and extent of the cracks. In the spring model, the Castigliano's theorem and the perturbation technique are used to derive a theoretical relationship between the eigenfrequency changes and the location and extent of the discrete cracks. In the continuum damage model, the effective stress concept coupled with the Hamilton's principle are used to derive the similar relationship that is cast in a continuum form. A unified g(β) function emerges from the two model approaches. The g(β) function can be determined through the mode shapes of an intact structure by means of the modal strain energy density. In the proposed integrated approach, the continuum damage model can be used first to identify the discretizing elements of a structure that contain cracks. Then, the spring damage model can be used to quantify the location and severity of the discrete crack in each damaged element. An example of a simply-supported beam containing two discrete cracks is given to illustrate the application and accuracy of the proposed approach.
109 citations
TL;DR: A neural network controller is developed to learn the inverse dynamics of unknown dynamic systems and to serve as a feedforward controller that is intelligent enough to learn from its experience.
Abstract: A neural network controller is developed to learn the inverse dynamics of unknown dynamic systems and to serve as a feedforward controller. Artificial neural networks, which consist of a set of processing units with interconnections between them, are used to get the desired output. The interconnections, known as weights, can be on-line tuned. Hence the controller is adaptive in nature. Neural networks can be used to represent the inverse dynamics of unknown dynamic systems. The error back propagation technique is used in the learning process. The controller is intelligent enough to learn from its experience. The performance of the intelligent controller for learning and control of dynamic systems is very successful.
54 citations
TL;DR: In this article, the authors propose an approach without causality resistors for linear systems, without such resistors, to compute the amplitude of the pulse and the value of the new variables.
Abstract: Modelling and simulation of switching devices with bond graphs is a subject which has no totally satisfying solutions. In this paper, switching devices are represented by flow or effort sources, with a variable circuit topology at switching time. For the simulation, the usual method uses causality resistors to insure integral causality to energy storage elements. The choice of those resistors is quite arbitrary and can lead to stiff systems. We propose, for linear systems, an approach without such resistors. When components lose the integral causality, the order of the state vector changes, provoking the use of pulse variables. A solution is proposed to compute the amplitude of the pulse and the value of the new variables.
45 citations
TL;DR: In this article, two different descriptions of an abstract n-dimensional dynamical system are discussed: a Sierpinski space setting and a statistical cellular space setting, and the results suggest that the phase space dynamics is peano-like and resembles an Anosov diffeomorphism of a compact manifold which is dense and quasi-ergodic.
Abstract: Two different descriptions of an abstract n-dimensional dynamical system are discussed: a Sierpinski space setting and a statistical cellular space setting. The results suggest that in four dimensions the phase space dynamics is peano-like and resembles an Anosov diffeomorphism of a compact manifold which is dense and quasi-ergodic. The Hausdorff capacity dimension in this case is d(4)C= 3.981 ≅ 4 and we conjecture that the simplest fully developed turbulence is related to d(5)C≅ 6.3. The corresponding Shannon information entropy of the second analysis are l (4)S = 3.68 and l (5)S = 6.12. The implications of the results for quantum spacetime are outlined and found to be consistent with Heisenberg uncertainty relationship and Bekenstein-Hawking entropy. Finally, the connection between strange nonchaotic behaviour and Godel theorem is discussed.
40 citations
TL;DR: In this article, a model-independent scenario for a dynamic system to possess strange nonchaotic behaviour in the presence of quasi-periodic forcing is presented, and the implications for ergodicity and turbulence are discussed in connection with Sierpenski and peano-Hilbert spaces.
Abstract: The work outlines a fairly model-independent scenario for a dynamic system to possess strange nonchaotic behaviour in the presence of quasi-periodic forcing. Implications for ergodicity and turbulence are discussed in connection with Sierpenski and peano-Hilbert spaces.
27 citations
TL;DR: In this paper, the Schur-Cohn minors and inner determinants of polynomials with both real and complex-valued coefficients are extracted from the Bistritz table.
Abstract: The Bistritz tabular form may be utilized in determining discrete-time system stability with less computational effort as compared with the Jury tabular form. When appropriately constructed, the latter, however, provides the Schur-Cohn minors and the inner determinants related to the characteristic equation being tested. In this paper, we show that these quantities also may be extracted from the Bistritz tabular form. The cases of polynomials with both real- and complex-valued coefficients are studied. An important consequence of these relationships is the possibility of utilizing the Bistritz table in determining stability of two- and multi-dimensional discrete-time systems
27 citations
TL;DR: The optimal model of memoryless cascade system is derived and estimated by the recursive kernel regression estimate and nonlinear dynamical systems of Hammerstein and Wiener type with arbitrary nonlinearities are identified by means of nonparametric techniques.
Abstract: The identification of block-oriented systems by the kernel recursive estimate is discussed. Three types of system are considered: cascade of nonlinear memoryless system, Hammerstein system and Wiener system. The optimal model of memoryless cascade system is derived and estimated by the recursive kernel regression estimate. Nonlinear dynamical systems of Hammerstein and Wiener type with arbitrary nonlinearities are identified by means of nonparametric techniques. Convergence of identification procedures is investigated.
25 citations
TL;DR: In this article, a graph representation of geared kinematic chains is introduced, and a simple method is proposed to generate all possible (N+1)-link geared chain from N-link chain.
Abstract: This paper presents a systematic appoach, which is based on a new graph representation of geared kinematic chains, for the structural synthesis of geared kinematic chains. First, the new graph representation of geared kinematic chains is introduced. Next, a simple method is proposed to generate all possible (N+1)-link geared kinematic chains from N-link geared kinematic chains. Then, isomorphic geared kinematic chains are identified to obtain nonisomorphic geared kinematic chains by comparing their Structural Codes. Finally, an atlas of nonisomorphic geared kinematic chains for one degree-of-freedom planetary gear trains with up to seven links is constructed.
23 citations
TL;DR: In this article, an exhaustive catalogue of OTA-C oscillator topologies and methods of generating canonic oscillators has been presented, which provide independent control of the oscillation frequency.
Abstract: OTA-C oscillators offer many attractive features as compared to conventional op-amp based oscillators. They have now become increasingly important in view of their adaptability for implementing high frequency digitally programmable sinusoidal oscillators in CMOS technology. Although several OTA-C oscillator topologies and a few methods of generating OTA-C oscillators have been known earlier, the existing list of OTA-C oscillators is by no means complete. To cover this gap, following a systematic approach, an exhaustive catalogue of a class of canonic (employing only two capacitors and three OTAs) oscillator circuits has been generated which provide independent control of the oscillation frequency. Only a few of these oscillator structures have been known earlier, whereas the remainder of these are completely new. The workability of all the configurations has been confirmed experimentally and some sample results are included.
21 citations
TL;DR: In this article, a systematic method based on the concept of admissible graphs was developed for the synthesis of the kinematic structure of planetary gear trains with any number of degrees of freedom.
Abstract: This paper develops a systematic method, which is based on the concept of admissible graphs, for the synthesis of the kinematic structure of planetary gear trains with any number of degrees of freedom. First, the fundamental rules of admissible graphs of planetary gear trains are investigated. Next, acording to the number of links and gear pairs, all the admissible graphs of planetary gear trains can be listed from the atlas of admissible graphs. For each admissible graph, all possible graphs of planetary gear trains are synthesized by the process of edge transformation. Then, the Structural Codes of graphs are used to identify the isomorphism of the derived graphs. Finally, an atlas of the graphs of planetary gear trains with up to four gear pairs and three degrees of freedom has been constructed.
21 citations
TL;DR: A novel method of obtaining optimal reduced-order models of linear system transfer functions is presented, which uses the popular multipoint Pade approximation technique in an iterative way to generate efficiently the optimal models.
Abstract: A novel method of obtaining optimal reduced-order models of linear system transfer functions is presented. It uses the popular multipoint Pade approximation technique in an iterative way to generate efficiently the optimal models. Central to the method is a new way of calculating Pade approximants about many points by reducing them to equivalent Taylor series approximants. Optimal reduced-order models for impulse and step inputs are considered, and it is seen how the method may be extended to ramp and other polynomial inputs. Numerical examples are given to demonstrate the method.
TL;DR: In this article, the boundary control of a nonlinear elliptic partial differential equation with an integral performance criterion is considered, in which the goal is to minimize a linear form over a subset of the product of two measure spaces defined by linear equalities.
Abstract: We consider the boundary control of a nonlinear elliptic partial differential equation with an integral performance criterion. By means of a well-known process of embedding, this problem is replaced by another, in which we seek to minimize a linear form over a subset of the product of two measure spaces defined by linear equalities. This minimization is global, and the theory allows the development of a computational method consisting of the solution of large finite-dimensional linear programming problems. Nearly optimal controls can thus be constructed. An example is given.
TL;DR: In this article, the authors used temperature-correlated profiles to obtain the solution of optimum convective fin when the thermal conductivity and heat transfer coefficient are functions of temperature and the profile is shown to be convenient to obtain an analytical solution of the resulting nonlinear heat transfer equation.
Abstract: The method of temperature-correlated profiles is used to obtain the solution of optimum convective fin when the thermal conductivity and heat transfer coefficient are functions of temperature. The profile is shown to be convenient to obtain an analytical solution of the resulting nonlinear heat transfer equation. It is shown that the profile correctly predicts the optimization problems with spatial variation of the heat transfer coefficients reported in the literature. The effect of temperature dependence on heat transfer coefficients is found to be important in the design of optimum fins. Using the profile, an approximate solution for the optimum fin, including the effect of temperature dependence on convection heat transfer coefficient (useful for parametric study and design analysis), is obtained. The exact solution, using numerical integration of the resulting equations, is compared with the approximate solutions. The results are reported in terms of dimensionless quantities convenient in design analysis. The method is shown to be very useful for parametric study where the optimization problem is given in terms of two parameters: the tip temperature and a profile parameter.
TL;DR: In this article, the authors examined the mechanical efficiency of reciprocating heat engines in a general setting and derived an upper bound on the compression ratio under conditions relating the level of performance of the mechanism to the ratio of engine operating temperatures, which has implications for the design of engines intended for operation from low grade sources such as industrial waste heat or passive solar energy.
Abstract: This paper examines the mechanical efficiency of reciprocating heat engines in a general setting. From an abstract mathematical characterization of machines, the relation of the pressure-volume cycle of an engine and the characteristics of its mechanism to its useful work output is established. Using the ideal Stirling engine in conjunction with this relation, a functional upper bound on the mechanical efficiency of all engines is derived. This shows the existence of limits on compression ratio under conditions relating the level of performance of the mechanism to the ratio of engine operating temperatures. This has implications for the design of engines intended for operation from low grade sources, such as industrial waste heat or passive solar energy.
TL;DR: Based on the principle of minimum volume, an optimum shape of fin is proposed in this article, where the outer appearance is essentially like a cylindrical fin and the excavated part is in the inner portion of the fin.
Abstract: Based on the principle of minimum volume, an optimum shape of fin is proposed in this study. The outer appearance is essentially like a cylindrical fin and the excavated part is in the inner portion of the fin. First, the surface heat flux is assumed to follow a power-law dependence. With the aid of one-dimensional analysis, the temperature distributions and the profiles of the excavation hole are calculated for various single heat transfer modes. Secondly, the boiling curve of isopropyl alcohol on copper surface is used as an input to the model. The base temperature in the film boiling regine is taken and the optimum geometry is presented. Finally, the efficiency based on the volume and heat duty is discussed.
TL;DR: In this article, a method for the optimal control of linear time-varying systems with a quadratic cost functional is proposed, where state and control variables are expanded in the shifted Legendre series, and an algorithm is provided for approximating the system dynamics, boundary conditions and performance index.
Abstract: A method for the optimal control of linear time-varying systems with a quadratic cost functional is proposed. The state and control variables are expanded in the shifted Legendre series, and an algorithm is provided for approximating the system dynamics, boundary conditions and performance index. The necessary condition of optimality is then derived as a system of linear algebraic equations. Numerical examples are included to demonstrate the validitiy and applicability of the technique.
Abstract: The complexity of computation in a multidimensional digital filter stability test using resultant theory is reduced by exploiting a criterion for a polynomial having complex coefficients to be a Schur polynomial. The computational advantage is illustrated by nontrivial examples involving polynomials having both numerical and literal coefficients.
TL;DR: In this paper, the dynamics of a simply supported, spinning Timoshenko beam subjected to a moving load is solved analytically using a modal analysis technique, which yields eigenquantities such as natural frequencies and mode shapes.
Abstract: The dynamics of a simply supported, spinning Timoshenko beam subjected to a moving load is solved analytically using a modal analysis technique. In addition to obtaining the system transient response, this method also yields eigenquantities such as natural frequencies and mode shapes. Unlike the spinning Euler-Bernoulli and the simply supported spinning Rayleigh beams which have only one pair of natural frequencies corresponding to each mode shape, simply supported spinning Timoshenko beams possess two pairs of natural frequencies. It is also shown that the coupled differential equations are of the eighth-order which for most cases, can be reduced to a set of uncoupled fourth-order equations without introducing any significant errors. Closed-form expressions for natural frequencies and the system transient response are presented using this simplified theory. A linearized expression for the computation of natural frequencies, which retains the essential features of the Timoshenko beam theory is also proposed here.
TL;DR: In this paper, the problem of approximating an original rational matrix by means of a rational matrix of lower order according to the L 2 -norm criterion is considered, and a compact form of the necessary conditions for optimality is derived, which may be considered as the extension to the multivariable case of the interpolation conditions valid in the scalar case.
Abstract: The problem of approximating an original rational matrix by means of a rational matrix of lower order according to the L 2 -norm criterion is considered. In particular, a compact form of the necessary conditions for optimality is derived, which may be considered as the extension to the multivariable case of the interpolation conditions valid in the scalar case. On the basis of this form, an iterative numerical technique to find the optimal approximating model is suggested.
TL;DR: In this paper, a discrete-time multipoint Pade approximation method is presented that derives optimal reduced-order models, which can be easily implemented using a recently developed way of calculating Pade approximants.
Abstract: A discrete-time multipoint Pade approximation method is presented that derives optimal reduced-order models. The method is seen to be easily implemented using a recently developed way of calculating Pade approximants. An important result that relates the optimal model to multipoint Pade approximation is proved and the whole process isseen to consist of multiplying matrices and solving linear equations. Numerical examples are given to illustrate the application of the new method.
TL;DR: A new method is proposed for computing a relatively small number of points to define an approximate representation of the tradeoff set and a general algorithm embodying the method is outlined and analysed.
Abstract: The problem of efficiently approximating the tradeoff (Pareto-optimal) curve or set for optimization problems with two conflicting objectives is considered. In particular, a new method is proposed for computing a relatively small number of points to define an approximate representation of the tradeoff set. The efficiency of the method is established by showing the maximum number of points required to achieve a prescribed precision of approximation. Finally, a general algorithm embodying the method is outlined and analysed.
TL;DR: In order to attain a standard regular problem, some techniques to decompose the singular system into a reduced-order regular subsystem and a nondynamic subsystem are used.
Abstract: Design procedures are proposed for model conversion and digital redesign of a singular system, which is controllable at finite and impulsive modes. In order to attain a standard regular problem, we use some techniques to decompose the singular system into a reduced-order regular subsystem and a nondynamic subsystem. As a result, some well-known design methodologies for a regular system can be applied to the reduced-order regular subsystem. Finally, we transform the results obtained back to those of the original coordinate system.
TL;DR: In this article, the authors studied the phenomenon of false lock in second-order, Type I phase-locked loops (PLLs) with a constant frequency reference of ω i and a voltage controlled oscillator (VCO) quiescent frequency.
Abstract: New results are given on the phenomenon of false lock in second-order, Type I phase locked loops (PLLs) with a constant frequency reference of ω i and a voltage controlled oscillator (VCO) quiescent frequency of ω 0 . This loop has only one false lock state whose frequency error approaches ω i -ω 0 as loop gain δ approaches zero, and this false lock state is stable. This false lock state corresponds to a stable, hyperbolic limit cycle X s (t;δ) of the nonlinear equation describing the loop. As gain δ is increased from a value of zero, it is shown that a value δ 1 can be reached where X s becomes semi-stable and nonhyperbolic. Furthermore, saddle node bifurcation occurs at δ 1 , and a second limit cycle X u (t;δ) branches from this bifurcation point. Limit cycle X u is unstable, and it corresponds to an unstable false lock state of the PLL. Furthermore, X u can be continued as a function of gain on an interval δ 2 1 , for some δ 2 >0. Finally, X s and X u do not exist for δ>δ 1 . Two numerical algorithms are given to analyse the false locked PLL under consideration. The first is useful for computing the above-mentioned limit cycles and the bifurcation point δ 1 . The second algorithm can calculate a Poincare map and its derivative which are useful in studying the saddle node bifurcation which occurs at δ 1 . Also given is a detailed description of a laboratory experiment which was used to substantiate the theory and numerical techniques. The qualitative theory, numerical method and laboratory procedure are applied to a simple example. The numerical and empirical results are shown to be in close agreement.
TL;DR: In this paper, it was shown that all-terminal reliability polynomials of networks having the same number of nodes and links can cross twice as the edge operation probability ranges from 0 to 1.
Abstract: An example is given to demonstrate that all-terminal reliability polynomials of networks having the same number of nodes and the same number of links can cross twice as the edge operation probability ranges from 0 to 1 . A similar result is shown for two-terminal reliability.
TL;DR: In this article, the authors used the zero-order approximate solution for the currents along thin antennae to study the behavior of a received voltage pulse across the terminals of thin dipole placed at the far zone of a thin transmitting dipole excited by a single-cycle sinusoidal voltage.
Abstract: The zero-order approximate solution for the currents along thin antennae is used to study the behavior of a received voltage pulse across the terminals of a thin dipole placed at the far zone of a thin transmitting dipole excited by a single-cycle sinusoidal voltage. It is found that each of the four distinct electric field pulses which the transmitting dipole radiates, induces four distinct (although overlapping) voltage pulses at the discontinuities of the receiving dipole antenna. Although the exciting voltage is single-cycle, the time duration of the incident electric field and the induced received voltage is lengthened by 1.5 cycles and up to 2 cycles, respectively. The receiving antenna behaves like an integrating circuit. The spectra of the short-pulse radiated field and the received voltage have peak values at frequencies higher than the carrier frequency f 0 of the exciting single-cycle sinusoidal voltage.
TL;DR: The class of transformation noise generated by multivariate Gaussian underlying noise is proposed as a model for other second-order stationary transformation noise processes and three ad hoc methods are suggested to obtain the correlation function.
Abstract: Some properties are studied of the class of discrete time transformation noise which is generally non-Gaussian and correlated and is generated by passing another noise process through an invertible memoryless nonlinearity. In general, any discrete time noise process can be considered as transformation noise. The dependency structure of the transformation noise is described by the same set of parameters as the underlying noise, with closely related canonical eigenfunctions. The class of transformation noise generated by multivariate Gaussian underlying noise is proposed as a model for other second-order stationary transformation noise processes. While the nonlinearity is simple to determine, three ad hoc methods are suggested to obtain the correlation function. One method is found to be simple and reasonable.
TL;DR: An implementation of the integrated operational amplifier used in the design of an artificial CNN is studied and a fast algorithm for a CNN component detector is given which proves to be very simple and quite convenient.
Abstract: Cellular neural network (CNN) is a type of analog, nonlinear, real-time parallel processing network. The paper studies an implementation of the integrated operational amplifier used in the design of an artificial CNN. It improves the implementation of CNN proposed by Chua. A 4 x 4 artificial CNN circuit is designed, obtaining a better characteristic of a CNN connected component detector. Finally, a fast algorithm for a CNN component detector is given which proves to be very simple and quite convenient.
TL;DR: In this paper, the Extended Bond Graph (EBG) method is used to model a two-link flexible manipulator system, and the model is coupled with a DC motor and a revolute joint.
Abstract: The Extended Bond Graph (EBG) method is used to model a two-link flexible manipulator system. An EBG module is first derived to represent the dynamics of an elastic link undergoing large motions by applying the spatial discretization of the conjugate variable approximation method, the shadow-beam kinematic description and the principle of virtual work. Then, modules for a DC motor and a revolute joint are reticulated into the EBG format. Finally, the link, revolute joint and DC motor modules are coupled to form the EBG model for a two-link flexible manipulator system. Numerical simulations for a planar two-link flexible manipulator are presented, and the utility of this method is illustrated by the computation of the actuator torques and reaction forces at the joints.
TL;DR: A methodology is presented based on the alpha-beta expansion, so as to derive a bond graph model from any transfer function found, most of the time, using special techniques for the identification of dynamical systems.
Abstract: A methodology is presented based on the alpha-beta expansion, so as to derive a bond graph model from any transfer function (resp. matrix) found, most of the time, using special techniques for the identification of dynamical systems. The object is to take advantage of the whole set of bond graph techniques for structural analysis, sensors assignment, model reduction and control.
TL;DR: In this article, a recursive method for determining the state weighting matrix of a linear quadratic regulator problem in order to shift the open loop poles to the desired locations is presented.
Abstract: A recursive method for determining the state weighting matrix of a linear quadratic regulator problem in order to shift the open loop poles to the desired locations is presented. This method is capable of shifting the real and imaginary parts for continuous time systems. Aggregation is used in each step of the recursive process. Therefore each time the order of the system is reduced to first- or second-order, a constrained minimization problem with linear and nonlinear constraints has to be solved in order to find the state weighting matrix of the reduced-order system that will shift the open loop poles to the desired locations. An example is given to illustrate the theory.