on the solution of s ω x 0 by a newtonian procedure the method 1 developed for the solution of e a x 0 where e and a are real symmetric matrices and a is positive definite is extended to deal with s x 0 where s is a real symmetric structural dynamic stiffness matrix whose elements are trancendental functions of the radian natural frequency the method enables all natural frequencies latent roots 2 and mode shapes latent vectors x across a prescribed frequency range to be determined infallibly and in ascending frequency order at a speed approaching twice that associated with bisection and sign counting methods 3 it is ideally suited for use on micro and minicomputers where single precision working is the norm and on the commodore 4032 computer can cope with matrices s of order n and bandwidth p provided that np 4200 much larger problems of course may be dealt with on mainframe machines

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

design and analysis of a fuzzy proportional integral derivative controller abstract this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional integral pi plus a derivative d controller first the fuzzy pi d controller is derived from the conventional continuous time linear pi d controller then the fuzzification control rule base and defuzzification in the design of the fuzzy controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pi d controller which has the same linear structure in the proportional integral and derivative parts but has nonconstant gains the proportional integral and derivative gains are nonlinear functions of the input signals the new fuzzy pi d controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self tuning control capability computer simulation results have demonstrated the advantages of the fuzzy controller particularly when the process to be controlled is nonlinear after a brief stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are shown to compare with the conventional pi d controller computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance

tracking control of a manipulator under uncertainty by fuzzy p id controller one of the most important manipulator operations is the control of the manipulator to track a given trajectory most commercial robot systems currently are equipped with conventional pid controllers due to their simplicity in structure and ease of design using pid control however it is di cult to achieve a desired tracking control performance since the dynamic equations of a mechanical manipulator are tightly coupled highly nonlinear and uncertain in order to improve the tracking control performance under uncertainty this paper presents a new hybrid control scheme for the manipulator which consists of a fuzzy logic proportional controller and a conventional integral and derivative controller fuzzy p id in comparison with a conventional pid controller only one additional parameter has to be adjusted to tune the fuzzy p id controller the proposed control scheme has been implemented on a direct drive two link manipulator the outlined experimental results on tracking control under inertial parameters changes demonstrate the eaectiveness and the robustness of the new fuzzy p id controller c 2001 elsevier science b v all rights reserved

a general procedure for improving substructures representation in dynamic synthesis in the general substructure synthesis method for the dynamic analysis of complex flexible structures developed earlier by the authors the motion of each substructure is represented by a given number of substructure admissible functions and the otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of weighted residuals in this paper a general procedure for improving the admissible functions representing each substructure in the synthesis is developed the procedure is an iterative one and it leads to an improved eigensolution for the intermediate structure i e a fictitious structure defined by the approximate compatibility conditions where the improved eigensolution is obtained while always using the same number of degrees of freedom to represent a given substructure in any iteration the computations associated with each substructure are independent of those for all other substructures and they can be performed in parallel by increasing the number of iterations the eigensolution for the intermediate structure is approached the procedure is applicable to assembled structures that are either positive definite or positive semidefinite moreover the procedure represents an extension of the concept of subspace iteration to structures composed of substructures

eigenvalue convergence in the finite element method in static force deflection applications of the finite element method convergence rates for the p version in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed are superior to those for the h version in which the element degree remains fixed while the mesh is refined so that element size approaches zero in structural dynamics applications one does not seek to approximate a single solution as in static applications but seeks estimates for a number of the lower system eigenvalues this paper identifies factors responsible for poorer accuracy in higher computed eigenvalues in addition it explains why the p version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h version numerical examples demonstrate the superiority of the p version over the h version they also show the effects of various mechanisms limiting eigenvalue convergence

new design and stability analysis of fuzzy proportional derivative control systems this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional derivative pd controller first the fuzzy pd controller is derived from the conventional continuous time linear pd controller then the fuzzification control rule base and defuzzification in the design of the fuzzy pd controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pd controller which has the same linear structure in the proportional and the derivative parts but has nonconstant gains both the proportional and derivative gains are nonlinear functions of the input signals the new fuzzy pd controller thus preserves the simple linear structure of the conventional pd controller yet enhances its self tuning control capability computer simulation results have demonstrated this advantage of the fuzzy pd controller particularly when the process to be controlled is nonlinear after a detailed stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are compared with the conventional pd controller although the conventional and fuzzy pd controllers are not exactly comparable the authors compare them in order to have a sense of how well the fuzzy pd controller performs for this reason in the simulations several first order and second order linear systems with or without time delays are first used to test the performance of the fuzzy pd controller for step reference inputs the fuzzy pd control systems show remarkable performance as well as if not better than the conventional pd control systems moreover the fuzzy pd controller is compared to the conventional pd controller for a particular second order linear system showing the advantage of the fuzzy pd controller over the conventional one in the sense that in order to obtain the same control performance the conventional pd controller has to employ an extremely large gain while the fuzzy controller uses a reasonably small gain finally in the case of nonlinear systems the authors provide some examples to show that the fuzzy pd controller can track the set points satisfactorily but the conventional pd controller cannot

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral controllers with variable gains abstract the author analytically proves that the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral pi controllers with proportional gains and integral gains changing with inputs of the controllers the inference methods involved are mamdani s minimum inference method larsen s product inference method the drastic product inference method and the bounded product inference method configuration of the fuzzy controllers is minimal which includes two input fuzzy sets three output fuzzy sets four control rules zadeh fuzzy logic and lukasiewicz fuzzy logic or and a center of gravity defuzzification algorithm after analytically investigating properties of the nonlinear pi controllers the author reveals that the bounded product inference method is inappropriate for the control purpose while the other three inference methods are appropriate dynamic and static control behaviors of the fuzzy controllers with the appropriate inference methods are analytically compared with each other and are also compared with those of the linear pi controller finally it is analytically proven that the fuzzy control systems have the same local stability at the equilibrium point as the corresponding linear pi control system does

quantifiers in the formulation of multiple objective decision functions abstract we discuss the interpretation of linguistically quantified statements using fuzzy sets we indicate that there are two methods of interpreting these statements the algebraic approach and the substitution approach we then use quantified statements to express overall decision functions involving multiple objectives these statements are of the type a solution should satisfy many of the objectives using the algebraic and substitution approach we develop a whole family of forms for combining multiple objectives we show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction the substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives

substructure mode synthesis with overlapping connecting elements abstract an approach is presented to synthesize the modal properties of two substructures to obtain the modal properties of the combined structure the substructures are assumed to be fixed at the interfacing boundary and have overlapping elements the eigenproperties of the overlapping elements are also used in the synthesis process the approach can be used with any finite element discretization scheme the approach avoids the solution of a second eigenvalue problem by conventional means instead the eigenvalues are obtained as the solution of characteristic equations and eigenvectors are defined in closed form if the complete set of eigenproperties are used the approach provides the exact eigenproperties

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

dynamic substructure response abstract dynamic substructure methods enable one to analyze a large scale dynamic system by considering its constituents individually and the combined action afterwards steady state harmonic oscillation has been studied almost exclusively the methods are extended to general non steady state excitations the orthonormality condition of the modal vectors in terms of the masters is introduced a mixed mass matrix for initial conditions is derived the dynamic flexibility is expressed in spectral form for response calculation modal participation factors for both distributed and concentrated loads are given explicitly

on a new iterative approach of component mode synthesis a wholly new concept of intermediate structure is developed in this paper based on this a new component mode iteration cmi or subdomain subspace iteration method is proposed in the new cmi method the ordinarily required step of ensuring interface compatibility is eliminated an outstanding achievement of this method is that it retains the merit of the standard subspace iteration ssi technique concerning the number of vectors required in computation in the present method iteraton is carried out at subdomain levels on machines capable of parallel processing this work can be performed simultaneously numerical examples clearly demonstrate the excellence of this new method

matrix variate distributions for probabilistic structural dynamics matrix variate distributions are proposed to quantify uncertainty in the mass stiffness and damping matrices arising in linear structural dynamics the proposed approach is based on the so called wishart random matrices it is assumed that the mean of the system matrices are known a new optimal wishart distribution is proposed to model the random system matrices the optimal wishart distribution is such that the mean of the matrix and its inverse produce minimum deviations from their respective deterministic values the method proposed here gives a simple nonparametric approach for uncertainty quantification and propagation for complex aerospace structural systems the new method is illustrated using a numerical example it is shown that wishart random matrices can be used to model uncertainty across a wide range of excitation frequencies

the use of the karhunen loegve procedure for the calculation of linear eigenfunctions abstract it is shown that the karhunen loeve decomposition may be used to determine the eigenfunctions of a general class of linear operators from an ensemble of realizations that are derived from that system given a moderate size data set either numerical or experimental from a linear system good approximations to the eigenfunctions that characterize the underlying equations can be computed by performing the karhunen loeve procedure two numerical examples are presented the vibration of a thin membrane in a rectangular domain and in a stadium these are used to determine the convergence and accuracy of the method it is found that this method yields accurate results for the first few eigenfunctions with relatively few realizations eigenfunctions with less energy are accurately resolved as the size of the ensemble increase the method is shown to be an efficient and practical procedure for determining the eigenfunctions of systems in complex geometries and in cases where the governing equations are not known a priori the effect of random noise contamination of the data set is also investigated and it is found that the karhunen loeve procedure can still achieve accurate results despite the presence of substantial background noise

linear non linear dynamic substructures the dynamic substructure method is extended to linear and non linear coupling systems only those master co ordinates with non linear nature non linear co ordinates are retained other slave co ordinates relating to the linear part linear co ordinates are eliminated by the dynamic substructure method the dynamic flexibility matrix associated with the linear co ordinates is first expanded in terms of the fixed interface natural modes the condensed dynamic stiffness matrix associated with the non linear co ordinates is formed subsequently the convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and taylor series expansion to find the steady state solutions the non linear responses are expanded into a fourier series responses of the linear co ordinates are related to the non linear co ordinates analytically to solve for the unknown fourier coefficients the harmonic balance method gives a set of non linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients a newtonian algorithm is adopted to solve for the unknown fourier coefficients iteratively the computational cost of a non linear analysis depends heavily on the number of degrees of freedom encountered in the method the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced

on estimating frequency response function envelopes using the spectral element method and fuzzy sets abstract the influence of uncertain input data on response spectra of dynamic structures is considered traditionally frequency response analyses are based on finite or boundary element models of the objective structure in the case of the mid frequency range problem however a very fine mesh is required to correctly approximate the frequency response this is particularly problematic in uncertainty modeling where the computational effort is usually increased significantly by the need for multiple runs e g when conducting a monte carlo analysis to achieve reliable results in this paper the spectral element method combined with a fuzzy set based uncertainty modeling approach is presented as an appealing alternative provided that the models are simple enough to yield a spectral element representation to conduct the fuzzy analysis part three different implementations of the extension principle of fuzzy arithmetic are applied and compared the suitability of each method depends on the number of uncertain parameters the problem characteristics and the required accuracy of the results the performance of the proposed approach is illustrated by two test problems a simple coupled rod and a reinforced plate model to verify the fuzzy valued results a monte carlo simulation has also been included

representation similarity measures and aggregation methods using fuzzy sets for content based recommender systems representation of features of items and user feedback and reasoning about their relationships are major problems in recommender systems this is because item features and user feedback are subjective imprecise and vague the paper presents a fuzzy set theoretic method ftm for recommender systems that handles the non stochastic uncertainty induced from subjectivity vagueness and imprecision in the data and the domain knowledge and the task under consideration the research further advances the application of fuzzy modeling for content based recommender systems initially presented by ronald yager the paper defines a representation method similarity measures and aggregation methods as well as empirically evaluates the methods performance through simulation using a benchmark movie data ftm consist of a representation method for items features and user feedback using fuzzy sets and a content based algorithm based on various fuzzy set theoretic similarity measures the fuzzy set extensions of the jaccard index cosine proximity or correlation similarity measures and aggregation methods for computing recommendation confidence scores the maximum minimum or weighted sum fuzzy set theoretic aggregation methods compared to the baseline crisp set based method csm presented the empirical evaluation of the ftm using the movie data and simulation shows an improvement in precision without loss of recall moreover the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures

eigensolution of augmented graph products using shifted inverse iteration method two important matrices associated with graphs are adjacency and laplacian matrices in this paper efficient methods are presented for eigensolution of graph products augmented by other graphs for augmentations that do not destroy the symmetry of the graph products a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution for graphs composed of two non overlapping graph products joined through a small number of link members a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products owing to the availability of fast methods for eigensolution of graph products this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy

damped dynamic substructures the dynamic substructure method is extended to lightly or heavily damped systems both internal and external dampings are considered the damped dynamic flexibility associated with the slave co ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co ordinates is formed subsequently the convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices since the dynamic stiffness method is equivalent to the modal synthesis method the component mode method and kron s method the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices

improved fixed interface method for modal synthesis the paper takes a fresh look at the important topic of substructure synthesis an improved technique for synthesizing the modes obtained with fixed interface coordinates is proposed the reduction in the size of a substructure model is achieved through a higher order mode superposition approach for the first time an analytical rationale for the popular craig bampton hurty method is presented it is shown that the craigbampton hurty method is a special case of the proposed method the proposed approach can be used to improve the accuracy of the calculated eigenproperties by utilizing the higher order component modes but without calculating additional normal modes of the substructures numerical results are presented to demonstrate the effectiveness of the proposed method with the increasing order of the mode superposition approach used the approach is expected to be efficient if the degrees of freedom at the interface of the substructures are relatively small compared with the degrees of freedom of the substructures

a hierarchical non iterative extension of the guyan condensation method for damped structures abstract reduction methods are commonly employed for solving the eigenvalue problems of systems with a large number of degrees of freedom these methods are based upon dividing the system s degrees of freedom into masters and slaves and obtaining a reduced system which is in terms of the masters only since 1965 when the guyan condensation method for undamped structures was presented which neglects the dynamic effects of the slaves entirely there have been many efforts to overcome this by proposing various forms of dynamic condensation methods these methods take into account the dynamics of the slaves through an iterative procedure in this paper a hierarchical non iterative reduction method has been proposed for damped dynamic systems the method results in explicit forms of the effective stiffness viscosity and mass and also introduces higher order properties when third and higher order approximations are used furthermore a procedure for the automatic selection of master degrees of freedom has been proposed which assures the convergence and increases the efficiency of the method application of the method for obtaining low frequency eigenvalues of two example structures with and without damping reveals that results with good accuracy are obtained by using higher order approximations as they consider the dynamics of the slaves properly

dynamic condensation method for structural eigenvalue analysis an improved dynamic condensation approach is presented for accurate calculation of structural eigenproperties the approach is iterative the kept and reduced degrees of freedom in the approach are related through a condensation matrix that is used to form a condensed eigenvalue problem an initial condensation matrix can be defined in terms of the system submatrices the eigenproperties calculated in an iterative step are utilized to update the condensation matrix matrix inversions or gaussian eliminations are avoided in the updating process by employing the orthogonality of the eigenvectors the process of updating the condensation matrix and the eigenvalue problem is repeated until a desired convergence in the eigenvalues is achieved usually a few iterations are quite adequate iterations for both the lower as well as the higher modes can be performed as the condensation matrices for the two sets of modes are very simply related numerical examples are presented to show the applicability of the proposed approach several methods that have been used in practice to select the kept degrees of freedom for condensing are also evaluated numerically with respect to their effectiveness in providing accurate estimates of the eigenproperties with a minimum number of iterations

probabilities from fuzzy observations abstract we introduce a new definition for getting the probability of a fuzzy event from a collection of fuzzy observations this definition is based upon the use of the compatibility of the target event with the observation we show that this new definition satisfies the komolgoroff conditions we show how it naturally extends all the properties of the classical probability theory

design of a hybrid fuzzy logic proportional plus conventional integral derivative controller presents approaches to the design of a hybrid fuzzy logic proportional plus conventional integral derivative fuzzy p id controller in an incremental form this controller is constructed by using an incremental fuzzy logic controller in place of the proportional term in a conventional pid controller by using the bounded input bounded output small gain theorem the sufficient condition for stability of this controller is derived based on the condition we modify the ziegler and nichols approach to design the fuzzy p id controller in this case the stability of a system remains unchanged after the pid controller is replaced by the fuzzy p id controller without modifying the original controller parameters when a plant can be described by any modeling method the fuzzy p id controller can be determined by an optimization technique finally this controller is used to control a nonlinear system numerical simulation results demonstrate the effectiveness of the fuzzy p id controller in comparison with the conventional pid controller especially when the controlled object operates under uncertainty or in the presence of a disturbance

a receptance formula for general second degree square lambda matrices abstract a computational algorithm utilizing the free vibration modes of a structure is presented for calculating receptances the usual eigen system computed for large structural models is incomplete hence the receptances are approximate the formulas developed here increased receptance accuracy compared to classical spectral representations receptances are used extensively in eigensolution reanalysis design and synthesis and also for forced harmonic response studies in these areas receptance approaches offer a popular alternative to rayleigh ritz subspace type methods structural models represented by non symmetric mass damping and stiffness matrices which occur frequently in rotating structures may be treated using the receptance formulas presented the receptance matrix derived is applicable to general 2nd degree square lambda matrices this generalizes the receptance matrix commonly associated with matrix pencils author

gibbs phenomenon in structural mechanics the concepts of complementary boundary condition and interior condition are discussed guidelines are developed to eliminate the gibbs effect when selecting trial functions for the series expansion

independent component analysis to enhance performances of karhunen loeve expansions for non gaussian stochastic processes application to uncertain systems abstract in the context of engineering systems an essential step in uncertainty quantification is the development of accurate and efficient representation of the random input parameters for such input parameters modeled as stochastic processes karhunen loeve expansion is a classical approach providing efficient representations using a set of uncorrelated but generally statistically dependent random variables the dependence structure among these random variables may be difficult to estimate statistically and is thus ignored in many practical applications this simplifying assumption of independence may lead to considerable errors in estimating the variability in the system state thus limiting the effectiveness of karhunen loeve expansion in certain cases in this paper independent component analysis is exploited to linearly transform the random variables used in karhunen loeve expansion resulting into a set of random variables exhibiting higher order decorrelation the stochastic wave equation is investigated for numerical illustration whereby the random stiffness coefficient is modeled as a non gaussian stochastic process under the assumption of independence among the random variables used in the karhunen loeve expansion and independent component analysis representations the latter provides more accurate statistical characterization of the output process for the specific cases examined

compatibility relations for the representation of associations between variables in knowledge based systems and their use in approximate reasoning abstract compatibility relations are proposed as formal representations of the production if then rules capturing associations between a primary a and a secondary b variable the most general form of the if then rule considered is if a takes on its value in a set then b takes on its value in a set or in different possible sets each with its associated degree of belief conviction moreover with each rule is associated a degree of belief as to its validity we consider an approximate reasoning scheme stated as we know a possibility distribution representing the value of a premise and an association between a and b represented by an if then rule and we seek the induced possibility distribution representing the value of b consequence the approach to approximate reasoning proposed is based on possibility theory and possibility measures induced by multivalued mappings

an accurate error estimator for guyan reduction the objective of this study is to develop an error estimator that accurately predicts relative eigenvalue errors in finite element models reduced by guyan reduction we present a derivation procedure for the error estimator in which kidder s transformation matrix for guyan reduction is employed we demonstrate the excellent performance of the proposed error estimator through various numerical examples rectangular plate cylindrical panel hyperboloid panel and shaft shaft interaction problems c

application of hybrid fuzzy logic proportional plus conventional integral derivative controller to combustion control of stoker fired boilers abstract combustion control of an industrial stoker fired boiler is to provide a continuous supply of steam at the desired condition of pressure because no efficient mathematical model of the stoker fired boiler is available it would be very hard to design its controller by using any traditional model based method therefore the most widely used controller for the boiler system is a conventional pid type controller due to its simple control structure and ease of design however control performance of the pid type controller suffers greatly from high uncertainty and nonlinearity of the system large disturbances and so on this paper presents a hybrid fuzzy logic proportional plus conventional integral derivative fuzzy p id controller to improve the control performance yielded by the pid type controller the proposed fuzzy p id controller is constructed by using an incremental fuzzy logic controller in place of the proportional term in the conventional pid controller the basic idea of this study is to reduce the parameters of a fuzzy controller to be tuned so that in comparison with the pid type controller only one additional parameter should be adjusted the proposed hybrid fuzzy p id controller is applied to several stoker fired boilers in order to demonstrate the effectiveness of the hybrid controller the real application results on control of the stoker fired boilers are reported and analyzed

uncertainty in structural dynamics experimental validation of a wishart random matrix model in the modeling of complex dynamical systems high resolution finite element models are routinely adopted to reduce the discretization error such an approach may fail to enhance the confidence in simulation based predictions when the dynamical systems exhibit significant variability in the parameterization and description of the mathematical model due to parametric data uncertainty and model uncertainty in contrast to parametric uncertainty model uncertainty poses significant challenges as no explicit parameter is available a priori to characterize its behavior in the current investigation a set of sprung mass oscillators randomly attached to a baseline system namely a homogeneous cantilever plate gives rise to model uncertainty contrary to model parametric uncertainty traditionally tackled using stochastic finite element method sfem the model uncertainty arising from randomly attached sprung masses gives rise to a new variant of dynamical system for every sample the feasibility of adopting a wishart random matrix to represent such ensemble of dynamical systems derived from model perturbation is investigated in this paper the experiments conducted on a vibrating plate with randomly attached sprung mass oscillators demonstrate that the wishart random matrix model may provide a reasonable representation of model uncertainty in linear dynamical systems in the medium and high frequency region

how many modes are acceptable and how do people improve the modes abstract in this paper an effective judgement and improvement regarding the truncation errors of the modal synthesis method are put forward the truncation errors estimated are considered as error forces and their reasonable bound is defined to determine the number of acceptable modes the initial eigenvalues and eigenvectors can be calculated from the modal synthesis method the renewed eigenvalues are obtained from rayleigh quotient and the renewed eigenvectors are obtained from an equation which is essentially the expression for error forces then the renewed eigenvectors are put into rayleigh quotient again as an iterative process until the permitted error forces or definite errors of eigenvalues are reached as a result the proposed approach is called an error force vector method obviously the process is also an accuracy improvement for eigenpair updating

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

new improved series expansion for solving the moving oscillator problem a new method able to evaluate the dynamic stress response of an elastic beam subject to moving oscillators is presented the proposed procedure improves the convergence and accuracy of the conventional eigenfunction series expansion of beam response taking into account the gravitational inertial and damping effects due to the moving oscillators the improvement of the conventional solution is obtained by means of an extension to continuous systems of the dynamic correction method originally proposed for discretized structures the proposed method is able to account for the truncated higher order eigenfunctions by adding a pseudo static term to the conventional series expansion numerical results are presented to demonstrate the capability of the method to accurately determine the discontinuity and jump in bending moment and shear force distributions respectively

domain decomposition methods for eigenvalue problems abstract this paper proposes several domain decomposition methods to compute the smallest eigenvalue of linear self adjoint partial differential operators let us be given a partial differential operator on a domain which consists of two nonoverlapping subdomains suppose a fast eigenvalue solver is available for each of these subdomains but not for the union of them the first proposed method is a scheme which determines an appropriate boundary condition at the interface separating the two regions this boundary condition can be derived from the zero of a nonlinear operator which plays the same role for the eigenvalue problem as the steklov poincare operator for the linear equation an iterative method can be used to solve this nonlinear equation yielding the exact boundary condition at the interface this enables the determination of the eigenpair on the whole domain the same concept can be applied to a schwarz alternating method for the eigenvalue problem in case the subdomains overlap a nonoverlapping scheme in the spirit of schur complement will also be discussed these ideas are also applicable to a domain imbedding algorithm

mid frequency structural dynamics with parameter uncertainty abstract in this paper a number of frequency domain dynamic analysis procedures of randomly disordered structural systems in the medium frequency range are integrated into the stochastic finite element method in all cases frequency domain model reduction strategies are used to minimize the computational effort in the mid frequency range firstly an energy operator approach eoa is investigated in this procedure an energy operator adapted to a fixed medium frequency band is defined whose dominant eigensubspace is used to construct a reduced model using a ritz galerkin method secondly the proper orthogonal decomposition method is used to extract the spatial dominant coherent structures in the vibration wave field in the mid frequency band the coherent structures are the eigenvectors corresponding to the dominant eigenvalues of the spatial autocorrelation function of the system response consequently a close relationship between the energy operator approach and the proper orthogonal decomposition method is identified although these two approaches are not mathematically identical the proper orthogonal decomposition method appears to be more straightforward compared to the energy operator method from the viewpoint of numerical implementation thirdly another approach namely the dynamic element method based on frequency dependent finite element shape functions is considered a stochastic reduction method is then utilized to represent the uncertain parameters modelled as stochastic processes in terms of their dominant scales of fluctuation the karhunen loeve and the polynomial chaos decompositions are used to that effect in the context of a stochastic finite element formalism the methodology adopted in the paper thus integrates efficient dynamical reduction techniques with a reduction scheme of stochastic processes for the mid frequency vibration of linear random systems the formulation is exemplified by its application to the analysis of the dynamics of a coupled uncertain rod assembly subjected to an external excitation the example is also used to highlight some of the relative features of the three dynamic reduction strategies

fuzzy control theory a nonlinear case abstract sources of nonlinearity in a fuzzy controller include the fuzzification algorithm used for the controller inputs fuzzy control rules type of fuzzy logic used for evaluating the fuzzy control rules and the defuzzification algorithm used for the controller output we analyze the performance of a simple fuzzy controller with linear and nonlinear defuzzification algorithms we prove theoretically that such a fuzzy controller the smallest possible with two inputs error and rate change of error and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional integral pi controller with proportional gain and integral gain changing with error and rate change of error about a setpoint furthermore this fuzzy controller is precisely equivalent to a conventional linear pi controller if a linear defuzzification algorithm is employed computer simulation showed that the performance of the fuzzy controller was almost the same as that of the pi controller when first order and second order linear processes were used furthermore the fuzzy controller was significantly better when a first order with a time delay model was used more importantly the simulated result illustrated that the fuzzy controller was stable when a nonlinear process model was controlled but the pi controller was unstable

component mode iteration for frequency calculations this paper presents component mode iteration a new method for carrying out a form of subspace iteration on the substructure level for structures composed of substructures in component mode iteration substructure displacement is in terms of component modes with the interface displacements as coefficients component modes are chosen such that exact compatibility is assured throughout the structure the reduced structure eigenvalue problem is assembled and solved for lower mode approximations the resulting estimates of lower mode interface motion are used to refine the component modes by approximating the dynamic response of substructures to interface motion with a vector iteration process for this step the substructures are independent and can be processed in parallel reassembly and solution of the reduced structure problem yields improved lower mode estimates further iterations of refinement and reassembly are performed until convergence takes place the initial component modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent yielding very accurate results after only one iteration indeed convergence is shown to be significantly faster than in the standard subspace iteration method

space time approach to numerical analysis of a string with a moving mass inertial loading of strings beams and plates by mass travelling with near critical velocity has been a long debate typically a moving mass is replaced by an equivalent force or an oscillator with rigid spring that is in permanent contact with the structure such an approach leads to iterative solutions or imposition of artificial constraints in both cases rigid constraints result in serious computational problems a direct mass matrix modification method frequently implemented in the finite element approach gave reasonable results only in the range of relatively low velocities in this paper we present the space time approach to the problem the interaction of the moving mass supporting structure is described in a local coordinate system of the space time finite element domain the resulting characteristic matrices include inertia coriolis and centrifugal forces a simple modification of matrices in the discrete equations of motion allows us to gain accurate analysis of a wide range of velocities up to the velocity of the wave speed numerical examples prove the simplicity and efficiency of the method the presented approach can be easily implemented in the classic finite element algorithms copyright 2008 john wiley sons ltd

generalized probabilities of fuzzy events from fuzzy belief structures abstract we extend shafer s theory of evidence to include the ability to have belief structures involving fuzzy sets we then obtain under the condition of bayesian belief structure a whole family of possible definitions for the probability of fuzzy sets we also suggest a procedure for including belief qualification in pruf

semi active control of 1d continuum vibrations under a travelling load abstract the paper presents a method for computing the response of a 1d elastic continuum supported by a set of semi active viscous dampers and induced by a load travelling over it the magnitude of the moving force has been assumed to be constant by neglect of the inertia forces full analytical solution is based on the power series method and is given in an arbitrary time interval the time marching scheme allows us to continue a solution in successive layers with initial conditions taken from the end of previous stages the semi active open loop control strategy is proposed shapes of damping functions are defined as a form of piecewise constant function the control strategy is suboptimal and it outperforms the passive case numerical results are presented for the cases of a string and a bernoulli euler beam

a correction method for the analysis of continuous linear one dimensional systems under moving loads a new correction procedure for dynamic analysis of linear proportionally damped continuous systems under traveling concentrated loads is proposed both cases of non parametric moving forces and parametric moving mass loads are considered improvement in the evaluation of the dynamic response is obtained by separating the contribution of the low frequency lf modes from that of the high frequency hf modes the former is calculated as usual by classical modal analysis while the latter is taken into account using a new series expansion of the corresponding particular solution the advantage of the suggested method is immediately shown in the calculation of the stress distribution since it is able to capture the stress discontinuities due to the nature of the applied loads themselves numerical results are presented to discuss the convergence of the proposed series and to show the accuracy of the calculated response compared to the classical series expansion solution

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

a multivariable self tuning pid controller abstract a multivariable self tuning controller with a proportional plus integral plus derivative pid structure is derived the algorithm features a combination of the self tuning property in which the controller parameters are tuned automatically on line and also the structure of a multivariable pid controller making it more favourable to be used in industry a stability proof of the algorithm is also presented here comparison of the performance of the algorithm with a fixed tuned multivariable pid controller in the simulation examples demonstrates the effectiveness of the proposed algorithm

reduced models in the medium frequency range for general external structural acoustic systems this paper presents a theoretical approach for constructing a reduced model in the medium frequency range in the area of structural acoustics for a general three dimensional dissipative structure made of an anisotropic inhomogeneous viscoelastic bounded medium coupled with an external acoustic fluid all the results presented can be used if the structure is made of beams plates and shells the boundary value problem in the frequency domain and its variational formulation are presented for a fixed medium frequency band an energy operator related to the structural acoustic system is introduced this operator is symmetric positive definite and has a countable set of positive eigenvalues its dominant eigensubspace allows a reduced model to be constructed using the ritz galerkin method a finite dimension approximation of the three dimensional continuous case is presented and an effective construction of the dominant subspace using the subspace iteration method is developed as an example the reduced model is used for constructing the time stationary random response of the structural acoustic system submitted to a random wall pressure field finally the theory is validated for a finite length circular cylindrical shell coupled with several dashpots and springs and immersed in a gas air and in a liquid water

elicitation assessment and pooling of expert judgments using possibility theory the problem of modeling expert knowledge about numerical parameters in the field of reliability is reconsidered in the framework of possibility theory usually expert opinions about quantities such as failure rates are modeled assessed and pooled in the setting of probability theory this approach does not seem to always be natural since probabilistic information looks too rich to be currently supplied by individuals indeed information supplied by individuals is often incomplete imprecise rather than tainted with randomness moreover the probabilistic framework looks somewhat restrictive to express the variety of possible pooling modes in this paper the authors formulate a model of expert opinion by means of possibility distributions that are thought to better reflect the imprecision pervading expert judgments they are weak substitutes to unreachable subjective probabilities assessment evaluation is carried out in terms of calibration and level of precision respectively measured by membership grades and fuzzy cardinality indexes finally drawing from previous works on data fusion using possibility theory the authors present various pooling modes with their formal model under various assumptions concerning the experts a comparative experiment between two computerized systems for expert opinion analysis has been carried out and its results are presented in this paper

revisiting the moving force problem abstract the problem of the vibration of a beam subject to a travelling force is considered the purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force it is shown that for given boundary conditions there exists a unique response velocity dependence function a technique to determine this function is suggested which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode to illustrate this the maximum response function is calculated analytically for a simply supported ss beam and constructed numerically for a clamped clamped beam the effect of the higher modes on the maximum response is investigated and the relative error of the one mode approximation for a ss beam is constructed the estimates obtained substantiate the assumption about adequacy of the one mode approximation in a wide range of velocities in particular the relative error in the neighborhood of the velocity that results in the largest response is less than one percent

kron s method for symmetric eigenvalue problems kron s method has been used successfully by engineers for over 30 years to find eigenvalues of large symmetric matrices these matrices arise from domain decomposition of nonoverlapping domains of self adjoint partial differential operators this paper discusses some theoretical aspects of kron s method specifically the poles and zeroes of eigenvalues of the kron matrix and their relationships with the eigenvalues of the original matrix are given

a substructure approach for the midfrequency vibration of stochastic systems a novel substructure coupling technique based on the proper orthogonal decomposition method is presented for the midfrequency range vibration of linear dynamical systems with parameter uncertainty for a given frequency band the methodology permits the derivation of an adaptive basis for each subsystem and the construction of a reduced order model of the global structure the formulation is directed toward the efficient probabilistic characterization of model based predictions in the framework of a stochastic finite element method the efficiency of the substructure method has been contrasted both from the viewpoint of adopting free free and fixed fixed substructure proper orthogonal modes in order to arrive at a reduced subsystem model the distinction as well as similarity of the present methodology with the component mode synthesis is also pointed out the proper orthogonal modes are obtained from both frequency and time domain approaches and their suitability is discussed in relation to the behavior of a specific system the substructure approach elegantly integrates with a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes

aggregating evidence using quantified statements abstract starting with a collection of experts opinions as to the value of some unknown variable in the form of fuzzy subsets we are concerned with the problem of aggregating the opinions with regard to what values for the unknown variable are possible certain or probable we first show that linguistically quantified propositions provide a framework in which to aggregate the opinions we provide two methodologies for implementing the aggregation in terms of quantified statements the first method involves a consensory aggregation and is based upon an algebraic interpretation of a quantified statement the second involves a competitive type aggregation and is based upon substitution interpretation of a quantified statement we also provide for the ability to include differing importances to the experts as well as differing degrees of confidence in an opinion

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

dynamic condensation with synthesis of substructure eigenproperties abstract for structures divided into substructures which are defined by their eigenproperties a combination of the node synthesis and condensation techniques is presented to obtain a first few important eigenproperties of the combined system accurately the accuracy of the calculated modal properties can be increased by iteratively solving an improved and condensed eigenvalue problem if desired the higher modal properties can also be obtained by solving a complementry eigenvalue problem associated with the higher modes the availability of the substructure modes in this approach also provides a very convenient and efficient means of selecting the most appropriate kept degrees of freedom in the condensed eigenvalue problem to expediate the convergence to the correct eigenproperties the methods for coupling of the substructure eigenproperties obtained with different boundary conditions at the interface are described several examples are presented to demonstrate the application of the approach

fuzzy self tuning of pid controllers abstract this paper presents a novel fuzzy self tuning pid control scheme for regulating industrial processes the essential idea of the scheme is to parameterize a ziegler nichols like tuning formula by a single parameter then to use an on line fuzzy inference mechanism to self tune the parameter the fuzzy tuning mechanism with process output error and error rate as its inputs adjusts in such a way that it speeds up the convergence of the process output to a set point y r and slows down the divergence trend of the output from y r a comparative simulation study on various processes including a second order process processes with long dead time and non minimum phase processes shows that the performance of the new scheme improves considerably in terms of set point and load disturbance responses over the pid controllers well tuned using both the classical ziegler nichols formula and the more recent refined ziegler nichols formula

on three modal synthesis variants abstract a unified formulation of fixed free and loaded interface variants of modal synthesis is presented a formal proof of the exactness of all three variants in the absence of modal truncation is established the sensitivity of the truncation error to the different interface conditions is studied

a critical assessment of truth functional modification and its use in approximate reasoning abstract we examine the inconsistencies in the current notion of fuzzy truth values and show how these have arisen from an attempt to equate two separate concepts we argue that any approximate reasoning system based on truth functional modification is redundnat and inefficient

another look at admissible functions abstract problems associated with using global admissible functions in boundary value problems are discussed it is shown that if care is not taken it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge the concept of complementary boundary conditions is introduced and their existence is established complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries it is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions a revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration

absolute versus relative formulations of the moving oscillator problem in the general framework of the bridge vehicle dynamic interaction the so called moving oscillator problem is revisited in order to provide a deeper insight into some analytical and physical aspects not specifically analyzed in previous investigations without lack of generality the case of a stream of moving oscillators crossing a simply supported beam with arbitrary time law is considered the formulations in terms of both absolute and relative displacements of the moving oscillators are critically reviewed and compared and alternative sets of differential equations with time dependent coefficients are derived the study enlightens both theoretically and numerically that impulsive contributions to the dynamic response appear in the relative displacement formulation at the time instants in which each vehicle enters or exits the bridge it is demonstrated that such contributions somehow hidden in the absolute displacement formulation may have a significant influence on the vibration of the moving oscillators and thus cannot be a priori neglected in the analysis it is also shown that the analytical and computational difficulties associated with these additional impulses make preferable the use of the absolute displacement formulation far from being restricted to the case of simply supported beams these findings are valid for any type of bridge structure which induces a discontinuity in the slope of the road profile experienced by the vehicles

substructure synthesis method for frequency response of viscoelastic structures the method of substructure synthesis previously applicable to undamped and viscously damped systems has been extended to systems with viscoelastic damping in hereditary integral form differential operator form and steady state corm based on a variational principle for symmetric systems the corresponding substructure synthesis method is formulated in the frequency domain each substructure is represented by a set of admissible trial vectors in the rayleigh ritz method eigenvectors of the corresponding undamped substructure and ritz vectors obtained by spatial discretization of admissible functions are recommended as trial vectors the traditional state space formulation is avoided by the proposed substructure synthesis method so that the approach is independent of the form of viscoelastic models the effectiveness of the proposed method in terms of reducing the size of final equations is illustrated through numerical examples

analytical structures for fuzzy pid controllers in this paper analytical structures for fuzzy proportional integral derivative pid controllers are derived by using triangular membership functions for inputs singletons or triangular membership functions for output minimum triangular norm maximum or drastic sum triangular conorm mamdani minimum drastic or larsen product inference nonlinear control rules and center of sum defuzzification it is shown that these analytical structures are not suitable for control purpose in this context it is extremely important to note that the analytical structures reported by carvajal et al are also not valid for control

self learning fuzzy controllers based on temporal backpropagation a generalized control strategy that enhances fuzzy controllers with self learning capability for achieving prescribed control objectives in a near optimal manner is presented this methodology termed temporal backpropagation is model sensitive in the sense that it can deal with plants that can be represented in a piecewise differentiable format such as difference equations neural networks gmdh structures and fuzzy models regardless of the numbers of inputs and outputs of the plants under consideration the proposed approach can either refine the fuzzy if then rules of human experts or automatically derive the fuzzy if then rules if human experts are not available the inverted pendulum system is employed as a testbed to demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired fuzzy controller

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation