theoretical study of moving force identification on continuous bridges a method to identify moving forces on a continuous bridge has been developed in this paper the bridge is modelled as a bernoulli euler beam and the boundary value problem of the beam is solved to get the exact mode shape functions of the vibrating beam with intermediate supports as the number of spans of the bridge increases the identification accuracy decreases and at the same time more execution time is needed to finish one case study to minimize this problem a method has been developed to identify moving forces on a selected span of interest from the continuous bridge the singular value decomposition svd of the coefficient matrix of the overdetermined equation is used in the solution to evaluate the method simulations of two moving forces on a continuous bridge and on one selected span from the continuous bridge are studied white noise is added to the simulated bending moment and acceleration responses to study the effect of noise in moving forces identification problem for different numbers and arrangements of sensors the results obtained from the simulation study show that the method is effective in identifying moving forces and acceptable results can be obtained

pollutant transport by shallow water equations on unstructured meshes hyperbolization of the model and numerical solution via a novel flux splitting scheme abstract the purpose of this paper is twofold first using the cattaneo s relaxation approach we reformulate the system of governing equations for the pollutant transport by shallow water flows over non flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms the proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection diffusion models this turns out to give a larger stability range for the choice of the time step second following a flux splitting approach we derive a novel numerical method to discretise the resulting problem in particular we propose a new flux splitting and study the associated two systems of differential equations called the hydrodynamic and the relaxed diffusive system respectively for the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the godunov type these schemes are simple to implement robust accurate and fast when compared with existing methods the resulting method is implemented on unstructured meshes and is systematically assessed for accuracy robustness and efficiency on a carefully selected suite of test problems including non flat topography and wetting and drying problems formal second order accuracy is assessed through convergence rates studies

realization of stable models with subspace methods abstract subspace methods for system identification estimate the dynamics of state space models either by using the shiftinvariance property of an estimated observability or controllability matrix or by estimating a state sequence and then solving a least squares problem to obtain the system matrices in either case it is possible for the estimated system to be unstable we present algorithms to find stable approximants to a least squares problem which can then be applied to subspace methods to ensure stability either asymptotic or marginal stability can be ensured in the latter case a pole or a pair of poles being forced to lie on the unit circle in addition some results on a sufficient condition for stability for least squares solutions obtained by the shift invariance approach are derived

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

reformulations for general advection diffusion reaction equations and locally implicit ader schemes following cattaneo s original idea in this article we first present two relaxation formulations for time dependent non linear systems of advection diffusion reaction equations such formulations yield time dependent non linear hyperbolic balance laws with stiff source terms then we present a locally implicit version of the ader method to solve these stiff systems to high accuracy the new ingredient of the numerical methodology is a locally implicit solution of the generalised riemann problem we illustrate the formulations and the resulting numerical approach by solving the compressible navier stokes equations

brief paper enforcing stability constraints in set membership identification of linear dynamic systems in this paper we consider the identification of linear systems a priori known to be stable from input output data corrupted by bounded noise by taking explicitly into account a priori information on system stability a formal definition of the feasible parameter set for a stable linear system is provided on the basis of a detailed analysis of the geometrical structure of the feasible set convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameter uncertainty intervals properties of the computed relaxed bounds are discussed a simulated example is presented to show the effectiveness of the proposed technique

subspace identification with eigenvalue constraints standard subspace methods for the identification of discrete time linear time invariant systems are transformed into generalized convex optimization problems in which the poles of the system estimate are constrained to lie within user defined convex regions of the complex plane the transformation is done by restating subspace methods such as the minimization of a frobenius norm affine in the estimate parameters allowing the minimization to be augmented with convex constraints the constraints are created using linear matrix inequality regions which generalize standard lyapunov stability to arbitrary convex regions of the complex plane the algorithm is developed for subspace methods based on estimates of the extended observability matrix and methods based on estimates of state sequences but it is extendable to all subspace methods simulation examples demonstrate the utility of the proposed method

natural frequency changes of a cracked timoshenko beam by modified fourier series a new method is presented in this paper for computing the natural frequencies of a timoshenko beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is developed particularly for a timoshenko beam having an arbitrary number of transverse open cracks unlike the conventional fourier series the modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked timoshenko beam in the usual way and thus reduces the problem to a simple one by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form that renders the task of computer coding quite straightforward

a global mathematical model for the simulation of stenoses and bypass placement in the human arterial system this paper is concerned with a global mathematical model for the human circulation we describe its construction its validation and its application to study the haemodynamical effect of stenoses and bypass placement in the arterial system a geometric multiscale approach is adopted combining one dimensional 1d descriptions to represent 55 major arteries and zero dimensional 0d compartmental descriptions for the heart lungs the venous system and the microcirculation modern non linear numerical methods are implemented for solving the 1d systems of hyperbolic partial differential equations and high order rungekutta methods are used to solve the systems of ordinary differential equations resulting from the compartmental models the complete global mathematical model is then validated for healthy and stenotic cases comparing numerical predictions from the model against in vivo measurements results show overall satisfactory agreement in addition a sensitivity analysis is conducted in order to assess the influence of the most important parameters on some haemodynamical quantities of interest we then apply the model to simulate the haemodynamics for healthy controls and subjects with arterial stenosis we study the haemodynamical effect of bypass placement considering different locations in the arterial system different degrees of severity for both single and multiple arterial stenoses haemodynamical quantities of interest in the study are local pressure and flow rate we observe that large stenotic plaques near the heart cause abnormally strong pressure waves in the circulatory system and two adjacent occlusions worsen the phenomenon we find that the mathematical model is capable of predicting the most convenient bypass location and graft dimensions consistent with normal haemodynamics

nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load this paper focuses on the geometrically nonlinear dynamic analysis of an eccentrically prestressed simply supported damped beam subjected to a concentrated moving harmonic load the nonlinear dynamic deflections of the beam are obtained by polynomial functions the kelvin voigt model for the material of the beam is used two coupled nonlinear systems of equations of motion are derived using lagrange s equations under the assumptions of the euler bernoulli beam theory with the von karman s nonlinear strain displacement relationships the rotary inertia axial displacement and axial inertia are included in the formulation the nonlinear equations of motion are solved by using the implicit time integration method of newmark in conjunction with the newton raphson iteration method in this study the effects of large deflections the internal damping of the beam the velocity of the moving harmonic load the prestress load the eccentricity of the prestress load and the excitation frequency on the dynamic response of the beam are discussed the obtained results are compared with the results based on the linear beam theory convergence studies are performed numerical results show that the above mentioned effects play a very important role in the deflections of the beam

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

vibration of multi span non uniform beams under moving loads by using modified beam vibration functions based on hamilton s principle the vibration of a multi span non uniform beam subjected to a moving load is analysed by using modified beam vibration functions as the assumed modes the modified beam vibration functions satisfy the zero deflection conditions at all the intermediate point supports as well as the boundary conditions at the two ends of the beam numerical results are presented for both uniform and non uniform beams under moving loads of various velocities examples show that this method converges very quickly and good results are obtained

implicit semi analytical solution of the generalized riemann problem for stiff hyperbolic balance laws we present a semi analytical implicit solution to the generalized riemann problem grp for non linear systems of hyperbolic balance laws with stiff source terms the solution method is based on an implicit time taylor series expansion and the cauchy kowalewskaya procedure along with the solution of a sequence of classical riemann problems our new grp solver is then used to construct locally implicit ader methods of arbitrary accuracy in space and time for solving the general initial boundary value problem for non linear systems of hyperbolic balance laws with stiff source terms analysis of the method for model problems is carried out and empirical convergence rate studies for suitable tests problems are performed confirming the theoretically expected high order of accuracy

subspace model identification part 2 analysis of the elementary output error state space model identification algorithm the elementary moesp algorithm presented in the first part of this series of papers is analysed in this paper this is done in three different ways first we study the asymptotic properties of the estimated state space model when only considering zero mean white noise perturbations on the output sequence it is shown that in this case the moespl implementation yields asymptotically unbiased estimates an important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the hankel matrices constructed from the input and output data at the beginning of the computations depends on the number of non zero markov parameters this analysis however leads to a second implementation of the elementary moesp scheme namely moesp2 the latter implementation has the same asymptotic properties without the finite impulse response constraint secondly we compare the moesp2 algorithm with a classical state space model identification scheme the latter

low dissipation centred schemes for hyperbolic equations in conservative and non conservative form abstract we propose a one parameter family of low dissipation centred numerical schemes for solving hyperbolic equations in conservative or non conservative form using finite volume or discontinuous galerkin finite element methods the new schemes spring out from the multi dimensional force method and are determined by a single parameter 1 given an increasing sequence of real numbers 1 1 2 k there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of courant numbers 1 c 1 c 2 c k 0 and a decreasing sequence of corresponding numerical viscosity functions d 1 d 2 d k for a given courant number c k 1 there is a real number k 0 and a corresponding stable scheme with minimal numerical viscosity d k the proposed schemes suit very well the family of high order discontinuous galerkin finite element methods and the recently proposed class of ader tr schemes whose orders of accuracy define decreasing sequences of courant numbers as the order of accuracy increases the centred methods of this paper are stable in 2d and 3d in the frame of simultaneous updating formulae unlike other centred methods such as 1d force which are not furthermore the schemes are highly accurate for slowly moving waves which is precisely the kind of waves that traditional centred methods smear disastrously additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non conservative form here the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system for the euler equations in one and two space dimensions and for the baer nunziato equations for compressible two phase flow

kernels for linear time invariant system identification in this paper we study the problem of identifying the impulse response of a linear time invariant lti dynamical system from the knowledge of the input signal and a finite set of noisy output observations we adopt an approach based on regularization in a reproducing kernel hilbert space rkhs that takes into account both continuous and discrete time systems the focus of the paper is on designing spaces that are well suited for temporal impulse response modeling to this end we construct and characterize general families of kernels that incorporate system properties such as stability relative degree absence of oscillatory behavior smoothness or delay in addition we discuss the possibility of automatically searching over these classes by means of kernel learning techniques so as to capture different modes of the system to be identified

orthogonality condition for a multi span beam and its application to transient vibration of a two span beam abstract this paper treats the orthogonality condition for a multi span beam and its application to forced transient vibration of a two span beam the beam is modeled as a bernoulli euler beam the boundary conditions for the particular case of two span beam are clamped pinned pinned an exact closed form solution is obtained for this problem even though there has been an enormous amount of work on beam vibration most of the studies are conducted on a single span beam there are some studies on the multi span beam vibration however their treatment is rather specialized in terms of the applied loading and the initial conditions none of the studies in the past treats an exact solution for a forced transient vibration of a general two span beam with arbitrary initial conditions and arbitrary forcing functions therefore the solution obtained in this paper is new the key development in the solution is the orthogonality condition for a multi span beam the method of solution developed in this paper establishes a general methodology for the forced transient vibration of a multi span beam the closed form solution obtained in this paper can be used as a benchmark solution for the transient vibration of a two span beam

identification of positive real models in subspace identification by using regularization in time domain subspace methods for identifying linear time invariant dynamical systems the model matrices are typically estimated from least squares based on estimated kalman filter state sequences and the observed outputs and or inputs it is well known that for an infinite amount of data this least squares estimate of the system matrices is unbiased when the system order is correctly estimated however for a finite amount of data the obtained model may not be positive real in which case the algorithm is not able to identify a valid stochastic model in this note positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm the regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix

a unifying theorem for three subspace system identification algorithms the aim of this paper is to indicate and explore the similarities between three different subspace algorithms for the identification of combined deterministic stochastic systems the similarities between these algorithms have been obscured due to different notations and backgrounds it is shown that all three algorithms are special cases of one unifying theorem the comparison also reveals that the three algorithms use exactly the same subspace to determine the order and the extended observability matrix but that the weighting matrix used to calculate a basis for the column space of the observability matrix is different in the three cases

vibration and stability of cracked hollow sectional beams this paper presents simple tools for the vibration and stability analysis of cracked hollow sectional beams it comprises two parts in the first the influences of sectional cracks are expressed in terms of flexibility induced each crack is assigned with a local flexibility coefficient which is derived by virtue of theories of fracture mechanics the flexibility coefficient is a function of the depth of a crack the general formulae are derived and expressed in integral form it is then transformed to explicit form through 128 point gauss quadrature according to the depth of the crack the formulae are derived under two scenarios the first is for shallow cracks of which the penetration depth is contained within the top solid sectional region the second is for deeper penetration in which the crack goes into the middle hollow sectional region the explicit formulae are best fitted equations generated by the least squares method the best fitted curves are presented from the curves the flexibility coefficients can be read out easily while the explicit expressions facilitate easy implementation in computer analysis in the second part the flexibility coefficients are employed in the vibration and stability analysis of hollow sectional beams the cracked beam is treated as an assembly of sub segments linked up by rotational springs division of segments are made coincident with the location of cracks or any abrupt change of sectional property the crack s flexibility coefficient then serves as that of the rotational spring application of the hamilton s principle leads to the governing equations which are subsequently solved through employment of a simple technique it is a kind of modified fourier series which is able to represent any order of continuity of the vibration buckling modes illustrative numerical examples are included

brief paper constrained state space system identification with application to structural dynamics constrained identification of state space models representing structural dynamic systems is addressed based on physical insight transfer function constraints are formulated in terms of the state space parametrization a simple example shows that a method tailored for this application which utilizes the non uniqueness of a state space model outperforms the classic sequential quadratic programming method in terms of robustness and convergence properties the method is also successfully applied to real experimental data of a plane frame structure

on consistency of subspace methods for system identification subspace methods for identification of linear time invariant dynamical systems typically consist of two main steps first a so called subspace estimate is constructed this first step usually consists of estimating the range space of the extended observability matrix secondly an estimate of system parametersis obtained based on the subspace estimate in this paper the consistency of a large class of methods for estimating the extended observability matrix is analyzed persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise for systems with process noise it is shown that a persistence of excitation condition on the input is not sufficient more precisely an example for which the subspace methods fail to give a consistent estimate of the transfer function is given this failure occurs even if the input is persistently exciting of any order it is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed

junction generalized riemann problem for stiff hyperbolic balance laws in networks in this paper we design a new implicit solver for the junction generalized riemann problem j grp which is based on a recently proposed implicit method for solving the generalized riemann problem grp for systems of hyperbolic balance laws we use the new j grp solver to construct an ader scheme that is globally explicit locally implicit and with no theoretical accuracy barrier in both space and time the resulting ader scheme is able to deal with stiff source terms and can be applied to non linear systems of hyperbolic balance laws in domains consisting on networks of one dimensional sub domains in this paper we specifically apply the numerical techniques to networks of blood vessels we report on a test problem with exact solution for a simplified network of three vessels meeting at a single junction which is then used to carry out a systematic convergence rate study of the proposed high order numerical methods schemes up to fifth order of accuracy in space and time are implemented and tested we then show the ability of the ader scheme to deal with stiff sources through a numerical simulation in a network of vessels an application to a physical test problem consisting of a network of 37 compliant silicon tubes arteries and 21 junctions reveals that it is imperative to use high order methods at junctions in order to preserve the desired high order of accuracy in the full computational domain for example it is demonstrated that a second order method throughout gives comparable results to a method that is fourth order in the interior of the domain and first order at junctions we are concerned with stiff hyperbolic balance laws in networks an implicit solver for the junction generalized riemann problem is proposed ader schemes of arbitrary accuracy in space and time for networks are constructed convergence rates studies of schemes up to fifth order are carried out it is necessary to match the accuracy at junctions to that of the rest of the domain

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

a convex entropy for a hyperbolic system with relaxation abstract we explicitly construct a convex entropy function for a hyperbolic system with relaxation this entropy is defined in the sense of chen levermore and liu which resembles boltzman s h theorem for kinetic equations this construction follows the idea of suliciu s energy function for a rate type mixed hyperbolic elliptic system such an entropy will be useful in proving the entropy property of the relaxation schemes introduced by jin and xin for conservation laws

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

on line structured subspace identification with application to switched linear systems this article is concerned with the identification of switched linear multiple inputs multiple outputs state space systems in a recursive way first a structured subspace identification scheme for linear systems is presented which turns out to have many attractive features more precisely it does not require any singular value decomposition but is derived using orthogonal projection techniques it allows a computationally appealing implementation and it is closely related to input output models identification second it is shown that this method can be implemented on line to track both the range space of the extended observability matrix and its dimension and thereby the system matrices third by making use of an on line switching times detection strategy this method is applied to blindly identify switched systems and to label the obtained submodels simulation results on noisy data illustrate the abilities and the benefits of the proposed approach

solution of the generalized riemann problem for advection reaction equations we present a method for solving the generalized riemann problem for partial differential equations of the advection reaction type the generalization of the riemann problem here is twofold firstly the governing equations include nonlinear advection as well as reaction terms and secondly the initial condition consists of two arbitrary but infinitely differentiable functions an assumption that is consistent with piecewise smooth solutions of hyperbolic conservation laws the solution procedure local and valid for sufficiently small times reduces the solution of the generalized riemann problem of the inhomogeneous nonlinear equations to that of solving a sequence of conventional riemann problems for homogeneous advection equations for spatial derivatives of the initial conditions we illustrate the approach via the model advection reaction equation the inhomogeneous burgers equation and the nonlinear shallow water equations with variable bed elevation

brief a fast algorithm for the computation of an upper bound on the µ norm a fast algorithm for the computation of the optimally frequency dependent scaled h norm of a finite dimensional lti system is presented it is well known that this quantity is an upper bound to the m norm furthermore it was recently shown to play a special role in the context of slowly time varying uncertainty numerical experimentation suggests that the algorithm generally converges quadratically

vibrations of non uniform continuous beams under moving loads abstract the dynamic behavior of multi span non uniform beams transversed by a moving load at a constant and variable velocity is investigated the continuous beam is modelled using bernoulli euler beam theory the solution is obtained by using both the modal analysis method and the direct integration method the natural frequencies and mode shapes used in the solution of this problem are obtained exactly by deriving the exact dynamic stiffness matrices for any polynomial variation of the cross section along the beam using the exact element method the mode shapes are expressed as infinite polynomial series using the exact mode shapes yields the exact solution for general variation of the beam section in case of constant and variable velocity numerical examples are presented in order to demonstrate the accuracy and the effectiveness of the present study and the results are compared to previously published results

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

subspace identification with guaranteed stability using constrained optimization in system identification the true system is often known to be stable however due to finite sample constraints modeling errors plant disturbances and measurement noise the identified model may be unstable we present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods in subspace identification we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters to ensure asymptotic stability of the identified model we write the least squares optimization problem as a convex linear programming problem with mixed equality quadratic and positive semidefinite constraints suitable for existing convex optimization codes such as sedumi we present examples to illustrate the method and compare to existing approaches

identification methods in a unified framework the paper derives a framework suitable to discuss the classical koopmans levin kl and maximum likelihood ml algorithms to estimate parameters of errors in variables linear models in a unified way using the capability of the unified approach a new parameter estimation algorithm is presented offering flexibility to ensure acceptable variance in the estimated parameters the developed algorithm is based on the application of hankel matrices of variable size and can equally be considered as a generalized version of the kl method gkl or as a reduced version of the ml estimation the methodology applied to derive the gkl algorithm is used to present a straightforward derivation of the subspace identification algorithm

natural frequencies of a non uniform beam with multiple cracks via modified fourier series abstract a new method is presented in this paper for computing the natural frequencies of a non uniform beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is specially developed for a beam with transverse open cracks unlike conventional fourier series modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked beam in the most usual way and thus reduce the problem to a simple one the beam can be of non uniform cross section and the number of cracks can be arbitrary by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form which renders the programming quite straightforward

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

convex parameterizations and fidelity bounds for nonlinear identification and reduced order modelling model instability and poor prediction of long term behavior are common problems when modeling dynamical systems using nonlinear black box techniques direct optimization of the long term predictions often called simulation error minimization leads to optimization problems that are generally nonconvex in the model parameters and suffer from multiple local minima in this paper we present methods which address these problems through convex optimization based on lagrangian relaxation dissipation inequalities contraction theory and semidefinite programming we demonstrate the proposed methods with a model order reduction task for electronic circuit design and the identification of a pneumatic actuator from experiment

high order ader schemes for a unified first order hyperbolic formulation of newtonian continuum mechanics coupled with electro dynamics abstract in this paper we propose a new unified first order hyperbolic model of newtonian continuum mechanics coupled with electro dynamics the model is able to describe the behavior of moving elasto plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro magnetic fields it is actually a very peculiar feature of the proposed pde system that viscous fluids are treated just as a special case of elasto plastic solids this is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix a which in the case of purely elastic solids maps the current configuration to the reference configuration the model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by ohm s law via formal asymptotic analysis we show that in the stiff limit the governing first order hyperbolic pde system with relaxation source terms tends asymptotically to the well known viscous and resistive magnetohydrodynamics mhd equations furthermore a rigorous derivation of the model from variational principles is presented together with the transformation of the euler lagrange differential equations associated with the underlying variational problem from lagrangian coordinates to eulerian coordinates in a fixed laboratory frame the present paper hence extends the unified first order hyperbolic model of newtonian continuum mechanics recently proposed in 110 42 to the more general case where the continuum is coupled with electro magnetic fields the governing pde system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics hence it belongs to the so called class of symmetric hyperbolic thermodynamically compatible systems shtc which have been studied for the first time by godunov in 1961 61 and later in a series of papers by godunov and romenski 67 69 119 an important feature of the proposed model is that the propagation speeds of all physical processes including dissipative processes are finite the model is discretized using high order accurate ader discontinuous galerkin dg finite element schemes with a posteriori subcell finite volume limiter and using high order ader weno finite volume schemes we show numerical test problems that explore a rather large parameter space of the model ranging from ideal mhd viscous and resistive mhd over pure electro dynamics to moving dielectric elastic solids in a magnetic field

a finite element formulation for a convection diffusion equation based on cattaneo s law a number of contributions have been made during the last decades to model pure diusive transport problems by using the so called hyperbolic diusion equa on problems based on a cattaneo type law the finite element solution of the proposed equations is addressed the performance of the algorithm is verified by solving some 2d test cases some interesting features of the proposed model can be observed from these examples and we conclude that the proposal is a feasible alternative to the parabolic model for real engineering simulations

dynamic stability of stepped beams under moving loads abstract the dynamic stability of a stepped beam subjected to a moving mass is investigated in this study the equations of motion for transverse vibrations of the beam are developed in distributed parameter and finite element forms the impulsive parametric excitation theory is used to predict the stability of the beam when subjected to periodic parametric excitations the accuracy of the theory is verified by obtaining the stability boundaries of a simply supported beam and comparing the results with the results reported in the literature stability maps are then obtained for clamped free uniform beams as well as clamped free stepped beams it is found that the stability of certain beam modes can be improved by providing the beam with appropriately spaced steps it is shown that better stability characteristics can be obtained by using piezoelectric actuators stability analyses of beams with periodic piezoelectric and or viscoelastic steps are a natural extension of the present work

maximum likelihood identification of stable linear dynamical systems this paper concerns maximum likelihood identification of linear time invariant state space models subject to model stability constraints we combine expectation maximization em and lagrangian re

choice of state space basis in combined deterministic stochastic subspace identification this paper describes how the state space basis of models identified with subspace identification algorithms can be determined it is shown that this basis is determined by the input spectrum and by user defined input and output weightings through the connections between subspace identification and frequency weighted balancing the state space basis of the subspace identified models is shown to coincide with a frequency weighted balanced basis

precise time step integration for the dynamic response of a continuous beam under moving loads abstract the dynamic response of a non uniform continuous euler bernoulli beam is analyzed with hamilton s principle and the eigenpairs are obtained by the ritz method a high precision integration method is used to calculate the dynamic responses of this beam numerical results show that the method is more accurate in the prediction of the vibration responses under the moving loads than the newmark method

stochastic dynamic finite element analysis of bridge vehicle system subjected to random material properties and loadings abstract this paper performs the statistical dynamic analysis on the bridge vehicle interaction problem with randomness in material properties and moving loads the bridge is modeled as a laminated composite beam with gaussian random elastic modulus and mass density of material with random moving forces on top the mathematical model of the bridge vehicle system is established based on the finite element model in which the gaussian random processes are represented by the karhunen loeve expansion some statistical response such as the mean value and standard deviation of the deflections of the beam are obtained and checked by monte carlo simulation

improved accuracy for time splitting methods for the numerical solution of parabolic equations in this work we study time splitting strategies for the numerical approximation of evolutionary reaction diffusion problems in particular we formulate a family of domain decomposition splitting methods that overcomes some typical limitations of classical alternating direction implicit adi schemes the splitting error associated with such methods is observed to be o 2 in the time step in order to decrease the size of this splitting error to o 3 we add a correction term to the right hand side of the original formulation this procedure is based on the improved initialization technique proposed by douglas and kim in the framework of adi methods the resulting non iterative schemes reduce the global system to a collection of uncoupled subdomain problems that can be solved in parallel computational results comparing the newly derived algorithms with the crank nicolson scheme and certain adi methods are presented

identification of stable models in subspace identification by using regularization in subspace identification methods the system matrices are usually estimated by least squares based on estimated kalman filter state sequences and the observed inputs and outputs for a finite number of data points the estimated system matrix is not guaranteed to be stable even when the true linear system is known to be stable in this paper stability is imposed by using regularization the regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive semi definite weighting matrix the amount of regularization can be determined from a generalized eigenvalue problem the data augmentation method of chui and maciejowski 1996 is obtained by using specific choices for the weighting matrix in the regularization term

brief consistency analysis of subspace identification methods based on a linear regression approach in the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions unfortunately a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does not include important model structures such as e g box jenkins based on a simple least squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure

vibration of multi span non uniform bridges under moving vehicles and trains by using modified beam vibration functions abstract based on the lagrangian approach the vibration of a multi span non uniform bridge subjected to a moving vehicle is analyzed by using modified beam vibration functions as the assumed modes the vehicle is modelled as a two degree of freedom system the method is extended to the action of a moving train by modelling it as a series of two degree of freedom systems all the derived formulae are expressed in matrix form and therefore programming is quite straightforward the total number of unknowns for this method is very small compared with that of the finite element method convergence is very quick and in almost all cases 12 16 terms are sufficient to give satisfactory results

subspace model identification part 1 the output error state space model identification class of algorithms in this paper we present two novel algorithms to realize a finite dimensional linear time invariant state space model from input output data the algorithms have a number of common features they are classified as one of the subspace model identification schemes in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input output data this structure is then exploited in the calculation of a realization another common feature is their algorithmic organization an rq factorization followed by a singular value decomposition and the solution of an overdetermined set or sets of equations the schemes assume that the underlying system has an output error structure and that a measurable input sequence is available the latter characteristic indicates that both schemes are versions of the mimo output error state space model identification moesp approach the first algorithm is denoted in particular as the elementary moesp scheme

a substructure approach tailored to the dynamic analysis of multi span continuous beams under moving loads abstract the paper deals with the dynamic analysis of multiply supported continuous beams subjected to moving loads which in turn can be modelled either as moving forces or moving masses a dedicated variant of the component mode synthesis cms method is proposed in which the classical primary secondary substructure approach sa is tailored to cope with slender i e euler bernoulli continuous beams with arbitrary geometry to do this the whole structure is ideally decomposed in primary and secondary spans with convenient restraints whose exact eigenfunctions are used as assumed local modes the representation of the internal forces is improved with the help of two additional assumed modes for each primary span while primary secondary influence functions allow satisfying the kinematical compatibility between adjacent spans the continuous beam is then re assembled and the lagrange s equations of motion are derived in a compact block matrix setting for both moving force and moving mass model numerical examples demonstrate accuracy and efficiency of the proposed procedure an application with a platoon of high speed moving masses confirms that the inertial effects neglected in the moving force model may have a significant impact in the structural response

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

a birkhoff contraction formula with applications to riccati equations in this paper we show that the symplectic hamiltonian operators on a hilbert space give rise to linear fractional transformations on the open convex cone of positive definite operators that contract a natural invariant finsler metric the thompson or part metric on the convex cone more precisely the constants of contraction for the hamiltonian operators satisfy the classical birkhoff formula the lipschitz constant for the corresponding linear fractional transformations on the cone of positive definite operators is equal to the hyperbolic tangent of one fourth the diameter of the image by means of the close connections between hamilitonian operators and riccati equations this result and the associated machinery are applied to obtain convergence results for discrete algebraic riccati equations and riccati differential equations

a new frequency domain subspace algorithm with restricted poles location through lmi regions and its application to a wind tunnel test abstractin this paper an innovative method is presented to identify models with a modified frequency domain subspace method this new approach allows to introduce in the subspace resolution constraints on the identified model poles location here a very general formulation is proposed to take into account regions in continuous discrete map this formulation is based on an lmi linear matrix inequalities description where the stability domain represents a particular case these lmi constraints are combined with the frequency domain subspace resolution to obtain identified models whose poles are situated in the specified lmi regions this approach is benchmarked with the loewner one which belongs to the class of frequency domain input output model identification and approximation methods besides the fact that they both belong to the data driven model approximation class they result to have slightly different objectives and show complementary performances this discussion is illustrated in practice wit

brain venous haemodynamics neurological diseases and mathematical modelling a review behind medicine m is physiology p behind physiology is physics p and behind physics is always mathematics m for which i expect that the symmetry of the quadruplet mppm will be compatible with the characteristic bias of hyperbolic partial differential equations a theme of this paper i start with a description of several idiopathic brain pathologies that appear to have a strong vascular dimension of which the most prominent example considered here is multiple sclerosis the most common neurodegenerative disabling disease in young adults other pathologies surveyed here include retinal abnormalities transient global amnesia transient monocular blindness meniere s disease and idiopathic parkinson s disease it is the hypothesised vascular aspect of these conditions that links medicine to mathematics through fluid mechanics in very complex networks of moving boundary blood vessels the second part of this paper is about mathematical modelling of the human cardiovascular system with particular reference to the venous system and the brain a review of a recently proposed multi scale mathematical model then follows consisting of a one dimensional hyperbolic description of blood flow in major arteries and veins coupled to a lumped parameter description of the remaining main components of the human circulation derivation and analysis of the hyperbolic equations is carried out for blood vessels admitting variable material properties and with emphasis on the venous system a much neglected aspect of cardiovascular mathematics veins unlike their arterial counterparts are highly deformable even collapsible under mild physiological conditions we address mathematical and numerical challenges regarding the numerical analysis of the hyperbolic pdes we deploy a modern non linear finite volume method of arbitrarily high order of accuracy in both space and time the ader methodology in vivo validation examples and brain haemodynamics computations are shown we also point out two preliminary but important new findings through the use of mathematical models namely that extracranial venous strictures produce chronic intracranial venous hypertension and that augmented pressure increases the blood vessel wall permeability

a five equation model for the simulation of miscible and viscous compressible fluids abstract typical multispecies compressible navier stokes computations employ conservative equations for mass fraction transport upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces between gases of differing ratio of specific heat capacities which degrade the convergence rate of the algorithm adding quasi conservative equations for volume fraction can solve this error however this approach has been derived only for immiscible fluids here a five equation quasi conservative model is proposed that includes the effects of species diffusion viscosity and thermal conductivity the derivation of the model is presented along with a numerical method to solve the governing equations at second order accuracy in space and time formal convergence studies demonstrate the expected order of accuracy is achieved for three benchmark problems cross validated against two standard mass fraction models in these test cases the new model has between 2 and 10 times lower error for a given grid size simulations of a two dimensional air sf6 richtmyer meshkov instability demonstrate that the new model converges to the solution with four times fewer points in each direction when compared to the mass fraction model in an identical numerical framework this represents an 40 times lower computational cost for an equivalent error in two dimensional computations the proposed model is thus very suitable for direct numerical simulation and large eddy simulation of compressible mixing

moving forces identification on a multi span continuous bridge abstract a continuous bridge is modelled as a multi span continuous timoshenko beam with non uniform cross section the vibration behaviour of this beam subjected to moving loads is analyzed by hamilton s principle with the intermediate point constraints represented by very stiff linear springs a method based on the modal superposition and optimization technique is developed to identify the moving forces in the time domain the damped least squares method is used in the identification to provide bounds to the results the errors in the moving force identification are discussed in the paper both computation simulations and laboratory tests show that the method is effective for identifying the moving loads using different combinations of measured responses

study on different beam models in moving force identification abstract several methods have been developed recently to identify moving forces on a beam the results from all of them exhibit fluctuations at the beginning and end of the time history and they are natural outcomes of the ill conditioned inverse problem accuracy of the identified forces also depends on the parameters of the beam force system which have not been systematically studied this paper employs tikhonov regularization technique to provide bounds to the ill conditioned results in the identification problem the calculation of the optimal regularization parameter is discussed the improved algorithm is then used to study the effect of different parameters on the identification results through single force and multi forces identification both the timoshenko beam theory and the euler bernoulli beam theory are included in the study for a comparison laboratory results on two moving forces identification are also presented for illustration timoshenko beam model is found better than the euler bernoulli beam model in the identification and the limits of applications of the moving force identification method are also reported

reconstructed discontinuous galerkin methods for linear advection diffusion equations based on first order hyperbolic system abstract newly developed reconstructed discontinuous galerkin rdg methods are presented for solving linear advection diffusion equations on hybrid unstructured grids based on a first order hyperbolic system fohs formulation benefiting from both fohs and rdg methods the developed hyperbolic rdg methods are reliable accurate efficient and robust achieving higher orders of accuracy than conventional dg methods for the same number of degrees of freedom superior accuracy is achieved by reconstruction of higher order terms in the solution polynomial via gradient variables introduced to form a hyperbolic diffusion system and least squares variational reconstruction unsteady capability is demonstrated by an l stable implicit time integration scheme a number of advection diffusion test cases with a wide range of reynolds numbers including boundary layer type problems and unsteady cases are presented to assess accuracy and performance of the newly developed hyperbolic rdg methods numerical experiments demonstrate that the hyperbolic rdg methods are able to achieve the designed optimal order of accuracy for both solutions and their derivatives on regular irregular and heterogeneous grids indicating that the developed hyperbolic rdg methods provide an attractive and probably an even superior alternative for solving the linear advection diffusion equations

vibration of viscoelastic beams subjected to an eccentric compressive force and a concentrated moving harmonic force abstract the problem of lateral vibration of a beam subjected to an eccentric compressive force and a harmonically varying transverse concentrated moving force is analyzed within the framework of the bernoulli euler beam theory the lagrange equations are used to examine the free vibration characteristics of an axially loaded beam and the dynamic response of a beam subjected to an eccentric compressive force and a moving harmonic concentrated force the constraint conditions of supports are taken into account by using the lagrange multipliers in the study trial function denoting the deflection of the beam is expressed in a polynomial form by using the lagrange equations the problem is reduced to the solution of a system of algebraic equations results of numerical simulations are presented for various combinations of the value of the eccentricity the eccentric compressive force excitation frequency and the constant velocity of the transverse moving harmonic force convergence studies are made the validity of the obtained results is demonstrated by comparing them with exact solutions based on the bernoulli euler beam theory obtained for the special cases of the investigated problem

a novel subspace identification approach with enforced causal models subspace identification methods sims for estimating state space models have been proven to be very useful and numerically efficient they exist in several variants but all have one feature in common as a first step a collection of high order arx models are estimated from vectorized input output data in order not to obtain biased estimates this step must include future outputs however all but one of the submodels include non causal input terms the coefficients of them will be correctly estimated to zero as more data become available they still include extra model parameters which give unnecessarily high variance and also cause bias for closed loop data in this paper a new model formulation is suggested that circumvents the problem within the framework the system matrices a b c d and markov parameters can be estimated separately it is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles

damage identification of supporting structures with a moving sensory system abstract an innovative approach to identify local anomalies in a structural beam bridge with an instrumented vehicle moving as a sensory system across the bridge accelerations at both the axle and vehicle body are measured from which vehicle bridge interaction force on the structure is determined local anomalies of the structure are estimated from this interaction force with the newton s iterative method basing on the homotopy continuation method numerical results with the vehicle moving over simply supported or continuous beams show that the acceleration responses from the vehicle or the bridge structure are less sensitive to the local damages than the interaction force between the wheel and the structure effects of different movement patterns and moving speed of the vehicle are investigated and the effect of measurement noise on the identified results is discussed a heavier or slower vehicle has been shown to be less sensitive to measurement noise giving more accurate results

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

the behavior of hyperbolic heat equations solutions near their parabolic limits standard energy methods are used to study the relation between the solutions of one parameter families of hyperbolic systems of equations describing heat propagation near their parabolic limits which for these cases are the usual diffusive heat equation in the linear case it is proven that given any solution to the hyperbolic equations there is always a solution to the diffusion equation which after a short time stays very close to it for all times the separation between these solutions depends on the square of the ratio between the assumed very short decay time appearing in cattaneo s relation and the usual characteristic smoothing time initial data dependent of the limiting diffusive equation the techniques used in the linear case can be readily used for nonlinear equations as an example we consider the theories of heat propagation introduced by coleman fabrizio and owen and prove that near a solution to the limiting diffusive equation there is always a solution to the nonlinear hyperbolic equations for a time which usually is much longer than the decay time of the corresponding cattaneo relation an alternative derivation of the heat theories of divergence type which are consistent with thermodynamic principles is given as an appendix

semi analytic solution in the time domain for non uniform multi span bernoulli euler beams traversed by moving loads abstract this paper presents a semi analytic solution of the moving load problem which is of great interest for the analysis of multi span uniform and non uniform beams subjected to moving forces such as high speed trains the solution is based on the response of the structure to a unit load circulating at a constant speed of the train viscous modal damping is considered using bernoulli euler beam elements with variable cross sectional properties the structure is discretized and the mode shapes are computed using standard procedure the moving load is represented by a unitary dirac delta function and the modal loads are obtained in terms of cubic hermitian polynomials this leads in a straightforward manner to the closed form solution for the unit load in the time domain the solution is expressed in terms of 10 coefficients per element and per mode the values of which are independent of the speed of the moving load finally the response to a series of loads is built simply by adding the contribution of each the overall procedure is fast and accurate depending only on the spatial discretization and the time step selected for evaluating the solution without the need of any integration step numerical tests have been included in order to show the efficiency of this technique