identification of shear buildings using an instrumental variable method and linear integral filters abstract this paper develops a method for estimating the parameters of a seismically excited building acceleration measurements of the ground and of the building floors containing offsets and noise are used for identification purposes the proposed scheme estimates the complete model of the building if all the floors are equipped with accelerometers moreover it also estimates a reduced model of the structure if only some floors are instrumented the methodology is based on the combined use of the instrumental variable method and linear integral filters the instrumental variable method employs as instrument an auxiliary model of the structure and it is able to directly identify the continuous time structure model using discrete time data without resorting on model transformations from continuous time to discrete time and vice versa using linear integral filters allows obtaining a linear in the parameters expression that depends only on acceleration measurements suitable for parameter identification purposes these filters eliminate measurement offsets and attenuate high frequency measurement noise the above features together with the use of the instrumental variable method reduce the likelihood of biased parameter estimates experiments on a testbed employing a reduced scale five story structure allow comparing the results obtained using the instrumental variable method and those produced by the standard least squares method

full analytical sensitivities in nurbs based isogeometric shape optimization abstract non uniform rational b spline nurbs has been widely used as an effective shape parameterization technique for structural optimization due to its compact and powerful shape representation capability and its popularity among cad systems the advent of nurbs based isogeometric analysis has made it even more advantageous to use nurbs in shape optimization since it can potentially avoid the inaccuracy and labor tediousness in geometric model conversion from the design model to the analysis model although both positions and weights of nurbs control points affect the shape until very recently usually only control point positions are used as design variables in shape optimization thus restricting the design space and limiting the shape representation flexibility this paper presents an approach for analytically computing the full sensitivities of both the positions and weights of nurbs control points in structural shape optimization such analytical formulation allows accurate calculation of sensitivity and has been successfully used in gradient based shape optimization the analytical sensitivity for both positions and weights of nurbs control points is especially beneficial for recovering optimal shapes that are conical e g ellipses and circles in 2d cylinders ellipsoids and spheres in 3d that are otherwise not possible without the weights as design variables

irreducible model estimation for mimo systems abstract estimation of the parameters of a reducible inflated common denominator model for the transfer function matrix of mimo systems is well known however the reduction of the model to the minimal form by pole zero cancellation is possible only in the noise free case this paper presents an algorithm for the estimation of the minimal continuous time transfer function matrix model monte carlo simulation results are presented for discrete time and continuous time models least squares and generalized least squares methods have been used in both cases an asymptotic analysis of convergence has also been provided for these models in the noise free case the computation times and space complexities of different variants of the algorithm are compared the results show that in noisy situations obtaining a discrete time model by discretizing an estimated continuous time model may be a viable proposition

asymptotic formation and orbital stability of phase locked states for the kuramoto model abstract we discuss the asymptotic formation and nonlinear orbital stability of phase locked states arising from the ensemble of non identical kuramoto oscillators we provide an explicit lower bound for a coupling strength on the formation of phase locked states which only depends on the diameters of natural frequencies and initial phase configurations we show that when the phases of non identical oscillators are distributed over the half circle and the coupling strength is sufficiently large the dynamics of kuramoto oscillators exhibits two stages transition and relaxation stages in a transition stage initial configurations shrink to configurations whose diameters are strictly less than 2 in a finite time and then the configurations tend to phase locked states asymptotically this improves previous results on the formation of phase locked states by chopra spong 2009 26 and ha ha kim 2010 27 where their attention were focused only on the latter relaxation stage we also show that the kuramoto model is l 1 contractive in the sense that the l 1 distance along two smooth kuramoto flows is less than or equal to that of initial configurations in particular when two initial configurations have the same averaged phases the l 1 distance between them decays to zero exponentially fast for the configurations with different phase averages we use the method of average adjustment and translation invariant of the kuramoto model to show that one solution converges to the translation of the other solution exponentially fast this establishes the orbital stability of the phase locked states our stability analysis does not employ any standard linearization technique around the given phase locked states but instead we use a robust l 1 metric functional as a lyapunov functional in the formation process of phase locked states we estimate the number of collisions between oscillators and lower upper bounds of the transversal phase differences

shape optimization of shell structures based on nurbs description using automatic differentiation the consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work surfaces based on nurbs non uniform rational b spline mathematical optimization the finite element method fem in structural analysis and automatic differentiation ad are applied in shape optimization of shells this problem is performed taking into account the fact that material and mechanical characteristics influence both the structural shape and the thickness variation in order to obtain the best performance with respect to a specific criterium some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation the shape modification is carried out using an optimization code based on the data obtained by a finite element analysis and gradients evaluation in this work the optimization procedure is performed using an sqp sequential quadratic programming algorithm where the variables are the control points in homogeneous coordinates the knot vectors and the thickness the functional value is determined by the fem and gradients are evaluated using ad some examples are analyzed and discussed as a consequence of the shape optimization shells with high structural performance and aesthetically beautiful shapes can be obtained copyright 2011 john wiley sons ltd

identification of continuous time models the paper considers the problem of estimation of the transfer function of a continuous time dynamic system in the presence of colored noise the author introduces an operator transformation that allows for keeping a continuous time parametrization whereas the parameter estimation can be made by means of a discrete time maximum likelihood algorithm a comparison is made between the performance of the new method in comparison with a standard identification of an armax model the method is useful in cases where it is important to estimate the coefficients of a continuous time transfer function and where it is important to maintain a physical interpretation of the transfer function results

lyapunov function for the kuramoto model of nonlinearly coupled oscillators a lyapunov function for the phase locked state of the kuramoto model of non linearly coupled oscillators is presented it is also valid for finite range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes for the kuramoto model a minimum of the lyapunov function corresponds to a ground state of a system with frustration the interaction between the oscillators xy spins is ferromagnetic whereas the random frequencies induce random fields which try to break the ferromagnetic order i e global phase locking the ensuing arguments imply asymptotic stability of the phase locked state up to degeneracy and hold for any probability distribution of the frequencies special attention is given to discrete distribution functions we argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results but that a partial locking of some but not all sublattices is not to be expected the order parameter of the phase locked state is shown to have a strictly positive lower bound r 1 2 so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded

synchronization of globally coupled phase oscillators singularities and scaling for general couplings abstract the onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling the effect of a stochastic temporal variation in the frequencies is also included the fokker planck equation for the coupled langevin system is reduced to a kinetic equation for the oscillator distribution function instabilities of the phase incoherent state are studied by center manifold reduction to the amplitude dynamics of the unstable modes depending on the coupling the coefficients in the normal form can be singular in the limit of weak instability when the diffusive effect of the noise is neglected a detailed analysis of these singularities to all orders in the normal form expansion is presented physically the singularities are interpreted as predicting an altered scaling of the entrained component near the onset of synchronization these predictions are verified by numerically solving the kinetic equation for various couplings and frequency distributions

laguerre domain adaptive filters using a tapped delay line as an adaptive fitter the complexity of the filter increases with increasing correlation length of input and reference signal the author seeks simple adaptive filter structures such that for a long correlation length only a minor complexity of the filter is needed he considers adaptive mechanisms governed by an exponentially weighted squared error criterion laguerre domain adaptive filters are introduced which lead to a tapped iir filter line these filters contain a discount factor as a free variable which makes it possible to set the memory and the number of adaptive coefficients independently convergence properties of the proposed adaptive filters are discussed

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

paper unprejudiced optimal open loop input design for identification of transfer functions the problem to estimate transfer functions of linear systems is considered the quality of the resulting estimate depends among other things on the input used during the identification experiment we measure the quality using a quadratic norm in the frequency domain the problem to determine optimal inputs i e inputs that minimize the chosen norm subject to constrained input variance has long been studied we point out that such procedures may involve a prejudice that the system is to be found in a certain model set that may have some surprising effects we discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set we also calculate explicit expressions for the resulting unprejudiced optimal inputs these expressions relate the signal to noise ratio as a function of frequency to the chosen weighting function in the quadratic norm we also point out the role of the employed noise model for the design

least squares parameter estimation of continuous time arx models from discrete time data when modeling a system from discrete time data a continuous time parameterization is desirable in some situations in a direct estimation approach the derivatives are approximated by appropriate differences for an arx model this lead to a linear regression the well known least squares method would then be very desirable since it can have good numerical properties and low computational burden in particular for fast or nonuniform sampling it is examined under what conditions a least squares fit for this linear regression will give adequate results for an arx model the choice of derivative approximation is crucial for this approach to be useful standard approximations like euler backward or euler forward cannot be used directly the precise conditions on the derivative approximation are derived and analyzed it is shown that if the highest order derivative is selected with care a least squares estimate will be accurate the theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation

parameter estimation of continuous time bilinear systems based on numerical integration and separable non linear least squares this paper considers the problem of estimating the parameters in continuous time bilinear systems the system identification approach is based on numerical integration and separable non linear least squares the situation where the output signal is contaminated with noise is also discussed the suggested estimation method uses a bias compensating approach and the model parameters together with parameters associated with the noise are estimated by solving an overdetermined system of equation in a least squares sense

online identification of the bilinear model expansion on laguerre orthonormal bases this paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input to the output and to the crossed product on three independent laguerre orthonormal bases compared to classical bilinear model the resulting model entitled bilinear laguerre model ensures a significant parameter number reduction as well as simple recursive representation however this reduction is still subject to an optimal choice of the laguerre poles defining the three laguerre bases therefore we propose an analytical solution to optimise the laguerre poles which depend on fourier coefficients defining the bilinear laguerre model and that are identified using the regularised square error the identification procedures of the laguerre poles and fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the bilinear laguerre model the bilinear laguerre model as well as the proposed algorithm are illustrated and tested

variance error quantifications that are exact for finite model order this paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order in the interests of improved accuracy this paper provides new expressions whose accuracy depends only on data length they are therefore exact for arbitrarily small true model order other authors have recognized the importance of such expressions and have derived them for the case of finite impulse response like model structures in which denominators are fixed at true values and only numerator terms are estimated this paper progresses beyond this situation to address the more general output error and box jenkins structures in which full dynamics models both numerator and denominator terms and noise models may be estimated a key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed

nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators a mean field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit when the frequency distribution isbimodal new results include subcritical spontaneous stationary synchronization of the oscillators supercritical time periodic synchronization bistability and hysteretic phenomena bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength and theirnonlinear stability properties ascertained

stress adapted numerical form finding of pre stressed surfaces by the updated reference strategy in this paper we present the updated reference strategy for numerical formfinding of pre stressed membranes which is based on standard finite elementdiscretization the singularities of the inverse problem are regularizedby a homotopy mapping a projection scheme is proposed where anisotropicpre stress is defined with respect to an additional reference plane whichreflects the initially developable surface of membrane strips in the productionprocess physically problematic combinations of edge geometry and surfacestress are solved by a self adaptive stress correction scheme the algorithmis based on a local criterion derived from differential geometry severalexamples illustrate the success of each idea and implementation

recursive formula for the multiple integral using block pulse functions the recursive formula for the multiple integral using block pulse functions is derived with this algorithm not only the accumulated truncation errors but also the size of the computations involved in the multiple integral are significantly reduced an example which is solved by different algorithms is given the result shows that in solving the multiple integration problems this new recursive method has both the advantages of the generalized operational matrices and the recursive formula for single integral

integral equation approach to system identification this paper presents an integral equation approach to the problem of parameter identification in continuous linear siso mimo and linear in parameters nonlinear systems parameter estimates are deduced from an appropriate set of overdetermined equations which are solved in a least squares sense the effects of deterministic disturbances at system input and output are also included in the analysis

higher dimensional generalizations of the watanabe strogatz transform for vector models of synchronization we generalize the watanabe strogatz ws transform which acts on the kuramoto model in d 2 dimensions to a higher dimensional vector transform which operates on vector oscillator models of synchronization in any dimension for the case of identical frequency matrices these models have conserved quantities constructed from the cross ratios of inner products of the vector variables which are invariant under the vector transform and have trajectories which lie on the unit sphere s d 1 application of the vector transform leads to a partial integration of the equations of motion leaving independent equations to be solved for any number of nodes n we discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on s d 1 we further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball and leaves invariant the cross ratios constructed from inner products of vectors in this mapping can be used to partially integrate a system of vector oscillators with trajectories in and for d 2 leads to an extension of the kuramoto system to a system of oscillators with time dependent amplitudes and trajectories in the unit disk we find an inequivalent generalization of the mobius map which also preserves but leaves invariant a different set of cross ratios this time constructed from the vector norms this leads to a different extension of the kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations

the effects of rapid sampling in system identification this paper deals with the effects of rapid sampling in system identification in continuous time noise models of non zero relative degree imply that one has to differentiate the measured data to find the prediction error parameter estimate this problem can be avoided by using noise models of relative degree zero or by introducing prefilters the corresponding difficulty for the discrete time case is less obvious however by linking the discrete time and continuous time parameter estimation problem we show that the same problem arises for rapid sampled systems

on the global well posedness of bv weak solutions to the kuramoto sakaguchi equation abstract the kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit cycle oscillators when the number of oscillators is sufficiently large the dynamics of kuramoto ensemble can be effectively approximated by the corresponding mean field equation namely the kuramoto sakaguchi ks equation this ks equation is a kind of scalar conservation law with a nonlocal flux function due to the mean field interactions among oscillators in this paper we provide a unique global solvability of bounded variation bv weak solutions to the kinetic ks equation for identical oscillators using the method of front tracking in hyperbolic conservation laws moreover we also show that our bv weak solutions satisfy local in time l 1 stability with respect to bv initial data for the ensemble of identical kuramoto oscillators we explicitly construct an exponentially growing bv weak solution generated from bv perturbation of incoherent state for any positive coupling strength this implies the nonlinear instability of incoherent state in a positive coupling strength regime we provide several numerical examples and compare them with our analytical results

a fictitious energy approach for shape optimization this paper deals with shape optimization of continuous structures as in early works on shape optimization coordinates of boundary nodes of the fe domain are directly chosen as design variables convergence problems and problems with jagged shapes are eliminated by a new regularization technique an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design the energy constraint defines a feasible design space whose size can be varied by one parameter the upper energy limit by construction the proposed regularization is applicable to a wide range of problems although in this paper the application is restricted to linear elastostatic problems

robust filtering and feedforward control based on probabilistic descriptions of model errors abstract a new approach to robust estimation of signals prediction of time series and robust feedforward control is considered modelling errors are parametrized by random variables with known covariances a robust design is obtained by minimizing the squared estimation error averaged both with respect to model errors and the noise a polynomial equations approach based on averaged spectral factorizations and averaged diophantine equations is derived mild solvability conditions guarantee the existence of stable optimal filters and feedforward regulators the robust design turns out to be no more complicated than the design of an ordinary wiener filter or lqg regulator the proposed approach avoids two drawbacks of minimax design first probabilistic descriptions of model uncertainties may have soft bounds these are more readily obtainable in a noisy environment than the hard bounds required for minimax design furthermore not only the range of uncertainties but also their likelihood is taken into account common model deviations will have a greater impact on an estimator design than do very rare worst cases the conservativeness is thus reduced

on the finiteness of collisions and phase locked states for the kuramoto model synchronization phenomenon is ubiquitous in our complex systems and many phenomenological models have been proposed and studied analytically and numerically among them the kuramoto model serves as a prototype model for the phase synchronization of weakly coupled oscillators in this paper we study the finiteness of collisions crossings among kuramoto oscillators in the relaxation process toward the phase locked states and the total number of phase locked states with positive kuramoto order parameters for identical oscillators it is well known that collisions between distinct oscillators cannot occur in finite time and we show that there are only a finite number of phase locked states with positive order parameters however for non identical oscillators oscillators with different natural frequencies can cross each other in their relaxation process and estimating the total number of phase locked states is a nontrivial matter we show that for the non identical case asymptotic phase locking is equivalent to the finiteness of collisions and the total number of phase locked states with positive order parameters is bounded above by 2 n where n is the number of oscillators

recursive identification of transfer function matrix in continuous systems via linear integral filter a method is presented for identifying the transfer function matrix of a continuous time multivariate system with unknown initial conditions from sampled data of input output measurements using the so called linear integral filter an operation of numerical integration for handling time derivatives of measurements leads to an identification model without involving the unknown initial conditions and thus they do not require estimation together with the system parameters both a theoretical analysis and simulation study show that the least squares estimates are asymptotically biased even when the system outputs are corrupted by white noise an instrumental variable method where instrumental variables are composed of combinations of input signals is proposed to give consistent estimates of system parameters for open loop operation and it is also thoroughly evaluated by monte carlo simulation analysis

shape optimization of thin walled structures governed by geometrically nonlinear mechanics this paper introduces a structural optimization strategy that combines fe based parametrization with nonlinear kinematics in order to optimize the shape of thin shell structures the optimization is based on gradient based strategies where the required derivatives are formulated by the adjoint approach the applied solution algorithm combines the well known nonlinear path following strategies with the design update procedure of the shape optimization this results in robust and flexible methods that require only a minimum of system evaluations the proposed optimization goals improve the load carrying behavior of the structure and minimize displacements and stresses it is shown that such efficient designs also exhibit an improved limit load this contribution illustrates the application of the proposed method by several shape optimization problems the presented results prove the exceptional performance of the optimized designs even if the optimal design is disturbed by unavoidable imperfections it is shown that the application of nonlinear kinematics in the shape optimization of thin shell structures allows for a much more realistic system response and gradient data the proposed approach is applicable to all kind of optimization strategies like topology sizing or material optimization respectively

numerical integration approach to on line identification of continuous time systems abstract the problem of estimating the parameters in linear continuous differential equation models from sampled data is treated using a linear integral filter we can obtain an identification model that is parametrized directly in the continuous time model parameters the unknown initial states of the system do not require estimation the choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden by applying the results from discrete time model identification with the obtained identification model a discrete time parameter estimation method is developed and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations a simulation study is also included to confirm the theoretical results

on the mathematical foundations of stable rkhss abstract reproducing kernel hilbert spaces rkhss are key spaces for machine learning that are becoming popular also for linear system identification in particular the so called stable rkhss can be used to model absolutely summable impulse responses in combination e g with regularized least squares they can then be used to reconstruct dynamic systems from input output data in this paper we provide new structural properties of stable rkhss the relation between stable kernels and other fundamental classes like those containing absolutely summable or finite trace kernels is elucidated these insights are then brought into the feature space context first it is proved that any stable kernel admits feature maps induced by a basis of orthogonal eigenvectors in l 2 the exact connection with classical system identification approaches that exploit such kind of functions to model impulse responses is also provided then the necessary and sufficient stability condition for rkhss designed by formulating kernel eigenvectors and eigenvalues is obtained overall our new results provide novel mathematical foundations of stable rkhss with impact on stability tests impulse responses modeling and computational efficiency of regularized schemes for linear system identification

use of two stage least squares algorithms for identification of continuous systems with time delay based on pulse responses this paper presents the so called two stage least squares algorithms to deal with practical identification difficulties often encountered in field testing such as unsteady initial states unknown load disturbances and noise corrupted measurement for step and ramp responses a general linear regression equation is derived from multiple integration of the differential system equation four types of pulse inputs are then considered each of which has its specific advantage in applications and can be represented as a combination of step or ramp inputs based on any of these pulse responses the algorithms are able to overcome those difficulties and yield accurate parameter estimates in a sequential manner the resulting identification scheme provides a convenient way to give the delay estimate along with system parameters and is robust with respect to noise and model structure mismatch

approximation of stable systems by laguerre filters laguerre methods are used to develop concrete techniques and results for approximating stable infinite dimensional systems both hankel norm and l approximation by laguerre filters are studied the infimum of the hankel norm approximation error when the system is approximated by laguerre filters of given maximum order is given by the norm of a certain shifted hankel operator and the best laguerre filter to approximate the system is obtained essentially from the associated eigenproblem for the shifted hankel operator hankel optimal laguerre filters are here called cf laguerre filters as there is a certain connection to the caratheodory fejer interpolation problem and typically provide near best solutions to related l approximation problems a time domain compressed laguerre shift method for solving certain nehari problems for delay systems is used to determine analytically the achievable hankel error norms and thus also to obtain bounds for the achievable l error norm for delay systems a result on a laguerre filter approximation problem in the hilbert schmidt norm is given as well

a new bias compensating ls method for continuous system identification in the presence of coloured noise a new bias compensating least squares ls method is presented for the parameter estimation of linear single input single output siso continuous time systems a discrete time model obtained by using the linear integral filter is augmented by introducing a pre filter on the input and then the parameters of the augmented model are estimated by the conventional ls method the distinct characteristic roots of the pre filter are used to estimate the bias in the ls estimate the pre filter should be chosen so that its frequency bandwidth is wider than those of the system and the input signals since the new method requires minimal information on the noise characteristics it is easily applicable to the case of coloured noise

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

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

brief parameter identification with derivative shift operator parametrization a way of parametrizing linear systems using an operator which combines the two commonly used operators the shift q and the delta d operators is proposed it is shown that the proposed parametrization improves the numerical property of parameter identification process by using the proposed operator the condition number of the information matrix in the identification algorithm is significantly lower than that using the q or d operator it is also shown that accurate and fast converging parameter identification can be achieved by using the new operator at fast sampling rates especially for systems with relatively wide bandwidth the numerical superiority of the new parametrization is demonstrated by simulation results

continuous time system representation with exact macro difference expressions a macro difference equation representation is proposed which is a mixture of finite difference quotients and integrals over finite time intervals the choice of the micro or sampling interval length for the numerical integration accuracy and representation bandwidth and the choice of the macro interval length for numerical conditioning accuracy of the difference quotients and of the resulting equations are independent this approach does not need the assumption which in practical situations is quite unnatural of zero initial conditions

irreducible continuous model identification via markov parameter estimation abstract this paper presents a new approach to irreducible model identification of continuous time mimo systems via markov parameter estimation owing to the chosen linear in parameters model structure the estimation becomes linear and is aymptotically robust to zero mean additive disturbances this paper proposes a generalization and flexible parametrization of the markov parameter model structure removes the existing limitations in the case of systems with low or zero damping extends the formulation to mimo systems and analyses the algorithm establishing identifiability conditions thus rendering the proposed approach to continuous time system identification quite general and particularly attractive for finite dimensional system identification

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

a gradient based shape optimization scheme using an interface enriched generalized fem abstract a gradient based shape optimization scheme using an interface enriched generalized finite element method igfem is presented wherein the design geometry is projected onto a fixed mesh and the igfem is used for analysis this approach eliminates the mesh distortion present in conventional lagrangian shape optimization methods as well as the need for remeshing an analytical sensitivity analysis using both the adjoint or direct approaches is presented to compute derivatives of the objective and constraint functions due to the fixed nature of the mesh the so called design velocity field only needs to be computed on the structure boundary interface a comparison between igfem and conventional fem based shape optimization schemes is presented showing an improved precision for the igfem approach finally we solve various numerical examples to demonstrate the capability of the method including the computational design of particulate and microvascular composites

optimal shapes of mechanically motivated surfaces abstract subject of this contribution is form finding of optimal structural shapes with regard to the load carrying behaviour of surface structures under certain load cases in general those optimal shapes prefer a membrane state of stress to transfer loading bending is omitted as much as possible it will be focused on two different disciplines and related numerical approaches which deal with solutions of the mentioned task form finding of prestressed membranes and general shape optimization as design is an inverse problem both approaches share similar problematic properties as e g indeterminate in plane location of surface discretization or necessary regularization and filtering of sensitivity and other data as it will turn out those remedies found for the very special methods of membrane design can be abstracted and transferred to general optimization procedures that merges into elegant numerical shape optimal design techniques which combine advantages of both approaches and allow for effective and efficient shape optimization of free formed surfaces directly on the finite element mesh and for a large number of variables typical applications are for example membrane design free form architecture and structural engineering and metal sheet design

shape optimisation with multiresolution subdivision surfaces and immersed finite elements abstract we develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation similar to wavelets multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness during shape optimisation the vertex coordinates of control meshes are updated using the computed shape gradient information by virtue of the multiresolution editing semantics updating the coarse control mesh vertex coordinates leads to large scale geometry changes and conversely updating the fine control mesh coordinates leads to small scale geometry changes in our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum this approach effectively prevents the appearance of non physical boundary geometry oscillations and control mesh pathologies like inverted elements independent of the fineness of the control mesh used for optimisation on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution with the immersed finite element method there is no need to maintain an analysis suitable domain mesh in some of the presented two and three dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain the merging or removing of holes is not considered

brief continuous time approaches to identification of continuous time systems a fundamental continuous time approach to identification of continuous time systems is considered a consequent and coherent continuous time analysis leads to parameter estimation schemes expressed in the continuous time domain for the purpose of digital realization the estimators are discretized leading to various discrete time recursive procedures and exercised numerically

a shocking display of synchrony abstract this article explores the kuramoto model describing the synchronization of a population of coupled oscillators two versions of this model are considered a discrete version suitable for a population with a finite number of oscillators and a continuum model found in the limit of an infinite population when the strength of the coupling between the oscillators exceeds a threshold the oscillators partially synchronize we explore the transition in the continuum model which takes the form of a bifurcation of a discrete mode from a continuous spectrum we use numerical methods and perturbation theory to study the patterns of synchronization that form beyond transition and compare with the synchronization predicted by the discrete model there are similarities with instabilities in ideal plasmas and inviscid fluids but these are superficial

systems of matrix riccati equations linear fractional transformations partial integrability and synchronization we partially integrate a system of rectangular matrix riccati equations which describe the synchronization behavior of a nonlinear complex system of n globally connected oscillators the equations take a restricted form in which the time dependent matrix coefficients are independent of the node we use linear fractional transformations to perform the partial integration resulting in a system of reduced size which is independent of n generalizing the well known watanabe strogatz reduction for the kuramoto model for square matrices the resulting constants of motion are related to the eigenvalues of matrix cross ratios which we show satisfy various properties such as symmetry relations for square matrices the variables can be regarded as elements of a classical lie group not necessarily compact satisfying the matrix riccati equations trajectories lie either within or on the boundary of a classical domain and we show by numerical example that complete synchronization can occur even for the mixed case provided that certain unitarity conditions are satisfied we extend the definition of cross ratios to rectangular matrix systems and show that again the eigenvalues are conserved special cases are models with real vector unknowns for which trajectories lie on the unit sphere in higher dimensions with well known synchronization behavior and models with complex vector wavefunctions that describe synchronization in quantum systems possibly infinite dimensional we partially integrate a system of rectangular matrix riccati equations which describe the synchronization behavior of a nonlinear complex system of n globally connected oscillators the equations take a restricted form in which the time dependent matrix coefficients are independent of the node we use linear fractional transformations to perform the partial integration resulting in a system of reduced size which is independent of n generalizing the well known watanabe strogatz reduction for the kuramoto model for square matrices the resulting constants of motion are related to the eigenvalues of matrix cross ratios which we show satisfy various properties such as symmetry relations for square matrices the variables can be regarded as elements of a classical lie group not necessarily compact satisfying the matrix riccati equations trajectories lie either within or on the boundary of a classical domain and we show by numerical example that complete synchronization can occur even for the mixed ca

limit results for sampled systems properties of discrete time systems obtained by sampling continuous time systems are described by introducing prefilters we can treat different ways of sampling within one framework results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given these results are generalizations of the results of astrom hagander and sternby 1984 on the convergence of poles and zeros for zero order hold sampled transfer functions sampled noise models are also analysed knowledge of these properties is very important in for example discrete time simulations of continuous time systems and identification of continuous time models based on discrete time measurements

brief performance evaluation of methods for identifying continuous time autoregressive processes identification of continuous time autoregressive processes from discrete time data by replacing the differentiation operator by an approximation is considered a linear regression model can then be formulated the least squares method and the instrumental variables method must be used with some care to get parameter estimates of good quality the bias is studied explicitly in the paper together with the asymptotic distribution and expressions are presented for the covariance matrix of the estimated parameters it turns out that there are small differences in the dominating bias term for the different methods whereas the statistical properties are comparable overall the performance is similar to that of a prediction error method for short sampling intervals

isogeometric shape optimization of shells using semi analytical sensitivity analysis and sensitivity weighting abstract we present isogeometric shape optimization for shell structures applying sensitivity weighting and semi analytical analysis we use a rotation free shell formulation and all involved geometry models i e initial design analysis model optimization model and final design use the same geometric basis in particular nurbs a sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update a multilevel design approach is applied such that the design space can be chosen independently from the analysis space the use of semi analytical sensitivities allows having different polynomial degrees for design and analysis model different numerical examples are performed which confirm the applicability of the proposed method furthermore a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods

identification of continuous time multivariable systems from sampled data abstract several approaches to estimating the parameters of a continuous time model of a multivariable system from samples of input and output observations arc discussed these include indirect methods where a discrete time model is first obtained from the input output data and then transformed into a continuous time model as well as direct methods where the continuous time model is obtained straight from the samples of the observations an example is used to compare the methods

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

parameter and differentiation order estimation in fractional models this paper deals with continuous time system identification using fractional differentiation models an adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known then an optimization approach based on the use of the developed instrumental variable estimator is presented two variants of the algorithm are proposed either all differentiation orders are set as integral multiples of a commensurate order which is estimated or all differentiation orders are estimated the former variant allows to reduce the number of parameters and can be used as a good initial hit for the latter variant the performances of the proposed approaches are evaluated by monte carlo simulation analysis finally the proposed identification algorithms are used to identify thermal diffusion in an experimental setup

new class of discrete time models for continuous time systems digital computing in estimation control or signal processing for continuous time systems requires the use of discrete time models while conventional difference equation or z transfer function models are widely popular a class of methods exists that uses discrete approximations of continuous signals and operators retaining the continuous time parameters some important advantages of this class have been demonstrated in the contexts of parameter estimation adaptive control and controller design this paper proposes a new class of discrete time models that originates from the z transfer function but which is close to continuous time models in structure and parameters thereby retaining its advantageous features the recently proposed delta model is seen to be a member of this class the interrelations among various digital model types are brought out better sensitivity properties over z transfer function models are established finite word length properties of these models vis a vis the z transfer fu

design variables for bias distribution in transfer function estimation estimation of transfer functions of linear systems is one of the most common system identification problems several different design variables chosen by the user for the identification procedure affect the properties of the resulting estimate in this paper it is investigated how the choices of prefilters noise models sampling interval and prediction horizon i e the use of k step ahead prediction methods influence the estimate an important aspect is thai the true system is not assumed to be exactly represented within the chosen model set the estimate will thus be biased it is shown how the distribution of bias in the frequency domain is governed by a weighting function which emphasizes different frequency bands the weighting function in turn is a result of the previously listed design variables it is shown e g thai the common least squares method has a tendency to emphasize high frequencies and that this can be counteracted by prefiltering it is also shown that asymptotically it is only the prediction horizon itself and not how it is split up into sampling interval times number of predicted sampling instants that affects this weighting function

formation of phase locked states in a population of locally interacting kuramoto oscillators abstract in this paper we present an asymptotic formation of phase locked states from the ensemble of kuramoto oscillators with a symmetric and connected interaction topology for a limited interaction topology that does not have an all to all interaction lyapunov type approaches based on phase and frequency diameters do not work due to the lack of completeness thus we employ an energy method together with the connectedness of underlying interaction topologies to determine the complete synchronization estimates our synchronization estimation method consists of two parts first we establish that the uniform boundedness of fluctuations yields the asymptotic formation of phase locked states using ojasiewicz gradient inequality second we show that for the initial configurations lying in the half circle the uniform boundedness of fluctuations can be derived by a comparison with solutions to the linear gronwall s differential inequality for the total phase variance

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

a gradient based parameter free approach to shape optimization in shape optimization the independent node movement approach wherein finite element node coordinates are used directly as design variables allows the most freedom for shape change and avoids the time consuming parameterization preprocess however this approach lacks a length scale control that is necessary to ensure a well posed shape optimization problem and avoid numerical instability motivated by the success of filtering techniques that impose minimum length scales in topology optimization we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach

the spectrum of the locked state for the kuramoto model of coupled oscillators we analyze the linear stability of the phase locked state in the kuramoto model of coupled oscillators the main result is the first rigorous characterization of the spectrum and its associated eigenvectors for any finite number of oscillators all but two of the eigenvalues are negative and merge into a continuous spectrum as the number of oscillators tends to infinity one eigenvalue is always zero by rotational invariance the final eigenvalue corresponding to a collective mode determines the stability of the locked state

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

estimation of coefficients for multiple input system models without employing common denominator structure an instrumental variable iv parameter estimation scheme is presented for transfer function coefficient estimation it is applied to some elementary multiple input single output miso linear system models the discrete unit delay z transform model form is employed with both similar and dissimilar denominator polynomials the efficacy of the proposed scheme is illustrated by means of results obtained in single stochastic simulation experiments although more convergence difficulties are encountered with the dissimilar denominator model structure the is in a more general form because the independent auto regressive all components within the assumed noise disturbance dynamics are immediately available the dissimilar denominator miso model structure is formulated as superimposed single input single output siso models convergence difficulties are mainly experienced because of the need to estimate the individual output series associated with each of the siso models the present results suggest that t

frequency domain tracking characteristics of adaptive algorithms the problem of tracking time varying linear systems is discussed the focus is on the model quality in terms of the mean square error mse between the true momentary transfer function and the estimated one this mse is thus a function of frequency the exact expression for the mse is complicated but simple expressions that are asymptotic in the model order are developed for model structures of finite impulse response fir character simulations verify that these simple expressions are quite reliable and insightful even for moderate model orders expressions are developed for three basic adaptation algorithms recursive identification algorithms viz the least mean squares algorithm the recursive least squares algorithm with exponential forgetting and a tracking algorithm based on the kalman filter the results apply both to slowly time varying systems and to the model recovery after an abrupt change in the system dynamics

on the discrete variant of the traction method in parameter free shape optimization abstract one of the major challenges in the parameter free approach to computational shape optimization is the avoidance of oscillating i e non smooth boundaries in the optimal design trials in order to achieve this we investigate a method for regularization that corresponds to the discrete variant of the so called traction method in this approach the design updates are generated in terms of a displacement field which is obtained as the solution to an auxiliary boundary value problem that is defined on the actual design domain the main idea herein is to apply fictitious nodal forces corresponding to the discrete sensitivity of the objective function we propose an algorithm in which constraint functions will be taken into account by using an augmented lagrangian formulation and a step length control ensures a sufficient decrease condition in terms of the objective function within each iteration we examine the benefits of the proposed regularization method on the basis of some numerical examples in comparison to an unregularized steepest descent algorithm

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

constants of motion for superconducting josephson arrays abstract we show that series arrays of n identical overdamped josephson junctions have extremely degenerate dynamics in particular we prove that such arrays have n 3 constants of motion for all n 3 the analysis is based on a coordinate transformation that reduces the governing equations to an n 3 parameter family of low dimensional systems in the weak coupling limit the reduced equations can be analyzed completely either all solutions approach the synchronous state or they converge to a continuous family of incoherent oscillations depending on a certain parameter value at the transitional value of this parameter the system becomes completely integrable then the phase space is foliated by invariant two dimensional tori for any n 3 the infinite n limit of the system is an integro partial differential equation with rigorously low dimensional dynamics it supports solitons in the integrable case and chaotic waves in the non integrable case

transfer function matrix identification in mimo systems via shifted legendre polynomials a general algorithm is presented for the identification of the parameters in the transfer function matrix of a multi input multi output mimo system the approach adopted is that of expanding the system input and output variables in shifted legendre series the feasibility of the method lies in the generation of linear algebraic equations in the unknown parameters and initial conditions by means of an elegant operational matrix which relates shifted legendre polynomials to their integrals an example is included to illustrate the applicability of the proposed method

on a least squares based algorithm for identification of stochastic linear systems a new form of bias eliminated least squares bels algorithm is developed to identify transfer function parameters of a linear time invariant system irrespective of noise dynamics unlike the bels estimator previously presented the main feature with the developed algorithm is that the transfer function parameters are consistently estimated in such a direct way that there is no need to prefilter observed data or to deal with a high order augmented system this greatly simplifies implementation of the bels based algorithms and reduces numerical efforts whereas a desirable estimation accuracy can still be achieved two simulation examples are presented that clearly illustrate the good performances of the developed algorithm including its superiority over one type of simple instrumental variable method

partial entrainment in the finite kuramoto sakaguchi model abstract although modifications of the kuramoto model have been the subject of extensive research the model itself is not yet fully understood we offer several results and observations some analytic others through simulations we derive a sufficient condition for the existence of a solution exhibiting partial entrainment with respect to a given subset of oscillators the result also implies persistence of the entrainment behavior under perturbations the critical values of the coupling strength defining the transitions between different forms of partial entrainment are predicted by an analytical approximation based on the fact that oscillators with large differences in their natural frequencies have little influence on each other s entrainment behavior the predictions agree with the actual values obtained by simulations we indicate by simulations that entrainment can disappear with increasing coupling strength and that in arrays of josephson junctions a similar phenomenon can be observed where it is also possible that a junction leaving one entrained subset joins another entrained subset

on the complete synchronization of the kuramoto phase model abstract we discuss the asymptotic complete phase frequency synchronization for the kuramoto phase model with a finite size n we present sufficient conditions for initial configurations leading to the exponential decay toward the completely synchronized states our new sufficient conditions and decay rate depend only on the coupling strength and the diameter of initial phase and natural frequency configurations but they are independent of the system size n hence they can be used for the mean field limit for the complete synchronization estimates we estimate the time evolution of the phase and frequency diameters for configurations the initial phase configurations for identical oscillators located on the half circle will converge to the complete synchronized states exponentially fast in contrast for the non identical oscillators the complete frequency synchronization will occur exponentially fast for some restricted class of initial phase configurations our estimates are based on the monotonicity arguments of extremal phase and frequencies which do not employ any linearization procedure of nonlinear coupling terms and detailed information on the eigenvalue of the linearized system around the complete synchronized states we compare our analytical results with numerical simulations

estimation of continuous time ar process parameters from discrete time data the problem of estimating continuous time autoregressive process parameters from discrete time data is considered the basic approach used here is based on replacing the derivatives in the model by discrete time differences forming a linear regression and using the least squares method such a procedure is simple to apply computationally flexible and efficient and may have good numerical properties it is known however that all standard approximations of the highest order derivative such as repeated use of the delta operator gives a biased least squares estimate even as the sampling interval tends to zero some of our previous approaches to overcome this problem are reviewed then two new methods which avoid the shift in our previous results are presented one of them which is termed bias compensation is computationally very efficient finally the relationship of the above least squares approaches with an instrumental variable method is investigated comparative simulation results are also presented

bias compensating least squares method for identification of continuous time systems from sampled data abstract least squares ls techniques are applied to the identification problem of continuous time systems from sampled data of input output measurements the linear integral filter which solves the intial condition problem is employed for handling time derivatives the asymptotic bias in the ls estimator is derived and is compensated in a modified ls algorithm called a bias compensating ls method to obtain consistent estimates of the unknown parameters when it is unknown the variance of the noise can be estimated recursively together with the system parameters the bias compensating ls method not only has all merits of the ls method but also possesses good consistency properties it is applicable to both time invariant and time varying continuous time systems in the time varying case an adaptive ls algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly and the bias is compensated as is done in the time invariant case representative nu

orthogonal rational functions a transformation analysis finite impulse response fir models are among the most basic tools in control theory and signal processing and are routinely used in almost all fields of application the connections to orthogonal polynomials are well known however infinite impulse response iir models often provide much more compact descriptions and in many cases give improved performance the objective of this paper is to present a simple framework for the derivation and analysis of orthogonal iir transfer functions which are directly related to orthogonal rational functions orthogonality simplifies approximation analysis and leads to improved numerical properties the basic idea is to use a fractional transformation to map the problem to a new domain where an fir description is most appropriate this fir representation is then mapped back to the original domain to give an orthogonal iir representation it is then straightforward to extend many results for fir models to iir model structures with arbitrary stable poles i e prop

asymptotic properties of black box identification of transfer functions the problem of estimating the transfer function of a linear stochastic system is considered the transfer function is parametrized as a black box and no given order is chosen a priori this means that the model orders may increase to infinity when the number of observed data tends to infinity the consistency and convergence properties of the resulting transfer function estimates are investigated asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase it is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise to signal ratio at that frequency mulliplied by the model order to number of data points ratio