the effects of linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems the associated output frequency response function in the present study a new concept known as the associated output frequency response function aofrf is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems based on the aofrf concept the study has shown for the first time that the output frequency responses of a wide class of nonlinear systems that are described by the narx nonlinear auto regressive with exogenous input model can be represented by a polynomial function of both the system linear and nonlinear characteristic parameters of interests to the system analysis moreover an efficient algorithm is derived to determine the structure and coefficients of the aofrf based representation for system output frequency responses finally a case study is provided to demonstrate the effectiveness and advantages of the new aofrf based representation and the implication of the result to the analysis and design of nonlinear systems in the frequency domain

coupled bending torsional dynamic stiffness matrix of an axially loaded timoshenko beam element abstract analytical expressions for the coupled bending torsional dynamic stiffness matrix terms of an axially loaded uniform timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element the symbolic computing package reduce has been used to generate an analytical expression for each of the dynamic stiffness terms in a concise form for check purposes numerical values of the dynamic stiffness matrix terms were obtained using the derived explicit expressions as well as by an alternative nonanalytical method based on matrix inversions and matrix multiplications stiffnesses obtained from both methods agreed with each other to machine accuracy application of the developed theory is discussed with particular reference to an established algorithm the influence of axial force shear deformation and rotatory inertia on the natural frequencies of a bending torsion coupled beam with cantilever end conditions is demonstrated by numerical results such results are not generally available in the literature therefore results obtained by partially restricting the present theory are compared with the existing literature wherever possible the results indicate that the method is accurate and efficient

parametric and nonparametric identification of linear systems in the presence of nonlinear distortions a frequency domain approach this paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations in the first part a related linear dynamic system rlds approximation to the nonlinear system nls is defined and it is shown that the differences between the nls and the rlds can be modeled as stochastic variables with known properties in the second part a parametric model for the rlds is identified convergence in probability of this model to the rlds is proven a function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate

an asymptotic factorization method for inverse electromagnetic scattering in layered media we consider the inverse problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two layered background medium from near field measurements of time harmonic electromagnetic fields for this purpose we first study the direct scattering problem and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero integral equation methods and a factorization of the corresponding near field measurement operator are applied to prove this expansion in the second part of this work we use the asymptotic expansion to justify a noniterative reconstruction algorithm which is a combination of factorization methods and music type methods we illustrate the feasibility of this method by a numerical example

nearly cloaking the electromagnetic fields the approximate cloaking is investigated for time harmonic maxwell s equations via the approach of transformation optics the problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an asymptotically small support but an arbitrary content enclosed by a thin high conducting layer sharp estimates are established in terms of the asymptotic parameter which are independent of the material tensors of the small electromagnetic inclusion the result implies that the blow up a small region construction via the transformation optics approach yields a near cloak for the electromagnetic waves a novelty lies in the fact that the geometry of the cloaking construction of this work can be very general moreover by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region arbitrary electromagnetic contents can be nearly cloaked our mathematical technique extends the general one developed in h y

least squares lti approximation of nonlinear systems and quasistationarity analysis least squares linear time invariant lti approximation of discrete time nonlinear systems is studied in a generalized harmonic analysis setting extending an earlier result based on quasistationary signals the least squares optimal lti model is such that the crosscorrelation between the input and the lti model output equals the crosscorrelation between the input and the output of the nonlinear system new results for limits of sample averages of signals are derived via riemann stieltjes integration theory these results are applied to crosscorrelation and quasistationarity analysis of input output signals for several important classes of nonlinear systems including stable finite memory wiener and hammerstein systems this analysis demonstrates that the assumptions used in the least squares lti approximation setup are fairly mild finally an illustrative example is provided

coupled vibrations of beams an exact dynamic element stiffness matrix a uniform linearly elastic beam element with non coinciding centres of geometry shear and mass is studied under stationary harmonic end excitation the euler bernoulli saint venant theory is applied thus the effect of warping is not taken into account the frequency dependent 12 12 element stiffness matrix is established by use of an exact method the translational and rotational displacement functions are represented as sums real of complex exponential terms where the complex exponents are numerically found built up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines

on linear models for nonlinear systems best linear time invariant lti approximations are analysed for several interesting classes of discrete nonlinear time invariant systems these include nonlinear finite impulse response systems and a class of nonsmooth systems called bi gain systems the frechet derivative of a smooth nonlinear system is studied as a potential good lti model candidate the frechet derivative is determined for nonlinear finite memory systems and for a class of wiener systems most of the concrete results are derived in an signal setting applications to linear controller design to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed

on coupled bending and torsional vibration of uniform beams abstract it is known that the bernoulli euler theory of beam flexure may be combined with the saint venant theory of torsion to describe the coupled antisymmetric free vibration of uniform beams having a plane of symmetry 1 the principal modes may be expressed in terms of tabulated functions this paper extends the theory to allow for warping of the beam cross section for this can make a large difference to results for thin walled beams of open section

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

on robustness in control and lti identification near linearity and non conic uncertainty robustness issues are studied in the context of linear models in linear controller design and in system identification when the true system is nonlinear the notion of nearly linear system is generalized to include time varying and open loop unstable systems this class of systems although it presents the simplest possible global generalization of linear systems is in many ways nontrivial for the purpose of linear controller design and linear model identification from input output data this is mainly due to the presence of non conic uncertainty which is not included in standard treatments of robust control theory and stochastic system identification theory signal distribution theory a realistic non stochastic signal analysis tool is used to study the limiting least squares estimates of linear finite impulse response fir and autoregressive with external input arx model parametrizations for two classes of nonlinear systems some connections to worst case analysis of linear model identification are also discussed

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

deterministic and random vibration of an axially loaded timoshenko beam resting on an elastic foundation abstract a method is presented to perform the deterministic and random vibration analysis of a rayleigh timoshenko beam on an elastic foundation which may simulate bridges runways rails roadways pipelines etc the rayleigh timoshenko beam is assumed to be uniform damped with generalized boundary conditions and subjected to axial load also the rayleigh timoshenko beam includes the effect of shear deformation and rotatory inertia which are usually important if the span depth ratio of the beam is relatively small once the natural frequencies and mode shapes of the beam are obtained modal analysis is used to compute the dynamic responses of the structure such as the displacement and bending moment and some statistical responses such as mean square values of the dynamic displacement and bending moment these dynamic responses are quite useful for structural design while the statistical dynamic responses play an important role in structural reliability analysis

dynamic stability of a thin walled beam subjected to axial loads and end moments the dynamic stability problem of thin walled beams subjected to combined action of axial loads and end moments is studied each force and moment consists of a constant part and a time dependent stochastic function closed form analytical solutions are obtained for simply supported boundary conditions by using the direct liapunov method almost sure asymptotic stability and uniform stochastic stability conditions are obtained as the function of stochastic process variance damping coefficient and geometric and physical parameters of the beam the almost sure stability regions for i cross section and narrow rectangular cross section are shown in the plane of variances of stochastic parts axial force and end moment uniform stochastic stability regions are shown in intensity of stochastic loadings and constant parts of axial loads and end moments

stochastic vibration of axially loaded monosymmetric timoshenko thin walled beam abstract an analytical method is presented to perform the flexure torsion coupled stochastic response analysis of monosymmetric axially loaded timoshenko thin walled beam subjected to various kinds of concentrated and distributed stochastic excitations with stationary and ergodic properties the effects of warping stiffness axial force shear deformation and rotary inertia are included in the present formulations first the damped general governing differential equations of motion of axially loaded timoshenko thin walled beam are developed and the free vibration analysis is performed once the natural frequencies and mode shapes are obtained mode superposition method in conjunction with receptance method is used to compute the mean square displacement response of the axially loaded thin walled beam finally the method is illustrated by its application to two test examples to investigate the effects of warping stiffness axial force shear deformation and rotary inertia on the stochastic response of the thin walled beams

on optimal lti approximation of nonlinear systems optimal linear time invariant lti approximation of discrete time nonlinear systems is studied using a quasi stationary signal description the optimality of the lti approximation is quantified as a least average squared error condition reminescent of recent studies on the performance of least squares type identification methods for lti models of nonlinear systems

nonlinear gray box identification using local models applied to industrial robots in this paper we study the problem of estimating unknown parameters in nonlinear gray box models that may be multivariable nonlinear unstable and resonant at the same time a straightforward use of time domain predication error methods for this type of problem easily ends up in a large and numerically stiff optimization problem we therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem the procedure is based on the estimation of the nonparametric frequency response function frf in a number of operating points the nonlinear gray box model is linearized in the same operating points resulting in parametric frfs the optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric frfs the procedure is illustrated by estimating elasticity parameters in a six axis industrial robot different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure the weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control

recovery of an embedded obstacle and the surrounding medium for maxwell s system abstract in this paper we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far field data the complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting pec obstacle the far field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation but frequencies from an open interval it is shown that the embedded obstacle can be uniquely recovered by the aforementioned far field data independent of the surrounding medium furthermore if the surrounding medium is piecewise homogeneous then the medium can be recovered as well those unique recovery results are new to the literature our argument is based on low frequency expansions of the electromagnetic fields and certain harmonic analysis techniques

beam bending torsion dynamic stiffness method for calculation of exact vibration modes abstract the exact dynamic stiffness matrix is derived for a straight and uniform beam element whose elastic and inertial axes are not coincident elementary bending torsion beam theory is used and bending translation is restricted to one direction the element matrix can be used in the dynamic stiffness method for calculation of exact natural frequencies mode shapes and generalized masses for planar assemblages of connected bending torsion beams the dynamic stiffness method is outlined and details pertinent to the bending torsion beam element are given an example of a three beam assemblage representing an airplane wing is posed and exact numerical solutions are tabulated for natural frequencies and generalized masses solutions calculated by the finite element method are also tabulated for comparison

lti approximation of nonlinear systems via signal distribution theory l 2 and l 1 optimal linear time invariant lti approximation of discrete time nonlinear systems such as nonlinear finite impulse response nfir systems is studied via a signal distribution theory motivated approach the use of a signal distribution theoretic framework facilitates the formulation and analysis of many system modelling problems including system identification problems specifically a very explicit solution to the l 2 least squares lti approximation problem for nfir systems is obtained in this manner furthermore the l 1 least absolute deviations lti approximation problem for nfir systems is essentially reduced to a linear programming problem active lti modelling emphasizes model quality based on the intended use of the models in linear controller design robust stability and lti approximation concepts are studied here in a nonlinear systems context numerical examples are given illustrating the performance of the least squares ls method and the least absolute deviations lad method with lti models against nonlinear unmodelled dynamics

lti modelling of nfir systems near linearity and control ls estimation and linearization linear time invariant lti modelling of nonlinear finite impulse response nfir systems is studied from a control point of view nearly linear nfir systems and their control relevant properties are analysed in detail the main modelling interest is in the analysis of least squares ls lti identification when the true system is an nfir system which is possibly nearly linear linearization is used for comparison purposes as the second lti modelling technique nearly linear systems provide a natural generalization of lti systems to include nonlinearities that allow globally good lti approximations while at the same time such nonlinearities can have a very dramatic effect on the local characteristics of the system several control oriented examples illustrate the possible weaknesses and strengths of the studied lti modelling techniques linearization is found to be especially vulnerable to the presence of even very small only locally significant nonlinearities ls estimation can largely avoid such difficulties but input design becomes a more critical issue than in standard linear estimation theory certain counter intuitive properties of commonly used input output stability notions such as 2 stability are discussed via the concept of near linearity

squared and absolute errors in optimal approximation of nonlinear systems optimal squared error and absolute error based approximation problems for static polynomial models of nonlinear discrete time systems are studied in detail these problems have many similarities with other linear in the parameters approximation problems such as with optimal approximation problems for linear time invariant models of linear and nonlinear systems nonprobabilistic signal analysis is used close connections between the studied approximation problems and certain classical topics in approximation theory such as optimal l 2 1 1 and l 1 1 1 approximation are established by analysing conditions under which sample averages of static nonlinear functions of the input converge to appropriate riemann integrals of the static functions these results should play a significant role in the analysis of corresponding system identification and model validation problems furthermore these results demonstrate that optimal modelling based on the absolute error can offer advantages over squared error based modelling especially modelling problems in which some signals possess heavy tails can benefit from absolute value based signal and error analysis

linear approximations of nonlinear fir systems for separable input processes nonlinear systems can be approximated by linear time invariant lti models in many ways here lti models that are optimal approximations in the mean square error sense are analyzed a necessary and sufficient condition on the input signal for the optimal lti approximation of an arbitrary nonlinear finite impulse response nfir system to be a linear finite impulse response fir model is presented this condition says that the input should be separable of a certain order i e that certain conditional expectations should be linear for the special case of gaussian input signals this condition is closely related to a generalized version of bussgang s classic theorem about static nonlinearities it is shown that this generalized theorem can be used for structure identification and for the identification of generalized wiener hammerstein systems

beam element matrices derived from vlasov s theory of open thin walled elastic beams a uniform beam element of open thin walled cross section is studied under stationary harmonic end excitation an exact dynamic transcendentally frequency dependent 14 14 element stiffness matrix is derived from vlasov s coupled differential equations special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross section zero warping stiffness etc the dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices a static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given modal masses are evaluated a fortran program and a numerical example are included

the axial torsional vibration of pretwisted beams we investigate the coupled axial torsional vibration of pretwisted beams the equations of motion governing the extension torsion and cross sectional warping of pretwisted beams are derived from hamiltons principle and the common assumptions used to simplify the equations are carefully examined through scaling analysis inconsistencies in previous works such as the neglect of spatial and time derivatives of torsion in the lagrangian functional are remedied giving rise to fourth order terms in the equations of motion that are significant for higher harmonics furthermore scaling analysis of the governing equations yields a set of objective criteria for checking the validity of the frequently misused assumption that the warping function under pretwist is locally identical to that of a prismatic beam we show that this simplification is responsible for the common poor prediction of axial resonance frequencies for pretwisted beams

measuring a linear approximation to weakly nonlinear mimo systems the paper addresses the problem of preserving the same lti approximation of a nonlinear mimo multiple input multiple output system it is shown that when a nonlinear mimo system is modeled by a multidimensional volterra series periodic noise and random multisines are equivalent excitations to the classical gaussian noise in a sense that they yield in the limit as the number of the harmonics m the same linear approximation to the nonlinear mimo system this result extends previous results derived for nonlinear siso single input single output systems based upon the analysis of the variability of the measured frf frequency response function due to the presence of the nonlinearities and the randomness of the excitations a new class of equivalent input signals is proposed allowing for a lower variance of the nonlinear frf measurements while the same linear approximation is retrieved

the uniqueness of the inverse obstacle scattering problem with transmission boundary conditions abstract in this paper we consider the uniqueness of the interior wavenumber for the inverse obstacle scattering problem with transmission boundary conditions we show that the interior wavenumber is uniquely determined by the far field pattern

identification of nonlinear systems using polynomial nonlinear state space models in this paper we propose a method to model nonlinear systems using polynomial nonlinear state space equations obtaining good initial estimates is a major problem in nonlinear modelling it is solved here by identifying first the best linear approximation of the system under test the proposed identification procedure is successfully applied to measurements of two physical systems