an inverse method to compute equivalent forces on a structure based on sound power measurements when modelling the dynamic response of an existing structure to predict the effects of design modifications many types of forces are difficult to characterize e g those due to unsteady flows or acoustic excitation to model the forcing function in such cases a method is presented which solves for an equivalent forcing function based on sound power measurements the method assumes that the equivalent forcing function may be represented with a superposition of force distributions on a mode by mode basis i e there is one force distribution per eigenvalue with the shape of the eigenvector the method is applied to cases where the structure is lightly damped and has low modal density experimental results show that the method accurately predicts the effect of design changes on the structure s radiated sound power the accuracy of the method is sensitive to small differences between the experimental and theoretical natural frequencies and thus it is important to match the damped natural frequencies of the physical structure as accurately as possible

finite element interval analysis of external loads identified by displacement input with uncertainty a finite element formulation is proposed for the interval estimation of the nodal forces identified by displacement input with uncertainty the stiffness matrix of the structural system in problem of linear elastic body under static loading is assumed to be known and determinate this assumption enables us to derive the governing equation of the nodal forces to be identified with respect to the nominal displacement input from the stiffness equation based on the moore penrose generalized inverse solution of the unknown remnant displacements we assume that the uncertain errors involved in the nodal displacements obtained somehow by measurement and used as input are confined in a convex hull the effect of the uncertainty on the identified nodal forces is evaluated by the sensitivity analysis of the forces with respect to the uncertain displacements how to estimate the scatter of the identified nodal forces corresponding to the uncertain displacements confined in the convex hull is devised by means of the lagrange multiplier method the validity of the proposed method for identification and interval estimation of the nodal forces is shown by the numerical example of an elastic square plate in the plane stress state and subject to in plane loading

coefficient ideals in and blowups of a commutative noetherian domain abstract the ratliff rush ideal associated to a nonzero ideal i in a commutative noetherian domain r with unity is n 1 in 1 rin is r s b i where b i r i a p a i 0 p spec r i a is the blowup of i we observe that certain ideals are minimal or even unique in the class of ideals having the same associated ratliff rush ideal if r m is local quasi unmixed and analytically unramified and if i is m primary then we show that the coefficient ideal i k of i i e the largest ideal containing i whose hilbert polynomial agrees with that of i in the highest k terms is also contracted from a blowup b i k which is obtained from b i by a process similar to s2 ification this allows us to generalise the notion of coefficient ideas we investigate these ideas in the specific context of a two dimentional regular local ring observing the interaction of these notions with the zariski theory of complete ideals

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

estimation of a common effect parameter from sparse follow up data breslow 1981 biometrika 68 73 84 has shown that the mantel haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications for cohort studies however estimation of a common risk ratio or risk difference can be of greater interest under a binomial sparse data model the mantel haenszel risk ratio and risk difference estimators are consistent in sparse stratifications while the maximum likelihood and weighted least squares estimators are biased under poisson sparse data models the mantel haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent while the weighted least squares estimators are again biased similarly of the common rate difference estimators the weighted least squares estimators are biased while the estimator employing mantel haenszel weights is consistent in sparse data variance estimators that are consistent in both sparse data and large strata can be derived for all the mantel haenszel estimators

input forces estimation of beam structures by an inverse method an on line recursive inverse method to estimate the input forces of beam structures is presented the inverse method is based on the kalman filter and a recursive least squares algorithm the filter models the system dynamics in a linear set of state equations the state equations of the beam structures were constructed using the finite element method the practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses in the numerical experiments the cantilever beam was subjected to five types of input forces i e sinusoidal triangular impulse rectangular impulse a series of impulses and random the simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements

time domain identification of loads on plate like structures using an array of acoustic velocity sensors the fat force analysis technique method has been developped to identify loads on beams or plates from the knowledge of their flexural displacements the method is based on a local discretisation of the differential operator of the studied structure all derivatives of the displacement field are assessed at a given point from a finite difference scheme the estimation of the operator gives as an output the value of the force distribution up to now applications of the fat method have been made in the frequency domain scanning the studied structure with accelerometers or with a laser vibrometer and using phase references to get the phase relation between different points the aim of the present study is to show that the fat method allows to identify loads in the time domain this operation requires the simultaneous measurement of at least 13 points on the plate that can be realized without contact using an array of acoustic velocity sensors in the very near field of the plate the method has been app

measurement of structural intensity using boundary element method based nearfield acoustical holography the regularization method for measurement of structural intensity si using boundary element method bem based nearfield acoustical holography nah is proposed spatial derivatives of normal displacement are necessary to obtain the structural intensity the derivative operations amplify high wavenumber component of measurement noise and contaminate the measurement result of si to overcome this difficulty regularization method for measurement of si using fast fourier transform based nah has been introduced in this paper this regularization method is modified for the bem based nah the bem based nah avoids the aperture replication problem therefore measurement aperture for bem based nah can be set smaller than that for fft based nah the effectiveness of the proposed method is demonstrated by experiments

a poynting vector formulation for thin shells and plates and its application to structural intensity analysis and source localization part i theory this paper deals with a formulation of the poynting vector structural intensity for thin shells and plates and its application to structural intensity analysis and source localization the procedure begins with the insertion of a taylor series expansion of the displacement components about the middle surface of the shell directly into the three dimensional representation of the poynting vector from this representation an average power flow per unit length or equivalently an intensity resultant is derived whose form permits expressibility in terms of force and moment resultants the corresponding equations of continuity for energy are derived for both body and surface forces and the time integral of the net outflow is developed yielding a technique for source localization this technique offers a method for the determination of the structural intensity of thin elastic shells and plates and is successful for source localization

generalized mantel haenszel estimators for k 2 x j tables mickey and elashoff 1985 biometrics 41 623 635 gave an extension of mantel haenszel estimation to log linear models for 2 x j x k tables their extension yields two generalizations of the mantel haenszel odds ratio estimator to k 2 x j tables this paper provides variance and covariance estimators for these generalized mantel haenszel estimators that are dually consistent i e consistent in both large strata and sparse data and presents comparisons of the efficiency of the generalized mantel haenszel estimators

an improved method for the reconstruction of a distributed force acting on a vibrating structure indirectly reconstructing distributed forces from measured structural response is necessary when the direct measurement of these dynamic forces is not possible an improved method for reconstructing distributed forces is developed in this paper unlike the traditional modal method for force reconstruction the forcing spatial function is decomposed only over the known forcing region numerical simulations illustrate that when compared with the traditional modal method this new method tends to obtain better reconstruction results while requiring fewer basis functions a theoretical proof is provided to reveal the applicability and limitations of this new method it turns out that this approach like other inverse methods can also be an ill posed method to address this issue a regularization process is introduced to increase the inverse stability numerical results show that when the regularization process is applied to simulated response measurements that include noise the new method is able to reconstruct spatially distributed external forces with improved accuracy

a generalization of the mantel haenszel estimator of partial association for 2 x j x k tables summary a generalization of the mantel haenszel estimator of a common odds ratio for a series of 2 x 2 tables is proposed for the estimation of log linear partial association parameters for a series of 2 x j j 2 tables the assumption of no three way interaction among row column and stratifying variables is made two approximate covariance estimators are presented small sample properties of these estimators are investigated by simulation studies the results indicate that use of the proposed partial association technique produces estimates with negligible bias both covariance estimation techniques provide confidence intervals for functions of partial association parameters for example odds ratios or adjusted rates a test of no three way interaction results from these procedures

inverse aeroacoustic problem for a streamlined body ii accuracy of solutions previously established methods for performing the aeroacoustic inversion for a fiat plate airfoil are tested to determine their sensitivity to errors in both the far field input data and the mean flow input parameters the results of the sensitivity analysis for the input data show that the magnification of input error due to ill posedness can be controlled by optimal choices of the regularization parameter and the input data locations a similar sensitivity analysis of the effect of mean flow parameters mach number and reduced frequency shows strong dependence of the inverse process on these parameters in this case improvements in the reconstructions can be obtained by using input data from the midfield

the conception of structure borne sound based near field holography abstract a procedure for the projection of structure borne sound fields is introduced following the basic idea behind near field acoustic holography it is shown that the bending wave field of an infinite plate subjected to point force excitation can be reconstructed by means of fourier transform based wave field extrapolation all required information on the wave field is obtained by vibrational response measurement in the near field of the excitation using a circular geometry with a limited number of positions the procedure is verified both numerically and experimentally to very satisfying results the experiments indicate that the reconstruction at the source becomes erratic when standoff distances greater than half of the minimum wavelength under consideration are used reconstruction of the far field plate response is found to be less restrictive

integrally closed and componentwise linear ideals in a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is cohen macaulay in higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do we restrict our attention to 0 dimensional homogeneous ideals in polynomial rings r of arbitrary dimension we identify a class of integrally closed ideals the goto class mathcal g which is closed under product and it has a suitable unique factorization property ideals in mathcal g have a cohen macaulay associated graded ring if either they are monomial or dim r 3 our approach is based on the study of the relationship between the notions of integrally closed contracted full and componentwise linear ideals

reconstruction of distributed dynamic loads on an euler beam via mode selection and consistent spatial expression this paper presents a convenient and efficient approach to reconstruct two dimensional distributed dynamic loads on a damped thin elastic plate from its steady state dynamic response the approach is based on a mode selection method which comes from an idea that an optimal range of frequency and mode exists for dynamic load reconstruction as well as on the consistent spatial expression of the distributed dynamic loads the criterion for mode selection is derived theoretically a comparison between the method of truncated singular value decomposition tsvd and the method of mode selection demonstrates that the former is unstable while the latter is not only stable but robust with the proposed criterion the method of mode selection enables one to find an optimal range for load reconstruction provided that the error bounds of both parameters and objective are given or estimated and hence to make a balance between the reconstruction range and the error control

a strategy to identify exciting forces acting on structures the strategy for identifying the external forces acting on structures sketched by turco comput method appl mech eng 1998 165 291 306 is extended to the dynamic case starting from the measurement of the stress or strain history in a suitable number of points of the structure the exciting forces are reconstructed this inverse problem is tackled in the frequency domain by using the standard tools of computational mechanics along with a classical approach to treat ill conditioned problems some numerical results relating to pin jointed trusses are discussed in order to validate the proposed strategy copyright 2005 john wiley sons ltd

reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering the localization and the magnitude of acting steady states forces resulting from the dynamic response of a cylindrical shell are investigated the derivatives present in the equation of motion are expressed in terms of displacements using finite difference schemes displacements of the structure are introduced into the equation of motion in order to calculate the distribution of these forces numerical simulations show that when the force distribution is calculated using well defined displacements the exact position of the force is easily determined however when the displacements are mixed with uncertainties noise appears and the real force is relatively inaccurate in order to handle this instability in the inverse problem a regularization method based on signal processing techniques such as windowing and filtering in the spatial wavenumber domain should be performed numerical examples that illustrate the regularization process show that when the local filtering is applied to the force distribution calculated from noisy data reasonable results are obtained experiments are performed on a cylindrical shell in order to measure its velocities unfortunately using the displacements derived from measured velocities high sensitivity to the noise in the measurements is observed overall the experimental identification gives also good results when the same technique of filtering is applied to the force distribution

inverse aeroacoustic problem for a streamlined body i basic formulation the inverse aeroacoustic problem associated with a flat plate airfoil in unsteady compressible flow is formulated in terms of a fredholm integral equation of the first kind the feasibility of determining the unsteady pressure along the airfoil surface from the radiated acoustic signal is demonstrated it is shown that the hadamard conditions of existence and uniqueness of the inverse solution can be satisfied the third hadamard condition for the continuous dependence of the solution on the input acoustic data shows the problem to be ill posed the singular value decomposition method with regularization is used to treat the associated ill conditioned algebraic problem discretization and collocation techniques are used to represent the unsteady pressure on the airfoil both methods give very accurate reconstructions when perfect input data are used the collocation method requires only a small amount of input data either from the far field or the near field thus making it more suitable for applications

vibration source identification using corrected finite difference schemes abstract this paper addresses the problem of the location and identification of vibration excitations from the measurement of the displacement field of a vibrating structure it constitutes an improvement of the force analysis technique published several years ago the development is based on the use of the motion equation which is discretized by finite difference schemes approximating spatial derivatives of the displacement in a first instance the error due to this approximation is analytically calculated in the case of beams and the low pass filtering effect of the finite difference schemes in the wavenumber domain is shown this filter also contains singularities implying bias errors especially if the spacing between sensors is chosen in order to regularize the problem in a second instance a corrected value is applied to the classic schemes used in the force analysis technique which suppresses completely the singularities of the filter after the complete description of the corrected force analysis technique on beams the extension to plates is described where simulations with noisy data show the very good accuracy one can obtain without the requirement of an added regularization for the excitation identification

depth of fiber cones of ideals with almost minimal mixed multiplicity let r m be a cohen macaulay local ring of dimension d 0 i an m primary ideal with almost minimal mixed multiplicity such that depth g i d 1 we show that fm i has almost maximal depth i e depth fm i d 1

extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem abstract an improvement of the force analysis technique fat an inverse method of vibration is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate this method is a significant progress since the usual techniques of measurements with flush mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high moreover the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate this underlines the need to extract the acoustic part in this work numerical experiments are performed to solve both the direct and inverse problems of vibration the excitation is a turbulent boundary layer and combines the pressure field of the corcos model and a diffuse acoustic field these pressures are obtained by a synthesis method based on the cholesky decomposition of the cross spectra matrices and are used to excite a plate thus the application of the inverse problem fat that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation indeed the discretization of the inverse operator motion equation of the plate acts as a low pass wavenumber filter in addition this method is simple to implement because it can be applied locally no need to know the boundary conditions and measurements can be carried out on the opposite side of the plate without affecting the flow finally an improvement of fat is proposed it regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution this optimized fat in the case of the turbulent flow has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise

a non linear inverse vibration problem of estimating the external forces for a system with displacement dependent parameters the conjugate gradient method i e the iterative regularization method is used in an inverse non linear force vibration problem of estimating the unknown time dependent external forces in a damped system with the displacement dependent spring constant and damping coefficients the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements since the system parameters are functions of displacement the present study from a purely mathematical viewpoint is thus a genuine non linear inverse vibration problem the numerical simulations are performed to test the validity of the present algorithm by using different types of system parameters external forces and measurement errors results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses with a couple of second s cpu time at pentium iii 500 mhz pc

identification of external structural loads from measured harmonic responses abstract in many practical situations it is difficult to perform direct measurements or calculations of the external forces acting on an existing vibrating structure instead the structural response may than be measured and the position and magnitude of the exciting forces be calculated from the measured response unfortunately the results from this inverse process are often highly sensitive to noise in the measurements of the response and errors in the model of the structure the present study is focussed on this sensitivity under the assumption of a linear relation between the unknown harmonic force amplitudes and the response at discrete measurement positions a scalar measure of the sensitivity is suggested numerical examples that illustrate the sensitivity and its correlation to the proposed sensitivity measure are given the present sensitivity measure can be calculated for different candidate experimental configurations prior to any actual measurements and hence assist in the experimental design

flexural intensity measurement on finite plates using modal spectrum ideal filtering abstract flexural intensities on various plate like structures with arbitrary boundary conditions are calculated using measured and fem yielded mobility in doing so a two dimensional spatial fourier transform has been implemented along with a refined k spectral filtering concept intensity is decomposed into individual contributions from bending moments twisting moments and shear forces the source and energy sink localization and energy flow have been analyzed through these contributions the effect of reflections from the plate edges and that of the uncorrelated noise on the intensity are discussed it is shown that the width of the k filters may have a non negligible influence on the shape of the intensity field damping in the structure can efficiently control the edge reflections and therefore help to localize the energy sources and sinks a link has been found at certain excitation conditions between the radiated acoustic intensity and the active flexural intensity it is also observed that the classical method of studying the vibration transmission using vibration amplitude measurements does not reflect the transmitted vibration energy but rather provides information on non propagating reactive energy the fem study further explains some of the experimental observations and suggests the possibility of applying intensity to complex analytical models

a novel approach for distributed dynamic load reconstruction by space time domain decoupling abstract a novel inverse approach based on green s function method and orthogonal polynomial fitting technique is presented in this paper to reconstruct the distributed dynamic load acting on a structure this approach enables one to identify the time history and reconstruct the spatial distribution function separately it is first assumed in this paper that the distribution function and the time history of the distributed dynamic load are separable modal analysis proves the sameness of the form between the modal loads and the actual time history with the knowledge of corresponding green s functions and modal responses the modal loads are identified later approximating the spatial distribution function by a set of chebyshev orthogonal polynomials new distributed dynamic loads are constructed with each orthogonal polynomial performing as the spatial distribution function and the previously identified modal load acting as the time history fitting the modal loads the coefficients of each orthogonal polynomial are achieved and then the spatial distribution function recovered to overcome the intrinsic ill conditioned characteristic appropriate regularization methods are adopted in both the modal load identification and the distribution function reconstruction numerical examples demonstrate the validity and accuracy of the proposed method

generalized hilbert coefficients and northcott s inequality abstract let r be a cohen macaulay local ring of dimension d with infinite residue field let i be an r ideal that has analytic spread l i d satisfies the g d condition and the weak artin nagata property a n d 2 we provide a formula relating the length i n 1 j i n to the difference p i n h i n where j is a general minimal reduction of i p i n and h i n are respectively the generalized hilbert samuel polynomial and the generalized hilbert samuel function we then use it to establish formulas to compute the generalized hilbert coefficients of i as an application we extend northcott s inequality to non m primary ideals furthermore when equality holds we prove that the ideal i enjoys nice properties indeed if this is the case then the reduction number of i is at most one and the associated graded ring of i is cohen macaulay we also recover results of g colome nin c polini b ulrich and y xie on the positivity of the generalized first hilbert coefficient j 1 i our work extends that of s huckaba c huneke and a ooishi to ideals that are not necessarily m primary

the encounter of interval and probabilistic approaches to structural reliability at the design point abstract the consideration of uncertainties in structural analysis has traditionally been made in the field of structural reliability within the framework of classical probability theory in many cases however there is no sufficient probabilistic information to substantiate such an approach in recent years several non probabilistic methods have been proposed as alternatives one of them is the interval analysis oriented to estimate the range of variation of output structural variables given the ranges of the input ones the method however requires the use of special arithmetics which renders its application unpractical for structural analysis based on finite elements or other numerical techniques in this paper a monte carlo method that can be applied to probabilistic as well as to interval approaches to reliability analysis is proposed it is based on the optimal properties of the classical design point of probabilistic structural reliability in particular it is shown that the order statistics of the output variable is concealed in a plot defined by the design point vector this facilitates the selection of the relevant samples for either interval or probability based analysis the examples show that the desired interval of the response or the failure probability can be accurately estimated on such a basis the paper also discusses the use of monte carlo methods for both reliability and interval analysis from the point of view of the proposed representation

a finite element method for computation of structural intensity by the normal mode approach abstract a method for numerical computation of structural intensity in thin walled structures is presented the method is based on structural finite elements beam plate and shell type enabling computation of real eigenvalues and eigenvectors of the undamped structure which then serve in evaluation of complex response the distributed structural damping is taken into account by using the modal damping concept while any localized damping is treated as an external loading determined by use of impedance matching conditions and eigenproperties of the structure emphasis is given to aspects of accuracy of the results and efficiency of the numerical procedures used high requirements on accuracy of the structural response displacements and stresses needed in intensity applications are satisfied by employing the swept static solution which effectively takes into account the influence of higher modes otherwise inaccessible to numerical computation a comparison is made between the results obtained by using analytical methods and the proposed numerical procedure to demonstrate the validity of the method presented

an estimating equation approach for the analysis of case control studies with exposure measured at several levels liang gave an extension of the mantel haenszel estimating procedure for a common odds ratio to logistic regression models it is applicable to case control studies with multiple exposure levels which yield k 2 j tables this paper provides variance and covariance estimators which are consistent in both sparse data and large strata for liang s estimating functions in the k 2 j tables case and proposes an approximate confidence interval method for the common odds ratios

interpretation and estimation of summary ratios under heterogeneity of the several types of summary odds ratios in use in epidemiology only those proposed by mantel and haenszel and miettinen do not assume homogeneity constancy of stratum specific parameters under heterogeneity miettinen s estimators consistently estimate meaningful epidemiologic parameters whereas the asymptotic expectation of the mantel haenszel odds ratio varies according to irrelevant features of the sampling design although one can modify the mantel haenszel summary to overcome the latter problem one can also extend the miettinen estimators to sparse data and thus limit the use of mantel haenszel summaries to situations in which the homogeneity hypothesis is reasonable this paper provides formulae for the extended miettinen estimators and large sample variances and confidence limits for summary ratios under heterogeneity

the problem of vibration field reconstruction statement and general properties abstract the paper addresses the problem of reconstructing the vibration field of a structure or the acoustic field of a bounded fluid from limited data the problem relates to practical situations when there is a need to know the dynamic stress and displacement distribution over the entire structure e g for estimating its remaining service life but the vibration may be measured only on accessible parts of the structure surface in the paper this problem is mathematically formulated and its general properties solvability uniqueness and continuity are studied most attention is paid to the analysis of the error of reconstruction one of the main results obtained is the proof of existence of the optimal vibration model of the structure which renders minimum to the reconstruction error the application of the results to discrete systems is discussed

elementary methods of cohort analysis with several exposure levels this paper proposes an extension of the mantel haenszel rate ratio for the dichotomous exposure to the multiple exposure levels this extension is based on the unbiased estimating function approach and yields closed form mantel haenszel rate ratio estimators dually consistent variance and covariance estimators of the estimating functions are given and a quasi score based confidence interval for individual common rate ratio is provided a similar extension to the common rate difference case is also given

vibratory source identification by using the finite element model of a subdomain of a flexural beam abstract this paper proposes the identification of vibration excitations by an inverse method the use of the local operator of a structure for which the vibration field is obtained by measurements is investigated this method has already been developed on analytically known structures but there are as yet few applications the goal of this paper is to adapt the same technique by using an operator obtained with the finite element method rather than a discretised differential motion equation the first difficulty is the measurement of rotational degrees of freedom a concept analogous to an observation matrix enabling only the measurement of displacements is then proposed the method of extracting the operator on a part of the structure is also discussed two variants are proposed an operator with free boundary conditions and a truncated operator without boundary conditions the first permits identifying internal forces at the boundaries of the subdomain whereas the second ignores them in order to regularise the inverse method a tikhonov approach is used an important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results the possibility of an a priori force only assumption is then demonstrated and recommended after illustrations obtained from numerical simulations on beams an experimental validation is provided for a beam excited by a shaker where several signals are used giving several signal to noise ratios the results are discussed and compared to the force measured directly by a piezoelectric sensor

confidence limits for the common odds ratio based on the asymptotic distribution of the mantel haenszel estimator this paper proposes a new approximate confidence limit method for the common odds ratio based on the asymptotic distribution of the mantel haenszel estimator the proposed method provides easily computed limits and is applicable to both sparse data and large strata cases monte carlo experiments compare its performance with that of a method based on the asymptotic distribution of the log mantel haenszel odds ratio applications of the proposed method to the common risk and rate ratio cases are given

on computing the forces from the noisy displacement data of an elastic body this study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise vision based minimally intrusive force sensing using elastically deformable grasping tools is the motivation for undertaking this problem since this problem involves incomplete and inconsistent displacement force of ail elastic body it leads to an ill posed problem known as cauchy s problem in elasticity vision based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy therefore we use geometrically non linear modelling of the elastic body which was not considered by others who attempted to solve cauchy s elasticity problem before we present two methods to solve the problem the first method uses the pseudo inverse of an over constrained system of equations this method is shown to be not effective when the noise in the measured displacement data is high we attribute this to the appearance of spurious forces at regions where there should not be any forces the second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples the performance of the two methods is compared using seven numerical examples all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements an experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces

a two stage method for nonlinear inverse problems in this work we are interested in the solution of nonlinear inverse problems of the form f x y we consider a two stage method which is third order convergent for well posed problems combining the method with levenberg marquardt regularization of the linearized problems at each stage and using the discrepancy principle as a stopping criterion we obtain a regularization method for ill posed problems numerical experiments on some parameter identification and inverse acoustic scattering problems are presented to illustrate the performance of the method

review of force reconstruction techniques abstract an important engineering problem is the recovery of the input of a system given its output this is a difficult problem to solve in that it is often an ill defined problem such ill posedness is problematic since noise becomes very influential and results in inaccurate or non unique solutions to combat this ill posedness additional constraints are typically applied to redefine the problem leading to a well defined problem with a unique solution current input reconstruction methods span the spectrum of analysis and computation and we have grouped them into three categories direct regularization and probabilistic statistical each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem our primary interests lie in the behavior of mechanical systems and as such we have focused on the literature in these fields however applicability includes other fields with the same and similar governing equations

identification of stiffness and damping properties of plates by using the local equation of motion this paper deals with the identification of stiffness and damping properties of vibrating structures by an inverse method inspired from the force analysis technique fat the proposed approach uses a local equation of motion assumed a priori which provides a relative straightforward relationship between the displacement field and material properties the spatial derivatives of the displacement in the equation are calculated using finite differences as this operation amplifies measurement noise a regularization step is applied before solving the inverse problem a procedure is proposed to automatically adjust the level of regularization the method also allows one to identify local stiffness and damping on a heterogeneous structure illustrations for both homogeneous and heterogeneous cases are shown using simulated and measured displacement fields

hilbert coefficients of hilbert filtrations adic filtrations see 7 11 18 21 wx in the first section of this paper we extend most of the techniques of 4 w5 to the case of hilbert filtrations and by doing so we are also able toxoffer alternative simple proofs of some results of 7 wxin the second section thanks to the setting just described if

dynamic force identification based on enhanced least squares and total least squares schemes in the frequency domain identifying dynamic forces from structural responses is necessary when direct measurement of those dynamic forces is impossible using conventional means a common approach to address this problem is to determine the frequency response function frf matrix measure the structural responses and calculate the dynamic forces based on least squares ls scheme this approach has been proven to be effective in reducing the random errors that occur in structural response signals unfortunately the accuracy of this approach is often hindered by the inversion of an ill conditioned frf matrix at frequencies near the structural resonances to overcome this inversion instability two regularization filters namely the truncated singular value decomposition tsvd filter and the tikhonov filter are used in conjunction with the conventional ls scheme at specific frequencies here a criterion for applying these enhanced ls schemes is proposed to aid in determining when the increase in computational effort is better utilized furthermore a new ls form of the morozov s discrepancy principle is formulated to aid in selecting the optimum regularization parameter for these filters at each frequency the accuracy in using conventional ls tsvd based ls and tikhonov filter based ls schemes are compared analytically and numerically in this paper it is found that for small sized frf matrices the tikhonov filter based ls scheme tends to work better than the tsvd filter based ls scheme since these approaches can only deal with the random errors in the measured structural responses a total least squares tls scheme that can also address errors associated with the frf matrix is proposed in this research numerical simulations demonstrate that under certain conditions the tls scheme is more effective in reducing the impact of these errors

extended mantel haenszel estimating procedure for multivariate logistic regression models a class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case control studies it reduces to the well known mantel haenszel estimator when there is a single binary risk factor large sample properties of the solutions to the proposed estimating equations are established for two distinct situations efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered application of the proposed method to family data and longitudinal data where the conditional likelihood approach fails is discussed two examples from case control studies and one example from a study on familial aggregation are presented

a new regularization method for the dynamic load identification of stochastic structures for the dynamic load identification for stochastic structures ill posedness and randomness are main causes that lead to instability and low accuracy monte carlo simulation mcs method is a robust and effective random simulation technique for the dynamic load identification problems of stochastic structures however it needs large computational cost and is also inefficient for practical engineering applications because of the requirement of a large quantity of samples in order to improve its computational efficiency this paper proposes a novel computational algorithm for the dynamic load identification of stochastic structures first the newly developed algorithm transforms dynamic load identification problems for stochastic structures into equivalent deterministic dynamic load identification problems second a new regularization method is proposed to realize the deterministic dynamic load identification third the assessments of the statistics of identified loads are obtained based on statistical theory finally the stability and robustness of the proposed algorithm are well validated by two engineering examples it is demonstrated that the newly developed regularization method outperforms the traditional tikhonov regularization method in computational accuracy moreover the newly proposed algorithm can significantly improve the computational efficiency of mcs and is very stable and effective in solving the dynamic load identification for stochastic structures

regularization method for measurement of structural intensity using nearfield acoustical holography the regularization method for measurement of structural intensity using nearfield acoustical holography is proposed spatial derivatives of normal displacement are necessary to obtain the structural intensity the derivative operations amplify high wave number components of measurement noise therefore the estimation of an appropriate wave number filter is crucial for implementation of the measurement of structural intensity in conventional methods this wave number filter is determined from the flexural wavelength and the same wave number filter is applied to obtain all spatial derivatives as a result structural intensity obtained from the pressure hologram whose signal to noise ratio is low is seriously contaminated by the noise to overcome this difficulty regularization theory is applied to determine the appropriate wave number filter for each order of derivatives the effectiveness of the proposed method is demonstrated by experiments

graded rings associated with contracted ideals the study of the ideals in a regular local ring r m of dimension 2 has a long and important tradition dating back to the fundamental work of zariski zs more recent contributions are due to several authors including cutkosky huneke lipman rees sally and teissier among others see c1 c2 h hs l lt r one of the main result in this setting is the unique factorization theorem for complete i e integrally closed ideals proved originally by zariski zs theorem 3 appendix 5 it asserts that any complete ideal can be factorized as a product of simple complete ideals in a unique way up to the order of the factors by definition an ideal is simple if it cannot be written as a product of two proper ideals another important property of a complete ideal i is that its reduction number is 1 which in turns implies that the associated graded ring gri r is cohen macaulay and its hilbert series is well understood this is due to lipman and teissier lt see also hs the class of contracted ideals plays an important role in the original work of zariski as well as in the work of huneke h an ideal i of r is contracted if i r ir m x for some x m m2 any complete ideal is contracted but not the other way round the associated graded ring gri r of a contracted ideal i need not be cohen macaulay and its hilbert series can be very complicated

sequential reconstruction of driving forces from nonlinear nonstationary dynamics abstract this paper describes a functional analysis based method for the estimation of driving forces from nonlinear dynamic systems the driving forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system the proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics we derive the estimator conditioned on the differentiability of the unknown system s mapping and smoothness of the driving force the proposed algorithm is an adaptive sequential realization of the blind prediction error method where the basic idea is to predict the observables and retrieve the driving force from the prediction error our realization of this idea is embodied by predicting the observables one step into the future using a bank of echo state networks esn in an online fashion and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages the adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving forces accurately which are illustrated by simulations logistic and moran ricker maps are studied in controlled experiments exemplifying chaotic state and stochastic measurement models the algorithm is also applied to the estimation of a driving force from another nonlinear dynamic system that is stochastic in both state and measurement equations the results are judged by the posterior cramer rao lower bounds the method is finally put into test on a real world application extracting sun s magnetic flux from the sunspot time series