a monte carlo based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type random set theory is a useful tool to quantify lower and upper bounds on the probability of the occurrence of events given uncertain information represented for example by possibility distributions probability boxes or dempster shafer structures among others in this paper it is shown that the belief and plausibility estimated by dempster shafer evidence theory are basically approximations by riemann stieltjes sums of the integrals of the lower and upper probability employed when using infinite random sets of indexable type in addition it is shown that the evaluation of the lower and upper probability is more efficient if it is done by pseudo monte carlo strategies this discourages the use of dempster shafer evidence theory and suggests the use of infinite random sets of indexable type specially in high dimensions not only because the initial discretization step of the basic variables is not required anymore but also because the evaluation of the lower and upper probability of events is much more efficient using the different techniques for multidimensional integration like monte carlo simulation

sparse second moment analysis for elliptic problems in stochastic domains we consider the numerical solution of elliptic boundary value problems in domains with random boundary perturbations assuming normal perturbations with small amplitude and known mean field and two point correlation function we derive using a second order shape calculus deterministic equations for the mean field and the two point correlation function of the random solution for a model dirichlet problem which are 3rd order accurate in the boundary perturbation size using a variational boundary integral equation formulation on the unperturbed nominal boundary and a wavelet discretization we present and analyze an algorithm to approximate the random solution s mean and its two point correlation function at essentially optimal order in essentially mathcal o n work and memory where n denotes the number of unknowns required for consistent discretization of the boundary of the nominal domain

comparison of dynamic response of structures with uncertain but bounded parameters using non probabilistic interval analysis method and probabilistic approach abstract now by combining the finite element analysis and interval mathematics a new non probabilistic set theoretical models that is interval analysis method is being developed in scientific and engineering communities to predict the variability or uncertainty resulting from the unavoidable scatter in structural parameters and the external excitations as an alternative to the classical probabilistic approaches interval analysis methods of uncertainty were developed for modeling uncertain parameters of structures in which bounds on the magnitude of uncertain parameters are only required not necessarily knowing the probabilistic distribution densities instead of conventional optimization studies where the minimum possible response is sought here an uncertainty modeling is developed as an anti optimization problem of finding the least favorable response and the most favorable response under the constraints within the set theoretical description in this study we presented the non probabilistic interval analysis method for the dynamical response of structures with uncertain but bounded parameters under the condition of the interval vector which contains the uncertain but bounded parameters determined from probabilistic statistical information or stochastic sample test through comparing between the non probabilistic interval analysis method and the probabilistic approach in the mathematical proof and the numerical examples we can see that the region of the dynamical response of structures with uncertain but bounded parameters obtained by the interval analysis method contains that produced by the probabilistic approach in other words the width of the maximum or upper and minimum or lower bounds on the dynamical responses yielded by the probabilistic approach is tighter than those produced by the interval analysis method this kind of results is coincident with the meaning of the probabilistic theory and interval mathematics

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

reverse order laws for the generalized strong drazin inverses various kinds of the reverse order laws for the strong drazin inverse are characterized in a ring then we define the generalized strong drazin inverse in a banach algebra and present similar results related to reverse order laws for this new inverse

biharmonic maps from r 4 into a riemannian manifold for a domain r 4 and a compact riemannian manifold n r k without boundary if u w 2 2 n is an extrinsic or intrinsic respectively biharmonic map then u c n

partial orders based on core nilpotent decomposition abstract in this paper we study partial orders in terms of the core nilpotent decomposition we derive some characterizations of the c n partial ordering create a new partial ordering the g drazin partial ordering which is a generalization of c n partial ordering and give some properties and characterizations of the g drazin partial ordering

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

contrasting probabilistic and anti optimization approaches in an applied mechanics problem probabilistic and non probabilistic anti optimization analyses of uncertainty are contrasted in this study specifically the comparison of these two competing approaches is conducted for an uniform column with initial geometric imperfection subjected to an impact axial load the reliability of the column is derived for the cases when the initial imperfections posses either a uniform probability density b truncated exponential density or c generic truncated probability density the problem is also analyzed in the context of an interval analysis it is shown that in the most important near unity reliability range these two approaches tend to each other since the interval analysis constitutes a much simpler procedure than the probabilistic approach it is argued that the former is advantageous over the latter in some circumstances

an algorithm to check the nonnegativity of singular systems in the literature an important class of generalized inverse matrices corresponds to the group inverse that is matrices of index 1 recently the nonnegativity of a singular system has been applied to different fields in this paper an algorithm to check the nonnegativity of a singular linear control system of index 1 is presented to this purpose the nonnegativity of this kind of systems is characterized using a block partition of the original matrices in this way we can work with matrices having smaller sizes and keeping the original information finally numerical examples illustrating the obtained results are shown

stationary biharmonic maps from rm into a riemannian manifold for m 5 we prove that a stationary extrinsic or intrinsic respectively biharmonic map u w2 2 n from rm into a riemnanian manifold n is smooth away from a closed set of m 4 dimensional hausdorff measure zero 2003 wiley periodicals inc

nonlinear partial differential equations of fourth order under mixed boundary conditions solutions to nonlinear partial differential equations of fourth order are studied boundary regularity is proved for solutions that satisfy mixed boundary conditions various geometric situations including so called triple points are considered regularity is measured in sobolev slobodeckii spaces and the results are sharp in this scale the approach is based on the use of a first order difference quotient method

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

probabilistic interval reliability of structural systems the probabilistic reliability approach is the most widely used method for reliability analysis the recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model it is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability in this study we introduce the interval approach into the conventional reliability theory we present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables this approach is a combination of the two techniques namely the classical reliability theory and the interval analysis in the end of this paper we show the feasibility of the proposed approach through two examples of the truss systems

convex models and interval analysis method to predict the effect of uncertain but bounded parameters on the buckling of composite structures a new non probabilistic set theoretical models that is interval analysis method is developed in this study to predict the variability or uncertainty in buckling loads of composite structures resulting from the unavoidable scatter in structural parameters by mathematically analyzing and proving the width of the upper and lower bounds on the critical buckling loads calculated by the interval analysis method is sharper than those that are obtained by convex models method moreover the interval analysis method has less computational cost than convex models method comparison between convex models and interval analysis method is performanced through numerical examples for the specific cases considered the results of numerical examples indicate that uncertainties in structural parameters have significant effect on the critical buckling loads of composite structures

the drazin inverses of sum and difference of idempotents in this note the drazin inverses of sum and difference of idempotents on a hilbert space are established under some conditions

nonnegative matrices a with aa 0 in this paper we obtain a decomposition of nonnegative matrices a such that aa 0 we then use this characterization to obtain the previous results known for nonnegative matrices a with a 3 0 we also consider nonnegative matrices a with a a 2 0

relationships between different sets involving group and drazin projectors and nonnegativity abstract this paper deals with nonnegativity of matrices and their group or drazin inverses firstly the nonnegativity of a square matrix a its group inverse a and its group projector aa is used to define different sets for which relationships and characterizations are given next an extension of the previous results for index greater than 1 is presented similar sets are introduced and studied for drazin inverses and drazin projectors considering the core nilpotent decomposition in addition the results are applied to study the l drazin periodic matrices for l 1

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

reanalysis of linear and nonlinear structures using iterated shanks transformation reanalysis of structures is a common task in two important fields of structural engineering namely optimization and reliability it implies the solution of the kinematic equations for each new set of data in order to simplify this task several approximate methods have been developed in this paper a simple method for reanalysis applicable to either linear or nonlinear structures is proposed it is based on the improvement of the neumann resolvent series which diverges beyond a certain radius by means of the iterated shanks transformation the method is compared with two relevant proposals intended to improve the convergence of the neumann series namely the pade series and the scaled approximation methods the accuracy and simplicity of the proposed method is demonstrated through some examples concerning linear and nonlinear structures

hybrid high dimensional model representation for reliability analysis abstract this paper presents a new probabilistic method based on hybrid high dimensional model representation hhdmr for predicting the failure probability of structural and mechanical systems subject to random loads material properties and geometry high dimensional model representation hdmr is a general set of quantitative model assessment and analysis tools for capturing the high dimensional relationships between sets of input and output model variables it is a very efficient formulation of the system response if higher order variable cooperative effects are weak and if the response function is dominantly of additive nature allowing the physical model to be captured by the first few lower order terms but if multiplicative nature of the response function is dominant then all right hand side components of hdmr must be used to be able to obtain the best result however if hdmr requires all components which means 2 n number of components to get a desired accuracy making the method very expensive in practice then factorized hdmr fhdmr can be used but in most cases the limit state performance function has neither additive nor multiplicative nature rather it has an intermediate nature this paper presents a new hhdmr based approximation for the limit state performance functions having an intermediate nature the proposed approximation of an implicit limit state performance function includes both hdmr and fhdmr expansions through a hybridity parameter as an alternative to the conventional methods for reliability analysis which are very computationally demanding when applied in conjunction with complex finite element models this study aims to assess how accurately and efficiently hhdmr technique can capture complex model output uncertainty once the approximate form of the original implicit limit state performance function is defined the failure probability can be obtained by statistical simulation results of six numerical examples involving mathematical functions and structural solid mechanics problems indicate that the failure probability obtained using hhdmr based approximation of an implicit limit state performance function provides significant accuracy when compared with the conventional monte carlo method while requiring fewer original model simulations

interval analysis of structures with uncertain but bounded axial stiffness abstract a method to evaluate the static response of structures with interval axial stiffnesses is proposed the procedure overcomes the drawbacks arising in traditional interval analysis due to dependency phenomenon the inversion of the interval stiffness matrix is pursued by means of a novel approximate relationship based on an interval valued sherman morrison woodbury formula numerical results on truss and frame structures evidence the accuracy and the effectiveness of the proposed approach to evaluate bounds of displacements and internal forces

reconstruction of radial dirac operators we study the inverse spectral problem of reconstructing the potential of radial dirac operators acting in the unit ball of r3 for each one dimensional partial dirac operator corresponding to a nonzero angular momentum we give a complete description of the spectral data eigenvalues and suitably defined norming constants prove existence and uniqueness of solutions to the inverse problem and present the reconstruction algorithm