splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

interval process model and non random vibration analysis abstract this paper develops an interval process model for time varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate by using the interval process model to describe a time varying uncertain parameter only its upper and lower bounds are required at each time point rather than its precise probability distribution which is quite different from the traditional stochastic process model a correlation function is defined for quantification of correlation between the uncertain but bounded variables at different times and a matrix decomposition based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis more importantly based on the interval process model a non random vibration analysis method is proposed for response computation of structures subjected to time varying uncertain external excitations or loads the structural dynamic responses thus can be derived in the form of upper and lower bounds providing an important guidance for practical safety analysis and reliability design of structures finally two numerical examples and one engineering application are investigated to demonstrate the feasibility of the interval process model and corresponding non random vibration analysis method

nonlinear modeling of time series using multivariate adaptive regression splines mars abstract multivariate adaptive regression splines mars is a new methodology due to friedman for nonlinear regression modeling mars can be conceptualized as a generalization of recursive partitioning that uses spline fitting in lieu of other simple fitting functions given a set of predictor variables mars fits a model in the form of an expansion in product spline basis functions of predictors chosen during a forward and backward recursive partitioning strategy mars produces continuous models for high dimensional data that can have multiple partitions and predictor variable interactions predictor variable contributions and interactions in a mars model may be analyzed using an anova style decomposition by letting the predictor variables in mars be lagged values of a time series one obtains a new method for nonlinear autoregressive threshold modeling of time series a significant feature of this extension of mars is its ability to produce models with limit cycles when modeling time series data that

error probability bounds for nuclear detection a collection of static and mobile radiation sensors is tasked with deciding within a fixed time interval whether a moving target carries radioactive material formally this is a problem of detecting weak time inhomogeneous poisson signals target radiation concealed in another poisson signal naturally occurring background radiation each sensor locally processes its observations to form a likelihood ratio which is transmitted once at the end of the decision interval to a fusion center the latter combines the transmitted information to optimally in the neyman pearson sense decide whether the measurements contain a radiation signal or just noise we provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection which are used to design threshold tests without the need for computationally intensive monte carlo simulations these analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection the network reconfigures itself in response to the target motion to allow more accurate collective decisions within the given time interval the approach is illustrated in numerical simulations and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser

correlation analysis of non probabilistic convex model and corresponding structural reliability technique compared with the probability approach the non probabilistic convex model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters and whereby makes the reliability analysis very convenient and economical in this paper we attempt to propose and create a correlation analysis technique mathematically for the non probabilistic convex model and based on it develop an effective method to construct the multidimensional ellipsoids on the uncertainty a marginal convex model is defined to describe the variation range of each uncertain parameter and a covariance is defined to represent the correlation degree of two uncertain parameters for a multidimensional problem the covariance matrix and correlation matrix can be created through all marginal convex models and covariances based on which the required ellipsoid on the uncertainty can be conveniently achieved by combining the correlation analysis technique and the reliability index approach a non probabilistic reliability analysis method is also developed for uncertain structures six numerical examples are presented to demonstrate the effectiveness of the present method

interval number and fuzzy number linear programmings abstract in this paper we focus on two kinds of linear programmings with fuzzy numbers they are called interval number and fuzzy number linear programmings respectively the problems of linear programmings with interval number coefficients are approached by taking maximum value range and minimum value range inequalities as constraint conditions reduced it into two classical linear programmings and obtained an optimal interval solution to it the problems of fuzzy linear programming with fuzzy number coefficients are approached in two ways i e fuzzy decisive set approach and interval number linear programming approach for several membership levels finally we gave the numerical solutions of the illustrative examples

trust region model management in multidisciplinary design optimization a common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques the use of approximation strategies is designed to reduce the number of detailed costly computer simulations required during optimization while maintaining the pertinent features of the design problem this paper overviews the current state of the art in model management strategies for approximate optimization model management strategies coordinate the interaction between the optimization and the fidelity of the approximation models so as to ensure that the process converges to a solution of the original design problem approximations play an important role in multidisciplinary design optimization mdo by offering system behavior information at a relatively low cost most approximate mdo strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence the move limits or trust region are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information in order to insure convergence of the sequence of approximate optimizations to a karush kuhn tucker solution a trust region model management or move limit strategy is required in this paper recent developments in approximate mdo strategies and issues of trust region model management in mdo are reviewed

interval k l expansion of interval process model for dynamic uncertainty analysis abstract the interval process model describes a time variant or dynamic uncertain parameter by the upper and lower bounds rather than the precise probability distribution at each time point providing an effective structural dynamic uncertainty quantification model with insufficient sample information by reference to the karhunen loeve k l expansion for stochastic process and random field models a novel expansion method for the interval process model namely the interval k l expansion is proposed in this work the interval k l expansion describes the continuous uncertainty of the interval process in time domain by superposition of infinite deterministic time related functions with uncorrelated interval coefficients which makes the interval process model much more convenient to use by introducing a splicing technique the interval k l expansion method for multiple correlated interval processes is also presented based on the interval k l expansion the vibration of structures subject to interval process excitations is analyzed where the analytic formulation of dynamic response bounds for linear elastic systems and continuum structures are derived finally several numerical examples are investigated to demonstrate the effectiveness of the proposed method

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

higher order failure probability calculation using nonlinear approximations use of approximations for calculating the structural failure probability under uncertainties is a necessary aspect but efficient use of suitable approximations at different stages of reliability prediction and design makes this valuable tool practical for many large scale structures the objective of this paper is to address the modern approximation concepts and their utility in structural reliability estimation emphasis is placed on building the higher order approximations using intervening variables to closely represent the nonlinear limit state functions the most probable failure point mpp search can be carried either in x space or u space for a wide variety of random variable distributions several test problems with highly nonlinear performance functions are used to demonstrate the accuracy of the proposed method

burmann expansion and test for additivity summary we propose a lagrange multiplier test for additivity based on the btirmann expansion of a conditional mean function the asymptotic null distribution of the test is shown to be x2 under some regularity conditions in contrast the lagrange multiplier test proposed by chen et al 1995 is based on the volterra expansion of the conditional mean function we discuss some desirable advantages of the bt rmann expansion over the volterra expansion for nonlinear time series modelling we also reported an empirical study which shows that in terms of empirical power the lagrange multiplier test motivated by the biirmann expansion outperforms the test of chen et al 1995 for the cases for which the lagrange multiplier test is designed for other cases for which none of the tests is specifically designed the empirical powers of the two tests are comparable finally we illustrated the use of the lagrange multiplier test with a blowfly experimental system

nonprobabilistic convex theoretic modeling of scatter in material properties nonprobabilistic convex modeling of uncertain material properties for viscoelastic structures is developed in this paper in particular the problem of forced vibrations of viscoelastic beams is studied first the analytic solution by inman is generalized for a deterministic set of variables describing material properties next these variables are treated as varying in a solid ball in the four dimensional space thus modeling the scatter in material properties the least favorable response needed for the design of the structure is determined

stability of elastic bars on uncertain foundations using a convex model a method is presented for evaluating the buckling load of weightless prismatic rigid bars resting on uncertain foundations which are modeled using linear extensional elastic springs the uncertainty in the spring elements is expressed in terms of a nonprobabilistic convex model an ellipsoidal bound is used which defines the uncertainty of the foundation in terms of a size parameter and the deviations of the elastic spring constants from their nominal values the size parameter represents the size of the ellipsoid and is analogous to the standard deviation magnitude in probabilistic analyses the semiaxes of the ellipsoid are the deviations of the foundation spring constants from their nominal values and they determine the shape of the ellipsoid a first order analysis shows that the reduction in the buckling load when uncertainty in the foundation s spring stiffnesses is present is a linear function of the size parameter and a nonlinear function of the semiaxes of the uncertainty ellipsoid for the same uncertainty in the spring elements different reductions in the buckling load result for beams with multimode buckling

linear programming with fuzzy objectives abstract this paper presents a new method for solving linear programming problems with fuzzy parameters in the objective function to determine a compromise solution the authors do not reduce the set of infinitely many objective functions to a single compromise objective function as done in classical deterministic or stochastic procedures here the problem is only reduced to a few extreme objective functions the information contained in the membership functions can be used to any extent by a method called level related pair formation moreover if different level sets are considered the stability of the optimal solution can be tested

identification of non linear additive autoregressive models summary we propose a lag selection method for non linear additive autoregressive models that is based on spline estimation and the bayes information criterion the additive structure of the autoregression function is used to overcome the curse of dimensionality whereas the spline estimators effectively take into account such a structure in estimation a stepwise procedure is suggested to implement the method proposed a comprehensive monte carlo study demonstrates good performance of the method proposed and a substantial computational advantage over existing local polynomial based methods consistency of the lag selection method based on the bayes information criterion is established under the assumption that the observations are from a stochastic process that is strictly stationary and strongly mixing which provides the first theoretical result of this kind for spline smoothing of weakly dependent data

optimum waveform signal sets with amplitude and energy constraints it is desirable to choose the waveforms making up a signaling alphabet so that they are maximally separated one from another this problem is considered in the space of square integrable functions for signals which have finite duration and are constrained in the ranges of their values as well as in energy corresponding to each of the following cases we establish sharp bounds for the minimum distance and for the average distance between elements of a fixed size signal set and construct sets of signals that attain both bounds simultaneously begin list item em case a energy constraint only the average energy of the waveforms in the signal set is at most sigma where 0 leq sigma item em case b energy and peak amplitude constraints the average energy of the waveforms in the signal set is leq sigma 0 leq sigma and the absolute value of each waveform is at most 1 item em case c energy and value constraints the average energy of the waveforms in the signal set is at most b 2 sigma a 2 1 sigma and each waveform takes values in the set a b where 0 leq a and 0 leq sigma leq 1 end list cases a and b are applicable to signal design for communication in channels with additive noise say gaussian and case c is applicable to signal design for optical channels where the signal represents the intensity of a photon stream the general character of the results is that the minimum distance behaves like gamma sigma in cases a and b and like gamma sigma 1 sigma in case c with gamma a suitable constant

nonparametric identification of nonlinear time series selecting significant lags abstract in this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series the procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series the procedure is illustrated by simulations and sunspot data lynx data and blowfly data are analyzed it is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model

optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval an optimization method for uncertain structures is suggested based on convex model and a satisfaction degree of interval in the investigated problem the uncertainty only exists in constraints convex model is used to describe the uncertainty in which the intervals of the uncertain parameters are only needed not necessarily to know the precise probability distributions a satisfaction degree of interval which represents the possibility that one interval is smaller than another is employed to deal with the uncertain constraints based on a predetermined satisfaction degree level the uncertain constraints are transformed to deterministic ones and the transformed optimization problem can be solved by traditional optimization methods for complex structural problems that the optimization model cannot be expressed in an explicit form the interval analysis method is adopted to calculate the intervals of the constraints efficiently and whereby eliminate the optimization nesting two numerical examples have been presented to demonstrate the efficiency of the suggested method

a new interval pattern analysis method of array antennas based on taylor expansion in this communication a new taylor expansion based interval pattern analysis method is developed to predict the impact of the small excitation amplitude uncertainty on the radiated array pattern the dependence problem of the classical interval arithmetic which may lead to overestimation of performance intervals is addressed in this communication the proposed method approximates by approximating the antenna power values to the first order with respect to the uncertain amplitude the new method is simpler and can produce more accurate bounds of the antenna pattern and the pattern features than the existing techniques several representative numerical examples are investigated to demonstrate the validity and efficiency of the proposed method

a nonlinear interval number programming method for uncertain optimization problems in this paper a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints based on an order relation of interval number the uncertain objective function is transformed into two deterministic objective functions in which the robustness of design is considered through a modified possibility degree the uncertain inequality and equality constraints are changed to deterministic inequality constraints the two objective functions are converted into a single objective problem through the linear combination method and the deterministic inequality constraints are treated with the penalty function method the intergeneration projection genetic algorithm is employed to solve the finally obtained deterministic and non constraint optimization problem two numerical examples are investigated to demonstrate the effectiveness of the present method

nonparametric transfer function models in this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between input and output time series the transfer function is smooth with unknown functional forms and the noise is assumed to be a stationary autoregressive moving average arma process the nonparametric transfer function is estimated jointly with the arma parameters by modelling the correlation in the noise the transfer function can be estimated more efficiently the parsimonious arma structure improves the estimation efficiency in finite samples the asymptotic properties of the estimators are investigated the finite sample properties are illustrated through simulations and one empirical example

response surface approximations for structural optimization response surface methodology can be used to construct global and midrange approximations to functions in structural optimization since structural optimization requires expensive function evaluations it is important to construct accurate function approximations so that rapid convergence may be achieved in this paper techniques to find the region of interest containing the optimal design and techniques for finding more accurate approximations are reviewed and investigated aspects considered are experimental design techniques the selection of the best regression equation intermediate response functions and the location and size of the region of interest standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size while the selection of a larger number of points is not necessarily cost effective in a further attempt to improve efficiency different regression models were investigated the results indicate that the use of the two methods investigated does not significantly improve the results finding an accurate global approximation is challenging and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space 1998 john wiley sons ltd

time variant random interval natural frequency analysis of structures abstract this paper presents a new robust method namely unified interval chebyshev based random perturbation method to tackle hybrid random interval structural natural frequency problem in the proposed approach random perturbation method is implemented to furnish the statistical features i e mean and standard deviation and chebyshev surrogate model strategy is incorporated to formulate the statistical information of natural frequency with regards to the interval inputs the comprehensive analysis framework combines the superiority of both methods in a way that computational cost is dramatically reduced this presented method is thus capable of investigating the day to day based time variant natural frequency of structures accurately and efficiently under concrete intrinsic creep effect with probabilistic and interval uncertain variables the extreme bounds of the mean and standard deviation of natural frequency are captured through the embedded optimization strategy within the analysis procedure three particularly motivated numerical examples with progressive relationship in perspective of both structure type and uncertainty variables are demonstrated to justify the computational applicability accuracy and efficiency of the proposed method

dynamic adaptive partitioning for nonlinear time series summary we propose a dynamic adaptive partitioning scheme for nonparametric analysis of stationary nonlinear time series it yields estimates of the whole probability distribution of the underlying process we use information from past values to construct adaptive partitioning in a dynamic fashion which is then different from the more common static schemes in the regression set up the idea of dynamic partitioning is new we make it constructive by an approach based on quantisation of the data and adaptively modelling partition cells with a parsimonious markov chain the methodology is formulated in terms of a new model class the so called quantised variable length markov chains it is a new extension of finite valued variable length markov chains to processes with values in rd we discuss estimation explore asymptotic properties of the new method and give some numerical results which reflect the finite sample behaviour

robust design of non linear structures using optimization methods abstract the robust design of non linear structures with path dependent response is stated as a two criteria optimization problem and is solved by the method of mathematical programming to this end the perturbation technique is applied in conjunction with the incremental loading procedure for the response moment analysis of path dependent non linear structural systems with random parameters furthermore the sensitivities of mean and variance of the structural performance function are evaluated using direct differentiation in the framework of perturbation based stochastic finite element analysis by introducing a weighting factor in the compound objective resp desirability function and feasibility indices in the constraints the mathematical model of structural robust design problem is formulated and is solved with a gradient based algorithm numerical examples demonstrate the applicability of the presented method

interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming abstract the modern trend in operations research methodology deserves modelling of all relevant vague or uncertain information involved in a real decision problem generally vagueness is modelled by a fuzzy approach and uncertainty by a stochastic approach in some cases a decision maker may prefer using interval numbers as coefficients of an inexact relationship as a coefficient an interval assumes an extent of tolerance or a region that the parameter can possibly take however its use in the optimization problems is not much attended as it merits this paper defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment on the basis of a comparative study on ordering interval numbers inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined a numerical example is also given

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

an interval algorithm for uncertain dynamic stability analysis abstract analysis on the stability of dynamic systems is a very important field in structural elasticity theory for possible engineering situations where the system parameters are uncertain but bounded the propagation from the initial uncertainties of parameters to the consequent uncertainty of dynamic stability of structure is elaborately investigated by interval analysis for the first time the interval dynamic stability issue is studied through the column structure as a generalized interval eigenvalue problem and an analytic theorem is rigorously derived and numerically verified for solving the generalized interval eigenvalue problem moreover to avoid the exaggeration on actual bounds of solution an effective approach is established to limit the dependency phenomenon in the interval dynamic stability analysis the interval relationships of the excitation parameter and the critical load frequency with five types of system parameters are further bridged according to the interval arithmetic to propose a three stage interval scheme for evaluating the effects of interval system parameters on the dynamic stability of structures numerical studies demonstrate that the uncertainty of the constant part of load influences the boundaries of principal instability region much more than that of the variable part of load within all structural parameters the uncertainty of column length has the most effect on the boundaries which could make the critical frequency of load be magnified about ten times the uncertainty of parameter in particular if all the system parameters are interval with an identical uncertainty degree the uncertainty of parameter would be propagated in the system of dynamic stability and enlarged as high as 20 times the uncertainty of parameter consequently the impacts of parameter uncertainties on the dynamic stability of structures are fairly significant

a sequential nonlinear interval number programming method for uncertain structures a sequential nonlinear interval number programming sninp method is suggested to deal with the uncertain optimization problems a general uncertain optimization model is investigated in which the objective function and constraints are both nonlinear and uncertain a nonlinear interval number programming ninp method is employed to transform the uncertain optimization problem into a deterministic two objective optimization problem then using the linear combination method and the constraint penalty function method a deterministic single objective and non constraint optimization problem is formulated in terms of a penalty function combining this ninp method with a modified approximation management framework amf an efficient sninp method is then constructed at each iterative step an approximation optimization problem is created based on the latin hypercube design lhd and the quadratic polynomial response surface approximation rsa and it can then be solved by the ninp method efficiently the trust region method is used to manage the sequence of the approximation optimization problems based on a reliability index an efficient method is suggested to calculate the actual penalty function and whereby the reliability index and based on it the current design space can be updated two numerical examples are presented to demonstrate the effectiveness of the present method

interval field model and interval finite element analysis uncertain parameters with inherent spatial variability are commonly encountered in engineering modeling of this kind of spatial uncertainty plays a fundamental role in structural uncertainty analysis which provides a necessary basis for subsequent uncertainty propagation through the system an interval field model for quantification of spatial uncertain parameters is proposed by which only the upper and lower bounds of the spatial uncertain parameters rather than their precise probability distributions are required the dependency can be fully considered by the proposed interval field model with the information of dependency an interval k l expansion is presented as a combination of deterministic functions with uncorrelated standard interval variables through which the continuous spatial interval field with dependency can be expressed only by very limited intervals necessary mathematical illustrations are provided for the proposed interval field model and the interval k l expansion the sampling method for the interval field model is given providing a robust numerical analysis basis for subsequent structural uncertainty analysis when the interval field model is applied in finite element analysis of structures with spatial uncertain parameters the non deterministic equilibrium equations with interval factors is then formulated the mcs method and the perturbation method are developed for solution of the derived interval equilibrium equations the feasibility and validity of the proposed interval field model and corresponding interval finite element methods are verified by numerical examples where the upper and lower bounds of the responses such as the displacements and the stresses of structures with spatial uncertain parameters are computed and compared

additivity tests for nonlinear autoregression summary additivity is commonly used in the statistical literature to simplify data analysis especially in analysis of variance and in multivariate smoothing in this paper we propose three procedures for testing additivity in nonlinear time series analysis the first procedure combines some smoothing techniques with analysis of variance the second is a lagrange multiplier test using nonparametric estimation and the third is a permutation test which uses smoothing techniques to obtain the test statistic and its reference distribution we investigate properties of the proposed tests and use simulation to check their performance in finite samples applications of the tests to nonlinear time series analysis are discussed and illustrated by real examples

volumetric locking issue with uncertainty in the design of locally resonant acoustic metamaterials abstract in the design of locally resonant acoustic metamaterials lrams the incompressible rubber is widely used however the physical behavior of lrams with a ternary structure is very sensitive to the poisson s ratio of incompressible rubber the slight variance of poisson s ratio could lead to a significant change of physical responses of lrams on the other hand the manufacturing error is unavoidable in the application of lrams therefore it is important to predict the upper and lower bounds of physical responses of lrams with uncertainty parameters for the first time the mathematical model to predict the upper and lower bounds of mechanical response of lrams with uncertainty parameters such as young s modulus poisson s ratio and density is established by the nonlinear interval perturbation hybrid node based smoothed finite element method niph ns fem one of the main features of niph ns fem with a softened effect in the discretized model is capable to overcome the volumetric locking issue of incompressible rubber in the standard finite element method fem the accuracy and effectiveness of niph ns fem have been validated by two numerical examples including lrams with binary and ternary structures

construction and application of an ellipsoidal convex model using a semi definite programming formulation from measured data abstract as a set theory based convex model the ellipsoidal model provides an attractive framework for treating uncertain but bounded variations in the structural reliability analysis and design optimization however improper modeling of the uncertainties may give rise to misleading non probabilistic reliability analysis thus result in either unsafe or over conservative designs this paper presents a systematic study on the mathematical formulation for constructing the minimum volume ellipsoidal convex model using a given set of sample data and shows its application in existing methods of non probabilistic reliability analysis and design optimization of structures with bounded uncertainties in this method the uncertain parameters are first divided into groups according to their sources for each individual group of uncertainties the minimum volume ellipsoid problem is reformulated into a semi definite programming sdp problem and thus can be efficiently solved to its global optimum further a linear transformation based on the eigenvalue analysis is employed to map the ellipsoidal model into a standard uncertainty space this uncertainty modeling technique enables a compact and differentiable bound description of the parameter variations moreover it has another useful property the affine invariance which is shown to be necessary for meaningful definition of a non probabilistic reliability index the effectiveness and efficiency of the present techniques for convex model construction and the corresponding reliability analysis are demonstrated with numerical examples of structural topology optimization problems with bounded variations arising from different sources

cutting plane method for multiple objective stochastic integer linear programming abstract this paper grapples with the problem of incorporating integer variables in the constraints of a multiple objective stochastic linear program moslp after representing uncertain aspirations of the decision maker by converting the original problem into a deterministic multiple objective integer linear program moilp a cutting plane technique may be used to compute all the efficient solutions of the last model leaving the decision maker to choose a solution according to his preferences a numerical example is also included for illustration

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

modeling long range dependence nonlinearity and periodic phenomena in sea surface temperatures using tsmars abstract we analyze a time series of 20 years of daily sea surface temperatures measured off the california coast the temperatures exhibit quite complicated features such as effects on many different time scales nonlinear effects and long range dependence we show how a time series version of the multivariate adaptive regression splines mars algorithm tsmars can be used to obtain univariate adaptive spline threshold autoregressive models that capture many of the physical characteristics of the temperatures and are useful for short and long term prediction we also discuss practical modeling issues such as handling cycles long range dependence and concurrent predictor time series using tsmars models for the temperatures are evaluated using out of sample forecast comparisons residual diagnostics model skeletons and sample functions of simulated series we show that a categorical seasonal indicator variable can be used to model nonlinear structure in the data that is changing with time of yea

multiple access channels with point process observations optimum demodulation the derivation and analysis of optimum multiuser detectors for additive rate and additive light poisson multiple access channels are studied the observed point process models the output of an ideal photodetector illuminated by several synchronous or asynchronous users who modulate coherent light of the same frequency dynamic programming based decision rules for the asynchronous multiple access channel exhibit the same computational complexity as their synchronous counterparts and are shown to be optimum under the criteria of minimum error probability and maximum likelihood sequence detection upper and lower bounds on the minimum uncoded bit error rate achievable with arbitrary signal constellations are obtained in terms of the error probability of binary hypothesis testing problems a particular case of these results namely the single user finite length intersymbol interference problem solves the error rate analysis of optimum direct detection systems for dispersive optical fibers

a nonlocal approach for asymptotic memoryless detection theory corresp previous literature on detector design has presented many tractable results using efficacy as a performance functional which is a small signal or local approach some nonlocal issues of memoryless detection are considered we argue that the asymptotic exponential rate of decrease of error probabilities or bayes risk provides the appropriate asymptotic measure of performance a main contribution is the development of an approximation for nonlocal design that retains the tractability of the efficacy approach we have proved the local consistency of our approximation also as a consequence of the analysis new proofs for pitman noether like theorems have been obtained

approximation in nonhierarchic system optimization this paper reports on the effectiveness of a nonhierarchic system optimization algorithm in application to complex coupled systems problems a second order nonhierarchic system optimization algorithm developed in earlier studies is modified in this study to provide for individual constraint state modeling a cumulative constraint formulation was used in previous implementation studies the test problems in this study are each complex coupled systems complex coupled systems require an iterative solution strategy to evaluate system states nonhierarchic algorithm development is driven by these types of problems and their study is imperative the algorithm successfully optimizes each of the complex coupled systems a significant reduction in the number of system analyses required for optimization is observed as compared with conventional optimization using the generalized reduced gradient method in the design database the design database stores design site information generated during the subspace optimizations a quadratic polynomial approximation to the design is formed using the strategy of vanderplaats 6 a weighted least squares solution strategy is employed to solve for the second order terms in vanderplaats strategy exact data in the design data base are more heavily weighted in the least squares solution procedure the resulting quadratic polynomial forms the basis function of accumulated approximation replacing the linear basis used in the original formulation in renaud and gabriele5 improved convergence is observed for the welded beam test problem the improved convergence is attributed to the im proved accuracy of cumulative constraint approximations when using second order based approximating functions additional studies using the second order based coordina tion procedure of system approximation indicated that replac ing the cumulative constraints with their component con straints may improve algorithm performance implementation of the second order based coordination procedure of system approximation was less effective in reducing cycling when applied to the golinski speed reducer problem the speed reducer cumulative constraints were composed of a large num ber of individual constraints as compared with the cumulative constraints in the welded beam test problem with a larger number of individual constraints assigned to a cumulative constraint it will more likely undergo a change in its active set during the coordination procedure it is difficult to approxi mate these changes in the cumulative constraints inaccurate cumulative constraint approximations reduce algorithm per formance and delay convergence approximating individual constraints states in the coor

a flexible coefficient smooth transition time series model we consider a flexible smooth transition autoregressive star model with multiple regimes and multiple transition variables this formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network this proposal has the major advantage of nesting several nonlinear models such as the self exciting threshold autoregressive setar the autoregressive neural network ar nn and the logistic star models furthermore if the neural network is interpreted as a nonparametric universal approximation to any borel measurable function our formulation is directly comparable to the functional coefficient autoregressive far and the single index coefficient regression models a model building procedure is developed based on statistical inference arguments a monte carlo experiment showed that the procedure works in small samples and its performance improves as it should in medium size samples several real examples are also addressed

weighted multiscale cumulative residual renyi permutation entropy of financial time series abstract in this paper based on cumulative residual entropy cre and renyi permutation entropy rpe multiscale cumulative residual renyi permutation entropy mcrrrpe and weighted multiscale cumulative residual renyi permutation entropy wmcrrpe are proposed as novelty measures to quantify the uncertainty of the nonlinear time series first the mcrrpe and wmcrrpe methods are performed on the synthetic data and the impact of the changes to parameters is discussed then the mcrrpe and wmcrrpe methods are applied to the closing prices of the us european and chinese stock markets we analyze the statistics and draw some conclusions from the comparison the stock markets can be divided into four categories 1 nasdaq and ftse100 2 s p500 dji and hsi 3 dax30 and cac40 and 4 sse and szse the standard deviation has a certain relationship with wmcrrpe compared with the mcrrpe method the wmcrrpe method can distinguish these financial stock markets effectively and better estimate the complexity of the time series containing amplitude information

non probabilistic convex model process a new method of time variant uncertainty analysis and its application to structural dynamic reliability problems in this paper we propose a method for time variant uncertainty analysis namely the non probabilistic convex model process which provides an effective mathematical tool for the analysis of structural dynamic uncertainty when lacking relevant information in the convex model process we express the variables at any time with intervals and establish the corresponding auto covariance function and correlation coefficient function to depict the correlation between variables at different times we also define several important characteristic parameters for the uni and bi dimensional convex model processes including the mid value function variance function auto covariance function and cross covariance function we provide the definition for the stationary convex model process and its ergodicity then by combining the convex model process with the first passage failure mechanism we propose a non probabilistic analysis model of structural dynamic reliability and formulate the solving algorithm based on monte carlo simulation finally through the analysis of numerical examples we verify the effectiveness of the convex model process and the model of dynamic reliability analysis proposed in this paper

asymptotic error probability of binary hypothesis testing for poisson point process observations corresp it is shown that the asymptotic probability of error of a binary equiprobable hypothesis test for observed poisson point processes with rates lambda i t b i t rho i t z 2 i 0 1 z rightarrow infty is equal to the error probability of optimum deterministic signal detection in additive white gaussian noise when the signals coincide with the square roots of the point process rates the implication of this result in the error rate analysis of optical digital communication systems is discussed

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

regularized local linear prediction of chaotic time series abstract local linear prediction based on the ordinary least squares ols approach is one of several methods that have been applied to prediction of chaotic time series apart from potential linearization errors a drawback of this approach is the high variance of the predictions under certain conditions here a different set of so called linear regularization techniques originally derived to solve ill posed regression problems are compared to ols for chaotic time series corrupted by additive measurement noise these methods reduce the variance compared to ols but introduce more bias a main tool of analysis is the singular value decomposition svd and a key to successful regularization is to damp the higher order svd components several of the methods achieve improved prediction compared to ols for synthetic noise corrupted data from well known chaotic systems similar results were found for real world data from the r r intervals of ecg signals good results are also obtained for real sunspot data compared to published predictions using nonlinear techniques

nonlinear additive arx models abstract we consider in this article a class of nonlinear additive autoregressive models with exogenous variables for nonlinear time series analysis and propose two modeling procedures for building such models the procedures proposed use two backfitting techniques the ace and bruto algorithms to identify the nonlinear functions involved and use the methods of best subset regression and variable selection in regression analysis to determine the final model simulated and real examples are used to illustrate the analysis

multidimensional parallelepiped model a new type of non probabilistic convex model for structural uncertainty analysis summary non probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions thus such models can be applied to uncertainty analysis of complex structures when experimental information is lacking the interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non probabilistic convex modeling however the former can only deal with independent variables while the latter can only deal with dependent variables this paper presents a more general non probabilistic convex model the multidimensional parallelepiped model this model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex multi source uncertainty problems in which dependent variables and independent variables coexist for any two parameters the concepts of the correlation angle and the correlation coefficient are defined through the marginal intervals of all the parameters and also their correlation coefficients a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters through the introduction of affine coordinates the parallelepiped model in the original parameter space is converted to an interval model in the affine space thus greatly facilitating subsequent structural uncertainty analysis the parallelepiped model is applied to structural uncertainty propagation analysis and the response interval of the structure is obtained in the case of uncertain initial parameters finally the method described in this paper was applied to several numerical examples copyright 2015 john wiley sons ltd

specification estimation and evaluation of smooth transition autoregressive models abstract this article considers the application of two families of nonlinear autoregressive models the logistic lstar and exponential estar autoregressive models this includes the specification of the model based on simple statistical tests linearity testing against smooth transition autoregression determining the delay parameter and choosing between lstar and estar models are discussed estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model the proposed techniques are illustrated by examples using both simulated and real time series

robust assessment of collapse resistance of structures under uncertain loads based on info gap model abstract the paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case and the best limit in the other case of rigid perfectly plastic structures subjected to uncertain but bounded applied loads using an info gap model the methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem and vice versa for the best collapse load limit the formulation for capturing the worst collapse load limit robust worst case solution takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm whilst that for the best collapse load limit is a standard linear programming problem the efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples

nonparametric identification of nonlinear time series projections abstract we study the possibility of identifying general linear and nonlinear time series models using nonparametric methods the kernel estimators of the conditional mean and variance are used as a basis and the properties of these quantities as model indicators are briefly discussed some drawbacks are pointed out and motivated by these we introduce projections as tools of identification the projections are especially useful for additive modeling expressions for the asymptotic bias and variance are obtained the projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series the results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance

tarso modeling of water table depths threshold autoregressive self exciting open loop tarso models are fitted to six time series of water table depths with precipitation excess as input variable basically these models are nonlinear in structure because they incorporate several regimes which are separated by so called thresholds for each well a subset tarso ss tarso model is selected using a bayes information criterion bic ss tarso models are used to simulate realizations of water table depths with lengths of 30 years from which characteristics such as durations of exceedance are computed the simulation performance of the fitted ss tarso models is compared with results obtained from transfer function noise tfn models dynamic regression dr models and with a physical descriptive model called swatre extended with additional autoregressive moving average arma processes for the noise swatre arma as compared to the linear tfn and dr models the ss tarso models perform better because they incorporate several regimes these regimes are the result of different soil layers or drainage levels furthermore it is interesting that ss tarso models show a good relative performance as compared to the swatre arma models a possible reason may be that inputs of swatre are uncertain

perturbation based stochastic fe analysis and robust design of inelastic deformation processes the study addresses the perturbation based stochastic finite element analysis and the robust design optimization of deformation processes of inelastic solids the perturbation equations for the stochastic moment analysis of both steady state and non stationary processes are presented an iteration scheme based on the secant system operator is given for the solution of the perturbation equations in case that a tangent matrix is not available the robust design of deformation processes is stated as a two criteria optimal design problem that attempts best mean properties of the outcome at minimum variability the task is solved using optimization techniques based on sequential quadratic programming in conjunction with the stochastic finite element analysis the proposed method is applied to the design of an extrusion die for robustness with respect to friction variability and to a workpiece preform design problem the numerical results show the potential of the method for applications regarding the design of robust deformation processes

performance bounds for mismatched decision schemes with poisson process observations abstract this paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time inhomogeneous poisson processes when some parameters characterizing the observation process are not known exactly key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true but intractable error probabilities the proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters using these tools it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making the results find direct application to problems of detecting illicit nuclear materials in transit

structural reliability analysis using non probabilistic convex model abstract by using the convex model approach the bounds of the uncertain parameters are only required rather than their precise probability distributions based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information in this paper a non probabilistic reliability model is given for structures with convex model uncertainty which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole convex model a monte carlo simulation is then formulated for the reliability model to obtain a reference solution a first order approximation method foam is proposed to solve the reliability model based on a linear approximation of the failure surface a second order approximation method soam is further formulated to improve the reliability analysis precision for limit state functions with relatively strong nonlinearity by introducing the suggested reliability model a convex model based system reliability method is also formulated eight numerical examples are provided to demonstrate the effectiveness of the present methods

a new nonlinear interval programming method for uncertain problems with dependent interval variables this paper proposes a new nonlinear interval programming method that can be used to handle uncertain optimization problems when there are dependencies among the interval variables the uncertain domain is modeled using a multidimensional parallelepiped interval model the model depicts single variable uncertainty using a marginal interval and depicts the degree of dependencies among the interval variables using correlation angles and correlation coefficients based on the order relation of interval and the possibility degree of interval the uncertain optimization problem is converted to a deterministic two layer nesting optimization problem the affine coordinate is then introduced to convert the uncertain domain of a multidimensional parallelepiped interval model to a standard interval uncertain domain a highly efficient iterative algorithm is formulated to generate an efficient solution for the multi layer nesting optimization problem after the conversion three computational examples are given to verify the effectiveness of the proposed method

bounds analysis of a beam based on the convex model of uncertain foundation a methodology of bounds analysis based on the convex set of uncertainty is presented an infinitely long beam on an uncertain foundation is subjected to a moving force with constant speed the steady state vibration is analysed in the context of the finite element method uncertainty variables representing the uncertain fluctuation of foundation stiffness is confined within a convex hull given as a hyperellipse the fluctuation of dynamic responses of the beam that is the vertical deflection and the bending moment are approximated to a first order with respect to the uncertainty variables the upper and lower bounds of the response fluctuations are identified on the boundary of the convex model by means of the lagrange multiplier method numerical analysis demonstrates the validity of the proposed formulation for various constant speeds of the moving force the analysis is summarized in terms of the worst response which is the maximum absolute value of the response within the identified bounds

log barrier method for two stage quadratic stochastic programming in this paper we present a log barrier method for solving two stage quadratic stochastic programs the mathematical model considered here can be used to present several real world applications including financial and production planning problems we discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm

inelastic deformation processes with random parameters methods of analysis and design methods of analysis and design for inelastic deformation processes with random input parameters are exposed stochastic analysis makes use either of function evaluations for a synthetic statistical input sample monte carlo technique or of a taylor series expansion of the response around the mean input the latter relates to the perturbation method extended over the duration of the deformation process following temporal integration tasks concerning process design are defined and the employment of the stochastic analysis techniques is discussed for exploring the parameter space as well as for design improvement and optimization the suitability of either analysis technique for performing the particular tasks is pointed out the design problem raises the issue of robustness to input scatter robust optimization respects both the mean and the variance of the design objective via the desirability function a weighted combination of the two quantities the exploration potential of synthetic sampling is demonstrated by an application where sensitivity based techniques prove inadequate because of the local nature of the approximation

spectral stochastic isogeometric analysis for linear stability analysis of plate abstract a spectral stochastic isogeometric analysis ssiga scheme is proposed for the stochastic linear stability analysis of plate with uncertain material properties within the proposed ssiga scheme the first order shear deformation theory of plate is adopted for modelling the kinematic relationship both homogeneous and functionally graded material fgm models can be incorporated the considered spatially dependent uncertainties i e young s modulus and poisson s ratio are modelled as random fields with gaussian and lognormal distributions and the spatially independent uncertainty i e gradient index of fgm is modelled as random variable the generalized isogeometric basis function is adopted for both the random field geometry representation and random field discretization through the karhunen loeve k l expansion an extended support vector regression x svr with a new generalized gegenbauer polynomial kernel is developed to model the nonlinear relationship between the structural uncertainties and the buckling load by further implementing various nonparametric statistical inference methods the mean standard deviation probability density function pdf and cumulative distribution function cdf of the buckling load can be effectively established to determine the strength limit of the plate the accuracy efficiency and applicability of the proposed approach are illustrated through two numerical examples

hybrid high dimensional model representation hhdmr on the partitioned data a multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid one way to construct the solution of this problem is to partition the given multivariate data into low variate data high dimensional model representation hdmr and generalized high dimensional model representation ghdmr methods are used to make this partitioning using the components of the hdmr or the ghdmr expansions the multivariate data can be partitioned when a cartesian product set in the space of the independent variables is given the hdmr expansion is used on the other hand if the nodes are the elements of a random discrete data the ghdmr expansion is used instead of hdmr these two expansions work well for the multivariate data that have the additive nature if the data have multiplicative nature then factorized high dimensional model representation fhdmr is used but in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature they have a hybrid nature so a new method is developed to obtain better results and it is called hybrid high dimensional model representation hhdmr this new expansion includes both the hdmr or ghdmr and the fhdmr expansions through a hybridity parameter in this work the general structure of this hybrid expansion is given it has tried to obtain the best value for the hybridity parameter according to this value the analytical structure of the sought multivariate function can be determined via hhdmr

efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering in this study we describe the algebraic computations required to implement the stochastic finite element method for solving problems in which uncertainty is restricted to right hand side data coming from forcing functions or boundary conditions we show that the solution can be represented in a compact outer product form which leads to efficiencies in both work and storage and we demonstrate that block iterative methods for algebraic systems with multiple right hand sides can be used to advantage to compute this solution we also show how to generate a variety of statistical quantities from the computed solution finally we examine the behavior of these statistical quantities in one setting derived from a model of acoustic scattering

multiobjective programming in optimization of the interval objective function abstract in this paper the mathematical programming problem whose objective function has interval coefficients is investigated to maximize the interval objective function the order relations which represent the decision maker s preference between interval profits are defined by the right limit the left limit the center and the width of an interval the maximization problem with the interval objective function is converted into a multiobjective problem using the order relations the minimization problem is also converted into a multiobjective problem using the order relations which represent the decision maker s preference between interval costs