variable selection for gaussian process models in computer experiments in many situations simulation of complex phenomena requires a large number of inputs and is computationally expensive identifying the inputs that most impact the system so that these factors can be further investigated can be a critical step in the scientific endeavor in computer experiments it is common to use a gaussian spatial process to model the output of the simulator in this article we introduce a new simple method for identifying active factors in computer screening experiments the approach is bayesian and only requires the generation of a new inert variable in the analysis however in the spirit of frequentist hypothesis testing the posterior distribution of the inert factor is used as a reference distribution against which the importance of the experimental factors can be assessed the methodology is demonstrated on an application in material science a computer experiment from the literature and simulated examples

an innovative eigenvalue problem solver for free vibration of euler bernoulli beam by using the adomian decomposition method this paper deals with free vibration problems of euler bernoulli beam under various supporting conditions the technique we have used is based on applying the adomian decomposition method adm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis

computer model calibration using high dimensional output this work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out statistical inference of particular interest here is determining uncertainty in resulting predictions this typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator the problem is complicated by the fact that simulation code is sufficiently demanding that only a limited number of simulations can be carried out we consider applications in characterizing material properties for which the field data and the simulator output are highly multivariate for example the experimental data and simulation output may be an image or may describe the shape of a physical object we make use of the basic framework of kennedy and o hagan however the size and multivariate nature of the data lead to computational challenges in implementing the framework to overcome these challenges we make use of basis repre

calculating centroids in constrained mixture experiments in constrained mixture experiments the centroid of a constraint region has traditionally been defined as the average of all extreme vertices of the region this differs from the classical physics definition of a centroid as the center of mass or volume of a region an algorithm for calculating a centroid based on the center of mass definition is discussed and illustrated with an example this centroid calculation technique can be used to calculate centroids of various dimensional faces and edges of the constraint region as well as of the overall centroid results of the center of mass and averaged extreme vertices centroid computation techniques are compared using examples from the literature

an innovative eigenvalue problem solver for free vibration of uniform timoshenko beams by using the adomian modified decomposition method this paper deals with free vibration problems of uniform timoshenko beams under various supporting boundary conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis

additivity and interaction in three component experiments with mixtures summary additivity and interaction are defined for a three component mixture experiment and studied both for polynomial models and factorial models the notion of the blandness of a component is introduced linear blending is equivalent to the combination of no interaction and the blandness of all three components

design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using adomian decomposition method the theory for designing distributed piezoelectric modal sensors is well established for beam structures however the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions i e either clamped free simply supported or sliding in this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed using the adomian decomposition method adm a general expression for designing the shape of a piezoelectric modal sensor is presented in which the output signal of the designed sensor is proportional to the response of the target mode other modes are filtered out the modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function based on the adm and employing some simple mathematical operations the closed form series solution of the second spatial derivative of the mode shapes can be determined then the shapes of the designed modal sensors are obtained finally some numerical examples are given to demonstrate the feasibility of the proposed modal sensors it is shown that for classical boundary conditions the shapes of the modal sensors based on the adm agree well with analytical and numerical results given in the literature for general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another the modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band

biplot displays for looking at multiple response data in mixture experiments in the analysis of mixture experiments it is not unusual to have many response variables or physical characteristics of the end product under investigation simultaneously generally these responses are correlated with one another and the analyst must compromise by concentrating on what he or she considers the most important characteristics at the expense of others in selecting the optimum formulation furthermore in those situations in which some responses are positively correlated while others are negatively correlated it can be very difficult to understand the relative importance of the different components in such situations a biplot display can help the analyst not only to understand the underlying structure of the data better but also to understand the roles played by the different components biplots are so named because both row mixture formulation and column response information are displayed in a single plot this graphical technique has been applied successfully to mixture experimen

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

mixture models based on neural network averaging a modified version of the single hidden layer perceptron architecture is proposed for modeling mixtures a particular flexible mixture model is obtained by implementing the box cox transformation as transfer function in this case the network response can be expressed in closed form as a weighted power mean the quadratic scheffe k polynomial and the exponential wilson equation turn out to be special forms of this general mixture model advantages of the proposed network architecture are that binary data sets suffice for training and that it is readily extended to incorporate additional mixture components while retaining all previously determined weights

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

free vibration analysis of a type of tapered beams by using adomian decomposition method abstract the adomian decomposition method adm is employed in this paper to investigate the free vibrations of tapered euler bernoulli beams with a continuously exponential variation of width and a constant thickness along the length under various boundary conditions based on adm the governing differential equation for the tapered beam becomes a recursive algebraic equation by using the boundary condition equations the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously the computed results for different boundary conditions and non uniformity ratios are presented the accuracy is assured from the convergence and comparison published results

methods for assessing curvature and interaction in mixture experiments the terms curvature and interaction traditionally are not defined or used in the context of mixture experiments because curvature and interaction effects are partially confounded due to the mixture constraint that the component proportions sum to 1 instead the term nonlinear blending traditionally is defined and used however just as the concept of a component effect is defined specifically for mixture experiments the concepts of curvature and interaction can be also these special definitions lead to special sets of points for assessing the curvature and interaction of mixture components an interaction plot for mixture components is obtained by plotting measured or predicted response values at the special points for assessing interaction together with response trace component effects plots the new mixture component interaction plots provide for graphically assessing the linear curvature and interaction effects of mixture components these methods provide a more complete picture of how mixture

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

analytic solution of nonlinear boundary value problems in several dimensions by decomposition abstract nonlinear partial differential equations are systematically solved by the decomposition method of g adomian for general boundary conditions described by boundary operator equations linear partial differential equations and linear or nonlinear ordinary differential equations become special cases all dealt with by a single procedure

on the convergence of adomian decomposition method here a simple method to determine the rate of convergence of adomian decomposition method is introduced the proposed method is used to compare between the rate of convergence of standard and modified proposed by wazwaz a m wazwaz a new method for solving singular initial value problems in the second order ordinary differential equations appl math comput 128 2002 45 57 adomian methods for solving lane emden singular problem furthermore with providing some examples the aforementioned cases are dealt with numerically

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

free vibration analysis of stepped beams by using adomian decomposition method abstract the adomian decomposition method adm is employed in this paper to investigate the free vibrations of a stepped euler bernoulli beam consisting of two uniform sections each section is considered a substructure which can be modeled using adm by using boundary condition and continuity condition equations the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously the computed results for different boundary conditions step ratios and step locations are presented comparing the results using adm to those given in the literature excellent agreement is achieved

log contrast models for experiments with mixtures summary a new form of expected response function involving log contrasts of the proportions is introduced for experiments with mixtures the advantages and disadvantages of log contrast models are discussed and illustrated in applications in particular the parameters of the model are related to certain useful hypotheses about mixtures and some relevant contrasts are identified

measuring component effects in constrained mixture experiments in a mixture experiment the response to a mixture of q components is a function of the proportions x 1 x 2 x q of components in the mixture the proporitons satisfy the constraint x i 1 and the nature of a particular situation may impose other restrictions the problem considered is the measurement of the effect each component has on the response a new mixture component effect measure is presented and compared to previously suggested measures this new measure incorporates more information concerning the size shape and location of the constraint region than do the previous suggestions a distinction between partial and total effects is made and the uses of these effects in modifying and interpreting mixture response prediction equations are considered the methods of the article are illustrated in an example from a glass development study in a waste vitrification program

noncollapsing space filling designs for bounded nonrectangular regions many researchers use computer simulators as experimental tools especially when physical experiments are infeasible when computer codes are computationally intensive nonparametric predictors can be fitted to training data for detailed exploration of the input output relationship the accuracy of such flexible predictors is enhanced by taking training inputs to be space filling if there are inputs that have little or no effect on the response it is desirable that the design be noncollapsing in the sense of having space filling lower dimensional projections this article describes an algorithm for constructing noncollapsing space filling designs for bounded input regions that are of possibly high dimension online supplementary materials provide the code for the algorithm examples of its use and show its performance in multiple settings

probabilistic sensitivity analysis of complex models a bayesian approach summary in many areas of science and technology mathematical models are built to simulate complex real world phenomena such models are typically implemented in large computer programs and are also very complex such that the way that the model responds to changes in its inputs is not transparent sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs this may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application a broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model s output to variation in its inputs in practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs an approach which is known as probabilistic sensitivity analysis we present a bayesian framework which unifies the various tools of prob abilistic sensitivity analysis the bayesian approach is computationally highly efficient it allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard monte carlo methods furthermore all measures of interest may be computed from a single set of runs

equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations abstract we consider the solution of partial differential equations for initial boundary conditions using the decomposition method the partial solutions obtained from the seperate equations for the highest ordered linear operator terms are shown to be identical when the boundary conditions are general and asymptotically equal when the boundary conditions in one independent variable are independet of other variables

a comparison between adomian decomposition method and taylor series method in the series solutions in this work we will compare the performance of the adomian decomposition method and the taylor series method applied to the solution of linear and nonlinear ordinary differential equations the comparison shows that the decomposition method is reliable efficient and easy to use from a computational viewpoint although the two methods provide the solution in an infinite series the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by taylor series method

the application of ridge techniques to mixture data ridge analysis the response surface technique ridge analysis was developed within the context of unconstrained or nonmixture explanatory variables it has apparently been generally considered nonapplicable to mixture data in this discussion two methods are introduced for analyzing quadratic mixture response surfaces with ridge analysis the first may be useful with standard response surface designs e g draper and lawrence 1965a b thompson and myers 1968 and the second offers an alternative method of examining the effects of individual components in constrained designs both methods are demonstrated on real data

vibration of beams with generally restrained boundary conditions using fourier series this work presents a method to find accurate vibration frequencies of beams with generally restrained boundary conditions using fourier series the suggested method is very convenient to find an accurate frequency parameter for beams with not only classical boundary conditions but also non classical boundary conditions restrained by rotational and translational springs numerical results for various degenerate cases are compared with existing results for natural frequency obtained by conventional analysis the results indicate that the present method can be used very effectively in the design of beams with various supporting conditions

general blending models for data from mixture experiments we propose a new class of models providing a powerful unification and extension of existing statistical methodology for analysis of data obtained in mixture experiments these models which integrate models proposed by scheffe and becker extend considerably the range of mixture component effects that may be described they become complex when the studied phenomenon requires it but remain simple whenever possible this article has supplementary material online

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

an approximate method for one dimensional structures with strong nonlinear and nonhomogenous boundary conditions abstract there is a lack of analytic methods for vibration analysis of structures with strong nonlinear and non homogenous boundary conditions this paper proposes such a method a distinct feature of the method is to introduce the generalized coordinates for nonlinear and nonhomogeneous boundary conditions the total solution of the structure consists of a sum of a spatial particular solution for the boundary conditions and a field solution satisfying linear and homogeneous boundary conditions the field solution can be obtained in terms of the modal expansion the modal coefficients together with the generalized coordinates for the boundary conditions satisfy a set of nonlinear ordinary differential equations which are solved with the harmonic balance method two examples are presented to study the convergence and accuracy of the solution the first example is the longitudinal vibration of a bar subject to a base excitation on the left and restrained by a damper on the right the wave method and the differential quadrature method dqm are compared with the proposed method and are found in good agreement the second example is a beam with nonlinear torsional boundary absorbers the method shows a good accuracy to deal with the complex boundary conditions as compared with the differential quadrature element method dqem the proposed method is also compared with the multi scale method msm and shows an advantage to deal with strong nonlinearities the proposed method is highly promising for vibration analysis of complex structures with nonlinear and nonhomogeneous boundary conditions

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

choosing the sample size of a computer experiment a practical guide we provide reasons and evidence supporting the informal rule that the number of runs for an effective initial computer experiment should be about 10 times the input dimension our arguments quantify two key characteristics of computer codes that affect the sample size required for a desired level of accuracy when approximating the code via a gaussian process gp the first characteristic is the total sensitivity of a code output variable to all input variables the second corresponds to the way this total sensitivity is distributed across the input variables specifically the possible presence of a few prominent input factors and many impotent ones i e effect sparsity both measures relate directly to the correlation structure in the gp approximation of the code in this way the article moves toward a more formal treatment of sample size for a computer experiment the evidence supporting these arguments stems primarily from a simulation study and via specific codes modeling climate and ligand activa

the modified decomposition method applied to unsteady flow of gas through a porous medium in this paper an analytic solution for the unsteady flow of gas through a porous medium is constructed our approach rests on the recently developed modification of the adomian decomposition method the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of y x and to determine the initial slope y 0 the proposed scheme avoids the complexity provided by using perturbation techniques

the decomposition method for approximate solution of the goursat problem abstract in this paper the adomian s decomposition method is effectively implemented to establish an analytic solution and a reliable numerical approximation to the goursat partial differential equation linear and nonlinear goursat examples are examined and the method supplied quantitatively reliable results for these types of problems the accuracy level of the results obtained indicates the superiority of the decomposition method over existing numerical methods that were applied to the goursat problem

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

defining consistent constraint regions in mixture experiments physical theoretical and economic considerations in mixture experimentation often impose constraints on the levels of components in the mixture these constraints define the region of interest and hence play an important role in the design and analysis of the mixture experiment because of this important role sufficient care must be taken in developing the set of constraints this article discusses several guidelines for developing mixture constraints and presents techniques for checking the consistency of the constraints developed the guidelines and techniques are illustrated using several examples

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

a general approach to ridge analysis with confidence intervals in response surface methodology ridge analysis is a graphical technique for interpreting response surfaces particularly those of three or more dimensions standard ridge analysis techniques employ a second order polynomial regression model an approach to ridge analysis is presented here that generalizes its current scope this approach allows the use of a general regression model for the response surface within the class of linear models conservative or approximate simultaneous confidence intervals about the optimal mean responses for varying radii can be obtained these simultaneous confidence intervals form a guidance band to aid the experimenter in determining optimal levels of operation a variety of explanatory variable constraints including mixture constraints can also be imposed for the standard quadratic model these confidence intervals can be easily modified to obtain confidence bounds about the maximum or minimum eigenvalues of b the matrix of second order regression coefficients

a new approach to the nonlinear advection problem an application of the decomposition method abstract in this paper the nonlinear advection problem is solved easily and elegantly by using the adomian s decomposition method the exact solution is quickly obtained by observing the appearance of the self canceling noise terms whose sum vanishes in the limit comparison with other existing techniques shows that the present approach is highly accurate

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

global sensitivity analysis for mixture experiments a mixture experiment is characterized by having two or more inputs that are specified as a percentage contribution to a total amount of material in such situations the input variables are correlated because they must sum to one consequently additional care must be taken when fitting statistical models or visualizing the effect of one or more inputs on the response in this article we consider the use of a gaussian process to model the output from a computer simulator taking a mixture input we introduce a procedure to perform global sensitivity analysis of the code output providing main effects and revealing interactions the resulting methodology is illustrated using a function with analytically tractable results for comparison a chemical compositional simulator and a physical experiment supplementary materials providing assistance with implementing this methodology are available online