testing quasi independence of failure and truncation times via conditional kendall s tau truncated survival data arise when the failure time is observed only if it falls within a subject specific truncating set most analysis methods rely on the key assumption of quasi independence that is factorization of the joint density of failure and truncation times into a product proportional to the individual densities in the observable region unlike independence of failure time and censoring time quasi independence can be tested tests of quasi independence are available for one sided truncation and for truncation that depends on a measured covariate but not for more complex truncation schemes here tests of quasi independence based on a multivariate conditional kendall s tau are proposed for doubly truncated data bivariate left truncated data and other forms of truncated survival data that arise when initiating or terminating event times are interval censored asymptotic properties under the null are derived the tests are illustrated using several real datasets and evaluated via simulation

modeling age and nest specific survival using a hierarchical bayesian approach recent studies have shown that grassland birds are declining more rapidly than any other group of terrestrial birds current methods of estimating avian age specific nest survival rates require knowing the ages of nests assuming homogeneous nests in terms of nest survival rates or treating the hazard function as a piecewise step function in this article we propose a bayesian hierarchical model with nest specific covariates to estimate age specific daily survival probabilities without the above requirements the model provides a smooth estimate of the nest survival curve and identifies the factors that are related to the nest survival the model can handle irregular visiting schedules and it has the least restrictive assumptions compared to existing methods without assuming proportional hazards we use a multinomial semiparametric logit model to specify a direct relation between age specific nest failure probability and nest specific covariates an intrinsic autoregressive prior is employed for the nest age effect this nonparametric prior provides a more flexible alternative to the parametric assumptions the bayesian computation is efficient because the full conditional posterior distributions either have closed forms or are log concave we use the method to analyze a missouri dickcissel dataset and find that 1 nest survival is not homogeneous during the nesting period and it reaches its lowest at the transition from incubation to nestling and 2 nest survival is related to grass cover and vegetation height in the study area

design of spl lscr sub 1 optimal controllers with flexible disturbance rejection level this note presents a new design methodology that allows for flexible management of the tradeoff between the ability of a system to attenuate disturbance signals versus its expected worst peak to peak amplification the proposed strategy applies to linear time invariant systems which are subject to persistent disturbance signals and combines a recently developed quasi robust linear programming concept with a well known spl lscr sub 1 optimal controller synthesis approach the benefit of the resulting technique is demonstrated using an example

interval analysis theory and applications we give an overview on applications of interval arithmetic among others we discuss verification methods for linear systems of equations nonlinear systems the algebraic eigenvalue problem initial value problems for odes and boundary value problems for elliptic pdes of second order we also consider the item software in this field and give some historical remarks

robust truss topology design via semidefinite programming we present and motivate a new model of the truss topology design problem where the rigidity of the resulting truss with respect both to given loading scenarios and small occasional loads is optimized it is shown that the resulting optimization problem is a semidefinite program we derive and analyze several equivalent reformulations of the problem and present illustrative numerical examples

confidence structural robust optimization by non linear semidefinite programming based single level formulation structural robust optimization problems are often solved via the so called bi level approach this solution procedure often involves large computational efforts and sometimes its convergence properties are not so good because of the non smooth nature of the bi level formulation another problem associated with the traditional bi level approach is that the confidence of the robustness of the obtained solutions cannot be fully assured at least theoretically in the present paper confidence single level non linear semidefinite programming nlsdp formulations for structural robust optimization problems under stiffness uncertainties are proposed this is achieved by using some tools such as s procedure and quadratic embedding for convex analysis the resulted nlsdp problems are solved using the modified augmented lagrange multiplier method which has sound mathematical properties numerical examples show that confidence robust optimal solutions can be obtained with the proposed approach effectively copyright 2010 john wiley sons ltd

inverse optimization for the recovery of constraint parameters abstract most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set we propose two approaches to impute unspecified left hand side constraint coefficients in addition to a cost vector for a given linear optimization problem the first approach identifies parameters minimizing the duality gap while the second minimally perturbs prior estimates of the unspecified parameters to satisfy strong duality if it is possible to satisfy the optimality conditions exactly we apply these two approaches to the general linear optimization problem we also use them to impute unspecified parameters of the uncertainty set for robust linear optimization problems under interval and cardinality constrained uncertainty each inverse optimization model we propose is nonconvex but we show that a globally optimal solution can be obtained either in closed form or by solving a linear number of linear or convex optimization problems

a linear decision based approximation approach to stochastic programming stochastic optimization especially multistage models is well known to be computationally excruciating moreover such models require exact specifications of the probability distributions of the underlying uncertainties which are often unavailable in this paper we propose tractable methods of addressing a general class of multistage stochastic optimization problems which assume only limited information of the distributions of the underlying uncertainties such as known mean support and covariance one basic idea of our methods is to approximate the recourse decisions via decision rules we first examine linear decision rules in detail and show that even for problems with complete recourse linear decision rules can be inadequate and even lead to infeasible instances hence we propose several new decision rules that improve upon linear decision rules while keeping the approximate models computationally tractable specifically our approximate models are in the forms of the so called second order cone soc programs which could be solved efficiently both in theory and in practice we also present computational evidence indicating that our approach is a viable alternative and possibly advantageous to existing stochastic optimization solution techniques in solving a two stage stochastic optimization problem with complete recourse

robustness analysis of trusses with separable load and structural uncertainties this paper discusses evaluation techniques of the robustness function of trusses which is regarded as one of measures of structural robustness under the uncertainties of member stiffnesses and external forces by using quadratic embedding of the uncertainty and the s procedure we formulate a quasiconvex optimization problem which provides lower bounds of the robustness functions a bisection method is proposed where we solve a finite number of semidefinite programming problems in order to obtain a global optimal solution to the proposed quasiconvex optimization problem the lower bounds of the robustness functions are computed for various trusses under several uncertainty circumstances

extreme structural response analysis of truss structures under material uncertainty via linear mixed 0 1 programming this paper concerns the extreme structural response analysis of truss structures taking the possible uncertainties of young s moduli of the bars into consideration the uncertainty of young s modulus is described by a non probability but bounded interval model with the use of this uncertain model it is shown that the structural responses such as nodal displacement and bar stress will attain their extreme values when young s moduli of the bars take either their upper or lower bound value based on this conclusion and simultaneous analysis and design formulation a linear mixed 0 1 programming problem can be constructed to find the extreme values of the structural response by the well established branch and bound approach with global optimality the proposed approach is applied to several test problems for the demonstration of its validity

a survey of non probabilistic uncertainty treatment in finite element analysis the objective of this paper is to critically review the emerging non probabilistic approaches for uncertainty treatment in finite element analysis the paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis first the applicability of the non probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint the necessary conditions for a useful application of the non probabilistic concepts are determined and are proven to be complementary rather than competitive to the classical probabilistic approach the second part of the paper focuses on numerical aspects of the interval finite element method it describes two principal strategies for the implementation i e the anti optimisation and the interval arithmetic approach and gives a state of the art of the interval finite element algorithms available from literature it is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output and the main sources of this conservatism are identified a numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built up benchmark structure

from cvar to uncertainty set implications in joint chance constrained optimization we review and develop different tractable approximations to individual chance constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional value at risk cvar measure we extend the idea to joint chance constrained problems and provide a new formulation that improves upon the standard approach our approach builds on a classical worst case bound for order statistics problems and is applicable even if the constraints are correlated we provide an application of the model on a network resource allocation problem with uncertain demand

confidence structural robust design and optimization under stiffness and load uncertainties abstract most of the structural behavior constraints involved in structural robust design and optimization are non convex in nature therefore if local optimality criteria based optimization algorithms are employed to find the worst case structural responses that are used for examining the feasibility of a given design it is highly possible that the optimization process will get stuck in a local optimum if this is the case the reliability of a robust design cannot be guaranteed at least theoretically the aim of the present paper is to develop some new formulations and the corresponding numerical algorithms to find the confidence optimal design under non probabilistic stiffness and load uncertainties to this end two bi level program formulations for confidence robust design are proposed in order to ensure the strict feasibility of the optimal solution in the lower level of program the constraints are imposed on the confidence upper bounds of the structural responses which can be obtained efficiently by solving some convex linear semi definite programs lsdps based on the sensitivity analysis of the lower level lsdp problem the upper level programs are then solved by employing the classical gradient based nonlinear optimization algorithms furthermore for the case of stiffness uncertainty a single level nonlinear semi definite programming nsdp formulation is also proposed and its mathematical properties are analyzed numerical examples show that confidence robust optimal design can be obtained via the proposed approaches effectively without resorting to too many computational efforts

tractable approximations to robust conic optimization problems in earlier proposals the robust counterpart of conic optimization problems exhibits a lateral increase in complexity i e robust linear programming problems lps become second order cone problems socps robust socps become semidefinite programming problems sdps and robust sdps become np hard we propose a relaxed robust counterpart for general conic optimization problems that a preserves the computational tractability of the nominal problem specifically the robust conic optimization problem retains its original structure i e robust lps remain lps robust socps remain socps and robust sdps remain sdps and b allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

a novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty abstract in today s business environments the high importance of economic benefits and environmental impacts of using scrapped products has caused most companies to move to designing the closed loop supply chain network this paper considers the closed loop supply chain network design problem under hybrid uncertainty while there are two sources of uncertainty for most parameters thus require fortifying of the robustness of the decision the first source is that some uncertain parameters may be based on the future scenarios which are considered according to the probability of their occurrence the second source is that the values of these parameters in each scenario are usually imprecise and can be specified by possibilistic distributions in this case the best robust decision has some additional properties in terms of mean value and variability of the objective function we introduced two types of the variability named scenario variability and possibilistic variability possibility theory is used to choose a solution in such a problem and a novel robust fuzzy stochastic programming approach is proposed that has significant advantages the performance of the proposed model is also compared with that of other models in term of the mean cost and variability by simulation

biases in the pollock and cornelius method of estimating nest survival pollock and cornelius 1988 biometrics 44 397 404 present a distribution free nest survival model that is applicable when survival is age specific as well as constant we show that this model can produce survival estimates that have a substantial bias the estimates for the constant survival model are always positively biased for the age specific survival model there is often a positive bias to examine the source of the bias we derive an explicit maximum likelihood estimator for the constant survival model this shows the bias can be interpreted as arising from implicitly assuming hatched nests are at risk until the end of the grouping interval rather than treating them as right censored we use simulation to examine the bias for the age specific survival model the em algorithm is used to constrain the estimates there is a general tendency for the bias to increase as the proportion of hatched nests in the sample increases finer grouping should reduce the bias but increases the number of parameters that must be estimated in this age specific model

modelling age specific survival in nesting studies using a general approach for doubly censored and truncated data in typical nest survival studies the observed sample of nests is usually biased by left truncation i e only active nests enter the study additionally the failure data may be doubly censored because the exact dates of nest initiation and failure are uncertain we present a general bivariate contingency table approach for analyzing such data we use weakly structured step spline hazard models which avoid estimability problems encountered in a strictly nonparametric approach yet still permit flexibility our method eliminates a potential source of bias noted by heisey and nordheim 1990 biometrics 46 855 862 in the nest survival method of pollock and cornelius 1988 biometrics 44 397 404 we compare our approach to related techniques developed for estimating the incubation distribution of aids

a unified approach to uncertain optimization abstract in this paper we consider uncertain scalar optimization problems with infinite scenario sets we apply methods from vector optimization in general spaces set valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming these methods provide new insights on the interrelation between different concepts for handling uncertainties and naturally lead to new concepts of robustness

model order reduction techniques with a posteriori error control for nonlinear robust optimization governed by partial differential equations we consider a nonlinear optimization problem governed by partial differential equations with uncertain parameters it is addressed by a robust worst case formulation the resulting optimization problem is of bilevel structure and is difficult to treat numerically we propose an approximate robust formulation that employs linear and quadratic approximations to speed up the computation reduced order models based on proper orthogonal decomposition in combination with a posteriori error estimators are developed the proposed strategy is then applied to the optimal placement of a permanent magnet in the rotor of a synchronous machine with moving rotor numerical results are presented to validate the presented approach

covariate analysis of competing risks data with log linear models a general system of log linear modeling is proposed for analysis of competing risks data with discrete covariates the instantaneous cause specific failure rates approximated by step functions are analyzed by techniques for multidimensional contingency tables censored observations are accommodated counts of failures of each type and the amount of follow up are summarized in two arrays in which each cell denotes a distinct combination of failure type time interval and covariate value maximum likelihood estimators for the parameters of the model are derived by iterative proportional fitting the resulting estimates of the number of failures in each cell are used for goodness of fit tests the principal advantages of this approach are its simple display of data its computational ease for the fitting and comparison of models and its provision of explicit goodness of fit tests interpretation of the models is facilitated by reference to several alternative models for survivorship and competing risks the basic model is extended to incorporate stochastic covariates whose values change during follow up and to accommodate quantitative covariates

robust structural topology optimization considering boundary uncertainties in classical deterministic topology optimization the effect of the possible boundary variations on the performance of the structure is not taken into account which may lead to designs that are very sensitive to manufacturing errors as a consequence the performance of the real structure may be far from optimal and even not meet the design requirements in the present paper structural topology optimization considering the uncertainty of boundary variations is considered via level set approach in order to make the optimal designs less sensitive to the possible boundary variations we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution with use of the schwarz inequality the original bi level optimization problem is transformed to a single level optimization problem which can be solved efficiently numerical examples demonstrate the effectiveness of the proposed approach

a novel method of non probabilistic reliability based topology optimization corresponding to continuum structures with unknown but bounded uncertainties abstract a new non probabilistic reliability based topology optimization nrbto method for detailed design of continuum structures is proposed in this paper in which the unknown but bounded ubb uncertainties existing in material and external loads are considered simultaneously based on the interval set theoretic model traditional displacement constraint is transformed into the non probabilistic reliability format in which a novel measuring index namely the optimization feature distance is defined by a combination of the area ratio ideas thus the optimal layout issue is converted by the lightweight design problem with displacement reliability constraints moreover the interval parametric vertex approach and the adjoint vector method are also employed to obtain the sensitivity information between the reliability measurement and design variables by utilizing the method of moving asymptotes mma the optimization problem that is investigated can be solved iteratively two engineering examples are eventually presented to demonstrate the validity and effectiveness of the methodology that has been developed and numerical results show that considering the ubb uncertainty effects during the whole procedure of topology optimization may have a significant influence on the final structural configurations

verifying exactness of relaxations for robust semi definite programs by solving polynomial systems abstract in this paper robust semi definite programs are considered with the goal of verifying whether a particular lmi relaxation is exact a procedure is presented showing that verifying exactness amounts to solving a polynomial system the main contribution of the paper is a new algorithm to compute all isolated solutions of a system of polynomials standard techniques in computational algebra often referred to as stetter s method h j stetter numerical polynomial algebra siam 2004 involve the computation of a grobner basis of the ideal generated by the polynomials and further require joint eigenvector computations in order to arrive at the zeros of the polynomial system our algorithm does neither require structural knowledge on the polynomial system nor does it rely on the computation of joint eigenvectors

stochastic control with uncertain parameters via chance constrained control chance constrained methods handle problem uncertainty by formulating the constraints probabilistically and only guaranteeing their satisfaction up to a given violation level this paper extends existing chance constrained methods to handle both uncertainty in the system state as well as in the constraint parameters due to the imperfect knowledge of the system state caused by motion sensor and environment uncertainty the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically prior work has primarily only dealt with uncertainty in the system state or constraint parameters but not both simultaneously however in many motivating applications both frequently occur to handle this case previous approaches either approximate the distribution leading to a nonconvex optimization program or use sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution to address these limitations a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty it is shown that under certain conditions the resulting optimization program using this hybrid representation is convex to check the convexity an efficient a priori sufficient condition is developed furthermore by using this hybrid representation this method drastically reduces the computational complexity over previous methods which is demonstrated through two examples consequently this method has the ability to enable real time stochastic control for the motivating applications

optimal design for multi item auctions a robust optimization approach in this paper we revisit the auction design problem for multi item auctions with budget constrained buyers by introducing a robust optimization approach to model a concepts such as incentive compatibility and individual rationality that are naturally expressed in the language of robust optimization and b the auctioneer s beliefs on the buyers valuations of the items rather than using probability distributions the classical probabilistic approach or an adversarial model to model valuations we introduce an uncertainty set based model for these valuations we construct these uncertainty sets to incorporate historical information available to the auctioneer in a way that is consistent with limit theorems of probability theory or knowledge of the probability distribution in this setting we formulate the auction design problem as a robust optimization problem and provide a characterization of the optimal solution as an auction with reservation prices thus extending the work of myerson myerson rb

optimization under probabilistic envelope constraints chance constraints are an important modeling tool in stochastic optimization providing probabilistic guarantees that a solution succeeds in satisfying a given constraint although they control the probability of success they provide no control whatsoever in the event of a failure that is they do not distinguish between a slight overshoot or undershoot of the bounds and more catastrophic violation in short they do not capture the magnitude of violation of the bounds this paper addresses precisely this topic focusing on linear constraints and ellipsoidal gaussian like uncertainties we show that the problem of requiring different probabilistic guarantees at each level of constraint violation can be reformulated as a semi infinite optimization problem we provide conditions that guarantee polynomial time solvability of the resulting semi infinite formulation we show further that this resulting problem is what has been called a comprehensive robust optimization problem in the literature as a byproduct we provide tight probabilistic bounds for comprehensive robust optimization thus analogously to the connection between chance constraints and robust optimization we provide a broader connection between probabilistic envelope constraints and comprehensive robust optimization

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

robust ccmv model with short selling and risk neutral interest rate abstract robust optimization is a powerful tool for managing uncertainty in financial optimization problems in this paper we study the cardinality constraints mean variance portfolio optimization model with short selling and risk neutral interest rate under the return and covariance matrix uncertainty equivalent mixed integer second order cone programming formulation of its robust counterpart is given for the interval uncertainty finally using s p 500 index data original and robust models are compared in terms of sharpe ratios

the vertex solution theorem and its coupled framework for static analysis of structures with interval parameters summary this work gives new statement of the vertex solution theorem for exact bounds of the solution to linear interval equations and its novel proof by virtue of the convex set theory the core idea of the theorem is to transform linear interval equations into a series of equivalent deterministic linear equations then the important theorem is extended to find the upper and lower bounds of static displacements of structures with interval parameters following discussions about the computational efforts a coupled framework based on vertex method vm is established which allows us to solve many large scale engineering problems with uncertainties using deterministic finite element software compared with the previous works the contribution of this work is not only to obtain the exact bounds of static displacements but also lay the foundation for development of an easy to use interval finite element software numerical examples demonstrate the good accuracy of vm meanwhile the implementation of vm and availability of the coupled framework are demonstrated by engineering example copyright 2017 john wiley sons ltd

modelling topology optimization problems as linear mixed 0 1 programs this paper deals with topology optimization of discretized continuum structures it is shown that a large class of non linear 0 1 topology optimization problems including stress and displacement constrained minimum weight problems can equivalently be modelled as linear mixed 0 1 programs the modelling approach is applied to some test problems which are solved to global optimality

robust and adaptive network flows we study network flow problems in an uncertain environment from the viewpoint of robust optimization in contrast to previous work we consider the case that the network parameters e g capacities are known and deterministic but the network structure e g nodes and arcs is subject to uncertainty in this paper we study the robust and adaptive versions of the maximum flow problem and minimum cut problems in networks with node and arc failures and establish structural and computational results the adaptive two stage model adjusts the solution after the realization of the failures in the network this leads to a more flexible model and yields less conservative solutions compared to the robust model we show that the robust maximum flow problem can be solved in polynomial time but the robust minimum cut problem is np hard we also prove that the adaptive versions are np hard we further characterize the adaptive model as a two person zero sum game and prove the existence of an equilibrium in such g

a branch and cut decomposition algorithm for solving chance constrained mathematical programs with finite support we present a new approach for exactly solving chance constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints such problems have been notoriously difficult to solve due to nonconvexity of the feasible region and most available methods are only able to find provably good solutions in certain very special cases our approach uses both decomposition to enable processing subproblems corresponding to one possible outcome at a time and integer programming techniques to combine the results of these subproblems to yield strong valid inequalities computational results on a chance constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed integer programming formulation and a simple decomposition approach that does not use strong valid inequalities we also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels as would be done when solving for the efficient frontier of risk and cost

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

unified response probability distribution analysis of two hybrid uncertain acoustic fields abstract for the response analysis of uncertain acoustic fields with limited information two hybrid uncertain models have been developed one is the hybrid probability and interval model in which the probability and interval variables exist simultaneously the other one is the hybrid interval probability model in which some distribution parameters of probability variables are expressed as interval variables for the unified response probability distribution analysis of acoustic fields under two hybrid uncertain models an inverse mapping hybrid perturbation method imhpm is proposed in imhpm the responses of two hybrid uncertain acoustic fields are converted to invertible functions of probability variables based on the taylor series expansion according to the inverse mapping relationships between responses and probability variables the formal expressions of the response probability distributions are yielded on the basis of the change of variable technique the variational ranges of the response probability distributions are estimated by the interval perturbation technique the effectiveness and efficiency of the proposed method for the unified response probability distribution analysis of two hybrid uncertain acoustic fields are investigated by a numerical example

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

a distributionally robust perspective on uncertainty quantification and chance constrained programming the objective of uncertainty quantification is to certify that a given physical engineering or economic system satisfies multiple safety conditions with high probability a more ambitious goal is to actively influence the system so as to guarantee and maintain its safety a scenario which can be modeled through a chance constrained program in this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry unimodality or independence patterns we delineate the watershed between tractability and intractability in ambiguity averse uncertainty quantification and chance constrained programming using tools from distributionally robust optimization we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones

robust nonlinear optimization with conic representable uncertainty set the robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints this methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty in this paper the robust optimization methodology is applied to the general nonlinear programming nlp problem involving both uncertain inequality and equality constraints the uncertainty set is defined by conic representable sets the proposed uncertainty set is general enough to include many uncertainty sets which have been used in literature as special cases the robust counterpart rc of the general nlp problem is approximated under this uncertainty set it is shown that the resulting approximate rc of the general nlp problem is valid in a small neighborhood of the nominal value furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far the resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

semidefinite programming for uncertain linear equations in static analysis of structures abstract this paper presents a method for computing a minimal bound that contains the solution set to the uncertain linear equations particularly we aim at finding a bounding ellipsoid for static response of structures where both external forces and elastic moduli of members are assumed to be imprecisely known and bounded by using the s lemma we formulate a semidefinite programming sdp problem which provides an outer approximation of the minimal bounding ellipsoid bounding ellipsoids are computed for nodal displacements of uncertain braced frames as the solutions of the presented sdp problems by using the primal dual interior point method

ellipsoidal bounds for uncertain linear equations and dynamical systems abstract in this paper we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations the proposed technique is based on the combination of a quadratic embedding of the uncertainty and the s procedure this formulation leads to convex optimization problems that can be essentially solved in o n3 n being the size of unknown vector by means of suitable interior point barrier methods as well as to closed form results in some particular cases we further show that the uncertain linear equations paradigm can be directly applied to various state bounding problems for dynamical systems subject to set valued noise and model uncertainty

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

reliable approximations of probability constrained stochastic linear quadratic control here we consider a state constrained stochastic linear quadratic control problem this problem has linear dynamics and a quadratic cost and states are required to satisfy a probabilistic constraint in this paper the joint probabilistic constraint in the model is converted to a conservative deterministic constraint using a multi dimensional chebyshev bound a maximum volume inscribed ellipsoid problem is solved to obtain this probability bound using the probability bound we develop a recursive state feedback control algorithm for a special class of state constrained stochastic linear quadratic regulator lqr the performance of this approach is explored in a numerical example

interval and subinterval perturbation finite element boundary element method for low frequency uncertain analysis of structural acoustic systems abstract uncertainties exist widely in the structural acoustic systems due to the physical imperfections model inaccuracies and system complexities to deal with the uncertainties the interval perturbation and subinterval perturbation techniques for the first time are extended and integrated into the hybrid finite element boundary element method ipfem bem in this work firstly the structural part of structural acoustic systems is modeled using finite element method fem and acoustic cavity is modeled by boundary element method bem then the interval perturbation technique is introduced to establish the interval perturbation equations of the system for large uncertainty levels the interval of parameters is divided into smaller sub intervals to improve the accuracy of proposed ipfem bem sub interval perturbation finite element boundary element method sipfem bem the proposed ipfem bem and sipfem bem are verified by two numerical examples the results obtained by ipfem bem sipfem bem and monte carlo method are compared it is found that ipfem bem and sipfem bem is reliable for the frequency response analysis of structural acoustic systems with small or large uncertain levels

a mixed integer programming for robust truss topology optimization with stress constraints this paper presents a mixed integer programming mip formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load a design dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization for a truss with the discrete member cross sectional areas it is shown that the robust topology optimization problem can be reduced to an mip problem which is solved globally numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

confidence ellipsoids for static response of trusses with load and structural uncertainties abstract this paper presents a semidefinite relaxation technique for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain truss we assume that the parameters both of member stiffnesses and external forces are uncertain but bounded by using a combination of the quadratic embedding technique of the uncertainty and the s procedure we formulate a semidefinite programming sdp problem which provides an outer approximation of the minimal bounding ellipsoid our approach has polynomial computational complexity of the problem size if the sdp problem presented is solved by using the primal dual interior point method the minimum bounding ellipsoids are computed for various trusses under several uncertain circumstances

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

compromise solutions for robust combinatorial optimization with variable sized uncertainty in classic robust optimization it is assumed that a set of possible parameter realizations the uncertainty set is modeled in a previous step and part of the input as recent work has shown finding the most suitable uncertainty set is in itself already a difficult task we consider robust problems where the uncertainty set is not completely defined only the shape is known but not its size such a setting is known as variable sized uncertainty in this work we present an approach how to find a single robust solution that performs well on average over all possible uncertainty set sizes we demonstrate that this approach can be solved efficiently for min max robust optimization but is more involved in the case of min max regret where positive and negative complexity results for the selection problem the minimum spanning tree problem and the shortest path problem are provided we introduce an iterative solution procedure and evaluate its performance in an experimental comparison

semidefinite programming for dynamic steady state analysis of structures under uncertain harmonic loads this paper presents semidefinite programming approaches for computing confidential bounds for the dynamic steady state responses of a damped structure subjected to uncertain driving loads we assume that amplitudes of harmonic driving loads obey a non probabilistic uncertainty model the semidefinite programming problems are formulated for finding confidential bounds for various characteristic amounts of dynamic steady state response including the modulus and phase angle of the complex amplitude of the displacement and stress numerical examples demonstrate that sufficiently tight bounds can be obtained by solving the presented semidefinite programming problems

conservative methods for structural optimization a method is introduced which adds a padding term to each constraint that is proportional to the gradient of the constraint one way to implement this approach is to determine the gradients of the constraints at the unpadded optimum design to modify the constraint allowables and then to restart the optimization a second implementation is proposed which imbeds the padding calculation into the optimization process by updating the padding term periodically during the optimization process finally an implementation which uses nonlinear constraint approximations and a second order update method is described

analysis of uncertain structural systems using interval analysis the imprecision or uncertainty present in many engineering analysis design problems can be modeled using probabilistic fuzzy or interval methods this work considers the modeling of uncertain structural systems using interval analysis by representing each uncertain input parameter as an interval number a static structural analysis problem can be expressed in the form of a system of linear interval equations in addition to the direct and gaussian elimination based solution approaches a combinatorial approach based on an exhaustive combination of the extreme values of the interval numbers and an inequality hased method are presented for finding the solution of interval equations the range or interval of the solution vector response parameters is found to increase with increasing size of the problem in all of the methods an interval truncation approach is proposed to limit the growth of intervals of response parameters so that realistic and accurate solutions can be obtained in the presence of large amounts of uncertainty numerical examples are presented to illustrate the computational aspects of the methods and also to indicate the importance of the truncation approach in practical problems the utility of interval methods in predicting the extreme values of the response parameters of structures is discussed

the rate of convergence of the augmented lagrangian method for nonlinear semidefinite programming we analyze the rate of local convergence of the augmented lagrangian method in nonlinear semidefinite optimization the presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices an implicit function theorem for semismooth functions and variational analysis on the projection operator in the symmetric matrix space without requiring strict complementarity we prove that under the constraint nondegeneracy condition and the strong second order sufficient condition the rate of convergence is linear and the ratio constant is proportional to 1 c where c is the penalty parameter that exceeds a threshold overline c 0

development of a simple and efficient method for robust optimization robust optimization problems are newly formulated and an efficient computational scheme is proposed both design variables and design parameters are considered as random variables about their nominal values to ensure the robustness of objective performance we introduce a new performance index bounding the performance together with a constraint limiting the performance variation the constraint variations are regulated by considering the probability of feasibility each probability constraint is transformed into a sub optimization problem by the advanced first order second moment afosm method for computational efficiency the proposed robust optimization method has the advantages that the mean value and the variation of the performance function are controlled simultaneously and rationally and the second order sensitivity information is not required even in case of gradient based optimization process the suggested method is examined by solving three examples and the results are compared with those for the deterministic case and those available in the literature copyright 2002 john wiley sons ltd

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

generalized online routing new competitive ratios resource augmentation and asymptotic analyses we consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints the problems are online because the set of locations are revealed incrementally over time we consider two main problems 1 the online traveling salesman problem tsp with precedence and capacity constraints and 2 the online tsp with m salesmen for both problems we propose online algorithms each with a competitive ratio of 2 for the m salesmen problem we show that our result is best possible we also consider polynomial time online algorithms we then consider resource augmentation where we give the online servers additional resources to offset the powerful offline adversary advantage in this way we address a main criticism of competitive analysis we consider the cases where the online algorithm has access to faster servers servers with larger capacities additional servers and or advanced information we derive improved competitive ratios we also give lower bounds on the competitive ratios under resource augmentation which in many cases are tight and lead to best possible results finally we study online algorithms from an asymptotic point of view we show that under general stochastic structures for the problem data unknown and unused by the online player the online algorithms are almost surely asymptotically optimal furthermore we provide computational results that show that the convergence can be very fast

outage constrained robust transmit optimization for multiuser miso downlinks tractable approximations by conic optimization in this paper we study a probabilistically robust transmit optimization problem under imperfect channel state information csi at the transmitter and under the multiuser multiple input single output miso downlink scenario the main issue is to keep the probability of each user s achievable rate outage as caused by csi uncertainties below a given threshold as is well known such rate outage constraints present a significant analytical and computational challenge indeed they do not admit simple closed form expressions and are unlikely to be efficiently computable in general assuming gaussian csi uncertainties we first review a traditional robust optimization based method for approximating the rate outage constraints and then develop two novel approximation methods using probabilistic techniques interestingly these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex gaussian quadratic form and they provide convex restrictions or safe tractable approximations of the original rate outage constraints in particular a feasible solution from any one of these methods will automatically satisfy the rate outage constraints and all three methods involve convex conic programs that can be solved efficiently using off the shelf solvers we then proceed to study the performance complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses finally simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature the results show that all three methods offer significantly improved solution quality and much lower complexity

sequential convex approximations to joint chance constrained programs a monte carlo approach when there is parameter uncertainty in the constraints of a convex optimization problem it is natural to formulate the problem as a joint chance constrained program jccp which requires that all constraints be satisfied simultaneously with a given large probability in this paper we propose to solve the jccp by a sequence of convex approximations we show that the solutions of the sequence of approximations converge to a karush kuhn tucker kkt point of the jccp under a certain asymptotic regime furthermore we propose to use a gradient based monte carlo method to solve the sequence of convex approximations

robust optimization methodology and applications robust optimization ro is a modeling methodology combined with computational tools to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set the paper surveys the main results of ro as applied to uncertain linear conic quadratic and semidefinite programming for these cases computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations of these counterparts are proposed making ro a useful tool for real world applications we discuss some of these applications specifically antenna design truss topology design and stability analysis synthesis in uncertain dynamic systems we also describe a case study of 90 lps from the netlib collection the study reveals that the feasibility properties of the usual solutions of real world lps can be severely affected by small perturbations of the data and that the ro methodology can be successfully used to overcome this phenomenon

bayesian modeling of age specific survival in nesting studies under dirichlet priors summary there has been much work done in nest survival analysis using the maximum likelihood ml method the ml method suffers from the instability of numerical calculations when models having a large number of unknown parameters are used a bayesian approach of model fitting is developed to estimate age specific survival rates for nesting studies using a large class of prior distributions the computation is done by gibbs sampling some latent variables are introduced to simplify the full conditional distributions the method is illustrated using both a real and a simulated data set results indicate that bayesian analysis provides stable and accurate estimates of nest survival rates

the generalized eigenvalue problem for tridiagonal symmetric interval matrices an algorithm to compute the eigenintervals of the generalized eigenvalue problem for tridiagonal symmetric matrices a b with interval entries is developed the algorithm is based on the sturm sequences and requires twice as much computational effort as for point matrices the algorithm is applied to the problem of computing the natural frequencies of a vibrating beam where the manufacturing tolerance is taken into consideration

interval analysis of vibrating systems interval calculus is a tool to evaluate a mathematical expression for ranges of values of its parameters the basic mathematical operations are defined in the interval algebra vibrating systems having system parameters initial conditions or forcing functions defined as intervals rather than single valued quantities have been modelled using interval calculus the eigenvalue problem for determining natural frequencies and vibrating modes of a system in the case of system matrix elements given as a range of values cannot be solved by exhaustion due to the prohibitively large number of solutions of the point number eigenvalue problem eigenvalue solution with interval evaluation of the commonly used numerical techniques is not feasible because if they are applied directly the solution intervals diverge an optimization technique was used to obtain the minimum radius intervals of the solution for the eigenvalue sensitivity problem to assure monotonicity and absolute inclusion necessary for convergence to the exact interval a converging interval halving sequence was developed for finite width interval matrices for numerical tests of the method a monte carlo solution was developed the results showed that interval analysis can predict the range of the eigenvalues with sufficient accuracy the response of a linear system to general excitation for interval matrices of the system parameters cannot be found with interval evaluation of the commonly used numerical techniques because if they are applied directly the solution intervals diverge interval modal analysis and the interval solution of the eigenvalue problem were developed an application is presented for the dynamic response of a rotor with interval bearing properties

robust solutions to multi facility weber location problem under interval and ellipsoidal uncertainty in this paper we consider the multi facility weber location problem mfwp with uncertain location of demand points and transportation cost parameters equivalent formulations of its robust counterparts for both the euclidean and block norms and interval and ellipsoidal uncertainty sets are given as conic linear optimization problems

capacity bounds for two dimensional asymmetric m ary 0 κ and d α runlength limited channels we present bounds on the two dimensional capacity for two sets of symmetric and asymmetric m ary runlength limited constraints based on simple constructions the bounds extend and generalize previous work on binary constraints

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

robust optimization in discrete design space for constrained problems robust design in discrete design space is defined as a discrete design that is insensitive to external uncertainties or variations the application of robust discrete design is not prevalent yet due to high computational cost a relatively simple method is proposed to select discrete and robust optimum at first the discrete design is achieved as the postprocess of conventional optimization an orthogonal array is established around a conventional optimum and the characteristic functions are evaluated the characteristic function is defined by considering the robustness of the objective and constraints the parameter design of the taguchi method is introduced to obtain the robust solution in discrete space the present method has insensitive performance to variations of the design variables within the selected discrete values enhancing the feasibility of constraints to enhance feasibility ranking the estimators of the characteristic function is developed several structural problems are solved to show the usefulness of the present method

interval static displacement analysis for structures with interval parameters in this paper a new method to solve the uncertain static displacement problem of structures with interval parameters is presented it is difficult to obtain all possible solutions with sharp bounds even if an optimum scheme is adopted when there are many uncertain parameters with the interval mathematics the interval finite element equation is developed based on the perturbation and the interval extension the upper and lower bounds of the static displacements are obtained in which the sharp bounds are guaranteed by the interval calculation operators two numerical examples a box cantilever beam and an automobile frame are given to illustrate the validity of the present method copyright 2001 john wiley sons ltd

robust control of partially observable failing systems this paper is concerned with optimal maintenance decision making in the presence of model misspecification specifically we are interested in the situation where the decision maker fears that a nominal bayesian model may be miss specified or unrealistic and would like to find policies that work well even when the underlying model is flawed to this end we formulate a robust dynamic optimization model for condition based maintenance in which the decision maker explicitly accounts for distrust in the nominal bayesian model by solving a worst case problem against a second agent nature who has the ability to alter the underlying model distributions in an adversarial manner the primary focus of our analysis is on establishing structural properties and insights that hold in the face of model miss specification in particular we prove i an explicit characterization of nature s optimal response through an analysis of the robust dynamic programming equation ii convexity results for both the robust va

a bayesian collocation method for static analysis of structures with unknown but bounded uncertainties abstract this paper proposes a bayesian collocation method bcm for static analysis of structures with unknown but bounded uncertainties or interval uncertainties unlike the existing collocation methods which construct surrogate model using preselected samples at fixed points the bcm chooses samples sequentially and adaptively based on bayesian inference theorem the bcm constructs a crude gaussian process surrogate model of structural response with selected samples then two acquisition functions named upper expected improvement ei up function and lower expected improvement ei lo function are defined simultaneously to guide the selection of next samples the samples will be collocated to the place where extrema of structural response are most likely to be found the procedure will repeat until the convergence criterion is met the extrema of the selected samples can be regarded as structural response bounds fewer samples are needed compared with existing collocation methods two numerical examples are used to demonstrate the accuracy and efficiency of the proposed method the results are compared with those obtained by existing methods the application of the method is performed by an engineering example the results show the validity of the proposed method

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

a distribution free nest survival model un modele de survie a temps discret est etudie qui permet d estimer la distribution de la survie des nids calculee a partir de leur date de creation il est applique a la survie des nids d une variete de colombes

modal analysis of structures with uncertain but bounded parameters via interval analysis in this paper the modal interval analysis method to estimate modal parameters frequency response function frf and mode shapes of structures with uncertain but bounded is presented although the system parameters or properties are uncertain in many engineering problems but their probable range of values i e upper and lower bounds can be provided from practical experience and engineering knowledge moreover to avoid the resonance of a structure and to consider the dynamic response of an uncertain one and also for reliability and stability analysis we often need the bounds of the ranges of structural characteristic parameters such as natural frequency and normal mode by using modal analysis and interval calculus we investigate the method of computing upper and lower bounds of paramenters such as natural frequencies modal shapes and frfs theoretically it is possible to analyze the uncertain but bounded of a structure by using modal analysis and interval calculus they can be estimated by modal interval analysis on the basis of the estimated intervals the engineering structure parameters can be applied into engineering design a numerical example is presented for a tower structure and the results illustrate that the proposed method is effective a comparison of the modal interval method with the results of monte carlo simulation serves to validate the solutions and to identify the bounded ranges of parameters

optimization for minimum sensitivity to uncertain parameters a procedure to design a structure for minimum sensitivity to uncertainties in problem parameters is described the approach is to directly minimize the sensitivity derivatives of the optimum design with respect to fixed design parameters using a nested optimization procedure the procedure is demonstrated for the design of a bimetallic beam for minimum weight with insensitivity to uncertainties in structural properties the beam is modeled with finite elements based on two dimensional beam analysis a sequential quadratic programming procedure used as the optimizer supplies the lagrange multipliers that are used to calculate the optimum sensitivity derivatives the procedure is validated by comparing the optimization results to parametric studies

a dynamic evolution scheme for structures with interval uncertainties by using bidirectional sequential kriging method abstract this paper proposes a bidirectional sequential kriging bsk method for nonlinear interval uncertainty quantification of dynamic systems different from existing surrogate based methods which build surrogate model at preselected samples the proposed method constructs surrogate models sequentially small amount of initial samples are generated by latin hypercube sampling lhs and a crude kriging surrogate model ksm is constructed then two index functions named lower confidence bound lcb and upper confidence bound ucb respectively are defined for sample collocation the index functions guide the search for the optima of structural response after iterations a sophisticated surrogate model will be obtained and the interval bounds of dynamic response can be calculated quickly with some auxiliary algorithms such as genetic algorithm ga numerical examples and engineering application are studied to verify the effectiveness of bsk the results show that compared with existing methods the proposed method can achieve higher accuracy with good efficiency in nonlinear interval analysis

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

antioptimization of structures with large uncertain but non random parameters via interval analysis non probabilistic interval modeling of uncertain but non random parameters for structures is developed in this paper for antioptimization analysis consisting in determining the least favorable responses the uncertain but non random parameter is considered to be a deterministic variable belonging to a set modeled as an interval the least favorable static displacement bound estimation for structures with uncertain but non random parameters is transformed into solving interval linear equations for small interval parameters the width of interval being small the uncertainties of interval parameters are treated as the perturbed quantities around the midpoint of interval parameters by means of the interval matrix central notation and the natural interval extension interval perturbation method for estimating the static displacement bound of structures with interval parameters was presented in the recent study by qiu et al 1 for large interval parameters a subinterval perturbation method for estimating the static displacement bound of structures with interval parameters is put forward in the study the numerical results show that a subinterval perturbation method yields tighter bounds than those yielded by the interval perturbation method

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