calculus for interval valued functions using generalized hukuhara derivative and applications this paper is devoted to studying differential calculus for interval valued functions by using the generalized hukuhara differentiability which is the most general concept of differentiability for interval valued functions conditions examples and counterexamples for limit continuity integrability and differentiability are given special emphasis is set to the class f t c g t where c is an interval and g is a real function of a real variable here the emphasis is placed on the fact that f and g do not necessarily share their properties underlying the extra care that must be taken into account when dealing with interval valued functions two applications of the obtained results are presented the first one determines a delta method for interval valued random elements in the second application a new procedure to obtain solutions to an interval differential equation is introduced our results are relevant to fuzzy set theory because the usual fuzzy arithmetic extension functions and mathematical analysis are done on a cuts which are intervals

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

a modified hybrid uncertain analysis method for dynamic response field of the lsoaac with random and interval parameters abstract for the prediction of dynamic response field of the luffing system of an automobile crane lsoaac with random and interval parameters a hybrid uncertain model is introduced in the hybrid uncertain model the parameters with certain probability distribution are modeled as random variables whereas the parameters with lower and upper bounds are modeled as interval variables instead of given precise values based on the hybrid uncertain model the hybrid uncertain dynamic response equilibrium equation in which different random and interval parameters are simultaneously included in input and output terms is constructed then a modified hybrid uncertain analysis method mhuam is proposed in the mhuam based on random interval perturbation method the first order taylor series expansion and the first order neumann series the dynamic response expression of the lsoaac is developed moreover the mathematical characteristics of extrema of bounds of dynamic response are determined by random interval moment method and monotonic analysis technique compared with the hybrid monte carlo method hmcm and interval perturbation method ipm numerical results show the feasibility and efficiency of the mhuam for solving the hybrid lsoaac problems the effects of different uncertain models and parameters on the lsoaac response field are also investigated deeply and numerical results indicate that the impact made by the randomness in the thrust of the luffing cylinder f is larger than that made by the gravity of the weight in suspension q in addition the impact made by the uncertainty in the displacement between the lower end of the lifting arm and the luffing cylinder a is larger than that made by the length of the lifting arm l

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

dynamic response analysis of stochastic truss structures under non stationary random excitation using the random factor method abstract the dynamic characteristics and responses of stochastic truss structures under non stationary random excitation are investigated using a new method called the random factor method rfm using the rfm the structural physical parameters and geometry can be considered as random variables based on the assumption that the randomness on each element is the same for all elements the structural stiffness and mass matrices can then respectively be described by the product of two parts corresponding to the random factor and the deterministic matrix from the expressions of structural random response in the frequency domain computational expressions for the mean value standard deviation and variation coefficient of the mean square value of the non stationary random displacement and stress response are developed by means of the random variable s functional moment method and the algebra synthesis method the influences of the randomness of the structural parameters on the dynamic characteristics structural displacement and stress responses are demonstrated using a truss structure

multiobjective programming in optimization of interval objective functions a generalized approach abstract we generalize known concepts those introduced by ishihuchi and tanaka 1 and rommerlfanger et al 2 of the solution of the linear programming problem with interval coefficients in the objective function based on preference relations between intervals we unify all the discussed concepts as well as the corresponding solution methods into one general framework

numerical methods for the topology optimization of structures that exhibit snap through the inclusion of non linear elastic analyses into the topology optimization problem is necessary to capture the finite deformation response e g the geometric non linear response of compliant mechanisms in previous work the non linear response is computed by standard non linear elastic finite element analysis here we incorporate a load displacement constraint method to traverse non linear equilibrium paths with limit points to design structures that exhibit snap through behaviour to accomplish this we modify the basic arc length algorithm and embed this analysis into the topology optimization problem copyright 2002 john wiley sons ltd

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

interval dynamic response analysis of vehicle bridge interaction system with uncertainty abstract interval dynamic response analysis of vehicle bridge interaction system with uncertain parameters is studied in this paper the bridge s and vehicle s parameters are considered as interval variables a half car model is used to represent a moving vehicle and the bridge is assumed as a simply supported euler bernoulli beam by introducing the interval algorithm into the dynamic analysis of vehicle bridge interaction system the expressions of the midpoint value interval width lower and upper bounds of interval bridge dynamic response are developed the lower and upper bounds are respectively the minimum and maximum values of bridge dynamic response which can also be determined by optimization approaches a heuristic optimization method a new particle swarm optimization method with low discrepancy sequence initialized particles and high order nonlinear time varying inertia weight and constant acceleration coefficients lhnpso is then developed to find the bounds of bridge displacement examples are used to illustrate the effectiveness of the presented methods and monte carlo simulations are implemented to validate the computational results the effects of individual system parameters on bridge response are also investigated

a meshfree level set method for topological shape optimization of compliant multiphysics actuators abstract this paper proposes a topology optimization method for compliant multiphysics actuators of geometrically nonlinear structures using meshfree galerkin weak forms and level set methods the design boundary is implicitly represented as the zero level set of a higher dimensional level set function leading to a level set model capable of handling complex shape and topological changes with flexibilities a family of compactly supported radial basis functions csrbfs is firstly used to interpolate the level set function of lipschitz continuity and then augmented to construct the shape function for meshless approximation by satisfying basic requirements in particular the predetermined consistency and the kronecker delta function property a meshless galerkin method mgm with global weak forms is established to implement the discretization of the state equations the design of actuators is transformed into an easier size optimization from a more difficult shape and topology optimization the design boundary evolution is just a question of advancing the discrete level set function in time by updating the design variables of the size optimization compared to most conventional level set methods the proposed meshless level set method is able to implement the free moving boundary discontinuities without remeshing and unify two different numerical procedures in propagating the discrete level set function e g eulerian grid and approximating the state equation e g lagrangian mesh respectively this method can also avoid numerical difficulties in solving a series of complicate hamilton jacobi partial differential equations pdes with explicit time schemes two typical numerical examples are used to demonstrate the effectiveness of the proposed method

on multiplicativity of the bernstein operator for continuous functions f and g we prove that the bernstein operator b n is multiplicative for all n 1 and all email protected 2 0 1 if and only if at least one of the functions f and g is a constant function some other variants of multiplicativity are also considered

hybrid uncertain analysis for structural acoustic problem with random and interval parameters abstract in this paper hybrid perturbation monte carlo method hpmcm and hybrid perturbation vertex method hpvm are developed for the hybrid uncertain structural acoustic problem with random and interval variables the random variables are used to treat the uncertain parameters with sufficient information whereas the interval variables are used to treat the uncertain parameters with limited information in hpmcm the intervals of expectation and variance of the frequency response vector are calculated by a combination of random interval matrix perturbation method random interval moment method and monte carlo method in hpvm a monotonicity analysis is conducted for the frequency response vector based on the random interval matrix perturbation method and then the intervals of expectation and variance of the frequency response vector are calculated by employing the random interval moment method and the vertex method numerical results on a shell structural acoustic problem verify the effectiveness and high efficiency of hpvm compared with hpmcm

stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters the research work presents the study on non deterministic problems in the presence of the multiple imprecise random field uncertainties by extending the spectral stochastic finite element framework the standard random field is expanded to characterize the behaviour of physical model with imprecise randomness more appropriately for real engineering problems based on available sources of uncertainty the young s modulus and body force of structures are considered as imprecise random fields with bounded statistical moments mathematical expressions and solution procedure are developed to produce the uncertain but bounded statistical characteristics of responses namely interval mean value interval standard deviation and bounding distribution functions the bounding probability density and cumulative distribution of the imprecise random response are then effectively visualized by means of polynomial chaos expansion the feasibility and effectiveness of the presented method are illustrated by three numerical examples

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

dynamic response analysis of structure under time variant interval process model abstract due to the aggressiveness of the environmental factor the variation of the dynamic load the degeneration of the material property and the wear of the machine surface parameters related with the structure are distinctly time variant typical model for time variant uncertainties is the random process model which is constructed on the basis of a large number of samples in this work we propose a time variant interval process model which can be effectively used to deal with time variant uncertainties with limit information and then two methods are presented for the dynamic response analysis of the structure under the time variant interval process model the first one is the direct monte carlo method dmcm whose computational burden is relative high the second one is the monte carlo method based on the chebyshev polynomial expansion mcm cpe whose computational efficiency is high in mcm cpe the dynamic response of the structure is approximated by the chebyshev polynomials which can be efficiently calculated and then the variational range of the dynamic response is estimated according to the samples yielded by the monte carlo method to solve the dependency phenomenon of the interval operation the affine arithmetic is integrated into the chebyshev polynomial expansion the computational effectiveness and efficiency of mcm cpe is verified by two numerical examples including a spring mass damper system and a shell structure

semiclassical treatment of the path integral approach to special effects in superconductivity abstract distinctive features of the flux mode regime in the anderson josephson potential are analyzed using both semiclassical path integral and instanton techniques this potential governs the behavior of a superconducting ring interrupted by a weak josephson junction after establishing the relation between wkb and functional integral approximations semiclassical expansions are derived from a discretized version of the feynman propagator the physical meaning of instantons is extended to the condensed matter problem of energy spectrum for weak link ring states localized near the minimum energy regions under certain circumstances an improved wkb approximation enables us to find expression for the decay rates of metastable states performing the reduction of the original anderson josephson shape to a double hump structure although we have not discussed here the temperature dependence of the josephson plasma frequency our calculations are consistent with recent theories for systems at finite temperatures with two metastable states separated by a potential energy barrier

quasi random initial population for genetic algorithms the selection of the initial population in a population based heuristic optimizationmethod is important since it affects the search for several iterations and often has an influence on the final solution if no a priori information about the optima is available the initial population is often selected randomly using pseudorandom numbers usually however it is more important that the points are as evenly distributed as possible than that they imitate random points in this paper we study the use of quasi random sequences in the initial population of a genetic algorithm sample points in a quasi random sequence are designed to have good distribution properties here a modified genetic algorithm using quasi random sequences in the initial population is tested by solving a large number of continuous benchmark problems from the literature the numerical results of two implementations of genetic algorithms using different quasi random sequences are compared to those of a traditional implementation using pseudorandom numbers the results obtained are promising

feynman propagator for time dependent lagrangians possessing an invariant quadratic in momentum a class of time dependent classical lagrangians possessing an invariant quadratic in momentum is considered from a quantal point of view quantum mechanics is introduced through the feynman propagator defined as a path integral involving the classical action it is shown without carrying out an explicit path integration that the propagator for such a time dependent system is related to the propagator of an associated time independent problem the expansion of the propagator in terms of the eigenfunctions of the invariant operator is derived and the equivalence of the present theory to that of lewis and reisenfeld 1969 is discussed explicit analytic forms of propagators are obtained for some cases to illustrate the application of the present approach

topology design optimization of geometrically non linear structures using meshfree method a topology optimization method using meshfree methods is developed for geometrically non linearly structures a density approach is used to optimally distribute the bulk material densities in a continuum design domain the reproducing kernel rk shape function is employed to discretize both displacement and bulk density fields thus the points can be located at any part of the design domain and be easily included in or excluded from the response analysis the well known convergence difficulty which normally occurs in the sub domain of low bulk density can be avoided by excluding the sub domain the numerical instability of bulk density solution due to the rank deficiency of system matrix is effectively prevented by properly selecting the number of independent design variables through numerous numerical examples we confirm that the developed method works very well even in the large deformation problems the sub domain exclusion scheme is found to be greatly beneficial in terms of computational costs compared with the results without the scheme

evolutionary algorithms with preference polyhedron for interval multi objective optimization problems multi objective optimization problems mops with interval parameters are ubiquitous in real world applications existing evolutionary optimization methods however aim to obtain a set of well converged and evenly distributed pareto optimal solutions in this paper we presented a novel evolutionary algorithm ea that interacts with a decision maker dm during the optimization process to obtain the most preferred solution the theory of preference polyhedron for the optimization problem with interval parameters was developed first an interactive evolutionary algorithm iea for mops with interval parameters was then proposed based on the theory of preference polyhedron the algorithm periodically provides a set of non dominated solutions to the dm a preference polyhedron is constructed in the objective space by taking the worst solution chosen by the dm as the vertex the solutions with the same rank are sorted based on the polyhedron constructed finally our method was empirically evaluated on several mops with interval parameters where the value functions were used to simulate the dm s responses the numerical results indicated that our method is simpler and more efficient than the a posteriori method

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

a general formula for the calculation of gaussian path integrals in two and three euclidean dimensions abstract the method which was used in a preceding article for the analytical evaluation of gaussian path integrals in one euclidean dimension is generalized as before the final results are formulae directly applicable to all gaussian path integrals this time in two and in three euclidean dimensions respectively the classical action is almost entirely integrated and the proportionality factor f tb ta in front of the exponential part is expressed in terms of a number of time dependent functions which one encounters in the description of the motion along the classical path the quadratic lagrange function is kept as general as possible e g involving twenty eight terms in the three dimensional case the well known time discretization procedure for path integrals has been avoided instead one of the main steps in the theoretical development consists in applying the convolution property of quantum mechanical green s functions i e in three euclidean dimensions k r b t b r a t a k r b t b r t k r t r a t a d r this equality leads to a non linear algebraic relation between f tb ta f tb t and f t ta the solution of this equation yields the f factor which appears in the propagator represented by the gaussian path integral at two locations the use of some remarkable determinantal identity previously unknown to the author has been indispensable in order to attain the desired final result in the appendix the n dimensional generalization of these identities is formulated

structural shape and topology optimization using a meshless galerkin level set method summary this paper aims to propose a meshless galerkin level set method for shape and topology optimization of continuum structures to take advantage of the implicit free boundary representation scheme the design boundary is represented as the zero level set of a scalar level set function to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface compactly supported radial basis functions csrbfs are used to parameterize the level set function and construct the shape functions for meshfree approximations based on a set of unstructured field nodes the meshless galerkin method with global weak form is used to implement the discretization of the state equations this provides a pathway to unify the two different numerical stages in most conventional level set methods 1 the propagation of discrete level set function on a set of eulerian grid and 2 the approximation of discrete equations on a set of lagrangian mesh the original more difficult shape and topology optimization based on the level set equation is transformed into a relatively easier size optimization to which many efficient optimization algorithms can be applied the proposed level set method can describe the moving boundaries without remeshing for discontinuities the motion of the free boundary is just a question of advancing the discrete level set function in time by solving the size optimization several benchmark examples are used to demonstrate the effectiveness of the proposed method the numerical results show that the proposed method can simplify numerical process and avoid numerical difficulties involved in most conventional level set methods it is straightforward to apply the proposed method to more advanced shape and topology optimization problems copyright 2011 john wiley sons ltd

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

transient waves in composite laminated plates with uncertain load and material property a method is suggested to deal with the wave propagation problems in composite laminated plates subjected to uncertainty in load and material property based on the interval analysis method and the hybrid numerical method hnm the uncertain parameters are treated as intervals in which only their bounds of the uncertainty are needed using the first order taylor expansion the transient responses can be approximated as a linear function of the uncertain parameters in this function the transient responses at the midpoints of the uncertain parameters can be obtained directly through the hnm a sensitivity analysis technique is suggested to calculate the first derivative of the transient responses with respect to each uncertain parameter based on two cases that the parameter exists in load or material property applying the interval extension in interval mathematics the lower and upper bounds of the transient responses caused by the uncertainty can be finally obtained the present method is applied to a numerical example in which the uncertainty of the load elastic constants of the layer material and ply orientations are all investigated and the results demonstrate the effectiveness of the present method

interval uncertain method for multibody mechanical systems using chebyshev inclusion functions this study proposes a new uncertain analysis method for multibody dynamics of mechanical systems based on chebyshev inclusion functions the interval model accounts for the uncertainties in multibody mechanical systems comprising uncertain but bounded parameters which only requires lower and upper bounds of uncertain parameters without having to know probability distributions a chebyshev inclusion function based on the truncated chebyshev series rather than the taylor inclusion function is proposed to achieve sharper and tighter bounds for meaningful solutions of interval functions to effectively handle the overestimation caused by the wrapping effect intrinsic to interval computations the mehler integral is used to evaluate the coefficients of chebyshev polynomials in the numerical implementation the multibody dynamics of mechanical systems are governed by index 3 differential algebraic equations daes including a combination of differential equations and algebraic equations responsible for the dynamics of the system subject to certain constraints the proposed interval method with chebyshev inclusion functions is applied to solve the daes in association with appropriate numerical solvers this study employs hht i3 as the numerical solver to transform the daes into a series of nonlinear algebraic equations at each integration time step which are solved further by using the newton raphson iterative method at the current time step two typical multibody dynamic systems with interval parameters the slider crank and double pendulum mechanisms are employed to demonstrate the effectiveness of the proposed methodology the results show that the proposed methodology can supply sufficient numerical accuracy with a reasonable computational cost and is able to effectively handle the wrapping effect as cosine functions are incorporated to sharpen the range of non monotonic interval functions copyright 2013 john wiley sons ltd

path integral formulation for levy flights evaluation of the propagator for free linear and harmonic potentials in the over and underdamped limits levy flights can be described using a fokker planck equation which involves a fractional derivative operator in the position coordinate such an operator has its natural expression in the fourier domain starting with this we show that the solution of the equation can be written as a hamiltonian path integral though this has been realized in the literature the method has not found applications as the path integral appears difficult to evaluate we show that a method in which one integrates over the position coordinates first after which integration is performed over the momentum coordinates can be used to evaluate several path integrals that are of interest using this we evaluate the propagators for a free particle b particle subjected to a linear potential and c harmonic potential in all the three cases we have obtained results for both overdamped and underdamped cases doi 10 1103 physreve 86 061105

optimal layout design of three dimensional geometrically non linear structures using the element connectivity parameterization method the topology design optimization of three dimensional geometrically non linear continuum structures is still difficult not only because of the size of the problem but also because of the unstable continuum finite elements that arise during the optimization to overcome these difficulties the element connectivity parameterization ecp method with two implementation formulations is proposed in ecp structural layouts are represented by inter element connectivity which is controlled by the stiffness of element connecting zero length links depending on the link location ecp may be classified as an external ecp e ecp or an internal ecp i ecp in this paper i ecp is newly developed to substantially enhance computational efficiency the main idea in i ecp is to reduce system matrix size by eliminating some internal degrees of freedom associated with the links at voxel level as for ecp implementation with commercial software e ecp developed earlier for two dimensional problems is easier to use even for three dimensional problems because it requires only numerical analysis results for design sensitivity calculation the characteristics of the i ecp and e ecp methods are compared and these methods are validated with numerical examples copyright 2006 john wiley sons ltd

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

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

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

topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system abstract this paper proposes a topology optimization for a linear elasticity design problem subjected to an uncertain load the design problem is formulated to minimize a robust compliance that is defined as the maximum compliance induced by the worst load case of an uncertain load set since the robust compliance can be formulated as the scalar product of the uncertain input load and output displacement vectors the idea of aggregation used in the field of control is introduced to assess the value of the robust compliance the aggregation solution technique provides the direct relationship between the uncertain input load and output displacement as a small linear system composed of these vectors and the reduced size of a symmetric matrix in the context of a discretized linear elasticity problem using the finite element method introducing the constraint that the euclidean norm of the uncertain load set is fixed the robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix according to the rayleigh ritz theorem for symmetric matrices moreover the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix the proposed structural optimization method is implemented using topology optimization and the method of moving asymptotes mma the numerical examples provided illustrate mechanically reasonable structures and establish the worst load cases corresponding to these optimal structures

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

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

fuzzy programming with fuzzy decisions and fuzzy simulation based genetic algorithm this paper provides a spectrum of chance constrained programming as well as chance constrained multiobjective programming and chance constrained goal programming with fuzzy rather than crisp decisions which will seek a fuzzy set from the given reference collection as an optimal solution the technique of fuzzy simulation is also presented to check fuzzy chance constraints and to handle fuzzy objective and goal constraints finally a fuzzy simulation based genetic algorithm for solving these models will be designed and illustrated by some numerical examples

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

stochastic multiresonance and correlation time controlled stability for a harmonic oscillator with fluctuating frequency the long time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force and an additive thermal noise is considered analytically the colored fluctuations of the oscillator frequency are modeled as a three level markovian noise using the shapiro loginov formula the exact expressions of several stochastic resonance sr characteristics such as the spectral amplification the variance of the output signal the signal to noise ratio and the sr gain have been calculated the nonmonotonic dependence of the sr characteristics versus the noise parameters as well as versus the input signal frequency and also the conditions for the appearance of energetic instability are analyzed in particular the multiresonancelike behavior of the variance and the signal to noise ratio as functions of the noise correlation time are observed and the connection between the occurrence of energetic instability and the phenomenon of stochastic multiresonance is established some unexpected effects such as the hypersensitive response of the spectral amplification to small variations of the noise amplitude encountered in the case of a large flatness of the colored noise are also discussed

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

integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems heuristic optimization provides a robust and efficient approach for solving complex real world problems the aim of this paper is to introduce a hybrid approach combining two heuristic optimization techniques particle swarm optimization pso and genetic algorithms ga our approach integrates the merits of both ga and pso and it has two characteristic features firstly the algorithm is initialized by a set of random particles which travel through the search space during this travel an evolution of these particles is performed by integrating pso and ga secondly to restrict velocity of the particles and control it we introduce a modified constriction factor finally the results of various experimental studies using a suite of multimodal test functions taken from the literature have demonstrated the superiority of the proposed approach to finding the global optimal solution

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

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

phase space path integral approach to harmonic oscillator with a time dependent force constant the quantum statistical mechanical propagator for a harmonic oscillator with a time dependent force constant m omega 2 t has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest in a previous work we had obtained the exact propagator for motion in an arbitrary time dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of levy flights a result that can be easily extended to brownian motion in this paper we make a connection between the overdamped brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly we find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time dependent force constant has the form omega 2 t lambda 2 t d lambda t dt where lambda t is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously we also employ this method to arrive at a formal solution of the propagator for both levy flights and brownian subjected to a time dependent harmonic potential in the underdamped limit of friction c 2015 elsevier b v all rights reserved

a new measure of irregularity of distribution and quasi monte carlo methods for global optimization measures of irregularity of distribution such as discrepancy and dispersion play a major role in quasi monte carlo methods for integration and optimization in this paper a new measure of irregularity of distribution called volume dispersion is introduced its relation to the discrepancy and traditional dispersion and its applications in global optimization problems are investigated optimization errors are bounded in terms of the volume dispersion also the volume dispersion is generalized to the so called f volume dispersion and quasi f volume dispersion they are reasonable measures of representation of point sets for given probability distributions on general domains and have potential applications in optimization problems when prior knowledge about the possible location of the optimizer is known and in the problems of experimental designs methods of generating point sets with low quasi f volume dispersion are described

damping mechanisms in the path integral approach to special effects in superconductivity abstract previous work on semiclassical approximations in squids which involved feynman s path integral technique is here extended to damped josephson systems quantum decay rates of unstable energy levels near the bottom of the quartic potential well are examined rates diagram is compared with that obtained for the undamped case agreement with caldeira leggett results is discussed a description of continuous flux measurements is developed the spreading of the wave function leads to the treatment of flux and charge as canonically conjugate variables

interval robust multi objective algorithm abstract this paper introduces a method for solving multi objective optimization problems in uncertain environment when the uncertainty factors of the optimization problem can be included into the mathematical model through bounded intervals i rmoa interval robust multi objective algorithm can find an enclosure of the robust pareto frontier in this approach the robust pareto solutions are the ones that have the best performance when the worst case scenario characterized by the uncertainty parameters is considered i rmoa has some positive aspects it does not require the calculus of derivatives it has only two input parameters it is a reliable tool for solving different robust optimization problems which can be nonlinear and discontinuous or have nonconvex pareto frontier for instance the success of the method depends only on the quality of the objective inclusion functions and the precision parameters its disadvantage lies in the fact that it requires high computational effort when high dimensional problems are considered or when a very accurate enclosure is needed two analytical robust test functions are proposed to be treated by i rmoa and to validate the results provided by a stochastic multi objective optimization method the results are satisfactory

optimization based on reliability and confidence interval design for the structural acoustic system with interval probabilistic variables abstract in practice the uncertain parameters whose unique distributions cannot be identified on the basis of limited data existed in the structural acoustic system extensively the uncertain parameters with limited data can be modeled as interval probabilistic variables whose distribution parameters are expressed as interval variables instead of unique values for the optimization of the structural acoustic system with interval probabilistic variables a new optimization technique named as the optimization based on reliability and confidence interval design o rcid is developed o rcid is a nested loop optimization whose computational cost during the evaluation of the confidence interval of sound pressure response and the system reliability is considerable to improve the computational efficiency of o rcid a change of variable interval probabilistic perturbation method cv ippm which is based on the perturbation approach and change of variable technique is proposed to calculate the confidence interval of sound pressure response and the system reliability by introducing cv ippm the nested loop o rcid is converted into an approximate single loop one which can be efficiently solved numerical examples demonstrate the effectiveness and efficiency of o rcid based on cv ippm for the optimization of the structural acoustic system with interval probabilistic variables

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

robust topology optimization under multiple independent unknown but bounded loads abstract the optimal designs obtained from the deterministic topology optimization without considering the loading uncertainties may become vulnerable or even lead to catastrophic failures a two level optimization formulation is often used in the robust topology optimization rto under uncertain loads various approaches have been reported to identify the critical loads associated with the worst structure responses because convex model approaches apply convex approximations to the original non convex model at the lower level the optimal designs obtained by these methods are greatly dependent on the quality of the approximation in this paper a new formulation based on the wolfe duality for the rto problems with multiple independent unknown but bounded loads is proposed following the two level formulation the lower level optimization problem for the worst multiple independent uncertain loading case is transformed by the wolfe duality both the first order necessary conditions and the second order sufficient conditions are derived rigorously to validate the solution optimality despite of the non convexity associated with the lower level formulation numerical examples are also presented to demonstrate the proposed approach

level set topology optimization for mechanical metamaterials under hybrid uncertainties abstract this paper proposes a level set based robust topology optimization rto method for computational design of metamaterials under hybrid uncertainties e g auxetics with negative poisson s ratio where the young s modulus of the solid is described as a random variable while the poisson s ratio is regarded as an interval variable firstly the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function secondly the interval mean and interval variance are computed by a hybrid uncertain analysis approach termed as polynomial chaos chebyshev interval pcci method thirdly the design sensitivities of the robust objective function are obtained after the implementation of the pcci method finally a powerful parametric level set method plsm in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems this method is non intrusive and general and can be easily extended to a range of design problems of micro structured metamaterials

non probabilistic reliability based topology optimization of geometrically nonlinear structures using convex models this paper describes a non probabilistic reliability based topology optimization method for the design of continuum structures undergoing large deformations the variation of the structural system is treated with the multi ellipsoid convex model which is a realistic description of the parameters being inherently uncertain but bounded or lacking sufficient probabilistic data the formulation of the optimal design is established as a volume minimization problem with non probabilistic reliability constraints on the geometrically nonlinear structural behaviour in order to circumvent numerical difficulties in solving the nested double loop optimization problem a performance measure based approach is employed to transform the constraint on the reliability index into one on the concerned performance in conjunction with an efficient adjoint variable scheme for the sensitivity analysis of reliability constraints the optimization problem is solved by gradient based mathematical programming methods three numerical examples for the optimization design of planar structures are presented to illustrate the validity and applicability of the proposed method the obtained optimal solutions show the importance of incorporating various uncertainties in the design problem moreover it is also revealed that the geometrical nonlinearity needs to be accounted for to ensure satisfaction of the reliability constraints in the optimal design of structures with large deformation

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

adaptive random search in quasi monte carlo methods for global optimization abstract quasi monte carlo random search is useful in nondifferentiable optimization borrowing ideas of population evolution from genetic algorithms we introduce an adaptive random search in quasi monte carlo methods aqmc for global optimization adaptive technique is used such that local search can head for local maximum points quickly because the search direction and search step size are adjusted according to the previous search result new individuals will be imported into the population adaptively according to population evolution degree for quasi random sequences with low discrepancy the new generated successive points fill in the gaps in the previously generated distribution in e the domain of function f which ensures that e can be searched evenly and the global extremum can be found in conclusion the aqmc method not only speeds up the random search but also balances the global and local demand adaptive equalization

coupled fuzzy interval model and method for structural response analysis with non probabilistic hybrid uncertainties abstract in many engineering practices with uncertainty the non probabilistic methods play an increasing important role to overcome the limitation of traditional single uncertainty modeling methods in handling coupled uncertain problems this paper develops a more general hybrid uncertainty analysis framework the non probabilistic hybrid uncertainties are expressed as coupled fuzzy interval variables where the bounds of interval are interpreted as fuzzy sets instead of deterministic values by means of the cut set strategy and decomposition theorem in fuzzy set theory the hybrid uncertain problem is transformed into a series of dual interval problems the conservative and radical extreme value predictions in different variable subspaces are adopted to characterize the coupled uncertainty in output response to further improve the computational efficiency of extreme value prediction an adaptive response surface model using radial basis function is proposed where the potential global optimum points are introduced as the new sample points in the sequential sampling process finally the effectiveness of the proposed method on dealing with non probabilistic hybrid uncertainties is validated by two examples

robust topology optimization minimization of expected and variance of compliance robust topology optimization has long been considered computationally intractable as it combines two highly expensive computational strategies this paper considers simultaneous minimization of expectancy and variance of compliance in the presence of uncertainties in loading magnitude using exact formulations and analytically derived sensitivities it shows that only a few additional load cases are required which scales in polynomial time with the number of uncertain load cases the approach is implemented using the level set topology optimization method shape sensitivities are derived using the adjoint method several examples are used to investigate the effect of including variance in robust compliance optimization

memory enhanced energetic stability for a fractional oscillator with fluctuating frequency the long time limit behavior of the variance and the correlation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered the influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean the viscoelastic type friction kernel with memory is assumed as a power law function of time the exact expressions of stochastic resonance sr characteristics such as variance and signal to noise ratio snr have been calculated it is shown that at intermediate values of the memory exponent the energetic stability of the oscillator is significantly enhanced in comparison with the cases of strong and low memory a multiresonancelike behavior of the variance and snr as functions of the memory exponent is observed and a connection between this effect and the memory induced enhancement of energetic stability is established the effect of memory induced energetic stability encountered in case the harmonic potential is absent is also discussed

small sample uniformity in random number generation nonstatistical notions of uniformity suitable for small samples are proposed and studied new algorithms are presented for generation of small samples of quasi random points good with respect to distance plane projection or plane section uniformity examples are presented for visual evaluation of uniformity in small samples on the screen of computers the methods can be used for generation of quasi random lattices for nonconvex global optimization multiple integration and other applications

topology optimization of structures using meshless density variable approximants this paper proposes a new structural topology optimization method using a dual level point wise density approximant and the meshless galerkin weak forms totally based on a set of arbitrarily scattered field nodes to discretize the design domain the moving least squares mls method is used to construct shape functions with compactly supported weight functions to achieve meshless approximations of system state equations the mls shape function with the zero order consistency will degenerate to the well known shepard function while the mls shape function with the first order consistency refers to the widely studied mls shape function the shepard function is then applied to construct a physically meaningful dual level density approximant because of its non negative and range restricted properties first in terms of the original set of nodal density variables this study develops a nonlocal nodal density approximant with enhanced smoothness by incorporating the shepard function into the problem formulation the density at any node can be evaluated according to the density variables located inside the influence domain of the current node second in the numerical implementation we present a point wise density interpolant via the shepard function method the density of any computational point is determined by the surrounding nodal densities within the influence domain of the concerned point according to a set of generic design variables scattered at field nodes an alternative solid isotropic material with penalization model is thus established through the proposed dual level density approximant the lagrangian multiplier method is included to enforce the essential boundary conditions because of the lack of the kronecker delta function property of mls meshless shape functions two benchmark numerical examples are employed to demonstrate the effectiveness of the proposed method in particular its applicability in eliminating numerical instabilities copyright 2012 john wiley sons ltd

a multicriteria fuzzy linear programming method for water supply system development planning abstract a method is presented for solving a multicriteria linear program where the coefficients of the objective functions and the constraints are fuzzy numbers of the l r type assuming the aspiration levels for particular criteria to be fuzzy and basing on comparison of fuzzy numbers the original problem is transformed into a multicriteria linear fractional program the latter is solved using an interactive technique involving a linear programming procedure in the calculation phase this method has been elaborated with a view to the application to the development of a water supply system

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

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

on the multiplicativity of linear operators abstract inspired by the well known gruss inequality we study the multiplicativity of linear operators satisfying certain conditions applications to some classical operators will be given

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

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique abstract this paper presents a simple but effective additive hyperelasticity technique to circumvent numerical difficulties in solving the material density based topology optimization of elastic structures undergoing large displacements by adding a special hyperelastic material to the design domain excessive distortion and numerical instability occurred in the low density or intermediate density elements are thus effectively alleviated during the optimization process the properties of the additional hyperelastic material are established based on a new interpolation scheme which allows the nonlinear mechanical behaviour of the remodelled structure to achieve an acceptable approximation to the original structure in conjunction with the adjoint variable scheme for sensitivity analysis the topology optimization problem is solved by a gradient based mathematical programming algorithm numerical examples are given to demonstrate the effectiveness of the proposed method

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

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

entropies and heun functions associated with positive linear operators we consider a parameterized probability distribution p x p 0 x p 1 x and denote by s x the squared l2 norm of p x the properties of s x are useful in studying the renyi entropy the tsallis entropy and the positive linear operator associated with p x we show that for a family of distributions including the binomial and the negative binomial distributions s x is a heun function reducible to the gauss hypergeometric function 2f1 several properties of s x are derived including integral representations and upper bounds examples and applications are given concerning classical positive linear operators

introducing loading uncertainty in topology optimization uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions this paper introduces an efficient and accurate approach to robust structural topology optimization the objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction where uncertainties are assumed normally distributed and statistically independent this new approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities illustrative examples using a level set based topology optimization method are then used to demonstrate the proposed approach

product demand forecasts using wavelet kernel support vector machine and particle swarm optimization in manufacture system demand forecasts play a crucial role in supply chain management the future demand for a certain product is the basis for the respective replenishment systems aiming at demand series with small samples seasonal character nonlinearity randomicity and fuzziness the existing support vector kernel does not approach the random curve of the sales time series in the l 2 r n space quadratic continuous integral space in this paper we present a hybrid intelligent system combining the wavelet kernel support vector machine and particle swarm optimization for demand forecasting the results of application in car sale series forecasting show that the forecasting approach based on the hybrid psowv svm model is effective and feasible the comparison between the method proposed in this paper and other ones is also given which proves that this method is for the discussed example better than hybrid psov svm and other traditional methods

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

a concept of the optimal solution of the transportation problem with fuzzy cost coefficients abstract in the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed

safety margin analysis of buckling for structures with unknown but bounded uncertainties abstract a safety margin of buckling for structures with unknown but bounded uncertainties is proposed in this paper the perturbation matrixes consisting of the elastic stiffness matrix and the geometric stiffness matrix are introduced to derive the concept of safety margin the concept of safety margin of buckling is first proposed to quantify the influence of uncertain parameters on structural buckling based on the spectrum norm and the singular value analysis the mathematical basis of the safety margin is expounded furthermore to obtain a more accurate estimation of safety margin the correction factor for the safety margin is introduced through the interval extension of interval analysis two engineering examples compared with traditional interval analysis method are utilized to demonstrate the validity of the proposed safety margin and numerical results indicate that the safety margin can provide a relatively accurate index to indicate the allowable perturbation range of the perturbation matrix of a structure under given loads

the analytical evaluation of one dimensional gaussian path integrals abstract in the introductory section 1 it is outlined how path integrals have made their appearance in quantum mechanics through feynman s formalism in section 2 it is recalled that gaussian path integrals defined as those in which the action is an integral whose integrand is a polynomial of at most the second degree in every dynamical variable involved can be cast into the form f t b t a exp i s cl b a where f t b t a is a coefficient solely depending on the initial time instant t a and the final time instant t b and s cl b a denotes the classical action section 3 is devoted to the calculation of a simple formula for the factor f t b t a in the case of a single particle in one euclidean dimension whereby the most general quadratic form of the lagrange function is considered the method is based upon successive transformations of various related auxiliary gaussian path integrals which are introduced applying feynman s theorem and making use of the well known property k x b t b x a t a k x b t b x t k x t x a t a dx satisfied by quantummechanical green s functions constitute important steps in the theoretical development at the end f t b t a is expressed solely in terms of two functions which one encounters in the description of the classical particle trajectory in section 4 four examples of practical application are given the last one concerns the linear harmonic oscillator with time dependent period and damping subject to a time dependent perturbative force

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