Multipoint approximation development: thermal structural optimization case study

Function approximation is one of the most important fields of research in design optimization. Accurate function approximation reduces the repetitive cost of finite element analysis. Many local approximations, such as one‐ and two‐point local approximations, are already available. These are, however, only valid in a small domain and require stringent move‐limits on design variables. The objective of this research is to achieve an efficient and accurate multipoint approximation to constraints by integrating the most accurate segment of all local approximations previously constructed. The proposed multipoint approximation is constructed by combining weighting functions with local function approximations. With function and gradient information at a series of points, local approximations are established at those points. Once established, all local approximations are blended into a multipoint approximation by use of a weighting function. Function and gradient values of this multipoint approximation correspond directly with exact counterparts at the points where the local approximations were generated. Finally, the multipoint approximation is applied to a plate and wing box thermal‐structural optimization. Published in 2000 by John Wiley & Sons, Ltd.     

Hierarchical adaptive experimental design for Gaussian process emulators

Large computer simulators have usually complex and nonlinear input output functions. This complicated input output relation can be analyzed by global sensitivity analysis; however, this usually requires massive Monte Carlo simulations. To effectively reduce the number of simulations, statistical techniques such as Gaussian process emulators can be adopted. The accuracy and reliability of these emulators strongly depend on the experimental design where suitable evaluation points are selected. In this paper a new sequential design strategy called hierarchical adaptive design is proposed to obtain an accurate emulator using the least possible number of simulations. The hierarchical design proposed in this paper is tested on various standard analytic functions and on a challenging reservoir forecasting application. Comparisons with standard one-stage designs such as maximin latin hypercube designs show that the hierarchical adaptive design produces a more accurate emulator with the same number of computer experiments. Moreover a stopping criterion is proposed that enables to perform the number of simulations necessary to obtain required approximation accuracy.     

一种用于毫米波器件本征在片S参数校准的新方法

提出一种用于毫米波器件本征在片S参数校准的新方法.对于毫米波频段电路而言,准确已知的仿真模型是必需的,因此,精确地去嵌入测试技术就显得尤为重要.在传统开路短路去嵌入算法的基础上,建立了新型去嵌入模型和求解算法.通过增加开路短路标准的传输线长度近似得到理想开路和短路,降低测试误差;同时在模型中增加了毫米波频段逐渐变大的微...     

TRAX: An approach for the time rational analysis of complex dynamic systems

This paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems. The proposed approach combines four main components: analytical expressions of the average of the system's transfer functions in the frequency domain, precise and convergent rational approximations of these exact expressions, exact evaluation of these approximations through model reduction in rational Krylov subspaces and semi‐analytical interpolation at just a few frequency points. The resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward: one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses. The time response of the reduced model implicitly provides a precise evaluation of that of the original system. The properties of the reduced models and the precision of the proposed approach are studied, and applications on complex matrix systems are presented and discussed. While the theory and numerical algorithms are presented in a matrix context, they are also transposable in a continuous functional context. Copyright © 2015 John Wiley & Sons, Ltd.     

Structural reliability analysis by univariate decomposition and numerical integration

This paper presents a new and alternative univariate method for predicting component reliability of mechanical systems subject to random loads, material properties, and geometry. The method involves novel function decomposition at a most probable point that facilitates the univariate approximation of a general multivariate function in the rotated Gaussian space and one-dimensional integrations for calculating the failure probability. Based on linear and quadratic approximations of the univariate component function in the direction of the most probable point, two mathematical expressions of the failure probability have been derived. In both expressions, the proposed effort in evaluating the failure probability involves calculating conditional responses at a selected input determined by sample points and Gauss–Hermite integration points. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure.     

Numerical evaluation of Hankel transforms for oscillating functions

Six methods for the numerical calculation of zero-order Hankel transforms of oscillating functions were evaluated. One method based on Filon quadrature philosophy, two published projection-slice methods, and a third projection-slice method based on a new approach to computation of the Abel transform were implemented; alternative versions of two of the projection-slice methods were derived for more accurate approximations in the projection step. These six algorithms were tested with an oscillating sweep signal and with the calculation of a three-dimensional diffraction-limited point-spread function of a fluorescence microscope. We found that the Filon quadrature method is highly accurate but also computationally demanding. The projection-slice methods, in particular the new one that we derived, offer an excellent compromise between accuracy and computational efficiency.     

基于ARMA模型和时空kriging插值联合模拟大跨结构的脉动风速时程

采用ARMA模型模拟具有时间和空间相关性的大跨结构的随机风速时程。并对Whittle递推算法进行了改进,求解出自回归系数和滑动回归系数矩阵。利用MATLAB软件编制了模拟大跨桥梁的风速时程模拟程序,运行结果表明: 改进的方法计算效率高,模拟精度符合要求。然后又利用时空Kriging插值法对控制点区域内节点的脉动风速时程进行模拟,其模拟精度较好且求解过程快,可用于大跨空间结构、超高层建筑等含有大量节点的结构风场模拟。     

Analysis of distortion in A/D converters by time-domain andcode-density techniques

Two new methods for measuring the total harmonic distortion of an A/D converter are described. One is based on time-domain analysis, the other on modified code density analysis. Experiments show that these methods give results comparable to the ones provided by FFT analysis. It is then shown, by both experiments on a flash converter and computer simulations, that the conventional code density analysis does not provide accurate signal-to-noise-plus-distortion ratio (SNDR) estimates at the highest frequencies, while the proposed methods do     

Higher-order sensitivity analysis of finite element method by automatic differentiation

To design optimal mechanical structures, design sensitivity analysis technique using higher order derivatives are important. However, usual techniques for computing the derivatives, for example numerical differentiation methods, are hard to apply to real scale structures because of the large amount of computational time and the accumulation of computational errors.To overcome the problem, we have studied a new approach for higher order sensitivity analysis of the finite element method using automatic differentiation techniques. The method automatically transforms FORTRAN code to special purpose code which computes both the value of the given functional dependence and their derivatives. The algorithm used in the method automatically and efficiently computes accurate values of higher order partial derivatives of a given functional dependence on many variables.This paper reports the basic principles of the automatic differentiation method and some experiments on the sensitivity analysis of mechanical structures. The original program of structural analysis by the finite element method is implemented in FORTRAN, which is developed by the first author. Using the proposed method, we get more accurate sensitivity and prediction values compared with usual numerical differentiation. We also discuss the effectiveness of the proposed approach for the sensitivity analysis of the mechanical structures.     

非比例阻尼线性体系基于规范反应谱的CCQC法

根据平稳随机过程理论和抗震设计反应谱,对具有非比例阻尼特性的线性体系,给出了实数形式的复振型反应谱叠加法和复振型完全平方组合(CCQC)计算公式。式中除了包含一般CQC方法中振型间的位移相关系数以外,还包含了新的速度相关系数和位移-速度相关系数。公式推导按照与一般CQC法同样的原理和假定,形式也同样简洁、明了,易于工程设计人员掌握和使用。用实例分析对比了基于设计反应谱的CCQC法、CSRSS法及强迫解耦法,并以人工地震波作为地震输入,用逐步积分法对计算结果进行了验证。结果表明:提出的CCQC法比CSRSS法具有更好的精度。实例分析还表明,对于一般的强非比例阻尼结构,抗震设计规范中采用的强迫解耦方法也具有较好的精度。     

Analysis of observer performance in unknown-location tasks for tomographic image reconstruction

Our goal is to optimize regularized image reconstruction for emission tomography with respect to lesion detectability in the reconstructed images. We consider model observers whose decision variable is the maximum value of a local test statistic within a search area. Previous approaches have used simulations to evaluate the performance of such observers. We propose an alternative approach, where approximations of tail probabilities for the maximum of correlated Gaussian random fields facilitate analytical evaluation of detection performance. We illustrate how these approximations, which are reasonably accurate at low probability of false alarm operating points, can be used to optimize regularization with respect to lesion detectability.     

Numerical approximation of a thermally driven interface using finite elements

A two‐dimensional finite element model for dendritic solidification has been developed that is based on the direct solution of the energy equation over a fixed mesh. The model tracks the position of the sharp solid–liquid interface using a set of marker points placed on the interface. The simulations require calculation of the temperature gradients on both sides of the interface in the direction normal to it; at the interface the heat flux is discontinuous due to the release of latent heat during the solidification (melting) process. Two ways to calculate the temperature gradients at the interface, evaluating their interpolants at Gauss points, were proposed. Using known one‐ and two‐dimensional solutions to stable solidification problems (the Stefan problem), it was shown that the method converges with second‐order accuracy. When applied to the unstable solidification of a crystal into an undercooled liquid, it was found that the numerical solution is extremely sensitive to the mesh size and the type of approximation used to calculate the temperature gradients at the interface, i.e. different approximations and different meshes can yield different solutions. The cause of these difficulties is examined, the effect of different types of interpolation on the simulations is investigated, and the necessary criteria to ensure converged solutions are established. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermal optimization in transient thermoelasticity using response surface approximations

Response surface methodology is used to construct approximations to temperature and stress in transient thermoelastic analysis of non-linear systems. The analysis forms the core component of a heating/cooling rate maximization problem in which the ordinates of the ambient temperature at equally spaced time intervals are chosen as the design variables. Polynomials or cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis. An experimental design method based on D-optimality and a genetic algorithm was used to select the design points used to create the approximations. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Two examples of which one is a thick-walled pressure vessel are used to illustrate the methodology. © 1998 John Wiley & Sons, Ltd.     

Efficient time stepping for the multiplicative Maxwell fluid including the Mooney‐Rivlin hyperelasticity

A popular version of the finite‐strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of the Mooney‐Rivlin type; it is a special case of the viscoplasticity model proposed by Simo and Miehe in 1992. A simple, efficient, and robust implicit time‐stepping procedure is suggested. Lagrangian and Eulerian versions of the algorithm are available, with equivalent properties. The numerical scheme is iteration free, unconditionally stable, and first order accurate. It exactly preserves the inelastic incompressibility, symmetry, and positive definiteness of the internal variables and w‐invariance. The accuracy of the stress computations is tested using a series of numerical simulations involving a nonproportional loading and large strain increments. In terms of accuracy, the proposed algorithm is equivalent to the modified Euler backward method with exact inelastic incompressibility; the proposed method is also equivalent to the classical integration method based on exponential mapping. Since the new method is iteration free, it is more robust and computationally efficient. The algorithm is implemented into MSC.MARC, and a series of initial boundary value problems is solved to demonstrate the usability of the numerical procedures.     

A comparative study of methodologies for vibro-acoustic FE model updating of cavities using simulated data

The structural dynamic modeling errors, which at times are difficult to eliminate in a structural FE model, can affect the accuracy and reliability of the vibro-acoustic FE models for NVH design of the cavities. A large number of methods have been proposed for structural finite element model updating. However, most of the studies conducted are mainly focused on structural dynamic applications and no work is reported on vibro-acoustic systems. The objective of this paper is to compare through a simulated study two recently proposed methodologies for vibro-acoustic FE model updating of cavities with weak acoustic coupling to address structural dynamic modeling errors. These methodologies utilize a direct and an iterative method of model updating developed for purely structural systems. A simulated example of a 2D rectangular cavity with a flexible surface is presented. Cases of incomplete and noisy data are considered. The comparison is done on the basis of accuracy of prediction of vibro-acoustic natural frequencies and the responses both inside and outside the frequency range of interest. It is concluded that both the methodologies give an accurate prediction of the vibro-acoustic natural frequencies and the response inside the updating frequency range. However, beyond this range, the predictions based on the direct updated vibro-acoustic models are not accurate. It is noted that the success of updating using IESM is dependent on the correct knowledge of the modeling inaccuracies, uncertainties or approximations and also on the choice of the suitable updating parameters, which could be very challenging for complex cavities. The vibro-acoustic FE model updating using the direct method could be handy in such situations where the iterative methods are difficult to be effectively applied.     

基于Campbell模型的卡车与防撞柱最大碰撞力修正计算方法

为探究卡车冲击防撞柱过程中的最大碰撞力,开展了63组碰撞数值试验。根据碰撞后卡车变形特征分析,采用卡车等效变形对Campbell模型进行参数修正,提出了卡车与防撞柱最大碰撞力的修正计算方法,并对国内外相关规范建议的最大碰撞力计算方法的适用性进行了评估。研究表明,碰撞后卡车变形沿宽度呈中间大、两端小的不均匀分布。卡车等效变形不仅受卡车碰撞速度影响,还与防撞柱高度和直径、钢管屈服强度和厚度以及基础深度有关。与实车碰撞试验和数值模拟试验得到的最大碰撞力对比表明,《欧规1》附录B建议方法计算结果严重偏小,《欧规1》附录C和《公路规范》建议方法计算结果离散性较大,该文建议方法计算结果更加准确保守,适用于防撞柱结构设计。     

Uncertainty quantification of high‐dimensional complex systems by multiplicative polynomial dimensional decompositions

The central theme of this paper is multiplicative polynomial dimensional decomposition (PDD) methods for solving high‐dimensional stochastic problems. When a stochastic response is dominantly of multiplicative nature, the standard PDD approximation, predicated on additive function decomposition, may not provide sufficiently accurate probabilistic solutions of a complex system. To circumvent this problem, two multiplicative versions of PDD, referred to as factorized PDD and logarithmic PDD, were developed. Both versions involve a hierarchical, multiplicative decomposition of a multivariate function, a broad range of orthonormal polynomial bases for Fourier‐polynomial expansions of component functions, and a dimension‐reduction or sampling technique for estimating the expansion coefficients. Three numerical problems involving mathematical functions or uncertain dynamic systems were solved to corroborate how and when a multiplicative PDD is more efficient or accurate than the additive PDD. The results show that indeed, both the factorized and logarithmic PDD approximations can effectively exploit the hidden multiplicative structure of a stochastic response when it exists. Since a multiplicative PDD recycles the same component functions of the additive PDD, no additional cost is incurred. Finally, the random eigensolutions of a sport utility vehicle comprising 40 random variables were evaluated, demonstrating the ability of the new methods to solve industrial‐scale problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Models and solving procedures for continuous-time production planning

The goal of this paper is to solve a continuous time production planning problem, where production rates are assumed to be piecewise constant. The problem is then to determine not only the rates, but also the times, called switching times, at which these rates may change. An iterative procedure is proposed where, at the first step, optimal rates are determined given the switching times and, at the second step, new switching times are added given the rates. A linear programming model is proposed and discussed for the first step. Several rules to remove or add switching times are also analyzed. Computational experiments are presented comparing two versions of the procedure and showing its efficiency     

MULTIVARIATE HERMITE APPROXIMATION FOR DESIGN OPTIMIZATION

An approximation based on multiple function and gradient information is developed using Hermite interpolation concepts. The goal is to build a high-quality approximation for complex and multidisciplinary design optimization problems employing analysis such as aeroservoelasticity, structural control, probability, etc. The proposed multidimensional approximation utilizes exact analyses data generated during the course of iterative optimization. The approximation possesses the property of reproducing the function and gradient information of known data points. The accuracy of the new approach is compared with linear, reciprocal and other standard approximations. Because the proposed algorithm uses more data points, its efficiency has to be compared in the context of iterative optimization.     

TORT/MCNP coupling method for the calculation of neutron flux around a core of BWR

For the analysis of BWR neutronics performance, accurate data are required for neutron flux distribution over the In-Reactor Pressure Vessel equipments taking into account the detailed geometrical arrangement. The TORT code can calculate neutron flux around a core of BWR in a three-dimensional geometry model, but has difficulties in fine geometrical modelling and lacks huge computer resource. On the other hand, the MCNP code enables the calculation of the neutron flux with a detailed geometry model, but requires very long sampling time to give enough number of particles. Therefore, a TORT/MCNP coupling method has been developed to eliminate the two problems mentioned above in each code. In this method, the TORT code calculates angular flux distribution on the core surface and the MCNP code calculates neutron spectrum at the points of interest using the flux distribution. The coupling method will be used as the DOT-DOMINO-MORSE code system. This TORT/MCNP coupling method was applied to calculate the neutron flux at points where induced radioactivity data were measured for 54Mn and 60Co and the radioactivity calculations based on the neutron flux obtained from the above method were compared with the measured data.