Optimal cross-sectional area distribution of a high-speed train nose to minimize the tunnel micro-pressure wave

Optimization of the cross-sectional area distribution of a high-speed train nose is conducted for various nose lengths in order to minimize the micro-pressure wave intensity at a tunnel exit. To this end, an inviscid compressible flow solver is adopted with an axi-symmetric patched grid system. To improve the shape of the train nose, multi-step design optimization is performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with a response surface model. The optimization reveals that the optimal nose shapes differ for different nose lengths. For a short nose, the shape has an extremely blunt front end, and the cross-sectional area decreases in the middle section. As the nose length increases, the nose shape flattens around the middle section. These optimal shapes divide one large compression wave into two small waves by causing a strong expansion effect between the front and rear ends. As a result, through the nose shape optimization, the intensity of the micro-pressure wave is reduced by 18–27% compared to a parabolic nose, which has a minimum variation of the cross-sectional area change. The optimized distribution of the cross-sectional area can be used as a guideline for the design of three-dimensional nose shapes of high-speed trains, further improving their aerodynamic performance.     

An interior-point sequential approximate optimization methodology

The use of optimization in a simulation-based design environment has become a common trend in industry today. Computer simulation tools are commonplace in many engineering disciplines, providing the designers with tools to evaluate a designs performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior-point approach for trust-region-managed sequential approximate optimization. The interior-point approach will ensure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.     

SVM参数优化的AFMC算法

支持向量机的参数选择仍未有系统的理论指导,其优化选择一直是支持向量机的一个重要研究方向。考虑到人工鱼群算法优化支持向量机参数往往易陷入最优参数组合微小邻域的问题,构造了用于支持向量机参数优化的AFMC算法。该算法前期利用鱼群算法较好的并行寻优性能,能快速寻得问题的近似最优解,而后利用MonteCarlo法进行局部寻优,以实现快速、有效地获取强近优解。数值实验结果表明,该算法具有较好的分类性能和较快的寻优速度,验证了在支持向量机参数寻优中的有效性和可行性。     

Optimum design of nonlinear structures with path dependent reponse

Optimum design of structures with path dependent response is studied in this paper. The direct differentiation and the adjoint structure methods of design sensitivity analysis are summarized. The reference volume concept is used to unify the conventional and shape design problems. It is concluded that the direct differentiation method is more effective for this class of problems. The design sensitivity analysis — developed with continuum formulation — is discretized using the finite element method. Two cases for an example problem are optimized using a sequential quadratic programming algorithm to demonstrate how the developed procedures work and to study the optimization process for the problems with path dependent response.     

回归支持向量机的改进序列最小优化学习算法

支持向量机(support vector machine,简称SVM)是一种基于结构风险最小化原理的学习技术,也是一种新的具有很好泛化性能的回归方法,提出了实现回归支持向量机的一种改进的SMO(sequential minimal optimization)算法,给出了两变量子优化问题的解析解,设计了新的工作集选择方法和停止条件,仿真实例说明,所提出的SMO算法比原始SMO算法具有更快的运算速度.     

果蝇耦合均匀设计算法及其优化SVM参数

支持向量机的参数选择仍无系统的理论指导,且参数优化一直是支持向量机的一个重要研究方向。传统果蝇优化算法能够较快寻得一个较优的近似最优解,随后在该解的邻域继续迭代而造成寻优时间的严重增加。针对该问题构建了果蝇优化算法与均匀设计相耦合的果蝇耦合均匀设计算法,并将其用于支持向量机的参数优化。该算法首先利用果蝇优化算法并行寻优以快速得到所研究问题的一个较优近似最优解,然后跳转执行均匀设计的局部寻优,以获得一个更优的近似最优解。数值实验结果表明:该算法具有较快的寻优效率和较高的分类精度,验证了其在支持向量机参数优化中的有效性和可行性。     

A sequential coupling of optimal topology and multilevel shape design applied to two-dimensional nonlinear magnetostatics

In this paper, a sequential coupling of two-dimensional (2D) optimal topology and shape design is proposed so that a coarsely discretized and optimized topology is the initial guess for the following shape optimization. In between, we approximate the optimized topology by piecewise Bézier shapes via least square fitting. For the topology optimization, we use the steepest descent method. The state problem is a nonlinear Poisson equation discretized by the finite element method and eliminated within Newton iterations, while the particular linear systems are solved using a multigrid preconditioned conjugate gradients method. The shape optimization is also solved in a multilevel fashion, where at each level the sequential quadratic programming is employed. We further propose an adjoint sensitivity analysis method for the nested nonlinear state system. At the end, the machinery is applied to optimal design of a direct electric current electromagnet. The results correspond to physical experiments. This research has been supported by the Austrian Science Fund FWF within the SFB “Numerical and Symbolic Scientific Computing” under the grant SFB F013, subprojects F1309 and F1315, by the Czech Ministry of Education under the grant AVČR 1ET400300415, by the Czech Grant Agency under the grant GAČR 201/05/P008 and by the Slovak Grant Agency under the project VEGA 1/0262/03.     

A decoupling approach for evidence-theory-based reliability design optimization

For the problem of evidence-theory-based reliability design optimization (EBDO), this paper presents a decoupling approach which provides an effective tool for the reliability design of some complex structures with epistemic uncertainty. The approach converts the original nested optimization into a sequential iterative process including design optimization and reliability analysis. In each iteration step, through the uniformity algorithm, the original EBDO is firstly transformed to a conventional reliability-based design optimization (RBDO) and an optimal solution is obtained by solving it. At the solution, the first-order approximate reliability analysis method (FARM) is then used to perform the evidence-theory-based reliability analysis for each constraint. In addition, the RBDO solving and the evidence-theory-based reliability analysis are carried out alternately until reaching the convergence. Finally, two numerical examples and a practical engineering application show the effectiveness of the proposed method.     

Data driven surrogate-based optimization in the problem solving environment WBCSim

Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate-based optimization algorithm that uses a trust region-based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling, and central composite design—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process.     

Parametric shape modification and application in a morphological biomimetic design

Biomimetic design performed to develop a solution-shape has been offered as a successful approach for overcoming the limitations of typical design methods. Especially for the nose-shape of high-speed trains, the morphological characteristics of a superior bio-model were used in the design process. However, current design methods using the biomimetic approach, particularly in the morphological domain, do not support a technique to evaluate how close the new solution is to the optimal one; nor do they support alternative methodologies used to validate and verify the solution-shape being developed. Solution optimization in a biomimetic design means not only preserving the original shape of a bio-model but also validating and verifying it. Shape optimization for a design problem should accompany shape evaluation and modification conducted according to criteria involving both evolutionary traits and technological constraints. In this research we suggest a method to verify the original shape, and to validate the solution, using theoretical backgrounds from both systematic biology and evolutionary biology. In this paper, the morphological characteristics of a bio-model are verified and modified using a quantitative method. To validate the solution developed, new criteria are applied for high-speed-train design.     

Sequential approximate optimization of industrial hammer peening using finite element simulations

In this paper, the industrial hammer peening process is optimized using multi-objective, sequential approximate optimization, which is a mathematics- plus finite element- based algorithm. Since the number of design and objective variables is significant, the global optimization problem is split into two, more manageable multi-objective subproblems. The use of surrogate modelling together with an intensification and diversification strategy for solving the optimization subproblems allows for significant computational cost savings without loss of accuracy. Additionally, we propose a Bayesian inference criterion-based sensitivity approach for “filtering-out” design variables which do not significantly affect objectives variables. Finally, guidelines for selecting appropriate Pareto optima are given using \(N-1\) Pareto diagrams, where N is the number of objective variables.     

Reliability-based design optimization for problems with interval distribution parameters

Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.     

PSO-based intelligent integration of design and control for one kind of curing process

In this paper, a PSO-based intelligent integration of design and control is proposed for one kind of nonlinear curing process. This method combines the merits of both fuzzy modeling/control and PSO method, where fuzzy modeling/control is proposed to approximate/control the nonlinear process in a large operating region and the PSO-based intelligent optimization method is developed to solve non-convex and non-differential integration problem with design and control optimized simultaneously. Finally, the proposed method is compared with the traditional sequential method on controlling the temperature profile of a nonlinear curing process.     

Successive overrelaxation for support vector machines

Successive overrelaxation (SOR) for symmetric linear complementarity problems and quadratic programs is used to train a support vector machine (SVM) for discriminating between the elements of two massive datasets, each with millions of points. Because SOR handles one point at a time, similar to Platt's sequential minimal optimization (SMO) algorithm (1999) which handles two constraints at a time and Joachims' SVM(light) (1998) which handles a small number of points at a time, SOR can process very large datasets that need not reside in memory. The algorithm converges linearly to a solution. Encouraging numerical results are presented on datasets with up to 10 000 000 points. Such massive discrimination problems cannot be processed by conventional linear or quadratic programming methods, and to our knowledge have not been solved by other methods. On smaller problems, SOR was faster than SVM(light) and comparable or faster than SMO.     

Optimization of a sheet metal forming process using successive multipoint approximations

An automated optimization method based on multipoint approximations and applied to the design of a sheet metal forming process is presented. Due to the highly complex nature of the design functions, it was decided to focus on the characterization of the final product thickness distribution as a function of the preforming die shape variables. This was achieved by constructing linear approximations to the noisy responses usingresponse surface methodology (RSM). These approximations are used to obtain an approximate solution to an optimization problem. Successive approximations are constructed, which improve the solution. An automated panning-zooming scheme is used to resize and position the successive regions of approximation. The methodology is applied to optimally design the preforming die shape used in the manufacture of an automotive wheel centre pressing from a sheet metal blank. The die shape is based on a cubic spline interpolation and the objective is to minimize the blank weight, subject to minimum thickness constraints. A weight saving of up to 9.4% could be realized for four shape variables. Restart is introduced to escape local minima due to the presence of noise and to accelerate the progress of the optimization process.     

Second-order SMO improves SVM online and active learning

Iterative learning algorithms that approximate the solution of support vector machines (SVMs) have two potential advantages. First, they allow online and active learning. Second, for large data sets, computing the exact SVM solution may be too time-consuming, and an efficient approximation can be preferable. The powerful LASVM iteratively approaches the exact SVM solution using sequential minimal optimization (SMO). It allows efficient online and active learning. Here, this algorithm is considerably improved in speed and accuracy by replacing the working set selection in the SMO steps. A second-order working set selection strategy, which greedily aims at maximizing the progress in each single step, is incorporated.     

Optimization of forging processes using Finite Element simulations

During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to the design of feasible forming processes. Coupling FEM to mathematical optimization algorithms offers a promising opportunity to design optimal metal forming processes rather than just feasible ones. In this paper Sequential Approximate Optimization (SAO) for optimizing forging processes is discussed. The algorithm incorporates time-consuming nonlinear FEM simulations. Three variants of the SAO algorithm—which differ by their sequential improvement strategies—have been investigated and compared to other optimization algorithms by application to two forging processes. The other algorithms taken into account are two iterative algorithms (BFGS and SCPIP) and a Metamodel Assisted Evolutionary Strategy (MAES). It is essential for sequential approximate optimization algorithms to implement an improvement strategy that uses as much information obtained during previous iterations as possible. If such a sequential improvement strategy is used, SAO provides a very efficient algorithm to optimize forging processes using time-consuming FEM simulations.     

An integrated approach to structural shape optimization of linearly elastic structures. Part II: Shape definition and adaptivity

In this paper we initially study how the number of design variables used affects the final optimum shape of the structure when employing two different types of curves to describe the boundary of the structure, i.e. quadratic Bezier and cubic B-spline curves. The advantage of using better shape definition is highlighted with several examples. An adaptive mesh refinement (AMR) procedure using six-node triangular elements is adopted in the structural shape optimization process. The procedure makes use of an h-version adaptive refinement technique based on error estimates determined from either best-guess stress values or residual terms in the governing equation. An example is presented to illustrate the performance of these error estimators with respect to their convergence, accuracy and cost of computation. Different strategies for the inclusion of AMR procedures in the shape optimization process are also proposed. Anomalies in predicting the optimum shape due to discretization errors are demonstrated using several examples.     

Arch shape optimization using force approximation methods

The objective of this paper is to provide a method of optimizing areas of the members as well as the shape of both two-hinged and fixed arches. The design process includes satisfaction of combined stress constraints under the assumption that the arch ribs can be approximated by a finite number of straight members.In order to reduce the number of detailed finite element analyses, the Force Approximization Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces (axial, bending moment) are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the arch with information from the approximate structural analysis.Numerical examples are presented to demonstrate the efficiency and reliablity of the proposed method for shape optimization. It is shown that the number of finite element analysis is minimal and the procedure provides a highly efficient method of arch shape optimization.     

A computational procedure for response statistics-based optimization of stochastic non-linear FE-models

An approach for an efficient solution of response statistics-based optimization problems of non-linear FE systems under stochastic loading is presented. A sequential approximate optimization approach, where approximate stochastic analyses are used during portions of the optimization process, is implemented in the proposed formulation. In this approach, analytical approximations of the performance functions in terms of the design variables are considered during the optimization process. The analytical approximations are constructed by combining a mixed linearization approach with a stochastic response sensitivity analysis. The state of the system is defined in terms of the statistical second-moment characteristics of the structural response. The stochastic loading and the response of the system are represented by an orthogonal series expansion of the corresponding covariance matrices. In particular, a truncated Karhunen-Loève (K-L) expansion is applied. The system of non-linear equations is replaced by a statistical equivalent linear system. The evaluation of the K-L vectors is carried out by an efficient procedure that combines local linearization, modal analysis and static response of higher structural modes. An illustrative example is presented that shows the efficiency of the proposed methodology: it considers a building finite element model enforced with non-linear hysteretic devices and subject to a stochastic ground acceleration. Two types of problems are considered: a minimum structural weight design problem and an optimal non-linear device design problem.