Approximate optimization of high-speed train nose shape for reducing micropressure wave

The paper deals with the nose shape design of high-speed railways to minimize the maximum micropressure wave, which is known to be mainly affected by train speed, train-to-tunnel area ratio, slenderness and shape of train nose, etc. It is advantageous to develop a proper approximate metamodel for replacing the real analysis code in the context of approximate design optimization. The study has adopted a newly introduced regression technique; the central of the paper is to develop and examine the support vector machine (SVM) for use in the sequential approximate optimization process. In the sequential approximate optimization process, Owen’s random orthogonal arrays and D-optimal design are used to generate training data for building approximate models. The paper describes how SVM works and how efficiently SVM is compared with an existing Kriging model. As a design result, the present study suggests an optimal nose shape that is an improvement over current design in terms of micropressure wave.     

Minimal area cross-sectional shape for a bar with prescribed lower bounds on stiffness in bending and torsion

This paper establishes the minimum cross-sectional area for an externally convex, hollow, prismatic bar subjected to minimum constraints on the second moment of area and on torsional rigidity. Some properties of the solution established by previous workers are assumed. Prandtl's stress function is expressed as a series in polar coordinates and the cross-sectional shapes are found by the semi-inverse method. The convexity constraint is expressed in a form suitable for application of mathematical programming methods. The optimal shapes were found by quadratic programming and generalized reduced gradient methods. Numerical results are given for typical examples, both for a circular hole and with the hole shape included in the optimization.     

On the optimal shape of a compressed column subjected to restrictions on the cross-sectional area

By using Pontryagin’s principle we study the optimal shape of an elastic compressed column with clamped ends and restrictions on cross-sectional area. The restrictions are imposed on either maximum or both minimal and maximum value of the cross-sectional area. We analyzed a column on elastic foundation of Winkler type and a column without foundation. It is shown that the optimization can be both bimodal and unimodal. We determine the transition value between unimodal and bimodal optimization for specified values of parameters.     

基于闭塞区间的高速列车运行时间与节能协同优化方法

提出了一种高速列车运行时间与节能协同优化方法.针对由动态调度层、优化控制层、跟踪控制层组成的列车运行控制与动态调度一体化结构,设计了面向动态调度层和优化控制层的列车运行时间调整策略和节能速度位置曲线.基于高速铁路闭塞区间,建立了列车区间模型和列车速度曲线节能优化模型.利用模型预测控制方法对列车区间运行时间进行调整,优化列车总延误时间;根据调整后的区间运行时间设计列车运行优化速度位置曲线,减少列车运行能耗.仿真算例验证了设计的运行时间与节能协同优化策略的有效性.     

A shape optimization study for tool design in resistance welding

The purpose of this study is to apply shape optimization tools for design of resistance welding electrodes. The numerical simulation of the welding process has been performed by a simplified FEM model implemented in COMSOL. The design process is formulated as an optimization problem where the objective is to prolong the life-time of the electrodes. Welding parameters like current, time and electrode shape parameters are selected to be the design variables while constraints are chosen to ensure a high quality of the welding. Surrogate models based on a Kriging approximation has been used in order to simplify the calculation of shape sensitivities and to generate a generic tool that can be interfaced with other simulation tools. An example numerical study shows the potential of applying optimal design techniques in this area. Part of this work was presented at WCSMO7 in Seoul Korea, May 21–25, 2007, in the paper titled ‘Some optimization aspects of resistance welding’ (CD-ROM, pp 2687–2695).     

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.     

Optimum shapes of bar cross-sections

In this paper, the problems of optimization of cylindrical bar cross sections are formulated. The functional considered characterizes rigidities, maximum stress and the areas of the cross-section of the bar. The shape of the boundary of the cross-section is taken as a design variable and is found in the case of regular polygonal contours. Using minimax approaches optimal designs have been obtained for simply connected and doubly connected cross-sections having given convex holes. Investigations performed and complete solutions derived from the cross-sectional area minimization under rigidity and strength constraints show the changes of the optimal shapes as functions of the problem parameter. Received September 29, 2000     

On an optimization problem for elastic rods

Optimal shape of an elastic rod loaded by extensional force is determined. It is assumed that the rod is described by a classical Bernoulli–Euler rod theory. The optimality conditions are obtained by using Pontriyagin's maximum principle. It is shown that the optimal shape (cross-sectional area as a function of an arc length) is determined from the solution of a nonlinear second-order differential equation. The solution of this equation is given in the closed form. It is shown that for the same buckling force, the savings of the material are of the order of 30%. An interesting feature of the problem is that for certain values of parameters, there is no optimal solution.     

Shape optimization of screwdriver handle for improving grasping comfort of precision and power grips

Improving grasping comfort is a significant factor in enhancing the value of industrial products, as most products are handled by human hands. Our aim was to optimize hand tool shapes and maximize grasping comfort, considering multiple‐shape parameters and grasping types. A screwdriver handle was used as the reference tool for this case study. The measurements of handle length, end diameter, and middle diameter were utilized as the shape parameters of the handle. Twelve participants were included in this study. We measured the participants' subjective perceptions of comfort while grasping the precision and power grips during screw‐driving and screw‐tightening tasks, respectively. The design of the screwdriver handle was formulated as a bi‐objective optimization problem with respect to the grasping comfort of the precision and power grips. A Pareto frontier was determined by optimizing the formulated problem. Well‐balanced and optimal shapes for the precision and power grips were identified.     

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

This paper discusses a new structural optimization method, based on topology optimization techniques, using frame elements where the cross-sectional properties can be treated as design variables. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush–Kuhn–Tucker (KKT) conditions and a complementary strain energy-based approach. Based on the above, the optimal rotational angle of each frame element is obtained as a function of the balance of the internal moments. The above methodologies are applied to problems of minimizing the mean compliance and maximizing the eigen frequencies. Several examples are provided to show the utility of the presented methodology.     

Optimal damping of a membrane and topological shape optimization

We consider a shape optimization problem of finding the optimal damping set of a two-dimensional membrane such that the energy of the membrane is minimized at some fixed end time. Traditional shape optimization is based on sensitivities of the cost functional with respect to small boundary variations of the shapes. We use an iterative shape optimization scheme based on level set methods and the gradient descent algorithm to solve the problem and present numerical results. The methods presented allow for certain topological changes in the optimized shapes. These changes can be realized in the presence of a force term in the level set equation. It is also observed that the gradient descent algorithm on the manifold of shapes does not require an exact line search to converge and that it is sufficient to perform heuristic line searches that do not evaluate the cost functional being minimized.     

Effects of operation type and handle shape of the driver controllers of high-speed train on the drivers' comfort

The design of a high-speed train controller affects the driver's health, operating performance and even safety. Understanding the effects of the design factors on the physical ergonomics of a high-speed train driver controller is essential for optimizing performance and safety. This study experimentally investigated the role of the operation type and handle shape on the physical ergonomics of a driver controller for a high speed train. Two controllers and six handles with pyriform shape, T-shape, sphere shape, cylinder shape and conical frustum shape were used in the experiment. The results indicated that a controller of the sagittal rotation operation type could significantly reduce the workload of the upper limbs compared to a horizontal rotation operation type controller. The handle shape had significant effect on the wrist angles, hand pressures and subjective assessment scores of upper limb fatigue, wrist discomfort and palm discomfort. The handle shape influenced the wrist angles and hand pressures depending on how the participants held the handle. The results demonstrated that the preferred operation type was rotation in the parasagittal plane and that the handle shape should be convenient for operating with a downward-facing palm posture. Among the tested shapes, the pyriform shape and T-shape were considered to be preferable.     

Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation

This paper presents an adaptive weighted sum (AWS) method for multiobjective optimization problems. The method extends the previously developed biobjective AWS method to problems with more than two objective functions. In the first phase, the usual weighted sum method is performed to approximate the Pareto surface quickly, and a mesh of Pareto front patches is identified. Each Pareto front patch is then refined by imposing additional equality constraints that connect the pseudonadir point and the expected Pareto optimal solutions on a piecewise planar hypersurface in the -dimensional objective space. It is demonstrated that the method produces a well-distributed Pareto front mesh for effective visualization, and that it finds solutions in nonconvex regions. Two numerical examples and a simple structural optimization problem are solved as case studies. Presented as paper AIAA-2004-4322 at the 10th AIAA-ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, August 30–September 1, 2004     

鼻尖状态对高速列车气动性能的影响

基于三维定常不可压N-S方程以及k-ε两方程湍流模型,分别在无横风和有横风环境下,用有限体积法研究高速列车车头鼻尖不同开闭状态对列车明线运行时气动性能的影响.用FLUENT分析车头鼻尖全开、全闭和半开半闭等3种不同开闭状态的高速列车气动性能,发现车头鼻尖开闭状态对列车侧向力和升力几乎没有影响,但对头车的阻力影响较大,这主要是由于头车鼻尖部分阻力变化较大引起的.在无横风环境下,车头鼻尖开闭状态对头车的气动力矩影响不大,但对尾车的点头力矩有一定影响.在横风环境下,车头鼻尖开闭状态对列车气动力矩影响不大.     

Shape optimization of the cavitator for a supercavitating torpedo

The torpedo is a vital component of the naval arsenal, and efforts are continually directed toward improving the technology to make the torpedo more lethal and more stealthy. Recently, a new direction of research is considering the high-speed torpedo, which is capable of reaching up to 200 mph underwater. When a torpedo travels at this speed, the flow around the body separates and a cavity is formed. This cavity generation due to high speeds is called supercavitation. And the drag force acting on this supercavitating torpedo dictates the thrust requirements for the propulsion system, to maintain a required cavity at the operating speed. Therefore, any reduction in the drag force, obtained by modifying the shape of the cavitator or the nose of the torpedo, would result in lower propulsion requirements. In this work, shape optimization techniques were employed to determine the optimum (minimum-drag) shape of the cavitator given certain operating conditions. Shape optimization was also used to determine the shape of the cavity for any given cavitator, using potential flow theory. Analytical sensitivities were derived for various parameters in order to implement a gradient-based optimization algorithm. The developed methodology is an optimization process where the cavity and cavitator shapes are determined simultaneously. The cavitator shape that induces minimum drag and the corresponding cavity shape can be used to model a supercavitating torpedo that fits in the generated cavity and satisfies the required performance characteristics.     

Target vector optimization of composite box beam using real-coded genetic algorithm: a decomposition approach

This paper aims to obtain the optimal composite box-beam design for a helicopter rotor blade. The cross-sectional dimensions and the ply angles of the box beam are considered as design variables. The objective is to optimize the box beam to attain a target vector of stiffness values and maximum elastic coupling. The target vector is the optimal stiffness values of helicopter rotor blade obtained from a previous aeroelastic optimization study. The elastic couplings introduced by the box beam have beneficial effects on the aeroelastic stability of helicopter. The optimization problem is addressed by decomposing the optimization into two levels, a global level and a local level. The box-beam cross-sectional dimensions are optimized at the global level. The local-level optimization is a subproblem which finds optimal ply angles for each cross-sectional dimension considered in the global level. Real-coded genetic algorithm (RCGA) is used as the optimization tool in both the levels of optimization. Hybrid operators are developed for the RCGA, thereby enhancing the efficiency of the algorithm. Min–max method is used to scalarize the multiobjective functions used in this study. Optimal geometry and ply angles are obtained for composite box-beam designs with ply angle discretization of 1010, 1515, and 45^o45^o.     

On body shapes providing maximum depth of penetration

The problem of maximization of the depth of penetration of rigid impactor into semi-infinite solid media (concrete shield) is investigated analytically and numerically using two-stage model and experimental data of Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997). The shape of the axisymmetric rigid impactor has been taken as an unknown design variable. To solve the formulated optimization problem for nonadditive functional, we expressed the depth of penetration (DOP) under some isoperimetric constraints. We apply approaches based on analytical and qualitative variational methods and numerical optimization algorithm of global search. Basic attention for considered optimization problem was given to constraints on the mass of penetrated bodies, expressed by the volume in the case of penetrated solid body and by the surface area in the case of penetrated thin-walled rigid shell. As a result of performed investigation, based on two-term and three-term two stage models proposed by Forrestal et al. (Int J Impact Eng 15(4):396–405, 1994), Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997) and effectively developed by Ben-Dor et al. (Comp Struct 56:243–248, 2002, Comput Struct 81(1):9–14, 2003a, Int J Solids Struct 40(17):4487–4500, 2003b, Mech Des Struct Mach 34(2): 139–156, 2006), we found analytical and numerical solutions and analyzed singularities of optimal forms.     

String‐Based Synthesis of Structured Shapes

We propose a novel method to synthesize geometric models from a given class of context‐aware structured shapes such as buildings and other man‐made objects. The central idea is to leverage powerful machine learning methods from the area of natural language processing for this task. To this end, we propose a technique that maps shapes to strings and vice versa, through an intermediate shape graph representation. We then convert procedurally generated shape repositories into text databases that, in turn, can be used to train a variational autoencoder. The autoencoder enables higher level shape manipulation and synthesis like, for example, interpolation and sampling via its continuous latent space. We provide project code and pre‐trained models.     

Design study of hole positions and hole shapes for crack tip stress releasing

The method of hole drilling near or at the crack tip is often used in fatigue damage repair. From a design optimization point of view, two questions are posed: Where should the hole(s) be drilled? And is there a better shape of the hole than a circular one? For the first question, we extend earlier results for isotropic material and in general study the influence of having orthotropic material. Optimal shapes are by no means circular, and we focus on the shape of a single hole centered at (or in front of) the crack tip. It is shown that the stress field at the crack boundary can be significantly improved by noncircular shapes. As a byproduct, an alternative method for extracting the stress intensity factor from a finite element analysis is presented.     

Multiobjective shape optimization of speed humps

This paper presents a new approach to the shape optimization of road speed humps. The proposed approach is based on multiobjective genetic optimization of the hump profile while taking into account the separation phenomenon, which occurs when the front tires of the vehicle momentarily lose contact with the road surface. The optimization is carried out for speeds up to twice the authorized speed (throughout this article, the term authorized speed refers to speed limits enforced in speed reduction [bump] areas of the roads) rather than for illegally high speeds as adopted by many of the previous works. A 6-degree of freedom non-linear dynamic model is used to identify the speeds at which separation occurs, and hump profiles associated with these speeds are discarded as infeasible solutions. Three independent objective functions are selected for optimization. They include the maximum vertical acceleration experienced by the driver when crossing the hump below the authorized speed limit (to be minimized), the same vertical acceleration at speeds above the authorized speed (to be maximized), and the ascending ratio of the “speed—vertical acceleration” curve (to be maximized). These objective functions are evaluated for more than 10,000 humps of two popular profile types (sinusoidal and flat top with straight ramps) and optimum profiles for three speed limits of 20, 25, and 30km/h are determined using the multiobjective nondominated sorting genetic algorithm II. As a result, a Pareto front of at least ten optimal points is achieved for each of the two hump profile types. Furthermore, to incorporate the economical aspects of the real-world problem, Pareto optimal points for the two profile types were compared based on their lateral section areas (an indication of the manufacturing cost). The comparison shows that sinusoidal humps more often than not outdo their flat top rivals economically.