遗传算法在供热管道直埋弯头优化设计的应用

采用遗传算法对直埋水平弯头进行优化设计。以弯头造价最低为优化目标,采用惩罚函数法处理复杂的非线性约束,求出最优的曲率半径和壁厚,结果可直接应用于工程设计。     

Database for the optimum design of semi-fan composite cable-stayed bridges based on genetic algorithms

The optimum design solution of cable-stayed bridges is a complicated task. The large number of design parameters, strict design constraints imposed by design codes, highly geometrically nonlinear behaviour and robust effect of post-tensioning cable forces make traditional design methods not capable of achieving this task. In this study, an optimisation technique that integrates a finite element model, a genetic algorithm and polynomial functions for evaluating post-tensioning cable forces is adopted to develop a database for the optimum design of cable-stayed bridges. The database describes the variations of the optimum design parameters, including the main span length, height of the pylon, number of stay cables and cross-sectional dimensions of all elements with the total length of the bridge. The study concerns the optimisation of three-span composite cable-stayed bridges with semi-fan cable arrangements. The study covers bridge lengths ranging from 250 to 700 m. The database is presented in the form of simple design charts and tables. Such database is useful in the preliminary design and cost estimation for this type of bridges.     

基于全局优化设计的桁架结构优化设计研究

桁架结构优化设计中普遍存在约束的作用.现有优化设计一般采用满应力法和遗传优化等优化方法,编程复杂.本文介绍了优化设计软件LINGO10.0的功能、特点、使用方法和使用注意事项等,建立了桁架结构优化设计的数学模型.采用LINGO软件的全局优化方法求解.实例计算表明,采用LINGO的全局优化方法能获得全局优化解,且方法简单,值得推广应用.     

Application of the orthogonal design method in geotechnical parameter back analysis for underground structures

The back analysis method has been widely used as an indirect method of determining geotechnical parameters based on field measurements. The number of parameters and their initial values greatly influence the reliability and efficiency of back analysis. Therefore, sensitivity analysis is often employed to select high sensitivity parameters that have more greater impact on measured back analysis values. The orthogonal design method was first utilized to select geotechnical parameters for back analysis. The optimized parameter values obtained from an orthogonal design table can be used as the initial back analysis values, so as to avoid optimisation algorithm searching in local parameter spaces. By introducing a penalty function to the objective function, back analysis of the geotechnical parameters is changed into an unconstrained optimisation problem, whereby the Nelder–Mead method can then be employed. To verify the feasibility of the proposed back analysis method, a case study was conducted to determine the rock mass parameters for the Houziyan underground powerhouse complex.     

基于安全度约束的多次预应力钢结构优化设计

建立了多次预应力钢结构优化设计的模型,考虑了应力、位移等安全性约束,将线性规划与满约束准则法相结合,提出了效率较高的新优化策略和方法,可以得出每一级的预应力值和各个构件的优化截面。分别对具有局部布索或整体布索的大跨度钢屋架、平行钢桁架进行了优化计算分析,验证了本文的理论和方法。     

Robust optimum design of tuned liquid column damper in seismic vibration control of structures under uncertain bounded system parameters

The optimum design of a tuned liquid column damper (TLCD) considering system parameter uncertainty is usually performed by minimising the performance measure obtained by the total probability theory without any consideration to the variation of its performance due to parameter uncertainty. However, such a design method does not necessarily correspond to an optimum design in terms of maximum response reduction as well as its minimum dispersion. Furthermore, such approach cannot be applied in many real situations when the required detailed information about the uncertain parameters is limited. The robust design optimisation (RDO) of a TLCD system to mitigate seismic vibration effect in which the bounds on the magnitude of the uncertain properties of the structural and ground motion model parameters are only required is attempted in this study. The RDO is formulated as a two-criterion optimisation problem where the weighted sum of the maximum root mean square displacement of the structure and its dispersion is minimised. The conventional interval analysis-based bounded optimum solution is also obtained to demonstrate the effectiveness of the proposed RDO approach. A numerical study elucidates the effect of parameter uncertainty on the RDO of TLCD parameters by comparing the RDO results with the bounded optimum results.     

Genetic evolutionary structural optimization

Evolutionary structural optimization (ESO) is based on a simple idea that an optimal structure (with maximum stiffness but minimum weight) can be achieved by gradually removing ineffectively used materials from design domain. In general, the results from ESO are likely to be local optimums other than the global optimum desired. In this paper, the genetic algorithm (GA) is integrated with ESO to form a new algorithm called Genetic Evolutionary Structural Optimization (GESO), which takes the advantage of the excellent behavior of the GA in searching for global optimums. For the developed GESO method, each element in finite element analysis is an individual and has its own fitness value according to the magnitude of its sensitivity number. Then, all elements in an initial domain constitute a whole population in GA. After a number of generations, undeleted elements will converge to the optimal result that will be more likely to be a global optimum than that of ESO. To avoid missing the optimum layout of a structure in the evolution, an interim thickness is introduced into GESO and its validity is demonstrated by an example. A stiffness optimization with weight constraints and a weight optimization with displacement constraints are studied as numerical examples to investigate the effectiveness of GESO by comparison with the performance of ESO. It is shown through the examples that the developed GESO method has powerful capacity in searching for global optimal results and requires less computational effort than ESO and other existing methods.     

基于动力可靠性约束的基础隔震结构抗震优化控制设计研究

对基础隔震结构的抗震优化设计往往以结构隔震效果指标为优化目标函数,对隔震装置的参数取值进行优化,而这种常规的优化方法无法反映出结构参数和作用荷载两者之一的随机性对结构优化设计的影响。基于可靠性的结构优化设计是在常规优化方法基础上发展起来的一种全新的结构优化设计方法,它的基本思路产生于结构可靠性理论与数学规划方法的有机结合。在结构可靠性优化中,将对结构的可靠性要求作为追求的目标或限制条件,运用最优化方法寻求结构在概率意义下的最佳设计。基于以上分析,提出了以结构最大位移响应的期望值为目标函数,控制装置响应的动力可靠性为约束条件,运用罚函数法进行优化求解的基础隔震结构抗震优化控制设计方法,最后给出了算例分析。     

A coupled finite element genetic algorithm for optimum design of stiffened liquid-filled steel conical tanks

In the current study an optimum design technique of stiffened liquid-filled steel conical tanks subjected to global and local buckling constraints is developed using a numerical tool that couples a non-linear finite element model developed in-house and a genetic algorithm optimization technique. This numerical tool is an extended version of an earlier one, adapted for the optimum design of unstiffened conical tanks. The design variables considered in the current study are the shell thicknesses, the geometry of the steel vessel as well as the dimensions and number of stiffeners. The developed numerical tool is capable of selecting the set of design variables that leads to optimum safe design. The analysis is conducted twice; first, case of stiffeners free at their bottom edge, which represents the case of retrofitting an existing tank. In the second case the stiffeners are assumed to be anchored to the bottom slab of the tank, which represents the situation of a newly designed tank. Finally, the optimum design of the stiffened tanks is compared to the optimum design of unstiffened tanks computed in a previous study.     

On the application of natural algorithms to structural design optimization

Powerful computational methods based on metaphors of ‘urvival of the fittest’ (the genetic algorithm) and human brain activity (the neural network) have made significant progress in engineering where there are needs for search and learning mechanisms. The principal subject of the paper is the ‘genetic algorithm’, a ‘population-based’ method of searching large combinatorial (design) spaces to find the optimum combination of design variables. Attention needs to be given to the form and organization of the algorithm if it is to be applied to large-scale problems. Consideration is given to the development of a space condensation heuristic which progressively reduces the size of the multidimensional space being searched thus leading to a more economical application of the algorithm. The approach to adaptivity of controls and the type of penalty function used for the design constraints are explained. Some results from a study of optimum design of a multistorey frame are included by way of illustration.     

考虑结构整体稳定性的单层网壳优化设计

提出了把近似满应力设计方法、弧长法和相对差商法结合起来的改进的离散变量两级优化方法,给出了同时考虑应力约束、位移约束和结构整体稳定性约束的优化算法。在考虑几何非线性的基础上,研究了单层网壳结构以结构质量最轻为目标函数的优化问题,编制了相应的计算程序,并通过算例进行了分析验证。     

Application of particle swarm optimisation to construction planning for cable-stayed bridges by the cantilever erection method

The optimum construction planning of cable-stayed bridges using the cantilever erection method is modelled by setting the objective function as the minimisation of deviation between structural displacement upon completion and the pre-planned construction targets. The constraints on the axial forces of each cable during each erection stage are set to not exceed allowable values and the design variables of post-tensioning force of the dominated cable at each erection stage. Particle swarm optimisation (PSO) and simulated annealing (SA) in the mutation operation of a conventional genetic algorithm (GA) are integrated to improve the ability to escape a local minimum. The PSO–SA–GA is designed to work with the Midas Civil commercial software to determine variables automatically. The newly constructed SheZi Bridge in Taipei, Taiwan, was chosen as a case study and the obtained results were compared to planned results determined by the bridge contractor. The results obtained show that the method developed in this study can be applied effectively for optimum planning of cable-stayed bridges using cantilever erection.     

Initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners

This paper provides an approach to perform initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners. The method divides the optimisation problem into two steps. At the first step, composite optimisation is performed using mathematical programming, where the skin and the stiffeners are modelled using lamination parameters accounting for their anisotropy. Skin and stiffener laminates are assumed to be symmetric, or mid-plane symmetric laminates with 0°, 90°, 45°, or −45° ply angles. The stiffened panel is subjected to a combined loading under strength, buckling and practical design constraints. Buckling constraints are computed using closed form solutions and an energy method (Rayleigh-Ritz). Conservatism is partially removed in the buckling analysis by considering the skin-stiffener flange interaction and decreasing the effective width of the skin. Furthermore, the manufacture of the stiffener is embedded within the design variables. At the second step, the actual skin and stiffener lay-ups are obtained using genetic algorithms, accounting for manufacturability and design practices. This two step approach permits the separation of the structural analysis (strength, buckling, etc.), which is performed at the first step, from the laminate stacking sequence combinatorial problem, which is dealt efficiently with genetic algorithms at the second step.     

Optimal scheduling of booster disinfection in water distribution networks

Booster disinfection stations are the solution alternative to maintain required disinfectant residual concentration in water distribution networks. In the present study, an optimisation problem to determine the optimum injection rates is solved. The minimisation of the total injected mass is considered as the objective function which is subjected to bound constraints on chlorine concentration. Two formulations are used for the linear optimisation problem, with and without considering the initial concentrations as unknowns. Determination of variable network hydraulics and chlorine concentrations is achieved by EPANET. A C++ code was developed to interface with EPANET by means of the EPANET Programmer's Toolkit for optimisation of the disinfectant mass applied to the network. Finally, a cross check is achieved in EPANET software for both disinfectant residual concentrations and linear superposition principle.     

Ant colony optimisation of spatial steel structures under static and earthquake loading

Optimisation is the process of trying to find out the best possible solution to any problem satisfying constraints. Soft computing is the class of methods which have been inspired by the biological computational methods and nature's problem-solving strategies. Currently, these methods include neural networks, evolutionary computational models such as genetic algorithms, random cost and linguistic models such as fuzzy logic. Ant colony optimisation (ACO) is one such method applied for large engineering combinatorial optimisation problems. A design procedure utilising an ACO technique is developed for discrete optimisation of reticulated steel space trusses. The ACO algorithm is motivated by the analogy with natural phenomena, in particular the ability of a colony of ants to ‘optimise’ their collective endeavours. In this paper, the computational implementation of ACO is presented in a structural design context. The objective function considered is the total weight/cost of the structure subjected to material and performance constraints in the form of stress and deflection limits. In the case of reticulated space trusses, the design variables are the cross-sectional areas of members belonging to various groups. The objective function and constraints are obtained by using structural analysis package FEAST (Anonymous, 1995. FEAST user manual. Trivandrum, India: SEG, SDS Group, ISRO, VSSC) in case of structures subjected to static loading and SAP90 (Anonymous, 1990. SAP90, ETABS, SAFE – computer software for structural and earthquake engineering. Berkeley, CA: Computers and Structures) for earthquake loading for reticulated steel space trusses. The numerical examples presented demonstrate the computational advantage of the ACO for large-scale optimisation problems.     

独立基础优化设计及应用

在分析目前常规设计存在的一些缺陷基础上,给出一种独立基础优化设计新方法,有效地解决了现行规范存在的诸如强度和变形影响无法同时考虑等问题。导出了偏心荷载作用下的独立基础底面尺寸设计及独立基础设计的优化数学模型,并编制了求其优化解的复合形法和罚函数法的最优化算法程序及独立基础设计绘图程序。通过算例分析表明,将最优化方法用于基础设计会交大的经济效益。     

Time-domain dynamic drift optimisation of tall buildings subject to stochastic wind excitation

Wind-resistant design of tall buildings has been traditionally treated using the equivalent static load approach. In order to account for the uncertainties in random wind excitation, it is necessary to develop a comprehensive and reliable dynamic optimisation technique in the time domain. The optimal lateral stiffness design problem of wind-excited tall buildings consists of (1) identifying the critical dynamic drift response in the time domain and (2) searching for the optimal distribution of element stiffness of the building subject to multiple drift design constraints. The critical time-history drift constraints of a wind-excited building are first treated by the worst-case formulation and then explicitly expressed in terms of element sizing variables using the principle of virtual work. The extreme value distribution and the Gaussian assumption are employed to formulate and simplify the probabilistic drift constraints, which are explicitly considered in the dynamic optimisation problem. The system reliability associated with the interstory drift is estimated approximately by the bound approach to ensure that the most cost-efficient solution also attains an acceptable reliability level. A full-scale 45-story building example under wind tunnel derived time history wind loading is presented to illustrate the effectiveness and practicality of the reliability-based dynamic optimisation technique.     

A novel hybrid cellular automata–linear programming approach for the optimal sizing of planar truss structures

This paper presents a novel hybrid cellular automata (CA) linear programming (LP) methodology for the size optimisation of planar truss structures. The method uses the nodal displacements and internal forces of the truss as the design variables of the optimisation problem. The objective function is the volume of the structure and the constraints of the original optimisation problem are recast in terms of the new decision variables in the two-phase step. Starting with an arbitrary set of nodal displacements and internal forces, these are updated in turn in an iterative two-phase process. In the first phase, the internal forces are kept fixed and the nodal displacements are found using a CA approach. In the second phase, a LP is used to find the set of internal forces of truss elements which minimises the total volume of the structure. The effectiveness and efficiency of the methodology is also examined with its application to some benchmark truss structures.     

Border-search and jump reduction method for size optimization of spatial truss structures

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.     

Meshing and integrated optimisation for free-form reticulated shells

Presented herein is a study on the meshing and the integrated optimisation technique combined with configuration and mechanical behaviour for free-form reticulated shells. It focuses on the realisation of the practical layouts of meshes and improves the evaluation criteria for grid quality. For the preparation for the integrated optimisation, the bicubic quasi-uniform B-spline surface is applied to describe the free-form surface, and the energy method is introduced to smooth free-form reticulated shell through fairing factors. In order to perform optimisation automatically, a novel integrated optimisation system is established including fairing, finite element analysis (FEA) and optimisation programme modules. Based on the relationship between the fairing factors and the structural configuration, the zoned fairing factors are chosen as design variables (DVs). The FEA module is introduced to analyse and calculate the total structural strain energy of the structural components. By using the optimisation module, the optimum structural configuration can be found when the total structural strain energy reaches the minimum. Numerical results demonstrate that the proposed optimisation technique is convenient and feasible.