COST OPTIMIZATION OF STEEL STRUCTURES

While the weight of a steel structure is a major component of the total cost, the minimization of the cost should be the final objective for optimum use of available resources. The total cost of a steel structure includes (a) the material cost of structural members such as beams, columns, and bracings, (b) the fabrication cost including the material costs of connection elements, bolts, and electrodes and the labor cost, (c) the cost of transporting the fabricated pieces to the construction field, and (d) the erection cost including the material costs of connection elements, bolts, and electrodes and the labor cost. In this article, a chronological review of the journal articles on cost optimization of steel structures is presented. Articles on deterministic, reliability-based, and fuzzy logic-based optimization of steel structures are reviewed. Research on cost optimization can encourage the use of the optimization approach in structural steel design practice by providing a more realistic way of modeling structural steel design and resulting in additional savings compared with the weight optimization problem.     

Reliability‐based robust design optimization: A multi‐objective framework using hybrid quality loss function

In this globally competitive business environment, design engineers are constantly striving to establish new and effective tools and techniques to ensure a robust and reliable product design. Robust design (RD) and reliability‐based design approaches have shown the potential to deal with variability in the life cycle of a product. This paper explores the possibilities of combining both approaches into a single model and proposes a hybrid quality loss function‐based multi‐objective optimization model. The model is unique because it uses a hybrid form of quality loss‐based objective function that is defined in terms of desirable as well as undesirable deviations to obtain efficient design points with minimum quality loss. The proposed approach attempts to optimize the product design by addressing quality loss, variability, and life‐cycle issues simultaneously by combining both reliability‐based and RD approaches into a single model with various customer aspirations. The application of the approach is demonstrated using a leaf spring design example. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability-based optimization of direct and indirect LCC of RC bridge elements under coupled fatigue-corrosion deterioration processes

An optimal bridge design should minimize the life cycle cost (LCC) of the structure without compromising its safety. Various cost components need to be evaluated when assessing the life cycle cost of a reinforced concrete bridge. When the structure is subjected to performance degradation due to aging, the probabilistic modeling of degradation is required. In this paper, the reliability-based design optimization RBDO is performed on the life cycle cost of the structure subject to deterioration processes of fatigue and corrosion. This paper advances the state of the art by: considering the coupled corrosion fatigue model in the design optimization and by developing a new approach to evaluate the user delay costs on a bridge, based on direct and indirect costs related to degradation and failure. Also, a sensitivity analysis of optimal costs and design variables is performed. The improved life cycle cost analysis presented herein can be applied to select the optimal design of reinforced concrete bridge elements, by minimizing both agency and bridge user costs, while providing the required safety along the structure lifetime, taking into account the most severe degradation processes.     

An enhanced genetic algorithm for structural topology optimization

Genetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problem‐specific knowledge. The original discrete black‐and‐white (0–1) problem is directly solved by using a bit‐array representation method. To address the related pronounced connectivity issue effectively, the four‐neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well‐posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge‐free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM‐based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near‐optimum solutions and viable topologies with checkerboard free, mesh independent and hinge‐free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem‐specific knowledge can be a powerful global search tool for structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.     

Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis

Accelerated life testing (ALT) design is usually performed based on assumptions of life distributions, stress–life relationship, and empirical reliability models. Time‐dependent reliability analysis on the other hand seeks to predict product and system life distribution based on physics‐informed simulation models. This paper proposes an ALT design framework that takes advantages of both types of analyses. For a given testing plan, the corresponding life distributions under different stress levels are estimated based on time‐dependent reliability analysis. Because both aleatory and epistemic uncertainty sources are involved in the reliability analysis, ALT data is used in this paper to update the epistemic uncertainty using Bayesian statistics. The variance of reliability estimation at the nominal stress level is then estimated based on the updated time‐dependent reliability analysis model. A design optimization model is formulated to minimize the overall expected testing cost with constraint on confidence of variance of the reliability estimate. Computational effort for solving the optimization model is minimized in three directions: (i) efficient time‐dependent reliability analysis method; (ii) a surrogate model is constructed for time‐dependent reliability under different stress levels; and (iii) the ALT design optimization model is decoupled into a deterministic design optimization model and a probabilistic analysis model. A cantilever beam and a helicopter rotor hub are used to demonstrate the proposed method. The results show the effectiveness of the proposed ALT design optimization model. Copyright © 2015 John Wiley & Sons, Ltd.     

基于应变能的预应力平面实体结构拓扑优化设计

研究了预应力平面实体钢结构拓扑优化设计问题。建立了以索力值和结构拓扑为设计变量,以结构储存应变能为约束条件,以结构重量最小为目标函数的数学优化模型。在求解方法上,首先以结构储存应变能最小(刚度最大)确定施加在结构上的索力值,然后采用渐进结构优化法(ESO方法)删除低应变能的单元实现结构的拓扑优化并减轻结构重量。算例结果与相应体系受力性能的结论相吻合,表明本文所提出的优化方法是可行的。     

Condition‐based Maintenance Optimization Using Neural Network‐based Health Condition Prediction

Artificial neural network (ANN)‐based methods have been extensively investigated for equipment health condition prediction. However, effective condition‐based maintenance (CBM) optimization methods utilizing ANN prediction information are currently not available due to two key challenges: (i) ANN prediction models typically only give a single remaining life prediction value, and it is hard to quantify the uncertainty associated with the predicted value; (ii) simulation methods are generally used for evaluating the cost of the CBM policies, while more accurate and efficient numerical methods are not available, which is critical for performing CBM optimization. In this paper, we propose a CBM optimization approach based on ANN remaining life prediction information, in which the above‐mentioned key challenges are addressed. The CBM policy is defined by a failure probability threshold value. The remaining life prediction uncertainty is estimated based on ANN lifetime prediction errors on the test set during the ANN training and testing processes. A numerical method is developed to evaluate the cost of the proposed CBM policy more accurately and efficiently. Optimization can be performed to find the optimal failure probability threshold value corresponding to the lowest maintenance cost. The effectiveness of the proposed CBM approach is demonstrated using two simulated degradation data sets and a real‐world condition monitoring data set collected from pump bearings. The proposed approach is also compared with benchmark maintenance policies and is found to outperform the benchmark policies. The proposed CBM approach can also be adapted to utilize information obtained using other prognostics methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Fatigue design of railway wheels: a probabilistic approach

This paper deals with a method to evaluate and optimize the design of railway wheels subjected to multiparameter variable fatigue loading. The fatigue loads are statistically evaluated from in‐service measurements. Representative realistic loading paths are built from the knowledge of the influence of various factors (such as train speed and track curvature). Using these paths, the method combines finite element computations and the fatigue equivalence method for damage evaluation in the structure. An extension of the Dang Van fatigue criterion in the high‐cycle fatigue finite life domain associated with a damage accumulation law is adopted. The probability of failure of the structure is directly obtained from the interference between a local fatigue equivalent stress and fatigue strength distributions (based on the stress–strength interference approach). The result is useful for the optimization during the design stage or the validation of the fatigue strength of structures.     

A human‐like numerical technique for design of engineering systems

Because of the necessity for considering various creative and engineering design criteria, optimal design of an engineering system results in a highly‐constrained multi‐objective optimization problem. Major numerical approaches to such optimal design are to force the problem into a single objective function by introducing unjustifiable additional parameters and solve it using a single‐objective optimization method. Due to its difference from human design in process, the resulting design often becomes completely different from that by a human designer. This paper presents a novel numerical design approach, which resembles the human design process. Similar to the human design process, the approach consists of two steps: (1) search for the solution space of the highly‐constrained multi‐objective optimization problem and (2) derivation of a final design solution from the solution space. Multi‐objective gradient‐based method with Lagrangian multipliers (MOGM‐LM) and centre‐of‐gravity method (CoGM) are further proposed as numerical methods for each step. The proposed approach was first applied to problems with test functions where the exact solutions are known, and results demonstrate that the proposed approach can find robust solutions, which cannot be found by conventional numerical design approaches. The approach was then applied to two practical design problems. Successful design in both the examples concludes that the proposed approach can be used for various design problems that involve both the creative and engineering design criteria. Copyright © 2005 John Wiley & Sons, Ltd.     

Using the sequential linear integer programming method as a post‐processor for stress‐constrained topology optimization problems

This paper deals with topology optimization of load‐carrying structures defined on discretized continuum design domains. In particular, the minimum compliance problem with stress constraints is considered. The finite element method is used to discretize the design domain into n finite elements and the design of a certain structure is represented by an n‐dimensional binary design variable vector. In order to solve the problems, the binary constraints on the design variables are initially relaxed and the problems are solved with both the method of moving asymptotes and the sparse non‐linear optimizer solvers for continuous optimization in order to compare the two solvers. By solving a sequence of problems with a sequentially lower limit on the amount of grey allowed, designs that are close to ‘black‐and‐white’ are obtained. In order to get locally optimal solutions that are purely {0, 1}ⁿ, a sequential linear integer programming method is applied as a post‐processor. Numerical results are presented for some different test problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Balancing Multiple Criteria Incorporating Cost using Pareto Front Optimization for Split‐Plot Designed Experiments

Finding a D‐optimal design for a split‐plot experiment requires knowledge of the relative size of the whole plot (WP) and sub‐plot error variances. Since this information is typically not known a priori, we propose an optimization strategy based on balancing performance across a range of plausible variance ratios. This approach provides protection against selecting a design which could be sub‐optimal if a single initial guess is incorrect. In addition, options for incorporating experimental cost into design selection are explored. The method uses Pareto front multiple criteria optimization to balance these objectives and allows the experimenter to understand the trade‐offs between several design choices and select one that best suits the goals of the experiment. We present new algorithms for populating the Pareto front for the split‐plot situation when the number of WPs is either fixed or flexible. We illustrate the method with a case study and demonstrate how considering robustness across variance ratios offers improved performance. The Pareto approach identifies multiple promising designs, and allows the experimenter to understand trade‐offs between alternatives and examining their robustness to different ways of combining the objectives. New graphical summaries for up to four criteria are developed to help guide improved decision‐making. Copyright © 2012 John Wiley & Sons, Ltd.     

大展弦比复合材料机翼气动弹性优化

使用遗传/ 敏度混合优化算法对大展弦比复合材料机翼进行气动弹性优化设计研究。在满足强度、位移、发散速度和颤振速度等约束条件的前提下, 以机翼各部件复合材料铺层的厚度为设计变量, 对结构进行重量最小化设计。研究表明: 弯曲变形严重影响最终的优化重量, 是设计大展弦比复合材料机翼结构时应该重点考虑的问题; 按照应力设计准则对这类结构进行设计, 往往很难满足弯曲变形的要求; 使用遗传/ 敏度混合优化算法对大展弦比复合材料机翼进行气动弹性优化设计能够在可以接受的计算耗费下获得满意的结果。      

Discussion of “Reliability‐based design optimization with dependent interval variables” by Xiaoping Du,International Journal for Numerical Methods in Engineering 2012; 91:218–228

In the subject paper, a reliability‐based design optimization (RBDO) model with both random and dependent interval uncertainties was proposed based on the First Order Reliability Method. The lower bound of reliability defined in Equation (9) of the subject paper was utilized as the constraint in this RBDO model. The author claimed that it is the minimum reliability with both random and interval variables. However, we prove that it is not the minimum value. It is therefore suggested that the minimum reliability should be used in the RBDO model. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete size optimization of steel trusses using a refined big bang–big crunch algorithm

This article presents a methodology that provides a method for design optimization of steel truss structures based on a refined big bang–big crunch (BB-BC) algorithm. It is shown that a standard formulation of the BB-BC algorithm occasionally falls short of producing acceptable solutions to problems from discrete size optimum design of steel trusses. A reformulation of the algorithm is proposed and implemented for design optimization of various discrete truss structures according to American Institute of Steel Construction Allowable Stress Design (AISC-ASD) specifications. Furthermore, the performance of the proposed BB-BC algorithm is compared to its standard version as well as other well-known metaheuristic techniques. The numerical results confirm the efficiency of the proposed algorithm in practical design optimization of truss structures.     

Fatigue remaining life estimation for remanufacturing truck crane Jib structure based on random load spectrum

For remanufacturing truck cranes with the characteristic of single piece production, the coupling effect of multi‐physical fields and the correlation of multi‐defect modes are also faced in service. This causes that the safety of crane jib structures has great volatility and uncertainty and is difficult to be judged by fatigue test and damage test. To solve the above problems, an approach of fatigue remaining life evaluation based on random load spectrum is presented. By collecting operating cycle times corresponding to characteristic parameter values during the given time period, the small‐sample measured load spectrum is acquired. Six probability distribution models are used to fit the lifting weight sample in characteristic parameters and the optimal distribution model based on Akaike's information criterion (AIC) is obtained. With the Latin hypercube sampling (LHS) method, a random sample of lifting weight is determined within the fixed inspection cycle. In addition, combining with the rated lifting weight table of truck crane, the corresponding jib length and working range are confirmed. Through defining random values of character parameters and matched operating cycle times, a random load spectrum is gained, thus enabling the extension of measured load spectrum. Depending on the remanufacturing information database, the remanufacturing information of truck crane are retrieved to determine fatigue dangerous cross sections and critical points of jib structures. In order to reflect the variation of structure stress level, the equivalent cross sections of dangerous cross sections are constructed. The first principal stress–time history simulation model for critical points is established, and the rain‐flow counting technology is adopted to extract the two‐dimensional stress spectrum from simulation results. Using the Paris formula combined with the greatest risk principle, the fatigue residual life of jib structure is estimated. Furthermore, the fatigue remaining life evaluation system for jib structure of remanufacturing truck crane is developed for easier application of the proposed method. Finally, as an illustrative example, jib structures of ZLJ5551JQZ110V remanufacturing truck crane are provided to demonstrate the validity and feasibility of this method and system.     

Reliability Based Design Optimization Using Design Explorer

Experimental design methods can be applied to engineering design activities to understand which variables affect the system under consideration, how these variables affect the system, and how to select variable settings that will give uniformly long life to the system. The objective of this paper is to demonstrate the use of Design and Analysis of Computer Experiment (DACE) methods (Sacks, J. et al., 1989) and design optimization via the Surrogate Management Framework (Booker, A. J. et al., 1999; Audet, C. et al., 2000) on reliability optimization problems. Reliabilities are calculated using the Probabilistic Structural Analysis Method (Palle Thoft–Christensen and Baker, 1982; Achintya Haldar and Sankaran Mahadevan, 2000), a method for estimation of reliabilities and reliability indices for a structural model given probability distributions for design variables and “environmental” variables such as loads. By maximizing reliability, or minimizing the probability of failure, we attempt to achieve a minimum cost design that is affected minimally by the variability in the design variables.     

Composite‐Structure Material Design for High‐Energy Lithium Storage

High‐energy storage devices are in demand for the rapid development of modern society. Until now, many kinds of energy storage devices, such as lithium‐ion batteries (LIBs), sodium‐ion batteries (NIBs), and so on, have been developed in the past 30 years. However, most of the commercially exploited and studied active electrode materials of these energy storage devices possess a single phase with low reversible capacity or unsatisfied cycle stability. Continuous and extensive research efforts are made to develop alternative materials with a higher specific energy density and long cycle life by element doping or surface modification. A novel strategy of forming composite‐structure electrode materials by introducing structure units has attracted great attention in recent years. Herein, based on previous publications on these composite‐structure materials, some important scientific points focusing on the design of composite‐structure materials for better electrochemical performances reveal the distinction of composite structures based on average and local structure analysis methods, and an understanding of the relationship between these interior composite structures and their electrochemical performances is discussed thoroughly. The lithiation/delithiation mechanism and the remaining challenges and perspectives for composite‐structure electrode materials are also elaborated.     

An isogeometric approach to topology optimization of multi‐material and functionally graded structures

A new isogeometric density‐based approach for the topology optimization of multi‐material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric non‐uniform rational B‐spline‐based parameterization leading to exact modeling of the geometry, removing numerical artifacts and full analytical computation of sensitivities in a cost‐effective manner. An extension of the perimeter control technique is introduced where restrictions are imposed on the perimeters of density fields of all phases. Consequently, not only can one control the complexity of the optimal design but also the minimal lengths scales of all material phases. This leads to optimal designs with significantly enhanced manufacturability and comparable performance. Unlike the common element‐wise or nodal‐based density representations, owing to higher order continuity of density fields in this method, their gradients required for perimeter control restrictions are calculated exactly without additional computational cost. The problem is formulated with constraints on either (1) volume fractions of different material phases or (2) the total mass of the structure. The proposed method is applied for the minimal compliance design of two‐dimensional structures consisting of multiple distinct materials as well as functionally graded ones. Copyright © 2016 John Wiley & Sons, Ltd.     

Cost optimal design of R/C buildings

A systematic approach is proposed for evaluating the cost-effectiveness of existing or proposed design criteria from the standpoint of life-cycle cost consideration. A series of alternative designs of a model structure representing a class of R/C buildings would be developed following an existing code procedure, except that the code requirements or parameters will be varied for the alternative designs so that a suite of different structures will be obtained each with a different level of safety or reliability. For each of the designed structures, the probability of exceeding the various damage levels under a given earthquake intensity may be calculated. Aggregating and integrating all the cost components with the damage probability density functions for each of the designed structures, as well as with the probabilities of all possible earthquake intensities over a given life will yield the expected life-cycle costs for the respective structures as a function of structural reliability. From these results, the design with the minimum expected life-cycle cost may then be identified; its underlying safety or reliability can also be determined. The approach is illustrated for a class of reinforced concrete buildings under earthquake loading.     

Improving the efficiency of large scale topology optimization through on‐the‐fly reduced order model construction

Topology optimization of large scale structures is computationally expensive, notably because of the cost of solving the equilibrium equations at each iteration. Reduced order models by projection, also known as reduced basis models, have been proposed in the past for alleviating this cost. We propose here a new method for coupling reduced basis models with topology optimization to improve the efficiency of topology optimization of large scale structures. The novel approach is based on constructing the reduced basis on the fly, using previously calculated solutions of the equilibrium equations. The reduced basis is thus adaptively constructed and enriched, based on the convergence behavior of the topology optimization. A direct approach and an approach with adjusted sensitivities are described, and their algorithms provided. The approaches are tested and compared on various 2D and 3D minimum compliance topology optimization benchmark problems. Computational cost savings by up to a factor of 12 are demonstrated using the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.