基于改进PSO算法的结构损伤检测

结构的损伤检测常转化为求解约束优化问题,针对粒子群算法容易出现早熟问题,增大算法后期的粒子位置的改变量,从而增加粒子位置的差异,因而能够增强其在求解约束优化问题时抵抗局部极小的能力。两层刚架单损伤和多损伤识别的数值结果和收敛曲线表明了改进后的粒子群算法优于传统的带惯性因子的粒子群算法。三层框架结构的4种损伤工况的试验研究进一步说明了该算法应用于结构损伤检测领域的有效性。     

结构损伤检测的人工鱼群算法

结构损伤检测实际上属于系统识别的问题,其最终目标是识别结构损伤前后物理参数的变化。可利用实测结构模态参数建立方程求解得到结构物理参数,该过程在数学上往往转化为求解约束优化问题。由此,尝试采用人工鱼群算法来求解这类大型土木工程约束优化问题,首先介绍了算法的参数定义、行为描述及算法流程,然后利用经典测试函数对算法计算性能进行测试,最后给出了结构损伤识别这类约束优化问题的目标函数并通过数值仿真验证了该算法的有效性和鲁棒性。考虑测量噪声影响并通过不同损伤工况的数值仿真,研究结果表明,人工鱼群算法能有效地检测出损伤单元所处位置和损伤程度,因而将其应用到结构损伤检测领域是可行的。     

基于POS算法的结构模型修正与损伤检测

结构模型修正与损伤检测是结构健康监测过程中必须解决的多学科研究课题，常常转化为求解约束优化问题。介绍粒子群优化（PSO）算法，并在此基础上利用带惯性权重因子的全局版PSO算法对结构模型修正和损伤检测等约束优化问题进行研究。通过两层刚架单损伤和多损伤数值仿真以及三层建筑框架结构四种损伤试验研究，结果表明PSO算法对结构模型修正能够起到非常好的效果，采用PSO算法对结构损伤进行检测不仅能够准确定位结构损伤而且能够有效识别损伤程度。由此可见，PSO算法应用于该领域的效果是显而易见的。     

Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design—determining well placement, number of fracturing stages, and fracture lengths—is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.     

A different view of ridge analysis from numerical optimization

This research falls into the gap between applied statistics and numerical optimization in a specific topic—Ridge Analysis (RA). This article proposes using the trust-region (TR) methods in numerical optimization to solve the RA problem, arising from the literature of response surface methodology (RSM) in applied statistics, where its goal is to help engineers for ‘process improvement’ to find the better response value of the predicted response function within the boundary of experimentation. In the field of numerical optimization, as the family of TR approaches always exhibits excellent mathematical properties during optimization steps, thus the algorithm presented in this study guarantees global optima for the RA problem. Two examples found in the RSM literature are included to illustrate the algorithm, demonstrating its capability of locating better operating conditions than existing computing methods and pointing out particular circumstances (termed the ‘hard case’) where the classical RA procedure fails. An important application to the response modeling problem arising from the philosophy of Taguchi's quality engineering illustrates the hard case. Finally, the utility of the presented TR algorithm is demonstrated through a sequential framework with iterative updates of the TR model under local approximation provided that the predicted response model is a high-order or even non-polynomial function.     

An efficient approach for reliability-based topology optimization

This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15–30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.     

A cloud theory-based particle swarm optimization for multiple decision maker vehicle routing problems with fuzzy random time windows

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.     

Finite-circle method for component approximation and packing design optimization

In this article, the finite-circle method is introduced for 2D packing optimization. Each component is approximated with a group of circles and the non-overlapping constraints between components are converted into simple constraints between circles. Three new algorithms—the bisection algorithm, the three-step algorithm, and the improved three-step algorithm with gap—are developed to automatically generate fewer circles approximating the components. The approximation accuracy, the circle number, and the computing time are analyzed in detail. Considering the fact that packing optimization is an NP-hard problem, both genetic and gradient-based algorithms are integrated in the finite-circle method to solve the problem. A mixed approach is proposed when the number of components is relatively large. Various tests are carried out to validate the proposed algorithms and design approach. Satisfactory results are obtained.     

Structural damage detection using time domain responses and an optimization method

An efficient method is proposed to determine the location and severity of structural damage using time domain responses and an optimization method. The time domain responses utilized here are the nodal accelerations measured at the limited points of a structure subjected to an impulse load. The nodal accelerations of the structure are obtained by Newmark time integration method. Firstly, using nodal accelerations extracted for the damaged structure and an analytical model of the structure, an objective function is defined for optimization. Then, the optimization-based damaged detection problem is solved via a differential evolution algorithm for finding the location and severity of damage. In order to assess the accuracy of the proposed method, four numerical examples are considered. Simulation results reveal the efficiency of the method for properly identifying damage with considering measurement noise.     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

OPTIMAL STRUCTURAL DESIGN BY ANT COLONY OPTIMIZATION

Ant colony optimization (ACO) is a relatively new heuristic combinatorial optimization algorithm in which the search process is a stochastic procedure that incorporates positive feedback of accumulated information. The positive feedback (;i.e., autocatalysis) facility is a feature of ACO which gives an emergent search procedure such that the (common) problem of algorithm termination at local optima may be avoided and search for a global optimum is possible.

The ACO algorithm is motivated by analogy with natural phenomena, in particular, the ability of a colony of ants to ‘optimize’ their collective endeavours. In this paper the biological background for ACO is explained and its computational implementation is presented in a structural design context. The particular implementation of ACO makes use of a tabu search (TS) local improvement phase to give a computationally enhanced algorithm (ACOTS).

In this paper ACOTS is applied to the optimal structural design, in terms of weight minimization, of a 25-bar space truss. The design variables are the cross-sectional areas of the bars, which take discrete values. Numerical investigation of the 25-bar space truss gave the best (i.e., lowest to-date) minimum weight value. This example provides evidence that ACOTS is a useful and technically viable optimization technique for discrete-variable optimal structural design.     

Computational fluid dynamics and interactive multiobjective optimization in the development of low-emission industrial boilers

A CFD-based model is applied to study emission formation in a bubbling fluidized bed boiler burning biomass. After the model is validated to a certain extent, it is used for optimization. There are nine design variables (nine distinct NH₃ injections in the selective non-catalytic reduction process) and two objective functions (which minimize NO and NH₃ emissions in flue gas). The multiobjective optimization problem is solved using the reference-point method involving an achievement scalarizing function. The interactive reference-point method is applied to generate Pareto optimal solutions. Two inherently different optimization algorithms, viz. a genetic algorithm and Powell's conjugate-direction method, are applied in the solution of the resulting optimization problem. It is shown that optimization connected with CFD is a promising design tool for combustion optimization. The strengths and weaknesses of the proposed approach and of the methods applied are discussed from the point of view of a complex real-world optimization problem.     

Short communication optimal replacement scheduling in multi‐state series–parallel systems

The paper generalizes a replacement schedule optimization problem to multi‐state systems, where the system and its components have a range of performance levels—from perfect functioning to complete failure. The multi‐state system reliability is defined as the ability to satisfy a demand which is represented as a required system performance level. The reliability of system elements is characterized by their lifetime distributions with hazard rates increasing in time and is specified as expected number of failures during different time intervals. The optimal number of element replacements during the study period is defined as that which provides the desired level of the system reliability by minimum sum of maintenance cost and cost of unsupplied demand caused by failures. To evaluate multi‐state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Examples of the optimal replacement schedule determination are demonstrated. Copyright © 2000 John Wiley & Sons, Ltd.     

Investigation of static transmission expansion planning using the symbiotic organisms search algorithm

Transmission expansion planning (TEP) has become a complex problem in restructured electricity markets. This article presents the symbiotic organisms search (SOS) algorithm, a novel metaheuristic optimization technique for solving TEP problems in power systems. The SOS algorithm is inspired by the interactions among organisms in an ecosystem. The TEP problem is formulated here as an optimization problem to determine the cost-effective expansion planning of electrical power systems. Several constraints, such as power flow of the lines, right-of-way validity and maximum line addition, are taken into consideration. First, the SOS algorithm is tested with several benchmark functions. Then, it is applied on three standard power system networks (IEEE 24-bus system, Brazilian 46-bus system and Brazilian 87-bus system) in a TEP study to demonstrate the optimization capability of the proposed SOS algorithm. The results are compared with those produced by other state-of-the-art algorithms.     

An inverse finite‐element algorithm for parameter identification of thermoelastic damage models

In this contribution an algorithm for parameter identification of thermoelastic damage models is proposed, in which non‐uniform distributions of the state variables such as stresses, strains, damage variables and temperature are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite‐element method. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled variational problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a non‐homogeneous shear problem with thermal loading. Copyright © 2000 John Wiley & Sons, Ltd.     

A multiscale flaw detection algorithm based on XFEM

We present a novel multiscale algorithm for nondestructive detection of multiple flaws in structures, within an inverse problem type setting. The key idea is to apply a two‐step optimization scheme, where first rough flaw locations are quickly determined, and then, fine tuning is applied in these localized subdomains to obtain global convergence to the true flaws. The two‐step framework combines the strengths of heuristic and gradient‐based optimization methods. The first phase employs a discrete‐type optimization in which the optimizer is limited to specific flaw locations and shapes, thus converting a continuous optimization problem in the entire domain into a coarse discrete optimization problem with limited number of choices. To this end, we develop a special algorithm called discrete artificial bee colony. The second phase employs a gradient‐based optimization of the Broyden–Fletcher–Goldfarb–Shanno type on local well‐defined and bounded subdomains determined in the previous phase. A semi‐analytical approach is developed to compute the stiffness derivative associated with the evaluation of objective function gradients. The eXtended FEM (XFEM), with both circular and elliptical void enrichment functions, is used to solve the forward problem and alleviate the costly remeshing of every candidate flaw, in both optimization steps. The multiscale algorithm is tested on several benchmark examples to identify various numbers and types of flaws with arbitrary shapes and sizes (e.g., cracks, voids, and their combination), without knowing the number of flaws beforehand. We study the size effect of the pseudo grids in the first optimization step and consider the effect of modeling error and measurement noise. The results are compared with the previous work that employed a single continuous optimization scheme (XFEM–genetic algorithm and XFEM–artificial bee colony methods). We illustrate that the proposed methodology is robust, yields accurate flaw detection results, and in particular leads to significant improvements in convergence rates compared with the previous work. Copyright © 2014 John Wiley & Sons, Ltd.     

A damage identification method for truss structures using a flexibility-based damage probability index and differential evolution algorithm

An efficient method for the multiple damage detection of truss systems using a flexibility-based damage probability index (FBDPI) and differential evolution algorithm (DEA) is proposed. In the first step, a new FBDPI is introduced to find the potentially damaged elements of truss systems. The proposed FBDPI is based on the changes of elemental strain, due to damage, computed by the flexibility matrix of the structure. The flexibility matrix of the structure is dynamically estimated using modal analysis data. In the second step, the reduced damage problem is transformed into a standard optimization problem having few damage variables. Then, the DEA is employed to solve the optimization problem for determining the actual location and severity of damaged elements. Simulation results considering measurement noise demonstrate the high efficiency of the proposed method for the damage detection of truss structures.     

Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching

This article proposes a new multiobjective optimization method for structural problems based on multiobjective particle swarm optimization (MOPSO). A gradient-based optimization method is combined with MOPSO to alleviate constraint-handling difficulties. In this method, a group of particles is divided into two groups—a dominated solution group and a non-dominated solution group. The gradient-based method, utilizing a weighting coefficient method, is applied to the latter to conduct local searching that yields superior non-dominated solutions. In order to enhance the efficiency of exploration in a multiple objective function space, the weighting coefficients are adaptively assigned considering the distribution of non-dominated solutions. A linear optimization problem is solved to determine the optimal weighting coefficients for each non-dominated solution at each iteration. Finally, numerical and structural optimization problems are solved by the proposed method to verify the optimization efficiency.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

Conceptual design optimization of rectilinear building frames: A knapsack problem approach

This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.