Reliability-Based Optimal Design of Series Structural Systems

A robust approach for approximately solving reliability-based optimal design problems, for series structural systems, is developed. The approach reformulates the problems by replacing reliability terms with deterministic functions. The reformulated problems can be solved by existing semiinfinite optimization algorithms, producing solutions that are identical to those of the original problems, when the limit-state functions are affine, or when first-order reliability approximations are used. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, allowing flexibility in the choice of the optimization algorithm and the reliability method. Three sets of examples demonstrate applications of the approach.     

Design Philosophy Issues of Fiber Reinfored Polymer Reinforced Concrete Structures

The conventional design philosophy for reinforced concrete (RC) relies heavily on the ductile properties of steel. These ductile properties are used as a “fuse” and conceal the large uncertainty in the determination of modes of failure caused directly by concrete. Current design guidelines for fiber reinforced polymer (FRP) RC structures have inappropriately adopted the same design philosophy used for steel RC, leading either to the adoption of conservative safety factors or reduced structural reliability. A reliability-based analysis of FRP RC beams shows that the current, very conservative partial safety factors for FRP reinforcement on their own do not influence the structural safety of overreinforced concrete elements. Proposals are made for the modification of the material partial safety factors to achieve target safety levels.     

Overtopping Probability Constrained Optimal Design of Composite Channels Using Swarm Intelligence Technique

In this paper swarm intelligence based methodology is proposed for optimal and reliable design of irrigation channels. The input parameters involved in channel design are prone to uncertainty and the solution of deterministic model may result in flooding risk and affect the stability of the channel. To provide reliability in the design, an overtopping probability constrained design is presented in this study. The deterministic equivalent of the probabilistic constraint is derived by following the principle of first order uncertainty analysis. In order to account for the uncertainty of design parameters in the objective function, a modified cost function is proposed. A methodology is propounded to solve it in a metaheuristic environment and solved it using elitist-mutated particle swarm optimization (EMPSO) method. The EMPSO based solutions are found to be quite successful and better than the classical optimization methods. Finally, it is concluded that the proposed methodology has a good potential for reliable design of composite channels for designer specified reliability values.     

Reliability-Based Optimization Considering Manufacturing and Operational Uncertainties

This paper presents approaches for integrating multidisciplinary optimization and probabilistic methods to perform reliability-based multidisciplinary optimization. The approaches are built into a framework that allows solution of optimization problems, wherein system parameters including dimensional tolerances, material properties, boundary conditions, loads, and model predictions are uncertain or variable. This approach directly supports quality engineering because it allows engineers to specify manufacturing tolerances required to achieve the desired product reliability, and it results in robust designs that are optimal over the range of variable conditions because it considers uncertainties during the optimization process. The basic reliability-based multidisciplinary optimization methodology has been demonstrated to design engine components, aircraft lap joints, and transport aircraft wings. Herein this methodology is reviewed and then the focus is on demonstrating a new framework that makes it possible to use these methods with commercial CAD∕CAE tools and support commercial shape parameterization to enable shape optimization and consideration of manufacturing uncertainties.     

Optimal Design with Probabilistic Objective and Constraints

Significant challenges are associated with solving optimal structural design problems involving the failure probability in the objective and constraint functions. In this paper, we develop gradient-based optimization algorithms for estimating the solution of three classes of such problems in the case of continuous design variables. Our approach is based on a sequence of approximating design problems, which is constructed and then solved by a semiinfinite optimization algorithm. The construction consists of two steps: First, the failure probability terms in the objective function are replaced by auxiliary variables resulting in a simplified objective function. The auxiliary variables are determined automatically by the optimization algorithm. Second, the failure probability constraints are replaced by a parametrized first-order approximation. The parameter values are determined in an adaptive manner based on separate estimations of the failure probability. Any computational reliability method, including first-order reliability and second-order reliability methods and Monte Carlo simulation, can be used for this purpose. After repeatedly solving the approximating problem, an approximate solution of the original design problem is found, which satisfies the failure probability constraints at a precision level corresponding to the selected reliability method. The approach is illustrated by a series of examples involving optimal design and maintenance planning of a reinforced concrete bridge girder.     

Reliability-Based Optimization of Design Code for Tension Piles

A reliability-based calibration of a design code for offshore tension pile foundations in clay is presented by an example. The design against pullout in ultimate loading is considered. The calibration is performed by means of a numerical optimization technique in conjunction with probabilistic and deterministic models for load and capacity. The probabilistic models allow for predictions of the reliability against pullout. The deterministic models express design load and design capacity in terms of characteristic values and partial safety factors. The code calibration consists of determination of the partial safety factors such that—over a specified scope of code—designs with reliabilities with minimum deviations from some prescribed target reliability result when applying the deterministic models with this particular set of partial safety factors. For tutorial purposes, the scope of code is represented by a limited number of design cases, and emphasis is placed on the demonstration of the code calibration principles and a proper formulation of the code format.     

Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

多目标粒子群优化算法研究综述

针对多目标粒子群优化算法的研究进展进行综述。首先,回顾了多目标优化和粒子群算法等基本理论;其次,分析了多目标优化所涉及的难点问题;再次,从最优粒子选择策略,多样性保持机制,收敛性提高手段,多样性与收敛性平衡方法,迭代公式、参数、拓扑结构的改进方案5个方面综述了近年来的最新成果;最后,指出多目标粒子群算法有待进一步解决的问题及未来的研究方向。      

用粒子群算法优化编制露天矿生产作业计划

从露天矿采掘和运输成本的最小化角度出发,构建露天矿生产作业计划模型.基于群体智能优化理论,提出了用粒子群算法对露天矿生产作业计划模型进行解算的方法,并在求解过程中设计了带核粒子及双吸引子的粒子搜索策略.以MATLAB软件为平台进行求解运算最佳作业计划.以某露天铁矿为工程背景进行实例研究,将研究结果与露天矿实际生产指标和非线性规划解算结果进行比较验证.结果表明,粒子群算法可用于露天矿生产作业计划的优化编制.      

Multiple Resistance Factor Design for Shallow Transmission Line Structure Foundations

This paper presents the development of simplified reliability-based design (RBD) equations that are suitable for spread foundations subjected to uplift. Emphasis is placed on the loading and foundation characteristics relevant to the electric utility industry. A general reliability calibration procedure is used to derive robust resistance/deformation factors for load and resistance factor design (LRFD) and multiple resistance factor design (MRFD) formats. Two target reliability indices of 3.2 and 2.6 are proposed based on an extensive study of existing designs for ultimate and serviceability limit state, respectively. The main advantage of using these RBD factors is that a known level of reliability can be consistently achieved over a wide range of design conditions. Simple design calculations using the MRFD format are shown to demonstrate their ability to account for parametric uncertainties in a rational manner.     

Reliability-based Calibration of Partial Safety Coefficients for Fiber-Reinforced Plastic

The scope of this paper is to present a possible methodology for the calibration of partial safety factors for the design of strengthening measures of reinforced-concrete (RC) members using fiber-reinforced plastic (FRP). The methodology is general and can be used for any type of strengthening measure, e.g., in flexure, shear, ductility, or for the design of anchorage zones. The approach considers the problem of strengthening an RC member from a current unsafe situation, where all involved quantities are known from assessment, though only in probabilistic terms, to a target safe one, of which only the desired reliability is known. All relevant random variables are attributed a predefined probability distribution, based on a statistical survey separately conducted on geometrical and mechanical characteristics of old-style components. A first-order reliability method based optimization procedure is used to seek the solution of such a problem so that the target reliability is attained with the optimal FRP quantity, the appropriate collapse mechanism of the strengthened member, and the FRP design strength, with the associated partial safety factor. From Monte Carlo design simulations, the partial safety factor is probabilistically characterized, thus allowing one to select an appropriate fractile value for it.     

Genetic Algorithms in Competitive Environments

Competition is introduced among the populations of a number of genetic algorithms (GAs) in solving optimization problems. The aim is to adapt the parameters of the GAs, by altering the resources of the system, so as to achieve better solutions. The evolution of the different populations, having different sets of parameters, is controlled at the level of metapopulation, i.e., the union of populations, on the basis of statistics and trends of the evolution of every population. An overall fitness measure is introduced that incorporates a diversity measure and the required resources to rank the populations. The fuzzy outcome of the conflict among the populations guides the evolution of the different GAs toward better solutions in the statistical sense. The proposed scheme is applied to two different problems—a multimodal function with six global and several near-global optima, and a reliability based optimal design of a simple truss. Numerical results are presented, and the robustness and computational efficiency of the proposed scheme are discussed.     

Reliability-Based Optimum Design of Glulam Cable-Stayed Footbridges

This work presents a procedure for finding the reliability-based optimum design of cable-stayed bridges. The minimization problem is stated as the minimization of stresses, displacements, reliability, and bridge cost. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. An equivalent multicriteria approach is used to solve the nondifferential, nonlinear optimization problem, turning the original problem into sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum is obtained. Examples are given illustrating the procedure.     

基于自适应搜索的免疫粒子群算法

经典粒子群算法由于多样性差而陷入局部最优,从而造成早熟停滞现象.为克服上述缺点,本文结合人工免疫算法,提出一种基于自适应搜索的免疫粒子群算法.首先,该算法改善了浓度机制;然后由粒子最大浓度值来控制子种群数目以充分利用粒子种群资源;最后对劣质子种群进行疫苗接种,利用粒子最大浓度值调节接种疫苗的搜索范围,不仅避免了种群退化现象,而且提高了算法的收敛精度和全局搜索能力.仿真结果表明该算法求解复杂函数优化问题的有效性和优越性.      

Numerical Approximations of Design Points in Reliability Analysis under Parametric Changes

Traditional approaches for repeatedly updating reliability estimates, as needed in reliability-based optimal designs or real-time system control, require the iterative application of a reliability method. This paper explores a new strategy for repeatedly estimating reliability under frequent parameter variations. The central idea is to update the design point in the parameter domain, rather than in the traditional random variable domain, by evaluating several parametric sensitivity measures which are systems of nonlinear first-order ordinary differential equations relating the design point to parameter changes. Four numerical algorithms for evaluating the sensitivity measures are developed using the Euler and the improved Euler algorithms. Two solution procedures are applied. One procedure solves for the updated design point directly, while the other solves for both the unit normal vector at the design point and the reliability index separately, and evaluates the product of these to determine the updated design point. The numerical techniques are thoroughly compared with the classical Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm in five numerical examples regarding efficiency and accuracy. It is found that they are efficient and robust under given conditions.     

Damage Detection and Damage Detectability— Analysis and Experiments

A technique to identify structural damage in real time using limited instrumentation is presented. Contrast maximization is used to find the excitation forces that create maximum differences in the response of the damaged structure and the analytical response of the undamaged structure. The optimal excitations for the damage structure are then matched against a database of optimal excitations to locate the damage. To increase the reliability of the approach under modeling and measurement errors, the contrast maximization approach is combined with an approach based on changes in frequency signature. The detectability of any particular damage with the proposed technique depends on the ratio of the magnitude of damage and the magnitude of errors in the measurements, as well as on how much the damage influences the measurements. A damage detectability prediction measure, that incorporates these effects, is developed. The technique is first tested numerically on a 36 degree-of-freedom space truss. To simulate experimental conditions, an extensive study is carried out in the presence of noise. A similar truss is then built and the finite-element method (FEM) model of the structure is corrected using experimental data. The technique is applied to locate the damage in several members. The experimental results indicate that this technique can robustly identify the damaged member with limited measurements and real-time computation. The effectiveness of the damage detection measure is also demonstrated.     

Particle Swarm Optimization-Supported Simulation for Construction Operations

This study proposes an integration of particle swarm optimization (PSO) and a construction simulation so as to determine efficiently the optimal resource combination for a construction operation. The particle-flying mechanism is utilized to guide the search process for the PSO-supported simulation optimization. A statistics method, i.e., multiple-comparison procedure, is adopted to compare the random output performances resulting from the stochastic simulation model so as to rank the alternatives (i.e., particle-represented resource combinations) during the search process. The indifference zone and confidence interval facilitate consideration of the secondary performance measure (e.g., productivity) when the main performance measures (e.g., cost) of the competing alternatives are close. The experimental analyses demonstrate the effectiveness and efficiency of the proposed simulation optimization. The study aims to providing an alternative combination of optimization methodology and general construction simulation by utilizing PSO and a statistics method so as to improve the efficiency of simulation in planning construction operations.     

Simultaneous Determination of Critical Slip Surface and Reliability Index for Slopes

This paper presents a new method for applying reliability-based design approaches to slope stability analysis. In this method the soil properties are considered to be random variables. The factor of safety of the slope is found using Bishop’s simplified method for noncircular slip surfaces. By considering the variability of the soil properties, the probability of failure is determined from the reliability index (β). The minimization problem (determination of the lowest β value for the range of variables and possible slip surfaces considered) is solved using a genetic algorithm approach, which simultaneously locates the critical slip surface and determines the reliability index. The performance of the new method is compared to some existing reliability approaches when applied to case histories of slope failures from the geotechnical literature. The new approach is seen to provide reasonable and consistent estimates of the reliability index and critical slip surface.     

Optimum Design of Cantilever Retaining Walls Using Target Reliability Approach

In this paper, an approach for reliability-based design optimization of reinforced concrete cantilever retaining wall is described. A parametric study is conducted to assess the effect of uncertainties in design parameters on the probability of failure of cantilever retaining walls. In total, ten modes of failure are considered, viz. overturning of the wall about its toe, sliding of the wall on its base, eccentricity, bearing capacity failure below the base slab, and shear and moment failure in the toe slab, heel slab, and stem. The analysis is performed by treating backfill and foundation soil properties, geometric properties of wall, and reinforcement and concrete properties as random variables. These results are used to develop a set of reliability-based design charts for different coefficients of variation of friction angle of backfill soil (5 and 10%) and targeting reliability index (βt) in the range of 3–3.2 for all failure modes. A comparative study is also presented, which shows that optimized sections have less areas of cross section compared to those obtained from specifications on dimensioning of retaining walls available in literature.