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.     

Approximate Reliability-Based Optimization Using a Three-Step Approach Based on Subset Simulation

A novel three-step approach is proposed to solve reliability-based optimization (RBO) problems. The new approach is based on a novel approach previously developed by the authors for estimating failure probability functions. The major advantage of the new approach is that it is applicable to RBO problems with high-dimensional uncertainties and with arbitrary system complexities. The basic idea is to transform the reliability constraint in the target RBO problem into nonprobabilistic one by first estimating the failure probability function and the confidence intervals using minimal amount of computation, in fact, using just a single subset simulation (SubSim) run for each reliability constraint. Samples of the failure probability function are then drawn from the confidence intervals. In the second step, candidate solutions of the RBO problems are found based on the samples, and in the third step, the final design solution is screened out of the candidates to ensure that the failure probability of the final design meets the target, which also only costs a single SubSim run. Four numerical examples are investigated to verify the proposed novel approach. The results show that the approach is capable of finding approximate solutions that are usually close to the actual solution of the target RBO problem.     

Efficient Spreadsheet Algorithm for First-Order Reliability Method

A new spreadsheet-cell-object-oriented algorithm for the first-order reliability method is proposed and illustrated for cases with correlated nonnormals and explicit and implicit performance functions. The new approach differs from the writers earlier algorithm by obviating the need for computations of equivalent normal means and equivalent normal standard deviations. It obtains the solution faster and is more efficient, robust, and succinct. Other advantages include ease of initialization prior to constrained optimization, ease of randomization of initial values for checking robustness, and fewer required optimization constraints during spreadsheet-automated search for the design point. Two cases with implicit performance functions, namely an asymmetrically loaded beam on Winkler medium and a strut with complex supports are analyzed using the new approach and discussed. Comparisons are also made between the proposed approach and that based on Rosenblatt transformation.     

Reliability-Based Optimal Design of Truss Structures Using Particle Swarm Optimization

In this work, the particle swarm optimization method is employed for the reliability-based optimal design of statically determinate truss structures. Particle swarm optimization is inspired by the social behavior of flocks (swarms) of birds and insects (particles). Every particle’s position represents a specific design. The algorithm searches the design space by adjusting the trajectories of the particles that comprise the swarm. These particles are attracted toward the positions of both their personal best solution and the best solution of the swarm in a stochastic manner. In typical structural optimization problems, safety is dealt with in a yes/no manner fulfilling the set of requirements imposed by codes of practice. Considering uncertainty for the problem parameters offers a measure to quantify safety. This measure provides a rational basis for the estimation of the reliability of the components and of the entire system. Incorporating the reliability into the structural optimization framework one can seek a reliability-based optimal design. For the problems examined herein, the reliability indexes of the structural elements are obtained from analytical expressions. The structure is subsequently analyzed as a series system of correlated elements and the Ditlevsen bounds are used for the calculation of its reliability index. The uncertain-random parameters considered in this work are the load, the yield-critical stress; and the cross sections of the elements. The considered design variables of the optimization problem are the cross-sectional areas of the groups, which control the size of the truss, and the heights and lengths that control the shape of the truss. The results of the optimization are presented for a 25-bar truss and a 30-bar arch and the robustness of the optimization scheme is discussed.     

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.     

Hybrid Time-Cost Optimization of Nonserial Repetitive Construction Projects

Time-cost trade-off analysis represents a challenging task because the activity duration and cost have uncertainty associated with them, which should be considered when performing schedule optimization. This study proposes a hybrid technique that combines genetic algorithms (GAs) with dynamic programming to solve construction projects time-cost trade-off problems under uncertainty. The technique is formulated to apply to project schedules with repetitive nonserial subprojects that are common in the construction industry such as multiunit housing projects and retail network development projects. A generalized mathematical model is derived to account for factors affecting cost and duration relationships at both the activity and project levels. First, a genetic algorithm is utilized to find optimum and near optimum solutions from the complicated hyperplane formed by the coding system. Then, a dynamic programming procedure is utilized to search the vicinity of each of the near optima found by the GA, and converges on the global optima. The entire optimization process is conducted using a custom developed computer code. The validation and implementation of the proposed techniques is done over three axes. Mathematical correctness is validated through function optimization of test functions with known optima. Applicability to scheduling problems is validated through optimization of a 14 activity miniproject found in the literature for results comparison. Finally implementation to a case study is done over a gas station development program to produce optimum schedules and corresponding trade-off curves. Results show that genetic algorithms can be integrated with dynamic programming techniques to provide an effective means of solving for optimal project schedules in an enhanced realistic approach.     

Reliability-Constrained Optimization of Water Treatment Plant Design Using Genetic Algorithm

A new approach that links genetic algorithm (GA) as an optimization tool with Monte Carlo simulation (MCS)-based reliability program is presented for reliability-constrained optimal design of water treatment plant (WTP). The reliability of a WTP is defined as the probability that it can achieve the desired effluent water quality standard (WQS). The objective function minimizes the treatment cost, subjected to design and performance constraints, and to achieve desired reliability level for meeting the given effluent WQS. The random variables used to generate the reliability estimates are suspended solids (SS) concentration, flow rate, specific gravity of floc particle, temperature of raw water, sedimentation basin performance index, and model coefficients. The application of GA-MCS approach for design of a WTP is illustrated with a hypothetical case study. The annualized cost of WTP is affected by the number of uncertain parameters included in the analysis, coefficient of variation of uncertain parameters, effluent WQS, and target reliability level. Analysis suggests that higher reliability at lower annual cost of treatment can be achieved by limiting the fluctuation of uncertain parameters. Results show that distribution of effluent SS is also affected by the uncertainty. The suggested GA-MCS approach is efficient to evaluate treatment cost-reliability tradeoff for WTP. Results demonstrate that the combination of GA with MCS is an effective approach to obtain the reliability-constrained optimal/near-optimal solution of WTP design problem consistently.     

Integrating Efficient Resource Optimization and Linear Schedule Analysis with Singularity Functions

Resources perform or enable physical operations and thus are vital on construction projects, yet are subject to various constraints. Their use within a project schedule must therefore be carefully planned. A major objective is optimizing when they are active within the float of noncritical activities to avoid disruptive and costly fluctuations. This paper builds on analyzing criticality of linear schedules with the unique singularity functions. The new approach keeps resources intact and derives one flexible equation for the complete resource profile of a schedule, including any timing or resource rate changes. Another equation models its first moment of area to minimize the objective function toward a level profile. A genetic algorithm is suitable for an iterative optimization. The parameters of its chromosomes are recombined evolutionarily and can model any permutation. Analyzing a road project illustrates how singularity functions integrate resource optimization with its linear schedule and facilitate a subsequent optimization.     

New Multidimensional Visualization Technique for Limit-State Surfaces in Nonlinear Finite-Element Reliability Analysis

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS.     

Glass Fiber Reinforced Polymer Pultruded Members: Constitutive Model and Stability Analysis

The increasingly widespread use of fiber-reinforced polymers as an alternative to conventional materials makes it necessary to formulate theoretical models which adequately evaluate the influence of the anisotropy of such composites on the structural behavior. While the cross section shapes adopted for compressed members are generally the same as in steel structures, the anisotropy which characterizes these polymers may reduce the critical loading threshold due to local buckling phenomena. A procedure to study the buckling of glass fiber reinforced polymer pultruded members by means of an homogenization approach is proposed here. A two-stage buckling model permits the determination of both global and local critical loads as explicit functions of the member geometry and its material behavior. These functions may be used for optimization of the shape of the above-mentioned members. Besides the model shows its reliability as it fits the results of experimental testson members with different slenderness ratios.     

Achieving Water Quality System Reliability Using Genetic Algorithms

This paper presents an efficient approach for obtaining wasteload allocation solutions that provide the optimal trade-off between treatment cost and reliability. This approach links a genetic algorithm (GA) with the first-order reliability method (FORM) for estimating the probability of system failure under a given wasteload allocation. The GA-FORM optimization approach is demonstrated for the case study of managing water quality in the Willamette River in Oregon. The objective function minimizes the sum of the treatment cost and the penalty associated with breaching a reliability target for meeting a water quality standard. The random variables used to generate the reliability estimates include streamflow, temperature, and reaeration coefficient values. The results obtained indicate that the GA-FORM approach is nearly as accurate as the approach that links the GA with Monte Carlo simulation and is far more efficient. The trade-off between total treatment cost and reliability becomes more pronounced at higher water quality standards and is most sensitive to the uncertainty in the reaeration coefficient. The sensitivity to the reaeration coefficient also increases at increased reliability levels.     

Reliability, Risk, and Uncertainty Analysis Using Generic Expectation Functions

In engineering design and analysis, mathematical models that generally involve a number of uncertain parameters are frequently employed for decision making. Over the years, a number of techniques have been developed to quantify model output uncertainty contributed by uncertain input parameters. Typically, the methods that are easy to apply may give inaccurate estimates of model output uncertainty. Other methods that reliably produce very accurate results are either difficult to apply or require intensive computational effort. This paper describes the development of generic expectation functions as a function of means and coefficients of variation of input random variables. The generic expectation functions are straightforward to develop, and apply to problems related to reliability, risk, and uncertainty analysis. Several expectation functions based on commonly used probability distributions have been developed. Using them, any order of moment can be estimated exactly. It is found that if exact moments of the model output are available, one can find a good estimate of reliability, risk, and uncertainty of a system without knowing its model output distribution exactly. This technique is applicable when an output variable is a function of several independent random variables in multiplicative, additive, or combined (multiplicative and additive) forms. A practical example is presented to demonstrate the application of generic expectation functions.     

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。      

Dynamic reliability models with conditional proportional hazards

A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a 'jump' from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution function of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.     

面向全局和工程优化问题的混合进化JAYA算法

为了更好求解复杂函数优化和工程约束优化问题,进一步增强JAYA算法的寻优能力,提出一种面向全局优化的混合进化JAYA算法.首先在计算当前最优和最差个体时引入反向学习机制,提高最优和最差个体跳离局部极值区域的可能性;然后在个体位置更新中引入并融合正弦余弦算子和差分扰动机制,不仅增加了种群的多样性,而且较好平衡与满足了算法在不同迭代时期对探索和挖掘能力的不同需求;最后在算法结构上采用奇偶不同的混合进化策略,有效利用不同演化机制的优势结果,进一步提升了算法的收敛性和精度.之后给出了算法流程伪代码,理论分析证明了改进算法的时间复杂度与基本JAYA相同,而通过6种代表性算法在包含和组合了30个基准函数的CEC2017测试套件上进行的多维度函数极值优化测试,以及对拉伸弹簧、波纹舱壁、管柱设计、钢筋混凝土梁、焊接梁和汽车侧面碰撞6个具有挑战性的工程设计问题的优化求解,都清楚地表明改进后算法的寻优精度、收敛性能和求解稳定性均有显著提升,在求解CEC复杂函数和工程约束优化问题上有着明显优势.     

A disagreement about within-group agreement: Disentangling issues of consistency versus consensus.

L. R. James et al (1984) developed an index, rWG, for assessing within-group agreement appropriate when only a single target is rated. F. L. Schmidt and J. E. Hunter (1989) criticized the conceptual foundation of rWG because it is not consistent with the classical model of reliability, and proposed an alternative approach, the use of the rating standard deviation (SDx), the standard error of the rating mean (SEM), and the associated confidence intervals for SEM to index interrater agreement. This comment argues that the critique of rWG did not clearly distinguish the concepts of interrater consensus (i.e., agreement) and interrater consistency (i.e., reliability). When the distinction between agreement and reliability is drawn, the critique of rWG is shown to divert attention from more critical problems in the assessment of agreement. The approach for assessing within-group agreement proposed by Schmidt and Hunter has several limitations. rWG should not be used as an index of interrater reliability but, within certain bounds, it is suitable as an index of within-group interrater agreement. SDx and SEM are not acceptable substitutes for extant indexes of interrater agreement. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Simultaneous Inverse Identification of Transient Thermal Properties and Heat Sources Using Sparse Sensor Information

A study is presented herein on the simultaneous inverse identification of transient internal heat generation, transient thermal diffusivity, and constant convection coefficients. The formulations of the direct and inverse problems are presented in the context of finite-element analysis and nonlinear optimization, respectively. A real-coded genetic algorithm was used to solve the inverse problem because of the global convergence properties of this optimization technique. It was found through numerical studies that heat generation and thermal conductivity as functions of time can be simultaneously and consistently estimated from sparse sensor information, as long as convection coefficients are known. However, treating convection coefficients as unknown may significantly affect the accuracy of the estimated thermal diffusivity function and to a lesser extent, the accuracy of the heat generation function. The numerical experiments showed, however, that the Biot number can be accurately estimated when the convection coefficients are not well known. These results can have wide and important implications in problems related to monitoring and quality control of structures.     

应急救援物资车辆运输路线多目标优化

运用运筹学中图论及多目标优化的理论和方法建立应急救援物资车辆最佳运输路线的选择模型,并基于启发式算法求解该模型.从静态网络应急物资车辆运输路线的双目标优化问题入手,设计适合本文模型的算法,并将之推广至含有三个及三个以上优化目标的路线选择问题.引入时间扩展图的概念,将动态网络中的最佳运输路线问题转化为静态网络中的路径选择问题.算法实质是通过构造辅助决策函数实现Dijstra算法的调用,并在辅助函数构成的搜索空间上寻找最优解,是一种快速的、近似的算法.利用随机路网和真实路网测试本文算法,测试结果与本文的理论分析一致,证明本文算法在应急救援物资车辆运输路线的多目标优化问题中可行且有较好的应用效果.      

Balancing Connectivity of Deteriorating Bridge Networks and Long-Term Maintenance Cost through Optimization

Due to aggressive environmental stressors and increasing traffic loads, highway bridges are undergoing significant deterioration in both condition and safety. Timely and adequate maintenance interventions are therefore crucial to ensure the functionality of existing bridges in a network. Under budget constraints, it is important to prioritize maintenance needs to bridges that are most significant to the functionality of the entire network. In this paper, the network-level bridge maintenance planning problem is posed as a combinatorial optimization and is automated by a genetic algorithm (GA) to select and allocate maintenance interventions of different types among networked bridges as well as over a specified time horizon. Two conflicting objective functions are considered simultaneously: (1) The overall performance of a bridge network expressed by the time-dependent reliability of connectivity between the origin and the destination locations and (2) the present value of total maintenance cost over the specified time horizon. A variety of maintenance types, which differ in unit costs as well as in effects on bridge performance in terms of improvement in structural reliability levels, are used in the optimization. An event tree analysis is carried out to obtain a closed-form expression for the network connectivity reliability. As an illustration example, the GA-based procedure is applied to deteriorating deck slabs of an existing 13-bridge network located in Colorado. It is shown that the proposed maintenance planning procedure has the capability of both prioritizing scarce maintenance needs to deteriorating bridges that are most crucial to the network performance and cost-effectively distributing maintenance interventions over the time horizon.     

Object-Oriented Optimization Approach Using Genetic Algorithms for Lattice Towers

A new approach is presented for the optimization of steel lattice towers by combining genetic algorithms and an object-oriented approach. The purpose of this approach is to eliminate the difficulties in the handling of large size problems such as lattice towers. Improved search and rapid convergence are obtained by considering the lattice tower as a set of small objects and combining these objects into a system. This is possible with serial cantilever structures such as lattice towers. A tower consists of panel objects, which can be classified as separate objects, as they possess an independent property as well as inherent properties. This can considerably reduce the design space of the problem and enhance the result. An optimization approach for the steel lattice tower problem using objects and genetic algorithms is presented here. The paper also describes the algorithm with practical design considerations used for this approach. To demonstrate the approach, a typical tower configuration with practical constraints has been considered for discrete optimization with the new approach and compared with the results of a normal approach in which the full tower is considered.