An integrated reliability-based design optimization of offshore towers

After recognizing the uncertainty in the parameters such as material, loading, geometry and so on in contrast with the conventional optimization, the reliability-based design optimization (RBDO) concept has become more meaningful to perform an economical design implementation, which includes a reliability analysis and an optimization algorithm. RBDO procedures include structural analysis, reliability analysis and sensitivity analysis both for optimization and for reliability. The efficiency of the RBDO system depends on the mentioned numerical algorithms. In this work, an integrated algorithms system is proposed to implement the RBDO of the offshore towers, which are subjected to the extreme wave loading. The numerical strategies interacting with each other to fulfill the RBDO of towers are as follows: (a) a structural analysis program, SAPOS, (b) an optimization program, SQP and (c) a reliability analysis program based on FORM. A demonstration of an example tripod tower under the reliability constraints based on limit states of the critical stress, buckling and the natural frequency is presented.     

Adaptive improved response surface method for reliability-based design optimization

Reliability-based design optimization (RBDO) requires the evaluation of probabilistic constraints (or reliability), which can be very time consuming. Therefore, a practical solution for efficient reliability analysis is needed. The response surface method (RSM) and dimension reduction (DR) are two well-known approximation methods that construct the probabilistic limit state functions for reliability analysis. This article proposes a new RSM-based approximation approach, named the adaptive improved response surface method (AIRSM), which uses the moving least-squares method in conjunction with a new weight function. AIRSM is tested with two simplified designs of experiments: saturated design and central composite design. Its performance on reliability analysis is compared with DR in terms of efficiency and accuracy in multiple RBDO test problems.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

Thermal–hydraulic passive system reliability-based design approach

In order to enhance the safety of new advanced reactors, optimization of the design of the implemented passive systems is required. Therefore, a reliability-based approach to the design of a thermal–hydraulic passive system is being considered, and a limit state function (LSF)-based approach elicited from mechanical reliability is developed. The concept of functional failure, i.e., the possibility that the load will exceed the capacity in a reliability physics framework, in terms of performance parameter is introduced here for the reliability evaluation of a natural circulation passive system, designed for decay heat removal of innovative light water reactors. Water flow rate circulating through the system is selected as passive system performance characteristic parameter and the related limit state or performance function is defined. The probability of failure of the system is assessed in terms of safety margin, corresponding to the LSF. Results help the designer to determine the allowable limits or set the safety margin for the system operation parameters, to meet the safety and reliability requirements.     

Reliability-based optimal design using sample average approximations

An algorithm for reliability-based optimal design is developed using sampling techniques for estimating the failure probability. The algorithm applies a new method for sensitivity calculations of the failure probability. Initially, the estimates of the failure probability are coarse. As the algorithm progresses towards an optimal design, the number of sample points is increased in an adaptive way leading to better estimates of the failure probability. The algorithm is proven to converge to an optimal design. The applicability of the algorithm is shown in an example from the area of highway bridge design.     

Reliable design space and complete single-loop reliability-based design optimization

Reliability-based design optimization (RBDO) has been intensively studied due to its significance and its conceptual and mathematical complexity. This paper proposes a new method for RBDO on the basis of the concept of reliable design space (RDS), within which any design satisfies the reliability requirements. Therefore, a RBDO problem becomes a simple, deterministic optimization problem constrained by RDS rather than its deterministic feasible space. The RDS is found in this work by using the partial derivatives at the current design point as an approximation of the derivatives at its corresponding most probable point (MPP) on the limit state function. This work completely resolves the double loop in RBDO and turns RBDO into a simple optimization problem. Well-known problems from the literature are selected to illustrate the steps of the approach and for result comparison. Discussions will also be given on the limitation of the proposed method, which is shown to be a common limitation overlooked by the research community on RBDO.     

Multi-objective system reliability-based optimization method for design of a fully parametric concept car body

This article investigates multi-objective optimization under reliability constraints with applications in vehicle structural design. To improve computational efficiency, an improved multi-objective system reliability-based design optimization (MOSRBDO) method is developed, and used to explore the lightweight and high-performance design of a concept car body under uncertainty. A parametric model knowledge base is established, followed by the construction of a fully parametric concept car body of a multi-purpose vehicle (FPCCB-MPV) based on the knowledge base. The structural shape, gauge and topology optimization are then designed on the basis of FPCCB-MPV. The numerical implementation of MOSRBDO employs the double-loop method with design optimization in the outer loop and system reliability analysis in the inner loop. Multi-objective particle swarm optimization is used as the outer loop optimization solver. An improved multi-modal radial-based importance sampling (MRBIS) method is utilized as the system reliability solver for multi-constraint analysis in the inner loop. The accuracy and efficiency of the MRBIS method are demonstrated on three widely used test problems. In conclusion, MOSRBDO has been successfully applied for the design of a full parametric concept car body. The results show that the improved MOSRBDO method is more effective and efficient than the traditional MOSRBDO while achieving the same accuracy, and that the optimized body-in-white structure signifies a noticeable improvement from the baseline model.     

Inverse reliability-based design of shear buildings supported by springs with stochastic stiffnesses

A straightforward and efficient stiffness design method is developed for a shear building supported by a pair of swaying and rocking springs with stiffnesses given as statistically independent normal variates. The story stiffnesses are determined with the use of the closed form stiffness solution for specified fundamental frequency and translational eigenmode so that the probability of the seismic mean maximum interstory drifts not exceeding prescribed values would coincide with the specified value. The proposed method consists of two steps: (1) find the stiffnesses of swaying and rocking springs that can achieve the constrained nonexceedance probability by derived approximate formulas; (2) determine the story stiffnesses of the shear building so that the mean maximum interstory drifts would coincide with the prescribed values. The validity and good accuracy of the proposed method are demonstrated by use of Monte Carlo simulation.     

Developing safety performance functions incorporating reliability-based risk measures

Current geometric design guides provide deterministic standards where the safety margin of the design output is generally unknown and there is little knowledge of the safety implications of deviating from these standards. Several studies have advocated probabilistic geometric design where reliability analysis can be used to account for the uncertainty in the design parameters and to provide a risk measure of the implication of deviation from design standards. However, there is currently no link between measures of design reliability and the quantification of safety using collision frequency. The analysis presented in this paper attempts to bridge this gap by incorporating a reliability-based quantitative risk measure such as the probability of non-compliance (P_nc) in safety performance functions (SPFs). Establishing this link will allow admitting reliability-based design into traditional benefit–cost analysis and should lead to a wider application of the reliability technique in road design. The present application is concerned with the design of horizontal curves, where the limit state function is defined in terms of the available (supply) and stopping (demand) sight distances. A comprehensive collision and geometric design database of two-lane rural highways is used to investigate the effect of the probability of non-compliance on safety. The reliability analysis was carried out using the First Order Reliability Method (FORM). Two Negative Binomial (NB) SPFs were developed to compare models with and without the reliability-based risk measures. It was found that models incorporating the P_nc provided a better fit to the data set than the traditional (without risk) NB SPFs for total, injury and fatality (I + F) and property damage only (PDO) collisions.     

Reliability analysis and reliability-based design optimization of roadway horizontal curves using a first-order reliability method

This article presents reliability analysis and reliability-based optimization of roadway minimum radius design based on vehicle dynamics, mainly focusing on exit ramps and interchanges. The performance functions are formulated as failure modes of vehicle rollover and sideslip. To accurately describe the failure modes, analytical models for rollover and sideslip are derived considering nonlinear characteristics of vehicle behaviour using the commercial software TruckSim. The probability of an accident is evaluated using the first-order reliability method and numerical studies are conducted using a single-unit truck model. To propose a practical application for the study, the reliability analysis for the minimum radius recommended by American Association of State Highway and Transportation Officials is conducted. The results show that, even if there are deviations from assumed design conditions of the current design guideline, the proposed design method can guarantee given target margins of safety against rollover and sideslip. Based on the reliability analysis, reliability-based design optimization is carried out and the results indicate new recommendations for minimum radii satisfying given target reliability levels.     

An inverse reliability analysis method for reliability-based design optimization with random and dependent interval variables constrained within ellipsoids

In practical design problems, interval variables exist. Many existing methods can handle only independent interval variables. Some interval variables, however, are dependent. In this work, dependent interval variables constrained within a multi-ellipsoid convex set are considered and incorporated into reliability-based design optimization (RBDO). An efficient RBDO method is proposed by employing the sequential single-loop procedure, which separates the coupled reliability analysis procedure from the deterministic optimization procedure. In the reliability analysis procedure, a single-loop optimization for the inverse reliability analysis is performed, and an efficient inverse reliability analysis method for searching for the worst-case most probable point (WMPP) is developed. The search method contains two stages. The first stage deals the situation where the WMPP is on the boundary of the feasible region, while the second stage accommodates the situation where the WMPP is inside the feasible region by interpolation. Three examples are used for a demonstration.     

Simulated variance optimization for robust design

A method to aid robust design in the presence of design parameter uncertainty is described. For a given relationship between a performance measure (or output parameter) and the uncertain design parameters a probabilistic simulation is used to obtain the variance of the performance measure as a function of the nominal design parameter values. The optimum values of the latter are then obtained as those corresponding to a minimum of the computed variance, determined by means of a particular non-linear optimization algorithm in the presence of constraints. The latter are in the form of limits on the nominal values of the design parameters and a specified value for the performance measure at the nominal design point, i.e. the deterministic design target. Some problems inherent in this type of procedure are discussed and methods of solution are described. A specific example is studied and the results from the present method are compared with those previously obtained by use of another procedure. © 1998 John Wiley & Sons, Ltd.     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.     

Tolerancing and optimization for model-based robust engineering design

There are various methods for performing tolerancing and robust design within a computer-aided design (CAD) framework. Recent work on fitting statistical emulators to CAD systems can be used to facilitate fast optimization geared towards robustness against input variation. After discussing available methods for tolerancing within a common framework, a comprehensive strategy for robust design is developed which involves a combination of circuit simulation, emulation and global optimization.     

Crashworthiness design optimization using successive response surface approximations

 Finite Element (FE) method is among the most powerful tools for crash analysis and simulation. Crashworthiness design of structural members requires repetitive and iterative application of FE simulation. This paper presents a crashworthiness design optimization methodology based on efficient and effective integration of optimization methods, FE simulations, and approximation methods. Optimization methods, although effective in general in solving structural design problems, loose their power in crashworthiness design. Objective and constraint functions in crashworthiness optimization problems are often non-smooth and highly non-linear in terms of design variables and follow from a computationally costly (FE) simulation. In this paper, a sequential approximate optimization method is utilized to deal with both the high computational cost and the non-smooth character. Crashworthiness optimization problem is divided into a series of simpler sub-problems, which are generated using approximations of objective and constraint functions. Approximations are constructed by using statistical model building technique, Response Surface Methodology (RSM) and a Genetic algorithm. The approximate optimization method is applied to solve crashworthiness design problems. These include a cylinder, a simplified vehicle and New Jersey concrete barrier optimization. The results demonstrate that the method is efficient and effective in solving crashworthiness design optimization problems. Received: 30 January 2002 / Accepted: 12 July 2002 Sponsorship for this research by the Federal Highway Administration of US Department of Transportation is gratefully acknowledged. Dr. Nielen Stander at Livermore Software Technology Corporation is also gratefully acknowledged for providing subroutines to create D-optimal experimental designs and the simplified vehicle model.     

Extreme response predictions for jack-up units in second order stochastic waves by FORM

An efficient procedure for the derivation of mean outcrossing rates for non-linear wave-induced responses in stationary sea states is presented and applied to an analysis of the horizontal deck sway of a jack-up unit. The procedure is based on the theory of random vibrations and uses the first order reliability method (FORM) to estimate the most probable set of wave components in the ocean wave system that will lead to exceedance of a specific response level together with the associated mean outcrossing rate. The procedure bears some resemblance to the Constrained NewWave methodology, but is conceptually simpler and makes efficient use of the optimisation procedures implemented in standard FORM software codes.

Due to the fast calculation procedure the analysis can be carried out taking into account all relevant non-linear effects. Specifically, the present analysis accounts for second order stochastic waves, not previously included in the analysis of jack-up units in stochastic seaways.     

某家具汇展中心气流组织的优化设计

合理的室内气流组织形式对提高空调系统的舒适性、降低系统能耗有着重要的作用。以某家具汇展中心为研究对象,建立展厅室内空气流动和换热的三维紊流数学模型,采用CFD技术对侧送侧回、上送下回和上送上回3种气流组织方式条件下的温度场和流场进行数值模拟。模拟结果表明,上送下回气流组织形式不但可以节省系统初投资,还可以达到更加节能的要求,是一种更为合理的气流组织方案。     

非正态变量情况下基于杂交SAPSO-SFLA的多目标稳健协同优化

为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性及灵敏度的问题,融合鞍点估计与线抽样法的优点,结合二分法的特点与黄金分割法的求解效率,提出基于黄金分割二分法的鞍点线抽样法,即可沿重要线抽样方向利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点,将结构失效概率转化为一系列线性功能函数失效概率的平均值,求出相关变量的可靠性灵敏度,从而导出失效概率对变量均值与方差的可靠性灵敏度及结构轻量化的多目标优化问题,并阐明了多目标协同优化的思想。同时,针对可靠性灵敏度作为目标函数因误差导致多目标协同优化难以收敛的问题,提出了利用误差的思想与方法;为提高算法的收敛性,对粒子群优化(Particle Swarm Optimization,PSO)算法与混合蛙跳算法(Shuffled Frog-Leaping Algorithm,SFLA)进行改进以后,再将两者进行杂交,提出杂交自适应粒子群优化-混合蛙跳算法(Self-Adaptive PSO-SFLA,SAPSO-SFLA),并用来求解上述多目标优化问题。算例表明：1) 基于黄金分割二分法的鞍点线抽样法在求解复杂非线性功能函数的可靠性及灵敏度时精度高,速度快;2) 与粒子群优化和混合蛙跳算法相比,所提杂交SAPSO-SFLA不仅具有更快的收敛速度,其鲁棒性还能使盾构行星减速器箱体体积减小8.42%。