Reliability-based life-cycle cost seismic design optimization of coastal bridge piers with nonuniform corrosion using different materials

Reinforcement corrosion is the main cause of performance deterioration of reinforced concrete(RC)structures.Limited research has been performed to investigate the life-cycle cost(LCC)of coastal bridge piers with nonuniform corrosion using different materials.In this study,a reliability-based design optimization(RBDO)procedure is improved for the design of coastal bridge piers using six groups of commonly used materials,i.e.,normal performance concrete(NPC)with black steel(BS)rebar,high strength steel(HSS)rebar,epoxy coated(EC)rebar,and stainless steel(SS)rebar(named NPC-BS,NPC-HSS,NPC-EC,and NPC-SS,respectively),NPC with BS with silane soakage on the pier surface(named NPC-Silane),and high-performance concrete(HPC)with BS rebar(named HPC-BS).First,the RBDO procedure is improved for the design optimization of coastal bridge piers,and a bridge is selected to illustrate the procedure.Then,reliability analysis of the pier designed with each group of materials is carried out to obtain the time-dependent reliability in terms of the ultimate and serviceability performances.Next,the repair time of the pier is predicted based on the time-dependent reliability indices.Finally,the time-dependent LCCs for the pier are obtained for the selection of the optimal design.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Random Forest-Based Fatigue Reliability-Based Design Optimization for Aeroengine Structures

Fatigue reliability-based design optimization of aeroengine structures involves multiple repeated calculations of reliability degree and large-scale calls of implicit high-nonlinearity limit state function,leading to the traditional direct Monte Claro and surrogate methods prone to unacceptable computing efficiency and accuracy.In this case,by fusing the random subspace strategy and weight allocation technology into bagging ensemble theory,a random forest(RF)model is presented to enhance the computing efficiency of reliability degree;moreover,by embedding the RF model into multilevel optimization model,an efficient RF-assisted fatigue reliability-based design optimization framework is developed.Regarding the low-cycle fatigue reliability-based design optimization of aeroengine turbine disc as a case,the effectiveness of the presented framework is validated.The reliabilitybased design optimization results exhibit that the proposed framework holds high computing accuracy and computing efficiency.The current efforts shed a light on the theory/method development of reliability-based design optimization of complex engineering structures.

A Multiscale Reliability-Based Design Optimization Method for Carbon-Fiber-Reinforced Composite Drive Shafts

Carbon fiber composites,characterized by their high specific strength and low weight,are becoming increasingly crucial in automotive lightweighting.However,current research primarily emphasizes layer count and orientation,often neglecting the potential of microstructural design,constraints in the layup process,and performance reliability.This study,therefore,introduces a multiscale reliability-based design optimization method for carbon fiber-reinforced plastic(CFRP)drive shafts.Initially,parametric modeling of the microscale cell was performed,and its elastic performance parameters were predicted using two homogenization methods,examining the impact of fluctuations in microscale cell parameters on composite material performance.A finite element model of the CFRP drive shaft was then constructed,achieving parameter transfer between microscale and macroscale through Python programming.This enabled an investigation into the influence of both micro and macro design parameters on the CFRP drive shaft’s performance.The Multi-Objective Particle Swarm Optimization(MOPSO)algorithm was enhanced for particle generation and updating strategies,facilitating the resolution of multi-objective reliability optimization problems,including composite material layup process constraints.Case studies demonstrated that this approach leads to over 30%weight reduction in CFRP drive shafts compared to metallic counterparts while satisfying reliability requirements and offering insights for the lightweight design of other vehicle components.

Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design

Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

A self-regulating pairwise swapping algorithm to search reliability-based user equilibrium

The violation of monotonicity on reliability measures(RMs)usually makes the mathematical programming algorithms less efficient in solving the reliability-based user equilibrium(RUE)problem.The swapping algorithms provide a simple and convenient alternative to search traffic equilibrium since they are derivative-free and require weaker monotonicity.However,the existing swapping algorithms are usually based on linear swapping processes which cannot naturally avoid overswapping,and the step-size parameter update methods do not take the swapping feature into account.In this paper,we suggest a self-regulating pairwise swapping algorithm(SRPSA)to search RUE.SRPSA comprises an RM-based pairwise swapping process(RMPSP),a parameter self-diminishing operator and a termination criterion.SRPSA does not need to check the feasibility of either solutions or step-size parameter.It is suggested from the numerical analyses that SRPSA is effective and can swap to the quasi-RUE very fast.Therefore,SRPSA offers a good approach to generate initial points for those superior local search algorithms.

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H-B parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H-B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H-B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.

Reliability-Based Shape Optimization of Tenon/Mortise in Aero-engines with Contact

Based on the theory of reliability-based structural shape optimization, exact expressions of the sensibility using the stochastic finite element method for contact problems were derived in detail, and the basic steps of structural optimization were given. A coattail-type tenon/mortise of an aero-engine was optimized. In this model, the maximum equivalent stress of the nodes on the boundary of the tenon was the objective function; the width of tooth’s neck and the side surface’s slope angle of a tenon were design variables, with constraints of tension stress, extrusion stress and reliability index. The result showed that the distributions of the contact pressure between tenon and mortise, the equivalence stress and reliability index were more reasonable. It validates the correctness of the optimization model and the reliability-based structural shape optimization, and provides valuable references for structural design of the tenon/mortise.

NEW APPROACH FOR RELIABILITY-BASED DESIGN OPTIMIZATION:MINIMUM ERROR POINT

Conventional reliability-based design optimization （RBDO） requires to use the most probable point （MPP） method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point （MEP） method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor＇s expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.

Reliability-based design optimization for flexible mechanism with particle swarm optimization and advanced extremum response surface method

To improve the computational efficiency of the reliability-based design optimization(RBDO) of flexible mechanism, particle swarm optimization-advanced extremum response surface method(PSO-AERSM) was proposed by integrating particle swarm optimization(PSO) algorithm and advanced extremum response surface method(AERSM). Firstly, the AERSM was developed and its mathematical model was established based on artificial neural network, and the PSO algorithm was investigated. And then the RBDO model of flexible mechanism was presented based on AERSM and PSO. Finally, regarding cross-sectional area as design variable, the reliability optimization of flexible mechanism was implemented subject to reliability degree and uncertainties based on the proposed approach. The optimization results show that the cross-section sizes obviously reduce by 22.96 mm^2 while keeping reliability degree. Through the comparison of methods, it is demonstrated that the AERSM holds high computational efficiency while keeping computational precision for the RBDO of flexible mechanism, and PSO algorithm minimizes the response of the objective function. The efforts of this work provide a useful sight for the reliability optimization of flexible mechanism, and enrich and develop the reliability theory as well.

Reliability-Based Topology Optimization of Fail-Safe Structures Using Moving Morphable Bars

This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.

Reliability-Based Optimum Design of a Simple Offshore Platform Based on Genetic Algorithms

In this paper, the problem of reliability-based optimal design of simple offshore platform is studied, and a nonlinear fatigue damage model based on damage mechanics and genetic algorithms are used in the fatigue reliability optimum design of the structure under stochastic wave load. The fatigue damage model and the yield failure reliability analyzing model are used in the paper. The reliability of the models and the effectiveness of genetic algorithm are shown by the results of optimum design.

Efficient Reliability-Based Optimization Scheme for Piezoelectric Composite Beams with Delamination under Axial Compression

An efficient computational framework for reliability analysis and reliability-based design optimization of piezoelectric composite beam with delamination is presented.In the proposed approach,the transverse shear deformation,delamination and piezoelectricity of the beam are taken into account.By introducing the Heaviside step function into the displacement components and using the Rayleigh-Ritz method,and the buckling governing equations for the piezoelectric composite beams is obtained.The reliability of the beams is obtained by integrating the support vector machine method and first order reliability method,further the reliability-based optimization is executed through employing genetic algorithm.The effects of ply style,delamination length and voltage are discussed in details.Numerical results indicate that the comprehensive computational scheme provides a unified numerical framework to analysis the nondeterministic buckling and reliability efficiently.

Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components

The reliability-based selective maintenance(RSM)decision problem of systems with components that have multiple dependent performance characteristics(PCs)reflecting degradation states is addressed in this paper.A vine-Copulabased reliability evaluation method is proposed to estimate the reliability of system components with multiple PCs.Specifically,the marginal degradation reliability of each PC is built by using the Wiener stochastic process based on the PC’s degradation mechanism.The joint degradation reliability of the component with multiple PCs is established by connecting the marginal reliability of PCs using D-vine.In addition,two RSM decision models are developed to ensure the system accomplishes the next mission.The genetic algorithm(GA)is used to solve the constraint optimization problem of the models.A numerical example illustrates the application of the proposed RSM method.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Reliability-Based Optimization:Small Sample Optimization Strategy

The aim of the paper is to present a newly developed approach for reliability-based design optimization. It is based on double loop framework where the outer loop of algorithm covers the optimization part of process of reliability-based optimization and reliability constrains are calculated in inner loop. Innovation of suggested approach is in application of newly developed optimization strategy based on multilevel simulation using an advanced Latin Hypercube Sampling technique. This method is called Aimed multilevel sampling and it is designated for optimization of problems where only limited number of simulations is possible to perform due to enormous com- putational demands.

MCS-based quantile value approach for reliability-based design of tunnel face support pressure

This paper develops a new approach for reliability-based design(RBD)of tunnel face support pressure from a quantile value perspective.A surrogate model is constructed to calculate the collapse pressures of the random samples generated by a single run of Monte Carlo simulation(MCS).The cumulative distribution function(CDF)of the collapse pressure is then obtained and the support pressure aiming at a target failure probability is chosen as the upper quantile value of the collapse pressures.The proposed approach does not require repetitive reliability analyses compared to the existing methods.Moreover,a direct relationship between the target failure probability and the required support pressure is established.An illustrative example is used to demonstrate the implementation procedure.The accuracy of the reliability-based support pressures is verified by direct MCS incorporating with three-dimensional numerical simulations.Finally,the influencing factors,including the sample size of MCS,the correlation coefficient between random variables,the choice of experimental points,and the surrogate model,are investigated.This method can play a complementary role to available approaches due to its advantages of simplicity and efficiency.

Reliability-based robust design optimization of vehicle components, Part Ⅱ： Case studies

The reliability-based optimization, the relia- bility-based sensitivity analysis and robust design method are employed to propose an effective approach for reliability-based robust design optimization of vehicle components in Part I. Applications of the method are further discussed for reliability-based robust optimization of vehicle components in this paper. Examples of axles, torsion bar, coil and composite springs are illustrated for numerical investigations. Results have shown the proposed method is an efficient method for reliability-based robust design optimization of vehicle components.

Reliability-based components, Part robust design optimization of vehicle I： Theory

The reliability-based design optimization, the reliability sensitivity analysis and robust design method are employed to present a practical and effective approach for reliability-based robust design optimization of vehicle components. A procedure for reliability-based robust design optimization of vehicle components is proposed. Application of the method is illustrated by reliability-based robust design optimization of axle and spring. Numerical results have shown that the proposed method can be trusted to perform reliability-based robust design optimization of vehicle components.