Reliability-based Design Optimization Method Research Articles

A novel non-probabilistic reliability-based design optimization method using bilevel accelerated microbial genetic algorithm

A novel non-probabilistic reliability-based design optimization method using bilevel accelerated microbial genetic algorithm

A reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model for nuclear fuel assembly bottom nozzle

The design of intricate systems such as the nuclear fuel assembly necessitates elevated levels of multi-disciplinary performance and reliability. In current reliability-based multidisciplinary design optimization methods, the decoupling strategy between optimization and reliability assessment involves sequential optimization and reliability assessment, with reliability serving as a constraint for optimization. This approach often suffers failure in locating the global optimal solution. In light of this issue, a reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model is hereby proposed, achieving parallel separation and global efficient optimization of deterministic disciplinary performances and reliability, while performing efficient and accurate calculation on the multi-disciplinary reliability numerical solution. This method has been implemented for the multi-disciplinary uncertain optimization of the nuclear fuel assembly bottom nozzle. In comparison to conventional optimization methods, this approach demonstrates enhanced global optimization effectiveness.

A two-loop RBDO approach for steel frame structures using EVPS, GWO, and Monte Carlo simulation

This paper evaluates Enhanced Vibrating Particle System (EVPS) and Grey Wolf Optimizer (GWO) algorithms for Reliability-based Design Optimization (RBDO) of steel frames. The two-loop RBDO method minimizes frame weight while satisfying strength, drift, and reliability constraints, considering uncertainties in material properties and loads. Both EVPS and GWO effectively reduce structure weight and ensure required reliability levels, demonstrating their applicability in sustainable steel frame design.

Life-cycle integrity design method considering load robustness of offshore oil and gas equipment: SCSSV as a case study

Components that are vulnerable to the external environment and harsh working conditions easily fail during their life cycle under variable loads of offshore oil and gas equipment. The reliability of the system in the life cycle is reduced, various risks are increased, and substantial maintenance costs are generated. However, the current reliability-based design optimization method has difficulty meeting the situation that the life cycle is taken as the time dimension of design considering reliability, risk, and maintenance. To solve the problem, a life cycle integrity design optimization method considering robustness is proposed. A simplified integrity model is established through random load sampling and global sensitivity analysis. A multiobjective particle swam hierarchical optimization algorithm is proposed, in which hierarchical optimization order is determined by the priority of objectives, and the optimization design with structural integrity as the optimization objective is completed. The method is applied in the design of pressure pipeline of all-electric surface-controlled subsurface safety valve system.

A sequential sampling-based Bayesian numerical method for reliability-based design optimization

For efficiently solving the Reliability-Based Design Optimization (RBDO) problem with multi-modal, highly nonlinear and expensive-to-evaluate limit state functions (LSFs), a sequential sampling-based Bayesian active learning method is developed in this work. The penalty function method is embedded to transform the constrained optimization problem into a non-constrained one to reduce the model complexity. The proposed method for solving RBDO problems starts by training a Gaussian process (GP) model, in the augmented space of random and design variables. It is then based on an efficient sampling scheme for simulating the GP model, the adaptive Bayesian optimization (BO) and Bayesian reliability analysis (BRA) procedures are combined in a collaborative way for sequentially producing the joint training points. BO driven by expected improvement (EI) function is used for inferring the global optimum in the design space with global convergence, and the BRA equipped with U function is implemented for inferring the failure probabilities at the identified design points with the desired accuracy. The superiority of the proposed method is demonstrated with two numerical and two real-world engineering examples.

A new Bayesian model averaging ensemble modeling method for surrogate-assisted reliability-based design optimization of FBTAM

A new Bayesian model averaging ensemble modeling method for surrogate-assisted reliability-based design optimization of FBTAM

An effective active learning strategy for reliability-based design optimization under multiple simulation models

This paper proposes an effective active learning strategy for reliability-based design optimization (RBDO) problems in which the constraint functions are acquired from multiple simulation models. To achieve this goal, a new active learning function (ALF) is derived by estimating the increased reliability of active constraint functions after adding one point to the train points of constraint functions in each simulation model. The proposed ALF distinguishes possibly active constraint functions that seem active near the current optimum and considers how the constraint functions are active. In the proposed RBDO method, a Kriging model is iteratively updated by adding the best point to the train points of constraint functions included in the crucial simulation model until the optimum converges and the Kriging model is sufficiently accurate. The best point and the crucial simulation model are obtained by comparing the proposed ALF. The ALF is further modified to apply to problems where the cost of each simulation model is different. To verify the effectiveness of the proposed method, two numerical and one engineering examples are analyzed. The results show that the proposed method efficiently and accurately obtains the RBDO optimum involving multiple simulation models, regardless of simulation cost.

A Coupled Simulated Annealing and Particle Swarm Optimization Reliability-Based Design Optimization Strategy under Hybrid Uncertainties

As engineering systems become increasingly complex, reliability-based design optimization (RBDO) has been extensively studied in recent years and has made great progress. In order to achieve better optimization results, the mathematical model used needs to consider a large number of uncertain factors. Especially when considering mixed uncertainty factors, the contradiction between the large computational cost and the efficiency of the optimization algorithm becomes increasingly fierce. How to quickly find the optimal most probable point (MPP) will be an important research direction of RBDO. To solve this problem, this paper constructs a new RBDO method framework by combining an improved particle swarm algorithm (PSO) with excellent global optimization capabilities and a decoupling strategy using a simulated annealing algorithm (SA). This study improves the efficiency of the RBDO solution by quickly solving MPP points and decoupling optimization strategies. At the same time, the accuracy of RBDO results is ensured by enhancing global optimization capabilities. Finally, this article illustrates the superiority and feasibility of this method through three calculation examples.

Reliability-based design optimization of the spiral water jacket for motorized spindle

Spiral water jackets are essential refrigeration units in motorized spindles. The design of spiral water jackets directly affects the machining accuracy and reliability of motorized spindles. In this regard, a reliability-based design optimization (RBDO) method is presented to obtain the optimal configuration of the spiral water jacket. The proposed RBDO algorithm aims to minimize the volume of the spiral water jacket and power loss of the cooling equipment while ensuring machining reliability. The geometric correlation and machining reliability are selected as constraints. The Kriging surrogate model is established to approximate the time-consuming finite element model for improving computational efficiency. An efficient metaheuristic algorithm is introduced to perform optimal exploration for the proposed RBDO problem. The risk speed of the motorized spindle is investigated by the experiment and finite element analysis. Subsequently, the effects of various cooling configurations on thermal error are investigated thoroughly. Eventually, the proposed RBDO is conducted on a motorized spindle. Through probabilistic evaluation, machining reliability is guaranteed by the proposed RBDO compared to deterministic design optimization. This paper provides a new design paradigm for cooling configurations in motorized spindles from the perspective of machining reliability.

A novel probabilistic feasible region method for reliability-based design optimization with varying standard deviation

A novel probabilistic feasible region method for reliability-based design optimization with varying standard deviation

An Overview of Adaptive-Surrogate-Model-Assisted Methods for Reliability-Based Design Optimization

Reliability-based design optimization (RBDO) is one of the most crucial techniques in complex and reliability-critical engineering systems. This has been a research hotspot over the past few decades. RBDO allows us to take into consideration the uncertainties from various sources, during the early design stage. It provides a design that satisfies various constraints as well as the reliability of the designed system performing the expected functions. Such capabilities can serve as countermeasures against the foreseeable uncertainties in the manufacturing or application process. Following a short preliminary overview of RBDO as well as the canonical strategies, this article sets out to review how surrogate models have been explored to streamline RBDO. This is done through a systematic study, outlining their respective advantages as well as disadvantages, and discussing the problems that need to be solved.

Reliability-based design optimization using adaptive Kriging-A single-loop strategy and a double-loop one

With the development of the surrogate-assisted Reliability-Based Design Optimization (RBDO) methods in recent decade, efficiency has been continuously improved by various state-of-the-art learning schemes. However, ensuring sufficient accuracy and feasibility at the optimum is still challenging, especially for real scenarios with complex probabilistic constraints and high fidelity. In order to achieve a good balance between efficiency and accuracy and feasibility at the optimum, both a single-loop and a double-loop adaptive Kriging-based RBDO methods are proposed. By directly approximating the probabilistic constraints using Kriging models in the single-loop method, the original RBDO problem is converted into a trivial deterministic optimization, which can be solved by any type of optimization method. The real values of failure probabilities are estimated by Generalized Subset Simulation (GSS) at the initial construction or during each update of the Kriging models. To further raise efficiency in the double-loop adaptive Kriging-based method, GSS is substituted by an inner-loop Kriging-based failure probability estimation, which includes each local enrichment at the limit states corresponding to the active probabilistic constraints based on an initial global enrichment within the augmented reliability space. Once a certain Kriging model meets the requirement during the refining of all, only the others are kept updating until the accuracy of all are accepted. Four examples are used to demonstrate the performance of the proposed two methods.

A two-stage Kriging estimation variance reduction method for efficient time-variant reliability-based design optimization

Adaptive Kriging modelling technique is an effective tool to reduce the computational burden for time-variant reliability-based design optimization (TRBDO) significantly. However, the existing methods may allocate sampling resources to unimportant regions and do not consider the correlations between time trajectories, both of which will waste some computationally expensive samples. In this paper, we propose a two-stage Kriging estimation variance reduction method (KEVAR2) to address these challenges. First, the expression of Kriging estimation variance is derived, which can quantify the contribution of correlations between time trajectories to the Kriging prediction uncertainty. Second, the global and local adaptive Kriging approaches are proposed based on the Kriging estimation variance reduction strategy. Meanwhile, two metrics, i.e., the expectation of wrong classification rate and the error of safe rate are proposed to quantify global and local errors of Kriging models respectively. After that, we propose a two-stage framework that integrates the global and local adaptive Kriging approaches together, where the first stage performs global adaptive sampling to quickly reduce the Kriging prediction error, and then the second stage performs local adaptive sampling in the region near the current optimal solution to achieve high efficiency. Finally, five case studies demonstrate the effectiveness of the proposed KEVAR2.

Reliability-based design method for marine structures combining topology, shape, and size optimization

The uncertainty and extremity of ocean conditions make the design of marine structures a challenging process. Reliability-based optimization is a powerful approach to enhance material utilization and ensure system survivability. In this paper, a novel reliability-based design optimization (RBDO) method that combines topology, shape, and size optimization is proposed to achieve the design of marine structures. Within the framework of decoupled sequence optimization and reliability assessment, the developed method employs an innovative multi-technology combined optimization Scheme and a new reliability assessment algorithm. The combined optimization Scheme is established by simultaneously incorporating topology, shape, and size optimization technologies to further improve the lightweighting effect. The advanced arc interpolation algorithm is developed, which dynamically selects the advanced mean value method or arc interpolation method based on the trend judgment criterion to accelerate the calculation for the most probable point in reliability assessments. The RBDO examples of the wind turbine jacket and platform stiffened plate are utilized to verify the proposed method's applicability and validity, and the results are compared with those of other approaches. The findings prove that this RBDO method can effectively address reliability-based design problems of marine structures and is superior in providing lightweighting structures compared with others.

Enhancing ball grid array (BGA) component design and reliability using a novel reliability-based design optimization (RBDO) methodology

In industry and research areas, the importance of reliable and optimally designed BGA components has remarkably grown. To tackle this challenge, we elaborated an innovative approach that optimizes of the BGA’s structure. By adopting the RBDO method, we assess the geometric design variables of the BGA component and determine the optimal variables that promote the structure’s efficiency level. Our approach considers technical and economic feasibility, ensuring an optimal design of the BGA solder joints. This work rests upon coupling Ansys and MATLAB software. The current paper reports our investigation’s results, highlighting our approach’s benefits and potential for practical applications.

Efficient adaptive reliability-based design optimization for geotechnical structures with multiple design parameters

Reliability-based design optimization (RBDO) aims to improve the reliability of geotechnical systems while minimizing the cost of design. However, the conventional RBDO method suffers from a large computational cost and intractable convergence problem due to the double-loop structure involving numerical optimization and repeated reliability analysis. To address this issue, this paper proposes an efficient adaptive RBDO framework for geotechnical structure with multiple design parameters. The proposed framework mainly includes two parts: a novel expanded inverse first-order reliability method (E-IFORM) for dealing with the inverse reliability problem with multiple design parameters, and an adaptive surrogate model to decouple the double-loop structure and improve the efficiency. The proposed methodology is applied to four geotechnical systems (i.e., a soil slope, an excavation pit, a strip footing and a retaining wall), and the results demonstrate the effectiveness and efficiency of the proposed framework.

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

Multi-level Reliability-Based Design Optimization (RBDO) study for electronic cooling: Application of heat sink based on multiple phase change materials enhanced with carbon nanoparticles

Phase change materials represent efficient performances in the thermal management field. However, the low thermal conductivity poses a serious restraint for electronic cooling applications. Recently, the use of multiple phase change materials and the dispersion of nanoparticles are the most recommended techniques to improve the performance of the heat sink. In this study, a developed heat sink filled with multiple phase change materials (PCMs) enhanced with carbon nanoparticles was proposed. First, a parametric study was carried out to determine the optimal pair of phase change materials and nanoparticles. Then, deterministic design optimization and various reliability-based design optimization methods are performed. The optimization and reliability problems are solved by coupling the MATLAB optimization toolbox and the ANSYS Finite Element Model. The optimization-reliability results prove the efficiency of the Robust Hybrid Method in proposing a reliable and optimal heat sink design filled with multiple nano-enhanced phase change materials. The temperature is reduced by 25 % (16,5 °C) and the discharge time is reduced by 8,69 % (14 min) compared to the baseline heat sink.

Belief reliability-based design optimization method with quantile index under epistemic uncertainty

Product reliability design optimization is affected by epistemic uncertainty greatly, which leaves significant risks in product use. In this paper, a new belief reliability-based design optimization (BRBDO) method under epistemic uncertainty is established to handle this problem. First, the belief reliability theory is introduced into the design optimization problem, and a quantile index is proposed to quantify belief reliability level based on uncertainty theory, through which a rapid analysis method called first order belief reliability analysis (FOBRA) method is developed. Then, according to the different trade-off strategies, two types of design optimization models are established, and corresponding FOBRA-based computation methods are also demonstrated. Finally, several case applications are studied to verify the effectiveness of the analysis and design optimization methods proposed in this paper. The results indicate that the BRODO method with the quantile index can save a lot of computational time with acceptable accuracy and can rationally cope with epistemic uncertainty.

An equivalent RBDO method under the hybrid of fuzzy and interval variables in the worst case

AbstractIn the reliability‐based design optimization (RBDO) problems of structures or systems, only a single type of variable involving is rare, and most of time are hybrid variables. Random variables are often used to describe uncertainty, and these random variables can usually be described by certain probability distributions. However, in practice, the probability distributions of some random variables are difficult or even impossible to be obtained, or the obtained probability distributions may be inaccurate, and can only be roughly described by fuzzy values or intervals. Therefore, this paper is committed to solving RBDO problems under the hybrid of fuzzy variables and interval variables. Firstly, the RBDO model of the structure under the hybrid variables is established. Secondly, the fuzzy variables are transformed to random variables according to entropy invariance. Finally, RBDO is carried out based on sequential single‐loop method in the worst case. A numerical example is presented to illustrate the feasibility of the proposed method.