Reliability-based Design Optimization Method Research Articles

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

A reliability-based design optimization strategy using quantile surrogates by improved PC-kriging

In recent years, the surrogate-assisted reliability-based design optimization (RBDO) methods have been continuously developed, and numerous advanced optimization strategies have boosted efficiency and accuracy. However, ensuring sufficient accuracy and feasibility at the optimal is still a challenge. In order to achieve a well-balanced between efficiency, accuracy, and optimal feasibility, in this work, a RBDO strategy using quantile surrogates by improved PC-Kriging model is proposed. The novelty of the proposed method lies in the following main aspects: Firstly, an improved learning function has been developed to significantly enhance the convergence efficiency during the construction of the PC-Kriging model. Secondly, in the RBDO analysis process, a novel "MP+EI" combination point addition strategy is adopted to enhance the approximation of the surrogate model to the optimum of the objective function. It can further improve optimization efficiency and accuracy. On the basis of the rough probability constrained surrogate model established by the global enrichment strategy, a local refinement strategy is introduced to guarantee the accuracy of the quantile evaluation of the probability constrained surrogate model for each iteration solution during the optimization process. Finally, the proposed method is validated by three typical RBDO test examples and one engineering application example.

An approximate decoupled reliability-based design optimization method for efficient design exploration of linear structures under random loads

Reliability-based design optimization (RBDO) provides a promising approach for achieving effective structural designs while explicitly accounting for the effects of uncertainty. However, the computational demands associated with RBDO, often due to its nested loop nature, pose significant challenges, thereby impeding the application of RBDO for decision-making in real-world structural design. To alleviate this issue, an approximate decoupled approach is introduced for a class of RBDO problems involving linear truss structures subjected to random excitations, with the failure event defined by compliance. This contribution aims to provide an approximate but efficient way for design exploration to facilitate decision-making during the initial design phase. Specifically, the proposed approach converts the original RBDO problem into a deterministic optimization problem through a modest number of reliability analyses by the probability density evolution method (PDEM). Once the deterministic optimization problem is obtained, the solution of the whole RBDO problem can be obtained by solving this equivalent problem without further reliability analysis, resulting in notable enhancement in terms of computational efficiency. In this way, this contribution expands the frontier of application of the operator norm theory within the RBDO framework. Numerical examples are conducted to illustrate the effectiveness and capabilities of the proposed approach.

Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear

Ball bearings operating at low speeds and under heavy loads are susceptible to wear failure, leading to significant economic losses. The existing reliability-based robust design optimization method of the fourth-moment method has high accuracy and does not need to determine the random distribution of the input variables, but it is not possible to apply it to ball bearing wear due to the complexity of the bearing wear state function that cannot be characterized as an explicit form. To address this issue, this paper proposes a novel design method for ball bearing wear. Firstly, a surrogate model is constructed using the Kriging model method to establish a relationship between the bearing design parameters and the mechanical response. Subsequently, a wear reliability model is developed on the basis of the fourth-moment method, and reliability sensitivity analysis is conducted. Finally, the ball bearing wear reliability-based robust design optimization is accomplished through the use of a genetic algorithm. The results of the case calculations demonstrate that the proposed method effectively calculates the ball bearing wear reliability and analyzes the impact of design parameter randomness on reliability. Furthermore, optimizing the design parameters reduces the sensitivity of wear reliability to parameter randomness.

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.