Reliability-based Design Optimization Method Research Articles

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.

A response band-based method for time-dependent reliability-based robust design optimization

In this paper, a response band-based method for time-dependent reliability-based robust design optimization is proposed. The proposed method provides a novel alternative framework, consist of a two-step transformation stage and a solving stage, to solve the time-dependent reliability-based robust design optimization problem. The original time-dependent reliability-based robust design optimization problem is transformed into an equivalent deterministic robust design optimization problem in the transformation stage, and the equivalent problem is settled in the solving stage. In the transformation stage, the dynamic modal decomposition technique and the kriging technique are combined to overcome the problem that there is no standard for both time division and observation sampling in the commonly used transformation methods. In the solving stage, an approach for constructing the response band of the objective function is presented, which significantly reduces the computational consumption of the variation evaluation of the objective function. Five cases are employed to verify the effectiveness of the proposed method.

An efficient reliability-based design of TMD & MTMD in nonlinear structures under uncertainty

One of the methods to improve the performance of tuned mass dampers is to combine the primary and auxiliary mass dampers in series, known as multiple tuned mass dampers. The mechanical properties of these dampers influence the seismic behavior of structures equipped with tuned mass dampers. Generally, the determination of TMD parameters to achieve optimal seismic behavior is defined in the framework of optimization problems. In structures with nonlinear behavior, there are several sources of uncertainty in the structure, which emphasizes the importance of using the reliability-based design optimization method. For this purpose, two strategies based on the meta-heuristic optimization and reliability-based design optimization method are used for the optimal design of TMD and MTMD. In the RBDO method, the optimal design is performed based on the objective function established on the target reliability of the structure. Furthermore, a hybrid metaheuristic method was developed based on BOA and CSS algorithms to increase search-ability. The results show the efficiency of the HBC algorithm in solving engineering design problems. Also, reliability analysis and sensitivity analysis are conducted on passive controlled structures to display the effect of uncertainty in mechanical parameters of the system and their importance in the reliability of the system. Also, the optimum design of TMD and MTMD was evaluated based on the target reliability using the efficient RBDO method. The results show that the RBDO strategy has an excellent ability to design TMD and MTMD with a good performance in reducing seismic responses.

An efficient time-variant reliability-based design optimization method based on probabilistic feasible region

An efficient time-variant reliability-based design optimization method based on probabilistic feasible region

Sequential most probable point update combining Gaussian process and comprehensive learning PSO for structural reliability-based design optimization

This paper proposes an efficient reliability-based design optimization (RBDO) method that advantageously decouples comprehensive learning particle swarm optimization (CLPSO) algorithm with Gaussian process regression (GPR) model, termed as GPR-CLPSO. The method iteratively performs the CLPSO with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) iteratively updated by the active learning reliability evaluation process. The GPR model approximates, from the design data given by CLPSO, the spectrum of LSFs under random parameters, and hence enables a significant computational reduction of Monte-Carlo simulations (MCSs) for failure probability approximation. The expected feasibility function is maximized using the CLPSO code to systematically refine the GPR model by adaptively adding new (intelligent) learning points in the region with high-reliability sensitivity leading to the more accurate prediction of failure probability. A novel inverse MCS constraint boundary method is developed to redefine the MPP assigned for the CLPSO algorithm in determining the new optimal design. The method efficiently leverages the decoupling approach, whilst significantly alleviating computing efforts, to quickly and accurately capture the optimal RBDO design. The resulting failure probability well satisfies the allowable limit. Four RBDO examples are provided to illustrate applications and robustness of the proposed decoupling GPR-CLPSO approach.

Unified reliability-based design optimization with probabilistic, uncertain-but-bounded and fuzzy variables

Reliability-based design optimization (RBDO) is critical in improving the design objective and guaranteeing the safety level of mechanical and engineering structures. However, a large number of multi-source uncertainties exist in the real-world, and their applications pose significant challenges owing to the lack of unity and generality of the RBDO theory and high performance computational methods. This study proposes a unified reliability-based design optimization (URBDO) method to deal with multi-source uncertainties, in which probabilistic, uncertain-but-bounded, and fuzzy parameters are simultaneously considered. First, a novel URBDO model is proposed by combining the probabilistic, non-probabilistic, and fuzzy theories, and it consists of nested quadruple optimization loops. Second, the single-loop URBDO method is further developed based on the Lagrangian function to ease the unaffordable computational burden, where the probabilistic analysis, non-probabilistic analysis, fuzzy analysis, and deterministic optimization are simultaneously implemented. Third, the directional properties of non-probabilistic and fuzzy computations are disclosed, and the directional chaos single-loop method (DCSLM) and conjugate gradient single-loop method (CGSLM) are constructed based on the chaos control theory and conjugate gradient method. Finally, three numerical examples and three practical engineering examples are tested to validate the effectiveness of the proposed URBDO model and the high performances of the DCSLM and CGSLM.

Anisotropy-Based Adaptive Polynomial Chaos Method for Hybrid Uncertainty Quantification and Reliability-Based Design Optimization of Structural-Acoustic System

The evaluation of objective functions and component reliability in the optimisation of structural-acoustic systems with random and interval variables is computationally expensive, especially when strong nonlinearity exhibits between the response and input variables. To reduce the computational cost and improve the computational efficiency, a novel anisotropy-based adaptive polynomial chaos (ABAPC) expansion method was developed in this study. In ABAPC, the anisotropy-based polynomial chaos expansion, namely the retained order of polynomial chaos expansion (PCE) differs from each variable, is used to construct the initial surrogate model instead of first-order polynomial chaos expansion in conventional methods. Then, an anisotropy-based adaptive basis growth strategy was developed to reduce the estimation of the coefficients of the polynomial chaos expansion method and increase its computational efficiency. Finally, to solve problems with probabilistic and interval parameters, an adaptive basis truncation strategy was introduced and implemented. Using the ABAPC method, the computational cost of reliability-based design optimisation for structural-acoustic systems can be efficiently reduced. The effectiveness of the proposed method were demonstrated by solving two numerical examples and optimisation problems of a structural-acoustic system.

A Transformation-Based Improved Kriging Method for the Black Box Problem in Reliability-Based Design Optimization

In order to overcome the drawbacks of expensive function evaluation in the practical reliability-based design optimization (RBDO) problem, researchers have proposed the black box-based RBDO method. The algorithm flow of the commonly employed RBDO method for the black box problem consists of the outer construction loop of the surrogate model of the constraint function and the inner surrogate model-based solving loop. To improve the solving ability of the black box RBDO problem, this paper proposes a transformation-based improved kriging method to increase the effectiveness of the two loops identified above. For the outer loop, a sample distribution-based learning function is suggested to improve the construction efficiency of the surrogate model of the constraint function. For the inner loop, a paired incremental sample-based limit reliability boundary construction approach is suggested to transform the RBDO problem into an equivalent deterministic design optimization problem that can be efficiently solved by classical optimization algorithms. The test results of five cases demonstrate that the proposed method can accurately construct the surrogate model of the constraint function and efficiently solve the black box RBDO problem.

Kriging-Based Performance Measure Function Approximation Method for Hybrid Reliability-Based Design Optimization

Hybrid reliability-based design optimization (HRBDO) can provide an effective way to obtain the optimum design in the presence of both random and interval variables. HRBDO is typically described as a nested optimization model. It is computationally expensive when directly solving the HRBDO problem by the nested optimization method. To address this issue, this paper develops an efficient decoupled HRBDO method that aims at performance measure function approximation by the adaptive Kriging model (KPMFA). The proposed KPMFA method includes three main blocks, namely hybrid inverse reliability analysis, performance measure function approximation, and equivalent deterministic optimization. In KPMFA, the adaptation of the adaptive chaos control (ACC) algorithm for inverse reliability analysis that accommodates interval variables is developed. Moreover, an adaptive strategy with two-stage of enrichment for the Kriging model is developed to approximate performance measure functions on the region of interest. Then, the optimization can be proceeded using the Kriging model of performance measure functions. Finally, five illustrative HRBDO problems are investigated to demonstrate the accuracy and efficiency of the proposed KPMFA 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.

A single-loop reliability-based design optimization using adaptive differential evolution

Reliability-based design optimization (RBDO) is an efficient tool for generating reliable and optimal solution under uncertainty of design variables. The major challenges in solving RBDO problems are generating optimal or near optimal reliable solution and higher computational cost. In this paper, a single-loop RBDO formulation is developed for addressing these challenges that uses shifting vector approach for achieving feasibility for violated constraints or performance functions. The formulation also incorporates target and trial vectors of differential evolution (DE) for guiding the algorithm. DE is also made adaptive by designing a heuristic parameter that controls two mutation operators for both exploration and exploitation of search space. The proposed RBDO method is tested on three mathematical and four engineering examples. The reliability of obtained solutions from RBDO methods are verified using Monte Carlo simulations with sample size of one million. The results of the proposed method are compared with various RBDO methods from the literature and a double-loop based DE method. It is found that the proposed method generates the best reliable solution for all examples.

A novel reliability index approach and applied it to cushioning packaging design

This paper is aimed at proposing a new approach to Reliability-based Design Optimization (RBDO) and applying it to cushioning packaging design with a highly nonlinear system. The problem is formulated as an RBDO problem, which is included a minimizing cost function and probabilistic constraints. Here, the thickness of the cushion material is dealt with uncertainty and uncontrolled parameters. The traditional reliability index approach (RIA) has evolved as a powerful tool to solve the RBDO problem; however, due to its convergence problem, the modified reliability index approach (MRIA) is proposed. Although the MRIA method solves the problems of the traditional RIA, it inherits the low efficiency of searching for the most probability point (MPP). Thus, we developed a novel RIA based on MRIA to improve the efficiency and robustness during the RBDO process. The innovation active set strategy is developed in reliability assessment, which is a strict inequality to determine whether the current constraint is active or inactive. An application example is presented, and the results are compared with MRIA to assess cost-effectiveness and efficiency. Results indicate the proposed method is feasible to solve the uncertainty problem of packaging materials in the processing process and is also an efficient RBDO method.

A New Framework for Efficient Sequential Sampling-Based RBDO Using Space Mapping

Abstract In engineering applications of sampling-based reliability-based design optimization (RBDO), the Monte Carlo simulation (MCS) using a surrogate model of the performance function is mainly used for the probability of failure calculation and sensitivity analysis. However, if an inaccurate surrogate model is used, the calculation result using MCS will also be inaccurate, so it is essential to improve the accuracy of the surrogate model using sequential sampling. Hence, various sampling-based RBDO methods and sequential sampling methods have been proposed and used in various fields, and space mapping may also be a new framework for sequential sampling. In this paper, sampling-based RBDO with the Gaussian process regression (GPR) and space mapping is proposed. Space mapping generally attempts to utilize high-fidelity samples to update the low-fidelity model in multi-fidelity model conditions. However, in the proposed method, it is used for sequential sampling to improve the accuracy of the existing surrogate model. The major advantage of the proposed space mapping-based RBDO is that the existing surrogate model and the finally updated surrogate model can be formulated with simple matrix and vector calculations. In particular, when there is only a surrogate model that has been built due to the loss of existing sample information since the space mapping updates the model, the accuracy of the surrogate model can be improved by sequential sampling. The proposed method is compared with sequential sampling-based RBDO using GPR, and the calculation accuracy and efficiency are demonstrated through a 2D highly nonlinear example and an engineering problem.

Grid Feature-Based Weighted Simulation Method for Multi-Objective Reliability-Based Design Optimization

Reliability analysis and reliability-based design have attracted huge attention since their origin, especially in the engineering design optimization field. Integrating a novel grid feature (GF) mechanism into the weighted simulation method (WSM), a grid feature-based weighted simulation method (GFWSM) is proposed in this paper. By sorting the samples in the random variable space, the GF mechanism serializes the failure probability calculation process, which can reduce the number of performance function evaluations required by the WSM. The proposed GFWSM is integrated into an efficient evolutionary multi-objective optimizer, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), for solving multi-objective reliability-based design optimization (MORBDO) problems. Different reliability analysis examples are employed to verify the advantages of the proposed GFWSM. Various constrained multi-objective reliability-based design optimization problems have been selected to test the effectiveness of the GFWSM-DMOEOA algorithm. The simulation results indicate that GFWSM and GFWSM-DMOEOA algorithm have achieved a good balance between accuracy and efficiency.

An enhanced finite step length method for structural reliability analysis and reliability-based design optimization

An enhanced finite step length method for structural reliability analysis and reliability-based design optimization

A practical and efficient reliability-based design optimization method for rock tunnel support

Uncertainty is an intrinsic feature in rock mechanics and engineering, and uncertainty analysis is an important challenge to stability analysis, design, and construction in the context of rock engineering. In this study, a reliability-based design optimization (RBDO) approach is developed to determine the design parameters for engineering by combining the moment method and high-dimensional model representation (HDMR). Multiplicative dimensional reduction (MDRM) is used to approximate and determine the statistical moment of a rock tunnel response. The first-order second moment is used to estimate the reliability index based on the MDRM model. The complex, high-dimensional, and nonlinear response of the engineering structure is determined by HDMR. Microsoft Solver is used as optimization technology for the RBDO. The proposed approach was applied to a circular tunnel with rock bolts and the procedure was examined using a Monte Carlo simulation. The results show that the proposed method can determine the reliability index and design variables in the RBDO, and provide a simple and feasible way to consider uncertainties in design, stability analysis, and construction in rock engineering.

An innovative reliability-based design optimization method by combination of dual-stage adaptive kriging and genetic algorithm

PurposeThis study aims to propose an efficient method for solving reliability-based design optimization (RBDO) problems.Design/methodology/approachIn the proposed algorithm, genetic algorithm (GA) is employed to search the global optimal solution of design parameters satisfying the reliability and deterministic constraints. The Kriging model based on U learning function is used as a classification tool to accurately and efficiently judge whether an individual solution in GA belongs to feasible region.FindingsCompared with existing methods, the proposed method has two major advantages. The first one is that the GA is employed to construct the optimization framework, which is helpful to search the global optimum solutions of the RBDO problems. The other one is that the use of Kriging model is helpful to improve the computational efficiency in solving the RBDO problems.Originality/valueSince the boundaries are concerned in two Kriging models, the size of the training set for constructing the convergent Kriging model is small, and the corresponding efficiency is high.