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1.
This paper develops an efficient methodology to perform reliability-based design optimization (RBDO) by decoupling the optimization
and reliability analysis iterations that are nested in traditional formulations. This is achieved by approximating the reliability
constraints based on the reliability analysis results. The proposed approach does not use inverse first-order reliability
analysis as other existing decoupled approaches, but uses direct reliability analysis. This strategy allows a modular approach
and the use of more accurate methods, including Monte-Carlo-simulation (MCS)-based methods for highly nonlinear reliability
constraints where first-order reliability approximation may not be accurate. The use of simulation-based methods also enables
system-level reliability estimates to be included in the RBDO formulation. The efficiency of the proposed RBDO approach is
further improved by identifying the potentially active reliability constraints at the beginning of each reliability analysis.
A vehicle side impact problem is used to examine the proposed method, and the results show the usefulness of the proposed
method. 相似文献
2.
Harish Agarwal Chandan K. Mozumder John E. Renaud Layne T. Watson 《Structural and Multidisciplinary Optimization》2007,33(3):217-227
Reliability-based design optimization (RBDO) is a methodology for finding optimized designs that are characterized with a
low probability of failure. Primarily, RBDO consists of optimizing a merit function while satisfying reliability constraints.
The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the
system or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing
a reliability analysis. During the last few years, a variety of different formulations have been developed for RBDO. Traditionally, these have been
formulated as a double-loop (nested) optimization problem. The upper level optimization loop generally involves optimizing a merit function subject to reliability constraints,
and the lower level optimization loop(s) compute(s) the probabilities of failure corresponding to the failure mode(s) that
govern(s) the system failure. This formulation is, by nature, computationally intensive. Researchers have provided sequential strategies to address this issue, where the deterministic optimization and reliability analysis are decoupled, and the process is performed iteratively until convergence is achieved. These methods, though attractive in terms of obtaining
a workable reliable design at considerably reduced computational costs, often lead to premature convergence and therefore
yield spurious optimal designs. In this paper, a novel unilevel formulation for RBDO is developed. In the proposed formulation, the lower level optimization (evaluation of reliability constraints
in the double-loop formulation) is replaced by its corresponding first-order Karush–Kuhn–Tucker (KKT) necessary optimality
conditions at the upper level optimization. Such a replacement is computationally equivalent to solving the original nested
optimization if the lower level optimization problem is solved by numerically satisfying the KKT conditions (which is typically
the case). It is shown through the use of test problems that the proposed formulation is numerically robust (stable) and computationally efficient compared to the existing approaches for RBDO. 相似文献
3.
Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias indicating the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty approximation in a product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias modeling approach is proposed and results are demonstrated by two vehicle design problems. 相似文献
4.
Traditional reliability-based design optimization (RBDO) requires a double-loop iteration process. The inner optimization loop is to find the reliability and the outer is the regular optimization loop to optimize the RBDO problem with reliability objectives or constraints. It is known that the computation can be prohibitive when the associated function evaluation is expensive. This situation is even worse when a large number of reliability constraints are present. As a result, many approximate RBDO methods, which convert the double loop to a single loop, have been developed. In this research, an engineering problem with a large number of constraints (144) is designed to test RBDO methods based on the first-order reliability method (FORM), including single- and double-loop methods. In addition to the number of constraints, this problem possesses many local minimums. Some original authors of the RBDO methods are also asked to solve the same problem. The results and the efficiencies for different methods are published and discussed. 相似文献
5.
Zeng Meng Dixiong Yang Huanlin Zhou Bo Ping Wang 《Structural and Multidisciplinary Optimization》2018,57(3):1079-1091
For solution of reliability-based design optimization (RBDO) problems, single loop approach (SLA) shows high efficiency. Thus SLA is extensively used in RBDO. However, the iteration solution procedure by SLA is often oscillatory and non-convergent for RBDO with nonlinear performance function. This prevents the application of SLA to engineering design problems. In this paper, the chaotic single loop approach (CLSA) is proposed to achieve the convergence control of original iterative algorithm in SLA. The modification involves automated selection of the chaos control factor by solving a novel one-dimensional optimization model. Additionally, a new oscillation-checking method is constructed to detect the oscillation of iterative process of design variables. The computational capability of CLSA is demonstrated through five benchmark examples and one stiffened shell application. The comparison of numerical results indicates that CSLA is more efficient than the double loop approach and the decoupled approach. CSLA also solves the RBDO problems with highly nonlinear performance function and non-normal random variables stably. 相似文献
6.
Single-loop system reliability-based topology optimization considering statistical dependence between limit-states 总被引:1,自引:1,他引:0
Tam H. Nguyen Junho Song Glaucio H. Paulino 《Structural and Multidisciplinary Optimization》2011,44(5):593-611
This paper presents a single-loop algorithm for system reliability-based topology optimization (SRBTO) that can account for
statistical dependence between multiple limit-states, and its applications to computationally demanding topology optimization
(TO) problems. A single-loop reliability-based design optimization (RBDO) algorithm replaces the inner-loop iterations to
evaluate probabilistic constraints by a non-iterative approximation. The proposed single-loop SRBTO algorithm accounts for
the statistical dependence between the limit-states by using the matrix-based system reliability (MSR) method to compute the
system failure probability and its parameter sensitivities. The SRBTO/MSR approach is applicable to general system events
including series, parallel, cut-set and link-set systems and provides the gradients of the system failure probability to facilitate
gradient-based optimization. In most RBTO applications, probabilistic constraints are evaluated by use of the first-order
reliability method for efficiency. In order to improve the accuracy of the reliability calculations for RBDO or RBTO problems
with high nonlinearity, we introduce a new single-loop RBDO scheme utilizing the second-order reliability method and implement
it to the proposed SRBTO algorithm. Moreover, in order to overcome challenges in applying the proposed algorithm to computationally
demanding topology optimization problems, we utilize the multiresolution topology optimization (MTOP) method, which achieves
computational efficiency in topology optimization by assigning different levels of resolutions to three meshes representing
finite element analysis, design variables and material density distribution respectively. The paper provides numerical examples
of two- and three-dimensional topology optimization problems to demonstrate the proposed SRBTO algorithm and its applications.
The optimal topologies from deterministic, component and system RBTOs are compared with one another to investigate the impact
of optimization schemes on final topologies. Monte Carlo simulations are also performed to verify the accuracy of the failure
probabilities computed by the proposed approach. 相似文献
7.
Traditional reliability-based design optimization (RBDO) requires a double loop iteration process. The inner optimization loop is to find the most probable point (MPP) and the outer is the regular optimization loop to optimize the RBDO problem with reliability objectives or constraints. It is well known that the computation can be prohibitive when the associated function evaluation is expensive. As a result, many approximate RBDO methods, which convert the double loop to a single loop, have been developed. In this work, several approximate RBDO methods are coded, discussed, and tested against a double loop algorithm through four design problems. 相似文献
8.
Efficient reliability-based design optimization using a hybrid space with application to finite element analysis 总被引:2,自引:0,他引:2
G. Kharmanda A. Mohamed M. Lemaire 《Structural and Multidisciplinary Optimization》2002,24(3):233-245
The design of high technology structures aims to define the best compromise between cost and safety. The Reliability-Based
Design Optimization (RBDO) allows us to design structures which satisfy economical and safety requirements. However, in practical
applications, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to
very high computational time and weak convergence stability. Traditionally, the solution of the RBDO model is achieved by
alternating reliability and optimization iterations. This approach leads to low numerical efficiency, which is disadvantageous
for engineering applications on real structures. In order to avoid this difficulty, we propose herein a very efficient method
based on the simultaneous solution of the reliability and optimization problems. The procedure leads to parallel convergence
for both problems in a Hybrid Design Space (HDS). The efficiency of the proposed methodology is demonstrated on the design
of a steel hook, where the RBDO is combined with Finite Element Analysis (FEA). 相似文献
9.
Z. L. Huang C. Jiang Y. S. Zhou J. Zheng X. Y. Long 《Structural and Multidisciplinary Optimization》2017,55(2):513-528
Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications. 相似文献
10.
This study developed a reliability-based design optimization (RBDO) algorithm focusing on the ability of solving problems with nonlinear constraints or system reliability. In this case, a sampling technique is often adopted to evaluate the reliability analyses. However, simulation with an insufficient sample size often possesses statistical randomness resulting in an inaccurate sensitivity calculation. This may cause an unstable RBDO solution. The proposed approach used a set of deterministic variables, called auxiliary design points, to replace the random parameters. Thus, an RBDO is converted into a deterministic optimization (DO, α-problem). The DO and the analysis of finding the auxiliary design points (β-problem) are conducted iteratively until the solution converges. To maintain the stability of the RBDO solution with less computational cost, the proposed approach calculated the sensitivity of reliability (in the β-problem) with respect to the mean value of the pseudo-random parameters rather than the design variables. The stability of the proposed method was compared to that of the double-loop approach, and many factors, such as sample size, starting point and the parameters used in the optimization, were considered. The accuracy of the proposed method was confirmed using Monte Carlo simulation (MCS) with several linear and nonlinear numerical problems. 相似文献
11.
Z. L. Huang C. Jiang Z. Zhang T. Fang X. Han 《Structural and Multidisciplinary Optimization》2017,56(3):647-661
For the problem of evidence-theory-based reliability design optimization (EBDO), this paper presents a decoupling approach which provides an effective tool for the reliability design of some complex structures with epistemic uncertainty. The approach converts the original nested optimization into a sequential iterative process including design optimization and reliability analysis. In each iteration step, through the uniformity algorithm, the original EBDO is firstly transformed to a conventional reliability-based design optimization (RBDO) and an optimal solution is obtained by solving it. At the solution, the first-order approximate reliability analysis method (FARM) is then used to perform the evidence-theory-based reliability analysis for each constraint. In addition, the RBDO solving and the evidence-theory-based reliability analysis are carried out alternately until reaching the convergence. Finally, two numerical examples and a practical engineering application show the effectiveness of the proposed method. 相似文献
12.
Zhenzhong Chen Haobo Qiu Liang Gao Peigen Li 《Structural and Multidisciplinary Optimization》2013,47(6):905-920
The application of reliability-based design optimization (RBDO) is hindered by the unbearable computational cost in the structure reliability evaluating process. This study proposes an optimal shifting vector (OSV) approach to enhance the efficiency of RBDO. In OSV, the idea of using an optimal shifting vector in the decoupled method and the notation of conducting reliability analysis in the super-sphere design space are proposed. The shifted limit state function, instead of the specific performance function, is used to identify the inverse most probable point (IMPP) and derive the optimal shifting vector for accelerating the optimization process. The super-sphere design space is applied to reduce the number of constraints and design variables for the novel reliability analysis model. OSV is very efficient for highly nonlinear problems, especially when the contour lines of the performance functions vary widely. The computation capability of the proposed method is demonstrated and compared to existing RBDO methods using four mathematical and engineering examples. The comparison results show that the proposed OSV approach is very efficient. 相似文献
13.
A. Mohsine A. El Hami 《Computer Methods in Applied Mechanics and Engineering》2010,199(17-20):1006-1018
Nowadays, the search in reliability-based design optimization is becoming an important engineering design activity. Traditionally for these problems, the objective function is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure. This paper focuses on the study of a particular problem with the failure mode on vibration of structure. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large-scale multidisciplinary systems which are likewise computationally intensive. With this in mind research, we propose in this paper a new method to treat reliability-based optimization methods under frequencies constraint. The goal of this development has resolved just one problem of optimization and reduced the cost of computation. Aircraft wing design typically involves multiple disciplines such as aerodynamics and structure; this numerical example demonstrated the different advantages of the proposed method. 相似文献
14.
Niclas Strömberg 《Structural and Multidisciplinary Optimization》2017,56(3):631-645
In this work a second order approach for reliability-based design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORM-based SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. For instance, it is shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach. 相似文献
15.
This paper presents an efficient reliability-based multidisciplinary design optimization (RBMDO) strategy. The conventional
RBMDO has tri-level loops: the first level is an optimization in the deterministic space, the second one is a reliability
analysis in the probabilistic space, and the third one is the multidisciplinary analysis. Since it is computationally inefficient
when high-fidelity simulation methods are involved, an efficient strategy is proposed. The strategy [named probabilistic bi-level
integrated system synthesis (ProBLISS)] utilizes a single-level reliability-based design optimization (RBDO) approach, in
which the reliability analysis and optimization are conducted in a sequential manner by approximating limit state functions.
The single-level RBDO is associated with the BLISS formulation to solve RBMDO problems. Since both the single-level RBDO and
BLISS are mainly driven by approximate models, the accuracy of models can be a critical issue for convergence. The convergence
of the strategy is guaranteed by employing the trust region–sequential quadratic programming framework, which validates approximation
models in the trust region radius. Two multidisciplinary problems are tested to verify the strategy. ProBLISS significantly
reduces the computational cost and shows stable convergence while maintaining accuracy. 相似文献
16.
The reliability-based design optimization (RBDO) presents to be a systematic and powerful approach for process designs under uncertainties. The traditional double-loop methods for solving RBDO problems can be computationally inefficient because the inner reliability analysis loop has to be iteratively performed for each probabilistic constraint. To solve RBDOs in an alternative and more effective way, Deb et al. [1] proposed recently the use of evolutionary algorithms with an incorporated fastPMA. Since the imbedded fastPMA needs the gradient calculations and the initial guesses of the most probable points (MPPs), their proposed algorithm would encounter difficulties in dealing with non-differentiable constraints and the effectiveness could be degraded significantly as the initial guesses are far from the true MPPs. In this paper, a novel population-based evolutionary algorithm, named cell evolution method, is proposed to improve the computational efficiency and effectiveness of solving the RBDO problems. By using the proposed cell evolution method, a family of test cells is generated based on the target reliability index and with these reliability test cells the determination of the MPPs for probabilistic constraints becomes a simple parallel calculation task, without the needs of gradient calculations and any initial guesses. Having determined the MPPs, a modified real-coded genetic algorithm is applied to evolve these cells into a final one that satisfies all the constraints and has the best objective function value for the RBDO. Especially, the nucleus of the final cell contains the reliable solution to the RBDO problem. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed cell evolution method in solving RBDOs. Simulation results reveal that the proposed cell evolution method outperforms comparative methods in both the computational efficiency and solution accuracy, especially for multi-modal RBDO problems. 相似文献
17.
André J. Torii Rafael H. Lopez Leandro F. F. Miguel 《Structural and Multidisciplinary Optimization》2016,54(2):317-332
There are available in the literature several papers on the development of methods to decouple the reliability analysis and the structural optimization to solve RBDO problems. Most of them focused on strategies that employ the First Order Reliability Method (FORM) to approximate the reliability constraints. Despite of all these developments, one limitation prevailed: the lack of accuracy in the approximation of the reliability constraints due to the use of FORM. Thus, in this paper, a novel approach for RBDO is presented in order to overcome such a limitation. In this approach, we use the concept of shifting vectors, originally developed in the context of the Sequential Optimization and Reliability Assessment (SORA). However, the shifting vectors are found and updated based on a novel strategy. The resulting framework is able to use any technique for the reliability analysis stage, such as Monte Carlo simulation, second order reliability methods, stochastic polynomials, among others. Thus, the proposed approach overcomes the aforementioned limitation of most of RBDO decoupling techniques, which required the use of FORM for reliability analysis. Several examples are analyzed in order to show the effectiveness of the methodology. Focus is given on examples that are poorly solved or even cannot be tackled by FORM based approaches, such as highly nonlinear limit state functions comprised by a maximum operator or problems with discrete random variables. It should be remarked that the proposed approach was not developed to be more computationally efficient than RBDO decoupling strategies based FORM, but to allow the utilization of any, including more accurate, reliability analysis method. 相似文献
18.
Xuchun Ren Vaibhav Yadav Sharif Rahman 《Structural and Multidisciplinary Optimization》2016,53(3):425-452
This paper puts forward two new methods for reliability-based design optimization (RBDO) of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, encompassing a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the AS-PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the AS-PDD approximation and score functions. In both methods, the failure probability and its design sensitivities are determined concurrently from a single stochastic simulation or analysis. When applied in collaboration with the multi-point, single-step framework, the proposed methods afford the ability of solving industrial-scale design problems. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new methods provide more computationally efficient design solutions than existing methods. Furthermore, shape design of a 79-dimensional jet engine bracket was performed, demonstrating the power of the AS-PDD-MCS method developed to tackle practical RBDO problems. 相似文献
19.
In the reliability-based design optimization (RBDO) model, the mean values of uncertain system variables are usually applied
as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical
programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide
an improved design but also a higher level of confidence in the design. In this paper, we present recent developments for
the RBDO model relative to two points of view: reliability and optimization. Next, we develop several distributions for the
hybrid method and the optimum safety factor methods (linear and nonlinear RBDO). Finally, we demonstrate the efficiency of
our safety factor approach extended to nonlinear RBDO with application to a tri-material structure. 相似文献
20.
Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method 总被引:2,自引:2,他引:0
In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical
distributions, known as epistemic uncertainty. Existing methods in uncertainty-based design optimization have difficulty in
handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties,
reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However,
Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability
predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver,
the eigenvector dimension reduction (EDR) method, for Bayesian reliability analysis. The EDR method takes a sensitivity-free
approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as
FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration. 相似文献