Sequential Optimization And Reliability Assessment Method Research Articles

An Efficient Decoupled Reliability-Based Topology Optimization Method Based on a Performance Shift Strategy

AbstractIn this paper, a new efficient reliability-based topology optimization (RBTO) method is proposed for structures, in which the double-loop optimization is equivalently decoupled into a sequential process based on a performance shift strategy. First, a volume minimization RBTO formulation is built for structures considering displacement or compliance reliability constraints. Second, an efficient decoupling scheme is proposed to turn the double-loop RBTO into a series of deterministic topology optimization and reliability analysis. For the reliability analysis, the reliability probability is calculated based on the probability distribution function of the performance function, and the probability distribution function can be solved by the maximum entropy method based on the raw moments calculated by the multiplicative dimension reduction method. A performance shift strategy is then applied to build an equivalence between probabilistic constraint and deterministic constraint to formulate the deterministic topology optimization. Thirdly, the adjoint variable method is applied to obtain the sensitivity information for topological design variables, and a gradient-based optimization algorithm is used to update the design variables. Finally, four typical numerical examples are used to verify the advantage of the proposed method. Compared with the traditional sequential optimization and reliability assessment (SORA) method, the proposed RBTO method results in a design with a 5.4% smaller volume value to reach the same reliability index requirement for the cantilever beam, and the function calls are 354 times less than that of the SORA method.

An Extended SORA Method for Hybrid Reliability-Based Design Optimization

In many practical engineering problems, distributions of some random variables may not be precisely known or even only the variation ranges can be given, due to which the Reliability-Based Design Optimization (RBDO) methods cannot be applied directly. In this paper, a hybrid RBDO model is established to deal with hybrid uncertainties including random variables with interval distribution parameters and coexistence of random and interval variables. The hybrid uncertainties lead to an interval of reliability, thus giving rise to a triple-loop optimization problem, which burdens the computational effort significantly. Therefore, an extended Sequential Optimization and Reliability Assessment (SORA) method is proposed, where the worst-case point over the bounded domain of interval uncertainty is employed to replace reliability constraint with deterministic optimization. Therefore, the hybrid RBDO problem can be efficiently solved by a series of deterministic optimization procedures. The efficiency and accuracy of the proposed method are illustrated through several numerical examples.

Reliability-based optimization of ship structure based on interest subdomain dynamic surrogate model

Objectives Aiming at the difficulty of ensuring the fitting accuracy and optimization efficiency of surrogate models due to the high nonlinearity in ship structure reliability-based optimization design, a reliability-based ship structure optimization method based on the interest subdomain dynamic surrogate model is proposed. Methods This method puts forward the concept of the interest subdomain based on the sequential optimization and reliability assessment (SORA) method, determines the range of interest subdomains and formulates adaptive spatial reduction rules based on information entropy function H, then proposes an adaptive spatial reduction sequential sampling strategy based on interest subdomains, thereby constructing a dynamic Kriging surrogate model that highly fits the subdomain of interest locally with as few sample points as possible, and embedding the surrogate model and multi-island genetic algorithm (MIGA) in the SORA method to undertake reliability-based optimization.This study proposes a probability constraint feasibility checking method to reduce unnecessary reliability assessment processes. A mathematical example is given to verify the reliability-based optimization method. Results The relative error between the optimal solution and theoretical solution is 0.066 8%, and the number of function calls is 40.6% less than those of the optimal method in the references, which proves the accuracy and efficiency of this method. Conclusions When the proposed method is applied to the reliability optimization design of a cabin structure, the total cabin mass is reduced by 0.511% compared with the references, and 94 fewer finite element calculations are required, proving the efficiency and applicability of this method.

Extending SORA method for reliability-based design optimization using probability and convex set mixed models

In many practical applications, probabilistic and bounded uncertainties often arise simultaneously, and these uncertainties can be described by using probability and convex set models. However, the computing cost becomes unacceptable when directly solving the reliability-based design optimization (RBDO) problem with these uncertainties involved. To address this issue, in this study, a sequential sampling strategy by extending classical sequential optimization and reliability assessment (SORA) method for RBDO is developed. The proposed strategy can successively select sample points to update the surrogate model at each step of the optimization process. New samples for reliability constraints are mainly chosen from the local region around the approximate minimum performance target point (MPTP) and worst-case point (WCP). Typical design examples, including one engineering application, are investigated to demonstrate the efficiency and accuracy of the proposed method.

A probabilistic feasible region approach for reliability-based design optimization

Reliability-based design optimization (RBDO) is a useful tool for design optimization when considering the probabilistic characteristics of the design variables. However, its use in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Sequential optimization and reliability assessment (SORA) method is one of the most popular methods used for RBDO. In this paper, the proposed probabilistic feasible region (PFR) approach is based on the SORA framework, and it is developed to enhance the efficiency of SORA. In PFR, the notion of probabilistic feasible region is created using the reliability assessment results; Rather than conducting reliability assessment for every movement of the design variables, when the design variables locate in the probabilistic feasibile region during the optimizaiton iterations, no new relibility assessment will be needed. The range of the probabilistic feasible region is updated and becaome larger during the interaion processes, and its creation does not need extra computational cost. The computation capability of the proposed PFR is demonstrated and compared to the SORA method using a mathematical example, a speed reducer design and a box girder structure design application. The comparison results show that the proposed PFR approach is very efficient.

An efficient approach to reliability-based design optimization within the enhanced sequential optimization and reliability assessment framework

Reliability based design optimization (RBDO) has been widely implemented in engineering practices for high safety and reliability. It is an important challenge to improve computational efficiency. Sequential optimization and reliability assessment (SORA) has made great efforts to improve computational efficiency by decoupling a RBDO problem into sequential deterministic optimization and reliability analysis as a single-loop method. In this paper, in order to further improve computational efficiency and extend the application of the current SORA method, an enhanced SORA (ESORA) is proposed by considering constant and varying variances of random design variables while keeping the sequential framework. Some mathematical examples and an engineering case are given to illustrate the proposed method and validate the efficiency.

Enhanced sequential optimization and reliability assessment for reliability-based design optimization

Reliability-based design optimization (RBDO) has been receiving increasing attention for achieving high safety and reliability in engi- neering design. Sequential optimization and reliability assessment (SORA), as one of the efficient single-loop methods, decouples an RBDO problem into sequential deterministic optimization and reliability analysis. An enhanced SORA (ESORA) method is proposed with the aim of further improving the computational efficiency for RBDO, considering both cases of constant and varying variances of random design inputs while keeping the single-loop framework. Vehicle side impact example is used to test and compare the efficiency of the proposed method with existing approaches.

Reliability-based design optimization using convex approximations and sequential optimization and reliability assessment method

In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. The sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the reliability analysis loop. In this study, the convex approximations for probabilistic constraint are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. Hence, the proposed method requires much less function evaluations of probabilistic constraints in the deterministic optimization than the original SORA method. The efficiency and accuracy of the proposed method were verified through numerical examples.

Enhanced sequential optimization and reliability assessment method for probabilistic optimization with varying design variance

The Sequential Optimization and Reliability Assessment (SORA) method is a single-loop method containing a serial of cycles of decoupled deterministic optimization and reliability assessment for improving the efficiency of probabilistic optimization. However, the original SORA method as well as some other existing single-loop methods do not take into account the effect of varying design variance (changing variance) in design problems. In this paper, to enhance the SORA method, three formulations are proposed in order to improve the efficiency for solving problems with changing variance. These formulations are categorized by the different strategies of Inverse Most Probable Point (IMPP) approximation. Mathematical examples and a speed reducer design problem are utilized to test and compare the effectiveness of the proposed formulations. The insight gained from our study on the applicability of different approaches can be extended and utilized in other probabilistic optimization strategies that require IMPP estimations.

Reliability-based multidisciplinary optimization for aircraft wing design

Aircraft wing design typically involves multiple disciplines such as aerodynamics and structure. Multidisciplinary design optimization (MDO) has been recently used to deal with the multidisciplinary efforts in wing design. When reliability is considered, MDO for the wing design becomes much more computationally intensive. To improve the efficiency, the strategy of using Sequential Optimization and Reliability Assessment (SORA) in MDO is proposed with the application of a simplified wing design problem. The overall reliability-based MDO is decomposed into sequential cycles of deterministic MDO and reliability analysis. The reliability analysis is therefore decoupled from the MDO loop, and the number of reliability analyses is then reduced significantly. It is shown that the use of the SORA method is efficient through the demonstration of a light aircraft wing design problem.

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

Probabilistic design, such as reliability-based design and robust design, offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. Since a probabilistic optimization often involves a double-loop procedure for the overall optimization and iterative probabilistic assessment, the computational demand is extremely high. In this paper, the sequential optimization and reliability assessment (SORA) is developed to improve the efficiency of probabilistic optimization. The SORA method employs a single-loop strategy with a serial of cycles of deterministic optimization and reliability assessment. In each cycle, optimization and reliability assessment are decoupled from each other; the reliability assessment is only conducted after the deterministic optimization to verify constraint feasibility under uncertainty. The key to the proposed method is to shift the boundaries of violated constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. The design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.