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Abstract Reliability-based design optimization (RBDO) is a powerful tool to handle the influence of various uncertainties during optimization. However, unbearable computation cost is one of the largest barriers for its application, especially for the finite element method (FEM)-based RBDO. In this paper, an efficient and accurate RBDO framework is established based on isogeometric analysis (IGA) for complex engineering problems. Furthermore, an enhanced step length adjustment (ESLA) iterative algorithm and a second-order reliability method-based stepped-up sequential optimization and reliability assessment approach (SSORA-SORM) are proposed to boost the efficiency of RBDO. According to the situation of iteration process, the step length of search the most probable target point can be adaptively updated by the proposed criterion to improve the robustness in ESLA. In the proposed framework, the analytical first-order sensitivity is derived based on IGA in the optimization process to substitute the time-consuming finite difference method. The robustness, accuracy and efficiency of proposed methods are verified via several numerical benchmarks. Besides, three complex IGA-based examples demonstrate that the proposed method is able to save much computational cost without losing accuracy, which is inherently suitable for the RBDO of complex engineering problems. [ABSTRACT FROM AUTHOR]

For non-probabilistic reliability-based design optimization (NRBDO), existing methods cannot satisfy both efficiency and robustness requirements, especially for complex engineering problems. In this study, an efficient adaptive-loop (EAL) method for NRBDO is proposed based on an improved single loop method and enhanced chaos control method, aiming to enhance the optimization efficiency without sacrifice of numerical stability. The constraint function is reconstructed to improve the efficiency of reliability analysis. Moreover, a criteria condition is defined to guarantee the rationality of rough optimum and eliminate redundant constraints. The proposed EAL method can adaptively switch to a proper method, thus both high efficiency and robustness can be guaranteed. Nonlinear numerical examples and complex engineering problems are utilized to demonstrate the effectiveness of the proposed method by comparison with other existing methods. [ABSTRACT FROM AUTHOR]

In this study, an efficient and robust algorithm of non-probabilistic reliability-based design optimization (NRBDO) is proposed based on convex model. In this double-nested optimization model, the inner loop concerns a Min–max problem for the evaluation of reliability index, where the target performance approach is applied to substitute the Min–max problem. To improve the convergence rate, an enhanced chaos control (ECC) method is developed on the basis of chaotic dynamics theory, which can check and re-update the control factor by the Wolfe–Powell criterion. To further enhance the optimization efficiency, a novel NRBDO algorithm is developed based on the proposed ECC, where HL–RF algorithm is applied at the initial stage of this algorithm, while ECC is used to improve the robustness once the oscillation or chaotic behavior is identified. Three mathematical examples, one numerical example and one complex engineering problem, i.e. axially compressed stiffened shells in launch vehicles, are utilized to demonstrate the robustness and efficiency of the proposed method by comparison with other existing methods. Results indicate that the proposed method is particularly suitable for complicated engineering problems without prior knowledge of uncertainty distributions, which is expected to be utilized in the structural design of future launch vehicles. [ABSTRACT FROM AUTHOR]

The statistical model is commonly used in the reliability-based design optimization (RBDO). However, it is difficult to obtain sufficient data to construct a reasonable statistical model in the practical engineering. The biased statistical model seriously reduces the accuracy of uncertainty modeling and further affects the validity of the optimal result of RBDO. In this paper, the uncertainty of statistical model caused by the insufficient data is taken into consideration, which is quantified by the confidence of failure probability. Confidence-based design optimization (CBDO) is used to ensure the validity of the optimal result, and thus the double-loop RBDO is replaced by the time-consuming treble-loop CBDO. To reduce the heavy computational cost, a complete performance measure approach (PMA) with single-loop strategy is proposed in this paper and performance measure value is applied in the whole optimization process. The modified second-order reliability method (SORM) is employed to replace the time-consuming MCS and calculate the minimum performance target point (MPTP) of the reliability constraint function. Then, the reliability analysis is integrated into the confidence level evaluation process by single-loop strategy. Four examples are used to verify the performance of the proposed method in this paper. All results have demonstrated that the proposed method only needs much lower computational cost but its accuracy is similar to the previous CBDO. [ABSTRACT FROM AUTHOR]

In practical engineering problems, it is frequently challenging to collect sufficient data to construct high-precision probabilistic models. In this case, probabilistic models typically contain cognitive uncertainty and may be biased. Confidence-based design optimization (CBDO) is an effective tool for solving optimization problems with insufficient input data. Therein, epistemic uncertainty is taken into account, and its propagation is quantified by the confidence level of reliability. However, the coupling of reliability analysis and confidence analysis (CA) results in low calculation accuracy and an unacceptable rise in computational cost. To improve the performance of CBDO, a sequential single-loop reliability optimization and confidence analysis method (SROCA) is proposed in this paper. Specifically, a decoupling strategy with a serial of cycles of complete single-loop method (CSLM) and CA is established. In each cycle, CSLM and CA are decoupled from each other. Therein, the CSLM integrates both the reliability and confidence constraints into the deterministic optimization loop, and the performance functions are not required to be evaluated in CA due to the application of a semi-analytic sensitivity method. Additionally, update strategies for both the reliability and confidence indexes are employed to neutralize the linear approximation errors based on the dimension reduction method. Finally, four mathematical and one engineering example are adopted to demonstrate the performance of the proposed SROCA. The results show that the efficiency and accuracy of implementing CBDO achieve significant improvement by the proposed method. [ABSTRACT FROM AUTHOR]

Surrogate models and adaptive methods can release the huge computational burden of structural reliability analysis. However, it is very difficult to guarantee the accuracy of uncertainty quantification, especially when noises are contained in samples, which may greatly reduce the confidence of reliability analysis. In this study, we propose a novel Nested Stochastic Kriging (NSK) model method with response noise parameters decoupled from other surrogate model parameters, which can significantly improve the accuracy of uncertainty quantification and modeling efficiency. The proposed NSK is for deterministic data with response noise, aiming at reliability analysis. Various types of uncertainty can be identified by the NSK, including the conditions of known and unknown, constant and variable variances. Moreover, a local sample verification method is established to improve the accuracy of uncertainty quantification. To further improve the accuracy of reliability analysis, an adaptive NSK framework is established with new samples added, and then reliability analysis can be conducted. Through several numerical examples, it can be seen that the NSK always provides the most accurate results with the fewest analysis calls. • A novel modular framework of Nested Stochastic Kriging (NSK) is proposed. • The proposed NSK can deal with response noise with kinds of variable variances. • An adaptive framework using the NSK for reliability analysis is established. • The reliability analysis with NSK considering both epistemic and response noise. [ABSTRACT FROM AUTHOR]