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.

在实际工程问题中，收集足够的数据来构建高精度概率模型通常具有挑战性。在这种情况下，概率模型通常包含认知不确定性并且可能存在偏差。基于置信度的设计优化（CBDO）是解决输入数据不足的优化问题的有效工具。其中，认知不确定性被考虑在内，其传播通过可靠性的置信水平来量化。然而，可靠性分析和置信度分析（CA）的耦合导致计算精度低，计算成本上升不可接受。为了提高 CBDO 的性能，顺序单环可靠性优化本文提出了置信度分析方法（SROCA）。具体而言，建立了具有一系列完整单循环方法（CSLM）和CA循环的解耦策略。在每个循环中，CSLM 和 CA 相互解耦。其中，CSLM 将可靠性和置信度约束都集成到确定性优化循环中，并且由于应用了半解析灵敏度方法，因此不需要在 CA 中评估性能函数。此外，采用可靠性和置信度指标的更新策略来抵消基于降维方法的线性近似误差。最后，采用四个数学和一个工程实例来证明所提出的 SROCA 的性能。