The development of surrogate models based on limited data is crucial in enhancing the speed of structural analysis and design optimization. Surrogate models are highly effective in alleviating the challenges between design variables and performance evaluation. Bidirectional Long Short-Term Memory (BiLSTM) is an advanced recurrent neural network that exhibits significant advantages in processing sequential data. However, the training of BiLSTM involves the adjustment of multiple hyperparameters (such as the number of layers, the number of hidden units, and the learning rate), which complicates the training process of the model. To enhance the efficiency and accuracy of neural network model development, this study proposes an Improved Whale Optimization Algorithm-assisted BiLSTM establishment strategy (IWOA-BiLSTM). The new algorithm enhances the initial population design and population position update process of the original Whale Optimization Algorithm (WOA), thereby improving both the global search capability and local exploitation ability of the algorithm. The IWOA is employed during the training process of BiLSTM to search for optimal hyperparameters, which reduces model training time and enhances the robustness and accuracy of the model. Finally, the effectiveness of the model is tested through a parameter optimization problem of a specific analog circuit. Experimental results indicate that, compared to traditional neural network models, IWOA-BiLSTM demonstrates higher accuracy and effectiveness in the optimal parameter design of analog circuit engineering problems.

The escalating need for reliability analysis (RA) and reliability-based design optimization (RBDO) within engineering challenges has prompted the advancement of saddlepoint approximation methods (SAM) tailored for such problems. This article offers a detailed overview of the general SAM and summarizes the method characteristics first. Subsequently, recent enhancements in the SAM theoretical framework are assessed. Notably, the mean value first-order saddlepoint approximation (MVFOSA) bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation (MVSOSA); the latter serves as an auxiliary approach to the former. Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method. Both the saddlepoint approximation and third-moment (SATM) and saddlepoint approximation and fourth-moment (SAFM) strategies model the cumulant generating function (CGF) by leveraging the initial random moments of the function. Although their optimal application domains diverge, each method consistently ensures superior relative precision, enhanced efficiency, and sustained stability. Every method elucidated is exemplified through pertinent RA or RBDO scenarios. By juxtaposing them against alternative strategies, the efficacy of these methods becomes evident. The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs. The main purpose and value of this article is to review the SAM and reliability-related issues, which can provide some reference and inspiration for future research scholars in this field.