As engineering systems become increasingly complex, reliability-based design optimization (RBDO) has been extensively studied in recent years and has made great progress. In order to achieve better optimization results, the mathematical model used needs to consider a large number of uncertain factors. Especially when considering mixed uncertainty factors, the contradiction between the large computational cost and the efficiency of the optimization algorithm becomes increasingly fierce. How to quickly find the optimal most probable point (MPP) will be an important research direction of RBDO. To solve this problem, this paper constructs a new RBDO method framework by combining an improved particle swarm algorithm (PSO) with excellent global optimization capabilities and a decoupling strategy using a simulated annealing algorithm (SA). This study improves the efficiency of the RBDO solution by quickly solving MPP points and decoupling optimization strategies. At the same time, the accuracy of RBDO results is ensured by enhancing global optimization capabilities. Finally, this article illustrates the superiority and feasibility of this method through three calculation examples.

With the engineering system becoming more and more complex, the uncertainty factors have a more and more profound influence on the reliability and security of the engineering system. In recent years, Reliability-Based Design Optimization (RBDO) has been studied extensively in complex engineering system design. The research on reliability optimization design considering stochastic uncertainty has been comprehensive and widely used. However, the reliability optimization design considering mixed uncertainty has the disadvantages of large computation and imprecise convergence. This study proposes an RBDO method based on Particle Swarm Optimization (PSO) and Simulated Annealing (SA) to overcome this challenge. In the method, PSO is used to solve the most probable point, while SA has excellent global optimization capability to acquire the global optimal solution. Finally, three examples are given to illustrate the advantages of the proposed method.

In uncertainty analysis and reliability-based multidisciplinary design and optimization (RBMDO) of engineering structures, the saddlepoint approximation (SA) method can be utilized to enhance the accuracy and efficiency of reliability evaluation. However, the random variables involved in SA should be easy to handle. Additionally, the corresponding saddlepoint equation should not be complicated. Both of them limit the application of SA for engineering problems. The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments. However, the traditional moment matching method is not very accurate generally. In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization, a fourth-moment saddlepoint approximation (FMSA) method is introduced into RBMDO. In FMSA, the approximate cumulative generating functions are constructed based on the first four moments of the limit state function. The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function. Furthermore, the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment, which is based on the performance measure approach strategy. Two engineering examples are introduced to verify the effectiveness of proposed method.

In this paper, the high temperature deformation behaviour of 17-4PH steel was studied. A new forming optimization method was proposed. The study will help guide the obtainment of high-precision and high-mechanical properties forging products in the aerospace industry. A hot compression test was carried out on a Gleeble1500D test machine (DUFFERS SCIENTFIC, Beijing, China). The stress–strain behaviour at a temperature of 1000 °C~1150 °C and strain rate of 0.1~10 s⁻¹ was analysed. Through the analysis of multiple heating tests, we come to the conclusion that the heating times should be controlled within 1 or 2 times in order to obtain a grain size above grade 6. Optimization analysis of the forming process was carried out to shorten the process and ensure the precision of the product. The preform shape was obtained quickly by fourth-order curve fitting. According to the method of finite element numerical simulation, the near net forming process within two heating procedures was determined. A 17-4PH forging product with precise shape and qualified structure was obtained through actual forming test.

Failure of critical train components (CTCs) affects normal train operation or can cause serious accidents, resulting in economic losses. The design and manufacture of large, complex and precise punches is critical for the manufacture of CTCs. During extrusion, punches are at high temperature, which has a negative influence on the processing accuracy and reliability of CTCs. Hot compound deformation due to a long punch stroke reduces the life of punches, increasing manufacturing costs. Therefore, ensuring the timely cooling of punches is important for machining accuracy. A cooling strategy for punches under hot compound extrusion of CTCs is proposed. Based on computer-aided engineering technology, the cooling process of a punch was numerically simulated. Then, the design of an auxiliary mould was optimised and the process parameters were adjusted. The theoretical temperature rise of the punch was calculated and a formula for temperature rise and cooling of the punch obtained. According to the forced convective heat transfer of cooling water, the convective heat transfer coefficients on the surface of the cooling pipe were calculated. The interior and external heat dissipation of the punch were simulated using finite elements and the production beat and compound extrusion parameters were calculated. Interior circulation cooling equipment was then designed. Variations in the temperature field distribution were obtained after punch extrusion and heat dissipation using infrared temperature measuring equipment. The experimental and theoretical results agreed.