# Optimization Design Method of Pipe-Insulating Joints Based on Surrogate Model and Genetic Algorithm
###### Abstract
Since the insulating joint is a new type of structure, research on this structure is still limited both domestically and internationally. The above-mentioned studies are mainly focused on traditional flanged or welded pipe joints, and most of them employ traditional finite element analysis methods for optimization, which makes it difficult to obtain the global optimal solution [18; 20; 23]. Currently, flange connections are widely used for pipes, and there is relatively little research on the new type of insulating joint discussed in this paper. Moreover, there are no mature design methods or design standards available, leading to relatively conservative designs for insulating joints. The few existing design methods are mostly based on empirical formulas [24; 25; 26]. To prevent stress concentrations from exceeding the allowable limits, the dimensions of insulating joints are often designed to be larger, resulting in high self-weight and substantial costs. Therefore, optimization re  
Figure 1: Installation of the insulating joint. search is necessary for the design of cross-sectional dimensions for insulation joints, aiming to minimize self-weight and reduce costs while ensuring that the insulation joints meet stress requirements. A genetic algorithm is a stochastic optimization algorithm based on [PERSON]'s theory of evolution, which seeks to find the optimal solution to a problem by simulating the processes of selection, crossover, and mutation in nature [27]. Genetic algorithms begin by establishing a set of potential solutions, known as a population, and then assessing the quality of each individual based on a fitness function. This process selects individuals with higher fitness for genetic recombination and mutation, generating a new generation. Over multiple generations, the individuals within the population gradually evolve towards the optimal solution of the problem. The fitness function is a critical factor influencing the optimization performance of a genetic algorithm. The fitness function represents the relationship between the optimized parameters and the optimization objectives. In the context of this study, this relationship corresponds to the connection between the dimensions of the insulation joint and the maximum stress. However, this relationship involves stress concentration, and the impact of each dimension of the insulation joint on maximum stress is not necessarily independent; there is a coupling between the various parameters. Obtaining an analytical solution through physical and mathematical theories and constructing a fitness function is challenging. Finite element analysis is a powerful problem-solving tool in modern engineering, which can be utilized for numerical computation to determine the stress in insulation joints [28; 29]. This method can be integrated with genetic algorithms, employing finite element calculations as the fitness function within the genetic algorithm and subsequently optimizing the problem [30; 31]. This method can yield satisfactory results when the model is simple and the number of calculation points is sufficient. However, when the model is  
Figure 2: Insulating joint. complex and involves numerous characteristics, a large number of data points are required to ensure optimal results. Each iteration implies that the finite element program must also perform a calculation, leading to a significant increase in computational time and costs. The hyperparameters of the optimization algorithm are also an essential factor affecting the performance of the optimization, and each adjustment of the hyperparameters necessitates corresponding calculations from the finite element program, making the optimization process exceptionally tedious. Moreover, implementing the integration of optimization algorithms and finite elements through programming demands a high level of expertise from designers in mechanics, mathematics, and computer languages, which currently hinders its routine use and promotion.