# Optimization Design Method of Pipe-Insulating Joints Based on Surrogate Model and Genetic Algorithm
###### Abstract  
Pipe-insulating joints are common cathodic protection devices in long-distance oil and gas pipeline infrastructures. To ensure safety, they are often designed too conservatively, resulting in large dimensions, high self-weight, and substantial costs. This study analyzed an insulating joint under the most unfavorable conditions to identify the component of the maximum stress in the insulating joint, which is the right flange. Then, using parameterized finite element calculations, five independent dimensions of the right flange were combined and arranged to obtain a dataset of the right flange dimensions and their maximum stress. Subsequently, four different fitting algorithms were trained with this dataset, and the ridge regression algorithm, which showed the best predictive performance, was used to establish a surrogate model for calculating the maximum stress of the right flange. Finally, the surrogate model was combined with a genetic algorithm to determine the optimal design dimensions of the right flange. This study also provides examples verifying the accuracy and reliability of the surrogate model and genetic algorithm. In these examples, the maximum stress under the design dimensions given by the optimization algorithm has a maximum error of 8.98% and an average error of 4.63% compared to the preset maximum stress target, while the stress predicted by the surrogate model has a maximum error of 9.65% and an average error of 5.33% compared to the actual stress. This improves the computational efficiency of the optimization algorithm by establishing a surrogate model, which can be used to optimize the dimensions of insulation joints. been developed to counteract the corrosive effects of these stray currents [7]. These include the use of corrosion-resistant materials for pipeline construction [8; 9], the application of protective coatings designed to resist corrosion [10; 11], and the implementation of cathode protection [12; 13]. The cathodic protection system is a commonly used and highly effective anti-corrosion measure in long-distance oil and gas pipelines. Insulated joints are an important part of the cathodic protection system for oil and gas pipelines [14] and are now widely used in long-distance oil pipelines. Insulation joints are the successors of insulating flanges and serve as connection devices that isolate pipeline sections with cathodic protection from those without. Insulation joints are typically installed at the outlet of the protected pipeline, at both ends of large crossings, in sections affected by stray currents, and at the connection points between the protected pipeline and other primary or branch pipelines that should not be subjected to cathodic protection. The installation of insulated joints is shown in Figure 1. The insulation joint primarily consists of a short pipe, fixing sleeve, right flange, insulating filler, sealing ring, and left flange, as shown in Figure 2.  
During the operation of pipelines, insulating joints are subjected to axial forces and bending moments primarily due to the flow of liquids within the pipeline and the deformation of the surrounding soil [15; 16; 17]. Therefore, insulating joints are not only required to possess excellent insulating and sealing properties but also to meet strength requirements. Composed of multiple components, insulating joints are prone to excessive stress at the edges where the parts intersect. Due to the numerous relevant dimensions of pipe joint components and the interdependence of these dimensions, rather than their independence [18], the optimization of insulating joints is also relatively difficult. However, many scholars have still proposed some methods for the optimization of pipe joints, including the stress analysis of various parts of the pipe joint, mechanical analysis under different types of loads, and optimization design combined with optimization algorithms [19; 20; 21; 22].