# Predicting the External Corrosion Rate of Buried Pipelines Using a Novel Soft Modeling Technique
## 1 Introduction  
The integrity and safety of pipelines play a crucial role in the oil and gas industry, especially given the massive exploitation of fossil fuels [1, 2]. Most pipelines are laid underground and are susceptible to corrosion due to long-term contact with soil. Pipeline corrosion will lead to the continuous thinning of the pipeline wall, and perforation and leakage may occur. This leads to safety accidents and threatens the safety of life and property [3]. According to statistics, corrosion factors account for over 50% of pipeline failures [4]. Incidents of pipeline failures due to corrosion occur not only in China but also in other countries. For instance, corrosion damage occurred in 20% of pipelines in the US, resulting in economic losses of USD 203 million [5]. The data suggest pipeline corrosion as a significant safety hazard [6]. While effective pipeline protection methods have been found, ensuring integrity during laying is difficult. Factors like technology and materials make this challenging [7]. Corrosion rates rise with service life. This can cause perforations and leaks before the expected end of life. Such early issues can sharply reduce lifespans. Precisely predicting the extent of transmission pipeline corrosion can lower damage and maintenance costs. It can also minimize environmental impacts. For these reasons, studying pipeline corrosion failure prediction is critical for safe and effective operations [8]. Corrosion prediction models canbe divided into mechanistic, statistical, and machine-learning-based intelligent models. Many scholars have extensively studied corrosion mechanisms [9]. Theoretical modeling is a popular method among them. However, the method relies on many mechanism parameters that also have poor replicability in terms of migration. This results in a costly and computationally inefficient model [10]. Machine learning is an important driver of industrial transformation and technological revolution [11]. It has the advantages of fast computation speeds, good model stability, and strong nonlinear data processing ability. Various new intelligent pipeline corrosion prediction methods have emerged, such as gray system theory (GM) [12], BP neural network (BPNN) [13], support vector machine (SVM) [14], and artificial neural network (ANN) [15]. While statistical and probabilistic methods can be used to build corrosion prediction models by taking corrosion data as inputs and outputting patterns of corrosion changes, they face some issues. These methods have problems such as poor generalization ability, narrow prediction scope, severe data dependence, and poor fitting capacity [16; 17]. To address these issues, people have proposed various methods to improve the accuracy and generalization of corrosion prediction models. KPCA is used for data dimension reduction to eliminate redundant information between factors and reduce modeling complexity [18]. KPCA is a nonlinear dimensionality reduction technique that effectively extracts the main features of the data [19]. It is able to map them to a low-dimensional space, thus simplifying the model training process and improving generalization [20]. Unlike traditional principal component analysis (PCA), KPCA can handle nonlinear data and better preserve its nonlinear structure [21]. In addition, there are various models and algorithms in the field of corrosion prediction [22]. These include artificial neural network models (such as FF, MLP, and RBF) [23; 24; 25] and optimization algorithms (such as WOA, Bat, Firefly, and GWO) [26; 27; 28]. Compared to other optimization algorithms (e.g., WOA, Bat, and Firefly), PSO has faster convergence and global search capability [29; 30; 31]. It is more suitable for solving corrosion prediction for complex nonlinear data and local optimal problems [32]. ELM is a single-hidden-layer feedforward neural network with the advantages of fast training and a strong generalization ability [33].