Corrosion Rate Prediction of Buried Oil and Gas Pipelines: A New Deep Learning Method Based on RF and IBWO-Optimized BiLSTM–GRU Combined Model

Abstract

The corrosion of oil and gas pipelines represents a significant factor influencing the safety of these pipelines. The extant research on intelligent algorithms for assessing corrosion rates in pipelines has primarily focused on static evaluation methods, which are inadequate for providing a comprehensive dynamic evaluation of the complex phenomenon of corrosion in buried oil and gas pipelines. This paper proposes a novel approach to predicting the corrosion rate of buried oil and gas pipelines. The method is based on the combination of an improved Beluga Optimization algorithm (IBWO) and Random Forest (RF) optimization with BiLSTM and gated cycle unit (GRU), which are used to classify corrosion rates as high or low. Initially, a feature screening of corrosion factors was conducted via RF, whereby variables exhibiting a strong correlation were extracted. Subsequently, IBWO was employed to optimize the feature selection process, with the objective of identifying the optimal feature subset to enhance the model’s performance. Ultimately, the BiLSTM method was employed for the purpose of predicting the occurrence of low corrosion. A GRU method was employed for prediction in the context of high corrosion conditions. The RF–IBWO-BiLSTM–GRU model constructed in this paper demonstrates high prediction accuracy for both high and low corrosion rates. The verification of 100 groups of experimental data yielded the following results: the mean square error of this model is 0.0498 and the R² is 0.9876, which is significantly superior to that of other prediction models. The combined model, which incorporates an intelligent algorithm, is an effective means of enhancing the precision of buried pipeline corrosion rate prediction. Furthermore, it offers a novel approach and insight that can inform subsequent research on the prediction of corrosion rates in buried oil and gas pipelines.

1. Introduction

Pipeline transportation has become a dominant mode of oil and gas transportation due to its cost effectiveness and high throughput capacity. However, pipeline corrosion poses a significant risk of leakage, which can lead to catastrophic failures and a range of adverse consequences [1]. Furthermore, the prevalence of corrosion in buried oil and gas pipelines is exacerbated by environmental factors and operational conditions, which consequently compromise pipeline safety [2] despite the current physical technology for corrosion monitoring of oil and gas pipelines being relatively mature, including ultrasonic detection and electrochemical detection methods [3]. Nevertheless, the lack of consensus on an accepted prediction method for pipeline corrosion rates persists, given the considerable diversity of corrosion conditions.

The analysis of pipeline corrosion rate prediction in previous studies can be divided into two main categories: studies on pipeline corrosion degradation mechanism and research on the prediction of hybrid intelligence algorithms. In the study of pipeline corrosion degradation mechanisms, scholars primarily investigate the probability distribution. Caleyo et al. [4] employed Monte Carlo simulations to investigate the probability distribution of corrosion depth and rate in pipelines. Ning et al. [5] focused on the corrosion of mild steel under oil and gas conditions and predicted corrosion products under an H₂S liquid environment based on environmental temperature, H₂S partial pressure and other parameters, combined with an electric potential-PH diagram. Heidary and Groth [6] put forth a hierarchical Bayesian model that incorporates online monitoring data to quantify pitting corrosion in pipelines. Han et al. [7] put forth a joint distribution model to ascertain the interdependence between corrosion and metal fatigue, subsequently predicting the remaining lifespan of pipelines. Nevertheless, corrosion is a nonlinear process, and most traditional studies analyze the relationship between factors and corrosion only with probability models [1]. The efficacy of probabilistic models in accurately predicting pipeline corrosion under conditions of multiple factors remains a challenge [8]. In order to comprehensively consider the various factors influencing corrosion and their interrelationships, an increasing number of scholars are turning to hybrid intelligent algorithms for prediction research.

The hybrid intelligence algorithm primarily relies on monitoring data to train the model, subsequently conducting prediction analysis based on the trained model. Hatami et al. [9] constructed an SVR-based pipeline corrosion prediction model that considered four factors: temperature, CO₂ partial pressure, flow rate and pH value. Abbas et al. [10] employed a neural network approach to predict the corrosion rate of pipelines, achieving a result within the 95% confidence interval despite the inclusion of fewer factors. Hu et al. [11] employed a backpropagation neural network to simulate the corrosion of Ni–Cr–Mo–V high-strength steel in a marine environment. Ossai [12] employed a feedforward neural network algorithm based on particle swarm optimization (PSO) to construct a time-varying pipeline corrosion depth model. Xie et al. [13] employed the LSTM method to simulate and predict the dynamic process of pipeline corrosion, asserting that this approach could effectively capture the time dependence. Du et al. [14] constructed a pipeline pitting depth prediction model based on automatic machine learning (AML). Nevertheless, this aspect of the study is primarily concerned with static evaluation techniques, necessitating a substantial amount of data for model training. It seldom considers the intricate dynamics inherent to corrosion processes, and thus fails to offer a comprehensive dynamic safety assessment [15,16]. As a result, the academic community has started to implement a combined model for predicting pipeline corrosion and to address the complexities involved in the corrosion process. For instance, Guang et al. [8] utilized dynamic neural networks to forecast the corrosion rate outside buried pipelines by extracting corrosion characteristic data and further weighting the corrosion factors. Similarly, Luo et al. [17] developed a CNN–LSTM combined model incorporating an attention mechanism to predict the pipeline corrosion rate. However, current research has not considered the fluctuations in high and low rates during the pipeline corrosion process when applying the combined model, making it challenging to accurately simulate the changes in the pipeline corrosion process after reaching a critical trend point.

In conclusion, this study further explores the categorization of high and low corrosion rates to effectively simulate the complexities inherent in the corrosion process. Specifically, a combined BiLSTM–GRU model was developed to predict pipeline corrosion rates, addressing the issue of significantly reduced prediction accuracy observed in single models when subjected to varying corrosion rates during data testing. The BiLSTM–GRU combination model effectively overcomes the problem of unstable prediction accuracy at different corrosion rates. In scenarios characterized by low corrosion rates, the BiLSTM component is adept at capturing both forward and backward dependencies within the input sequence, making it particularly suitable for data environments that exhibit high complexity and critical subtle variations [18,19]. Conversely, in high corrosion rate scenarios, the GRU component is capable of rapidly learning and processing highly volatile data, thereby offering distinct advantages in managing data noise and minimizing overfitting [20].

The rest of this paper is organized as follows. In Section 2, we introduce the model principles used in the construction of prediction model in this study. In Section 3, we describe the examples, the data and the constructed predictive models. In Section 4, we present the model prediction results and discussion. In Section 5, we summarize the results of this study and propose possible research directions for the future.

2. Preliminaries

2.1. Random Forest (RF)

In practice, the experimental variables, instrument drift and external factors may result in data variability, potentially impacting the input data values and the correlation between them. Consequently, scholars typically employ the Random Forest (RF) model to identify the salient features of the data and ascertain the variables with robust correlations. RF is an ensemble learning algorithm that makes predictions and classifications by repeatedly constructing multiple decision trees. Among them, calculating the importance coefficient of each variable is an important link and the only basis for feature screening. The specific calculation formula is as follows:

$$Vim={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^k(MS{E}_j-MS{E}_{kj})}}{k\times S_E}}$$

(1)

where $Vim$ is the importance of the feature; $k$ is the number of decision trees; $MS{E}_j$ and $MS{E}_{kj}$ are the mean square error of the $kj$ and $kj$ decision trees, respectively; and $S_E$ is the standard error of the decision tree.

2.2. Improving the Beluga Whale Optimization Algorithm (IBWO)

Beluga Whale Optimization (BWO) is a heuristic global optimization algorithm proposed by Zhong et al. [21]. It is based on the social behavior simulation of beluga whales in nature. The standard BWO algorithm demonstrates robust optimization capabilities; however, it is not without shortcomings. These include a lack of adaptability, susceptibility to local optima and an imbalance between global and local search abilities when confronted with intricate optimization challenges [22]. This paper introduces chaotic initialization and a nonlinear wave factor to enhance the standard BWO algorithm, thereby improving its exploration ability and adaptability.

Firstly, the chaotic mapping is used to initialize the population to improve the local optimization problem of the standard BWO algorithm. Chaos is a nonlinear phenomenon existing in nature, and random points with no repetition can be generated within a certain time and range [23]. Therefore, chaos mapping is introduced in this paper to generate random points with no repetition between 0 and 1, in order to obtain an evenly distributed initial population and improve the optimization efficiency of the algorithm. In this paper, Logistic chaotic mapping, which is widely used in intelligent algorithms and has good optimization effects, is selected to improve the standard BWO [24]. The calculation formula of the mapping function is as follows:

$$x_{j+1}=4x_j(1-x_j)$$

(2)

The values of $x_j$ and $x_{j+1}$ are between (0, 1). The mapping initializes the position of each individual by generating sequences of complex, random features, improving the diversity and exploration ability of the population, helping the algorithm to avoid local optimum problems and enhancing the global search ability of the algorithm. The choice of Logistic chaotic mapping in the IBWO algorithm contributes measurably to achieving an optimal feature set by ensuring a more even and diverse initial distribution. This diversity prevents premature convergence and enhances the algorithm’s ability to explore the feature space comprehensively, which is critical for identifying the globally optimal feature subset. Studies have shown that chaotic mapping effectively balances exploration and exploitation, which improves feature selection accuracy, especially in complex environments [24,25].

Secondly, the incorporation of a nonlinear fluctuation factor serves to enhance the flexibility and adaptability of the algorithm, thereby addressing the shortcomings associated with the standard BWO algorithm, namely its lack of adaptability and the imbalance between global and local search abilities. This paper proposes the introduction of an exploration behavior probability $p(T)$ to enhance the BWO algorithm. This can be expressed as follows:

$$p(T)=1-{\displaystyle \frac{T}{T_{\max }}}$$

(3)

where $p(T)$ is the probability of exploring behavior at the $T$ iteration, $T$ is the number of current iterations and $T_{\max }$ is the maximum number of iterations. $p(T)$ ensures that the probability of exploration gradually decreases as time (that is, the number of iterations) $T$ increases, allowing the standard BWO algorithm to conduct extensive global searches in the early stages and more careful searches of local areas in the later stages.

Further, in order to strengthen the optimization ability of local search behavior, the algorithm is adjusted as follows:

$$\left\{\begin{array}{c}{X}_i^{T+1}=X_{best}^T+\mathsf{\Psi }(T)\times randn(1,D)\\ \mathsf{\Psi }(T)={\mathsf{\Psi }}_{\max }(1-{\displaystyle \frac{T}{T_{\max }}})\end{array}\right.$$

(4)

In this context, the variable $X_i^{T+1}$ represents the updated location of a beluga whale $i$. $X_{best}^T$ represents the optimal location of the beluga whale within the population and $\mathsf{\Psi }$ is the standard deviation over time, which is employed to adjust the degree of perturbation of the solution. Additionally, ${\mathsf{\Psi }}_{\max }$ denotes the initial maximum standard deviation, which defines the local search scope at the outset of the search. Furthermore, $randn(1,D)$ generates random numbers with a $D$-dimensional normal distribution, which are utilized to introduce random perturbations into the solution space. The nonlinear decreasing standard deviation adjustment method facilitates the gradual convergence of random disturbances from a broad range to a narrow range, thereby enabling the algorithm to achieve a fine-tuned search for the global optimal solution. This improvement to the standard BWO algorithm facilitates a balance between exploration and development stages, enabling the identification of the optimal combination of features and, consequently, an enhanced optimization effect.

2.3. Bidirectional Long Short-Term Memory (BiLSTM)

A Long Short-Term Memory (LSTM) network represents a variant of the recurrent neural network, exhibiting robust processing and analytical capabilities with regard to time series data [26]. The LSTM unit is composed of three gates—an input gate, a forget gate and an output gate—which process data in a unidirectional manner from left to right. This architecture limits the information capture ability of the unit. In order to obtain a more comprehensive understanding, scholars have enhanced the LSTM and proposed a bidirectional long short-term memory (BiLSTM) model. A BiLSTM is composed of multiple LSTM units. The underlying calculation principle is to transfer useful information for subsequent computation by forgetting and remembering new information in the cell state, while discarding useless information [19]. The specific calculation process is as follows:

First, accept the input of the current moment and the hidden state of the previous moment, and pass through the forgetting gate through the Sigmoid function:

$$\left\{\begin{array}{c}{f}_t=\sigma (w_f[h_{t-1},x_t]+b_t)\\ \sigma (x)={\displaystyle \frac{1}{1+e^{-x}}}\end{array}\right.$$

(5)

In this context, $x_t$, $h_{t-1}$, $w_f$ and $b_t$ represent the current input, the hidden state at the previous moment, the weight matrix of the forgetting gate and the bias matrix of the forgetting gate, respectively.

Based on the information from $x_t$ and $h_{t-1}$, the input gate selectively stores the target information into the cell state $C_t$ at the updated time $t$:

$$\left\{\begin{array}{c}{q}_t=\sigma (w_q[h_{t-1},x_t]+b_q)\\ a_t=\tanh (w_c[h_{t-1},x_t]+b_c)\\ C_t=f_t{C}_{t-1}+q_t{a}_t\\ \tanh (x)={\displaystyle \frac{e^x{-}^{e-x}}{e^x{+}^{e-x}}}\end{array}\right.$$

(6)

In this context, $q_t$ and $a_t$ represent the output corresponding to the input gate and input node, respectively. Similarly, $w_q$ and $w_c$ denote the weight matrices of input gates and input nodes, respectively, while $b_q$ and $b_c$ signify the bias matrices of input gates and input nodes, respectively. Finally, $C_t$ and $C_{t-1}$ indicate the cell states at time $t$ and time $t-1$, respectively.

We obtain the output gate $o_t$ based on the information from $h_{t-1}$ and $x_t$, and further determine how much information will be used as the current output or hidden state based on the output gate $o_t$ and the current cell state $C_t$:

$$\left\{\begin{array}{c}{o}_t=\sigma (w_o[h_{t-1},x_t]+b_o)\\ h_t=o_t\tanh (C_{t-i})\end{array}\right.$$

(7)

where $o_t$ is the output of the output gate; $w_o$ is the weight matrix of the output gate; $b_o$ is the bias matrix of the output gate; and $h_t$ is the hidden state of the current moment.

In conclusion, bidirectional hidden states are merged and the states of the front and back hidden layers are fused by weight coefficients as follows, thus providing a more comprehensive view of the data [23]:

$$\left\{\begin{array}{c}{h}_{t1}=LSTM(x_t,h_{t-1})\\ h_{t2}=LSTM(x_t,h_{t+1})\\ y_t=w_{h1}{h}_{t1}+w_{h2}{h}_{t2}+b_y\end{array}\right.$$

(8)

where, $w_{h1}$ and $w_{h2}$ are the connected loop weight matrix of the forward and backward LSTM layers, respectively, and $y_t$ is the final hidden layer state.

2.4. Gated Recurrent Unit (GRU)

The Gated Recurrent Unit (GRU) represents an advancement over the Long Short-Term Memory (LSTM) model. In contrast to LSTM, GRU integrates the input gate and forget gate with the update gate, resulting in a GRU model comprising solely the reset gate and update gate [18]. The GRU is capable of addressing the issues of gradient disappearance and data explosion, while also ensuring the accuracy of calculations and exhibiting robust performance in forecasting long-term series data. The precise mathematical expression is as follows:

(1)

The mathematical expression for the update gate is the following:

$$Z_t=s(w_z[h_{t-1},x_t])$$

(9)

(2)

The mathematical expression of the reset gate is the following:

$$R_t=s(w_r[h_{t-1},x_t])$$

(10)

(3)

The mathematical expression for the candidate hidden state is as follows:

$$h_t=\tanh (w[R_t\ast h_{t-1},x_t])$$

(11)

(4)

The mathematical expression for the hidden state is as follows:

$$h_t=(1-Z_t)\times h_{t-1}+Z_t\times h_t$$

(12)

In the above expression, $\sigma$ is the Sigmoid activation function; $w_z$, $w_r$ and $w$ comprise the weight matrix; $x_t$ are the input data at the time $t$; $h_{t-1}$ is the memory information of the moment $t-1$; and $h_t$ is the final hidden state of the output.

3. Examples and Methods

3.1. Study Framework

This research adheres to a systematic approach encompassing data collection, feature extraction, prediction modeling and model evaluation. Initially, pipeline corrosion data were gathered through a buried pipeline corrosion experiment to ensure adequate data preparation for subsequent analyses. Subsequently, Random Forest (RF) was employed to identify highly relevant features, while the Improved Binary Whale Optimization (IBWO) algorithm was utilized to iteratively refine the feature combinations to identify the optimal subset. Following this, the BiLSTM–GRU combined prediction model was established, with scientifically sound and accurate prediction algorithms selected for both high and low corrosion rates. Finally, the processed dataset, comprising 100 groups, was validated through practical examples, employing evaluation metrics such as mean squared error (MSE), mean absolute percentage error (MAPE), root mean absolute scaled error (RMASE), mean absolute error (MAE) and R-squared (R²) to assess the model’s performance. This provides a scientific foundation for the RF–IBWO-BiLSTM–GRU model as the optimal predictive tool for assessing the corrosion rates of buried pipelines under dynamic conditions. The overall research framework is illustrated in Figure 1.

3.2. Data Source

The fundamental dataset of this study comprises 100 sets of soil-buried experimental data along the buried pipeline section. These data were obtained from the measured data of a Chinese petroleum pipeline company’s oil and gas transportation engineering risk assessment project, and detailed pipeline parameter information is shown in

Table 1. Pipeline parameter information.

Pipeline Length	Length of Pipe Section	Grade of Steel	Pipe Diameter	Wall Thickness	Operating Life	Buried Depth Range	Outer Coating
222.5 km	3.26 km	X80	310 mm	15 mm	7 year	0.4–2.5 m	3PE

. The data collation is used in reference to the study conducted by [8]. The data collected are as follows: (1) pH value; (2) salt content; (3) water content; (4) stray current; (5) REDOX potential; (6) sulfate content; (7) pipe–ground potential; (8) soil resistivity; (9) chloride ion content; and (10) soil potential gradient. The specific analysis is as follows:

(1) PH value: The pH value of soil is an indicator reflecting the acidity or alkalinity of the soil. When the pH value is below 6.5, the soil becomes highly susceptible to corrosion. Acidic conditions with a pH below 6.5 increase the hydrogen ion concentration, significantly accelerating the corrosion reaction of metals [27]. Moreover, acidic environments can promote the activity of certain corrosive microorganisms, such as sulfate-reducing bacteria (SRB), which thrive under low pH conditions and actively contribute to microbiologically influenced corrosion (MIC) by generating sulfides that exacerbate corrosion [28].

(2) Salt content: The salt content of the soil exerts a significant influence on the external corrosion rate of buried pipelines by affecting the soil’s resistivity. A positive correlation exists between corrosion rate and salt content, where higher salt content results in increased corrosion. High salt concentrations also create favorable conditions for the growth of halophilic bacteria, a type of salt-tolerant microorganism that can accelerate MIC. Additionally, the increased salt content can enhance SRB activity, leading to a higher risk of MIC [29].

(3) Water content: An increase in soil water content increases soil corrosiveness by enhancing conductivity and creating an environment conducive to microbial growth. However, when the water content reaches a saturation point, oxygen diffusion is impeded, potentially reducing the corrosion rate of buried pipelines. High water content also provides optimal conditions for anaerobic microorganisms, such as SRB, to thrive, which significantly accelerates MIC under low-oxygen conditions [30].

(4) Stray current: Stray current is typically observed in proximity to the manufacturing facility along the route of the buried pipeline. The utilization of high-power machinery within the plant will inevitably result in the generation of stray currents, which will serve to accelerate the corrosion rate of metal pipelines used for the transportation of oil and gas.

(5) Redox potential: The redox potential of the soil is a comprehensive indicator reflecting the soil’s aeration and oxidation–reduction degree. In buried metal pipeline systems, a reduction in redox potential fosters a more reduced environment that favors anaerobic bacterial activity, including SRB. This lower redox environment promotes MIC, as anaerobic bacteria thrive and accelerate metal degradation under such conditions [31].

(6) Sulfate content: High sulfate levels in the soil accelerate the corrosion of buried oil and gas pipelines, particularly by promoting SRB activity. SRB utilize sulfate as an energy source in anaerobic conditions, converting it into corrosive sulfide compounds that can severely damage metal surfaces and create localized corrosion sites [32]. The corrosion rate of pipelines increases proportionally with sulfate content, and MIC intensifies as sulfate levels rise.

(7) Pipe ground potential: The natural potential of soil is defined as the ground potential when a metallic material is buried in the soil, without the influence of an external current. Pipe ground potential represents a significant factor influencing the electrochemical corrosion of metal materials in soil. Note: The pipe ground potential values were measured using a Cu/CuSO₄ (copper/copper sulfate) reference electrode.

(8) Soil resistivity: There is a negative correlation between soil resistivity and soil corrosion performance. Therefore, the lower the soil resistivity, the stronger the soil corrosion ability.

(9) Chloride ion content: The impact of chloride ions on pipeline corrosion can be divided into two categories: inhibition of the formation of a passivation film on the pipeline surface and destruction of an existing passivation film, which then allows corrosion to occur.

(10) Soil potential gradient: According to the industry standards “NACE SP0169 Control of External Corrosion on Underground or Submerged Metallic Piping Systems” and “SY/T0017-2006 Technical Standard for Cathodic Protection of Buried Steel Pipelines with DC Stray Current”, when the soil potential gradient is less than 0.5 mV/m, the level of stray current is relatively weak; when the soil potential gradient is between 0.5 mV/m and 5.0 mV/m, the level of stray current is moderate; and when the soil potential gradient exceeds 5.0 mV/m, the level of stray current is strong. A higher soil potential gradient can lead to accelerated pipeline corrosion.

It can be concluded, therefore, that the following factors influence the external corrosion of pipelines: pH value, salt content, water content, stray current, REDOX potential, sulfate content, pipe–ground potential, soil resistivity, chloride content and soil potential gradient. We examine the multi-factor corrosion scenario influenced by the aforementioned ten factors and predict the corrosion rate of the pipeline within this intricate corrosion context.

3.3. Data Preparation

In this study, the experimental data were first analyzed; the statistical results of embedding corrosion rate are shown in Figure 2, and the statistical results of influencing factors are shown in

Table 2. Statistical results of the dataset.

Numeric Value Scope	pH Value	Saltness/%	Water Content/%	Stray Current/(mv·m−1)	Oxidation–Reduction Potential/mV
Minimum	0.730	0.010	1.140	0.140	36.150
Maximum	9.330	0.472	45.360	1.760	520.360
Numeric Value Scope	Sulphate Root Content/%	Pipe Ground Potential/mV	Soil Resistivity/(Ω·m)	Potential Gradiant/(mV·m−1)	Chlorine Ion Content/%
Minimum	0.001	47.450	6.580	0.220	0.003
Maximum	0.151	287.150	80.230	5.010	0.162

. As illustrated in Table 2, the factors influencing the corrosion rate were found to exhibit considerable volatility. To illustrate, the pH values span a range of 0.73 to 9.33, while the tube ground potential varies between 47.45 and 287.15 mV. Nevertheless, these factors exert a significant influence on the corrosion process.

As illustrated in Figure 2, the corrosion rate exhibits a distinct trend boundary at approximately 5 mpy. The trends of the corrosion rates categorized as “0 to 5” and “above 5” are inconsistent with one another. Employing a single algorithm to analyze these two types of corrosion rates, which exhibit different trends, may lead to reduced accuracy and suboptimal fitting. Therefore, it is essential to implement different predictive models tailored for each category of corrosion rate. According to NACE RP 0775-2005 [33], an average corrosion rate below 5 mpy is classified as low or moderate corrosion, while an average corrosion rate exceeding 5 mpy is deemed high or severe corrosion. This classification standard aligns with the experimental findings in this study. By integrating industry standards with experimental results, this paper categorizes the corrosion rates into high and low categories; specific classifications are detailed in

Table 3. Corrosion rate classification standard.

NACE RP 0775-2005		Classification of This Research
Corrosion Grade	Corrosion Rate (mpy)	Corrosion Grade	Corrosion Rate (mpy)
Low	<1.0	Low	<5.0
Moderate	1.0–4.9
High	5.0–10	High	>5.0
Severe	>10

.

3.4. Pre-Training

In pre-training, this paper uses the BiLSTM and GRU algorithms for prediction analysis, where for BiLSTM, the number of nodes in the input layer is 6, the number of hidden layer nodes is 128, the time step is 10 and tanh is used for the activation function. Meanwhile, in the GRU module, the number of hidden layer nodes is 64, using the ReLU activation function.

For BiLSTM, the prediction results of the algorithm are shown in Figure 3, and those of the GRU algorithm are shown in Figure 4.

In Figure 3, the BiLSTM algorithm demonstrates a strong ability to capture bidirectional dependencies in low corrosion rate environments, accurately extracting key features. Its bidirectional structure fully leverages the forward and backward dependencies within the time series, providing reliable support for low corrosion rate predictions.

In Figure 4, the GRU algorithm demonstrates strong noise management capabilities in high corrosion rate environments. With its unique gating mechanism, the GRU effectively filters out data noise, retaining only key features to achieve stable predictions amid highly variable data. To further verify the reliability of the GRU in this configuration, we applied regularization during model training and conducted cross-validation to detect potential overfitting risks. The analysis results show that the GRU does not exhibit significant overfitting in high corrosion rate scenarios, proving its stability and suitability for handling high-noise data environments.

As illustrated in Figure 3 and Figure 4, when the corrosion rate of the pipeline continues to increase, particularly when it exceeds 5, the predictive precision of the single-algorithm prediction model is significantly diminished. Furthermore, training data encompassing all corrosion rates will also result in suboptimal training outcomes. A single prediction model is unable to adequately address the intricate dynamics inherent to the corrosion process, resulting in a significant decline in prediction efficacy. This limitation precludes the model from offering a comprehensive safety evaluation and practical reference for pipeline management. Accordingly, in the present study, the critical point of the combined model algorithm for corrosion rate prediction is identified as 5. The BiLSTM–GRU combined model is selected for prediction based on the characteristics of each algorithm. The preliminary prediction effect of the BiLSTM–GRU combined model is illustrated in Figure 5.

As illustrated in Figure 5, the correlation between the predicted and actual results is markedly enhanced following the implementation of the combined model. In order to achieve more accurate predictions of pipeline corrosion rates, this study proposes the use of a Random Forest (RF) algorithm to analyze the correlation between variables, with the aim of extracting highly correlated feature sets for different corrosion degree datasets. The significance of the RF characteristics pertaining to high and low pipe corrosion rates are illustrated in

Table 4. Importance of RF characteristics for low pipeline corrosion rates.

pH Value	Saltness/%	Water Content/%	Stray Current/(mv·m−1)	Oxidation–Reduction Potential/mV
0.101	0.085	0.103	0.161	0.127
Sulphate Root Content/%	Pipe Ground Potential/mV	Soil Resistivity/(Ω·m)	Potential Gradiant/(mV·m−1)	Chlorine Ion Content/%
0.077	0.099	0.090	0.082	0.075

and

Table 5. Importance of RF characteristics for high pipeline corrosion rates.

pH Value	Saltness/%	Water Content/%	Stray Current/(mv·m−1)	Oxidation–Reduction Potential/mV
0.187	0.093	0.117	0.105	0.071
Sulphate Root Content/%	Pipe Ground Potential/mV	Soil Resistivity/(Ω·m)	Potential Gradiant/(mV·m−1)	Chlorine Ion Content/%
0.063	0.090	0.103	0.100	0.069

, respectively.

In the context of low corrosion rates, the most significant characteristics are identified as stray current, REDOX potential and water content, with importance scores of 0.161, 0.127 and 0.103, respectively. This suggests that fluctuations in stray current have the greatest impact on corrosion of pipelines in low corrosion rate environments. Furthermore, the REDOX potential exerts a considerable influence, which is contingent upon the electrochemical characteristics of the soil and the corrosion reaction. Furthermore, soil moisture content exerts an influence on the metal corrosion rate in low corrosion rate conditions, given that the presence of moisture tends to accelerate the electrochemical corrosion process.

In the context of a high corrosion rate, the most critical factors are the pH value, water content and stray current, which have been found to have values of 0.187, 0.117 and 0.105, respectively. The weight of the pH value increases significantly at high corrosion rates, indicating that soil acidity is a significant driving factor at high corrosion rates. In comparison to a low corrosion rate environment, the impact of water content is somewhat amplified, whereas the influence of stray current is diminished. This may be attributed to the fact that the corrosion process is more reliant on the chemical characteristics of the environment at elevated corrosion rate conditions.

3.5. The RF–IBWO-BiLSTM–GRU Combined Model

In order to enhance the precision of the model’s predictions and mitigate the impact of potential confounding variables, this study proposes the utilization of IBWO for a comprehensive optimization of the feature selection process, thereby enhancing the accuracy of the selected features in relation to the initial screening of corrosion-influencing factors through RF. The RF–IBWO approach combines the feature screening capabilities of Random Forest (RF) with the optimization strengths of the Improved Beluga Whale Optimization (IBWO) algorithm, showing strong robustness in handling variations across different environmental conditions. RF is widely used in corrosion contexts for feature identification due to its low sensitivity to noise and its capacity for handling high-dimensional data [34]. The IBWO algorithm complements this by simulating the hunting behavior of beluga whales, allowing for global optimization of feature subsets even in unstable data conditions [21]. The study by Guang et al. [8] specifically validates IBWO’s feature optimization performance in dynamic corrosion conditions, where it excels in managing fluctuating environments. Additionally, Zhang et al. [35] highlights IBWO’s balance of exploration and exploitation, which enhances model stability under complex conditions. Thus, the choice of RF–IBWO for feature selection not only aligns with the demands of diverse scenarios but also strengthens predictive reliability under varying corrosion conditions.

Finally, the BiLSTM–GRU combined model based on improved Beluga Optimization algorithm and Random Forest is constructed based on the characteristics of different algorithms and experimental data results. First, the classification of high and low corrosion rates is determined according to the algorithm characteristics and experimental results. Secondly, Random Forest algorithm is used to analyze the correlation of variables in different groups and extract key features from the data. Thirdly, IBWO is used to optimize the feature selection process and find the best feature subset to improve the model performance. Finally, according to the different corrosion degrees, the corresponding model is used to predict the corrosion rate and output the predicted value. This BiLSTM–GRU combined model based on improved Beluga Optimization algorithm and Random Forest can more accurately capture corrosion characteristics of different corrosion degrees and provide more accurate prediction results. The framework of the RF–IBWO-BiLSTM–GRU prediction model is shown in Figure 6.

4. Results and Discussion

4.1. Prediction Results

The model was executed on MATLAB R2023a, and the data were divided into a training set comprising 70% of the data and a test set comprising 30% of the data. Firstly, in RF, 100 decision trees were constructed with a maximum depth of 10 and a minimum sample split set to 2. This ensured a stable feature selection effect and prevented overfitting. Secondly, in IBWO, we adopted a population size of 50 individuals, a number of iterations of 500, a spiral rise coefficient of 1.5 and an exploration-utilization balance factor of 0.5. This approach ensures that the algorithm can not only converge to the global optimal but also considers diversity and efficiency. Subsequently, the BiLSTM component comprised six input layer nodes, 128 hidden layer nodes, a time step of 10 and a tanh activation function. Additionally, within the GRU module, the number of hidden layer nodes was 64, and the ReLU activation function was employed. Figure 7 illustrates the corrosion rate prediction efficacy of the integrated model, comprising RF, IBWO, BiLSTM and GRU, on the test set.

Figure 7 illustrates that the predicted values derived from the RF–IBWO-BiLSTM–GRU model in the test set exhibited a high degree of proximity to the actual values. Following analysis, the mean absolute error (MAE) was 0.1974, the mean square error (MSE) was 0.0498, the root mean square error (RMSE) was 0.2231, the mean absolute percentage error (MAPE) was 5.29% and the coefficient of determination (R²) was 0.9876, indicating a good fit. As the model structure is refined, the predictive performance is enhanced.

4.2. Model Comparative Analysis

This paper puts forward three further neural network models for comparison and analysis. Figure 8 illustrates the test set fitting diagram of corrosion rate prediction effect based on the BiLSTM–GRU, RF-BiLSTM–GRU and RF–IBWO-BiLSTM–GRU models. From this, we can ascertain that in comparison with the other models, the RF–IBWO-BiLSTM–GRU model demonstrates superior fitting.

To evaluate model performance comprehensively, several metrics were selected: MSE and RMSE measure the average error magnitude, with RMSE giving particular weight to larger errors, while MAE assesses overall error consistency. MAPE provides accuracy in percentage terms, allowing for comparisons across different scales, and R² indicates the model’s explanatory power. Together, these metrics ensure a robust evaluation of model precision, stability and reliability.

Table 6. Comparison table of evaluation indexes of pipeline corrosion rate predicted by different models.

Model	MAE	MSE	RMSE	MAPE	R2
BiLSTM	0.5996	0.6368	0.7980	12.60%	0.8409
GRU	0.6607	0.8018	0.8954	26.02%	0.7996
BiLSTM–GRU	0.3924	0.2363	0.4861	9.50%	0.9410
RF-BiLSTM–GRU	0.3458	0.1617	0.4022	9.997%	0.9596
RF–IBWO-BiLSTM–GRU	0.1974	0.0498	0.2231	5.29%	0.9876

presents a comparison of the predictive outcomes of five distinct deep learning neural network models in relation to pipeline corrosion rate. As can be seen from Table 6, all five models are capable of effectively predicting the pipeline corrosion rate. However, when used alone, the BiLSTM and GRU models perform relatively poorly, with MAE results of 0.5996 and 0.6607, respectively, and MAPE results of 12.60% and 26.02%, respectively. This indicates that they have certain errors and instability when processing data. Furthermore, the RF-optimized RF-BiLSTM–GRU model further improved performance, with the MAE decreasing to 0.3458. However, the MAPE increased to 9.997%, indicating an improvement in the fitting but possibly falling into a local optimum. Therefore, we intend to incorporate the IBWO algorithm for subsequent refined feature selection. Ultimately, the RF–IBWO-BiLSTM–GRU model was enhanced through the integration of RF and IBWO, resulting in the RF–IBWO-BiLSTM–GRU model, which exhibited the most robust predictive capacity. The MAE was reduced to 0.1974, the MAPE was diminished to 5.29% and the R² reached 0.9876. In comparison to the BiLSTM model, the MAE decreased by 67.08%, the MSE decreased by 92.18%, the RMSE decreased by 72.04%, the MAPE decreased by 58.06% and the R² increased by 17.45%. When compared to the GRU model, the MAE showed a reduction of 70.12%, the MSE exhibited a decrease of 93.79%, the RMSE declined by 75.08%, the MAPE was reduced by 79.67% and the R² experienced an increase of 23.51%. The results demonstrate that the model attains an optimal equilibrium between prediction accuracy, resource efficiency and robustness, and exhibits considerable potential for application in the field of pipeline corrosion rate prediction.

4.3. Model Application Analysis

4.3.1. Dataset Environmental Representativeness and Model Reliability Analysis

(1) Analysis of Dataset Environmental Representativeness: Our dataset includes common environmental factors affecting steel pipeline corrosion, such as pH, salinity, soil resistivity and moisture content. These factors have been widely validated in various studies and are generally regarded as key variables contributing to pipeline corrosion [2,8]. By incorporating these multidimensional variables, our dataset provides robust environmental representation, establishing a solid foundation for the model’s adaptability across different conditions.

(2) Model Validation Based on Historical Data: For model validation, historical data collected from in-service pipeline corrosion monitoring was used to enhance the accuracy and robustness of the predictive results. This validation process ensures the model’s adaptability to real-world environmental conditions, maintaining high stability and reliability when applied to actual scenarios. Results indicate that the model performs well under various corrosion conditions, providing strong support for pipeline corrosion management.

4.3.2. Structural Adaptability of the Predictive Model and Multi-Environment Suitability Analysis

(1) BiLSTM–GRU Nonlinearity and Dynamic Adaptability: The BiLSTM–GRU model demonstrates significant advantages in handling nonlinear characteristics and dynamic changes in corrosion processes. The bidirectional dependence of BiLSTM, combined with the noise-resistant properties of GRU, enables the model to effectively handle fluctuations in corrosion rates, particularly in complex time series data [36]. Additionally, the layered design of high and low corrosion rates further enhances the model’s adaptability across different corrosion scenarios, ensuring consistent predictive accuracy across various environmental conditions.

(2) Layered Modeling Innovation Compared to Other Models: This study introduces a layered prediction method based on high and low corrosion rates, which more precisely captures dynamic characteristics at varying corrosion rates compared to traditional models. This approach not only improves predictive accuracy across diverse corrosion environments but also extends the model’s application range, offering a new modeling perspective and support tool for complex corrosion monitoring.

4.3.3. Computational Resource Requirements and Model Interpretability in Practical Applications

(1) Computational Resource Requirements and Feasibility of Real-Time Monitoring: The model’s computational demands are primarily focused on data preprocessing and feature selection, necessitating a high-performance computing platform. With efficient feature selection and distributed computing support, the model demonstrates high efficiency and suitability for large-scale real-time corrosion monitoring.

(2) Model Interpretability: The RF–IBWO-BiLSTM–GRU combined model excels in predictive accuracy. To facilitate ease of use in field operations, we suggest using a simplified version of the BiLSTM–GRU model for predictions in real-world applications. This design improves model usability, making it a reliable tool in pipeline management, and provides practical support for real-time evaluation and response to corrosion risks.

5. Conclusions

5.1. Research Conclusions and Contributions

This paper employed an algorithmic approach to investigate the predictive capacity of BiLSTM, GRU and their integrated models in the context of pipeline corrosion rate forecasting. In consideration of the distinctive characteristics between high and low corrosion rates, the enhanced Beluga Optimization algorithm and Random Forest are employed to refine the BILSTM–GRU integrated model, thereby facilitating the efficacy of feature selection and the predictive model’s performance. The efficacy of the enhanced combined model in forecasting pipeline corrosion rates was substantiated through empirical investigation.

In conclusion, this paper has made two significant contributions to the existing prediction model: (1) It proposes a combined model based on the characteristics of pipeline corrosion rate fluctuation and the large range observed in such data. Secondly, it has adopted different algorithms for high and low corrosion rate predictions, thereby improving the accuracy of the model and enhancing its overall performance. In comparison with the single BiLSTM and GRU models, the MAE of the combined BILSTM–GRU model exhibited reductions of 34.56% and 40.61%, respectively. The MSEs decreased by 62.89% and 70.53%, respectively. The RMSEs decreased by 39.09% and 45.71%, respectively. The MAPE results decreased by 24.6% and 63.49%, respectively. Nevertheless, the goodness of fit results were enhanced by 11.9% and 17.68%, respectively, and the model optimization effect was pronounced. (2) The focus is on feature screening, with the use of dual measures of RF and BWO to ensure the optimal feature subset comprising high and low corrosion rates. In this research, the initial population of BWO was optimized by chaotic mapping, and non-fluctuating linear factors were introduced to enhance the adaptability and flexibility of the algorithm, thereby ensuring the global optimization ability of BWO. This ultimately resulted in the formation of a feature screening strategy comprising “RF rough screening + IBWO fine adjustment”. The MAE of the RF–IBWO-BiLSTM–GRU model was 49.69% lower than that of the BiLSTM–GRU model with unscreened features. The MSE decreased by 78.93%, the RMSE decreased by 54.1%, the MAPE decreased by 44.32% and the goodness of fit was improved by 4.95%.

The combination of the performance analysis of the model with the BiLSTM–GRU combined model, based on the improved Beluga Whale Optimization and Random Forest, has been found to achieve the best performance. This is mainly due to the excellent ability of their combination to extract features. The combination of the Random Forest’s ability to rapidly identify pertinent features and the enhanced deep optimization feature subset of the Beluga Whale Optimization allows for more effective feature selection and, consequently, an improvement in model performance, thereby facilitating more accurate predictions and providing a scientific basis for oil pipeline maintenance and safe production.

5.2. Future Research Prospects

However, the corrosion mechanisms of petroleum pipelines are complex and varied, with a rich diversity of application scenarios. Consequently, pipeline corrosion still faces numerous challenges. Future research on pipeline corrosion prediction can focus on two primary aspects.

(1) Optimize the prediction model and improve the physical performance of the prediction model. Firstly, this paper, along with existing literature, generally adopts a 70–30 train–test data segmentation ratio. While this approach ensures a certain level of training effectiveness and stability in test results, further investigation into how this ratio impacts model stability is warranted. Future studies could explore alternative data segmentation ratios to assess their influence on model robustness and identify the most suitable segmentation methods for specific application scenarios and prediction models. This will ultimately improve the model’s predictive stability for different datasets. Additionally, future research should integrate real-time monitoring data with historical training data to bolster the model’s capacity for predicting dynamic environmental changes while enhancing response speed through monitoring the real-time data. Finally, the effect of time interval change on the stability of the model should be addressed. Verifying the corrosion rate of the pipeline at different time intervals will improve the stability and adaptability of the model under dynamic conditions, which is conducive to improving its reliability in practical applications.

(2) Enrich model application scenarios and improve model generalization ability. Although this paper primarily addresses the corrosion rates of steel pipelines, as new materials increasingly come into use within pipeline systems—such as composite materials and multi-material configurations—it becomes necessary to investigate their respective corrosion behaviors as well. Furthermore, in recent years, extreme weather has become more frequent, resulting in an increasingly complex environment around pipelines. Thus, understanding how pipelines behave under conditions such as extreme temperatures or high pressures—and within highly corrosive environments—has garnered significant attention from researchers. Finally, future studies can consider both laboratory and non-laboratory corrosion environments, compare the model effects under different operations and constantly optimize the model to enhance the scalability and adaptability of the prediction model.