The economic performance of GIS equipment is typically assessed based on its Life Cycle Cost (LCC). As shown in Figure 1, the LCC of GIS equipment consists of several types of costs: initial investment cost, operation cost, maintenance cost, failure cost, and decommissioning cost. Among these, the initial investment cost and decommissioning cost can be largely determined when the substation is completed, making them fixed costs. However, the operation, maintenance, and failure costs require annual statistics and are considered variable costs.

From the perspective of actual data collection on variable annual costs, GIS equipment in substations only began to be widely used in China in the 21st century, and related data collection activities started relatively late. As a result, the quantity of LCC data collected across different years is limited, leading to a sparse overall LCC data sample. Additionally, in the early stages of LCC data collection and transmission, manual recording methods were commonly relied upon. Consequently, issues such as insufficient cost materials, data loss, and recording errors have occurred, resulting in anomalies within the collected LCC sample data.

In summary, these data issues have created significant challenges for accurately calculating LCC data. Therefore, it is necessary to identify an appropriate data prediction method based on the characteristics of the LCC data for GIS equipment in substations. This method should aim to expand the data sample size while minimizing the impact of anomalous data on the predictions.

As discussed in Section 1.1, to achieve accurate predictions of LCC data for GIS equipment in substations, it is essential first to expand the sample size as much as possible to address the issue of limited data samples. Then, the characteristics of the data samples should be analyzed to resolve the issue of data anomalies.

Currently, under the condition that sample data exhibit certain regular variations, an effective approach to address the issue of limited sample data for prediction is to introduce similar data of the same scale as the existing sample data, thereby expanding the original dataset (Zhang et al., 2022; Wang et al., 2022; Yang et al., 2023; Cheng et al , 2022). However, considering that the data characteristics of the existing samples and the similar data may not be entirely consistent, an attention mechanism with focused characteristics is employed to quantify the influence weights between the existing sample data and similar data. The weighted data is then used as the expanded sample dataset (Tao et al., 2018). However, the attention mechanism requires manually assigned data feature vectors to process and analyze the data around these vectors. Given that LCC data for GIS equipment in substations belongs to cost data, which is significantly influenced by the actual operational conditions of the equipment, the data distribution pattern is complex, and the data features are not prominent. Therefore, manual feature extraction lacks a solid basis and accuracy. As a result, directly using the attention mechanism to obtain influence weights between data may lead to low accuracy. If a method could calculate vector weights between data to automatically extract feature vectors, enhancing the reliability of feature extraction results, it would avoid the subjectivity associated with manual feature vector extraction. This would provide an objective basis for quantifying the influence weights between existing sample data and similar data, thus improving the accuracy of data predictions.

Regarding the issue of anomalous data, after performing data preprocessing based on data distribution characteristics, it is important to consider that GIS equipment LCC data is collected and arranged in chronological order, making it sequential data. Therefore, a Recurrent Neural Network (RNN), which can capture temporal relationships, is employed for time-series data prediction (Ye et al., 2023; Li and Lin, 2018). In processing time-series data such as LCC data, RNN adjusts neural network parameters by calculating gradients according to the backpropagation algorithm and the chain rule (Kong et al., 2020) to minimize the loss function (Kong et al., 2020), thereby reducing the overall error in the prediction results. However, according to the chain rule, each parameter’s gradient expression in RNN is a product of terms, which often causes the calculated values to converge exponentially toward zero or infinity as the period increases. This leads to the gradient vanishing or exploding problem in the LCC data, raising concerns about the accuracy of the predictions. The fundamental cause of gradient vanishing or exploding in RNN lies in the linear nature of its information transfer structure. Therefore, by optimizing the internal structure of the network to selectively retain long-span information, the non-linear relationship between data points can be enhanced, suppressing the occurrence of gradient vanishing or exploding during the network training and updating process.

In summary, to achieve accurate LCC data predictions for GIS equipment in substations, we can first introduce a self-attention mechanism to enhance the feature representation of existing sample data, quantifying the influence weights between existing sample data and similar data, thereby expanding the sample size. Then, a GRU model can be employed, leveraging its gated structure to suppress the gradient vanishing or exploding issues, further improving the accuracy of the prediction results and enabling precise LCC data predictions.

Given the limited number of existing sample data, it is feasible to introduce LCC-similar data from GIS equipment in substations of the same voltage level and similar environments to expand the sample size. However, since similar data cannot fully represent the characteristics of the existing sample data, directly adding similar data to the existing samples for cost prediction would fail to achieve precise LCC calculations. Therefore, it is necessary to apply weighting to similar data based on the characteristics of the existing samples. This approach addresses the issue of reduced prediction accuracy caused by the incomplete consistency between similar data and existing sample data characteristics.

Due to the complex distribution patterns of LCC data for GIS equipment in substations, identifying correlations between data for weighting purposes requires transforming both existing sample data and similar data into matrix form. Different years are used as the row labels of the data, and various types are used as the column labels of the matrix. Based on this, a matrix representation of the existing sample data is constructed as follows: H LCC = h 11 ⋯ h 1 n ⋮ ⋮ h t 1 ⋯ h tn . (1)

In this expression, H _LCC represents the constructed matrix of existing sample data; h _tn denotes the LCC data of the n-th type in the t-th year for GIS equipment; n = 1 , 2 , 3 … , N ;   t = 1 , 2 , 3 … , T .

Considering that the similar data includes LCC data from multiple GIS equipment in substations of the same scale, the matrix is divided into sub-blocks by different substations as column references. Each sub-matrix is constructed in a manner consistent with the matrix representation of the existing sample data. To facilitate correlation comparisons between different data sets, the existing sample data is included as a reference value within the similar data, so that the matrix form of the similar data can be represented as follows: L LCC = H LCC , H LCC 1 , H LCC 2 , ⋯ , H LCC m − 1 , H LCC m . (2)

In this expression, L _LCC In this expression; H m LCCdenotes the similarity data sub-matrix composed of the LCC data from the m-th GIS equipment in substations of the same scale. The number of rows and columns in H m LCC matches those of the existing sample data matrix.

Based on the matrix constructions in Equations 1 and 2, it can be seen that the task of identifying correlations between existing sample data and similar data has been transformed into a problem of determining correlations between matrix column vectors (Zhang, 2021). According to the attention mechanism’s solving algorithm (Yin et al., 2021), the correlation between matrix column vectors can be obtained using an attention scoring function, specifically: α m = Soft max s H LCC m , H LCC . (3)

In this expression, α _m represents the weight coefficient matrix between the m-th similar data sub-matrix and the existing sample data matrix, indicating the correlation between matrices; Softmax is a normalization function; and s(·) is the attention scoring function, Considering the long time sequence of LCC data and the suitability of the dot-product model for calculating vector weight coefficients between matrices, the attention scoring function in Equation 3 employs a scaled dot-product model.

In solving matrix correlations using the scoring function, the attention scoring function performs calculations directly based on the matrix elements. Given that the LCC data of GIS equipment has inconspicuous data features, the scoring results of the attention function may lack accuracy. Therefore, an algorithm based on the self-attention mechanism (Yin et al., 2021) is introduced to determine the weight relationships among elements within the H _LCC matrix, thereby enhancing data features. When solving for weight relationships with the self-attention mechanism, to better capture the correlations between any two elements in the matrix, the H _LCC matrix needs to be transformed into three matrices through linear mapping: the LCC data query vector matrix Q _LCC, the LCC data key vector matrix K _LCC, and the LCC data value vector matrix H _LCC. Here, matrices Q _LCC and K _LCC share the same dimensions and are used to calculate the weight coefficients between column vectors of matrix H _LCC, while matrix V _LCC is used to compute the output by combining them with the weight coefficients. At this point, the weight coefficients between Q _LCC and K _LCC represent the weight coefficients between elements of the H _LCC matrix, and these coefficients can also be obtained using a scoring function: A LCC = Softmax s K LCC , Q LCC . (4)

In this expression, A _LCC represents the weight coefficient matrix of the existing sample data; Softmax is a normalization function, and s(·) is the attention scoring function. Since both matrices Q _LCC and K _LCC are also sequential data and involve calculating vector weight coefficients between matrices, the scaled dot-product formula is similarly used in Equation 4.

Since the weight coefficient matrix A _LCC obtained from Equation 4 only represents the correlations between matrix elements, to obtain a matrix with enhanced data features, it is necessary to perform matrix multiplication between A _LCC and V _LCC. This results in the data feature matrix:

Since the weight coefficient matrix A _LCC obtained from Equation 4 only represents the correlations between matrix elements, to obtain a matrix with enhanced data features, it is necessary to perform matrix multiplication between A _LCC and V _LCC, resulting in the data feature matrix: H LCC ′ = V LCC A LCC (5)

In this expression, H ʹ_LCC is the data feature matrix, with the same rows and columns as matrix H _LCC.

Furthermore, by substituting the enhanced data feature matrix H ʹ_LCC of Equation 5 into Equation 3 for calculation, the weight coefficient matrix α ʹ _m between the m-th similar data sub-matrix and the data feature matrix can be obtained. On this basis, to reduce the impact of the partial inconsistency between the data features of matrices H ʹ_LCC and H m LC on prediction accuracy, matrix α ʹ _m is multiplied by matrix H m LCC. This yields the LCC data matrix for GIS equipment in substations after expanding the sample data in Equation 6. Y LCC = α 1 ′ H LCC 1 , ⋯ , α m ′ H LCC m . (6)

In this expression, Y _LCC represents the expanded sample data matrix.

Thus, the final LCC sample data expansion model based on the self-attention mechanism is constructed, as shown in Figure 2.

Since there are anomalies in the LCC data, directly using the expanded sample data for prediction would still affect the accuracy of data predictions. Therefore, to fundamentally improve prediction accuracy, it is necessary to handle the anomalies in the LCC data. Given that anomalies in LCC data only appear at specific points in the time series, classifying them as point anomalies (Li et al., 2023), a weighted moving average method is employed to process the expanded sample data to mitigate the impact of point anomalies in the original time series: Y LCC t + 1 = ∑ i = 1 t w i Y LCC i ∑ i = 1 t w i Y LCC ′ = Y LCC 1 , ⋯ , Y LCC T T . (7)

In this expression, Y i LCC represents the expanded sample data value for the i-th year; w _i denotes the data weight for the i-th year.; i∈[1, T];t is the year for which the weighted moving average method is used for data processing; and Yʹ LCC is the expanded sample data matrix after processing.

On this basis, considering that the recurrent structure of the RNN algorithm can effectively capture the overall trend of time-series data, the RNN algorithm is introduced to predict the processed expanded sample data (Yang et al., 2023). Matrix Y ʹ LCC is used as the data input, and the RNN algorithm performs network training and prediction on the input data through its gradient calculation process. ∂ L t ∂ V = ∑ k = 0 t ∂ L k ∂ y k ∂ y k ∂ h k ∏ j = k − 1 t ∂ h j ∂ h j − 1 ∂ h k ∂ V = ∑ k = 0 t ∂ L k ∂ y k ∂ y k ∂ h k ∏ j = k − 1 t tan ⁡ h ′ · U ∂ h k ∂ V . (8)

In this expression, L _t represents the loss function of the RNN network at time t; y _k is the output of the RNN network at time k; h _j is the hidden state of the RNN network’s hidden layer at time j; tanh is the activation function of the RNN hidden layer; V is the weight parameter from the RNN hidden layer to other layers; and U is the weight parameter between hidden layers of the RNN.

From the linear multiplicative relationship in Equation 8, it can be seen that if tanh^ʹ·U is less than 1, the gradient will converge exponentially to zero as the time span of the input LCC data increases. Conversely, if tanh^ʹ·U is greater than 1, the gradient will tend towards infinity as the time span increases. Therefore, during gradient calculations over long time spans, gradient vanishing or exploding issues may arise, resulting in decreased prediction accuracy. To address this issue, considering that the LCC data for GIS equipment in substations does not belong to a large dataset, and to facilitate computation, a GRU gating structure is added to the RNN algorithm’s architecture. This modification mitigates the gradient vanishing and exploding problems caused by the linear multiplicative relationship.

The network structure with the added GRU gating structure can be expressed as follows in Equation 9: r t = σ W r x t + U r h t ‐ 1 + b r z t = σ W z x t + U z h t ‐ 1 + b z h t ′ = tanh W h x t + U h h t ‐ 1 ⊙ r t + b h h t = 1 ‐ z t ⊙ h t ‐ 1 + z t ⊙ h t ′ . (9)

In this expression, r _t is the reset gate at the current time step; z _t is the update gate at the current time step; h ^ʹ _t represents the candidate state information at the current time step; x _t is the input information at the current time step; h _t is the hidden state information passed to the next time step; h _t-1 is the hidden state information from the previous time step; σ is the sigmoid activation function; tanh is the activation function; ⊙ denotes the Hadamard product, which is the element-wise multiplication of matrices; W _r, W _z, W _h, U _r, U _z, U _h are the weight parameter matrices corresponding to the reset gate, update gate, and candidate state; b _r, b _z, b _h are the bias parameter matrices for the reset gate, update gate, and candidate state, respectively.

Thus, the multiplicative relationship expression for gradient calculation in the GRU structure becomes: ∏ j = k − 1 t ∂ h j ∂ h j − 1 = ∏ j = k − 1 t 1 − z j + U z δ z j + U h δ h j r j + U r δ r j δ z j = ∂ L j ∂ z j = ∂ L j ∂ h j h j − h j − 1 z j 1 − z j δ r j = ∂ L j ∂ r j = δ h j U h h j − 1 r j 1 − r j δ h j = ∂ L j ∂ h j = ∂ L j ∂ h j z j 1 − h j 2 (10)

In this expression: δ _zj is the partial derivative of the loss function concerning the update gate; δ _rj is the partial derivative of the loss function concerning the reset gate; δ _hj is the partial derivative of the loss function concerning the hidden state information.

By substituting the multiplicative terms in Equation 10 into Equation 8, it can be observed that the original linear multiplicative relationship in Equation 8 has been replaced by a nonlinear relationship. Consequently, the gradient vanishing and exploding issues in data prediction are resolved. At this point, the processed expanded sample data matrix can be used as input to the network, and data prediction is performed through the GRU network.

After obtaining the prediction values from the GRU network, the most commonly used metrics in time series prediction—Root Mean Square Error (RMSE) in Equation 11, Mean Absolute Error (MAE) in Equation 12, and R ² (R-Square) in Equation 13—are selected for error validation: RMSE = 1 n ∑ i = 1 n y i − y ^ i 2 , (11) MAPE = 1 n ∑ i = 1 n y i − y ^ i y i × 100 % , (12) R 2 = 1 − ∑ i = 1 n y i − y ^ i 2 ∑ i = 1 n y i − y ¯ i 2 . (13)

In these expressions: y _i represents the true value of the sample; y ^ i denotes the predicted value;n is the number of true values in the sample, y ¯ i represents the mean of the predicted values.

Combining the above analyses of the self-attention mechanism and GRU, the process begins by applying weight processing to similar data based on the self-attention mechanism to obtain expanded sample data. Then, the expanded sample data is used to train model parameters with the GRU model. Finally, the LCC data prediction results are output, and the accuracy of the prediction results is validated. The complete LCC data prediction workflow in Figure 3 is as follows.

Taking the 110 kV GIS equipment of a substation in Henan Province as an example, this substation is selected as the sample substation, and the SA-GRU model proposed in this paper is applied to predict the LCC data of GIS equipment in this sample substation. The substation currently has two main transformers, and the 110 kV side distribution device uses outdoor GIS equipment. It is located in an E-grade pollution area. The basic information on the voltage level, environment, and scale of the sample substation is shown in Table 1.

To demonstrate that the SA-GRU model proposed in this paper is suitable for predicting the LCC data of GIS equipment in substations, three similar substations are introduced to expand the LCC data samples based on the basic conditions, such as the voltage level, electrical scale, and surrounding environment of the example substation. The basic information of the introduced similar substations is shown in Table 2.

Comparing the basic information of substations in Tables 1 and 2 reveals that the three introduced substations have the same voltage level as the sample substation, with altitudes below 1,000 m, are located in an E-grade pollution area, and all GIS equipment is arranged outdoors. Substations 1 and 2 have one more main transformer than the sample substation, while Substation 3 has the same number of main transformers as the sample substation. In terms of incoming and outgoing line circuits, Substation 1 has the same number as the sample substation, Substation 2 has 4 more, and Substation 3 has 2 fewer circuits. Among these, Substation 3 has the highest similarity to the sample substation in terms of basic information, while Substations 2 and 1 have lower similarity.

After identifying the sample substation and similar substations, raw LCC data were obtained through the PMS and ERP system platforms and multidimensional lean reports. This data collection primarily focused on cost-related data, including voltage level, service life, asset original value, routine maintenance and repair material costs, major repair material costs, maintenance fees, labor costs, and other expenses. As of 31 December 2023, a total of 886 LCC sample data entries for GIS equipment were collected for the sample substation. Additionally, 4,101 LCC sample data entries were gathered for GIS equipment from the three similar substations, facilitating the expansion of LCC data samples.

A portion of the collected sample data on cost-related information for 110 kV GIS equipment is shown in Table 3.

To clearly present the data foundation of this study, Table 4 lists representative samples of the LCC time-series data collected from a 110 kV GIS unit at a substation in Henan Province. The dataset contains cost records spanning the equipment’s entire life cycle, reflecting the continuity and complexity characteristic of time-series data.

The GRU model was configured with the following hyperparameters: 64 hidden units, a look-back window (time steps) of 10, a dropout rate of 0.3, a batch size of 16, the Adam optimizer with an initial learning rate of 0.001, and 200 training epochs. These hyperparameters were selected through preliminary tuning based on validation performance, and early stopping was employed during training to prevent overfitting.

Based on the LCC sample data expansion model using the self-attention mechanism, the influence weights of LCC data for GIS equipment in different substations can be obtained. A comparison of these weights with those obtained using the direct attention mechanism is shown in Figure 4.

As shown in Figure 4, the influence weights based on the self-attention mechanism for the sample substation, Substation 1, Substation 2, and Substation 3 are 0.588, 0.115, 0.102, and 0.195, respectively. The weight results indicate that, apart from the sample substation, Substation 3 has the highest weight, likely due to the similarity of its main transformer count, main transformer capacity, and the number of incoming and outgoing circuits with those of the sample substation, differing only by 2 fewer circuits. The weights of Substation 1 and Substation 2 are nearly 50% lower than that of Substation 3, likely because Substation 1 has a higher main transformer count and capacity, and Substation 2 has a higher main transformer count and a larger number of incoming and outgoing circuits than the sample substation. These quantitative differences lead to higher LCC data values for Substations 1 and 2. Substation 2 has the lowest weight, possibly because the number of incoming and outgoing circuits on the 110 kV side has a greater impact on the LCC data values.

Comparing the influence weights of the attention mechanism in Figure 5, it can be seen that the weight of the sample substation based on the self-attention mechanism is reduced by 0.038 compared to the attention mechanism. This may be because the attention mechanism directly uses the raw sample data as sample features, whereas the self-attention mechanism extracts sample features from the raw data, leading to some differences between the two types of sample features. Except for Substation 3, the influence weights of the other similar substations based on the self-attention mechanism are all reduced. This may be because the LCC data features of Substation 3 are closer to the features extracted by the self-attention mechanism. Additionally, Substation 2 still has the smallest weight result, while Substation 3 still has the largest.

Based on the typical lifespan of GIS equipment in substations, 40 years is selected as the overall time frame for LCC, with predictions made annually. Considering that the LCC data for substation GIS equipment, even after sample expansion, still constitutes a small dataset, no validation set is created. Instead, the sample data processed in Equation 7 is split into a training set and a test set in a traditional 7:3 ratio. The training set is used to train model parameters, and the test set is used to validate the model’s training results. To maintain continuity in the time-series data during training, a segmented approach is adopted for dividing the dataset: the first 32 consecutive years of data are used for model parameter training, and the last 8 consecutive years of data are used for validation. The divided training set is fed as input to the GRU model, with only LCC values as the output. Considering the components of the model in this paper, the SA-GRU model, ATT-GRU model (Attention combined with GRU model), and GRU model are selected for a comparative analysis of the training results from different models. The training results of the different models on the LCC data of substation GIS equipment are shown in Figure 5, and the evaluation metrics RMSE, MAE, and R ² are presented in Table 4.

As seen in Figure 5, from an overall training perspective, while the GRU model’s general trend aligns with the true values, the discrepancies between its predictions and the actual values are noticeably larger than those of the SA-GRU and ATT-GRU models. The ATT-GRU model, which is an improved version of the GRU model with the inclusion of similar data during modeling, shows certain advantages in small-sample data prediction. Although its performance is not as accurate as the SA-GRU model, the overall prediction results are still better than the GRU model, closely approximating the true values, with only slight deviations at certain sample points and towards the end of the training. The SA-GRU model used in this paper provides results that are even closer to the true values compared to the ATT-GRU model. This improvement is due to the SA-GRU model’s use of a self-attention mechanism to enhance sample data features, which increases the weights assigned to similar substations that closely match the sample data features. This adjustment reduces the negative impact on prediction accuracy caused by inconsistencies between the features of similar data and sample data.

From Table 5, it can be observed that the RMSE of the SA-GRU model is 715.93 yuan, the MAPE is 1.54%, and the R ² value is 94.86%; the RMSE of the ATT-GRU model is 1039.18 yuan, the MAPE is 2.35%, and the R ² value is 91.78%; while the GRU model’s RMSE is 1677.33 yuan, the MAPE is 3.83%, and the R ² value is 83.32%. Compared to the ATT-GRU model, the SA-GRU model improves the RMSE accuracy by 31.11% and the MAPE accuracy by 34.47%, with the R ² value increasing from 91.78% to 94.86%.

To validate the accuracy of the proposed method for LCC data prediction, the proposed method was compared with the optimized partial least squares method and the fuzzy neural network method mentioned in the introduction. The training results are shown in Figure 6.

According to the evaluation index calculation formulas, the RMSE, MAE, and R ² results of different prediction methods are presented in Table 4. Combined with Figure 6, it is evident that among time-series prediction methods, the SA-GRU model demonstrates superior training performance and evaluation results compared to other methods. The optimized partial least squares (PLS) method is significantly influenced by numerical fluctuations during training, resulting in an inability to accurately capture data trends. Although the fuzzy neural network method mitigates the impact of numerical fluctuations on training, it shows weaker capability in capturing data features. These limitations cause both methods to yield less accurate prediction results than the proposed method in this paper. As shown in Table 4, compared to the optimized PLS method, the proposed method reduces the RMSE by 672.18 yuan, decreases the MAPE by 1.83%, and improves the R ² by 7.55%. Compared to the fuzzy neural network method, the proposed method reduces the RMSE by 444.64 yuan, decreases the MAPE by 1.19%, and improves the R ² by 9.18%.

To visualize the predictive performance of the best model, Figure 7 plots observed versus predicted LCC on the held-out test set. The 45° bisector (y = x) is shown as the ideal reference, together with an ordinary-least-squares (OLS) fit of predicted on observed values. The legend reports R ², RMSE, MAE, and MAPE to complement the visual assessment.

In Figure 7, points cluster around the bisector. The OLS fit y ^ = − 2403 + 1.048   x has a slope close to 1 and a small intercept, indicating limited systematic bias. Quantitatively, on the test set we obtain R 2 = 0.764 , RMSE = 1,549 yuan, MAE = 1,157 yuan, and MAPE = 3.30%, which is consistent with Table Y. The slope slightly above 1 suggests a mild overestimation at higher LCC levels (and slight underestimation for low-cost years), but the deviation is small relative to the overall range. Overall, SA-GRU provides accurate and decision-grade LCC forecasts.

In summary, the SA-GRU model proposed in this paper can effectively improve the accuracy of LCC data prediction for GIS equipment in substations.