2.1 Feature preprocessing: Low variance invalid feature elimination

Among the raw monitoring indicators of power communication networks, some indicators exhibit negligible fluctuation over the 12‑month time series. Such indicators fail to capture dynamic risk variations, while increasing computational overhead and interfering with the learning of core features. Accordingly, invalid feature removal is implemented as an initial preprocessing step [8].

Indicator validity is evaluated using time‑series variance: a smaller variance corresponds to weaker temporal fluctuation and lower sensitivity to risk changes. A variance threshold is defined to remove indicators with variance below the threshold, retaining only effective features that characterize risk dynamics.

Let the original indicator set be , where: (corresponding to samples in 12 months); (corresponding to 50 initial monitoring indicators); represents “monitoring value of th indicator in the th month”. For each indicator , calculate its variance within 12 months:

(1)

(2)

The denominator of variance formula is “12-1”, which is to make unbiased variance estimation for small samples to avoid underestimation of fluctuations. Then set variance threshold , if , it is judged as “invalid feature” and eliminated; if , it is judged as “valid feature” and retained;

In this study, the variances of all 50 initial indicators exceed 0.001, so all indicators are ultimately retained. The primary purpose of this step is noise reduction and redundancy removal, thereby preventing invalid indicators from diluting the contributions of core risk indicators.

2.2 Lightweight Temporal Attention (LTA) module

Conventional models employ fixed weights that cannot adapt to month‑specific risk scenarios. Furthermore, their weight matrices require full reconstruction when new indicators are added, resulting in high adaptation overhead. The LTA module is designed to automatically compute dynamic monthly weights, enabling direct integration of new indicators without manual intervention. Its operating principle is to quantify the importance of each indicator in a given month based on the correlation between indicators and risk levels [9].

The LTA module computes indicator weights via a streamlined workflow: first, all indicators and risk values are normalized to eliminate dimensional disparities; second, correlation scores between each indicator and monthly risk values are calculated by integrating linear correlation and nonlinear interaction terms; third, scores are nonlinearly enhanced to emphasize high-impact indicators; finally, the Softmax function is applied to convert the scores into interpretable monthly dynamic weights.

Dimension differences of different indicators will affect correlation calculation, and they need to be normalized to the same magnitude first. The normalization formula is as follows:

(3)

(4)

is the normalized value of monitoring value of item j in month i; is the normalized value of real risk value in month i; is the real risk value in month i; and are global mean and global standard deviation of all effectiveness indicators; and are mean and standard deviation of real risk value in month 12; , avoid small constant with denominator 0.

For the th month, calculate the “correlation score” between each indicator j and the risk value of the month. The higher the score, the greater the impact of the indicator on the risk of the month. The score takes into account “linear correlation” and “nonlinear synergy effect”:

(5)

The linear correlation term reflects the direct linear relationship between indicators and risks, while the nonlinear interaction term captures the synergistic effect of indicators and risks.

The correlation score is processed in two steps to generate the final weight . First, is raised to the power of 1.5 to make the advantage of high-scoring indicators more significant and avoid weight averaging:

(6)

where is to ensure that the score is non-negative, and when the score of the unrelated index is < 0, it is treated as 0.

Then introduce the parameter to control the weight differentiation degree, the smaller , the more significant the weight difference, and convert it into weight through Softmax:

(7)

Multiply the original metrics by the weights so that the impact of the core metrics is amplified and the secondary metrics are weakened:

(8)

is a 12 × 50 weighted index matrix for subsequent regression prediction.

2.3 Elastic Net (EN) regression

The core of Elastic Net lies in the integration of L1 and L2 regularization. This combined formulation balances fitting accuracy, generalization capability, and feature selection, rendering the model well suited for small‑sample scenarios.

The objective function of the model is to find regression coefficients (predictive contribution of the indicator to risk) and bias term (adjustment for prediction bias) such that “prediction error is minimal” and “coefficients are not too large”:

(9)

The prediction error term (MSE) is a measure of the deviation between the predicted value and the true value, where is the sum of the weighted index multiplied by the coefficient, which is the core prediction term; is the bias term, and if the predicted value is generally low, is adjusted upward; is a small monthly adjustment term, and is a random number from 0 to 1, simulating actual fluctuations.

The L1 regularization term filters redundant features, and the logarithm sums the absolute values, forcing “the coefficients of unimportant indicators to shrink to 0”; where is the regularization strength, and the larger the value, the stricter the screening.

The L2 regularization term suppresses overfitting and squares the coefficients to avoid “excessive individual index coefficients”; the larger , the stronger the restriction on large coefficients.

Then there is the solution of the model, because our sample number is much smaller than the characteristic number, direct solution is easy to appear “matrix irreversibility”, using the minimum norm solution (lsqminnorm) to ensure stability:

(10)

Where is the weighted index matrix and 12-dimensional full 1 vector (incorporating bias term ); is the true risk-bias term-adjustment term vector; is the regularization parameter to ensure that the L2 constraint takes effect. After solving, the prediction value for the ith month is:

(11)

3.1 Risk index system of electric power communication network

To better illustrate the complexity of risk factors in power communication networks and the rationale underlying indicator system construction, this section elaborates on two dimensions: multi-source risk drivers and indicator screening criteria, with emphasis on the rationality of factor classification and validity of indicator selection [10].

Owing to the extensive coverage and diverse service types of power communication networks, fault risk arises from multi-factor synergistic effects. Risk level is not determined by a single variable, but by the combined influence of multidimensional factors including equipment and line quality, service distribution, external environmental interference, man-made damage, and operation and maintenance management. Based on attribute differences and impact pathways, risk factors are categorized into five core groups, whose definitions and key characteristics are described below.

First, optical cable risk factors are closely associated with the basic availability of service channels in power communication networks. They mainly stem from inherent cable faults and defects, including channel interruptions due to optical fiber breakage, insufficient service bearing capacity caused by fiber core shortages, fault repair efficiency reflected by average optical cable defect duration, and emergency response effectiveness indicated by the number of optical cable fault timeouts.

Second, communication equipment risk factors concern the stability of core transmission equipment. Key contributors include communication equipment failures, equipment N-1 defect rate (impact of single-equipment failure on system robustness), communication DC power redundancy rate (power supply backup capability), and average service life of communication equipment (failure probability escalation due to aging).

Third, service operation risk factors reflect the operational status and integrity of protection mechanisms for service channels. Major risk points include the number of service interruptions (direct measure of service impact), co-routing of critical services in the transmission network (failure chain risk caused by path uniformity), service dual-channel rate (redundant channel support capability), and transmission service channel availability (ratio of normal operating time to total time).

Fourth, operation and maintenance management risk factors arise from institutional gaps and inadequate implementation. They are mainly reflected in the number of unconfirmed alarms (risk warning response delay), unrectified defects (resolution delay for known issues), delayed maintenance tasks (insufficient preventive maintenance), and other similar indicators. Although such risks do not directly disrupt equipment or channels, they can exacerbate the consequences of other risk events.

Fifth, environmental risk factors encompass internal and external disturbances to network operation. These include indoor issues such as suboptimal equipment room conditions (e.g., failed temperature and humidity control) and outdoor threats such as improper construction (e.g., optical cable damage by external forces), severe weather (e.g., equipment malfunction due to rainstorms or snowstorms), and unauthorized sabotage.

Considering the complexity of the aforementioned risk factors and the availability of indicator data, this study adopts the core objectives of risk assessment and construction principles of the assessment system [11] as dual guidelines. Key variables that are directly related to risk levels and support quantitative measurement are selected from the five categories of risk factors, leading to the establishment of the power communication network risk assessment indicator system. The detailed composition is presented in Table 1.

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Table 1. Risk assessment index system.

https://doi.org/10.1371/journal.pone.0354026.t001

3.2 Risk assessment method based on LTA-EN model

The basic framework of the proposed LTA-EN model-based risk assessment method is shown in Fig 1, which is implemented mainly through the following two steps:

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Fig 1. Flow chart of risk assessment method.

https://doi.org/10.1371/journal.pone.0354026.g001

1. (1) The overall process of the LTA module for dynamically focusing on core risk indicators is divided into training and evaluation stages. First, based on monthly historical data from the training set, standardized monthly data of each indicator within the established risk indicator system and the true risk values of corresponding months are fed into the LTA module to calculate the correlation priors between each risk indicator and risk values. Specifically, the correlation score between each indicator and the risk value is computed first, followed by nonlinear enhancement of these scores. After introducing a weight differentiation coefficient, Softmax function normalization is performed to generate historical benchmarks reflecting the correlation strength between each indicator and risk values. For the month to be evaluated, only standardized indicator data of the current month is input into the LTA module. Combined with the above historical correlation priors and interactive features of current‑period indicators, the module generates dynamic weights for each indicator of the evaluated month. Finally, standardized indicator values are element‑wise multiplied by their corresponding dynamic weights to output a weighted indicator matrix that focuses on key risk points. This matrix retains original indicator information while enhancing the contribution of core indicators to risk assessment, providing precise inputs for subsequent model prediction.
2. (2) Taking the weighted indicator matrix obtained in the first step as input features and corresponding monthly true risk values as output labels, model training and prediction are implemented. The training set and validation set are partitioned at a ratio of 1:11 for cross‑validation to mitigate data partitioning bias under small‑sample conditions. The grid search method is adopted to traverse the intervals of L1 and L2 regularization coefficients, and the parameter combination with the minimum validation set error is selected. These parameters are substituted into the Elastic Net (EN) regression model, and the optimal regression coefficients and bias term are solved via the minimum‑norm solution method to complete model training. The weighted indicator matrix of the month to be evaluated is imported into the trained model to directly output the monthly risk prediction value, realizing the mapping from indicator data to quantitative risk assessment.

4.1 Experimental data and parameter settings

The data of each evaluation index in Table 1 consists of the following data: T45 ~ T46 are meteorological statistical data, and the rest index data are statistical data of communication network of a certain provincial company [12]. Each index has statistical data of twelve months, and the risk value of each month is calculated according to the scoring standard of a certain company.

In terms of evaluation indicators, three quantitative indicators commonly used in small sample scenarios are used to evaluate model performance to avoid the limitations of a single indicator:

1. (1) Mean absolute error (MAE): measures the average deviation between the predicted value and the true value . The smaller the value, the more accurate the prediction. The formula is:

(12)

1. (2) Root mean square error (RMSE): amplifies the effect of larger errors to better reflect the prediction accuracy in extreme scenarios. The formula is:

(13)

1. (3) Coefficient of determination (R²): measures the degree of fitting of the model to the data, and the value range is [0,1]. The closer R² is to 1, the better the fitting effect of the model is. The formula is:

(14)

where is the mean true risk value.

The experiment is implemented on MatlabR2022b platform, and the core parameters of LTA-EN model are determined after grid search optimization, as follows:

1. LTA module: nonlinear interaction coefficient 0.3, score enhancement power 1.5, weight differentiation coefficient T = 0.5;
2. EN regression module: L1 regularization coefficient , L2 regularization coefficient , solution method is minimum norm solution (lsqminnorm).

4.2 Performance analysis and result visualization of LTA-EN model

Experimental results obtained from code execution are presented using three types of core metrics: dynamic indicator weights, predicted risk values, and prediction errors. Dynamic indicator weights are visualized using a heatmap, as shown in Fig 2.

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Fig 2. Monthly indicator weights distribution chart.

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This heatmap illustrates the weight distribution of each monitoring indicator across the 12 months. A deeper blue color corresponds to a higher weight value, indicating that the corresponding indicator contributes more significantly to the risk assessment result in that month. By presenting the monthly indicator weight distribution, dynamic changes in risk scenarios can be tracked in a timely manner, enabling operation and maintenance personnel to identify key risk points requiring attention each month without excessive reliance on empirical judgment, thereby avoiding inefficient resource allocation to low-impact indicators. When abnormal fluctuations in risk values occur in a given month, the underlying causes can be rapidly identified by analyzing weight variations, reducing fault localization time. Meanwhile, the temporal trends of dynamic weights provide intuitive verification of the consistency between model behavior and actual operational characteristics. This framework also delivers a unified data reference for multiple departments including line inspection, equipment maintenance, and service management, supporting coordinated work focused on high-weight indicators each month and promoting improved efficiency in operation and maintenance as well as risk control.

The risk prediction values and prediction errors of the model run are then shown in the following Table 2:

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Table 2. Comparison of predicted and true values of this method.

https://doi.org/10.1371/journal.pone.0354026.t002

Three core evaluation metrics of the LTA-EN model were computed: the mean absolute error (MAE) is 0.0032, the root mean square error (RMSE) is 0.0049, and the coefficient of determination (R²) is 0.9999. The results indicate stable prediction performance of the model: both MAE and RMSE remain at low magnitudes, suggesting small average deviations between predicted and actual values. Even in March, September, and other months with relatively large absolute errors, deviations range only from 0.009 to 0.01, which meets the engineering precision requirements for risk assessment in power communication networks. The R² value is close to 1, implying that the model accounts for 99.99% of the variance in risk values and yields sound fitting performance. This reflects the capability of the LTA module in dynamically weighting core risk indicators and verifies the stable fitting performance of the EN regression model under small-sample conditions.

As part of the experimental evaluation, statistical analysis was performed to quantify prediction uncertainty, test statistical significance, and evaluate model robustness.Uncertainty quantification was implemented via bootstrap resampling with 1000 iterations. The original 12 month dataset was randomly resampled with replacement repeatedly, and the LTA EN model was retrained and validated on each resampled subset. The 95% confidence intervals of key metrics were derived from the 2.5th and 97.5th percentiles of the bootstrap distribution, yielding MAE = [0.0028, 0.0036], RMSE = [0.0045, 0.0053], and R² = [0.9997, 0.9999], which characterize the variability of prediction performance.

Two tailed t tests were further conducted to examine whether performance differences between the proposed model and comparative methods are statistically significant. The results show that the MAE reductions relative to the two baseline models are statistically significant at the 95% confidence level (p < 0.05), ruling out random chance as a primary cause.

In addition, a parameter sensitivity analysis was carried out to assess robustness. Key hyperparameters including L1/L2 regularization coefficients and the nonlinear interaction coefficient in the LTA module were varied within reasonable ranges, and minor Gaussian noise was added to input indicators. Performance fluctuations remained within 5%, indicating stable prediction behavior under slight input and parameter variations.

Overall, the results confirm that the proposed method presents reliable and stable performance in quantitative risk prediction. It can provide quantitative support with four decimal places of precision for operation and maintenance decision-making of power communication networks and helps enhance the refinement level of risk management.

Finally, to verify the performance of the proposed risk assessment method, comparative experiments against representative benchmark methods are conducted. First, the experiments use the same 12-month small-sample dataset from a provincial power communication network as used for the LTA-EN model, ensuring a consistent data basis. Second, two methods are selected for comparison: fixed-weight linear regression and complex attention-based ridge regression. The fixed-weight linear regression method employs expert experience to assign static indicator weights, which are invariant across months and involve no regularization. The complex attention-based ridge regression method adopts a multi-layer attention mechanism with three fully connected layers to compute weights and uses ridge regression (L2 regularization only); parameters of both benchmark methods are optimized via grid search to avoid bias from suboptimal parameter settings. Finally, three metrics are uniformly adopted for performance comparison: MAE, small-sample generalization error (standard deviation of leave-one-out cross-validation errors over 12 folds), and core indicator recognition efficiency (matching rate between the top 5 weighted indicators and the actual monthly core risk indicators), ensuring consistent comparison dimensions. The predicted values of each comparative experiment are listed in Table 3 below, with the corresponding error values shown in parentheses.

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Table 3. Comparison of predicted values under different assessment methods.

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Over the 12‑month period, apart from March, September and October where risk values fluctuate noticeably, prediction errors of the LTA‑EN model are kept within 0.001. Its overall error remains consistently lower than those of the two comparative models. For instance, in February, the error of the LTA‑EN model is only 0.00004, whereas that of the fixed‑weight model reaches 0.01178, representing a substantial performance gap that demonstrates the effectiveness of dynamic weighting and dual regularization in improving prediction accuracy.

Further comparisons among different models are conducted in terms of three core metrics: mean absolute error (MAE), small‑sample generalization error (SSGE), and core indicator recognition efficiency (CIRE), as summarized in Table 4.

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Table 4. Comparison of core performance indicators of different models.

https://doi.org/10.1371/journal.pone.0354026.t004

The MAE of the LTA-EN model is 23.4% lower than that of the fixed-weight model and 12.1% lower than that of the complex attention model. Its small-sample generalization error is 10% lower than those of the comparative models, indicating that the model does not exhibit overfitting and maintains higher stability under the 12-month small-sample condition. In terms of core indicator recognition efficiency, the LTA-EN model outperforms the fixed-weight model by 40%, showing better adaptability to dynamic risk scenarios.