A small sample data driven borehole wall strain trend prediction method

Abstract

This invention discloses a wellbore strain trend prediction method driven by small sample data. The method mainly includes five steps: data acquisition, data preprocessing, construction of a data augmentation module, construction of a hybrid prediction module, and verification of the trend prediction model. In step 3, the data augmentation module addresses the non-stationary nature and small sample size of wellbore strain data by designing a collaborative network architecture of "data augmentation-hybrid prediction." Through a three-stage processing flow of "stationarization-enhancement-reduction," it generates augmented data with consistent statistical features and diverse patterns, solving the problem of insufficient training samples. In step 4, the hybrid prediction module integrates the advantages of statistical methods and neural networks. Using a prediction framework of "statistical features as the core and neural networks as calibration," it adaptively adjusts the contribution of each prediction method through a dynamic weight allocation mechanism and introduces conservative post-processing to ensure the engineering rationality of the prediction results. The data augmentation module in step 3 and the hybrid prediction module in step 4 constitute the core wellbore strain trend prediction model of this method. This invention can effectively predict the long-term evolution trend of wellbore strain and, combined with a set safety threshold, achieve early warning functionality, making it suitable for proactive early warning in wellbore safety monitoring systems.

Description

Technical Field

[0001] This invention belongs to the field of time series prediction technology, and in particular relates to a method for predicting wellbore strain trends driven by small sample data. Background Technology

[0002] In recent years, my country's shaft construction has shown a significant trend towards "deepening," with drilling depths reaching nearly 2000 meters in 2024 and poised to advance to 3000 meters. As a crucial channel connecting the surface and underground mining spaces, the long-term stability of vertical shafts directly impacts the overall mine's production safety and operational efficiency. The long-distance, highly interfering underground transmission environment leads to high data transmission delays, further restricting the early warning capabilities of real-time monitoring. With the continuous increase in mining depth, the formation stress state becomes more complex. The combined effects of non-uniform ground pressure, strong seepage, and high geothermal temperatures on the shaft wall make its stress and deformation mechanisms increasingly complex, rendering traditional monitoring methods insufficient to meet the needs of advanced early warning for deep shafts. Therefore, to overcome the bottleneck caused by data transmission delays and enhance the ability to proactively perceive and predict shaft wall safety, predicting shaft wall strain trends can effectively compensate for the time lag in data acquisition, allowing for early assessment of shaft wall deformation trends. This transforms reactive, post-event responses into proactive, pre-event warnings, providing a new technological path for the long-term stability of shafts.

[0003] Currently, research on wellbore deformation prediction methods can be divided into two categories: one is based on establishing numerical prediction models according to mechanical theory. Liu Xiangjun established a two-dimensional plane strain numerical model to simulate the wellbore stress distribution under different wellbore sizes to evaluate wellbore deformation. For details, see "Liu Xiangjun, Ding Yi, Cao Guangfu, et al. Study on stability of large-size wellbore in upper part of ultra-deep well [J / OL]. Journal of Coal Science and Technology, 1-11 [2025-12-09].". Yang established an elliptical wellbore model based on strain softening behavior to quantify the deformation characteristics of the wellbore. For details, see "YANG XR, WANG Q, XU J, et al. Strain-Softening-BasedElliptical Wellbore Model for Horizontal In-Situ Stress Prediction and Wellbore Stability Analysis in the Wujiaping Formation of Kaijiang-LiangpingBlock, Eastern Sichuan Basin, Sichuan Province [J]. Processes, 2025, 13:3326.". Cheng Hua, based on the theory of random media and hydrophobic consolidation of soil, elucidated the formation deformation mechanism and inverted the calculation of shaft deformation displacement. For details, see "Cheng Hua, Zhang Liangliang, Yao Zhishu, et al. Shaft deviation mechanism in asymmetric mining of thick loose layer and thin bedrock [J]. Journal of Coal Science and Technology, 2022, 47(01):102-114." Secondly, a prediction model was trained based on historical monitoring data. Liu Hui used various deep learning models to realize the short-term prediction of vertical shaft tilt deformation in thick water-bearing loose layers, verifying the superior accuracy of the proposed 1DCNN model. For details, see "Liu Hui, Li Guoqiang, Zhu Xiaojun, et al. Shaft deformation prediction model and application based on deep learning [J]. Journal of Coal Science and Technology, 2025, 50(02):732-747." Zhang used a stacking ensemble algorithm to predict the fracture pressure of the wellbore. For details, see “ZHANG H, REN Y, ZHANG Y, et al. Intelligent prediction method for fracture pressure based on stacking ensemble algorithm[J]. Geomechanics, Geophysics, Geo-energy, Geo-resources, 2023, 9:149.”Gao's physical constraint-based deep learning framework introduces a uniform adoption strategy and displacement method to optimize the PINNs model, enabling the prediction of stress fields in heterogeneous wellbores. For details, see "GAO J, CHEN F, WANG Q, et al. Application of Physics-Informed NeuralNetworks Model to Determine the Stress Field Around the Wellbore[J]. International Journal of Applied Mechanics, 2025, 17(12).".

[0004] While current research has to some extent compensated for the time lag in data transmission and transformed safety assessment from a passive response that relies on "real-time status" to an active early warning based on "strain prediction," researchers' data-driven methods mostly rely on short-term data and have not explored the long-term evolution trend of wellbore stress and strain to study the process of wellbore deformation evolution. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method for predicting wellbore strain trends driven by small sample data. This method can effectively predict the long-term evolution trend of wellbore strain and, combined with a set safety threshold, achieve an early warning function, which can be used for proactive early warning in wellbore safety monitoring systems.

[0006] A method for predicting wellbore strain trends driven by small sample data, characterized by the following steps:

[0007] Step 1, Data Acquisition: Distributed optical fibers are laid on the inner wall of the wellbore to collect wellbore strain data at various measuring points inside the wellbore;

[0008] Step 2, Data Preprocessing: First, the absolute value of the collected wellbore strain data is taken, and then the maximum monthly strain value of each month within the collection period is taken to construct the wellbore strain dataset. The dataset is divided into a wellbore strain training set and a wellbore strain test set in a 7:3 ratio.

[0009] Step 3: Data Augmentation Module Construction: Input the wellbore strain training set into the sequence stabilization module of the wellbore strain trend prediction model driven by small sample data. The sequence stabilization module needs to calculate the following variables when performing stabilization:

[0010] The sequence is divided into three equal-length sub-segments. The mean and variance of the i-th sub-segment are calculated as a percentage of the entire sequence to compare the statistical characteristics of each segment. and ;

[0011] Calculate linear regression to assess trend strength First-order autocorrelation coefficient Through a comprehensive stationarity scoring mechanism, the following was determined: , , , We perform a weighted combination and select the method with the lowest score as the optimal sequence stabilization method.

[0012] The stabilized sequence is input into the pattern-aware data augmentation module of the wellbore strain trend prediction model driven by small sample data. Data augmentation is performed through the augmentation strategy matrix in the pattern-aware data augmentation module and the physical scale of the augmented data is restored through the scale restoration and reconstruction module.

[0013] Step 4: Construction of the Hybrid Prediction Module: The fused dataset constructed from the original data and augmented data is input into the hybrid prediction module of the wellbore strain trend prediction model driven by small sample data. This module performs fusion predictions of each branch and outputs the final prediction results via a conservative post-processing module based on a dynamic weight allocation strategy.

[0014] The hybrid prediction module predicts according to the following formula:

[0015] In the formula, This is the final predicted value. This is a trend forecast value. This is a seasonal forecast. The LSTM branch predictions are denoted by α, β, and γ, which represent the weights of each strategy's predictions. CV is the distortion coefficient. A threshold of 0.25 is used to measure sequence volatility and determine the weights of each strategy's predictions, i.e., α, β, and γ. The standard deviation of the sequence. The mean of the sequence. The base prediction is based on a weighted average, T is the final time step of the training sequence, and w i Let be the weight for the i-th time step, m be the moving window size, k be the recent slope trend, n be the trend calculation window, and h be the prediction step size. The average of the last 12 months of the training sequence. Determine the average skewness of the periodic position corresponding to the prediction time, s i Calculate the average skewness of each period position. The mean position of the i-th period in the training set. Let y be the overall mean of the sequence. min and y max These are the minimum and maximum values ​​of the training sequence, respectively. It is the value of the sequence normalization.

[0016] Step 5: Validation of the trend prediction model: Validate the final predicted value in Step 4 using the wellbore strain test set described in Step 2.

[0017] Furthermore, in step 3, the data augmentation module expands the original monitoring data of a small sample to generate enhanced data with consistent statistical characteristics and pattern diversity; the data augmentation module consists of a three-order augmentation framework of "sequence stabilization processing - pattern-aware data augmentation - scale restoration and reconstruction";

[0018] Furthermore, in step 3, the sequence stabilization module, while preserving the core fluctuation pattern and potential regularity of the sequence, analyzes the mean stability, variance stability, trend strength, and autocorrelation of the sequence. For each dataset, it automatically selects the optimal stabilization strategy from five stabilization strategies: linear detrending, first-order differencing, percentage change, moving average detrending, and polynomial detrending. A comprehensive stationarity scoring mechanism is designed to... , , , We perform a weighted combination and select the method with the lowest score as the optimal sequence stabilization method.

[0019] Further, in step 3, the pattern-aware data enhancement module first analyzes the sequence pattern: calculates the standard deviation and range of the stationary sequence; calculates the seasonal variance ratio for the original sequence period to detect its seasonality, and calculates the sequence autocorrelation to assess volatility clustering; then, based on the stabilization method, it designs an enhancement strategy matrix: for sequences using the moving average detrending strategy, noise is injected, cubic spline interpolation is used to scale the time axis, and the sequence amplitude is adjusted by combining rolling standard deviation to maintain short-term volatility characteristics; for sequences using the linear detrending strategy, a slight trend component is introduced on top of the basic enhancement; for sequences using the difference strategy, the incremental characteristics of the sequence are maintained through volatility scaling technology; for sequences using the percentage change strategy, their amplitude is adaptively adjusted; and through the above enhancement matrix, a stationary enhanced sequence is generated.

[0020] Furthermore, in step 3, the scale restoration and reconstruction module, through the forward-inverse transformation system, provides a corresponding inverse transformation algorithm for each stabilization strategy, restricts the physical scale consistency between the augmented data and the original data, and finally constructs a fused dataset containing the original data and the augmented data;

[0021] Furthermore, in step 4, the hybrid prediction module uses a prediction framework that is "based on statistical features and calibrated by neural networks". It integrates the results of each prediction branch through a dynamic weight allocation mechanism and outputs the final prediction value after conservative post-processing.

[0022] Furthermore, in step 4, the hybrid prediction module inputs a fusion dataset, uses statistical methods as the core of prediction, and an LSTM neural network as the correction, and performs fusion prediction through three branches: trend prediction, seasonal prediction, and lightweight LSTM. A dynamic weight allocation mechanism is introduced to automatically adjust the contribution weights of the three branches according to the data fluctuation characteristics to fuse the prediction results. At the same time, conservative post-processing combined with engineering practice is used to constrain and smooth the prediction results to ensure the physical rationality and temporal continuity of the output.

[0023] Furthermore, in step 4, the conservative post-processing module adopts a three-point center weighting strategy and threshold connection correction. The former suppresses high-frequency random noise, and the latter eliminates jump errors.

[0024] The beneficial effects of this invention are:

[0025] This invention proposes a small-sample data-driven method for predicting wellbore strain trends. First, strain data from various measuring points within the wellbore are collected using distributed optical fibers. Considering the non-stationary and small-sample characteristics of the wellbore strain dataset, data preprocessing is performed, and the training and test sets are divided in a 7:3 ratio. A data augmentation algorithm is designed, employing a three-order augmentation framework of "sequence stabilization processing - pattern-aware data augmentation - scale restoration and reconstruction." Augmented data is generated based on the original training set data to meet the data volume requirements of the prediction network. A comprehensive stationarity scoring mechanism is designed to analyze the mean stability, variance stability, trend strength, and autocorrelation of the sequence to automatically select the optimal stabilization strategy. Based on the characteristics of the stabilization method, an augmentation strategy matrix is ​​designed. A forward-inverse transformation system is used to restore the augmented sequence to its original physical scale. Finally, a fused dataset of "original training set data + augmented data" is constructed. Secondly, the aforementioned fused dataset is input, and statistical methods are used as the core of prediction, with an LSTM neural network as the correction mechanism. A fusion prediction is performed through three branches: trend prediction, seasonal prediction, and a lightweight LSTM network. A dynamic weight allocation mechanism is introduced to automatically adjust the contribution weights of the three branches based on data fluctuation characteristics, and the prediction results are then fused: for highly volatile data, the stability of moving averages is emphasized, while for stable data, seasonal patterns are utilized. The lightweight LSTM network captures the nonlinear dependencies of the sequence, and a conservative post-processing module, combined with engineering practice, performs range constraints and smoothing on the prediction results to ensure their physical rationality and temporal continuity. This wellbore strain trend prediction method can effectively predict the long-term evolution trend of wellbore strain and, combined with a set safety threshold, achieve an early warning function, which can be used for proactive early warning in wellbore safety monitoring systems. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a structural diagram of the data augmentation module of the trend prediction model in an embodiment of the present invention.

[0028] Figure 2 This is a structural diagram of the hybrid prediction module of the trend prediction model in an embodiment of the present invention.

[0029] Figure 3 This is the network architecture of the trend prediction model in this embodiment of the invention.

[0030] Figure 4 This is a prediction effect diagram of the trend prediction model in an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0032] A method for predicting wellbore strain trends driven by small sample data, characterized by the following steps:

[0033] Step 1, Data Collection:

[0034] Distributed optical fibers are laid on the inner wall of the wellbore to collect wellbore strain data at various measuring points inside the wellbore.

[0035] Step 2, Data Preprocessing:

[0036] First, the absolute value of the collected wellbore strain data is processed. Then, the maximum monthly strain value of each month within the collection period is taken to construct the wellbore strain dataset. The dataset is then divided into a wellbore strain training set and a wellbore strain test set in a 7:3 ratio.

[0037] Step 3: Building the data augmentation module:

[0038] The data augmentation module employs a three-tiered augmentation framework comprising sequence stabilization, pattern-aware data augmentation, and scale restoration reconstruction. This framework is designed for adaptive data augmentation of non-stationary time series, generating augmented data from the original time series data to address the insufficient data volume issue during the training of the hybrid prediction module. First, a comprehensive stationarity scoring mechanism is designed to analyze the mean stability, variance stability, trend strength, and autocorrelation of the sequence to automatically select the optimal stabilization strategy. Second, based on the characteristics of the stabilization method, an augmentation strategy matrix is ​​designed. Finally, using a forward-inverse transformation system, the augmented sequence is restored to its original physical scale, constructing a fused dataset of "original data + augmented data."

[0039] like Figure 1 As shown, the sequence stabilization module evaluates the stability of the original sequence through statistical characteristic analysis, trend strength detection, and seasonality identification modules. It automatically selects the optimal stabilization strategy from five options: linear detrending, first-order differencing, percentage change, moving average detrending, and multinomial detrending. The pattern-aware data augmentation module analyzes the pattern characteristics of the stationary sequence from three aspects: volatility analysis, seasonality detection, and autocorrelation analysis. Based on the characteristics of the stabilization methods for the stationary sequence, it designs an augmentation strategy matrix: for sequences using the moving average detrending strategy, noise is injected, and cubic spline interpolation is used to scale the time axis, combined with rolling standard deviation to adjust the sequence amplitude, maintaining short-term volatility characteristics; for sequences using the linear detrending strategy, a controllable slight trend component is introduced on top of the basic augmentation; for sequences using the differencing strategy, the incremental characteristics are maintained, and volatility scaling techniques are used; for sequences using the percentage change strategy, their relative change patterns are maintained, and amplitude adaptive adjustments are made. The scale restoration and reconstruction module constructs a forward-inverse transformation system of "trend reconstruction-integral restoration-moving average recovery" to restrict the physical scale consistency between the augmented data and the original data. For each stabilization strategy, a corresponding inverse transformation algorithm is given to construct a fused dataset composed of the original data and the augmented data.

[0040] An adaptive selection and best-fit stationarization method for wellbore strain training set is proposed, along with a comprehensive stationarity scoring mechanism. First, the sequence is divided into three equal-length sub-segments, and the proportion of the mean and variance of the i-th sub-segment to the entire sequence is calculated. , To compare the statistical characteristics of each segment, the trend strength TS is assessed through linear regression, and the first-order autocorrelation coefficient is calculated. .Will , , , A weighted combination is performed, and the method with the lowest score is selected as the optimal sequence stabilization method. The specific calculation method is shown in the following formula:

[0041]

[0042] in , Let be the mean and variance of the i-th segment, respectively. The slope is the linear regression slope, and n is the sequence length. The value of the time series at time t. The value is lagged by one period. Let n be the mean of the entire time series, and n be the length of the time series.

[0043] First, the sequence patterns are analyzed: the standard deviation and range of stationary sequences are calculated; for the period of the original sequence, the seasonal variance ratio is calculated to detect its seasonality; and the autocorrelation of the sequence is calculated to assess volatility clustering. Based on the characteristics of the stationarization method, an enhancement strategy matrix is ​​designed: for sequences using the moving average detrending strategy, noise is injected, cubic spline interpolation is used to scale the time axis, and the sequence amplitude is adjusted by combining rolling standard deviation to maintain short-term volatility characteristics; for sequences using the linear detrending strategy, a controllable slight trend component is introduced on the basis of basic enhancement; for sequences using the difference strategy, the incremental characteristics are maintained, and volatility scaling techniques are used; for sequences using the percentage change strategy, the relative change pattern is maintained, and the amplitude is adjusted adaptively.

[0044] Finally, a forward-inverse transformation system is employed to ensure that the augmented data expands sample diversity while strictly limiting its physical scale consistency with the original data. For each stabilization strategy, a corresponding inverse transformation algorithm is provided. Ultimately, a fused dataset containing both the original and augmented data is constructed.

[0045] Step 4: Construction of the hybrid prediction module:

[0046] like Figure 2 As shown, the hybrid prediction module takes into account a fused dataset consisting of original and augmented data. Using statistical methods as its core and an LSTM network as an auxiliary calibration tool, it performs fusion prediction through three branches: trend prediction, seasonal prediction, and a lightweight LSTM. A dynamic weight allocation mechanism is introduced to automatically adjust the contribution weights of the three branches based on data volatility characteristics, fusing the prediction results: high-volatile data emphasizes the stability of moving averages, while stable data utilizes seasonal patterns. The lightweight LSTM network captures nonlinear dependencies, and a conservative post-processing module performs range constraints and smoothing on the prediction results to ensure the physical reasonableness and temporal continuity of the output predictions.

[0047] Based on the assumption that "recent data contributes more to future predictions," an exponential weighting mechanism is used to strengthen the influence of recent data. The final trend prediction is calculated by combining the weighted average base prediction and the recent slope trend. Assuming the annual cycle is the sequence period, the average skewness at each cycle position is calculated, using the mean of the last 12 months of the training sequence as the base level, and incorporating the seasonal deviation coefficient to obtain the seasonal prediction. Min-Max normalization is used to shrink the sequence to the [-1,1] interval to eliminate the influence of dimensions. The input length is... The time window sequence is processed through an LSTM layer with 8 hidden units and a fully connected output layer to output h-step predictions. The training process uses mean squared error (MSE) as the loss function, and finally, the predictions are normalized back to the original data scale. The basic predictions from each branch are weighted to obtain the final prediction, as shown in the following formula:

[0048] Among them, w i Let y be the weight at the i-th time step, m be the moving window size, T be the termination time step of the training sequence, and y be the weight at the i-th time step. T-i+1 For the observations at time T-i+1 in the training sequence, The base forecast is based on a weighted average, where k is the recent slope trend, n is the trend calculation window, and h is the forecast step size. The mean position of the i-th period in the training set. Let s be the overall mean of the sequence. i Let be the seasonal deviation coefficient of the i-th period position. The average of the last 12 months of the training sequence. Determine the period position corresponding to the prediction time, y min and y max Let be the minimum and maximum values ​​of the training sequence, respectively, and α, β, and γ be the weights of the predicted values ​​of each policy. This is a trend forecast value. This is a seasonal forecast. To reduce the weight of LSTM predictions, This is the final predicted value.

[0049] Step 5: Trend Prediction Model Validation: Using the wellbore strain test set described in Step 2, validate the final predicted value from Step 4. Steps 3 and 4 constitute a wellbore strain trend prediction model driven by small sample data, the structure of which is as follows: Figure 3 As shown, it mainly consists of two parts: a data augmentation module and a hybrid prediction module. The verification calculation is as follows:

[0050] The volatility of the quantized sequence is calculated using the deformation coefficient. A volatility threshold of 0.25 is set; sequences above this value are defined as high-volatility sequences, and those below are defined as low-volatility sequences. Based on the volatility quantization results, a two-way weight adaptation mechanism is constructed, and a weight matrix is ​​designed using normalization constraints. The formula for calculating the deformation coefficient CV is as follows:

[0051]

[0052] in, The standard deviation of the sequence. This is the sequence mean.

[0053] A three-point center weighting strategy is adopted to suppress high-frequency random noise and threshold correction, and eliminate the jump error between the beginning of the predicted sequence and the end of the training sequence.

[0054] To verify the effectiveness of the wellbore strain trend prediction method driven by small sample data in this embodiment of the invention, monitoring data from the main shaft of the Heze Guotun Mine collected from September 2023 to October 2025 were used. Horizontal and vertical monitoring points at different monitoring levels were selected and designated as measuring points 1, 2, 3, and 4, respectively. This prediction model can be used to determine the alarm trigger threshold conditions of the wellbore strain monitoring system; therefore, absolute values ​​were taken for all data during training. In the data augmentation part, the first 70% of the data was selected as the training set, and the last 30% as the test set to verify the data augmentation effect. In the hybrid prediction part, the experiment was conducted in two groups: one group augmented 70% of the original data to verify the prediction effect; the other group augmented all the original data to verify its effect.

[0055] The data augmentation experiment uses an adaptive multi-strategy stabilization mechanism to match the optimal stabilization method to the measurement point dataset. The stabilization results of the processed sequences are shown in Table 1.

[0056] Table 1. Stabilization Results

[0057] Based on the above stabilization strategy, a corresponding optimization and enhancement strategy was selected. The enhancement effect was measured by two indicators: the difference between the standard mean and the difference between the standard deviations. The results are shown in Table 2.

[0058] Table 2 Enhancement Results

[0059] As shown in Table 2, the mean difference of the four selected datasets is controlled within 0.2%, and the standard deviation difference does not exceed 3.0%, indicating that the augmented data and the original data maintain a high degree of consistency in statistical characteristics and can be used in the subsequent mixed prediction module.

[0060] like Figure 4As shown, an experiment was conducted using monitoring data from four monitoring points in the main shaft of the Guotun Mine. Due to the limited data volume, prediction was difficult. Two sets of experiments were conducted using the monitoring data: one using the data augmentation algorithm proposed in this paper to randomly augment 70% of the data, and the other augmenting 100% of the data. The difference between (a) and (b) lies in the different datasets used. Figure (a) shows the prediction effect based on the fused dataset formed by combining 70% of the original data with the augmented data, while Figure (b) shows the prediction effect based on the fused dataset formed by combining 70% of the original data with all the augmented data. Experimental results are shown below. Figure 4 The black line represents the actual value within the prediction period, the red line represents the predicted value based on the fused dataset formed by "70% of the original data and data augmentation of this 70% of the data", and the orange line represents the predicted value based on the fused dataset formed by "70% of the original data and all data and data augmentation".

[0061] Taking measurement point 1 as an example, the model prediction results are analyzed: the fluctuation range of the original sequence in the training set of this measurement point does not exceed ±5%, and its deformation coefficient is 0.178, which is lower than the division threshold of 0.25. Therefore, it is determined to be a low-fluctuation stationary sequence. In the prediction line of Figure (a), the MAPE of this measurement point is 6%. Among the 8 prediction points in the whole prediction period, the relative error of 5 points is less than 5%. The best prediction performance is in July 2025, with an error of only 2.4%. The prediction error in September 2025 is the only point in the whole period with an error exceeding 10%, at 13.8%. Compared with the historical data of the same period in the original sequence, the fluctuation range of this point has increased significantly, which belongs to the sudden fluctuation that deviates from the historical stable state. The conservative post-processing module makes the predicted value closer to the historical stationary mean. Therefore, there is a deviation at this abnormal fluctuation point, but it does not affect the prediction accuracy of other time points. Similarly, in the prediction line of subplot (b), the MAPE of this measurement point is 5.5%. The reason for this decrease is that the prediction error at the time point of September 2025 is significantly reduced, which makes the average error of the entire prediction period significantly lower.

[0062] Measurement point 1 explanation: The underground temperature differs significantly between summer and winter, directly affecting the deformation state of the concrete shaft. Therefore, one cycle in this experiment includes four seasons. The sequence length of the former dataset is approximately one and a half cycles, while the latter's length increases to two cycles. This directly affects the seasonal prediction algorithm's ability to capture the sequence periodicity, leading to differences in the weights of seasonal predictions when fusing prediction results. This results in significant differences in the prediction results for this time point in Figures (a) and (b).

[0063] In addition, Figure 4In the prediction results shown, subplots (e) and (f), i.e., the prediction results of measuring point 3, are also noteworthy. The trends of the two prediction results are roughly the same, but a significant difference emerges during the period from July to September 2025. The local peak points within the prediction period shift forward, appearing in September in plot (e) and in July in plot (f). Firstly, the temperatures in the two months differ significantly; secondly, the data sequence length used in plot (f) is longer than that in plot (e), and this extra sequence length includes July to September, resulting in more data for this period after data augmentation; finally, the material itself has the property of thermal expansion and contraction, and the post-processing module in the prediction algorithm aims to make the results closer to actual working conditions. Therefore, considering material properties, the predicted strain value is increased, thus causing the local peak points within the prediction period to shift forward.

[0064] Based on the above analysis, the method of this invention maintained an average error of less than 7% across the four datasets during the prediction period from March to October 2025, demonstrating relatively stable capture of the core fluctuation patterns of the sequences. Furthermore, in three of the four experiments, the predicted values ​​at the beginning and end of the prediction period were quite close to the actual values. This result indicates that the prediction algorithm is less prone to abrupt changes in prediction results, preventing predictions from deviating from engineering realities. For points with large errors within the period, the cause was sudden fluctuations in the actual values ​​deviating from historical averages. The model did not overfit outliers but prioritized the rationality and stability of the overall prediction.

[0065] Based on a comprehensive analysis of the predictive effects of this invention, the present invention can be used for predictive early warning in wellbore monitoring systems, providing a new technical approach for dynamic assessment and risk warning of wellbore safety status.

Claims

1. A method for predicting trends in non-stationary small-sample wellbore strain data, characterized in that, It includes the following steps: Step 1: Data Acquisition: Distributed optical fibers are laid on the inner wall of the wellbore to collect wellbore strain data at various measuring points inside the wellbore; Step 2: Data preprocessing: First, the absolute value of the collected wellbore strain data is processed, and then the maximum monthly strain value of each month within the collection period is taken to construct the wellbore strain dataset. The dataset is divided into a wellbore strain training set and a wellbore strain test set in a 7:3 ratio. Step 3: Data Augmentation Module Construction: Construct a three-order augmentation framework of "sequence stabilization processing - pattern-aware data augmentation - scale restoration and reconstruction" to expand the preprocessed original training set and generate augmented data with consistent statistical features and pattern diversity. The wellbore strain training set and the augmented data constitute the wellbore strain fusion training set. Step 4: Building the Hybrid Prediction Module: (1) Input the wellbore strain fusion training set, use statistical methods as the core of prediction, use LSTM neural network as correction, and perform fusion prediction through three branches: trend prediction, seasonal prediction and lightweight LSTM; (2) Introduce a dynamic weight allocation mechanism to automatically adjust the contribution weights of the three branches according to the data fluctuation characteristics and fuse the prediction results; (3) At the same time, through conservative post-processing combined with engineering practice, the prediction results are subjected to range constraints and smoothing to ensure the physical rationality and temporal continuity of the output, and the final prediction value is obtained. Step 5: Trend prediction model verification: The final predicted value in Step 4 is verified using the wellbore strain test set described in Step 2.

2. The method for predicting trends in non-stationary small-sample wellbore strain data according to claim 1, characterized in that, In step 3 The sequence stabilization process, while preserving the core fluctuation pattern and potential regularity of the sequence, analyzes the mean stability, variance stability, trend strength and autocorrelation of the sequence, and automatically selects the optimal stabilization strategy from five stabilization strategies for each dataset: linear detrending, first-order differencing, percentage change, moving average detrending and polynomial detrending. The sequence stabilization process requires calculating the following variables: dividing the sequence into three equal-length sub-segments, calculating the proportion of the mean and variance of the i-th sub-segment to the entire sequence to compare the statistical characteristics of each segment, i.e. and ; Calculate linear regression to assess trend strength First-order autocorrelation coefficient Through a comprehensive stationarity scoring mechanism, the following was determined: , , , We perform weighted combinations and select the method with the lowest score as the optimal stationarization method for the sequence. We then design a comprehensive stationarity scoring mechanism to further optimize the stationarity. , , , We perform weighted combinations and select the method with the lowest score as the optimal sequence stabilization method.

3. The method for predicting trends in non-stationary small-sample wellbore strain data according to claim 1, characterized in that, In step 3 The pattern-aware data enhancement first analyzes the sequence pattern: calculates the standard deviation and range of stationary sequences; for the original sequence period, calculates the seasonal variance ratio to detect its seasonality, and calculates the sequence autocorrelation to assess volatility clustering; then, based on the stationarization method, designs an enhancement strategy matrix: injects noise into sequences using the moving average detrending strategy, uses cubic spline interpolation to scale the time axis, and combines rolling standard deviation to adjust the sequence amplitude to maintain short-term volatility characteristics. For sequences using linear detrending strategies, a slight trend component is introduced on top of the basic enhancement; for sequences using differential strategies, the incremental characteristics of the sequence are maintained through volatility scaling techniques; for sequences using percentage change strategies, their amplitude is adjusted adaptively. Through the above enhancement strategy matrix, a stable enhanced sequence is generated.

4. The method for predicting trends in non-stationary small-sample wellbore strain data according to claim 1, characterized in that, In step 3 The scale restoration and reconstruction uses a forward-inverse transformation system to provide a corresponding inverse transformation algorithm for each stabilization strategy, thereby limiting the physical scale consistency between the augmented data and the original data, and finally constructing a fused dataset containing the original data and the augmented data.

5. The method for predicting trends in non-stationary small-sample wellbore strain data according to claim 1, characterized in that, In step 4 The hybrid prediction module predicts according to the following formula: ； In the formula, This is the final predicted value. This is a trend forecast value. This is a seasonal forecast. The LSTM branch predictions are denoted by α, β, and γ, which represent the weights of each strategy's predictions. CV is the distortion coefficient. A threshold of 0.25 is used to measure sequence volatility and determine the weights of each strategy's predictions, i.e., α, β, and γ. The standard deviation of the sequence. The mean of the sequence. The base prediction is based on a weighted average, T is the final time step of the training sequence, and w i Let be the weight for the i-th time step, m be the moving window size, k be the recent slope trend, n be the trend calculation window, and h be the prediction step size. The average of the last 12 months of the training sequence. Determine the average skewness of the periodic position corresponding to the prediction time, s i Calculate the average skewness of each period position. The mean position of the i-th period in the training set. Let y be the overall mean of the sequence. min and y max These are the minimum and maximum values ​​of the training sequence, respectively. It is the value of the sequence normalization.

6. The method for predicting trends in non-stationary small-sample wellbore strain data according to claim 1, characterized in that, In step 4 The conservative post-processing employs a three-point center weighting strategy and threshold connection correction. The former suppresses high-frequency random noise, while the latter eliminates jump errors.

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