The measurement principle of BOTDR (Brillouin Optical Time Domain Reflectometry) distributed optical fiber sensing technology is as follows: When pulsed light is injected into an optical fiber, it interacts with acoustic phonons within the fiber, generating spontaneous Brillouin scattering. The backscattered Brillouin light propagates backward along the fiber to the incident end (Figure 1A), entering BOTDR’s receiver unit and signal processing module. A photodiode converts the optical signal into an electrical signal, which undergoes averaging via a digital signal processor to obtain the distributed Brillouin scattered light power at each sampling point along the fiber (Figure 1B). The Brillouin scattered light power peaks at a specific frequency offset with a Lorentzian line shape distribution (Figure 1C). By sweeping the output signal frequency, Brillouin scattered light power measurements at different frequencies are acquired, yielding the Brillouin scattering spectrum (Figure 1A). The strain measurement principle of BOTDR is illustrated in Figure 1 (Hong et al., 2017).

The distance Z between any scattering location along the optical fiber and the incident end of the pulsed light can be calculated using Equation 1: Z = c T 2 n (1)

Where: c denotes the speed of light in vacuum; n represents the refractive index of the optical fiber; T is the time interval between the emitted pulse and the received scattered light.

The frequency shift of backscattered Brillouin light is simultaneously influenced by strain and temperature variations. Under laboratory-controlled constant-temperature conditions, temperature effects on Brillouin frequency shift are eliminated using a temperature compensation method. Under these conditions, the relationship between fiber strain and Brillouin frequency shift is expressed by Equation 2 (Zhang et al., 2019). v B ε = v B 0 + d V B ε d ε ε (2)

Where: v B ε denotes the Brillouin frequency shift at strain ε ; v B 0 represents the initial Brillouin frequency shift in the unstrained state; d V B ε d ε is the strain sensitivity coefficient, with a magnitude of approximately 493 M H z / μ ε ; ε is the strain applied to the sensing fiber.

Based on geological conditions of mining-disturbed rock masses and monitoring objectives, sensing optical cables are installed via borehole implantation. After positioning cables at target strata levels, boreholes are sealed using concrete grouting materials to ensure effective coupling between fibers and rock masses. Communication cables connect the borehole-collar fibers to an optical demodulator in the monitoring room. This enables acquisition of full-section strain distribution in borehole strata during longwall face advancement, facilitating analysis of overburden deformation characteristics during underground coal extraction. The schematic diagram of this distributed optical fiber monitoring system for mining-induced overburden deformation is presented in Figure 2.

Deformation and failure of mining-induced overburden are governed by geological conditions of overlying strata and coal extraction parameters. This study selects seven primary governing factors influencing overburden deformation, as listed in Table 1.

The width-to-depth ratio in Table 1 reflects the extraction sufficiency of coal seam mining, while the compressive-to-tensile strength ratio characterizes the rock brittleness index.

Given the disparate measurement units among governing factors in Table 1, accurate assessment of their individual impacts on overburden prediction accuracy is challenging. To ensure equivalent feature representation, dimensionless processing of all data is implemented using z-score standardization (He et al., 2024). The mathematical formulation is given by Equation 3: y i = x i − x ¯ s (3)

Where: y i denotes the i -th value in the standardized data sequence; x i represents the i -th value in the original data sequence; x ¯ is the mean of the original data; s is the standard deviation of the original data.

According to dataset requirements for the BPNN model, the original data is partitioned into a training set and a testing set. The training set optimizes model parameters, while the testing set evaluates the model’s generalization capability. The workflow for establishing the prediction model is illustrated in Figure 3.

In BP neural networks, strain data propagation follows a unidirectional path. Strain data transmits from the input layer through activation functions to hidden layers, then propagates to the output layer, completing one forward propagation cycle. The output values are compared against actual strain measurements via a loss function to compute prediction errors. These errors subsequently undergo backpropagation to update neuronal weights and biases. This process iterates until model convergence. Given that coal seam extraction disrupts in situ stress in overlying strata, the resulting stress evolution exhibits complex nonlinear behavior. Consequently, utilizing overburden strain data as training inputs leverages BPNN’s nonlinear fitting capability to approximate continuous nonlinear functions with high precision, enabling accurate input-output mapping.

To mitigate overfitting risks inherent in stochastic neural network training, the root mean square error (RMSE) function is selected as the BPNN loss function, expressed in Equation 4: L o s s y ^ , y , W = 1 2 y ^ − y 2 2 (4)

Where: y ^ denotes the predicted value from the model; y represents the true value; W is the parameter matrix of the model.

To prevent overfitting, L₂ regularization is applied to Equation 4, yielding the regularized loss function in Equation 5: L o s s y ^ , y , W = 1 2 y ^ − y 2 2 + α 2 W 2 2 (5)

Where α is a non-negative hyperparameter that controls the penalty intensity of the L₂ regularization term on the model. Its value is determined through systematic hyperparameter optimization, which involves selecting the optimal value from a predefined parameter space based on the model’s average performance during 10-fold cross-validation. In this study, α is set to 0.001.

The coefficient of determination (R²) and root mean square error (RMSE) are adopted as complementary evaluation metrics to assess model accuracy. Their computational formulations are given by Equations 6, 7 (Rawal and Ahmad, 2024): R 2 = 1 − ∑ i = 1 n y i − y ^ i 2 ∑ i = 1 n y i − y ¯ 2 (6) R M S E = 1 n ∑ i = 1 n y i − y ^ i 2 (7)

Where y i represents the measured value of the i -th sample; y ^ i represents the model-predicted value of the i -th sample; y ¯ denotes the mean of all measured values; n is the total number of samples.

Higher values of the coefficient of determination (R²) and lower root mean square error (RMSE) indicate closer alignment between model predictions and actual measurements.

The key stratum refers to a rock layer that controls the movement of partially or entirely overlying strata up to the surface within the mining area. The methodology for identifying key stratum positions in overburden involves three sequential steps: first, locating competent strata upward from the coal seam; second, calculating the fracturing span of each competent stratum; and third, comparing these fracturing spans to determine key stratum positions (Zhang et al., 2021).

The criterion for identifying competent strata is given by Equation 8: E m + 1 h m + 1 2 ∑ i = 1 m h i γ i > γ m + 1 ∑ i = 1 m E i h i 3 (8)

Where: h i , γ i , E i denote the thickness, unit weight, and elastic modulus of the i-th stratum (i = 1,2, … ,m), respectively.

The fracturing span l k of the k -th competent stratum is calculated using Equation 9: l k = h k 2 σ k q k (9)

Where h k is the thickness (m) of the k -th competent stratum, σ k denotes its tensile strength (MPa), and q k represents the load borne (MPa) by the k -th competent stratum.

Based on Equations 8, 9, the positions of competent strata and their fracturing spans in the overburden were calculated, revealing four competent strata above the No. 2^–2 coal seam: Stratum (5) (fine sandstone), Stratum (7) (fine sandstone), Stratum (9) (medium sandstone), and Stratum (10) (siltstone), with fracturing spans of l 1 = 11.4 m, l 2 = 20.47 m, l 3 = 9.23 m, l 4 = 17.91 m. Because of l 2 > l 4 > l 1 > l 3 , Stratum (7) (fine sandstone) is identified as the primary key stratum while the remaining three constitute secondary key strata.

This study focuses on the vertically installed A3 sensing optical fiber within the overburden strata. Strain curves measured after the passage of the 2^–2 coal seam working face through the A3 monitoring cross-section were selected to analyze deformation and failure characteristics of the overburden. The corresponding mining-induced strain distribution curves in the overburden are presented in Figure 5.

Analysis of Figure 5 reveals that coal extraction induces overburden movement toward the goaf area, placing the strata under tensile stress. As the working face advances, the tensile strain zone progressively expands within the overburden. Based on measured strain data and applying the discrimination methodology for water-flowing fractured zone development height (Piao et al., 2021), the observed development heights of the caved zone and fractured zone are identified at 10 cm and 35 cm above the coal seam roof, respectively.

Deformation and failure characteristics of mining-induced overburden in the physical model are illustrated in Figure 6.

Based on Figures 5, 6, the deformation of mining-induced overburden strata undergoes three evolutionary stages following the passage of the 2^–2 coal seam working face through the A3 monitoring section: Stage I features minimal strain curve fluctuations as the immediate roof remains intact bearing overburden pressure when the face advances 15 cm beyond A3; Stage II exhibits strain concentration in the caved zone 10 cm above the coal seam roof due to immediate roof collapse at 20–25 cm advancement, coupled with progressive bed separation between the (5)th layer fine-grained sandstone (sub-key stratum) and underlying strata—induced by its stiff lithology—causing secondary strain concentration at 35 cm above the roof; Stage III shows strata above the fractured zone undergoing integral subsidence to form a bending subsidence zone as the (7)th layer fine-grained sandstone (primary key stratum) controls overlying movement, with strains asymptotically approaching zero while the caved zone height stabilizes near 9.5 cm above the roof. Analysis confirms that mining-induced overburden failure is principally governed by primary and sub-key strata, with measured strain magnitudes and gradients demonstrating fundamental consistency with physically modeled failure heights—validating the reliability of distributed optical fiber sensing (DOFS) for overburden deformation monitoring.

To construct and validate the Backpropagation Neural Network (BPNN) prediction model, this study utilized raw strain data acquired from the A3 sensing optical fiber throughout the full monitoring period as the total sample set. To ensure robust model generalization, the complete dataset was randomly partitioned into two independent subsets: a training set and a test set. Specifically, 70% of the total samples were allocated to the training set for model development and parameter tuning, while the remaining 30% were reserved as the test set, which was strictly isolated during training and solely used for final evaluation of the model’s predictive performance. This partitioning strategy adheres to standard machine learning protocols, effectively mitigating overfitting and ensuring the model’s applicability and reliability on unseen data.

Based on the factors influencing mining-induced overburden deformation and failure listed in Table 1, the number of input neurons in the neural network was set to seven. A 10-fold cross-validated grid search was employed to determine the network architecture, resulting in two hidden layers with 10 and 5 neurons, respectively, and a single-neuron output layer, thereby finalizing the 7-10-5-1 network topology. The structure of the BPNN-based overburden prediction model is illustrated in Figure 7.

Utilizing the BPNN-based overburden prediction model structure depicted in Figure 7, 70% of the strain data measured by the A3 sensing optical fiber in the similarity model test were designated as the training set, with the remaining 30% allocated as the test set. The model was trained using the training dataset to output predicted strain values, which were then compared against the test set data to evaluate prediction performance. For model parameter optimization, the training set underwent 10-fold cross-validation to solve numerically optimal solutions for nonlinear minimization (Cao et al., 2024). The relationship between training epochs and root mean square error (RMSE) for the prediction model is illustrated in Figure 8.

As shown in Figure 8, the prediction model demonstrates rapid convergence during training. The root mean square error (RMSE) decreases significantly and stabilizes after 10 epochs, reaching 0.03 by the 98th epoch—meeting model precision requirements. Fitting analysis of computational results yields test-set coefficients of determination (R²) consistently exceeding 0.98, with no severe overfitting or underfitting observed, indicating robust model generalization capability.

To evaluate prediction accuracy, model training results were compared against test dataset values. Following passage of the 2^–2 coal seam working face through the A3 monitoring section, mining-induced strain values within the 25–45 cm face advancement range were selected to predict overburden strain distribution during mining progression, as illustrated in Figure 9.

As evidenced in Figure 9, the strain values predicted by the BPNN-based model closely align with measured strain data in the overburden strata, demonstrating that the neural network effectively captures the actual deformation behavior of rock strata and exhibits strong applicability.

To ascertain model prediction accuracy, measured and predicted strain values at the caved zone (10 cm above coal seam roof) and fractured zone (35 cm above coal seam roof) were selected for relative error calculation, with comparative results presented in Figure 10.

As shown in Figure 10, the relative error between the predicted and measured overburden strain values is less than 5%, indicating high overall prediction reliability of the model. However, the error distribution exhibits slight spatial variations, characterized by “overestimation in the caved zone and underestimation in the fractured zone.” In the caved zone, the inadequate coupling between the optical fiber and the fractured rock mass results in the measured strain data representing averaged values over a certain length. This averaging effect leads to measured strains being smaller than the actual local strains, consequently causing the predicted values in the caved zone to appear relatively larger compared to the measurements. In the fractured zone, although the actual rock deformation is minor and the measured strains are generally low, localized high strains occur at fracture openings within limited areas. To achieve overall prediction stability, the model “sacrifices” accuracy at these localized high-strain peaks, effectively smoothing the predictions toward the predominant low-strain background. As a result, the predicted high-strain peaks in the fractured zone are “pulled down” closer to the surrounding broader low-strain regions, leading to the observed underestimation in this zone.

Model performance was evaluated using the coefficient of determination (R²) and root mean square error (RMSE) metrics. Predictive accuracy of both Backpropagation Neural Network (BPNN) and Kernel Ridge Regression (KRR) models for overburden strain is comparatively assessed, with model evaluation results presented in Figure 11.

As shown in Figure 11, the prediction models based on BPNN and Kernel Ridge Regression exhibit progressively declining R² values and increasing RMSE values with advancing mining steps. The BPNN model demonstrates R² values approaching 1 initially, which gradually decrease over time. Nevertheless, even at the fifth mining step, the BPNN achieves R² = 0.90 with RMSE<10%, confirming its high accuracy in predicting mining-induced overburden strain. Conversely, the Kernel Ridge Regression model yields test-set R² values consistently below 0.85 and higher RMSE than the BPNN model, indicating significantly inferior predictive performance for overburden strain.