Overall sensing method for the three-dimensional stress of roadway via machine learning on SHM data

Abstract

Monitoring roof stress is essential for identifying structural anomalies and preventing disasters during underground construction. However, current sensors mainly focus on monitoring in one dimension, and it is challenging to obtain the mechanical status of the overall roof owing to the limitations of sensor numbers and the working environment. Therefore, we aimed to present an overall sensing method for the three-dimensional stress status of a roadway roof through machine learning (ML) based on limited monitoring points. First, the framework of the overall sensing method was developed, where a three-dimensional stress sensor was created to obtain the mechanical behaviours of some sensitive positions, and an ML model driven by the physical mechanism and limited monitoring data was developed to derive the overall stress situation. The developed sensor was installed in a case study, and the ML model was formulated based on the field-monitoring data. A series of experiments were conducted to derive the stress distribution of the roadway roof in the study case. Furthermore, a numerical simulation was conducted to compare the reasonability of the deduction results. The experimental results indicated that the deduction results of roof stress were reasonable, and thus the proposed sensing method is reliable.

Keywords

Monitoring machine learning underground engineering sensor mechanical analysis

Introduction

With the continuous consumption of energy resources, the construction of underground spaces, such as underground transportation facilities and deep energy extraction, has developed rapidly.^1,2 However, most underground engineering structures are located in complex geological conditions and are prone to disasters in both the construction and operation stages.^3–5 A large number of engineering cases and research results have indicated that most underground engineering disasters are closely related to the mechanical state of the roof.^6,7 As a type of representative underground construction, roadway excavation, including tunnel boring and coal mining, can easily suffer from large deformations, roof falls and collapses owing to the effect of excavation disturbances on the stress redistribution of the roadway roof, which seriously affects the stability of the structure.⁸ Therefore, it is essential to measure the stress distribution characteristics of roadway roofs by installing monitoring elements.^9,10 However, existing monitoring elements are limited, and it is impossible to obtain stress information on the overall roof.¹¹ Therefore, the purpose of this study is to present a global sensing method using machine learning (ML) on limited field-monitoring data to characterise the stress distribution on the overall roadway roof.

The methods used to obtain the mechanical status of underground construction can be divided into two categories: field monitoring and numerical simulation.^12,13 Early monitoring technology was mainly manual measurement, which has low accuracy and poor timeliness.¹⁴ With the development of the Internet and computer science, structural health monitoring (SHM) technology has been widely used for real-time monitoring of structural mechanical behaviours, such as the strain and stress variation of the lining and surrounding rock, displacement of uneven settlement and opening of segments.^15,16 However, the number of sensors deployed in the field is limited, and the design of the monitoring scheme is mainly based on experience; thus, it is difficult to obtain the overall mechanical characteristics of the structure, especially the mechanical states at sensitive positions.¹¹ Although many scholars have made great efforts to optimise sensors and monitoring schemes, such as the representative application of distributed fibre sensors, there is still no effective solution to the above problems.¹⁷ In addition, the mechanical status of any point in space should be described by six stress components; however, most current sensors monitor this in one dimension.

In contrast to field monitoring, numerical calculation is a method used to obtain the mechanical response of the overall structure by simulating the boundary conditions at the site. In recent years, many types of numerical methods have been presented, such as the finite element method, finite difference method and universal distinct element code.^18,19 All these methods have been widely used to solve engineering problems and play significant roles in obtaining the overall mechanical information of underground construction. Nevertheless, because the boundary conditions applied to the numerical model are much simpler than the actual field conditions, there is always a certain difference between the calculated results and the actual mechanical status of the structure.²⁰ In any case, both SHM technology and numerical simulations provide an important basis for analysing the mechanical behaviours of the entire structure.

With the wide application of artificial intelligence (AI) technology, obtaining the mechanical behaviour of underground engineering through advanced intelligent technology is an accepted method.²¹ As an important component of AI, ML has been successfully applied in many fields such as medical research, financial markets and traffic engineering. In the field of civil engineering, the commonly used ML method is applied to pre-process the original monitoring data, identify outliers and predict future variation trends.^22–24 Furthermore, neural network models including recurrent neural networks, convolutional neural networks (CNNs) and their variants are commonly used algorithms.^25,26 It has been proven that these methods have obvious advantages in mining the complex spatio-temporal correlations hidden in structural mechanical responses.²⁷ To this end, we aim to sense the mechanical status of overall roadway roofs by using the ML algorithm to capture the mechanical correlation from limited monitoring data.

The remainder of this paper is organised as follows. First, the framework and methodology of the overall sensing method are presented. Then, the background of a case study, which is used to instantiate the presented method, is introduced. Subsequently, the presented model is formulated based on the monitoring data recorded by the study case, and experiments are conducted to deduce the stress distribution of the overall roadway roof. Finally, a numerical simulation is adopted to discuss the reliability of the proposed sensing method. This study can improve the intelligence level of underground construction and provide an important reference for maintaining structural stability.

Methodology

This section presents the overall monitoring method for stress distribution on the roadway roof. The flowchart is first developed, and then the methodologies of the core components involved in the flowchart are introduced in detail.

Flowchart for the overall monitoring

A flowchart for obtaining the stress distribution of the overall roof of the roadway is displayed in Figure 1, which is an integrated application of field monitoring, mechanical analysis and ML. First, a three-dimensional stress sensor was developed based on the fibre Bragg grating theory to perform real-time monitoring in the field. Then, the developed sensor was installed at some sensitive positions on the roadway roof to obtain the stress data and their variations. Based on the limited monitoring data, an ML model was developed to derive the three-dimensional stresses of the positions with no monitoring points, in which the mechanical correlation of stress components was employed in the objective function to guide model training. Finally, the stress distribution characteristics of the roof were obtained. The monitoring principle of the developed three-dimensional stress sensor and the ML algorithm adopted in this study are introduced as follows.

Figure 1.

Flowchart to obtain the stress distribution of the overall roof.

Three-dimensional stress monitoring on-site

Assuming that the rock mass is linearly elastic, homogeneous and continuous, if a hole is drilled in the rock, the stress state around the hole is as shown in Figure 2. According to the plane strain theory, the stress components at any point can be described as follows:

[\begin{matrix} σ_{xx} \\ σ_{yy} \\ σ_{zz} \end{matrix}] = {[\begin{matrix} s_{1}^{1} & s_{2}^{1} & s_{3}^{1} \\ s_{1}^{2} & s_{2}^{2} & s_{3}^{2} \\ s_{1}^{3} & s_{2}^{3} & s_{3}^{3} \end{matrix}]}^{- 1} [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}]

(1)

where

s_{1}^{k} = \frac{d (1 - v^{2})}{E} [1 + 2 \cos (2 α_{k})]

(2)

s_{2}^{k} = \frac{d (1 - v^{2})}{E} [1 - 2 \cos (2 α_{k})]

(3)

s_{3}^{k} = \frac{4 d (1 - v^{2})}{E} [\sin (2 α_{k})]

(4)

where $u_{k}, k = 1, 2, 3$ represents the diametrical displacements of the hole in the k direction. $α_{k}$ represents the angle of the k direction to the x-axis. E and v are the elasticity modulus and Poisson’s ratio, respectively. d denotes the hole diameter.

Figure 2.

Stress state around the drill hole in a plane strain condition.

Considering that the strain gauge is used to monitor the plane stress state in one direction, three strain gauges must be embedded in different directions to monitor the stress components $(σ_{xx}, σ_{yy}, σ_{zz})$ , as expressed in Equation (1). However, it is well known that the stress state of a rock mass can be described by a stress tensor with six independent components: $σ_{xx}$ , $σ_{yy}$ , $σ_{zz}$ , $τ_{xy}$ , $τ_{xz}$ , $τ_{yz}$ . Therefore, at least three other strain gauges should be embedded around the hole, with which to describe the relations of the other stress components $(τ_{xy}, τ_{xz}, τ_{yz})$ to the deformation. To avoid the effect of the survival rate on the monitoring results and ensure monitoring accuracy, nine strain gauges were embedded in different directions to obtain the maximum possible stress variation. Furthermore, to avoid the effect of temperature variation in the monitoring results, a temperature compensation grating was fixed on the measuring grating to ensure that it was not affected by external forces in the free deformation state. If every three strain gauges are regarded as one unit and embedded at the same point, the nine strain gauges can be divided into three units arranged in the same ring at the same spacing (120°). To this end, a fibre optical sensor was developed by our group to monitor the three-dimensional stress state on the roof of the roadway.²⁸ As shown in Figure 3, the main body of the developed sensor was a ring made of elastic steel with an external diameter of 36 mm and an internal diameter of 34 mm.

Figure 3.

Three-dimensional stress sensor installed in the site.

In addition, multiple-unit strain gauges were embedded in the hollow steel cylinder. The layout of the three units is shown in Figure 4, where the angle of every two units is 120°, and every two fibre optical strain gauges in one unit are embedded at an angle of 45°. The other technical parameters of this stress sensor are listed in Table 1. Based on the developed sensor, the in situ stress and its long-term variation can be obtained.

Figure 4.

Schematic diagram for the monitoring principle of the fibre optical sensor: (a) layout of the monitoring units and (b) layout of the strain gauges.

Table 1.

Technical parameters of the developed three-dimensional stress sensor.

Indicator	Values
Measuring range	0–200 MPa
Resolution ratio	<0.01%
Precision	<0.5%
Temperature condition	−20°C–80°C
IP rating	IP68
Packing technique	Steel armour
Installation technique	Hole mounting

ML algorithm for the spatial deduction of roof stress

To perceive the stress distribution of the overall roadway roof, an ML algorithm was adopted to deduce the stress information at the positions without monitoring points using limited monitoring data. Considering that the mechanical responses of different spatial positions hide complicated relations, a CNN was introduced to capture the spatio-temporal correlations hidden in the monitoring data. A CNN is a reliable deep learning algorithm for solving the problems of image recognition, high-level information reconstruction, automatic pilots and security protection.²⁹ This model mainly consists of an input layer, convolution layer, activation layer (ReLU function) and fully connected layer. As the core component of the CNN model, the convolution kernel contains the features that need to be captured from the objective area, and the convolution results represent the weight of the features in the objective area. The procedure for the convolution calculation is illustrated in Figure 5.

Figure 5.

Procedure for the convolution calculation in CNN.

Clearly, the essence of the convolution calculation is the process of dot multiplication between the convolution kernel and target matrix according to a certain step in different directions. Correspondingly, multiple convolution kernels are required when multiple features must be captured. If there are multiple target matrices, multiple channels are required to input this information, where each channel is used to input the data information of the target matrix. The convolution kernel can be represented as $K \in R^{M \times N \times W}$ , where M and N are the lengths of the learned region each time in the x and y direction, respectively, and W is the number of convolution kernels. In addition, the ReLU is a nonlinear mechanism for processing the convolution result, and the fully connected layer fuses multiple features captured from the objective area. Therefore, the recommended form of the convolution calculation is expressed as follows³⁰:

O_{w} = ReLU (\sum_{M} \sum_{N} P (i + M, j + N) K_{w} (M, N) + b)

(5)

where $K_{w}$ is the matrix of kernel w, and $w \in W$ . $O_{w}$ is the convolution result obtained from kernel w. P is the input matrix constituted by the limited monitoring data, and i and j represent the coordinates in x and y axes, respectively.

According to Equation (5), the fusion process of multiple features can be derived as follows:

O_{W} = \sum_{w = 1}^{W} O_{w} (i, j)

(6)

where $O_{W}$ is the fusing result of multiple features.

In this study, the stress monitoring data obtained from limited sensors installed in the field constituted the input layer and were fed into the CNN model. The procedure would terminate if the error between the deduction and monitoring results is minimal. We assume that the dataset constituted by the monitoring data is X , $X = (X^{1}, X^{2}, \dots X^{G})$ , where G is the number of monitoring points. The stress components at each monitoring point are represented as $X^{g} = (σ_{x x}^{g}, σ_{y y}^{g}, σ_{z z}^{g}, τ_{x y}^{g}, τ_{y z}^{g}, τ_{z x}^{g})$ , $g \in G$ . The commonly used objective function is expressed as follows³¹:

ℒ_{d} (X, \hat{X}) = \arg \min_{f} ‖ \hat{X} - X | |^{2}

(7)

where X is the monitoring data, and $\hat{X}$ is the deduction result calculated by the ML model.

In contrast to most application conditions, the six stress components used to describe the stress status of any point contain mechanical correlations. Therefore, it is crucial to introduce mechanical constraints into the traditional objective functions. The elasticity and plasticity theory has proven that there are three stress tensor invariants for the stress state of any point.³² These invariants can be expressed as follows:

I_{1} = σ_{xx} + σ_{yy} + σ_{zz}

(8)

I_{2} = σ_{x x} σ_{y y} + σ_{y y} σ_{z z} + σ_{x x} σ_{z z} - (τ_{x y}^{2} + τ_{y z}^{2} + τ_{z x}^{2})

(9)

I_{3} = σ_{x x} σ_{y y} σ_{z z} - (σ_{x x} τ_{y z}^{2} + σ_{y y} τ_{z x}^{2} + σ_{z z} τ_{x y}^{2}) + 2 τ_{x y} τ_{y z} τ_{z x}

(10)

The three invariants of the stress tensor describe the mechanical correlations between the different stress components. It is reasonable to introduce them into the existing objective function and perform a hybrid-driven model of big data and a mechanical mechanism to deduce the three-dimensional stress distribution of the overall roof. To this end, the improved objective function is derived in Equation (11) as follows:

\begin{matrix} L (X, \hat{X}) = \sum_{g \in G} ‖ X_{g} - {\hat{X}}_{g} ‖^{2} + \sum_{g \in G} {‖ I_{g}^{1} - {\hat{I}}_{g}^{1} ‖}^{2} \\ + \sum_{g \in G} {‖ I_{g}^{2} - {\hat{I}}_{g}^{2} ‖}^{2} + \sum_{g \in G} {‖ I_{g}^{3} - {\hat{I}}_{g}^{3} ‖}^{2} \end{matrix}

(11)

where $I_{g}^{k}$ and ${\hat{I}}_{g}^{k}$ , $k = 1, 2, 3$ are the three stress tensor invariants calculated by the monitoring and deduction results, respectively.

Background for a study case

In this section, a roadway in a coal mine is selected as a case study to install a stress sensor. The background of this coal mine and the monitoring scheme at the site are introduced.

Geological conditions

The panel of 6303 in the Dongtan coal mine was selected as a case study to analyse the stress distribution of the roadway roof. This panel was located in Jining, Shandong, China. The length of the panel is 1400 m, and the width and height of the working face are 245 and 5 m, respectively. Furthermore, this panel is buried 660 m deep, where the overlying strata are mainly sandstone, including lower Shihezi formation sand and lower Jurassic series sand, and the floor strata are mainly siltstone and silty-fine sand. The geological layers and thickness of the immediate and main roof of the roadway were extracted and are displayed in Figure 6(a), and the corresponding parameters are listed in Table 2. The geological conditions in which the study case was located are complex; therefore, it is vital to install the SHM system in site to sense the stress state and prevent disasters.

Figure 6.

Geological conditions of the study case.

Table 2.

Property parameters of different geological layers.

Layer	Density (kg/m³)	Shear elasticity (GPa)	Cohesion (MPa)	Internal friction angle (°)
Mudstone	2400	2.9	5.74	28
Medium stone	2500	6.2	9.2	32
Coal seam	1410	0.7	1.8	25
Siltstone	2510	6	6.41	30
Silt-fine sand	2580	9.8	12.9	40

Field monitoring and the results

To obtain the stress distribution and evolutionary trend of the roadway roof, the developed three-dimensional stress sensors were installed in the study case. Holes were drilled at an elevation of 30° from the free face to the roof, where the diameter of the hole was 110 mm and the depth was 18 m, as shown in Figure 6(b). Subsequently, the developed stress sensors were embedded into these holes. In total, eight stress sensors were installed in the field, and the space between two sensors was set to 90 m. The field installation was recorded, and two photos are shown in Figure 7.

Figure 7.

The on-site installation of the three-dimensional stress sensor: (a) drilling hole and (b) embedding sensor.

The stress state of the rock mass consists of two components: in situ stress and mining-induced stress, as expressed in Equation (12). The former is mainly derived from gravity and tectonic stresses, and its magnitude and direction remain the same. The latter is induced by roadway excavation and timely variations. The measurement method for the in situ stress was introduced in our previous study,³³ based on which the in situ stress for the study case is listed in Table 3, where the compressive stress is negative and the tensile stress is positive. The developed stress sensor was then used to monitor the variation in mining-induced stress, and the monitoring results are shown in Figure 8. This figure shows the stress status 110 m front of the working face with 5 m intervals; a total of 21 data points in each direction were recorded, and a dataset containing 6 × 21 data points was generated.

σ_{ij} = σ_{ij}^{0} + Δ σ_{ij}

(12)

where $σ_{ij}^{0}$ is the in situ stress, and $Δ σ_{ij}$ is the mining-induced stress.

Table 3.

In situ stress of the study case.

Stresscomponent	Value (MPa)	Stresscomponent	Value (MPa)
$σ_{xx}$	−16.96	$τ_{xy}$	−0.53
$σ_{yy}$	−33.09	$τ_{yz}$	−0.64
$σ_{zz}$	−22.43	$τ_{zx}$	−3.61

Figure 8.

Monitoring results of the three-dimensional stress on the roadway roof.

Overall sensing for the study case

In this section, the proposed sensing method is formulated based on the monitoring data, and the stress distribution of the overall roof is obtained.

Experimental preparation

The monitoring data of three-dimensional stress, as shown in Figure 8, were extracted to formulate the presented model. The monitoring result of each stress component was regarded as a time series; therefore, there were six time series in this dataset, and each time series contained 21 monitoring data points. First, all the time series were pre-processed by a standardised criterion to avoid the effect of magnitude difference, as expressed in Equation (13):

x_{i, j}^{normal} = \frac{x_{i, j} - {\bar{x}}_{i}}{x_{i, \max} - {\bar{x}}_{i}}

(13)

where ${\bar{x}}_{i}$ is the average value of time series i, $x_{i, j}$ is the jth value in time series i, and $x_{i, \max}$ is the maximum value of time series i.

A CNN model with one convolution layer was developed to conduct the data experiments. The monitoring data were fed into the CNN model with six channels because the stress information has six components, and each channel was used to input the data of one stress component. Correspondingly, the number of out channels was set to six. The kernel size was defined as $K \in R^{3 \times 3 \times 6}$ , and its stride was set to 1. To ensure that the size of the dataset was consistent before and after calculation, zero padding was adopted, and the number of padding layers was calculated according to Equation (14).

L_{M} = \frac{M - 1}{2}, L_{N} = \frac{N - 1}{2}

(14)

where $L_{M}$ and $L_{N}$ are the number of padding layers in terms of width and height, respectively, and $M = N = 3$ .

In the process of model learning, the learning rate was set to 0.001, and the stochastic gradient descent was used to optimise the learning results. Furthermore, the value of the loss function was defined as 0.05. If the error between the deduction results and the monitoring data was less than 0.05, the computation terminated. Otherwise, the model continued to iterate until a predefined maximum number of steps was reached, which was set to 1000 in this experiment.

Sensing results for the stress distribution of the overall roof

The stress information to be deduced is a range with length of 450 m and width of 270 m. This region was divided by cells with side lengths of 5 m, so a total $90 \times 54$ units were obtained, as displayed in Figure 9. Therefore, the input layer was a tensor $X \in R^{90 \times 54 \times 6}$ . If these units are numbered as $(i, j), i \in 90, j \in 54$ , the units recording the monitoring information are $G (i, j), (i = 45, j \in (11, 32))$ , and the other units that were empty were derived from the information in $G$ .

Figure 9.

Generation and numbering form of the units on roadway roof.

To avoid the overfitting problem, $G (i, j)$ was randomly separated into two sets according to the approximation ratios of 0.7 and 0.3, represented as $A$ and $B$ . In addition, $A \in G (i, j), B \in G (i, j)$ , and the numbers of units in $A$ and $B$ were 15 and 6, respectively. The monitoring data at the units of $A$ generated a training set to deduce the stress information of the overall roof, and that of $B$ generated a testing set to verify the reliability of the model calculation result. In the initial stage, the tensor that recorded the monitoring data of $A$ was first input into the CNN model to derive the stress information of all units, based on which the value of the loss function corresponding to the units of $B$ could be calculated. This procedure was repeated until this value was minimised. Driven by the pre-processed monitoring data and improved object function (Equation (11)), the overall stress distribution on the roof was deduced by the prepared CNN model, as displayed in Figure 10.

Figure 10.

Deduction results for stress distribution of roadway roof.

The deduction results show that the stress of the face pressure roof was the largest, and the stress in front of the face was smaller than the on-site stress. This is because the pressure of the overlying strata is loaded on the roof above the working face owing to roadway excavation; however, this leads to the stress release of the rock strata in front of the working face. With the advancement of the working face, the roof stress is redistributed and tends to be balanced, and the influence of the roadway excavation on the stress in front of the working face gradually decreases.

Comparison and discussion for the sensing results

Numerical simulation is the most commonly used method for obtaining the stress distribution of an overall roof. In this section, the numerical results are regarded as the baseline for a comparison with the deduction results.

Stress distribution obtained from numerical simulation

Based on the geological conditions (Figure 6) and property parameters (Table 2), a numerical model was developed using the finite difference method, as shown in Figure 11.

Figure 11.

Numerical model of the study case.

Geometric modelling

The length (dip direction), width (strike direction) and height of this model were 450, 270 and 260 m, respectively, which were consistent with the actual conditions at the site. In addition, two roadways were excavated at a spacing of 245 m, and both the width and height of the roadways were 5 m.

Calculation elements

The developed model was meshed into solid cubic elements with a side length of 5 m. The Mohr–Coulomb formula was used as the constitutive equation for these elements.

Boundary conditions

The constraints were applied on the bottom, left, right, front and back surfaces of the numerical model. The lateral pressure in dip and strike directions were 0.8 and 1.4, respectively. The even load applied to this model was calculated as follows:

F = \sum_{l = 1}^{L} γ_{l} h_{l}

(15)

where $γ_{l}$ and $h_{l}$ are the weight and height of layer l, L is the number of layers in the overlying rock, $l \in L$ and $L = 3$ in this model.

Based on the above numerical model, the simulated result of the stress distribution was calculated, and the numerical result on the plane corresponding to the sensor installation, which was 15 m above the roadway, was extracted, as shown in Figure 12. Obviously, some stress distribution characteristics were similar to those from the CNN, where the stress of the face pressure roof was the largest and that in front of the face was smaller than the on-site stress. However, the stress distribution characterised by the deduction result was more regular than that characterised by the proposed model, and the magnitudes of the three-dimensional stress obtained from these two methods were different because the former model was unable to consider all boundary conditions in the field.

Figure 12.

Numerical results of stress distribution on roadway roof.

Evaluation for the calculation result

To verify the reliability of the presented overall sensing method and highlight its superiority to the commonly used method, a comparison of the monitoring results with the numerical and deduction results is displayed in Figure 13. It can be observed that the stress variation trends of the monitoring data agreed better with the deduction result, and the deviation of the deduction result from the monitoring result was smaller than that of the numerical result.

Figure 13.

Comparison of calculation results of different models with the monitoring data.

To this end, two indicators, root mean square error (RMSE) and Pearson’s correlation coefficient (PCC), were adopted to evaluate the calculated results. Specifically, RMSE is an indicator used to evaluate the deviation of the calculated results from the actual data. Given the calculated result $\tilde{y} = ({\tilde{y}}_{1}, {\tilde{y}}_{2}, \dots, {\tilde{y}}_{G})$ and the actual data $y = (y_{1}, y_{2}, \dots, y_{G})$ , the RMSE is calculated as follows:

RMSE (y, \tilde{y}) = \sqrt{\frac{1}{G} \sum_{g = 1}^{G} {(y_{g} - {\tilde{y}}_{g})}^{2}}

(16)

where G is the number of monitoring data points in the testing set, which is equal to six in this experiment.

Furthermore, the PCC is a dimensionless parameter used to evaluate the correlations between the calculated result and actual data, and the recommended form to calculate this indicator is given as follows:

PCC (y, \tilde{y}) = \frac{\sum_{g = 1}^{G} (y_{g} - {\bar{y}}_{g}) ({\tilde{y}}_{g} - {\bar{\tilde{y}}}_{g})}{\sqrt{{\sum_{g = 1}^{G} (y_{g} - {\bar{y}}_{g})}^{2} \sqrt{\sum_{g = 1}^{G} {({\tilde{y}}_{g} - {\bar{\tilde{y}}}_{g})}^{2}}}}

(17)

Using Equations (16) and (17), the evaluation results of the different models were calculated, as shown in Figure 14. This figure shows that the RMSE value of the deduction results was far smaller than that of the numerical results for all stress components, whereas the correlation of the former was larger than that of the latter. Specifically, the average value of the calculation error of the overall sensing method was 2.83 MPa, and the correlation between the deduction results and monitoring data was 94.35%. However, the calculation error of the numerical results was greater than 15 MPa, and the correlations of some stress components were less than 75%. Therefore, the overall sensing method presented by integrating ML and SHM was reliable.

Figure 14.

Evaluation results of different models.

Conclusion

In this study, an overall sensing method is presented based on ML and limited monitoring points to obtain the stress distribution in underground construction. It effectively solves the problem of inadequate monitoring of regions and dimensions. The conclusions are as follows.

The overall sensing method is composed of on-site monitoring and the ML algorithm and is modified by mechanical theory. A three-dimensional stress sensor was developed by our group to monitor the stress information of six components, and a CNN model modified by the invariant of the stress tensor was adopted to deduce the stress information of the overall roof using the limited monitoring data. As a case study, the proposed model was applied to the Dongtan coal mine to obtain the three-dimensional stress of the roadway roof. A numerical simulation was adopted for comparison with the sensing results, and two indicators were used to evaluate the reliability of the overall sensing method. The experimental results indicate that the three-dimensional stress of the overall roadway roof can be deduced using the presented model. The deduction error was 2.83 MPa and the correlation was 94.35%, which is superior to the simulated results, whose calculation error was over 10 MPa. Therefore, the overall sensing method presented in this study was reliable.

However, this study focused on characterising the stress distribution in a two-dimensional plane. The stress distribution in the vertical direction of the roadway roof is also important. It is essential to optimise the presented method to characterise the stress distribution in three-dimensional space, which is one of the important tasks to be carried out in the future.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the Project for Research Assistant of Chinese Academy of Sciences, Key deployment projects of Chinese Academy of Sciences numbers ZDRW-ZS-2021-3-3, and National Natural Science Foundation of China under grant numbers 51991392.

ORCID iD

Xu-Yan Tan

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