# Karst Collapse Monitoring and Early Warning Evaluation Method Based on Multisensor Internet of Things

Authors: Xin Zhang; Longfu Deng; Na Li
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

The international community has paid extensive attention to the numerous engineering problems faced by karst areas caused by the increasingly frequent human activities. China has a wide variety of karst forms. Among them, carbonate karst is the most widely distributed, and the development of carbonate karst is relatively strong in many areas. Countless property losses are caused by karst disasters every year. This article aims to study the real-time monitoring and timely early warning of karst collapse through the use of multisensor Internet of Things technology. To this end, this article proposes an improved method for multisensor data fusion. It optimizes and improves the transmission and delivery efficiency of its data. This makes the improved multisensor more in line with the research content of this article in terms of monitoring efficiency. At the same time, related experiments and analyses are designed to compare and analyze the karst collapse and the monitoring efficiency of the sensor. The experimental results of this article show that after the improvement, the anti-interference ability of the monitoring system is increased by 34%. The frequency of early warning has also been improved by 24%, which has high practical application value.


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## Body

## 1. Introduction

Karst is the general term for the chemical dissolution and mechanical destruction of soluble rocks caused by water and various phenomena and forms caused by these effects. The distribution area of soluble rocks in China is 340 km2, accounting for about one-third of China’s land area. Karst areas are mainly composed of carbonate rock series. In Guizhou Province, Guangxi Zhuang Autonomous Region, and Yunnan Province, the outcropping area of carbonate rocks accounts for about half of the total area of the three provinces. Due to the humid climate and abundant rainfall in these provinces, karst is extremely developed. There are so many types; it can be called the crown of the world. In the areas along the railway in Southwest China, there are mountains, hills, plains, and other karst areas widely distributed. However, the stage of development and the degree of development are different.During the construction of karst tunnels, the shape, size, development degree, scale, and exact location of exposure of the karst in front can be accurately predicted. It recognizes the influence laws of environmental stability under different working conditions. In this way, the construction plan can be adjusted in time, and safety measures can be set to avoid the occurrence of karst collapse. Karst collapse may occur at any time if the advance geological forecast fails to be proved or the treatment plan is unreasonable during construction. Not only will the construction safety be seriously threatened, but the construction progress will be slowed down. And it will leave a safety hazard after completion. Even deteriorating the environment causes irreversible environmental impacts and economic losses. It can be seen that the mechanism of karst collapse and the influence of karst on structural stability are analyzed and studied. Therefore, it is of great theoretical and practical significance to propose the corresponding forecasting technology and prevention technology.The innovation of this article lies in how to improve the effective karst monitoring and early warning. It is used for multisensor Internet of Things technology and focuses on the analysis and research of data fusion between multisensors. This makes it possible to achieve better results in terms of data transmission and transmission frequency. It is effectively applied to the actual karst collapse monitoring and early warning evaluation.


## 2. Related Work

Xue et al. proposed a vision-centric multisensor fusion framework for traffic environment perception methods for autonomous driving. The framework consistently fuses camera, lidar, and GIS information through geometric and semantic constraints for efficient self-localization and obstacle perception [1]. A commercial system proposed by Seeberg™ to analyze movement patterns using data from an inertial measurement unit (IMU) has not yet been adapted to monitor the daily training of cross-country (XC) skiing. All sensor data are simultaneously sampled and synchronized with GNSS data from commercially available sports watches. And XC skiing is on a different track from amateur skiers and world-class athletes [2]. Liu et al. aimed at the problems of incomplete information and uncertainty in the diagnosis of single-parameter complex systems. They proposed a new method of multisensor information fusion fault diagnosis based on BP neural network and D-S evidence theory [3]. Hu et al. addressed the consistency deviation due to measurement noise uncertainty during virtual measurement sampling. They proposed a multisensor integrated Kalman filter algorithm based on Metropolis–Hastings sampling [4]. Nada believed that the data from the sensors are combined and used as input to an unscented Kalman filter (UKF). He proposed two data fusion architectures: Measurement Fusion (MF) and State Vector Fusion (SVF) are used to merge the available measurements. A comparative study of these two architectures shows that the state estimation provided by the MF architecture has relatively less uncertainty compared to the SVF [5]. Jeff Morgan and O’Donnell proposed that high-precision manufacturing requires the use of advanced signal processing and analysis to monitor, manage, and control the production process. These systems vary in size, scope, and complexity and traditionally require the skills of multidisciplinary personnel for end-to-end applications. Current research trends in digital manufacturing aim to remove this complexity through interoperability solutions encapsulated in cyberphysical systems [6]. Yi et al. proposed a new method for distributed multitarget tracking using a multistatic radar system. The method is based on the use of generalized covariance intersection (GCI) of multiobjective densities in a multiobjective Bayesian filtering scheme to fuse the posteriors. Their proposed solution is particularly suitable for sensor fusion with posterior density [7]. Subedi et al. provided a computationally efficient technique for centralized multisensor information fusion. The MTT filter performs data association according to the predefined target dynamic model, compensates for missed detection, removes clutter components, and improves the accuracy of multitarget state estimation. The technique deploys a recursive feedback mechanism so that the group sparse reconstruction algorithm also benefits from the prior mathContainer loaded with MathJax knowledge about the target dynamics [8]. The above-mentioned documents are very good for monitoring related IoT multisensor monitoring. The content description is also quite detailed, and some technical points are also explained separately. However, there is no description of the relevant experimental process, and even if there is, it is very brief and not detailed enough.


## 3. Multisensor Monitoring Method

### 3.1. Multisensor IoT Technology

According to the requirements of the monitoring and early warning system studied in this article, it is necessary to send the data of multiple wireless sensor nodes to the remote monitoring center. It is a multi-point-to-point communication method. The network topology can be divided into three types: star network, tree network, and mesh network. The wireless transmission of this system adopts a tree-type network structure, and Figure1 shows the system summary structure. Sensor nodes can be in routing mode or terminal mode and can transmit data directly with the coordinator node. If the distance between the two is relatively far, the data can be transferred through the adjacent sensor nodes [9]. The coordinator node is connected to the host computer through a USB cable [10].Figure 1
Overall structure of the system.The whole system can be divided into three parts: wireless sensor network node, coordinator node, and monitoring center. Wireless sensor nodes integrate multiple sensors and are responsible for measuring multiple parameters. After the data are processed, they are sent out through the wireless module. The monitoring center is the main console of the system. The received data can be saved and displayed in real time through the monitoring software, and the data exceeding the threshold can be alarmed in time. The user can monitor the work of each node through the monitoring center [11]. The coordinator node is responsible for building and managing the entire wireless network and monitoring the normal operation of each sensor node. It receives the data of each sensor node in real time and uploads it to the host of the monitoring center.A wireless sensor network node is a miniature embedded system. It consists of a hardware layer and software layer, and its architecture is shown in Figure2. From bottom to top, they are STM32 embedded microprocessor, peripheral hardware devices, μC/OS-II embedded real-time operating system, application program interface, and application program. The STM32-embedded microprocessor is the core of the node hardware layer. By connecting temperature and humidity sensors, air pressure sensors, accelerometers, and wireless communication modules, the hardware foundation of data acquisition, processing, and wireless transmission is formed. The software layer is built on the basis of the hardware layer, and μC/OS-II embedded real-time operating system is the core of the software layer. It provides a software platform and application programming interface. Based on this, applications can be easily written to achieve multitask parallelism [12].Figure 2
Wireless sensor node architecture.Multisensor network refers to the wireless interconnection and cooperation among many sensor units with communication and computing capabilities and interacts with the external environment to jointly complete a set of specific tasks [13, 14]. The multisensor network monitors and collects information about the surrounding external environment through real-time collaborative monitoring. This information is then processed and distributed to users [15, 16]. Compared with the traditional centralized processing method, the multisensor network has higher robustness, higher accuracy, higher flexibility, and stronger intelligence.The unit structure of the sensor consists of a sensing part, a processing part, a wireless transceiver part, and a power supply part. The structure of the sensor unit is shown in Figure3.Figure 3
Sensor unit structure.The sensing part is mainly used to perceive and collect the information in the monitoring area and convert the information into digital signals. It is mainly composed of sensors and A/D conversion subparts. The processing part is mainly responsible for controlling and coordinating the work of each sensor unit. It handles the specified tasks and executes the specified algorithms and is mainly composed of processor and memory subparts. The wireless transceiver part is mainly responsible for communicating with other sensor units and exchanging control signals and data information. It is mainly composed of buffer, transceiver, MAC, and network and can also carry a microprocessor in some specific applications [17]. The power supply part is mainly responsible for providing the energy required for the normal operation of the sensor unit, usually using a miniature battery.Therefore, each sensor unit has a dual function at the same time. It is not only about local information collection and data processing. At the same time, it also needs to store, manage, and fuse the data sent by other sensor units to complete specific collaborative tasks [18]. The network structure of the sensor consists of a sensor unit, aggregation unit, and management unit. The structure of the sensor network is shown in Figure 4.Figure 4
Sensor network structure.Numerous sensor units are randomly deployed near the monitoring area. It forms a multisensor network in a self-organizing manner. When there is data information in the sensor units in the network, it is transmitted one by one through the communication between the sensor units. Data information may be processed by multiple sensor units during the entire transmission process. Then it finally reaches the aggregation unit and reaches the management unit through the Internet or satellite [19]. The manager of the sensor network can configure and manage the sensor network through the management unit, publish monitoring tasks, and collect monitoring data information.Generally speaking, the processing capacity, storage capacity, and communication capacity of the aggregation unit are much stronger than other sensor units. It connects the sensor’s internal network and the external Internet at the same time and needs to perform protocol conversion between the two communication protocols. At the same time, the information monitored by the sensor units in the sensor network is forwarded to the external Internet [20, 21]. Therefore, the aggregation unit with enhanced functions requires a lot of storage and computation. And it carries a wireless communication interface and monitoring function [22].Multisensor network coordination mainly includes resource coordination, task coordination, and signal and information coordination, among which multisensor network task coordination mainly includes task description, task decomposition, task allocation and scheduling, and task execution. The main purpose of multisensor network task coordination is to reduce the communication volume and energy consumption between sensor units by optimizing the assignment of tasks, and prolong the life cycle of the sensor network.


### 3.2. Mathematical Basis of Multisensor Data Fusion

It assumes that multiple sensors estimate the same target value. LetXi and Xj be the data measured by the i-th sensor and the j-th sensor, respectively, and both Xi and Xj obey the Gaussian distribution. Their pdf curves are used as the characteristic function of the sensor, denoted as pix, pjx, so xi and xj are the first measurement values of Xi and Xj, respectively. In order to express the degree of difference between xi and xj, the confidence distance measure dij is introduced, and the value of dij represents the confidence distance measure between the i-th sensor and the j-th sensor value, and σi represents the mean square error. Let(1)dij=2∫xixjpix|xidx,dji=2∫xjxipx|xijdx,pi=x|xi=12πσiexp−12x−xiσi2,pjx|xj∍=12πσjexp−12x−xjσj2.pix|xi , pjx|xj are expressed as probability density, the smaller the value of dij is, the closer the measurement results between i and j, and vice versa, the greater the difference [23]. Through the error function erfθ, it can be obtained:(2)dij=erfxj−xi2σi,dji=erfxj−xi2σj.Assuming that there aren sensors measuring the same parameter, the confidence distance measure dij is as follows:(3)dij=i,j=1,2,…,n.It can form a multisensor confidence distance matrixDn, so(4)Dn=d11d12…d1nd21d22…d2n⋮⋮⋱⋮dn1dn2…dnn.When multiple sensors measure the same target from multiple orientations, a fusion upper limit valueφij will be obtained, and for dij, there are(5)rij=1,dij≤φij;0,dij≤φij.Like,(6)rij=1.Then the compatibility between sensor nodesi and j is good and the mutual support is high. Otherwise, the compatibility is poor. If the sampling data of a sensor are supported by all other sensors, the sampling data are valid. If the sampled data of a certain sensor are only supported by a very small number of sensors, it is considered that the sampling data of the sensor is invalid and should be eliminated in the fusion stage to improve the fusion efficiency [24] because in the actual environment, the choice of threshold is too subjective and absolute. It often leads to misjudgment of fusion results. Now a new improvement method is listed.Calculation ofdij shows that(7)0≤dij≤1.According to the statistical significance of the operation formula, the smallerdij is, the higher the degree of support of sensor i by sensor j is [25]. Therefore, applying fuzzy theory to define the correlation function, we get(8)fi|j=1−dij,i,j=1,2,…,n.The magnitude of the correlation functionfi|j represents how well sensor i is supported by sensor j. The correlation function is defined as(9)fi|j=fi|jmaxfi|j,fj|i.It constructs a matrix offi|j, which is a square matrix, denoted as(10)C=i,j=1,2,…,n.If the rank isn, then there are(11)Ci′=minfi|A,A=1,2,…,n.A represents the other sensors andCi′ represents the degree to which the i-th sensor is supported by other sensors.


#### 3.2.1. Basic Trust Distribution Function

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. If any function satisfies(12)Bel:2U⊂0,1,then for any A, if there is(13)BelA=∑B⊂AmB,Belφ=mφ=0,BelU=∑B⊂UmB=1,then Bel is called a confidence function, and Bel belongs to the Probability Density Function, which represents the sum of the basic probability distributions of all subsets in A and represents the overall degree of confidence in A.


#### 3.2.2. Trust Function

LetU be the recognition frame, power set 2U is the set of propositions composed of all subsets in U, A belongs to this set 2U, and function BelA satisfies(14)Bel:2U⟶0,1,BelA=∑x⊆Amx.Then Bel is called the trust function on the recognition frameU. For any A∈U, BelA is called the confidence of proposition A.


#### 3.2.3. Confidence Interval

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. The confidence intervals of the D-S evidence theory are shown in Figure 5:Figure 5
Confidence interval of evidence theory.If the interval is1,1, then all intervals are considered to be supportive evidence, and at this time, A has the maximum support. Then the following relationship can be derived:(15)BelA≤PA≤PlA.


#### 3.2.4. Basic Probability Assignment Function

LetU be a recognition frame and 2U be the power set of U. If function m:2U⟶0,1, and the following conditions are met:(16)∑A∈2UmA=1,mA≥0,mφ=0.The classic D-S evidence combination rule is as follows:(17)mA=11−K∑B∩C=Am1Bm2C,0.In the formula,K is described as follows:(18)K=∑B∩C=φm1Bm2C.K is often called the conflict factor, and its value range is [0, 1]. The K value reflects the degree of the irrelevance of the pairwise evidence. The larger the value of K, the higher the degree of conflict between the evidence, and the value of K cannot be 1.


### 3.3. Karst Collapse Mechanism

The karst (KARST) collapse mechanism includes many aspects. There are mainly subsurface erosion theory, vacuum absorption theory, vibration theory, liquefaction theory, and gas explosion theory. Hydrodynamic conditions are generally considered to be the external cause of the ground collapse. The change of groundwater level is the inducing factor of karst collapse, and the structure of the geological body is the internal cause of the ground collapse. The upper overburden and the lower karst development are necessary conditions for karst collapse. The main mechanisms of ground collapse are as follows.


#### 3.3.1. Underlying Corrosion

The generally covered karst road sections have unobstructed groundwater flow conditions. At the same time, as the groundwater level dropped sharply, unstable soil and rocks were also washed away. This, in turn, produces erosion and hollowing out, and the hollowed-out area gradually expands. That is, soil caves are generated in the quaternary overburden and the underlying karst bedrock. At this time, the top of the soil cave will collapse due to the gradual change of the original stress to form a surface collapse. Hydrodynamic action can be transverse or longitudinal. Underground erosion of water is generally the action of groundwater, but it is also mostly caused by the infiltration of surface water. Underground erosion can be formed one or more times, and it has become the main inducement for the formation of soil subsidence. Many experts believe that this form of subsidence is due to the increase of hydraulic gradient, which causes the action of subsurface erosion to transport the cave filling. Over time, the rate of latent corrosion is accelerated, and when the normal stress of the upper covering layer is greater than the original resistance, it will lead to collapse. It is easier to determine that karst collapse is caused by seepage and undercurrent, and soil particles are lost to form soil caves, which are unstable and then collapse.


#### 3.3.2. Vacuum Suction Effect

When the groundwater level in the confined karst stratum drops below the bottom of the quaternary overburden due to pumping and drainage, that is, vacuum suction can be formed in the voids of the karst fracture zone some scholars have used model experiments to calculate the magnitude of vacuum suction. They believed that the pressure difference effect caused by the change of groundwater level is the main reason for the formation of karst collapse. In “On the Formation Mechanism of Karst Collapse,” the viewpoint that the pressure difference caused by the water level change further causes the vacuum absorption effect is expressed. It has also been successfully used to explain the karst collapse phenomenon in the Liuzhi mining area in Guizhou and the coal mining area in Hubei.


#### 3.3.3. Latent Corrosion∼Vacuum Suction Corrosion

The change of groundwater will definitely cause the underground erosion of the soil layer to occur. This is a long-term process, and the vacuum suction effect caused by the pressure difference will collapse only when the critical condition is reached. From the viewpoint of latent erosion and vacuum absorption, it is believed that karst collapse is caused by the above two effects. Some scholars have also successfully analyzed and explained the causes of ground collapse in Lujia Street, Wuchang, using the viewpoint of “subsurface erosion-vacuum absorption.”


#### 3.3.4. Vibration Theory and “Liquefaction Theory”

Vibration will cause rock and soil mass to produce fracture displacement, soil mass liquefaction and other effects. It reduces the strength of rock and soil mass and leads to the formation of collapse, which is called vibration collapse. This collapse is often caused by external vibration.


#### 3.3.5. Mechanism of Soil Cave Formation

The formation of overburdened soil cavities (cavities) will directly lead to the occurrence of karst collapse. People have been focusing on the study of karst cavities but neglected the research on the formation mechanism and formation conditions of soil cavities. This led to remedial measures after the collapse. However, in the construction process, they only focus on efficiency and interests and forget the damage to the underground environment caused by construction activities. For example, excessive and rapid groundwater extraction damages the mechanical stability of the overburden soil, resulting in ground collapse.The formation and development of soil caverns without human interference and the collapse after reaching the critical soil cavern height have to go through a long process. However, the development of human society destroys the underground homeostasis, which greatly reduces this time period. Some activities can create and rapidly expand cavities to the surface hours after groundwater is pumped. The causes of karst collapse are shown in Figure6.Figure 6
Causes of karst collapse.There are three necessary conditions for the formation of soil caves:(1)
First, there should be karst voids, fissures, or faults under the quaternary overburden. That is, there is a place for the storage of land particles carried away by groundwater activity.(2)
The formation of soil caves must have a certain thickness of overburden rock and soil mass. The shear strength and compressive strength of the overburden covering limestone, dolomite, and other rock mass karsts are low, especially near the bedrock surface. Due to the long-term immersion of karst void water in the aquifer, the soil strength is even lower. The soil layer is basically soft or fluid-plastic with extremely low tensile and shear strengths. The high-frequency fluctuation of groundwater under the intervention of human activities increases its hydraulic gradient and velocity. As a result, the stress on the soil above the karst and the karst cave is greater than the critical shear stress of the soil itself, resulting in undercutting, scouring, and hollowing, and the fine soil particles are transported away. Larger soil particles are unstable and fall into the cracks in the lower karst cave. The result is a cavity at the karst opening at the bottom of the layer. This is the prototype of the cave.(3)
Groundwater activity is an important condition for the formation of soil caves. There are two effects of groundwater flow on soil particles. One is the positive pressure acting on the soil by vacuum water flow and static pore water pressure. The second is the shear force acting on the side of the soil, which is consistent with the direction of the water flow and is caused by the hydrodynamic pressure. The change in water level directly destroys the stability of the soil layer. The change of water level not only causes high-intensity scouring of soil. And as the water level continued to drop, the volume of the soil cavity increased. The air pressure in the cavity decreases continuously, making the cavity lower than the standard atmospheric pressure outside and forming a low-pressure state. Finally, the stress of the soil around the cavity is greater than its compressive and shear strength, resulting in collapse.


## 3.1. Multisensor IoT Technology

According to the requirements of the monitoring and early warning system studied in this article, it is necessary to send the data of multiple wireless sensor nodes to the remote monitoring center. It is a multi-point-to-point communication method. The network topology can be divided into three types: star network, tree network, and mesh network. The wireless transmission of this system adopts a tree-type network structure, and Figure1 shows the system summary structure. Sensor nodes can be in routing mode or terminal mode and can transmit data directly with the coordinator node. If the distance between the two is relatively far, the data can be transferred through the adjacent sensor nodes [9]. The coordinator node is connected to the host computer through a USB cable [10].Figure 1
Overall structure of the system.The whole system can be divided into three parts: wireless sensor network node, coordinator node, and monitoring center. Wireless sensor nodes integrate multiple sensors and are responsible for measuring multiple parameters. After the data are processed, they are sent out through the wireless module. The monitoring center is the main console of the system. The received data can be saved and displayed in real time through the monitoring software, and the data exceeding the threshold can be alarmed in time. The user can monitor the work of each node through the monitoring center [11]. The coordinator node is responsible for building and managing the entire wireless network and monitoring the normal operation of each sensor node. It receives the data of each sensor node in real time and uploads it to the host of the monitoring center.A wireless sensor network node is a miniature embedded system. It consists of a hardware layer and software layer, and its architecture is shown in Figure2. From bottom to top, they are STM32 embedded microprocessor, peripheral hardware devices, μC/OS-II embedded real-time operating system, application program interface, and application program. The STM32-embedded microprocessor is the core of the node hardware layer. By connecting temperature and humidity sensors, air pressure sensors, accelerometers, and wireless communication modules, the hardware foundation of data acquisition, processing, and wireless transmission is formed. The software layer is built on the basis of the hardware layer, and μC/OS-II embedded real-time operating system is the core of the software layer. It provides a software platform and application programming interface. Based on this, applications can be easily written to achieve multitask parallelism [12].Figure 2
Wireless sensor node architecture.Multisensor network refers to the wireless interconnection and cooperation among many sensor units with communication and computing capabilities and interacts with the external environment to jointly complete a set of specific tasks [13, 14]. The multisensor network monitors and collects information about the surrounding external environment through real-time collaborative monitoring. This information is then processed and distributed to users [15, 16]. Compared with the traditional centralized processing method, the multisensor network has higher robustness, higher accuracy, higher flexibility, and stronger intelligence.The unit structure of the sensor consists of a sensing part, a processing part, a wireless transceiver part, and a power supply part. The structure of the sensor unit is shown in Figure3.Figure 3
Sensor unit structure.The sensing part is mainly used to perceive and collect the information in the monitoring area and convert the information into digital signals. It is mainly composed of sensors and A/D conversion subparts. The processing part is mainly responsible for controlling and coordinating the work of each sensor unit. It handles the specified tasks and executes the specified algorithms and is mainly composed of processor and memory subparts. The wireless transceiver part is mainly responsible for communicating with other sensor units and exchanging control signals and data information. It is mainly composed of buffer, transceiver, MAC, and network and can also carry a microprocessor in some specific applications [17]. The power supply part is mainly responsible for providing the energy required for the normal operation of the sensor unit, usually using a miniature battery.Therefore, each sensor unit has a dual function at the same time. It is not only about local information collection and data processing. At the same time, it also needs to store, manage, and fuse the data sent by other sensor units to complete specific collaborative tasks [18]. The network structure of the sensor consists of a sensor unit, aggregation unit, and management unit. The structure of the sensor network is shown in Figure 4.Figure 4
Sensor network structure.Numerous sensor units are randomly deployed near the monitoring area. It forms a multisensor network in a self-organizing manner. When there is data information in the sensor units in the network, it is transmitted one by one through the communication between the sensor units. Data information may be processed by multiple sensor units during the entire transmission process. Then it finally reaches the aggregation unit and reaches the management unit through the Internet or satellite [19]. The manager of the sensor network can configure and manage the sensor network through the management unit, publish monitoring tasks, and collect monitoring data information.Generally speaking, the processing capacity, storage capacity, and communication capacity of the aggregation unit are much stronger than other sensor units. It connects the sensor’s internal network and the external Internet at the same time and needs to perform protocol conversion between the two communication protocols. At the same time, the information monitored by the sensor units in the sensor network is forwarded to the external Internet [20, 21]. Therefore, the aggregation unit with enhanced functions requires a lot of storage and computation. And it carries a wireless communication interface and monitoring function [22].Multisensor network coordination mainly includes resource coordination, task coordination, and signal and information coordination, among which multisensor network task coordination mainly includes task description, task decomposition, task allocation and scheduling, and task execution. The main purpose of multisensor network task coordination is to reduce the communication volume and energy consumption between sensor units by optimizing the assignment of tasks, and prolong the life cycle of the sensor network.


## 3.2. Mathematical Basis of Multisensor Data Fusion

It assumes that multiple sensors estimate the same target value. LetXi and Xj be the data measured by the i-th sensor and the j-th sensor, respectively, and both Xi and Xj obey the Gaussian distribution. Their pdf curves are used as the characteristic function of the sensor, denoted as pix, pjx, so xi and xj are the first measurement values of Xi and Xj, respectively. In order to express the degree of difference between xi and xj, the confidence distance measure dij is introduced, and the value of dij represents the confidence distance measure between the i-th sensor and the j-th sensor value, and σi represents the mean square error. Let(1)dij=2∫xixjpix|xidx,dji=2∫xjxipx|xijdx,pi=x|xi=12πσiexp−12x−xiσi2,pjx|xj∍=12πσjexp−12x−xjσj2.pix|xi , pjx|xj are expressed as probability density, the smaller the value of dij is, the closer the measurement results between i and j, and vice versa, the greater the difference [23]. Through the error function erfθ, it can be obtained:(2)dij=erfxj−xi2σi,dji=erfxj−xi2σj.Assuming that there aren sensors measuring the same parameter, the confidence distance measure dij is as follows:(3)dij=i,j=1,2,…,n.It can form a multisensor confidence distance matrixDn, so(4)Dn=d11d12…d1nd21d22…d2n⋮⋮⋱⋮dn1dn2…dnn.When multiple sensors measure the same target from multiple orientations, a fusion upper limit valueφij will be obtained, and for dij, there are(5)rij=1,dij≤φij;0,dij≤φij.Like,(6)rij=1.Then the compatibility between sensor nodesi and j is good and the mutual support is high. Otherwise, the compatibility is poor. If the sampling data of a sensor are supported by all other sensors, the sampling data are valid. If the sampled data of a certain sensor are only supported by a very small number of sensors, it is considered that the sampling data of the sensor is invalid and should be eliminated in the fusion stage to improve the fusion efficiency [24] because in the actual environment, the choice of threshold is too subjective and absolute. It often leads to misjudgment of fusion results. Now a new improvement method is listed.Calculation ofdij shows that(7)0≤dij≤1.According to the statistical significance of the operation formula, the smallerdij is, the higher the degree of support of sensor i by sensor j is [25]. Therefore, applying fuzzy theory to define the correlation function, we get(8)fi|j=1−dij,i,j=1,2,…,n.The magnitude of the correlation functionfi|j represents how well sensor i is supported by sensor j. The correlation function is defined as(9)fi|j=fi|jmaxfi|j,fj|i.It constructs a matrix offi|j, which is a square matrix, denoted as(10)C=i,j=1,2,…,n.If the rank isn, then there are(11)Ci′=minfi|A,A=1,2,…,n.A represents the other sensors andCi′ represents the degree to which the i-th sensor is supported by other sensors.


### 3.2.1. Basic Trust Distribution Function

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. If any function satisfies(12)Bel:2U⊂0,1,then for any A, if there is(13)BelA=∑B⊂AmB,Belφ=mφ=0,BelU=∑B⊂UmB=1,then Bel is called a confidence function, and Bel belongs to the Probability Density Function, which represents the sum of the basic probability distributions of all subsets in A and represents the overall degree of confidence in A.


### 3.2.2. Trust Function

LetU be the recognition frame, power set 2U is the set of propositions composed of all subsets in U, A belongs to this set 2U, and function BelA satisfies(14)Bel:2U⟶0,1,BelA=∑x⊆Amx.Then Bel is called the trust function on the recognition frameU. For any A∈U, BelA is called the confidence of proposition A.


### 3.2.3. Confidence Interval

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. The confidence intervals of the D-S evidence theory are shown in Figure 5:Figure 5
Confidence interval of evidence theory.If the interval is1,1, then all intervals are considered to be supportive evidence, and at this time, A has the maximum support. Then the following relationship can be derived:(15)BelA≤PA≤PlA.


### 3.2.4. Basic Probability Assignment Function

LetU be a recognition frame and 2U be the power set of U. If function m:2U⟶0,1, and the following conditions are met:(16)∑A∈2UmA=1,mA≥0,mφ=0.The classic D-S evidence combination rule is as follows:(17)mA=11−K∑B∩C=Am1Bm2C,0.In the formula,K is described as follows:(18)K=∑B∩C=φm1Bm2C.K is often called the conflict factor, and its value range is [0, 1]. The K value reflects the degree of the irrelevance of the pairwise evidence. The larger the value of K, the higher the degree of conflict between the evidence, and the value of K cannot be 1.


## 3.2.1. Basic Trust Distribution Function

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. If any function satisfies(12)Bel:2U⊂0,1,then for any A, if there is(13)BelA=∑B⊂AmB,Belφ=mφ=0,BelU=∑B⊂UmB=1,then Bel is called a confidence function, and Bel belongs to the Probability Density Function, which represents the sum of the basic probability distributions of all subsets in A and represents the overall degree of confidence in A.


## 3.2.2. Trust Function

LetU be the recognition frame, power set 2U is the set of propositions composed of all subsets in U, A belongs to this set 2U, and function BelA satisfies(14)Bel:2U⟶0,1,BelA=∑x⊆Amx.Then Bel is called the trust function on the recognition frameU. For any A∈U, BelA is called the confidence of proposition A.


## 3.2.3. Confidence Interval

LetU be the recognition frame, and the number of elements in U is N, then its power set is 2U. The confidence intervals of the D-S evidence theory are shown in Figure 5:Figure 5
Confidence interval of evidence theory.If the interval is1,1, then all intervals are considered to be supportive evidence, and at this time, A has the maximum support. Then the following relationship can be derived:(15)BelA≤PA≤PlA.


## 3.2.4. Basic Probability Assignment Function

LetU be a recognition frame and 2U be the power set of U. If function m:2U⟶0,1, and the following conditions are met:(16)∑A∈2UmA=1,mA≥0,mφ=0.The classic D-S evidence combination rule is as follows:(17)mA=11−K∑B∩C=Am1Bm2C,0.In the formula,K is described as follows:(18)K=∑B∩C=φm1Bm2C.K is often called the conflict factor, and its value range is [0, 1]. The K value reflects the degree of the irrelevance of the pairwise evidence. The larger the value of K, the higher the degree of conflict between the evidence, and the value of K cannot be 1.


## 3.3. Karst Collapse Mechanism

The karst (KARST) collapse mechanism includes many aspects. There are mainly subsurface erosion theory, vacuum absorption theory, vibration theory, liquefaction theory, and gas explosion theory. Hydrodynamic conditions are generally considered to be the external cause of the ground collapse. The change of groundwater level is the inducing factor of karst collapse, and the structure of the geological body is the internal cause of the ground collapse. The upper overburden and the lower karst development are necessary conditions for karst collapse. The main mechanisms of ground collapse are as follows.


### 3.3.1. Underlying Corrosion

The generally covered karst road sections have unobstructed groundwater flow conditions. At the same time, as the groundwater level dropped sharply, unstable soil and rocks were also washed away. This, in turn, produces erosion and hollowing out, and the hollowed-out area gradually expands. That is, soil caves are generated in the quaternary overburden and the underlying karst bedrock. At this time, the top of the soil cave will collapse due to the gradual change of the original stress to form a surface collapse. Hydrodynamic action can be transverse or longitudinal. Underground erosion of water is generally the action of groundwater, but it is also mostly caused by the infiltration of surface water. Underground erosion can be formed one or more times, and it has become the main inducement for the formation of soil subsidence. Many experts believe that this form of subsidence is due to the increase of hydraulic gradient, which causes the action of subsurface erosion to transport the cave filling. Over time, the rate of latent corrosion is accelerated, and when the normal stress of the upper covering layer is greater than the original resistance, it will lead to collapse. It is easier to determine that karst collapse is caused by seepage and undercurrent, and soil particles are lost to form soil caves, which are unstable and then collapse.


### 3.3.2. Vacuum Suction Effect

When the groundwater level in the confined karst stratum drops below the bottom of the quaternary overburden due to pumping and drainage, that is, vacuum suction can be formed in the voids of the karst fracture zone some scholars have used model experiments to calculate the magnitude of vacuum suction. They believed that the pressure difference effect caused by the change of groundwater level is the main reason for the formation of karst collapse. In “On the Formation Mechanism of Karst Collapse,” the viewpoint that the pressure difference caused by the water level change further causes the vacuum absorption effect is expressed. It has also been successfully used to explain the karst collapse phenomenon in the Liuzhi mining area in Guizhou and the coal mining area in Hubei.


### 3.3.3. Latent Corrosion∼Vacuum Suction Corrosion

The change of groundwater will definitely cause the underground erosion of the soil layer to occur. This is a long-term process, and the vacuum suction effect caused by the pressure difference will collapse only when the critical condition is reached. From the viewpoint of latent erosion and vacuum absorption, it is believed that karst collapse is caused by the above two effects. Some scholars have also successfully analyzed and explained the causes of ground collapse in Lujia Street, Wuchang, using the viewpoint of “subsurface erosion-vacuum absorption.”


### 3.3.4. Vibration Theory and “Liquefaction Theory”

Vibration will cause rock and soil mass to produce fracture displacement, soil mass liquefaction and other effects. It reduces the strength of rock and soil mass and leads to the formation of collapse, which is called vibration collapse. This collapse is often caused by external vibration.


### 3.3.5. Mechanism of Soil Cave Formation

The formation of overburdened soil cavities (cavities) will directly lead to the occurrence of karst collapse. People have been focusing on the study of karst cavities but neglected the research on the formation mechanism and formation conditions of soil cavities. This led to remedial measures after the collapse. However, in the construction process, they only focus on efficiency and interests and forget the damage to the underground environment caused by construction activities. For example, excessive and rapid groundwater extraction damages the mechanical stability of the overburden soil, resulting in ground collapse.The formation and development of soil caverns without human interference and the collapse after reaching the critical soil cavern height have to go through a long process. However, the development of human society destroys the underground homeostasis, which greatly reduces this time period. Some activities can create and rapidly expand cavities to the surface hours after groundwater is pumped. The causes of karst collapse are shown in Figure6.Figure 6
Causes of karst collapse.There are three necessary conditions for the formation of soil caves:(1)
First, there should be karst voids, fissures, or faults under the quaternary overburden. That is, there is a place for the storage of land particles carried away by groundwater activity.(2)
The formation of soil caves must have a certain thickness of overburden rock and soil mass. The shear strength and compressive strength of the overburden covering limestone, dolomite, and other rock mass karsts are low, especially near the bedrock surface. Due to the long-term immersion of karst void water in the aquifer, the soil strength is even lower. The soil layer is basically soft or fluid-plastic with extremely low tensile and shear strengths. The high-frequency fluctuation of groundwater under the intervention of human activities increases its hydraulic gradient and velocity. As a result, the stress on the soil above the karst and the karst cave is greater than the critical shear stress of the soil itself, resulting in undercutting, scouring, and hollowing, and the fine soil particles are transported away. Larger soil particles are unstable and fall into the cracks in the lower karst cave. The result is a cavity at the karst opening at the bottom of the layer. This is the prototype of the cave.(3)
Groundwater activity is an important condition for the formation of soil caves. There are two effects of groundwater flow on soil particles. One is the positive pressure acting on the soil by vacuum water flow and static pore water pressure. The second is the shear force acting on the side of the soil, which is consistent with the direction of the water flow and is caused by the hydrodynamic pressure. The change in water level directly destroys the stability of the soil layer. The change of water level not only causes high-intensity scouring of soil. And as the water level continued to drop, the volume of the soil cavity increased. The air pressure in the cavity decreases continuously, making the cavity lower than the standard atmospheric pressure outside and forming a low-pressure state. Finally, the stress of the soil around the cavity is greater than its compressive and shear strength, resulting in collapse.


## 3.3.1. Underlying Corrosion

The generally covered karst road sections have unobstructed groundwater flow conditions. At the same time, as the groundwater level dropped sharply, unstable soil and rocks were also washed away. This, in turn, produces erosion and hollowing out, and the hollowed-out area gradually expands. That is, soil caves are generated in the quaternary overburden and the underlying karst bedrock. At this time, the top of the soil cave will collapse due to the gradual change of the original stress to form a surface collapse. Hydrodynamic action can be transverse or longitudinal. Underground erosion of water is generally the action of groundwater, but it is also mostly caused by the infiltration of surface water. Underground erosion can be formed one or more times, and it has become the main inducement for the formation of soil subsidence. Many experts believe that this form of subsidence is due to the increase of hydraulic gradient, which causes the action of subsurface erosion to transport the cave filling. Over time, the rate of latent corrosion is accelerated, and when the normal stress of the upper covering layer is greater than the original resistance, it will lead to collapse. It is easier to determine that karst collapse is caused by seepage and undercurrent, and soil particles are lost to form soil caves, which are unstable and then collapse.


## 3.3.2. Vacuum Suction Effect

When the groundwater level in the confined karst stratum drops below the bottom of the quaternary overburden due to pumping and drainage, that is, vacuum suction can be formed in the voids of the karst fracture zone some scholars have used model experiments to calculate the magnitude of vacuum suction. They believed that the pressure difference effect caused by the change of groundwater level is the main reason for the formation of karst collapse. In “On the Formation Mechanism of Karst Collapse,” the viewpoint that the pressure difference caused by the water level change further causes the vacuum absorption effect is expressed. It has also been successfully used to explain the karst collapse phenomenon in the Liuzhi mining area in Guizhou and the coal mining area in Hubei.


## 3.3.3. Latent Corrosion∼Vacuum Suction Corrosion

The change of groundwater will definitely cause the underground erosion of the soil layer to occur. This is a long-term process, and the vacuum suction effect caused by the pressure difference will collapse only when the critical condition is reached. From the viewpoint of latent erosion and vacuum absorption, it is believed that karst collapse is caused by the above two effects. Some scholars have also successfully analyzed and explained the causes of ground collapse in Lujia Street, Wuchang, using the viewpoint of “subsurface erosion-vacuum absorption.”


## 3.3.4. Vibration Theory and “Liquefaction Theory”

Vibration will cause rock and soil mass to produce fracture displacement, soil mass liquefaction and other effects. It reduces the strength of rock and soil mass and leads to the formation of collapse, which is called vibration collapse. This collapse is often caused by external vibration.


## 3.3.5. Mechanism of Soil Cave Formation

The formation of overburdened soil cavities (cavities) will directly lead to the occurrence of karst collapse. People have been focusing on the study of karst cavities but neglected the research on the formation mechanism and formation conditions of soil cavities. This led to remedial measures after the collapse. However, in the construction process, they only focus on efficiency and interests and forget the damage to the underground environment caused by construction activities. For example, excessive and rapid groundwater extraction damages the mechanical stability of the overburden soil, resulting in ground collapse.The formation and development of soil caverns without human interference and the collapse after reaching the critical soil cavern height have to go through a long process. However, the development of human society destroys the underground homeostasis, which greatly reduces this time period. Some activities can create and rapidly expand cavities to the surface hours after groundwater is pumped. The causes of karst collapse are shown in Figure6.Figure 6
Causes of karst collapse.There are three necessary conditions for the formation of soil caves:(1)
First, there should be karst voids, fissures, or faults under the quaternary overburden. That is, there is a place for the storage of land particles carried away by groundwater activity.(2)
The formation of soil caves must have a certain thickness of overburden rock and soil mass. The shear strength and compressive strength of the overburden covering limestone, dolomite, and other rock mass karsts are low, especially near the bedrock surface. Due to the long-term immersion of karst void water in the aquifer, the soil strength is even lower. The soil layer is basically soft or fluid-plastic with extremely low tensile and shear strengths. The high-frequency fluctuation of groundwater under the intervention of human activities increases its hydraulic gradient and velocity. As a result, the stress on the soil above the karst and the karst cave is greater than the critical shear stress of the soil itself, resulting in undercutting, scouring, and hollowing, and the fine soil particles are transported away. Larger soil particles are unstable and fall into the cracks in the lower karst cave. The result is a cavity at the karst opening at the bottom of the layer. This is the prototype of the cave.(3)
Groundwater activity is an important condition for the formation of soil caves. There are two effects of groundwater flow on soil particles. One is the positive pressure acting on the soil by vacuum water flow and static pore water pressure. The second is the shear force acting on the side of the soil, which is consistent with the direction of the water flow and is caused by the hydrodynamic pressure. The change in water level directly destroys the stability of the soil layer. The change of water level not only causes high-intensity scouring of soil. And as the water level continued to drop, the volume of the soil cavity increased. The air pressure in the cavity decreases continuously, making the cavity lower than the standard atmospheric pressure outside and forming a low-pressure state. Finally, the stress of the soil around the cavity is greater than its compressive and shear strength, resulting in collapse.


## 4. Karst Collapse Susceptibility Zoning Experiment

### 4.1. Overlay Condition

It is based on statistics of karst collapse overburden conditions in the work area. The degree of susceptibility was graded by two factors, the thickness of the capping layer, and the structure of the capping layer. Overburden is the main body of overburden karst collapse. Its thickness and structure determine the danger of karst collapse.


#### 4.1.1. Thickness of Cover Layer

The work area is hilly and mountainous, with frequent terrain fluctuations and large slopes. The cover layer is very uneven in both plane distribution and thickness variation. Generally, it is distributed on the gentle slopes below the mountainside. The terrain is relatively steep, and the upper part of the mountainside is generally rarely distributed or the bedrock is exposed.


#### 4.1.2. Overlay Structure

For the overburden structure, the one-dimensional structure area accounts for 86% of the soil distribution area, and most of the karst collapses develop in the one-dimensional structure area. The binary structure is rarely distributed, the ternary structure is almost absent, and the distribution of karst collapse is relatively rare. Areas without soil cover are basically less likely to collapse. The single-factor hierarchical properties for the overlay are shown in Table1.Table 1
Single-factor hierarchical attribute table of the cover layer.
First-level indicatorSoil layerSecondary indicatorsSoil thicknessSoil structureEffects on karst collapseHigh<5Single-layer structureAssign44Middle5–10Double-layer structureAssign33LowExposed karst areaMultilayer structureAssign22NoNoncarbonate rockRock base areaAssign11


#### 4.1.3. Groundwater Conditions

Hydrogeological conditions are one of the main factors influencing the occurrence of karst collapse. It is based on the statistics of the hydrogeological conditions of karst collapse in the work area. The susceptibility is graded by two factors: karst groundwater type and water-rich. The classification is shown in Table2.Table 2
Single-factor classification attribute table of hydrogeological conditions.
First-level indicatorHydrogeologySecondary indicatorsGroundwater typeWater-richEffects on karst collapseHighCarbonate fissureRichAssign44MiddleCarbonate karstMediumAssign33LowCarbonate bedrockPoorAssign22NoNoncarbonate rock saltPoor-moderateAssign11There are various types of karst groundwater in the work area. The corresponding karst collapse development numbers are high, medium, and low, respectively. The bedrock fissure water in the nonsoluble rock area is regarded as a less prone area.


#### 4.1.4. Groundwater Level Fluctuations

The greater the frequency of groundwater level fluctuations, the greater the intensity of rock-soil deformation. The more frequent the fluctuation, the higher the rate, and the higher the rate of rock-soil deformation. Because these data require long-term detection statistics, due to this limitation, no assignment is made in the susceptibility partitioning.


### 4.2. Human Engineering Activities

Human engineering activities are the main inducing factors of karst ground collapse. An important activity type for karst collapse in the working area is underground mining and drainage of groundwater. The formed karst water drop funnels result in the decline of the groundwater level and the strong groundwater runoff zone. Therefore, the manifestations of human engineering activities are assigned according to the intensity of groundwater pumping and the distance from the pumping and drainage. Its classification is shown in Table3.Table 3
Single-factor hierarchical attribute table of human engineering activities.
First-level indicatorEngineering activitiesSecondary indicatorsPumping and drainage strengthPumping distanceEffects on karst collapseHighWater level drops<3000Assign44MiddleLess affected3000∼5000Assign33LowNot yet mined>5000Assign22NoKarst-free waterAssign11


#### 4.2.1. Karst Collapse Distribution

The distribution range, density, scale, and degree of damage are the most direct manifestations of the risk of karst collapse and indirect reflections of triggering factors. Generally speaking, the wider the distribution range and the greater the development density of the existing collapse, the higher the damage degree and the higher the corresponding risk level. A single collapse, and a collapse that does not appear as a group of pits, lasts for a long time and is dangerous. Its susceptibility is also low. According to the existing data level, evaluation scope, and precision requirements, this study selects karst collapse density as one of the indicators to evaluate the susceptibility of karst collapse. Karst collapse density refers to the number of karst collapses per unit area. The greater the density, the greater the susceptibility. It is divided into high-density area, medium-density area, and low-density area. The corresponding risk levels are high, medium, and low susceptibility. For nonsoluble rock, it is regarded as a less prone area; at the same time, according to the development scale of karst collapse and the distribution of group pits and single pits, different classifications and assignments are also given. The details are shown in Table4.Table 4
Single-factor classification attribute table of karst collapse density.
First-level indicatorKarst collapse densityScaleEffects on karst collapseHigh>1/km2Pit distributionAssign44Middle0.1–1/km2Single pitAssign33Low0.01/km2Single pitAssign22NoInsoluble rock areaNoneAssign11


#### 4.2.2. Geological Structure

Geological structure controls the development of karst. Generally speaking, due to the fault structure, the soluble rock mass is broken, and the fractures are highly developed, which is easy to conduct water and causes the karst phenomenon. The tensile fault has better water conductivity and strong groundwater activity. Compressive faults have poor water conductivity and tend to accumulate water at one end of the fault disk, and groundwater is relatively abundant. The more dense and developed the fault structure, the stronger the karst, and the stronger the groundwater activity, which is more conducive to the karst collapse. The greater the fault density, the greater the susceptibility. In addition, the closer the karst collapse is to the structure, the greater the probability of collapse is, and the greater the susceptibility is.In this study, the karst collapse risk degree is classified and assigned according to the nature of the fault and the distance from the structure. The details are shown in Table5.Table 5
Geological structure single-factor classification attribute table.
First-level indicatorGeological structureSecondary indicatorsFault properties and tectonic distanceEffects on karst collapseHighTensor100–200Assign44MiddleTension200–500Assign33LowPressure>500Assign22NoCrumbsRock areaAssign11


## 4.1. Overlay Condition

It is based on statistics of karst collapse overburden conditions in the work area. The degree of susceptibility was graded by two factors, the thickness of the capping layer, and the structure of the capping layer. Overburden is the main body of overburden karst collapse. Its thickness and structure determine the danger of karst collapse.


### 4.1.1. Thickness of Cover Layer

The work area is hilly and mountainous, with frequent terrain fluctuations and large slopes. The cover layer is very uneven in both plane distribution and thickness variation. Generally, it is distributed on the gentle slopes below the mountainside. The terrain is relatively steep, and the upper part of the mountainside is generally rarely distributed or the bedrock is exposed.


### 4.1.2. Overlay Structure

For the overburden structure, the one-dimensional structure area accounts for 86% of the soil distribution area, and most of the karst collapses develop in the one-dimensional structure area. The binary structure is rarely distributed, the ternary structure is almost absent, and the distribution of karst collapse is relatively rare. Areas without soil cover are basically less likely to collapse. The single-factor hierarchical properties for the overlay are shown in Table1.Table 1
Single-factor hierarchical attribute table of the cover layer.
First-level indicatorSoil layerSecondary indicatorsSoil thicknessSoil structureEffects on karst collapseHigh<5Single-layer structureAssign44Middle5–10Double-layer structureAssign33LowExposed karst areaMultilayer structureAssign22NoNoncarbonate rockRock base areaAssign11


### 4.1.3. Groundwater Conditions

Hydrogeological conditions are one of the main factors influencing the occurrence of karst collapse. It is based on the statistics of the hydrogeological conditions of karst collapse in the work area. The susceptibility is graded by two factors: karst groundwater type and water-rich. The classification is shown in Table2.Table 2
Single-factor classification attribute table of hydrogeological conditions.
First-level indicatorHydrogeologySecondary indicatorsGroundwater typeWater-richEffects on karst collapseHighCarbonate fissureRichAssign44MiddleCarbonate karstMediumAssign33LowCarbonate bedrockPoorAssign22NoNoncarbonate rock saltPoor-moderateAssign11There are various types of karst groundwater in the work area. The corresponding karst collapse development numbers are high, medium, and low, respectively. The bedrock fissure water in the nonsoluble rock area is regarded as a less prone area.


### 4.1.4. Groundwater Level Fluctuations

The greater the frequency of groundwater level fluctuations, the greater the intensity of rock-soil deformation. The more frequent the fluctuation, the higher the rate, and the higher the rate of rock-soil deformation. Because these data require long-term detection statistics, due to this limitation, no assignment is made in the susceptibility partitioning.


## 4.1.1. Thickness of Cover Layer

The work area is hilly and mountainous, with frequent terrain fluctuations and large slopes. The cover layer is very uneven in both plane distribution and thickness variation. Generally, it is distributed on the gentle slopes below the mountainside. The terrain is relatively steep, and the upper part of the mountainside is generally rarely distributed or the bedrock is exposed.


## 4.1.2. Overlay Structure

For the overburden structure, the one-dimensional structure area accounts for 86% of the soil distribution area, and most of the karst collapses develop in the one-dimensional structure area. The binary structure is rarely distributed, the ternary structure is almost absent, and the distribution of karst collapse is relatively rare. Areas without soil cover are basically less likely to collapse. The single-factor hierarchical properties for the overlay are shown in Table1.Table 1
Single-factor hierarchical attribute table of the cover layer.
First-level indicatorSoil layerSecondary indicatorsSoil thicknessSoil structureEffects on karst collapseHigh<5Single-layer structureAssign44Middle5–10Double-layer structureAssign33LowExposed karst areaMultilayer structureAssign22NoNoncarbonate rockRock base areaAssign11


## 4.1.3. Groundwater Conditions

Hydrogeological conditions are one of the main factors influencing the occurrence of karst collapse. It is based on the statistics of the hydrogeological conditions of karst collapse in the work area. The susceptibility is graded by two factors: karst groundwater type and water-rich. The classification is shown in Table2.Table 2
Single-factor classification attribute table of hydrogeological conditions.
First-level indicatorHydrogeologySecondary indicatorsGroundwater typeWater-richEffects on karst collapseHighCarbonate fissureRichAssign44MiddleCarbonate karstMediumAssign33LowCarbonate bedrockPoorAssign22NoNoncarbonate rock saltPoor-moderateAssign11There are various types of karst groundwater in the work area. The corresponding karst collapse development numbers are high, medium, and low, respectively. The bedrock fissure water in the nonsoluble rock area is regarded as a less prone area.


## 4.1.4. Groundwater Level Fluctuations

The greater the frequency of groundwater level fluctuations, the greater the intensity of rock-soil deformation. The more frequent the fluctuation, the higher the rate, and the higher the rate of rock-soil deformation. Because these data require long-term detection statistics, due to this limitation, no assignment is made in the susceptibility partitioning.


## 4.2. Human Engineering Activities

Human engineering activities are the main inducing factors of karst ground collapse. An important activity type for karst collapse in the working area is underground mining and drainage of groundwater. The formed karst water drop funnels result in the decline of the groundwater level and the strong groundwater runoff zone. Therefore, the manifestations of human engineering activities are assigned according to the intensity of groundwater pumping and the distance from the pumping and drainage. Its classification is shown in Table3.Table 3
Single-factor hierarchical attribute table of human engineering activities.
First-level indicatorEngineering activitiesSecondary indicatorsPumping and drainage strengthPumping distanceEffects on karst collapseHighWater level drops<3000Assign44MiddleLess affected3000∼5000Assign33LowNot yet mined>5000Assign22NoKarst-free waterAssign11


### 4.2.1. Karst Collapse Distribution

The distribution range, density, scale, and degree of damage are the most direct manifestations of the risk of karst collapse and indirect reflections of triggering factors. Generally speaking, the wider the distribution range and the greater the development density of the existing collapse, the higher the damage degree and the higher the corresponding risk level. A single collapse, and a collapse that does not appear as a group of pits, lasts for a long time and is dangerous. Its susceptibility is also low. According to the existing data level, evaluation scope, and precision requirements, this study selects karst collapse density as one of the indicators to evaluate the susceptibility of karst collapse. Karst collapse density refers to the number of karst collapses per unit area. The greater the density, the greater the susceptibility. It is divided into high-density area, medium-density area, and low-density area. The corresponding risk levels are high, medium, and low susceptibility. For nonsoluble rock, it is regarded as a less prone area; at the same time, according to the development scale of karst collapse and the distribution of group pits and single pits, different classifications and assignments are also given. The details are shown in Table4.Table 4
Single-factor classification attribute table of karst collapse density.
First-level indicatorKarst collapse densityScaleEffects on karst collapseHigh>1/km2Pit distributionAssign44Middle0.1–1/km2Single pitAssign33Low0.01/km2Single pitAssign22NoInsoluble rock areaNoneAssign11


### 4.2.2. Geological Structure

Geological structure controls the development of karst. Generally speaking, due to the fault structure, the soluble rock mass is broken, and the fractures are highly developed, which is easy to conduct water and causes the karst phenomenon. The tensile fault has better water conductivity and strong groundwater activity. Compressive faults have poor water conductivity and tend to accumulate water at one end of the fault disk, and groundwater is relatively abundant. The more dense and developed the fault structure, the stronger the karst, and the stronger the groundwater activity, which is more conducive to the karst collapse. The greater the fault density, the greater the susceptibility. In addition, the closer the karst collapse is to the structure, the greater the probability of collapse is, and the greater the susceptibility is.In this study, the karst collapse risk degree is classified and assigned according to the nature of the fault and the distance from the structure. The details are shown in Table5.Table 5
Geological structure single-factor classification attribute table.
First-level indicatorGeological structureSecondary indicatorsFault properties and tectonic distanceEffects on karst collapseHighTensor100–200Assign44MiddleTension200–500Assign33LowPressure>500Assign22NoCrumbsRock areaAssign11


## 4.2.1. Karst Collapse Distribution

The distribution range, density, scale, and degree of damage are the most direct manifestations of the risk of karst collapse and indirect reflections of triggering factors. Generally speaking, the wider the distribution range and the greater the development density of the existing collapse, the higher the damage degree and the higher the corresponding risk level. A single collapse, and a collapse that does not appear as a group of pits, lasts for a long time and is dangerous. Its susceptibility is also low. According to the existing data level, evaluation scope, and precision requirements, this study selects karst collapse density as one of the indicators to evaluate the susceptibility of karst collapse. Karst collapse density refers to the number of karst collapses per unit area. The greater the density, the greater the susceptibility. It is divided into high-density area, medium-density area, and low-density area. The corresponding risk levels are high, medium, and low susceptibility. For nonsoluble rock, it is regarded as a less prone area; at the same time, according to the development scale of karst collapse and the distribution of group pits and single pits, different classifications and assignments are also given. The details are shown in Table4.Table 4
Single-factor classification attribute table of karst collapse density.
First-level indicatorKarst collapse densityScaleEffects on karst collapseHigh>1/km2Pit distributionAssign44Middle0.1–1/km2Single pitAssign33Low0.01/km2Single pitAssign22NoInsoluble rock areaNoneAssign11


## 4.2.2. Geological Structure

Geological structure controls the development of karst. Generally speaking, due to the fault structure, the soluble rock mass is broken, and the fractures are highly developed, which is easy to conduct water and causes the karst phenomenon. The tensile fault has better water conductivity and strong groundwater activity. Compressive faults have poor water conductivity and tend to accumulate water at one end of the fault disk, and groundwater is relatively abundant. The more dense and developed the fault structure, the stronger the karst, and the stronger the groundwater activity, which is more conducive to the karst collapse. The greater the fault density, the greater the susceptibility. In addition, the closer the karst collapse is to the structure, the greater the probability of collapse is, and the greater the susceptibility is.In this study, the karst collapse risk degree is classified and assigned according to the nature of the fault and the distance from the structure. The details are shown in Table5.Table 5
Geological structure single-factor classification attribute table.
First-level indicatorGeological structureSecondary indicatorsFault properties and tectonic distanceEffects on karst collapseHighTensor100–200Assign44MiddleTension200–500Assign33LowPressure>500Assign22NoCrumbsRock areaAssign11


## 5. Numerical Simulation and Results of Sensor Simulation under Different Boundary Conditions

### 5.1. Numerical Simulation and Results of Beams Supported at Both Ends

When the horizontal section of the karst cave roof is rectangular and the width is close to the pile diameter, the karst cave roof can be considered as the force of the beam. The rock formations at both ends of the beam are complete and, in good contact, can be regarded as fixed support. In this section, the force model of the beam supported at both ends will be taken as the analysis object. Using the designed multisensor network, the relationship curve between the ultimate bearing capacity and displacement and span of the cave roof with different thicknesses collected is drawn as shown in Figure7.Figure 7
Relationship between ultimate bearing capacity and displacement and span.It can be seen from the figure that for a fixed beam with the same span, the greater the thickness of the roof, the greater the ultimate bearing capacity. For the karst roof with the same thickness, the ultimate bearing capacity decreases gradually with the increase of the span. And the decreasing trend will slow down. When the thickness of the roof is 1 m, the change of the ultimate bearing capacity with the span is more significant than when the thickness of the roof is 3 m. And under the same load conditions, the greater the thickness of the roof, the smaller the central displacement of the roof, and the less obvious the change. It can be inferred that when the karst roof reaches a certain thickness, the influence of the span on the ultimate bearing capacity can be ignored. The roof failure at this time tends to be without karst.


### 5.2. Numerical Simulation and Result Analysis of Clamped Circular Plate

When the horizontal section of the roof of the karst cave is circular and the surrounding rock formation is complete, the contact is good. It can consider the roof of the karst cave according to the force of the fixed circular plate. This section will take the force model of the clamped circular plate as the analysis object. It uses the designed multisensor network to draw the relationship curve between the ultimate bearing capacity and displacement and span of the roof of karst caves with different thicknesses, as shown in Figure8.Figure 8
Relationship between ultimate bearing capacity, displacement, and span.It can be seen from the figure that the ultimate bearing capacity of the clamped circular plate under the same thickness condition decreases with the increase of the span. The decreasing range also gradually becomes smaller, indicating that the influence of span on the ultimate bearing capacity of the karst roof is decreasing. Under the same span condition, the greater the thickness, the greater the ultimate bearing capacity. And under the same load conditions, the smaller the thickness of the roof, the more obvious the change of the center displacement of the roof, and there is a slowing trend.


### 5.3. Physical Layer Simulation Verification and Results

In the MATLAB7.1 simulation software, the algorithm of the physical layer in the cooperative communication protocol of the multisensor network is simulated and analyzed. The simulation parameters of the physical layer in the multisensor network cooperative communication protocol are as follows. The modulation method is BPSK, the pseudorandom code ism sequence, and the amplitude of the signal is 1. The information code rate is 10 Kbit/s, the carrier frequency is 100 MHz, the sampling frequency is 20 GHz, and the spreading code rate is 10 Mbit/s. In the multisensor network communication protocol, the time-domain waveform diagram before the spread spectrum and the time-domain waveform diagram after the spread spectrum is shown in Figure 9.Figure 9
Time-domain waveforms before and after spread spectrum.Figure10 shows the frequency domain waveforms before and after spreading in the multisensor network communication protocol:Figure 10
Frequency domain waveforms before and after spread spectrum.As can be seen from the figure, the spectrum of the physical layer signal after pseudorandom code spread and the physical layer signal without spectrum spread is broadened. Error-free transmission of such signals at low signal-to-noise ratios is possible. Thereby, the antijamming performance of the physical layer in the multisensor network communication system is improved.Based on the above analysis, it can be seen that the improved multisensor-based karst collapse monitoring and early warning evaluation improves the anti-interference performance by 34%. The frequency of early warning can be increased by 24%, which greatly prevents the loss of personnel and property caused by karst.


## 5.1. Numerical Simulation and Results of Beams Supported at Both Ends

When the horizontal section of the karst cave roof is rectangular and the width is close to the pile diameter, the karst cave roof can be considered as the force of the beam. The rock formations at both ends of the beam are complete and, in good contact, can be regarded as fixed support. In this section, the force model of the beam supported at both ends will be taken as the analysis object. Using the designed multisensor network, the relationship curve between the ultimate bearing capacity and displacement and span of the cave roof with different thicknesses collected is drawn as shown in Figure7.Figure 7
Relationship between ultimate bearing capacity and displacement and span.It can be seen from the figure that for a fixed beam with the same span, the greater the thickness of the roof, the greater the ultimate bearing capacity. For the karst roof with the same thickness, the ultimate bearing capacity decreases gradually with the increase of the span. And the decreasing trend will slow down. When the thickness of the roof is 1 m, the change of the ultimate bearing capacity with the span is more significant than when the thickness of the roof is 3 m. And under the same load conditions, the greater the thickness of the roof, the smaller the central displacement of the roof, and the less obvious the change. It can be inferred that when the karst roof reaches a certain thickness, the influence of the span on the ultimate bearing capacity can be ignored. The roof failure at this time tends to be without karst.


## 5.2. Numerical Simulation and Result Analysis of Clamped Circular Plate

When the horizontal section of the roof of the karst cave is circular and the surrounding rock formation is complete, the contact is good. It can consider the roof of the karst cave according to the force of the fixed circular plate. This section will take the force model of the clamped circular plate as the analysis object. It uses the designed multisensor network to draw the relationship curve between the ultimate bearing capacity and displacement and span of the roof of karst caves with different thicknesses, as shown in Figure8.Figure 8
Relationship between ultimate bearing capacity, displacement, and span.It can be seen from the figure that the ultimate bearing capacity of the clamped circular plate under the same thickness condition decreases with the increase of the span. The decreasing range also gradually becomes smaller, indicating that the influence of span on the ultimate bearing capacity of the karst roof is decreasing. Under the same span condition, the greater the thickness, the greater the ultimate bearing capacity. And under the same load conditions, the smaller the thickness of the roof, the more obvious the change of the center displacement of the roof, and there is a slowing trend.


## 5.3. Physical Layer Simulation Verification and Results

In the MATLAB7.1 simulation software, the algorithm of the physical layer in the cooperative communication protocol of the multisensor network is simulated and analyzed. The simulation parameters of the physical layer in the multisensor network cooperative communication protocol are as follows. The modulation method is BPSK, the pseudorandom code ism sequence, and the amplitude of the signal is 1. The information code rate is 10 Kbit/s, the carrier frequency is 100 MHz, the sampling frequency is 20 GHz, and the spreading code rate is 10 Mbit/s. In the multisensor network communication protocol, the time-domain waveform diagram before the spread spectrum and the time-domain waveform diagram after the spread spectrum is shown in Figure 9.Figure 9
Time-domain waveforms before and after spread spectrum.Figure10 shows the frequency domain waveforms before and after spreading in the multisensor network communication protocol:Figure 10
Frequency domain waveforms before and after spread spectrum.As can be seen from the figure, the spectrum of the physical layer signal after pseudorandom code spread and the physical layer signal without spectrum spread is broadened. Error-free transmission of such signals at low signal-to-noise ratios is possible. Thereby, the antijamming performance of the physical layer in the multisensor network communication system is improved.Based on the above analysis, it can be seen that the improved multisensor-based karst collapse monitoring and early warning evaluation improves the anti-interference performance by 34%. The frequency of early warning can be increased by 24%, which greatly prevents the loss of personnel and property caused by karst.


## 6. Conclusion

This article mainly studies how to improve the current karst collapse monitoring and early warning system through the use of multisensor Internet of Things technology. To this end, this article has made great efforts in the key multisensor data fusion. Through the data fusion problem faced by multisensor, this article has carried out a separate study to improve it. And in the analysis part, the verification and comparison analysis of its effect is carried out. At the same time, a detailed understanding of the causes of karst collapse was carried out. This facilitates better timely early warning in the actual monitoring and early warning work.



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*Source: 2099268-2022-05-18.xml*