Tensor-based mobile Internet of Things coverage reliability assessment method

Abstract

The present invention discloses a tensor-based mobile Internet of Things coverage reliability assessment method: a network model is established according to a monitoring scenario; node status, energy, connectivity robustness, coverage, and link reliability are considered to define trusted information coverage reliability; state and energy tensors are constructed, and a multimodal Markov state probability prediction model is used to predict node status; a coverage tensor is constructed to calculate coverage; communication links are enumerated to calculate connectivity robustness; and Monte Carlo simulation is used to assess the trusted information coverage reliability of a specified network until the number of simulations reaches an upper limit. The present invention comprehensively considers node status, energy, connectivity robustness, coverage, and link reliability to accurately measure coverage reliability, adopts a multimodal Markov state probability prediction model to dynamically predict node status, and uses tensors to perform high-dimensional unified representation of network heterogeneous factors, thereby realizing efficient calculation of mobile Internet of Things coverage reliability.

Description

Technical Field

[0001] The present invention belongs to the technical field of Internet of Things, and more specifically, relates to a tensor-based mobile Internet of Things coverage reliability assessment method. Background Art

[0002] Reliability characterizes and measures the ability of the Mobile Internet of Things to deliver its intended functions and services within specified conditions and timeframes. Due to its inherent characteristics and the unique nature of network application environments and scenarios, the Mobile Internet of Things can be impacted by factors such as the number of nodes, node failures, node polymorphism, connection interruptions, coverage holes, passive eavesdropping, and active malicious attacks. These factors can lead to network coverage failing to meet requirements, even causing normal operation failures and service interruptions. To avoid these adverse consequences and maintain long-term network functionality, network reliability is a crucial consideration.

[0003] Coverage reflects and characterizes the sensing status of the target area monitored by the IoT. Reliable coverage ensures network data perception and transmission, thereby improving the Quality of Service (QoS). Therefore, coverage reliability is one of the core factors affecting network reliability and is an important support for ensuring normal network operation.

[0004] The difficulties in assessing mobile IoT coverage reliability lie primarily in five areas. First, the impact of node multi-state, connectivity robustness, coverage area, energy efficiency, and link reliability on coverage reliability is not fully considered, resulting in a lack of accurate definitions for measuring coverage reliability. Second, reliable coverage of a target area depends not only on the node's deployment location, coverage range, sensing capabilities, and network coverage, but also on the node's ability to transmit data to the processing center and network connectivity. Based on the characteristics of the IoT and the requirements for network coverage and reliability, a reasonable coverage reliability model must be constructed to ensure the usability of network coverage reliability assessment. Third, the network coverage model defines the coverage capability of sensors, and the choice of coverage model directly affects the accuracy and applicability of reliability assessment methods for measuring network coverage in different scenarios. Fourth, when measuring network connectivity, one of the reference reliability indicators, a reasonable connectivity definition must be devised to avoid incomplete reliability assessments and improve the effectiveness of reliability assessment methods. Fifth, sensor status is affected by multiple factors and changes dynamically over time and in the environment, necessitating the development of models that accurately and dynamically predict sensor status. Summary of the Invention

[0005] In response to the aforementioned deficiencies or improvements in the existing technologies, the present invention provides a tensor-based method for assessing the coverage reliability of mobile IoT. This method aims to comprehensively and effectively assess the coverage reliability of mobile IoT and assist in the deployment of sensor networks. This reliability assessment method uses a trusted information coverage model to define sensor coverage from the perspectives of prediction and information reconstruction. It leverages the spatial correlation of monitored physical parameters and the collaboration between adjacent nodes. It introduces connectivity robustness to measure network fault tolerance, comprehensively considers factors affecting network reliability, and calculates network reliability through Monte Carlo simulation. This method improves assessment efficiency and application scope, thereby addressing IoT reliability assessment issues and providing valuable guidance and reference.

[0006] To achieve the above object, according to one aspect of the present invention, a tensor-based mobile Internet of Things coverage reliability assessment method is provided, comprising the following steps:

[0007] (1) Establish a network model based on the monitoring coverage scenario of the target area;

[0008] (1.1) The target area is divided into multiple reconstruction areas according to the correlation radius CR, and the center of each reconstruction area is the reconstruction point;

[0009] (1.2) Determine the sensor node’s sensing radius and communication radius. The sensor operates according to a random duty cycle and has the following states during operation: ACTIVE, RELAY, SLEEP, SLEEPr, and FAIL.

[0010] (1.3) The directed arrows between sensors represent the communication link CM i,j , the link working reliability is link r ;

[0011] (1.4) Record the number of mobile sink node κ and the number of sensor nodes N. According to the distribution of sensor nodes, record the number of sensor node i and location (x i ,y i );

[0012] (1.5) Mobile Internet of Things (MIoT) is modeled as a graph G = {{s sink}∪S∪CM i,j};

[0013] (2) Comprehensively consider node multi-state, connectivity robustness, coverage area, energy efficiency, and link reliability to define the reliability of trusted information coverage;

[0014] (3) Construct node state tensor and energy tensor, and use multimodal Markov sensor state probability prediction model to predict sensor state;

[0015] (4) Construct a network coverage tensor and calculate the network coverage rate based on the coverage tensor and the trusted information coverage model;

[0016] (5) Enumerate the network node connectivity matrix and calculate the network connectivity robustness;

[0017] (6) Monte Carlo simulation method is used to evaluate the reliability of the trusted information coverage of the specified network until the number of simulations reaches the set upper limit.

[0018] In one embodiment of the present invention, step (2) specifically includes the following sub-steps:

[0019] (2.1) Definition: Trusted Information Coverage Reliability (CICR) refers to the probability that the MIoT can successfully transmit at least the required CIC-oriented data to the mobile sink in the event of any k-1 sensor failures;

[0020] (2.2) According to step (2.1), obtaining a reliable network with trusted information coverage requires satisfying three conditions:

[0021] Condition 1: Remaining energy E of the sensor res Can support data perception E S 、Data reception E R and data transmission E T ;

[0022] Condition 2: Coverage meets network coverage requirements, C r ≥C req ;

[0023] Condition 3: Connectivity robustness meets the network connectivity robustness requirements, K r ≥k.

[0024] In one embodiment of the present invention, in condition 1 of step (2.2), the data receiving E R and data transmission E T The calculation formula is as follows:

[0025]

[0026] E R (l) = lE elec

[0027] Among them, l is the transmission data size, d is the transmission distance, E elec is the energy consumed by the transceiver circuit to process each bit of data, ε fs and ε mp They are the common parameters related to the free space channel model and the multipath fading model. is the distance threshold that determines the channel model;

[0028] The ACTIVE state sensor has the ability to perceive and communicate, and the RELAY state sensor has the ability to communicate. For the ACTIVE sensor, condition 1 is converted to: E res ≥E T +E R +E S ;For RELAY sensor, condition 1 is: E res ≥E T +E R .

[0029] In one embodiment of the present invention, the coverage C in condition 2 of step (2.2) is r The calculation formula is as follows:

[0030]

[0031] Among them, W L and W B are the length and width of the monitoring area respectively; C(X) is the network coverage area, which is the sum of the areas covered by the reconstruction points:

[0032]

[0033] Among them, x i is the reconstruction point, X is the reconstruction point x i The set of |X| is the number of reconstruction points;

[0034] For each reconstruction point x i , the ACTIVE sensors in the reconstruction area that meet condition 1 collaborate to i Information reconstruction is performed at the location. If the root mean square error RMSE is less than the threshold, it is covered by credible information, and its coverage area C(x i ):

[0035]

[0036] In one embodiment of the present invention, the connectivity robustness K in condition 3 of step (2.2) r The calculation of is as follows:

[0037] The communication link describes the network connectivity and is the basis of connectivity robustness; for sensors in ACTIVE or RELAY i , if it can transmit data to the sensor s located within the communication radius Rc j , then s i and s j There is a communication link CM i,j , link reliability is link r, generates a random number that follows a uniform distribution to determine the link CM i,j Whether it is available, 1 is available, 0 is unavailable:

[0038]

[0039] Network connectivity robustness K r Convert to graph G = {{s sink}∪S∪CM i,j The point connectivity of a graph is K(G), and the point connectivity of a graph is equal to the maximum internal non-intersecting path λ(s' i ,s' j ).

[0040] In one embodiment of the present invention, step (3) specifically includes the following sub-steps:

[0041] (3.1) Constructing a three-dimensional node state tensor S and the energy tensor E , whose element S itq and E itq They represent the state and residual energy of node i at the t-th time point in the q-th simulation;

[0042] (3.2) Construct a multimodal Markov sensor state probability prediction model;

[0043] (3.3) Iteratively adjust the joint state probability distribution tensor M , until M Stable, get the steady-state joint state probability distribution tensor M , the adjustment formula is as follows:

[0044] M i =β P ※ M i-1 +(1-β) G

[0045] Among them, β (0<β<1) is the adjustment parameter, G is the adjustment joint probability distribution tensor;

[0046] (3.4) According to the tensor S 、 E And the actual situation, get the state value of the previous m-1 moment, based on the state value from the steady state M Extract h-order tensor B ;

[0047] (3.5) Extract the Multistate fiber L from the tensor B. The state corresponding to the highest element value in L is sensor s i state.

[0048] In one embodiment of the present invention, the step (3.2) specifically includes the following sub-steps:

[0049] (3.2.1) Construct an h-element, m-order Markov model, assuming P is the state transition probability tensor, M is the joint state probability distribution tensor:

[0050]

[0051] Σ M =1

[0052] (3.2.2) According to the state transition principle of the m-order Markov model, using M Sensor state conversion is achieved through tensor uniform multiplication;

[0053]

[0054] Among them, D t represents the state of the sensor at time t, Represents a tensor uniform multiplication operation.

[0055] In one embodiment of the present invention, step (4) specifically includes the following sub-steps:

[0056] (4.1) Calculate the reconstruction point x i Coverage area C(x i );

[0057] (4.2) Constructing a three-dimensional covering tensor A Its element S itq represents the coverage area of ​​the reconstruction point i at the t-th time point in the q-th simulation, and the tensor is updated using the value obtained in step (4.1) A ;

[0058] (4.3) Extracting Sensor Fiber A (:,t,q), the sum of its elements represents the network coverage area at time t in the qth simulation; the network coverage rate is calculated as follows:

[0059]

[0060] In one embodiment of the present invention, the step (4.1) specifically includes the following sub-steps:

[0061] (4.1.1) Tensor-based S 、 E Find x i The ACTIVE sensor that meets condition 1 in the reconstruction area;

[0062] (4.1.2) In the trusted information coverage model, for the reconstruction point x i , use the ordinary Kriging interpolation function to calculate the reconstruction point x i The estimated value of the environmental variable is to reconstruct the neighborhood Z(x i ) is used to calculate the estimated value of the environmental variable by taking the weighted average of the measured values ​​of the sensors selected in step (4.1.1); the interpolation weight coefficient ω of the sensor nodes in the neighborhood i satisfy |Z(x i )| is the reconstruction neighborhood Z(x i ) sensor nodes s i the number of

[0063] (4.1.3) Combined with the ordinary kriging interpolation function, the root mean square error φ(x) of the reconstructed point x is calculated using the following expression: in and δ(x) are solved by steps (4.1.3.1) and (4.1.3.2);

[0064] (4.1.4) According to the definition of the trusted information coverage model, if φ(x)>μ, that is, the time-averaged root mean square error is greater than the set coverage threshold, then the reconstructed area is covered; otherwise, it is not covered; calculate the coverage area of ​​the reconstructed points.

[0065] In one embodiment of the present invention, the step (4.1.3) specifically includes the following sub-steps:

[0066] (4.1.3.1) Interpolation weight coefficient ω i A set of optimal solutions is obtained by minimum Kriging variance; the Lagrange multiplier δ(x) is introduced to generate a linear Kriging system consisting of n+1 equations with n+1 unknowns, and the interpolation weight coefficient ω is obtained after solving it i ;

[0067]

[0068] Among them, γ(s i ,s j ) and γ(s i ,x) is calculated by the variogram;

[0069] (4.1.3.2) Calculate γ(s in step (3.3.2) i ,s j ) and γ(s i ,x i ); Gaussian variogram is selected as the variogram of environmental variables to describe the sensor node s i Spatial correlation between collected data; the formula of Gaussian variogram is:

[0070]

[0071] Among them, d sx For sensor nodes s i and the reconstruction point x i The Euclidean distance of For sensor nodes s i and s j The Euclidean distance, H0 and H1 are both constants.

[0072] In one embodiment of the present invention, step (5) specifically includes the following sub-steps:

[0073] (5.1) According to condition 3, use fibers S(:,t,q) and E(:,t-1,q) to determine the sensors that can form a communication link;

[0074] (5.2) For each communication link CM i,j , its link reliability is link r ,Monte Carlo method is used to confirm link availability;

[0075] (5.3) Calculate network connectivity robustness;

[0076] In one embodiment of the present invention, the step (5.3) specifically includes the following sub-steps:

[0077] (5.3.1) Graph transformation; transformation graph G = {{s sink}∪S∪X∪CM i,j} is a graph θ={ξ∪β}. Specifically, the point s in G i Transformed into two points ξ in θ i and ξ i+n , and ξ i and ξ i+n The arc capacity between them is 1; the edge CM in G i,j =(s i ,s j )=1 is converted into two edges β in θ i+n,j =(ξ i+n ,ξ j ) and β i,j+n =(ξ i ,ξ j+n ), the arc capacity is infinite;

[0078] (5.3.2) Calculate the point connectivity of the graph G, that is, all the point pairs (ξ i+n ,ξ j ) The point connectivity of graph G is the connectivity robustness value of the network.

[0079] In one embodiment of the present invention, step (6) specifically includes the following sub-steps:

[0080] (6.1) Monte Carlo simulation method is used to calculate the reliability of network trusted information coverage. The calculation formula is as follows:

[0081]

[0082] Where Q represents the number of Monte Carlo simulations, T represents the number of cycles, that is, the time it takes for the mobile convergence point to move at the edge of the monitoring area;

[0083] (6.2) At the end of each simulation, the energy of each sensor node is updated and steps (3), (4) and (5) are repeated until the number of simulations reaches the set upper limit.

[0084] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0085] (1) High coverage reliability. This invention comprehensively explores the spatial correlation of monitoring and reconstruction points in the coverage target area from the perspective of information collaboration, and uses the root mean square error to estimate the coverage error, complete coverage prediction, improve coverage rate, and thus improve coverage reliability;

[0086] (2) Fast evaluation speed. The Monte Carlo simulation method used in this invention uses the simulation results of a certain number of simulations as the network coverage reliability value, avoiding the computational complexity caused by the full state enumeration of network nodes and saving evaluation time.

[0087] (3) Comprehensive evaluation indicators. This invention comprehensively considers the impact of factors such as multi-state nodes, node energy consumption, link reliability, network coverage area, and network connectivity robustness on network coverage reliability. Tensors are used to perform a high-dimensional unified representation of multi-source heterogeneous correlation factors in IoT coverage, integrating each factor into a framework. The tensor Markov state probability prediction model is used to dynamically predict sensor states, which can comprehensively reflect network coverage reliability.

[0088] (4) High versatility: The present invention uses Monte Carlo simulation to assess network coverage reliability, making it suitable for high-density, large-scale networks. Furthermore, the Internet of Things involved in the present invention is a universal network suitable for a variety of application scenarios. The trusted information coverage model used in the present invention can be used to cover different terrains, regions, and different data monitoring targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 This is a flow chart of a tensor-based mobile Internet of Things coverage reliability assessment method according to an embodiment of the present invention;

[0090] Figure 2Schematic diagram of a mobile Internet of Things network model according to an embodiment of the present invention;

[0091] FIG3 is a schematic diagram showing how coverage reliability is affected by duty cycle in embodiments of the present invention and the prior art (MCMc, ACR), wherein: FIG3(a) is a schematic diagram showing the number of nodes N=30; FIG3(b) is a schematic diagram showing the number of nodes N=40; FIG3(c) is a schematic diagram showing the number of nodes N=50; FIG3(d) is a schematic diagram showing the number of nodes N=60; and FIG3(e) is a schematic diagram showing the number of nodes N=70.

[0092] FIG4 is a schematic diagram showing how coverage reliability is affected by coverage rate in embodiments of the present invention and the prior art (MCMc, ACR), wherein: FIG4(a) is a schematic diagram showing the number of nodes N=30; FIG4(b) is a schematic diagram showing the number of nodes N=40; FIG4(c) is a schematic diagram showing the number of nodes N=50; FIG4(d) is a schematic diagram showing the number of nodes N=60; and FIG4(e) is a schematic diagram showing the number of nodes N=70.

[0093] FIG5 shows the coverage reliability perception radius R in the embodiment of the present invention and the prior art (MCMc, ACR) S Impact diagram, where: Figure 5(a) is a schematic diagram of the number of nodes N = 30; Figure 5(b) is a schematic diagram of the number of nodes N = 40; Figure 5(c) is a schematic diagram of the number of nodes N = 50; Figure 5(d) is a schematic diagram of the number of nodes N = 60; Figure 5(e) is a schematic diagram of the number of nodes N = 70;

[0094] Figure 6 2. It is a schematic diagram showing the influence of the root mean square error threshold μ on coverage reliability in an embodiment of the present invention;

[0095] Figure 7 In the embodiment of the present invention, coverage reliability is affected by link reliability. r Impact diagram;

[0096] Figure 8 Schematic diagram showing how coverage reliability is affected by a connectivity robustness threshold k in an embodiment of the present invention;

[0097] In all the drawings, the same reference numerals are used to represent the same elements or structures, where a hexagonal star represents a grid reconstruction point, a five-pointed star represents a movable sink node, a dot represents a sensor node, a directed line represents a communication link, CR represents a range, and N represents the number of sensor nodes in the current state of the network. DETAILED DESCRIPTION

[0098] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0099] The following first explains and illustrates the technical terms of the present invention:

[0100] Correlation Range (CR): A distance threshold that characterizes the spatial correlation of environmental variables. For a specific environmental variable and spatial point, only the values ​​of other spatial points within the range are correlated with the current spatial point.

[0101] Root mean square error (RMSE): It is used to measure and evaluate the quality of reconstruction and estimation of unused spatial environmental variable values, that is, the error measure between the estimated value and the reference point value.

[0102] Confident Information Coverage: In the target monitoring area, if the root mean square error of the reconstructed information at a spatial point in the area is less than or equal to the threshold μ required by the actual application, the spatial point is covered by credible information.

[0103] Euclidean distance: measures the absolute distance between two points or vectors in multidimensional space, that is, the square root of the difference between the vectors. i ,y i ) to point B(x j ,y j ) is

[0104] Kriging Interpolation: Kriging is essentially a sliding weighted average method with optimal, linear, and unbiased properties. Kriging is a regression algorithm that uses a covariance function to spatially model and predict (interpolate) random processes or fields. For certain random processes, such as inherently stationary processes, kriging can provide optimal linear unbiased estimates, and is therefore also known in geostatistics as a spatially optimal unbiased estimator.

[0105] Adjacent nodes: sensor nodes s i The Euclidean distance within its communication range R c Other sensor nodes in s i adjacent nodes.

[0106] Monte Carlo simulation method: When the problem to be solved is the probability of an event occurring, or the expected value of a random variable, we can grasp the geometric quantities and geometric characteristics of the movement of things, use mathematical methods to simulate them, and obtain the frequency of occurrence of such an event, or the average value of this random variable, and use them as approximate solutions to the problem.

[0107] Tensor: It is a multilinear map defined on the Cartesian product of some vector spaces and some dual spaces. It is a generalization of the concept of vector. Vector is a first-order tensor that can be used to represent multilinear functions of linear relationships between some vectors, scalars and other tensors.

[0108] The solutions to the difficulties in the prior art are:

[0109] Regarding the first challenge, existing research on IoT coverage reliability fails to comprehensively consider factors influencing coverage reliability to define coverage reliability. Trusted information coverage reliability is defined by comprehensively considering node multi-state, connectivity robustness, coverage area, energy efficiency, and link reliability to accurately measure coverage reliability. Regarding the second challenge, existing research on IoT coverage reliability fails to consider the spatial correlation of monitored variables and node collaborative sensing capabilities, nor does it consider the impact of factors such as network connectivity, multi-state nodes, and malicious node interference on network coverage reliability. Consequently, it fails to uniformly represent and model the numerous factors influencing coverage reliability. This paper comprehensively considers factors influencing network coverage reliability and constructs an IoT coverage reliability assessment model using tensors. This tensor-based reliability model enables a high-dimensional, unified representation of heterogeneous, multi-source correlation factors in IoT coverage, maintaining correlations across dimensions. Regarding the third challenge, most existing IoT coverage research uses an overly simplistic and idealized disk coverage model to characterize node coverage capability, which is not suitable for practical scenarios. The trusted information coverage model, however, allows for the definition of sensor coverage from the perspective of prediction and information reconstruction. The trusted information coverage model leverages the spatial correlation of monitored physical parameters and the collaborative collaboration of adjacent nodes, making it well-suited for practical application. To address the fourth difficulty, most existing methods measure network connectivity from the perspective of whether there is a valid path from the sensor to the sink node, as one of the reliability assessment criteria. However, these methods do not consider the significant impact of failures of key nodes in the connectivity path on network reliability. Using connectivity robustness as one of the coverage reliability criteria not only evaluates network connectivity but also measures the network's fault tolerance, thus better characterizing the reliability of network coverage. To address the fifth difficulty, most existing methods model sensor states as two modes, ignoring the impact of multiple factors on sensor polymorphism. Using a tensor-Markov state probability prediction model to dynamically predict sensor states can highly integrate the dynamic factors that affect node state changes, effectively characterizing the temporal changes of node states over a period of time and the connectivity relationship of the network.

[0110] like Figure 1 As shown, the tensor-based IoT coverage reliability assessment method of the present invention includes the following steps:

[0111] (1) Establish a network model based on the monitoring coverage scenario of the target area;

[0112] (1.1) The target area is divided into multiple reconstruction areas according to the correlation radius CR, and the center of each reconstruction area is the reconstruction point.

[0113] (1.2) Determine the sensing radius and communication radius of the sensor node. The sensor operates according to a random duty cycle and has the following states during operation: ACTIVE, RELAY, SLEEP, SLEEPr, and FAIL.

[0114] (1.3) The directed arrows between sensors represent the communication link CM i,j , the link working reliability is link r .

[0115] (1.4) Record the number of mobile sink node κ and the number of sensor nodes N. According to the distribution of sensor nodes, record the number of sensor node i and location (x i ,y i ).

[0116] (1.5) Mobile Internet of Things (MIoT) is modeled as a graph G = {{s sink}∪S∪CM i,j}

[0117] (2) Comprehensively consider node multi-state, connectivity robustness, coverage area, energy efficiency, and link reliability to define the reliability of trusted information coverage;

[0118] (2.1) Definition Trusted Information Coverage Reliability (CICR) refers to the probability that the MIoT can successfully transmit at least the required CIC-oriented data to the mobile sink in the event that any k-1 sensors fail.

[0119] (2.2) According to step (2.1), obtaining a reliable network with trusted information coverage requires satisfying three conditions:

[0120] Condition 1: Remaining energy E of the sensor res Can support data perception E S 、Data reception E R and data transmission E T ;

[0121] Data reception E R and data transmission E T The calculation formula is as follows:

[0122]

[0123] E R (l) = lE elec

[0124] Among them, l is the transmission data size, d is the transmission distance, E elec is the energy consumed by the transceiver circuit to process each bit of data, ε fs and ε mp They are the common parameters related to the free space channel model and the multipath fading model. It is the distance threshold that determines the channel model.

[0125] The ACTIVE state sensor has the ability to perceive and communicate, and the RELAY state sensor has the ability to communicate. For the ACTIVE sensor, condition 1 is converted to: E res ≥E T +E R +E S ;For RELAY sensor, condition 1 is: E res ≥E T +E R .

[0126] Condition 2: Coverage meets network coverage requirements, C r ≥C req ;

[0127] Coverage C r The calculation formula is as follows:

[0128]

[0129] Among them, W L and W B are the length and width of the monitoring area respectively. C(X) is the network coverage area, which is the sum of the areas covered by the reconstruction points:

[0130]

[0131] Among them, x i is the reconstruction point, X is the reconstruction point x i where |X| is the number of reconstruction points.

[0132] For each reconstruction point x i , the ACTIVE sensors in the reconstruction area that meet condition 1 collaborate to i Information reconstruction is performed at the location. If the root mean square error RMSE is less than the threshold, it is covered by credible information, and its coverage area C(x i ):

[0133]

[0134] Condition 3: Connectivity robustness meets the network connectivity robustness requirements, K r ≥k.

[0135] Connectivity robustness K r The calculation of is as follows:

[0136] The communication link describes the network connectivity and is the basis of connectivity robustness. i , if it can transmit data to the sensor s located within the communication radius Rc j , then s i and s j There is a communication link CM i,j , link reliability is link r Generate a random number that follows a uniform distribution to determine the link CM i,j Whether it is available, 1 is available, 0 is unavailable:

[0137]

[0138] Network connectivity robustness K r Convert to graph G = {{s sink}∪S∪CM i,j The point connectivity of a graph is K(G), and the point connectivity of a graph is equal to the maximum internal non-intersecting path λ(s' i ,s' j ).

[0139] (3) Construct node state tensor and energy tensor, and use multimodal Markov sensor state probability prediction model to predict sensor state;

[0140] (3.1) Constructing a three-dimensional node state tensor S and the energy tensor E , whose element S itq and E itq They represent the state and residual energy of node i at the t-th time point in the q-th simulation;

[0141] (3.2) Construct a multimodal Markov sensor state probability prediction model.

[0142] (3.2.1) Construct an h-element, m-order Markov model, assuming P is the state transition probability tensor, M is the joint state probability distribution tensor:

[0143]

[0144] Σ M =1

[0145] (3.2.2) According to the state transition principle of the m-order Markov model, using M Sensor state conversion is achieved through tensor uniform multiplication.

[0146]

[0147] Among them, D t represents the state of the sensor at time t, Represents a tensor uniform multiplication operation.

[0148] (3.3) Iteratively adjust the joint state probability distribution tensor M , until M Stable, get the steady-state joint state probability distribution tensor M , the adjustment formula is as follows:

[0149]

[0150] Among them, β (0<β<1) is the adjustment parameter, and G is the adjusted joint probability distribution tensor.

[0151] (3.4) According to the tensor S 、 E And the actual situation, get the state value of the previous m-1 moment, based on the state value from the steady state M Extract h-order tensor B ;

[0152] (3.5) Extract the Multistate fiber L from the tensor B. The state corresponding to the highest element value in L is sensor s i state.

[0153] (4) Construct a network coverage tensor and calculate the network coverage rate based on the coverage tensor and the trusted information coverage model;

[0154] (4.1) Calculate the reconstruction point x i Coverage area C(x i );

[0155] (4.1.1) Tensor-based S 、 E Find x i The ACTIVE sensor that meets condition 1 in the reconstruction area;

[0156] (4.1.2) In the trusted information coverage model, for the reconstruction point x i , use the ordinary Kriging interpolation function to calculate the reconstruction point x i The estimated value of the environmental variable is to reconstruct the neighborhood Z(x i) is used to calculate the estimated value of the environmental variable by taking the weighted average of the measured values ​​of the sensors selected in step (4.1.1); the interpolation weight coefficient ω of the sensor nodes in the neighborhood i satisfy |Z(x i )| is the reconstruction neighborhood Z(x i ) sensor nodes s i the number of

[0157] (4.1.3) Combined with the ordinary kriging interpolation function, the root mean square error φ(x) of the reconstructed point x is calculated using the following expression: in and δ(x) are solved by steps (4.1.3.1) and (4.1.3.2);

[0158] (4.1.4) According to the definition of the trusted information coverage model, if φ(x)>μ, that is, the time-averaged root mean square error is greater than the set coverage threshold, then the reconstructed area is covered; otherwise, it is not covered; calculate the coverage area of ​​the reconstructed points.

[0159] (4.1.3.1) Interpolation weight coefficient ω i A set of optimal solutions is obtained by minimum Kriging variance; the Lagrange multiplier δ(x) is introduced to generate a linear Kriging system consisting of n+1 equations with n+1 unknowns, and the interpolation weight coefficient ω is obtained after solving it i ;

[0160]

[0161] Among them, γ(s i ,s j ) and γ(s i ,x) is calculated by the variogram;

[0162] (4.1.3.2) Calculate γ(s in step (3.3.2) i ,s j ) and γ(s i ,x i ); Gaussian variogram is selected as the variogram of environmental variables to describe the sensor node s i Spatial correlation between collected data; the formula of Gaussian variogram is:

[0163]

[0164] Among them, d sx For sensor nodes s i and the reconstruction point x i The Euclidean distance of For sensor nodes s i and s jThe Euclidean distance, H0 and H1 are both constants.

[0165] (4.2) Constructing a three-dimensional covering tensor A Its element S itq represents the coverage area of ​​the reconstruction point i at the t-th time point in the q-th simulation, and the tensor is updated using the value obtained in step (4.1) A ;

[0166] (4.3) Extracting Sensor Fiber A (:,t,q), the sum of its elements represents the network coverage area at time t in the qth simulation. The network coverage is calculated as follows:

[0167]

[0168] (5) Enumerate the network node connectivity matrix and calculate the network connectivity robustness;

[0169] (5.1) According to condition 3, use fibers S(:,t,q) and E(:,t-1,q) to determine the sensors that can form a communication link;

[0170] (5.2) For each communication link CM i,j , its link reliability is link r ,Monte Carlo method is used to confirm link availability;

[0171] (5.3) Calculate network connectivity robustness;

[0172] (5.3.1) Graph transformation; transformation graph G = {{s sink}∪S∪X∪CM i,j} is a graph θ={ξ∪β}. Specifically, the point s in G i Transformed into two points ξ in θ i and ξ i+n , and ξ i and ξ i+n The arc capacity between them is 1; the edge CM in G i,j =(s i ,s j )=1 is converted into two edges β in θ i+n,j =(ξ i+n ,ξ j ) and β i,j+n =(ξ i ,ξ j+n ), the arc capacity is infinite.

[0173] (5.3.2) Calculate the point connectivity of the graph G, that is, all the point pairs (ξ i+n ,ξ j) The point connectivity of graph G is the connectivity robustness value of the network.

[0174] (6) Using the Monte Carlo simulation method, the reliability of the trusted information coverage of the specified network is evaluated until the number of simulations reaches the set upper limit;

[0175] (6.1) Monte Carlo simulation method is used to calculate the reliability of network trusted information coverage. The calculation formula is as follows:

[0176]

[0177] Where Q represents the number of Monte Carlo simulations, and T represents the number of cycles, that is, the time it takes for the mobile convergence point to move at the edge of the monitoring area.

[0178] (6.2) At the end of each simulation, the energy of each sensor node is updated and steps (3), (4) and (5) are repeated until the number of simulations reaches the set upper limit.

[0179] FIG3 is a schematic diagram showing the effect of duty cycle on coverage reliability in embodiments of the present invention (T-CICR) and prior art inventions (MCMc, ACR), wherein: FIG3(a) is a schematic diagram when the number of nodes N=30; FIG3(b) is a schematic diagram when the number of nodes N=40; FIG3(c) is a schematic diagram when the number of nodes N=50; FIG3(d) is a schematic diagram when the number of nodes N=60; and FIG3(e) is a schematic diagram when the number of nodes N=70.

[0180] FIG4 is a schematic diagram showing how coverage reliability is affected by coverage rate in embodiments of the present invention (T-CICR) and the prior art (MCMc, ACR), wherein: FIG4(a) is a schematic diagram when the number of nodes N=30; FIG4(b) is a schematic diagram when the number of nodes N=40; FIG4(c) is a schematic diagram when the number of nodes N=50; FIG4(d) is a schematic diagram when the number of nodes N=60; and FIG4(e) is a schematic diagram when the number of nodes N=70.

[0181] FIG5 is a schematic diagram showing how coverage reliability is affected by the sensing radius Rs in the embodiments of the present invention (T-CICR) and the prior art (MCMc, ACR), wherein: FIG5(a) is a schematic diagram when the number of nodes N=30; FIG5(b) is a schematic diagram when the number of nodes N=40; FIG5(c) is a schematic diagram when the number of nodes N=50; FIG5(d) is a schematic diagram when the number of nodes N=60; and FIG5(e) is a schematic diagram when the number of nodes N=70.

[0182] like Figure 6 FIG. 1 is a schematic diagram showing the influence of the root mean square error threshold μ on the coverage reliability in an embodiment of the present invention; FIG. Figure 7 The following is an example of coverage reliability affected by link reliability in the embodiment of the present invention. rImpact diagram; Figure 8 The figure shows a schematic diagram of how coverage reliability is affected by the connectivity robustness threshold k in an embodiment of the present invention. Figures 3-8 demonstrate the versatility of this method, allowing network designers to better understand the impact of random duty cycle, coverage, node communication radius, link reliability, root mean square error threshold, and connectivity robustness threshold on reliability. Those skilled in the art will readily appreciate that the foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A tensor-based mobile Internet of Things coverage reliability assessment method, characterized in that: The following steps are involved: (1) Establish a network model based on the monitoring coverage scenario of the target area; (1.1) The target area is divided into multiple reconstruction areas according to the correlation radius CR, and the center of each reconstruction area is the reconstruction point; (1.2) Determine the sensor node’s sensing radius and communication radius. The sensor operates according to a random duty cycle and has the following states during operation: ACTIVE, RELAY, SLEEP, SLEEPr, and FAIL. (1.3) The directed arrows between sensors represent the communication link CM i,j , the link working reliability is link r ; (1.4) Record the number of mobile sink node κ and the number of sensor nodes N. According to the distribution of sensor nodes, record the number of sensor node i and location (x i ,y i ); (1.5) The Mobile Internet of Things (MIoT) is modeled as a graph G = {{s sink }∪S∪CM i,j }; (2) Comprehensively consider node multi-state, connectivity robustness, coverage area, energy efficiency, and link reliability to define the reliability of trusted information coverage; (3) Construct node state tensor and energy tensor, and use multimodal Markov sensor state probability prediction model to predict sensor state; (4) Construct a network coverage tensor and calculate the network coverage rate based on the coverage tensor and the trusted information coverage model; (5) Enumerate the network node connectivity matrix and calculate the network connectivity robustness; (6) Monte Carlo simulation method is used to evaluate the reliability of the trusted information coverage of the specified network until the number of simulations reaches the set upper limit.

2. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 1, characterized in that: The step (2) specifically includes the following sub-steps: (2.1) Definition: Trusted Information Coverage Reliability (CICR) refers to the probability that the MIoT can successfully transmit at least the required CIC-oriented data to the mobile sink when any k-1 sensors fail. (2.2) According to step (2.1), obtaining a reliable network with trusted information coverage requires satisfying three conditions: Condition 1: Remaining energy E of the sensor res Can support data perception E S 、Data reception E R and data transmission E T ; Condition 2: Coverage meets network coverage requirements, C r ≥C req ; Condition 3: Connectivity robustness meets the network connectivity robustness requirements, K r ≥k.

3. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 2, characterized in that: In the condition 1 of step (2.2), data reception E R and data transmission E T The calculation formula is as follows: Among them, l is the transmission data size, d is the transmission distance, E elec is the energy consumed by the transceiver circuit to process each bit of data, ε fs and ε mp They are the common parameters related to the free space channel model and the multipath fading model. is the distance threshold that determines the channel model; The ACTIVE state sensor has the ability to perceive and communicate, and the RELAY state sensor has the ability to communicate. For the ACTIVE sensor, condition 1 is converted to: E res ≥E T +E R +E S ;For RELAY sensor, condition 1 is: E res ≥E T +E R .

4. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 2, wherein: The coverage C in condition 2 of the step (2.2) r The calculation formula is as follows: Among them, W L and W B are the length and width of the monitoring area respectively; C(X) is the network coverage area, which is the sum of the areas covered by the reconstruction points: Among them, x i is the reconstruction point, X is the reconstruction point x i The set of |X| is the number of reconstruction points; For each reconstruction point x i , the ACTIVE sensors in the reconstruction area that meet condition 1 collaborate to i Information reconstruction is performed at the location. If the root mean square error RMSE is less than the threshold, it is covered by credible information, and its coverage area C(x i ):

5. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 2, wherein: The connectivity robustness K in condition 3 of step (2.2) r The calculation of is as follows: The communication link describes the network connectivity and is the basis of connectivity robustness; for sensors in ACTIVE or RELAY i , if it can transmit data to the sensor s located within the communication radius Rc j , then s i and s j There is a communication link CM i,j , link reliability is link r , generates a random number that follows a uniform distribution to determine the link CM i,j Whether it is available, 1 is available, 0 is unavailable: Network connectivity robustness K r Convert to graph G = {{S sink }∪S∪CM i,j The point connectivity of a graph is K(G), and the point connectivity of a graph is equal to the maximum internal non-intersecting path λ(s' i ,s' j ).

6. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 4, characterized in that: The step (3) specifically includes the following sub-steps: (3.1) Constructing a three-dimensional node state tensor S and the energy tensor E , whose element S itq and E itq They represent the state and residual energy of node i at the t-th time point in the q-th simulation; (3.2) Construct a multimodal Markov sensor state probability prediction model; (3.3) Iteratively adjust the joint state probability distribution tensor M , until M Stable, get the steady-state joint state probability distribution tensor M , the adjustment formula is as follows: Where β is the adjustment parameter, 0<β<1, and G is the adjusted joint probability distribution tensor; Represents a tensor uniform multiplication operation; (3.4) According to the tensor S 、 E And the actual situation, get the state value of the previous m-1 moment, based on the state value from the steady state M Extract h-order tensor B ; (3.5) Extract the Multistate fiber L from the tensor B. The state corresponding to the highest element value in L is sensor s i state.

7. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 6, characterized in that: The step (3.2) includes the following sub-steps: (3.2.1) Construct an h-element, m-order Markov model, assuming P is the state transition probability tensor, M is the joint state probability distribution tensor: (3.2.2) According to the state transition principle of the m-order Markov model, using M Sensor state conversion is achieved through tensor uniform multiplication; Among them, D t Indicates the state of the sensor at time t.

8. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 6, characterized in that: The step (4) includes the following sub-steps: (4.1) Calculate the reconstruction point x i Coverage area C(x i ); (4.2) Constructing a three-dimensional covering tensor A Its elements S itq represents the coverage area of ​​the reconstruction point i at the t-th time point in the q-th simulation, and the tensor is updated using the value obtained in step (4.1) A ; (4.3) Extracting Sensor Fiber A (:,t,q), the sum of its elements represents the network coverage area at time t in the qth simulation; the network coverage rate is calculated as follows:

9. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 8, wherein: The step (4.1) includes the following sub-steps: (4.1.1) Tensor-based S 、 E Find x i The ACTIVE sensor that meets condition 1 in the reconstruction area; (4.1.2) In the trusted information coverage model, for the reconstruction point x i , use the ordinary Kriging interpolation function to calculate the reconstruction point x i The estimated value of the environmental variable is to reconstruct the neighborhood Z(x i ) is used to calculate the estimated value of the environmental variable by taking the weighted average of the measured values ​​of the sensors selected in step (4.1.1); the interpolation weight coefficient ω of the sensor nodes in the neighborhood i satisfy |Z(x i )| is the reconstruction neighborhood Z(x i ) sensor nodes s i the number of (4.1.3) Combined with the ordinary kriging interpolation function, the root mean square error φ(x) of the reconstructed point x is calculated using the following expression: in and δ(x) are solved by the following equations; (4.1.3.1) Interpolation weight coefficient ω i A set of optimal solutions is obtained by minimum Kriging variance; the Lagrange multiplier δ(x) is introduced to generate a linear Kriging system consisting of n+1 equations with n+1 unknowns, and the interpolation weight coefficient ω is obtained after solving it i ; Among them, γ(s i ,s j ) and γ(s i ,x) is calculated by the variogram; (4.1.3.2) Calculate γ(s in step (3.3.2) i ,s j ) and γ(s i ,x i ); Gaussian variogram is selected as the variogram of environmental variables to describe the sensor node s i Spatial correlation between collected data; the formula of Gaussian variogram is: Among them, d sx For sensor nodes s i and the reconstruction point x i The Euclidean distance of For sensor nodes s i and s j The Euclidean distance, H0 and H1 are both constants; (4.1.4) According to the definition of the trusted information coverage model, if φ(x)>μ, that is, the time-averaged root mean square error is greater than the set coverage threshold, then the reconstructed area is covered; otherwise, it is not covered; calculate the coverage area of ​​the reconstructed points.

10. The tensor-based mobile Internet of Things coverage reliability assessment method according to claim 5, characterized in that: The step (5) specifically includes the following sub-steps: (5.1) According to condition 3, use fibers S(:,t,q) and E(:,t-1,q) to determine the sensors that can form a communication link; (5.2) For each communication link CM i,j , its link reliability is link r ,Monte Carlo method is used to confirm link availability; (5.3) Calculate network connectivity robustness, including: (5.3.1)Graph conversion; Transformation graph G = {{s sink }∪S∪X∪CM i,j } is a graph θ={ξ∪β}. Specifically, the point s in G i Transformed into two points ξ in θ i and ξ i+n , and ξ i and ξ i+n The arc capacity between them is 1; the edge CM in G i,j =(s i ,s j )=1 is converted into two edges β in θ i+n,j =(ξ i+n ,ξ j ) and β i,j+n =(ξ i ,ξ j+n ), the arc capacity is infinite; (5.3.2) Calculate the point connectivity of the graph G, that is, all the point pairs (ξ i+n ,ξ j ) The point connectivity of graph G is the connectivity robustness value of the network.

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