Grey correlation degree-based climate environment factor sensor layout optimization method

Abstract

The application provides a climate environmental factor sensor layout optimization method based on grey correlation degree, which comprises the following steps: S1, checking time series data stability; S2, performing differential processing on unstable data and then checking stability; S3, performing normalization processing on stable time series data; S4, calculating grey correlation degree and constructing a correlation matrix; S5, constructing a correlation network diagram; S6, performing S7-S9 on each sub-diagram in the correlation network diagram; S7, preprocessing a single-chain special structure; S8, sorting nodes by using an improved K-shell algorithm; S9, obtaining a final sub-layout scheme by using a climate environmental factor sensor layout algorithm and the nodes reserved by S7; and S10, combining the final sub-layout schemes of all sub-diagrams and adding the nodes reserved in advance by S2 to obtain a final layout scheme. The application has a simple process and does not need a large number of complex operations, and provides a new idea for sensor layout optimization.

Description

Technical Field

[0001] This invention relates to the field of sensor layout optimization technology, and in particular to a method for optimizing the layout of climate and environmental factors sensors based on grey relational analysis. Background Technology

[0002] Modern equipment operates in complex and ever-changing environments. Environmental stress is a significant cause of equipment failure throughout the entire process, from storage and transportation to use. If equipment is not suited to its operating conditions, such as high and low temperatures, dry and humid environments, or salt spray, corrosion, fatigue, or even structural damage can occur, leading to reduced performance and lifespan. Therefore, monitoring environmental factors can provide better early warnings of potential failures, predict and assess the remaining lifespan of equipment, improve the environmental adaptability of products, and ensure product reliability during its use.

[0003] To accurately monitor different environmental factors, different types of sensors are required, and the number of sensors needed is also relatively large. This makes the problem of increasingly complex sensor networks more obvious. In order to ensure the high accuracy of monitoring environmental factors, more accurate sensors are often required. In order to simplify the sensor network while obtaining more and more accurate experimental data, it is necessary to conduct research on sensor layout.

[0004] Current research on sensor layout is widely used in equipment fault detection and structural health monitoring in fields such as aerospace, vehicles, and civil engineering. However, although the research covers a wide range of fields, most researchers focus only on specific equipment or models in their respective fields, with few general models or methods. On the other hand, current research on layout optimization mainly starts from the fault mechanism and simulation model of the monitored object itself, such as optimizing the layout with the goal of more accurately monitoring stress concentration areas, rather than studying environmental factors alone.

[0005] To meet more precise monitoring requirements and address the challenges posed by the increased number of sensors, numerous excellent layout optimization algorithms have been proposed in domestic and international research. Common examples include clustering algorithms, sequential heuristic optimization algorithms, modeling and simulation, and machine learning. These algorithms have improved the transmission efficiency, network coverage, and measurement accuracy of sensor networks, laying a theoretical foundation for subsequent research. However, most current optimization algorithms only consider improving measurement accuracy and network coverage, neglecting the impact of the number of sensors in actual experiments. Furthermore, most algorithms focus on monitoring the target itself rather than considering environmental factors. Some studies address sensor energy consumption by optimizing sensor layout and usage scheduling to reduce energy costs, but research on universal methods that reduce the number of sensors and are applicable to most real-world scenarios is limited. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis. After data preprocessing, a grey relational analysis method is used to study the spatiotemporal correlation between data sequences. Subsequently, a method for optimizing the number of environmental factor sensors based on graph theory clustering is proposed to optimize the sensor layout from the perspective of sensor quantity.

[0007] Specifically, this invention provides a method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis, the specific steps of which are as follows:

[0008] Step 1: Perform a stationarity test on the raw monitoring data of each sensor in a set of climate and environmental factor monitoring sensors. If the raw monitoring data is stationary, then the stationary time series is equal to the time series data and proceed to Step 3; otherwise, proceed to Step 2.

[0009] Step 2: Perform first-order and second-order differencing on the non-stationary raw monitoring data and perform stationarity testing again; for sensors that still fail the stationarity test after first-order and second-order differencing, directly retain the corresponding sensor and discard the data.

[0010] Step 3: Normalize each stationary time series data that passes the test using the range method to obtain the normalized stationary time series for each sensor;

[0011] Step 4: For the normalized stationary time series of different sensors, calculate the grey relational degree between each pair of normalized stationary time series, and construct a correlation matrix based on the calculation results;

[0012] Step 5: Based on the correlation matrix, nodes with a correlation degree exceeding the threshold are considered to have edges between them, thus obtaining the correlation network graph matrix, and constructing the correlation network graph accordingly.

[0013] Step 6: Perform steps 7-9 for each disjoint subgraph of the correlation network graph;

[0014] Step 7: Preprocess the special single-chain structures with a path length exceeding 3 in the correlation network subgraph, pre-reserving the central node, and treating the special single-chain structure as a virtual node in subsequent steps;

[0015] Step 8: Quantify and rank the importance of each node in the relevant network subgraph using the improved K-shell algorithm. This includes:

[0016] Step 81: Use the K-shell method to stratify the importance of each node in the correlation network subgraph;

[0017] Step 82: In each layer obtained in Step 81, the improved algorithm of the K-shell method is used to calculate the comprehensiveness, and the importance of the nodes is quantified and sorted according to the comprehensiveness. The formula for calculating the comprehensiveness is as follows:

[0018]

[0019] Where K(i) is the degree of each node in the correlation network subgraph, and N(i) is the total number of nodes of the node’s neighboring nodes and second-next neighboring nodes.

[0020] Step 83: Sort the nodes from the highest K-shell layer down to the highest level of integration, reduce the K-shell layer number and continue sorting by integration until all nodes are sorted from highest to lowest importance.

[0021] Step 9: Use the climate and environmental factor sensor layout algorithm to traverse the correlation network subgraph to obtain the sensor sub-layout scheme. Add the points reserved in step 7 to obtain the final sub-layout scheme.

[0022] Step 10: Merge the final sub-layout schemes of all related network subgraphs and add the nodes reserved in step 2 to obtain the final layout scheme.

[0023] Preferably, step 2 specifically includes:

[0024] Step 21: For the original monitoring data that is non-stationary in Step 1, perform first-order differencing to obtain first-order differencing monitoring data. Perform a stationarity test on the first-order differencing monitoring data. If it is stationary, proceed to Step 3; otherwise, continue to Step 22.

[0025] Step 22: Perform differential processing again on the first-order difference monitoring data that is still not stable after the first-order difference processing in step 21 to obtain second-order difference monitoring data. Perform a stationarity test on the second-order difference monitoring data. If it is stable, proceed to step 3; otherwise, continue to step 23.

[0026] Step 23: If the second-order differential monitoring data is still unstable, discard the data and save the corresponding sensor.

[0027] Preferably, the formula for normalization using the range method in step 3 is as follows:

[0028]

[0029] Where n represents the stationary time series X i There are n elements in total, X i '(κ) represents the k-th normalized data point in a normalized stationary time series, χ i (κ) represents a stationary time series X i The k-th element, minχ i (κ) represents a stationary time series X i The smallest element in the χ² value, maxχ i (κ) represents a stationary time series X i The largest element in the system.

[0030] Preferably, step 4 specifically includes:

[0031] Step 41: From the normalized stationary time series X i '(κ), select one as the reference sequence χ i (κ), the remaining ones are comparison sequences χ j (κ)(i≠j,i,j=1,2,...,N)) Calculate the correlation coefficient between each sample point using the following formula:

[0032]

[0033] In the formula, ζ i,j (κ) represents the reference sequence χ i (κ) and comparison sequence χ j (κ) is the correlation coefficient of the κ-th element; ζ is the discrimination coefficient, with a value range of ζ∈(0,1); |χ i (κ)-χ j (κ)| represents the absolute value of the difference between the κ-th element of the reference sequence and the κ-th element of the comparison sequence; minmin|χ i (κ)-χ j(κ)| indicates that the minimum value is first taken from the sequence of element differences between the reference sequence and one comparison sequence, and then the minimum value is taken from the sequence of element differences between the reference sequence and each comparison sequence; max max|χ i (κ)-χ j (κ)| indicates that the maximum value is first taken from the element difference sequence between the reference sequence and a comparison sequence, and then the maximum value is taken from the maximum value of the element difference sequence between the reference sequence and each comparison sequence.

[0034] Step 42: Take the average of the correlation coefficients of all elements in the reference sequence and the comparison sequence as the grey correlation degree between the two sequences. The calculation formula is as follows:

[0035]

[0036] Where, γ i,j Represents the reference sequence χ i (κ) is the comparison sequence χ j (κ) Grey correlation degree between two sequences, i.e., normalized stationary time series X i '(κ) and X j Grey relational degree between '(κ);

[0037] Step 43: Based on the calculation results of the grey relational degree between normalized stationary time series, construct the sensor relational degree matrix A as follows:

[0038]

[0039] Preferably, step 7 specifically comprises:

[0040] Step 71: For a single-chain structure composed of sensor nodes with a length greater than or equal to 3 in the correlation network subgraph, retain the central node for every 3 sensor nodes starting from any side of the single chain and place the sensor there; for the part of the single chain structure with less than 3 sensors remaining, retain the node on the side of the single chain furthest from the center of the single chain and place the sensor there; save the nodes retained in this step as nodes to be retained during preprocessing.

[0041] Step 72: Treat the preprocessed single-chain structure as a virtual sensor node.

[0042] Preferably, step 9 specifically comprises:

[0043] Step 91: After quantifying and ranking the importance of nodes in Step 8, the climate and environmental factors sensor layout algorithm is used to traverse and retain sensor nodes, resulting in a sensor sub-layout scheme that can predict and cover the information of the correlation network subgraph under constraints. The specific climate and environmental factors sensor layout algorithm is as follows:

[0044] Starting with one node, the nodes are traversed sequentially in descending order of importance. If a result satisfies the network graph information prediction coverage under the constraints, the result is output as the sensor sub-layout scheme. If none of the results can cover the entire network graph under the constraints, the number of nodes to be retained is increased and the traversal is repeated. If no result can be output, the process of increasing the number of nodes to be retained and traversing is repeated until a result can be output.

[0045] Step 92: Add the points reserved in step 7 to the obtained sub-layout scheme to obtain the final sub-layout scheme.

[0046] Preferably, the limiting condition for step 91 is:

[0047] Each sensor node can predict information from its nearest neighbor and second-next neighbor nodes.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] 1. This invention adopts a grey relational method and proposes an environmental factor sensor number optimization method based on graph theory clustering. It optimizes the sensor layout from the perspective of sensor number, reducing the number of sensors while ensuring the accuracy of data monitoring, and provides a new research idea for sensor layout optimization.

[0050] 2. The improved K-shell method used in this invention quantifies the importance of each node by calculating the comprehensiveness of the nodes in each layer, and sorts the nodes according to the quantification results.

[0051] 3. This invention uses a novel sensor layout algorithm for climate and environmental factors to optimize the correlation network graph. The process is simple and has high optimization efficiency. It does not require a lot of complex calculations and the traversal process is relatively simple. Attached Figure Description

[0052] Figure 1 This is a flowchart of the climate and environmental factor sensor layout optimization method based on grey relational degree according to the present invention;

[0053] Figure 2 This is the correlation network diagram generated in step 5 of the embodiment of the present invention;

[0054] Figure 3 This is a preprocessing result image generated in step 7 according to an embodiment of the present invention;

[0055] Figure 4 This is the final sensor layout diagram after step 10 optimization according to an embodiment of the present invention. Detailed Implementation

[0056] Exemplary embodiments, features, and aspects of the present invention will now be described in detail with reference to the accompanying drawings. Although various parameter values ​​and aspects of the embodiments are shown, the optimization process need not be performed with exactly the same parameters and aspects unless specifically indicated.

[0057] The present invention provides a method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis, such as... Figure 1 As shown, it includes:

[0058] Step 1: Use the unit root test to test the stationarity of the original monitoring data and obtain the stationarity test results of the original monitoring data.

[0059] A set of climate and environmental factor monitoring sensors consists of N sensors, where N is a positive integer. Each climate and environmental factor monitoring sensor acquires its own monitoring data within the same time period. The monitoring data of the i-th climate and environmental factor monitoring sensor is represented as X. i Where i = 1, 2, ..., N. The monitoring data from the climate and environmental factors monitoring sensors are all time-series data. For ease of description, the sensors mentioned in this paper refer to climate and environmental factors monitoring sensors.

[0060] Raw monitoring data X from each climate and environmental factor monitoring sensor t Perform a stationarity test, which involves testing the time series data for stationarity using the standard unit root test. If the unit root test indicates that the time series data is stationary, then the stationary time series is equal to the time series data, and step 3 is executed; otherwise, if the time series data is not stationary, step 2 is executed.

[0061] In this embodiment, a group of 15 sensors is used as an example. Table 1 shows the raw monitoring data of some of the sensors.

[0062]

[0063]

[0064] Using the unit root test function in MATLAB, the unit root test method is used to perform stationarity tests on the original monitoring data of each sensor, and the stationarity test results are obtained. In this embodiment, the original monitoring data of 15 sensors are all non-stationary time series, so step 2 needs to be performed.

[0065] Step 2: The non-stationary original monitoring data are processed by first-order and second-order differences, and the stationarity is tested again by unit root test.

[0066] The difference processing and re-stationarity test specifically include:

[0067] Step 21: Apply first-order differencing to the original monitoring data that was found to be non-stationary in Step 1 to obtain first-order differencing monitoring data. The first-order differencing monitoring data is still time series data. After equalizing the time series data with the first-order differencing monitoring data of the sensor, the unit root test method in Step 1 is used again to test the stationarity of the time series data.

[0068] In this embodiment, since the raw monitoring data from the 15 sensors are all non-stationary, the raw monitoring data in Table 1 need to be processed using first-order differencing. The non-stationary time series data are processed using first-order differencing with a MATLAB program, and then the unit root test procedure from step 1 is used again to test the stationarity of the data after first-order differencing. The results show that all the data are stationary time series data.

[0069] Table 2 shows the results of the first-order difference monitoring data obtained after first-order difference processing.

[0070] Table 2 First-order difference monitoring data

[0071]

[0072] It should be noted here that step 2 is only required if the original monitoring data is non-stationary. The original monitoring data that is determined to be stationary is directly the stationary time series of the corresponding sensor. In this embodiment, since the original monitoring data of the 15 climate and environmental factor monitoring sensors are all non-stationary, first-order difference processing is required.

[0073] Step 22: The first-order difference monitoring data, which is still not stationary after the first-order difference processing in Step 21, is differenced again to obtain second-order difference monitoring data. The time series data is then equalized to the data from each sensor in the second-order difference monitoring data, and the unit root test is performed again to check the stationarity of the time series data. In this embodiment, since the first-order difference monitoring data is already stationary, second-order difference processing is not performed.

[0074] Step 23: If, after second-order differencing, the time series data still exhibits non-stationarity, discard that time series data and retain the sensor corresponding to that time series data in the final result. The time series data that pass the stationarity test are called the stationary time series of each sensor, and the stationary time series of the i-th sensor is denoted as X. i .

[0075] Step 3: Normalize the stationary time series data of each sensor using the range method to obtain the normalized stationary time series of each sensor.

[0076] The stationary time series is obtained through the tests in steps 1 and 2. According to steps 1 and 2, the data in the stationary time series of different sensors are any one of the original monitoring data, first-order difference monitoring data, and second-order difference monitoring data. Therefore, the stationary time series must be normalized to remove the influence of different data magnitudes on the gray relational degree calculation results.

[0077] After normalizing the stationary time series using the range method, the normalized stationary time series X of the i-th sensor is obtained. i The stationary time series is normalized using the range method, as shown in the following formula.

[0078]

[0079] Where n represents the stationary time series X i There are n elements in total, X i '(κ) represents the k-th normalized data point in a normalized stationary time series, χ i (κ) represents a stationary time series X i The k-th element, minχ i (κ) represents a stationary time series X i The smallest element in the χ² value, maxχ i (κ) represents a stationary time series X i The largest element in the range. The purpose of normalization is to map the data to decimals between [0, 1].

[0080] In this embodiment, MATLAB programming is used to normalize the stationary time series data in step 2 using the range method to remove the influence of different data magnitudes on the gray relational degree calculation results. The normalized stationary time series is shown in Table 3.

[0081] Table 3 Normalized stationary time series

[0082]

[0083]

[0084] Step 4: For the normalized stationary time series of different sensors, calculate the grey relational degree between each pair of normalized stationary time series, and construct a correlation matrix A based on the calculation results to perform spatiotemporal correlation analysis between sensor nodes. This specifically includes the following steps:

[0085] Step 41: From the normalized stationary time series X i '(κ), select one as the reference sequence χ i (κ), the remaining ones are comparison sequences χ j(κ) (i≠j, i,j=1,2,...,N)) Calculate the correlation coefficient between each sample point using the following formula:

[0086]

[0087] In the formula, ζ i,j (κ) represents the reference sequence χ i (κ) and comparison sequence χ j (κ) is the correlation coefficient of the κ-th element; ζ is the discrimination coefficient, the value of which affects the extreme values ​​and the discrimination, and its range is ζ∈(0,1). In actual calculations, ζ is generally taken as ≤0.5; |χ i (κ)-χ j (κ)| represents the absolute value of the difference between the κ-th element of the reference sequence and the κ-th element of the comparison sequence; minmin|χ i (κ)-χ j (κ)| indicates that the minimum value is first taken from the sequence of element differences between the reference sequence and one comparison sequence, and then the minimum value is taken from the sequence of element differences between the reference sequence and each comparison sequence; max max|χ i (κ)-χ j (κ)| indicates that the maximum value is first taken from the element difference sequence between the reference sequence and a comparison sequence, and then the maximum value is taken from the maximum value of the element difference sequence between the reference sequence and each comparison sequence.

[0088] Step 42: Take the average of the correlation coefficients of all elements in the reference sequence and the comparison sequence as the grey correlation degree between the two sequences. The calculation formula is as follows:

[0089]

[0090] Where, γ i,j Represents the reference sequence χ i (κ) is the comparison sequence χ j (κ) Grey correlation degree between two sequences, i.e., normalized stationary time series X i '(κ) and X j Grey relational degree between '(κ)'.

[0091] Step 43: Based on the calculation results of the grey relational degree between normalized stationary time series, construct the sensor relational degree matrix A as follows:

[0092]

[0093] In this embodiment, MATLAB programming is used to calculate the grey correlation degree between pairs of normalized stationary time series from different sensors, and a correlation matrix A is constructed based on the calculation results. The correlation matrix A is as follows:

[0094]

[0095] Step 5: Based on the correlation matrix A obtained in Step 4, treat each sensor as a different node, and simplify the relationship between nodes with a correlation degree exceeding the threshold by treating them as having edges, thereby obtaining the correlation network graph matrix B, and constructing the correlation network graph accordingly.

[0096] Each environmental factor sensor is considered as a different node in the network graph. Then, two sensor nodes with a correlation degree exceeding a specified threshold are considered to have an edge between them. A correlation network graph matrix B is established, as shown below:

[0097]

[0098] The correlation network graph matrix B is a matrix consisting only of 0s and 1s, and its transformation formula is as follows:

[0099]

[0100] Where, γ i,j Let α be the element in the i-th row and j-th column of the sensor correlation matrix A, and α be the set threshold.

[0101] In this embodiment, the threshold α = 0.7 is set, and the correlation network matrix B is obtained based on the sensor correlation matrix A as follows:

[0102]

[0103] Correspondingly, the correlation network diagram is shown below. Figure 2 .

[0104] Step 6: Perform steps 7-9 for each disjoint subgraph of the correlation network graph;

[0105] In this embodiment, since there are no non-overlapping correlation network subgraphs in the correlation network graph, there is only one correlation network subgraph, which is the correlation network graph itself.

[0106] Step 7: Preprocess special structures with low correlation and single-chain path length exceeding 3 in the correlation network subgraph, and retain the central node in advance. In subsequent steps, the special structure will be regarded as a virtual node to prevent it from adding unnecessary steps in the subsequent algorithm traversal.

[0107] Special structural pretreatment specifically includes:

[0108] Step 71: For a single-chain structure composed of sensor nodes with a length greater than or equal to 3 in the correlation network subgraph, starting from any side of the single chain, retain the central node for every 3 sensor nodes and place the sensor there. For the portion of the single chain structure with fewer than 3 remaining sensors, retain the node furthest from the center of the single chain and place the sensor there. Save the nodes retained in this step as nodes to be retained during preprocessing.

[0109] In this embodiment, the special structure of the single-chain correlation degree with a path length exceeding 3 in the correlation network subgraph corresponds to nodes 5, 10, and 12, which are environmental factor sensors 5, 10, and 12, respectively. Therefore, preprocessing is required. Starting from any side of the single chain, sensors are arranged with the central node retained for every 3 sensor nodes, i.e., node 10 is retained. Therefore, the preprocessing result is as follows: Figure 3 As shown.

[0110] Step 72: Treat the preprocessed single-chain structure as a virtual sensor node.

[0111] In other words, nodes that participate in preprocessing on a single-chain structure will not participate in other processing. Treating a single-chain structure as a virtual sensor node means that nodes connected to the single-chain structure are considered to have an edge connected to the virtual sensor node.

[0112] Step 8: Employ an improved K-shell algorithm to quantify and rank the importance of each node in the relevant network subgraph. This includes:

[0113] Step 81: Use the K-shell method to stratify the importance of each node in the correlation network subgraph;

[0114] Step 82: In each layer obtained in Step 81, the improved algorithm of the K-shell method is used to calculate the comprehensiveness and further quantify and rank the importance. The comprehensiveness calculation formula is as follows:

[0115]

[0116] Where K(i) is the degree of each node in the correlation network subgraph, and N(i) is the total number of the node’s neighboring nodes and second-next neighboring nodes.

[0117] Step 83: Sort the nodes from the highest K-shell layer down to the highest level of integration, reducing the K-shell layer number and continuing to sort by integration until all nodes are sorted from highest to lowest importance.

[0118] In this embodiment, since nodes 5, 10, and 12 have been preprocessed, they are no longer involved in the importance ranking of each node here. An improved algorithm of the K-shell method is used to quantify the importance of each node in the correlation network subgraph and sort them. The comprehensive degree calculation results are shown in Table 5. The top 10 nodes are sorted by importance and then sorted down to the next layer. From high to low, they are 14, 13(9), 11, 6, 7, 8(3)(1), 4, 15, and 2.

[0119] Table 5. Results of Comprehensive Degree Calculation

[0120]

[0121] Step 9: Use a climate and environmental factor sensor placement algorithm to traverse the correlation network subgraph and optimize the number of sensors in the correlation network subgraph. Specifically, this includes:

[0122] Step 91: After quantifying and ranking the importance of nodes in Step 8, the climate and environmental factors sensor layout algorithm is used to traverse and retain sensor nodes, resulting in a sensor sub-layout scheme that can predict and cover the information of the correlation network subgraph under certain constraints. These constraints are preset conditions. For example, in this embodiment, each sensor node can predict information from its adjacent and second-to-last adjacent nodes. That is, information from unretained sensors can be inferred from the information from retained sensors. However, retained sensors are only allowed to infer information from their adjacent and second-to-last adjacent nodes. This constraint is used in this embodiment to ensure the accuracy of information prediction. Information prediction coverage means that based on the retained nodes, every unretained node in the correlation network subgraph can be predicted, thus completing the coverage. Typically, a functional relationship between two nodes is obtained based on historical data. Then, based on this functional relationship, the data from one node is used to predict the data from the other node. The predicted data is then compared with the actual collected data. As long as the error is within a set range, it is considered that one node can predict the other node.

[0123] The specific algorithms for deploying climate and environmental factor sensors include:

[0124] Starting with one node, traverse the nodes in descending order of importance. If a result satisfies the network graph information prediction coverage under the constraints, output the result as the sensor sub-layout scheme. If none of the results can cover the entire network graph under the constraints, increase the number of nodes to be retained and traverse again. If no result can be output, repeat the process of increasing the number of nodes to be retained and traversing until a result can be output.

[0125] For example, in this embodiment, after nodes 14, 13(9), 11, 6, 7, 8(3)(1), 4, 15, and 2 have been sorted from highest to lowest importance, the first step is to start by retaining one node and then iterate through the 12 nodes in descending order of importance, i.e., retaining node 14, node 13, node 9, ..., node 2. If there is one node that can satisfy the network graph information prediction coverage under the constraints, then the sensor layout scheme only needs to include this one node. In this embodiment, there is no such node, so the number of nodes retained is increased to two. The nine nodes are then selected in descending order of importance. Two nodes are selected for retention: first, nodes (14, 13), then (14, 9), then (14, 11), ..., then (4, 15), then (4, 5), and finally (15, 2). If the network graph information prediction coverage is still not satisfied under the constraints, the number of retained nodes is increased to three. From the nine nodes, two nodes are selected in descending order of importance for retention: first, nodes (14, 13, 9), then (14, 13, 11), then (14, 13, 6), ..., then (4, 15, 2), and so on. In this embodiment, since the network graph information prediction coverage is satisfied under the constraints when the retention node (14, 11) is reached, the traversal stops, and the sub-layout scheme is saved as the retention node (14, 11).

[0126] Step 92: Add the points reserved in step 71 to the sub-layout schemes obtained by the algorithm traversal, which is the final sub-layout scheme.

[0127] In this embodiment, node 10 is retained in step 71. Therefore, the final sub-layout scheme is to retain nodes (14, 11, 10).

[0128] Step 10: Merge the final sub-layout schemes of all relevant network subgraphs and add the nodes retained in step 23 to obtain the final layout scheme. The climate and environmental factor sensors corresponding to the nodes in the final layout scheme are the sensors retained after the climate and environmental factor sensor layout optimization.

[0129] In this embodiment, since there is only one subgraph of the correlation network, the final layout scheme is to retain nodes (14, 11, 10), as follows. Figure 4 As shown.

[0130] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions or parameters described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis, characterized in that: It includes the following steps: Step 1: Perform a stationarity test on the raw monitoring data of each sensor in a set of climate and environmental factor monitoring sensors. If the raw monitoring data is stationary, the stationary time series is equal to the time series data and proceed to Step 3; otherwise, proceed to Step 2. Step 2: Apply first-order and second-order differencing to the non-stationary raw monitoring data and perform stationarity testing again; for sensors that still fail the stationarity test after first-order and second-order differencing, retain the corresponding sensor and discard the sensor data. Step 3: Normalize each stationary time series data that passed the test using the range method to obtain the normalized stationary time series for each sensor; Step 4: For the normalized stationary time series of different sensors, calculate the grey relational degree between each pair of normalized stationary time series, and construct a correlation matrix based on the calculation results; Step 5: Based on the correlation matrix, nodes with a correlation degree exceeding the threshold are considered to have edges between them, thus obtaining the correlation network graph matrix, and constructing the correlation network graph accordingly. Step 6: Perform steps 7-9 for each disjoint subgraph of the correlation network graph; Step 7: Preprocess the special single-chain structures with a path length exceeding 3 in the correlation network subgraph, pre-reserve the central node, and treat the special single-chain structure as a virtual node in subsequent steps; Step 8: Quantify and rank the importance of each node in the relevant network subgraph using the improved K-shell algorithm. This includes: Step 81: Use the K-shell method to stratify the importance of each node in the correlation network subgraph; Step 82: In each layer obtained in Step 81, the improved algorithm of the K-shell method is used to calculate the comprehensiveness. The importance of the nodes is quantified and sorted according to the comprehensiveness. The formula for calculating the comprehensiveness is as follows: ； in, Let represent the degree of each node in the correlation network subgraph. This is the total number of nodes that are adjacent to and the next adjacent to a given node. Step 83: Sort from the highest K-shell layer node with the highest overall score downwards, reducing the K-shell layer number and continuing to sort by overall score again until all nodes are sorted from highest to lowest importance. Step 9: Use the climate and environmental factor sensor layout algorithm to traverse the correlation network subgraph to obtain the sensor sub-layout scheme. Add the points saved in step 7 to obtain the final sub-layout scheme; Step 9 is specifically as follows: Step 91: After quantifying and ranking the importance of nodes in Step 8, the climate and environmental factors sensor layout algorithm is used to traverse and retain sensor nodes, resulting in a sensor sub-layout scheme that can predict and cover the information of the correlation network subgraph under constraints. The specific climate and environmental factors sensor layout algorithm is as follows: Starting with one node, the nodes are traversed sequentially in descending order of importance. If a result satisfies the network graph information prediction coverage under the constraints, the result is output as the sensor sub-layout scheme. If none of the results can cover the entire network graph under the constraints, the number of nodes to be retained is increased and the traversal is repeated. If no result can be output, the process of increasing the number of nodes to be retained and traversing is repeated until a result can be output. The constraint is that each sensor node can predict information from at most its adjacent node and the second-to-last adjacent node. Step 92: Add the points reserved in step 7 to the obtained sub-layout scheme to obtain the final sub-layout scheme; Step 10: Merge the final sub-layout schemes of all related network subgraphs and add the nodes reserved in step 2 to obtain the final layout scheme.

2. The method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis according to claim 1, characterized in that: Step 2 is as follows: Step 21: For the original monitoring data that is non-stationary in Step 1, perform first-order differencing to obtain first-order differencing monitoring data. Perform a stationarity test on the first-order differencing monitoring data. If it is stationary, proceed to Step 3; otherwise, continue to Step 22. Step 22: Perform differential processing again on the first-order difference monitoring data that is still not stable after the first-order difference processing in step 21 to obtain second-order difference monitoring data. Perform a stationarity test on the second-order difference monitoring data. If it is stable, proceed to step 3; otherwise, continue to step 23. Step 23: If the second-order differential monitoring data is still unstable, discard the sensor data and save the corresponding sensor.

3. The method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis according to claim 1, characterized in that: The formula for normalization using the range method in step 3 is as follows: ； Where n represents a stationary time series There are n elements in total. This represents the k-th normalized data point in a normalized stationary time series. Representing stationary time series The k-th element, Representing stationary time series The smallest element in the middle, Representing stationary time series The largest element in the system.

4. The method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis according to claim 1, characterized in that: Step 4 specifically involves: Step 41: From the normalized stationary time series Select one as the reference sequence The remaining ones are comparison sequences. The correlation coefficient between each sample point is calculated using the following formula: ； In the formula, Represents the reference sequence Comparison sequence In the The correlation coefficient of each element; The resolution coefficient has a range of values. ; Indicates the reference sequence number The element and the comparison sequence The absolute value of the differences between the elements; This means first taking the minimum value from the sequence of element differences between the reference sequence and a comparison sequence, and then taking the minimum value from the sequence of element differences between the reference sequence and each comparison sequence. This means first taking the maximum value from the element difference sequence between the reference sequence and a comparison sequence, and then taking the maximum value from the maximum values ​​of the element difference sequences between the reference sequence and each comparison sequence. Step 42: Take the average of the correlation coefficients of all elements in the reference sequence and the comparison sequence as the grey correlation degree between the two sequences. The calculation formula is as follows: ； in, Represents the reference sequence The comparison sequence is . Grey correlation between two series, i.e., normalized stationary time series and The degree of grey relational relationship between them; Step 43: Based on the calculation results of the grey relational degree between normalized stationary time series, construct the correlation matrix as follows: 。 5. The method for optimizing the layout of climate and environmental factor sensors based on grey relational analysis according to claim 1, characterized in that: Step 7 specifically includes: Step 71: For a single-chain structure composed of sensor nodes with a length greater than or equal to 3 in the correlation network subgraph, retain the central node for every 3 sensor nodes starting from any side of the single chain and place the sensor there; for the part of the single chain structure with less than 3 sensors remaining, retain the node on the side of the single chain furthest from the center of the single chain and place the sensor there; save the nodes retained in this step as nodes to be retained during preprocessing. Step 72: Treat the preprocessed single-chain structure as a virtual sensor node.

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