Safety early warning method for collapsible loess slope

Abstract

The invention provides a collapsible loess slope safety early warning method, which belongs to the technical field of geotechnical engineering risk, and comprises the following steps: constructing a network structure model of slope risk factors, identifying a dependency relationship between elements through an ANP method, and constructing a judgment matrix of the slope risk factors; calculating the local weight of each element of the judgment matrix and constructing a weight matrix; constructing an unempowerment hypermatrix and an empowerment hypermatrix according to the network structure model; calculating a limit sorting vector of the empowerment hypermatrix through multiple times of power operation to obtain a global weight of each element; and determining a risk matter element matrix, constructing a correlation function, and taking the global weight of each element as an extension operation weight weighting coefficient to obtain a risk level. The method has the advantages that by constructing the network structure model and calculating the global weight, the dynamic dependency relationship between the slope risk factors can be more effectively captured, and the limitation of a traditional method on factor interaction modeling is overcome, so that the comprehensiveness and adaptability of risk assessment are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of geotechnical engineering risk, and particularly relates to a collapsible loess slope safety early warning method. BACKGROUND

[0002] The widely distributed collapsible loess in China (covering about 640,000 square kilometers, of which 60% is collapsible) has significant water sensitivity. Its strength is relatively high in the natural state, but the structure is quickly destroyed after encountering water, the strength drops sharply, the compressibility increases dramatically, and it is extremely easy to induce collapsible deformation and even landslide disasters under extreme rainfall and other conditions, which seriously threatens the safety of infrastructure and people's lives and property. Although domestic and foreign scholars have widely applied various mathematical models for slope stability evaluation and early warning, and have explored the potential of BIM technology in information integration and risk visualization (such as geological monitoring information attachment, risk level color display), these methods still face significant challenges in dealing with the numerous, complex and dynamic time-varying factors (such as topography, crack development, slope structure, groundwater, rainfall, artificial disturbance, freezing and thawing, earthquake, etc.) that affect the stability of loess slopes and their dynamic interaction with the degree of correlation and hierarchical structure evolving over time. Therefore, it is urgent to develop a safety early warning method that can effectively integrate the special geological properties of collapsible loess, real-time monitoring data, and clearly display the dynamic risk state, in order to improve the prevention and control ability of slope instability SUMMARY

[0003] Therefore, the collapsible loess slope safety early warning method provided by the present application solves the above technical problems. The technical scheme adopted by the present application is as follows: A network structure model of slope risk factors is constructed, the dependence relationship between elements is identified by the ANP method, and a judgment matrix between slope risk factors is constructed by using the 1-9 scale method; The local weights of each element of the judgment matrix are calculated and a weight matrix is constructed; An unweighted supermatrix is constructed according to the network structure model, and a weighted supermatrix is obtained by weighting the unweighted supermatrix through the weight matrix; The limit ordering vector of the weighted supermatrix is obtained by multiple power operations to obtain the global weight of each element; A risk matter-element matrix is determined, a correlation function is constructed, the global weight of each element is taken as the weight coefficient of the extension operation, and the risk level is obtained by extension operation.

[0004] Further, the method of constructing a network structure model of slope risk factors, identifying the dependence relationship between elements by the ANP method, and constructing a judgment matrix between slope risk factors by using the 1-9 scale method comprises: Identify and define all the elements related to slope risk, and distribute these elements in different levels; compare the importance of elements by two, use 1-9 quantification scale method to compare two by two in the group or between groups, form a judgment matrix, and then perform consistency test, calculate the maximum eigenvalue and consistency ratio of the judgment matrix; require CR<0.1, otherwise adjust the judgment matrix.

[0005] Further, the method for processing the interdependence relationship between the group and the group includes: The judgment matrix that passes the consistency test is normalized to obtain the local weight vector of each element, and the weight matrix A is combined; If there is no influence between elements, the weight obtained is 0, and if there is a dependence relationship between elements, the weight vectors of the group and the group are calculated respectively.

[0006] Further, the method for constructing the unweighted super matrix and the weighted super matrix includes: The weight vector of the influence degree of each element on a certain element is obtained from the judgment matrix, and the vector matrix is obtained; the mutual influence of each element in the network structure model is considered comprehensively, the local vector matrix is integrated by super matrix operation, and the unweighted super matrix W is obtained after multiple iterations until convergence; the elements of the super matrix W are weighted according to the weight matrix A, and the weighted super matrix is obtained.

[0007] Further, the method for obtaining the global weight of each element by multiple power operations on the weighted super matrix includes: The weighted super matrix is operated by multiple power operations, the normalized limit ordering vector of the weighted super matrix is obtained, and finally the weight value of each index element is sorted, and the column vector of the limit matrix is the global weight of each element.

[0008] Further, the method for determining the risk matter element matrix and constructing the correlation function includes: Determine the classical domain, the section domain and the matter element to be evaluated: define the classical domain based on the network structure model, the classical domain R j is defined as each risk level K j The value range of the index u, wherein the risk level includes K1 level indicating danger, K2 level indicating more danger, K3 level indicating more safety, and K4 level indicating safety, and the corresponding threshold interval is 、 、 and ; the section domain R P is defined as the range of all possible values of the index, that is The object element R0 to be evaluated is obtained through actual monitoring data or expert scoring, and the specific value comes from the actual quantitative results of slope risk factors. Constructing the correlation function K j (v i ), used to calculate indicators actual value Risk level The degree of correlation; the correlation function is: ; Among them; among them As an indicator The actual measured value, i.e., the value of the object to be evaluated; As an indicator In level The classic domain interval; As an indicator The segmental range; For point to the interval The distance; Let represent the positional relationship of a point with respect to the interval.

[0009] Furthermore, the calculation of the correlation function includes point distance. and positional relationship The derivation ensures that the correlation reflects the degree of deviation of the indicator value from the level range, including: Given an interval V = ⟨a, b> and a real point v, where a and b are the upper and lower limits of the interval, and v is a real number; calculate the distance between the points. : Use point v i Distance to interval V: ;when When inside the interval, ; Based on point distance The calculation result is input point v i Classical domain interval and the interval Calculate positional relationships : in .

[0010] Furthermore, the method of obtaining the risk level of each region and level through extension operations by using the global weight of each element as the weighting coefficient of the extension operation includes: Step 1: Calculate the comprehensive correlation of the primary indicators. ;in; Primary Indicator Belonging to a rank The overall correlation; It belongs to the first-level indicator. A certain secondary indicator Global weights; Secondary indicators Belonging to a rank The degree of correlation; For those belonging to the first-level indicators Sum of all secondary indicators; Step 2: Calculate the overall correlation degree of the target layer. ;in; The target layer belongs to the hierarchy. The final overall correlation; The kth primary indicator The weights; The k-th primary indicator belongs to the level. The overall correlation degree; m: the number of primary indicators.

[0011] Step 3: Extract the maximum value from the comprehensive correlation vector. And assign the level K corresponding to the maximum value. j The slope was determined to be at an overall risk level.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This application effectively integrates the special geological characteristics of collapsible loess, real-time monitoring data, and clearly shows the dynamic risk status. By constructing a network structure model and calculating global weights, it can more effectively capture the dynamic dependencies between slope risk factors (such as topography, groundwater, rainfall, etc.), overcome the limitations of traditional methods in factor interaction modeling, thereby improving the comprehensiveness and adaptability of risk assessment and providing more reliable support for slope stability analysis under complex geological conditions.

[0013] 2. Regarding the accuracy and dynamism of risk assessment, this application achieves quantitative transformation and hierarchical aggregation of indicator values ​​through correlation functions and extension operations, which helps to obtain more accurate risk level judgment results. This weighted extension operation supports the integration of real-time monitoring data, can dynamically respond to changes in slope status, enhance the timeliness and pertinence of early warning, and provide timely decision-making basis for engineering prevention and control. Attached Figure Description

[0014] The present invention will now be described in further detail with reference to the accompanying drawings.

[0015] Figure 1 : Schematic diagram of the process of this invention. Detailed Implementation

[0016] To better understand the present invention, the content of the invention is further clearly illustrated below with reference to embodiments and accompanying drawings. However, the scope of protection of the present invention is not limited to the embodiments described below. Numerous specific details are set forth in the following description to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the present invention can be practiced without one or more of these details.

[0017] Example 1: See Figure 1 This embodiment provides a safety early warning method for collapsible loess slopes, which includes: S1. Construct a network structure model of slope risk factors. Identify dependencies between elements using the ANP method and construct a judgment matrix between slope risk factors using the 1-9 scaling method. This includes: identifying and defining all relevant elements in the slope risk problem and distributing these elements across different levels or components. This step aims to systematically decompose slope risk factors (such as topography, groundwater, rainfall, etc.). ANP (Network Analysis Method) allows for the formation of complex network structure models between elements. Unlike AHP, which only considers hierarchical relationships between elements, ANP allows for the formation of complex network structure models, including dependencies within and between elements. Compared to traditional AHP, which only considers hierarchical relationships, ANP better reflects the actual situation of dynamic interactions of multiple factors in collapsible loess slopes. Pairwise comparison of element importance: Using a specific element as a criterion, pairwise comparisons are made between elements within or between groups using the 1-9 quantification scaling method to form a judgment matrix. The 1-9 scaling method transforms subjective judgments into quantifiable values, making the comparison of element importance consistent and operable. The advantage of this method is that it standardizes the scoring process of experts or engineers, reduces subjectivity and arbitrariness, and supports cross-group element comparison, enhancing the flexibility of the network model. Then, a consistency test is performed: the maximum eigenvalue and consistency ratio of the judgment matrix are calculated to ensure that CR < 0.1; otherwise, the judgment matrix needs to be adjusted. The consistency test (CR test) is a crucial step in ensuring the logical consistency of the judgment matrix. The threshold of CR < 0.1 is derived from statistical standards, indicating that the degree of deviation of the matrix from random consistency is within an acceptable range. If CR ≥ 0.1, it indicates that there are contradictions in the comparison results, and the judgment matrix needs to be readjusted to avoid distortion in weight calculation.

[0018] S2. Calculate the weight vector, including normalizing the judgment matrix to obtain local weights and handling intra-group and inter-group dependencies. S21: Normalize the judgment matrix that passes the consistency test to obtain the local weight vector of each element. Combine these vectors to form a weight matrix, denoted as A. The normalization process transforms the element values ​​in the judgment matrix into relative weights. Standardization of the matrix rows is achieved through summation or scaling to ensure that the local weight vector of each element has consistency and additivity, eliminating the influence of scale differences in the original data and making the weight values ​​within a comparable range. For example, consider a fourth-order matrix: (1.1) S22: If elements have no mutual influence, the calculated weight is 0. If there is a dependency relationship between elements, the weight vectors within and between groups need to be calculated separately. S21 yields the basic weights without considering the networked dependencies between elements. S22 supplements the weight data based on whether the dependencies between elements interact and the degree of interaction, adjusting or enriching the local weights of S21. Intra-group weights refer to the mutual influence weights within the same group of elements, while inter-group weights refer to the cross-influence weights between elements in different groups. These weights are obtained by identifying the dependencies between elements using the ANP method described in S1 and then by the "pairwise comparison" in the 1-9 quantization scaling method. Intra-group weights and inter-group weights will respectively obtain the intra-group weight vector and the inter-group weight judgment matrix in the ANP method. The intra-group weight vector handles the mutual influence between elements in the same group, while the inter-group weight vector captures the cross-dependencies between elements in different groups. This reflects the advantage of the ANP model over AHP, which can more realistically simulate slope risk factors (such as the dynamic interaction between rainfall and groundwater). By calculating separately, the hierarchical and networked representation of the weights is ensured, which improves the precision of risk assessment, makes the output results more in line with actual engineering scenarios, and avoids assessment distortion caused by simplifying dependencies.

[0019] S3. Construct unweighted and weighted hypermatrices; By using a judgment matrix, weight vectors representing the degree of influence of each element on a given element are obtained, thus yielding a vector matrix. Based on the principle of ANP (Aspect-Neutral Programming), the local weight vectors of each element within all elements are derived through pairwise comparisons of the judgment matrix, forming a vector matrix. This vector matrix reflects the quantitative relationship of relative importance between elements. For example, in the risk assessment of collapsible loess slopes, the mutual influence of factors such as topography and groundwater can be systematically represented in matrix form. Considering the mutual influence of each element in the network structure model, the local vector matrices are integrated through operations such as supermatrix. After multiple iterations until convergence, an unweighted supermatrix W is obtained. Supermatrix operations are used to integrate multiple vector matrices to handle feedback and cross-dependencies between elements in the network structure model. The iterative process until convergence stabilizes the supermatrix through repeated matrix multiplication, ensuring that the weight results reflect global influence rather than local bias. The detailed expansion of the unweighted supermatrix W, using a fourth-order matrix as an example, is shown in the following equation: The elements of the supermatrix W are weighted according to the weight matrix A, resulting in a weighted supermatrix. The weight matrix A originates from the normalized local weights of S21. The weighting process of the supermatrix W essentially combines local weights with network dependencies, adjusting the elements of the supermatrix to reflect overall importance. The weighted supermatrix more accurately balances intra-group and inter-group influences, for example, giving higher weights to the main driving factors in slope risk factors, improving the accuracy of subsequent limit ordination vector calculations, and ultimately supporting more accurate slope safety early warning. The expansion can be obtained through the formula: .

[0020] S4. Obtain the limit ranking vector of the weighted hypermatrix through multiple exponentiation operations to obtain the global weight of each element. This includes: performing multiple exponentiation operations on the weighted hypermatrix to obtain the normalized limit ranking vector. Multiple exponentiation is an iterative calculation process. By repeatedly performing matrix multiplication, the weighted hypermatrix gradually converges to a stable state, thus obtaining the limit ranking vector. This ensures that the eigenvalues ​​of the matrix tend to be consistent after the exponentiation operation, and the vector no longer changes with iteration. Finally, the weight values ​​of each indicator element are obtained and ranked. The column vector of the limit matrix is ​​the global weight of each element, reflecting its comprehensive influence on the overall goal. The limit ranking vector represents the final relative importance of each element in the network structure model, and its column vector form facilitates the direct extraction of global weight values. The global weight integrates all direct and indirect dependencies between elements. For example, in the collapsible loess slope model, the weights of factors such as topography and groundwater reflect their contribution to the overall risk. S5. Determine the risk element matrix, construct the correlation function, and use the global weight of each element as the weighting coefficient of the extension operation. Obtain the risk level of each region and level through extension operation, which includes: S51. Determine the risk element matrix and construct the correlation function: S511. Determine the classical domain, section domain, and unit to be evaluated: Classical domain R j Describe each risk level K j Regarding the range of values ​​for a certain indicator u Rj=(Kj,c,Vj)=(Kj,u,⟨aj,bj>) For example, for the indicator u11 topography: K1 (Danger): K2 (More dangerous): K3 (relatively safe): K4 (Security): The classic domain is set based on risk level classification. By discretizing continuous index values ​​through threshold intervals, it provides a standardized benchmark for risk assessment. This ensures the objectivity and consistency of level determination, eliminates subjective arbitrariness, makes the model more adaptable to comparison and integration of different slope scenarios, and improves the repeatability of the assessment.

[0021] Section R P : Describes the range of all possible values ​​for the indicator.

[0022] ; The section is ; Setting the domain to <0,1> normalizes the index values, unifies data of different dimensions to the same scale, facilitates mathematical calculations and comparisons, and eliminates data heterogeneity. It also simplifies the calculation of correlation functions, enhances the robustness of the model when processing multi-source data (such as monitoring data and expert scores), and avoids errors caused by unit mismatch.

[0023] The object element to be evaluated, R0, is a specific numerical value of the indicator obtained from actual monitoring or expert scoring. This makes the model output more consistent with the actual engineering situation, improves the credibility of decision-making, and supports real-time early warning through dynamic data updates, adapting to changes in slope conditions.

[0024] S512, Constructing the correlation function K j (v i ): For indicators Its relation to rank The correlation function is defined as: in :index Actual measured value (value of the object to be evaluated), actual measured value It is the input to the correlation function, representing the specific indicator status (such as topographic and geomorphological scores), ensuring that the calculation is based on empirical data; :index In level Classical domain intervals, classical domain intervals The levels were defined. The boundary, through upper and lower limits and Capture the typical characteristics of this level; :index The segmental interval, the segmental interval As a global reference, the global range of index values ​​is defined to ensure that correlation functions are operated in a unified context; :point to the interval The distance; The positional relationship of a point with respect to an interval, D, combined with the point distance and the node region, reflects the relative position of the point with respect to multiple intervals.

[0025] a) Calculate the distance between the point and the interval. For interval and points : when When inside the interval, ; This property ensures that when the indicator value falls within a specific risk level range, the point distance is non-positive, indicating a high degree of matching; conversely, a positive number indicates deviation, enhancing the model's sensitivity to boundary conditions, enabling risk assessment to accurately capture critical states and supporting timely early warning. Where a and b are the upper and lower limits of the interval; v is a real number; the definition of interval V originates from the classical field or section field, such as the classical field. Indicates risk level The threshold range, the actual value point v is the index u i Measurement data.

[0026] b) Based on point distance The calculation result is input point v i Classical domain interval and the interval Calculate positional relationships : in ; The calculation of positional relationship D integrates the results of point distance ρ, capturing its relative position by comparing the deviation of the index value from the classical domain and the section domain. Input parameter v i , and Ensuring that calculations are based on actual data and predefined intervals avoids arbitrariness, improves the adaptability of the correlation function to complex risk scenarios, and enables the model to handle the transition of indicator values ​​between multiple levels.

[0027] S52. Successive calculation process of extension operations: The essence of this process is "bottom-up weighted synthesis", with the following hierarchical structure: secondary indicators → primary indicators → target layer (overall risk); Step 1: Calculate the overall correlation of the primary indicators. This is the most crucial step. Using the correlation of the secondary indicators and their global weights, calculate the degree to which the primary indicators belong to each risk level.

[0028] Calculation formula: Primary Indicator Belonging to a rank The overall correlation; It belongs to the first-level indicator. A certain secondary indicator Global weights; Secondary indicators Belonging to a rank The degree of correlation; For those belonging to the first-level indicators Sum of all secondary indicators; By using a weighted summation method, the correlation of secondary indicators is determined. With the corresponding global weight Combining these factors, it is calculated that the primary indicator U belongs to the level K. j The overall correlation; weight The global weights derived from the ANP-EWM model ensure that the differences in the importance of indicators are fully considered, reflecting the dynamic dependencies between elements in the network structure model. This improves the hierarchy and accuracy of risk assessment, enabling the model to capture the contributions of risk factors at different levels more precisely and avoiding assessment bias caused by ignoring weights.

[0029] Step 2: Calculate the overall correlation degree of the target layer After obtaining the overall correlation of all primary indicators, we treat them as new "data" and summarize them to the target layer (overall risk).

[0030] Calculation formula: The target layer belongs to the hierarchy. The final overall correlation; The kth primary indicator The weights; The k-th primary indicator belongs to the level. The overall correlation (and the calculation results from the previous step); m: the number of primary indicators; This step further aggregates the overall correlation of the primary indicators, using the weights of the primary indicators. Weighted summation yields the grade to which the target layer (overall slope) belongs. The final overall correlation. Weight Also derived from the ANP-EWM model, it reflects the relative importance of different primary indicators to the overall goal, ensuring the scientific rigor and consistency of the aggregation process.

[0031] Step 3: Final Risk Level Determination 1. Find the comprehensive correlation vector of the target layer; 2. Take the maximum value n among them; 3. The level corresponding to the maximum value n is K. j ; 4. Therefore, the final overall risk level of this slope was determined to be K. j ; The overall risk level of the slope is determined by comparing the maximum value in the comprehensive correlation vector of the target layer; the maximum value corresponds to the most matching risk level. Based on the principle of maximum correlation in extension set theory, the objectivity and uniqueness of the judgment result are ensured, and a clear risk judgment output is provided.

[0032] Technical effects of this embodiment: 1. This application addresses the technical bottlenecks in risk assessment of collapsible loess slopes, namely, the difficulty of traditional methods in effectively handling the dynamic interaction of multiple factors, lack of real-time performance, and insufficient visualization support. It proposes a solution integrating the ANP-EWM-Extenics model. By constructing a networked structural model and extension theory, this application can systematically integrate the complex dependencies of slope risk factors, overcome the limitations of existing technologies in medium- and long-term early warning and dynamic adaptability, and provide a more reliable theoretical basis for engineering protection.

[0033] 2. This application achieves hierarchical and precise risk assessment through the deep integration of ANP-EWM weight calculation and extension operations. Specifically, the construction of the correlation function and the derivation of point-distance relationships ensure the objectivity of indicator quantification. This design enhances the interpretability of early warning results, significantly improves the timeliness of decision support, and enables engineers to quickly identify risk areas and take targeted measures.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A safety early warning method for collapsible loess slopes, characterized in that, include, A network structure model of slope risk factors was constructed, the dependencies between elements were identified by the ANP method, and the judgment matrix between slope risk factors was constructed by the 1-9 scaling method. Calculate the local weights of each element in the judgment matrix and construct the weight matrix; An unweighted supermatrix is ​​constructed based on the network structure model. The weighted supermatrix is ​​obtained by weighting the unweighted supermatrix with a weight matrix. The limit sorting vector of the weighted hypermatrix is ​​obtained by exponentiation, and the global weight of each element is obtained. Determine the risk element matrix, construct the correlation function, use the global weight of each element as the weighting coefficient of the extension operation, and obtain the risk level through the extension operation.

2. The safety early warning method for collapsible loess slopes as described in claim 1, characterized in that, The method for constructing a network structure model of slope risk factors, identifying dependencies between elements using the ANP method, and constructing a judgment matrix between slope risk factors using the 1-9 scaling method includes: Identify and define all slope risk-related elements and distribute them across different levels; compare the importance of elements pairwise, using a 1-9 quantification scale as a criterion to compare elements within or between groups to form a judgment matrix; then perform a consistency test, calculating the maximum eigenvalue and consistency ratio of the judgment matrix; CR < 0.1 is required, otherwise the judgment matrix is ​​adjusted.

3. The safety early warning method for collapsible loess slopes as described in claim 2, characterized in that, The calculation of the weight vector includes obtaining local weights by normalizing the judgment matrix, and the methods for handling intra-group and inter-group dependencies include: Normalize the judgment matrix that passes the consistency test, obtain the local weight vector of each element, and combine them to form the weight matrix A; If the elements have no influence on each other, the weight is 0. If there is a dependency relationship between the elements, the weight vectors within and between groups are calculated separately.

4. The safety early warning method for collapsible loess slopes as described in claim 3, characterized in that, Methods for constructing unweighted and weighted hypermatrices include: By judging the matrix, the weight vectors of the influence of each element on a certain element are obtained, resulting in a vector matrix. Taking into account the mutual influence of each element in the network structure model, the local vector matrices are integrated through super matrix operations. After multiple iterations until convergence, an unweighted super matrix W is obtained. The elements of the super matrix W are weighted according to the weight matrix A to obtain a weighted super matrix.

5. The safety early warning method for collapsible loess slopes as described in claim 4, characterized in that, The method for obtaining the global weights of each element by calculating the limiting sorting vector of the weighted hypermatrix through multiple exponentiation operations includes: By performing multiple exponentiation operations on the weighted hypermatrix, the normalized limit sorting vector of the weighted hypermatrix is ​​obtained. Finally, the weight values ​​of each index element are obtained and sorted. The column vector of the limit matrix is ​​the global weight of each element.

6. The safety early warning method for collapsible loess slopes as described in claim 1, characterized in that, Methods for determining the risk element matrix and constructing correlation functions include: Determine the classical domain, the section domain, and the object element to be evaluated: Define the classical domain R based on the network structure model. j Defined as each risk level K j Regarding the value range of indicator u, the risk levels include K1 (representing danger), K2 (representing moderate danger), K3 (representing moderate safety), and K4 (representing safety), with corresponding threshold ranges as follows: , , and ; Section R P Defined as the range of all possible values ​​that the indicator can take, i.e. The object element R0 to be evaluated is obtained through actual monitoring data or expert scoring, and the specific value comes from the actual quantitative results of slope risk factors. Constructing the correlation function K j (v i ), used to calculate indicators actual value Risk level The degree of correlation; the correlation function is: ； Among them; among them As an indicator The actual measured value, i.e., the value of the object to be evaluated; As an indicator In level The classic domain interval; As an indicator The segmental range; For point to the interval The distance; Let represent the positional relationship of a point with respect to the interval.

7. The safety early warning method for collapsible loess slopes as described in claim 6, characterized in that, The calculation of the correlation function includes point distance. and positional relationship The derivation ensures that the correlation reflects the degree of deviation of the indicator value from the level range, including: Given an interval V = ⟨a, b> and a real point v, where a and b are the upper and lower limits of the interval, and v is a real number; calculate the distance between the points. : Use point v i Distance to interval V: ;when When inside the interval, ; Based on point distance The calculation result is input point v i Classical domain interval and the interval Calculate positional relationships : in .

8. The safety early warning method for collapsible loess slopes as described in claim 6, characterized in that, The method of obtaining the risk level of each region and level by using the global weight of each element as the weighting coefficient of the extension operation includes: Step 1: Calculate the comprehensive correlation of the primary indicators. ;in; Primary Indicator Belonging to a rank The overall correlation; It belongs to the first-level indicator. A certain secondary indicator Global weights; Secondary indicators Belonging to a rank The degree of correlation; For those belonging to the first-level indicators Sum of all secondary indicators; Step 2: Calculate the overall correlation degree of the target layer. ;in; The target layer belongs to the hierarchy. The final overall correlation; The kth primary indicator The weights; The k-th primary indicator belongs to the level. The overall correlation degree; m: the number of primary indicators.

9. Step 3: Extract the maximum value from the comprehensive correlation vector. And assign the level K corresponding to the maximum value. j The slope was determined to be at an overall risk level.

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