Underground cavern site selection method based on comprehensive index system
By establishing a hierarchical evaluation model and combining the AHP method with exponential scaling and the entropy weight method, the problems of expert opinion disagreement and poor consistency of judgment matrix in underground cavern site selection were solved, achieving more accurate and reliable cavern site selection decisions and improving engineering application efficiency and decision-making scientificity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-17
- Publication Date
- 2026-03-31
AI Technical Summary
Existing methods for selecting underground cavern sites rely on expert experience, leading to disagreements and a lack of scientific integration. Traditional quantitative methods suffer from poor consistency in the judgment matrix and strong subjectivity in weight allocation, making it difficult to scientifically handle disagreements among multiple experts, resulting in low decision-making efficiency and low credibility.
A hierarchical evaluation model based on a comprehensive index system was established, which includes geological, topographical, hydrological, investment, and construction conditions. Subjective and objective weights were determined by the AHP method with an exponential scale and the entropy weight method. Combined with a group decision-making disagreement handling mechanism, the comprehensive score was calculated using a linear weighting method to obtain the optimal cavern site selection scheme.
It improves the scientific nature and consistency of decision-making, enhances the reliability of group decision-making, reduces errors and efficiency losses caused by repeated adjustments, provides clear decision support, shortens the design cycle, and improves engineering quality and economy.
Smart Images
Figure CN121766596A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of underground cavern site selection technology, and in particular to an underground cavern site selection method based on a comprehensive index system. Background Technology
[0002] In hydropower station design practice, the site selection of underground caverns is a complex, multi-criteria decision-making problem involving multiple factors such as geology, topography, hydraulics, construction, and economy. Existing site selection decision-making methods suffer from two major pain points: First, they rely on qualitative judgments based on expert experience. In this case, the lack of a scientific integration mechanism when different experts disagree leads to a subjective decision-making process and conclusions that are difficult to convince others. Second, they employ quantitative methods such as the traditional Analytic Hierarchy Process (AHP). However, the inherent limitations of traditional scaling methods often result in failure to pass the consistency test of the judgment matrix. Furthermore, problems such as poor consistency of the judgment matrix, strong subjectivity in weight allocation, and difficulty in scientifically handling disagreements among multiple experts require repeated adjustments, leading to inefficiency and undermining the original judgment intentions of the experts. This results in insufficient scientific rigor and low credibility of the decision, impacting the safety and economy of the project. Summary of the Invention
[0003] The purpose of this invention is to provide a method for selecting underground cavern sites based on a comprehensive index system, which can make the decision-making results for underground cavern site selection more accurate.
[0004] The technical solution adopted by this invention to solve its technical problem is as follows: A method for selecting the location of underground caverns based on a comprehensive index system includes the following steps: Establish a hierarchical evaluation model that includes five primary indicators (geological conditions, topographical conditions, hydrological conditions, investment conditions, and construction conditions) and twenty-five secondary indicators under the corresponding primary indicators. The subjective weights of each indicator in the hierarchical evaluation model are determined by the AHP method based on the exponential scale, and the objective weights of each indicator in the hierarchical evaluation model are determined by the entropy weight method. The subjective and objective weights are weighted and combined to obtain the combined weights. Establish a mechanism for handling group decision-making disagreements and calculate the degree of disagreement index; The comprehensive score of the candidate cavern site selection schemes is calculated by linear weighting method, and the optimal cavern site selection scheme is obtained based on the comprehensive score.
[0005] In some embodiments, in the hierarchical evaluation model, when the primary index is geological conditions, the secondary indexes include: integrity of the surrounding rock mass, the angle between the axis and the geostress strike should not be too small, the rock softening coefficient should not be too large, the angle between the axis and the structural plane strike should not be too small, the angle between the axis and the rock strata strike should not be too large, the cross-sectional shape is conducive to cavern stability, the presence of a high-pressure, high-flow-rate aquifer and the degree of development of rock orientation and fractures; When the primary indicator is topographic conditions, the secondary indicators include: reasonable layout of construction adits, thickness of surrounding rock at the top and walls of the tunnels, near-straight layout of the tunnel group axes, ease of layout of entrance and exit structures, and topographic uncertainty index. When the primary indicator is hydrological conditions, the secondary indicators include: reasonable geothermal gradient and lateral pressure coefficient, smooth connection between inlet and outlet and cave group water flow, sufficient submersion depth at inlet and outlet, degree of chemical corrosion of groundwater and sufficient pressure relief in cave group. When the primary indicator is an investment condition, the secondary indicators include: low project investment and effective control of project risks; When the primary indicator is the construction conditions, the secondary indicators include: advanced construction technology, reasonable construction progress and intensity configuration, reasonable allocation of construction resources, suitable cross-sectional and longitudinal profiles for construction, and minimal environmental pollution from the construction team.
[0006] In some embodiments, determining the subjective weights of each indicator in the hierarchical evaluation model using the AHP method based on an exponential scale includes the following steps: For each primary and secondary indicator in the hierarchical evaluation model, experts make pairwise comparisons of the importance of the secondary indicators at the same level relative to the primary indicator. The comparison judgments are converted into numerical values using an exponential scale, and a judgment matrix is constructed. The exponential scales used are: 1, 1.315, 1.732, 3, and 9. Based on the judgment matrix, the subjective weights of each indicator are calculated using the AHP method.
[0007] In some embodiments, calculating the subjective weights of each indicator using the AHP method based on the judgment matrix means: The judgment matrix is normalized column by column; The normalized judgment matrix is summed row by row to obtain an approximate value of the eigenvector; The result of summing by row is then normalized again to obtain the subjective weight.
[0008] In some embodiments, determining the objective weights of each indicator in the hierarchical evaluation model using the entropy weight method includes the following steps: The original scores of the candidate cavern site selection schemes on the corresponding secondary indicators under the primary indicators were obtained by expert scoring, and a scoring matrix was obtained. The original scores in the rating matrix are standardized to obtain a standardized matrix. Calculate the information entropy of each secondary indicator; The difference coefficient of the secondary indicators is calculated based on information entropy, and the objective weight of the corresponding secondary indicators is calculated based on the difference coefficient.
[0009] In some embodiments, the weighted fusion of subjective weights and objective weights to obtain combined weights includes the following steps: Set the fusion coefficient; The fusion weight of the corresponding secondary indicators under the primary indicator is calculated based on the fusion coefficient.
[0010] In some embodiments, establishing a group decision-making disagreement handling mechanism and calculating a disagreement index includes the following steps: Obtain the judgment matrix corresponding to each expert, and transform it into an antisymmetric matrix by taking the logarithm, thus obtaining the group antisymmetric matrix; Calculate the standard deviation of the group antisymmetric matrix and use it as an indicator of divergence.
[0011] In some embodiments, after calculating the divergence index, the method further includes: Obtain the preset threshold for the divergence index; The divergence index is compared with a preset divergence index threshold, and the corresponding synthesis strategy is adopted based on the comparison result.
[0012] In some embodiments, comparing the divergence index with a preset threshold for the divergence index and adopting a corresponding synthesis strategy based on the comparison result means: When the divergence index is less than or equal to the preset divergence index threshold, it indicates that the divergence is small. In this case, the synthesis strategy adopts the arithmetic mean method. When the divergence index is greater than the preset divergence index threshold, it indicates that the divergence is large. In this case, the synthesis strategy adopts the optimal transfer matrix method.
[0013] In some embodiments, the step of calculating the comprehensive score of the candidate cavern site selection schemes using a linear weighted method and obtaining the optimal cavern site selection scheme based on the comprehensive score includes the following steps: Obtain the weights of the primary and secondary indicators of the candidate cavern site selection schemes, and calculate the global weight of the secondary indicators relative to the overall objective based on the weights of the primary and secondary indicators. Obtain standardized scores for the candidate cavern site selection schemes on the secondary indicators; Using the linear weighting method, the standardized score of the secondary indicator is multiplied by the global weight of the indicator to obtain the comprehensive score of each candidate cavern site selection scheme; The candidate cavern site selection scheme with the highest comprehensive score is selected as the optimal cavern site selection scheme.
[0014] The beneficial effects of this invention are: (1) Significantly improved scientific decision-making: A 5+25 indicator evaluation system specifically for the site selection of underground power plants was established, which solved the problem of incomplete consideration of influencing factors. This resulted in a significant improvement in the scientific nature of decision-making and high efficiency in engineering applications. The comprehensive indicator system and the weighting method that combines subjective and objective factors ensured the comprehensiveness of the decision-making basis and the rationality of the weights. (2) Improved decision accuracy and consistency: The introduction of the exponential scale greatly improves the consistency of the judgment matrix, reduces the error and efficiency loss caused by repeated adjustment of judgment values, and makes the decision results more accurate and reliable. (3) Enhanced reliability of group decision-making: The provided group decision-making disagreement handling mechanism can effectively integrate the opinions of multiple experts, especially when there are large differences of opinion, it can still draw scientific conclusions, thereby improving the credibility and acceptability of the decision results; (4) High efficiency in engineering application: The method has a clear process and strong operability, which can provide designers with clear decision support, reduce unnecessary disputes and rework, shorten the design cycle, and improve the quality and economy of the project from the source. Attached Figure Description
[0015] Figure 1 This is a flowchart of an underground cavern site selection method based on a comprehensive index system according to Embodiment 1 of the present invention; Figure 2 This is a system structure diagram of the underground cavern site selection evaluation system in Embodiment 1 of the present invention. Detailed Implementation
[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0017] Example 1
[0018] This embodiment provides a method for selecting the location of underground caverns based on a comprehensive index system. See the flowchart below. Figure 1 The method may include the following steps: S1. Establish a hierarchical evaluation model that includes five primary indicators (geological conditions, topographical conditions, hydrological conditions, investment conditions, and construction conditions) and twenty-five secondary indicators under the corresponding primary indicators. S2. The subjective weights of each indicator in the hierarchical evaluation model are determined by the AHP method based on the exponential scale, and the objective weights of each indicator in the hierarchical evaluation model are determined by the entropy weight method. S3. Weight the subjective weights and objective weights to obtain the combined weights; S4. Establish a group decision-making disagreement handling mechanism and calculate the disagreement index; S5. Calculate the comprehensive score of the candidate cavern site selection schemes using the linear weighting method, and obtain the optimal cavern site selection scheme based on the comprehensive score.
[0019] In the above steps of this embodiment, firstly, the established hierarchical evaluation model includes five primary indicators and twenty-five secondary indicators, namely geological conditions, topographical conditions, hydrological conditions, investment conditions, and construction conditions, systematically covering all key influencing factors; secondly, the AHP method based on an index scale is introduced: using 1, The exponential scales of 1.315, 1.732, 3, and 9 replace the traditional 1-9 scale for pairwise comparisons, more accurately characterizing the differences in expert judgments and fundamentally improving the consistency of the judgment matrix, keeping the consistency ratio stably controlled within 0.05. Furthermore, this embodiment integrates subjective and objective weights, using the AHP method to calculate the subjective weights of each indicator, while simultaneously using the entropy weight method to calculate the objective weights based on the original data of each scheme. Finally, the subjective and objective weights are weighted and integrated to obtain the combined weights, overcoming the limitations of a single weighting method. Next, this embodiment uses a group decision-making divergence handling mechanism to calculate the antisymmetric matrix and standard deviation of each expert's judgment. Based on the magnitude of the standard deviation (with 1 as the boundary), different strategies are used to synthesize group judgments: the optimal transfer matrix method is used when the divergence is large, and the arithmetic mean method is used when the divergence is small, ensuring the scientific nature and robustness of the group decision-making results. Finally, this embodiment performs quantitative optimization decision-making, calculating the comprehensive score of each scheme using a linear weighting method to achieve quantitative ranking and optimization of the schemes.
[0020] See Figure 2 The system structure diagram of the underground cavern site selection evaluation system is shown. For the hierarchical evaluation model in this embodiment, the optimal underground cavern site selection scheme is defined as the target layer. This indicates that the five primary indicators are used as sub-objective layers, and respectively... ~ This indicates that the twenty-five secondary indicators under all primary indicators serve as the criterion layer, each using... ~ This indicates that the various solutions under the final secondary indicators are considered as the solution layer, and the corresponding solution under each primary indicator is... Each is represented as . ~ .
[0021] Specifically, different primary indicators correspond to different secondary indicators. In this embodiment, in the hierarchical evaluation model, when the primary indicator is geological conditions... At that time, the secondary indicators include: the integrity of the surrounding rock mass. The angle between the axis and the direction of ground stress should not be too small. The rock softening coefficient should not be too large. The angle between the axis and the structural surface should not be too small. The angle between the axis and the strike of the rock strata should not be too large. The cross-sectional shape is conducive to the stability of the cavern. Does a high-pressure, high-flow-rate aquifer exist? and the degree of development of rock orientation and fractures ; When the primary indicator is terrain conditions At that time, the secondary indicators include: reasonable layout of construction adits. Thickness of the surrounding rock in the cave roof and walls The tunnel group's axis is arranged in a near-straight line. Facilitates the layout of entrance and exit buildings and terrain uncertainty index ; When the primary indicator is hydrological conditions At that time, the secondary indicators include: the geothermal gradient and the lateral pressure coefficient are reasonable. The inlet and outlet are smoothly connected to the water flow in the cave system. The inlet and outlet have sufficient submersion depth. Degree of chemical corrosion of groundwater The cave complex has enough pressure for Yufu ; When the primary indicator is an investment condition At that time, the secondary indicators included: less engineering investment Effective control of engineering risks ; When the primary indicator is construction conditions At that time, the secondary indicators include: advanced construction techniques. Reasonable construction schedule and intensity configuration Reasonable allocation of construction resources The cross-section / longitudinal section is suitable for construction. Construction teams cause less environmental pollution .
[0022] It should be noted that in this embodiment, the exponential scaling method does not directly process the final output value of the schemes (i.e., the comprehensive score of each scheme), but is applied to the front end of the method to determine the weight of each indicator in the hierarchical evaluation model. It is the scaling standard used by experts when making pairwise comparisons.
[0023] In this embodiment, determining the subjective weights of each indicator in the hierarchical evaluation model using the AHP method based on an exponential scale may include the following steps: For each primary and secondary indicator in the hierarchical evaluation model, experts make pairwise comparisons of the importance of the secondary indicators at the same level relative to the primary indicator. The comparison judgments are converted into numerical values using an exponential scale, and a judgment matrix is constructed. The exponential scales used are: 1, 1.315, 1.732, 3, and 9. Based on the judgment matrix, the subjective weights of each indicator are calculated using the AHP method.
[0024] In practical applications, the specific steps for determining the subjective weights of each indicator in the hierarchical evaluation model using the AHP method based on the exponential scale can be achieved through the following steps: Step 1: Make a judgment based on the evaluation system. Within the established hierarchical evaluation model framework, invite experts to compare the importance of each indicator at the same level relative to the indicator at the next higher level.
[0025] Step 2: Quantification using exponential scales. Experts use the exponential scales (1, 1.315, 1.732, 3, and 9) specified in this embodiment to replace the traditional 1-9 scale, transforming qualitative comparisons into quantitative values, thereby constructing a judgment matrix.
[0026] Step 3: Output the improved weight values. Using this judgment matrix built on an exponential scale, calculate the subjective weights of each indicator using the AHP method. Because the exponential scale better reflects human judgment and effectively improves matrix consistency, the weight values calculated in this way are more accurate and reliable than those calculated using traditional methods.
[0027] Step 4: Incorporating weights into subsequent calculations. These weights, optimized using the exponential scaling method (whether subjective weights or combined weights after fusion with the entropy weight method), will be used in the final comprehensive score calculation.
[0028] Therefore, the exponential scaling method applied in this embodiment indirectly but decisively affects the final output value (comprehensive score) of each scheme in the hierarchical evaluation model by outputting more scientific weights, making the ranking and optimization results of the schemes more reliable. The exponential scaling method is the core means introduced in this embodiment to solve the technical difficulty of "poor consistency of the judgment matrix". It acts on the weight determination stage, and its output (a highly consistent judgment matrix and the accurate weights obtained therefrom) is the key input for the hierarchical evaluation model to perform scientific and reliable calculations. This improvement enhances the scientificity and accuracy of the entire optimization process from the source.
[0029] Example 2
[0030] Based on Example 1, this example compares the exponential scaling method with the traditional 1-9 scaling method. The poor consistency of the judgment matrix stems from the contradiction between the linear characteristics of the traditional 1-9 scaling and the non-linear perception of humans when comparing importance. Humans perceive a much greater difference between "slightly important" and "significantly important" than between "strongly important" and "extremely important".
[0031] The traditional 1-9 scale (linear): It forces the use of linear values (1,2,3...,9) to express a non-linear psychological judgment process, which itself introduces inherent logical conflicts. This often leads to the constructed matrix violating the transitivity rule. For example, if A is 3 times more important than B, and B is 3 times more important than C, but A is 9 times more important than C instead of 10 times, this will produce inconsistency under the 1-9 scale.
[0032] In this embodiment, the exponential scaling (non-linear) has a scaling value sequence of (1, 1.315, 1.732, 3, 9), corresponding to roughly equal intervals in the perceived psychological intensity. This sequence is essentially close to a... A geometric sequence, in which .
[0033] The core mechanism for ensuring consistency in this embodiment lies in "transitability": Under the index scaling system, if experts believe that the index... Compared to indicators The degree of importance is a scaling value , and indicators Compared to indicators The importance is So, the indicators Compared to indicators The importance should theoretically be Therefore, the exponential scale value selected in this embodiment precisely satisfies this multiplication transitive relationship.
[0034] For example: Suppose that the expert makes the following logically coherent judgment: Indicators Comparison Indicators "Clearly important," according to the scale of this embodiment, is taken as... ; Indicators Comparison Indicators "Slightly important", take .
[0035] Logically, experts should therefore believe that the indicators Comparison Indicators The importance is In the scaling system of this embodiment, this result is very close to a scale value of "5" (between "significantly important" 3 and "strongly important" 9), rather than a linear superposition under traditional scaling. It cannot be explained.
[0036] Because expert judgments inherently possess a certain degree of transitivity in the subconscious, using a scaling system that conforms to the multiplication transitivity law naturally results in a judgment matrix that closely approximates the "ideal consistency matrix," thus making the calculated consistency ratio ( The value can be consistently less than the strict threshold of 0.05.
[0037] The following simulated controlled experiment illustrates the significant differences between the two scales: Experimental Design: 1000 sets of virtual expert comparison data that conform to human judgment patterns were randomly generated. Judgment matrices were constructed using both the traditional 1-9 scale and the exponential scale of this invention, and the consistency ratio of each matrix was calculated. ), and then calculate its pass rate ( ) and high standard pass rate ( ).
[0038] Table 1 Comparison between the traditional 1-9 scale method and the exponential scale method of this embodiment. The table above clearly shows that: Traditional 1-9 scale: The constructed judgment matrix is of unstable quality, with approximately 35% of the matrices failing the conventional consistency test. Furthermore, approximately 70% of the matrices fail to meet the high standard of consistency sought by this invention. This is precisely the fundamental reason why existing technologies require repeated matrix adjustments and are inefficient.
[0039] The exponential scaling of this invention: the vast majority (85%) of the judgment matrices can be directly satisfied without any adjustment. The high standards have significantly improved consistency. This allows experts to focus entirely on professional judgment without the need for subsequent tedious and subjective matrix correction processes.
[0040] Therefore, this embodiment solves the consistency problem of the judgment matrix from the source by adopting an exponential scale that is more in line with human nonlinear judgment perception. The principle is that the scaling system itself approximately satisfies the multiplication transitivity law, which is consistent with the expert's internal judgment logic. Simulation control experimental data fully demonstrates that, compared with the traditional 1-9 scale, this method can stably control the consistency ratio within 0.05, thus laying a solid foundation for achieving scientific, objective and efficient group decision optimization.
[0041] Example 3
[0042] Based on Examples 1 and 2, after the hierarchical evaluation model is established, it is necessary to calculate subjective weights, objective weights, and combined weights. Therefore, in this example, calculating the subjective weights of each indicator using the AHP method based on the judgment matrix means: The judgment matrix is normalized column by column; The normalized judgment matrix is summed row by row to obtain an approximate value of the eigenvector; The result of summing by row is then normalized again to obtain the subjective weight.
[0043] The determination of the objective weights of each indicator in the hierarchical evaluation model using the entropy weight method includes the following steps: The original scores of the candidate cavern site selection schemes on the corresponding secondary indicators under the primary indicators were obtained by expert scoring, and a scoring matrix was obtained. The original scores in the rating matrix are standardized to obtain a standardized matrix. Calculate the information entropy of each secondary indicator; The difference coefficient of the secondary indicators is calculated based on information entropy, and the objective weight of the corresponding secondary indicators is calculated based on the difference coefficient.
[0044] The process of weighting and fusing subjective and objective weights to obtain combined weights includes the following steps: Set the fusion coefficient; The fusion weight of the corresponding secondary indicators under the primary indicator is calculated based on the fusion coefficient.
[0045] It should be noted that this embodiment uses a simplified scenario to illustrate the entire weight calculation and fusion process. Assume that three underground cavern site selection schemes need to be considered ( ) to select the best option, focusing on "geological conditions ( The primary indicator "rock quality" has two secondary indicators: "rock quality ( ")" and "fault influence ( )".
[0046] Through expert scoring and on-site inspection, the original scores (out of 100) for the three schemes on two secondary indicators were obtained, with higher scores being better. The data matrix is shown in Table 2 below: Table 2 Data Matrix Given the above known data, we can first calculate the subjective weights. In this embodiment, we use an exponential scale (1, 1.315, 1.732, 3, 9) to construct the judgment matrix, and determine the weights by solving for the eigenvectors of the matrix. The specific calculation steps are as follows: (1) Constructing a judgment matrix: Assuming that experts use an exponential scale to make pairwise comparisons, they believe that for "geological conditions ( Regarding "rock quality ()", ")" is more accurate than "fault influence" ")" is slightly more important. Assignment is based on the scale. Correspondingly With diagonal elements all set to 1, we obtain the judgment matrix. : .
[0047] (2) Calculate the weights (approximation method): Step 1: Normalize the judgment matrix column by column.
[0048] Step 1: Normalize the judgment matrix column by column.
[0049] The sum of the first column is: 1 + 0.577 = 1.577; The sum of the second column is: 1.732 + 1 = 2.732; The normalized matrix is: .
[0050] Step 2: Sum the normalized matrix row by row to obtain approximate values of the eigenvectors.
[0051] Line 1: 0.634 + 0.634 = 1.268; Line 2: 0.366 + 0.366 = 0.732.
[0052] Step 3: Normalize the rows and results again to obtain the subjective weights.
[0053] Total: 1.268 + 0.732 = 2.000.
[0054] Therefore, the obtained subjective weight is : .
[0055] Therefore, the conclusion is: rock mass ( The subjective weight of ) is 0.634, and the impact of faults ( The subjective weight of ) is 0.366.
[0056] Secondly, the objective weights can be calculated. In this embodiment, the objective weights are calculated based on the entropy weight method. In this embodiment, the weights can be calculated based on the degree of dispersion of the data of each scheme under a certain indicator. The greater the degree of data dispersion, the greater the degree of differentiation of the scheme by the indicator, and the greater its weight should be.
[0057] Here, the calculation process for objective weights is as follows: (1) Data standardization (positive indicators): Since the scores are all positive indicators (the higher the better), the following formula is used for standardization to form a standardization matrix. : ,in The number of schemes.
[0058] Column: sum=85+75+95=255; ; Column: sum=90+70+80=240; ; Therefore, the standardized matrix .
[0059] (2) Calculate information entropy: in, ; entropy : entropy :
[0060] (3) Calculate the coefficient of difference and objective weight: Coefficient of difference ; ; ; Objective weight ; The sum of the coefficients of difference is: 0.014 + 0.011 = 0.025; therefore, .
[0061] Therefore, it can be concluded that: rock mass ( The objective weight of fault influence is 0.56. The objective weight of ) is 0.44.
[0062] Next, weighted fusion can be performed to calculate the combined weights. In this embodiment, subjective weights and objective weights are fused using a linear weighting method to take into account both expert experience and the information in the data itself. The specific process is as follows: (1) Setting the fusion coefficient: Assuming that subjective weights and objective weights are given equal importance, i.e., the fusion coefficient .
[0063] (2) Calculate the portfolio weights: The combined weights are: 0.5 * 0.634 + 0.5 * 0.56 = 0.317 + 0.28 = 0.597; The combined weights are: 0.5 * 0.366 + 0.5 * 0.44 = 0.183 + 0.22 = 0.403; Therefore, the final conclusion can be drawn: under "geological conditions ( Under the ")" indicator, the combined weights used for final solution selection are: Rock quality ( ): 0.597; Fault influence ( ): 0.403.
[0064] The combined weight in this embodiment includes both the subjective experience of experts that "rock quality is slightly more important than fault influence" and the objective fact that "rock quality" has slightly larger data dispersion and slightly stronger distinguishing ability among the three schemes in this batch. This weight will be used to calculate the comprehensive score of each scheme in the subsequent calculation to complete the final selection.
[0065] Example 4 Based on Examples 1, 2, and 3, after the combined weights are calculated, the divergence index can be calculated. In this example, the establishment of the group decision-making divergence handling mechanism and the calculation of the divergence index include the following steps: Obtain the judgment matrix corresponding to each expert, and transform it into an antisymmetric matrix by taking the logarithm, thus obtaining the group antisymmetric matrix; Calculate the standard deviation of the group antisymmetric matrix and use it as an indicator of divergence.
[0066] It should be noted that after calculating the divergence index, the following are also included: Obtain the preset threshold for the divergence index; The divergence index is compared with a preset divergence index threshold, and the corresponding synthesis strategy is adopted based on the comparison result.
[0067] Specifically, comparing the divergence index with a preset divergence index threshold and adopting a corresponding synthesis strategy based on the comparison result means: When the divergence index is less than or equal to the preset divergence index threshold, it indicates that the divergence is small. In this case, the synthesis strategy adopts the arithmetic mean method. When the divergence index is greater than the preset divergence index threshold, it indicates that the divergence is large. In this case, the synthesis strategy adopts the optimal transfer matrix method.
[0068] The group decision disagreement handling mechanism in this embodiment is a step-by-step, data-driven process. Its core idea is: instead of simply averaging all expert judgments, it first quantifies the degree of disagreement among the expert group's opinions, and then intelligently selects the most appropriate synthesis strategy based on the size of the disagreement, so as to ensure that the group decision result not only includes different viewpoints but also maintains internal logical consistency.
[0069] In this embodiment, it is assumed that there is Experts (e.g.) For the same level Individual indicators (e.g.) Indicators and Pairwise comparisons were performed, and each expert provided a judgment matrix using an exponential scale. ,in, 。
[0070] In this embodiment, the judgment matrix is first converted into an antisymmetric matrix. Because the judgment matrix... It is a positive reciprocal matrix (i.e.) Directly calculating its standard deviation is mathematically inconvenient. Converting it to an antisymmetric matrix, where the elements are symmetric about 0, facilitates statistical analysis. In this embodiment, the conversion rule is: for each expert... Judgment matrix Transform it into an antisymmetric matrix by taking its logarithm. ,in, .
[0071] because ,therefore .matrix satisfy And diagonal elements .
[0072] Suppose the judgment matrix given by the first expert is .
[0073] Then its antisymmetric matrix for: .
[0074] Secondly, calculate the standard deviation of the group antisymmetric matrix ( In this embodiment, the standard deviation is... It is quantification The core indicator of the degree of disagreement among experts is the same pair of indicators, and this embodiment only considers the opinions of all experts on the same pair of indicators. To determine whether there is a discrepancy, due to the antisymmetry of the matrix, only the upper triangular (or lower triangular) portion needs to be calculated. Therefore, the calculation process is as follows: For each pair of indicators ,in There is a A set consisting of expert judgments: And calculate the standard deviation of this set. : ,in Is this it? The average of the values.
[0075] final standard deviation : Get all For the calculated The average value is used as the overall degree of disagreement among the entire group regarding the indicators at this level, i.e.: .
[0076] The above calculations yielded a quantitative index of divergence. , The larger the value, the greater the difference in experts' judgments on the relative importance of the indicators.
[0077] After calculating the overall degree of divergence Then, the system will determine the threshold value based on the preset threshold. (as a boundary) Automatically select the synthesis strategy.
[0078] Strategy selection rules: Scenario 1: Minor disagreements ( ) Assessment: The experts are largely in agreement, and the differences are within an acceptable range.
[0079] Synthesis strategy: Arithmetic average method is used.
[0080] Specific operations: 1. Directly to The original judgment matrix of the experts The geometric mean is calculated for the elements at corresponding positions in the matrix (since the judgment matrix is a ratio scale, the geometric mean is more reasonable than the arithmetic mean).
[0081] 2. Calculate the group judgment matrix : .
[0082] 3. Regarding the obtained Perform a consistency check (at this point, because an exponential scale is used), (usually already very low), and calculate the group weight.
[0083] At this point, the advantages are: the calculation is simple and quick, and it can well preserve the collective consensus.
[0084] Scenario 2: Significant disagreement ( ) Judgment: There are significant disagreements among the experts. A simple averaging would mask the contradictions and could lead to very poor consistency in the synthesized matrix.
[0085] Synthesis strategy: The optimal transfer matrix method is adopted.
[0086] Specific operations: 1. Calculate the judgment matrix for each expert. The corresponding antisymmetric matrix (As mentioned above).
[0087] 2. Calculate the average matrix of all expert antisymmetric matrices. : ,in, It is also an antisymmetric matrix.
[0088] 3. Finding the optimal transfer matrix: The goal is to find an "optimal" judgment matrix. Its antisymmetric matrix With the average antisymmetric matrix The difference is minimized (usually using the Frobenius norm), this The analytical solution can be obtained by solving an optimization problem, and its solution is: In other words, the average antisymmetric matrix It is itself a completely consistent (transferable) matrix.
[0089] 4. Transform back to the judgment matrix: transform the optimal antisymmetric matrix Convert back to group judgment matrix : .
[0090] At this point, the advantage is that this method can forcibly guarantee the synthesized group judgment matrix. It has perfect consistency ( Instead of smoothing the data, it constructs a mathematically logically consistent decision-making model based on respecting the average opinion of all experts, thus effectively solving the decision-making dilemma in highly divergent situations.
[0091] Therefore, the group decision-making divergence handling mechanism in this embodiment calculates the standard deviation of the antisymmetric matrix. This objectively quantifies disagreements and intelligently switches the synthesis strategy accordingly. This ensures that, regardless of whether there is consensus or conflict, a scientific, robust, and logically rigorous group decision weight can be derived, significantly improving the credibility and reliability of site selection.
[0092] Example 5 Based on Examples 1, 2, 3, and 4, this example calculates the comprehensive score of the candidate cavern site selection schemes using a linear weighted method. Specifically, in this example, the calculation of the comprehensive score of the candidate cavern site selection schemes using a linear weighted method, and the acquisition of the optimal cavern site selection scheme based on the comprehensive score, includes the following steps: Obtain the weights of the primary and secondary indicators of the candidate cavern site selection schemes, and calculate the global weight of the secondary indicators relative to the overall objective based on the weights of the primary and secondary indicators. Obtain standardized scores for the candidate cavern site selection schemes on the secondary indicators; Using the linear weighting method, the standardized score of the secondary indicator is multiplied by the global weight of the indicator to obtain the comprehensive score of each candidate cavern site selection scheme; The candidate cavern site selection scheme with the highest comprehensive score is selected as the optimal cavern site selection scheme.
[0093] In this embodiment, it is assumed that three underground cavern site selection schemes are required ( The optimal solution is selected from the options. The following work has been accomplished using the method in this embodiment: a complete evaluation index system has been established (for simplicity, this example only uses 3 primary indicators); the combined weights of all indicators have been obtained by integrating subjective and objective weights; and standardized scores of the three solutions on all the lowest-level (secondary) indicators have been obtained through expert scoring and data processing.
[0094] In this embodiment, the known data is shown in Table 3: Table 3 Known Data Here, both the primary and secondary indicator weights are combined weights obtained by fusing AHP and entropy weighting methods. The "global weight" is the final weight of the secondary indicator relative to the overall goal, obtained by multiplying its respective primary and secondary weights.
[0095] Based on the known data above, the standardized scores of each scheme on the secondary indicators can be calculated. All scores have been normalized, with values ranging from 0 to 1, and higher scores being better. Cost-related indicators such as "project cost" have been positively normalized, as shown in Table 4. Table 4 Forward Processing Therefore, this embodiment can perform the process of calculating the comprehensive score using the linear weighting method. In this embodiment, the calculation rule is: the comprehensive score of each scheme. Based on its standardized scores on different indicators With the global weight of this indicator The sum of the products is calculated here. ,in: For the first The overall score of each option For the first The global combined weight of each indicator, For the first The first scheme is in the Standardized scores on each indicator The total number of the lowest-level (secondary) indicators (in this embodiment) ).
[0096] Therefore, the calculation process for calculating the comprehensive score using the linear weighting method is as follows: 1. Calculation scheme Overall score:
[0097] 2. Calculation Scheme Overall score:
[0098] 3. Calculation Scheme Overall score:
[0099] Then, the calculation results are summarized as shown in Table 5, and the optimal solution is selected based on the calculation results: Table 5 As shown in Table 5, the comprehensive score calculated using the linear weighting method indicates that the scheme... The optimal solution is the one with the highest score of 0.8145. and They had the same score and were tied for second place.
[0100] Therefore, the decision recommendation in this embodiment is: Preferred solution: This scheme has a clear advantage in geological conditions (especially rock quality) and a relatively reasonable investment cost. Although it has slight shortcomings in construction conditions, it is the best choice overall. Further analysis: Due to and If scores are the same, decision-makers can further examine their performance on different primary indicators. For example, It may be superior in terms of geological and hydrological conditions, and It may be better in terms of construction and investment conditions. Depending on the specific focus of the project, a final choice can be made between the two, or they can be listed as alternatives.
[0101] This embodiment clearly demonstrates how to use a linear weighting method to combine the global weights of each indicator with the standardized scores of the schemes, ultimately calculating the comprehensive score for each scheme. This process is quantifiable and transparent, providing a clear and objective decision-making basis for the optimal selection of underground cavern site selection schemes, fully demonstrating the scientific nature and practicality of the method in this embodiment.
[0102] Example 6 Based on Examples 1, 2, 3, 4 and 5, this example introduces a comparative example to simulate the decision-making process of traditional methods.
[0103] Scene setup and basic data (same as Example 5) Objective: From , , The preferred option is the one chosen from the three options.
[0104] Indicator System and Weights: This embodiment assumes two different sets of weights were obtained using traditional methods (such as purely subjective expert weighting) and the method described in this embodiment. The standardized scores for each scheme on the secondary indicators remain unchanged. 1. Using the traditional method (highly subjective, with unbalanced weights): Assuming weights: In the traditional method, a senior structural engineer, based on personal experience, believes that geological conditions are absolutely important, while investment and construction conditions can be appropriately sacrificed. Therefore, he assigns weights that are extremely biased towards geological conditions, as shown in Table 6: Table 6. Weights heavily biased towards geological conditions The calculation process (linear weighting, but with unreasonable weights) is as follows: The results of the traditional method are shown in Table 7: Table 7 Results of Traditional Methods Therefore, the traditional method of decision-making is: selection This method is entirely driven by the expert's personal preferences, ignoring... The plan is based on the construction conditions ( , The obvious shortcomings in geology may not have been adequately considered in terms of investment costs. Such a "geology-only" decision-making approach could lead to significantly increased construction difficulty, project delays, and budget overruns in reality.
[0105] 2. The method adopted in this embodiment (combining subjective and objective factors, with balanced weights): The weights determined in this embodiment (combining subjective and objective factors, with scientific balance) are shown in Table 8: Table 8. Weights determined by the method in this embodiment. The calculation process (linear weighting, weight science) is as follows:
[0106] The results of this embodiment are shown in Table 9: Table 9 Results of the Method in this Embodiment Therefore, the method decision in this embodiment is: to select the same method. However, the robustness and scientific validity of the conclusions are quite different.
[0107] The advantages of this embodiment are clearly highlighted by the above comparison, as shown in Table 10: Table 10 Advantages Therefore, this embodiment uses objective data (entropy weight method) to counteract subjective biases and employs a scientific weighting system to ensure a balanced consideration of all influencing factors. Ultimately, the comprehensive score calculated based on linear weighting can accurately, comprehensively, and robustly reflect the overall merits of the proposed solution, thereby significantly improving the scientific rigor and engineering reliability of underground cavern site selection decisions. In contrast, traditional nonlinear methods that rely on one-sided experience or have inherent consistency flaws are highly prone to biased or even dangerous decisions.
[0108] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for site selection of underground caverns based on an integrated index system, characterized in that, The method comprises the following steps: An evaluation model is established, which comprises five first-level indexes including geological conditions, topographical conditions, hydrological conditions, investment conditions and construction conditions, and twenty-five second-level indexes corresponding to the first-level indexes; Subjective weights of each index in the evaluation model are determined by an AHP method based on an index scale, and objective weights of each index in the evaluation model are determined by an entropy weight method; The subjective weights and the objective weights are fused by weighting to obtain combined weights; A group decision-making divergence processing mechanism is established, and a divergence index is calculated; A comprehensive score of a selected cavern site selection scheme is calculated by a linear weighting method, and an optimal cavern site selection scheme is obtained according to the comprehensive score.
2. The underground cavern site selection method based on a comprehensive index system according to claim 1, characterized in that, In the evaluation model, when the first-level index is geological conditions, the second-level indexes include: integrity of surrounding rock mass, angle between axis and ground stress direction not too small, rock softening coefficient not too large, angle between axis and structure surface direction not too small, angle between axis and rock stratum direction not too large, cross section shape beneficial to cavern stability, existence of high pressure and large flow aquifer and rock occurrence and fracture development degree; When the first-level index is topographical conditions, the second-level indexes include: rational arrangement of construction branch holes, thickness of surrounding rock of cavern roof and wall, straight line arrangement of cavern group axis, convenient arrangement of entrance and exit buildings and topographical uncertainty index; When the first-level index is hydrological conditions, the second-level indexes include: rationality of ground temperature gradient and lateral pressure coefficient, smooth connection of water inlet and outlet with water flow of cavern group, sufficient submergence depth of water inlet and outlet, chemical corrosion degree of underground water and sufficient pressure margin of cavern group; When the first-level index is investment conditions, the second-level indexes include: less engineering investment and effective control of engineering risk; When the first-level index is construction conditions, the second-level indexes include: advanced construction technology, rational configuration of construction progress and intensity, rational configuration of construction resources, administrative suitability of horizontal / vertical section to construction and small environmental pollution of construction team.
3. The underground cavern site selection method based on a comprehensive index system according to claim 1, characterized in that, The subjective weights of each index in the evaluation model are determined by the AHP method based on the index scale, and the method comprises the following steps: For each first-level index and second-level index in the evaluation model, two-by-two comparison and judgment are made by experts on the second-level indexes under the same level with respect to the importance of the second-level indexes relative to the first-level index; An index scale is used to convert the comparison and judgment into numerical values, and a judgment matrix is constructed, wherein the index scale used is: 1, 1.315, 1.732, 3 and 9; Based on the judgment matrix, the subjective weights of each index are calculated by the AHP method.
4. The underground cavern site selection method based on a comprehensive index system according to claim 3, characterized in that, The subjective weights of each index are calculated by the AHP method based on the judgment matrix, and the method comprises the following steps: The judgment matrix is normalized by column; The normalized judgment matrix is summed by row to obtain an approximate value of a characteristic vector; The summing result is normalized again to obtain the subjective weights.
5. The underground cavern site selection method based on a comprehensive index system according to claim 1, characterized in that, The objective weights of each index in the evaluation model are determined by the entropy weight method, and the method comprises the following steps: Original scores of the selected cavern site selection scheme on the second-level indexes under the first-level indexes are obtained by expert scoring to obtain a scoring matrix; The original scores in the scoring matrix are standardized to obtain a standardized matrix; Information entropy of each second-level index is calculated; The difference coefficient of the secondary indexes is calculated based on information entropy, and the objective weight of the corresponding secondary index is calculated according to the difference coefficient.
6. The underground cavern site selection method based on a comprehensive index system according to claim 1, characterized in that, The subjective weight and the objective weight are weighted and fused to obtain a combination weight, including the following steps: A fusion coefficient is set. The fusion weight of the corresponding secondary index under the primary index is calculated based on the fusion coefficient.
7. The underground cavern site selection method based on a comprehensive index system according to claim 1, characterized in that, The group decision-making divergence processing mechanism is established, and a divergence index is calculated, including the following steps: A judgment matrix corresponding to each expert is obtained, and the judgment matrix is converted into an anti-symmetric matrix by taking logarithm to obtain a group anti-symmetric matrix. The standard deviation of the group anti-symmetric matrix is calculated and taken as the divergence index.
8. The underground cavern site selection method based on a comprehensive index system according to claim 7, characterized in that, After the divergence index is calculated, the following steps are further included: A preset threshold of the divergence index is obtained. The divergence index is compared with the preset threshold of the divergence index, and a corresponding synthesis strategy is adopted according to the comparison result.
9. The underground cavern site selection method based on a comprehensive index system according to claim 8, characterized in that, The divergence index is compared with the preset threshold of the divergence index, and a corresponding synthesis strategy is adopted according to the comparison result, which means that: When the divergence index is less than or equal to the preset threshold of the divergence index, it indicates that the divergence is small, and at this time, the synthesis strategy adopts the arithmetic mean method; when the divergence index is greater than the preset threshold of the divergence index, it indicates that the divergence is large, and at this time, the synthesis strategy adopts the optimal transfer matrix method.
10. The underground cavern site selection method based on the comprehensive index system according to any one of claims 1-9, characterized in that, The comprehensive score of the selected cave site scheme is calculated by the linear weighting method, and the optimal cave site scheme is obtained according to the comprehensive score, including the following steps: The primary index weight and the secondary index weight of the selected cave site scheme are obtained, and the global weight of the secondary index relative to the total target is calculated according to the primary index weight and the secondary index weight. The standardized score of the selected cave site scheme on the secondary index is obtained. The standardized score on the secondary index is multiplied with the global weight of the index by using the linear weighting method to obtain the comprehensive score of each selected cave site scheme. The selected cave site scheme with the highest comprehensive score is taken as the optimal cave site scheme.