Subway station deep foundation pit construction risk assessment method based on bilateral probability language

Abstract

The invention relates to the technical field of construction risk management of constructional engineering, in particular to a subway station deep foundation pit construction risk assessment method based on bilateral probability language, which comprises the following steps: step 1, constructing an evaluation set in a bilateral probability language term set form; 2, performing objective standardization processing on evaluation information; 3, determining a combination weight of subjective and objective combination; step 4, hierarchical information aggregation based on a weighted average operator; and step 5, risk quantification and grade determination. According to the method, a bilateral probability language term set (DPLTS) is introduced to completely describe expert group opinion distribution, and an LCM objective standardization method and a fuzzy entropy-cross entropy-BWM combined weighting model are combined to construct a risk assessment system which is complete in information, scientific in weight and robust in decision making; the defects of the prior art in the aspects of expressing complex uncertainty and fusing subjective and objective information are effectively overcome, and the reliability, the distinction degree and the practical value of a risk assessment result are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of construction risk management technology, and in particular to a risk assessment method for deep foundation pit construction of subway stations based on bilateral probabilistic language. Background Technology

[0002] Currently, risk assessment methods for deep foundation pit construction in subway stations have evolved from qualitative to quantitative approaches. Early methods commonly employed expert surveys (Delphi method) and checklists. While simple and intuitive, these methods relied excessively on expert experience, were highly subjective, lacked quantitative evidence, and resulted in inconsistent assessment results.

[0003] To improve the objectivity of assessments, the Analytic Hierarchy Process (AHP) and its fuzzy version, the Fuzzy Analytic Hierarchy Process (FAHP), are widely used. These methods construct judgment matrices to compare and rank risk factors pairwise, thus addressing the fuzziness of judgments to some extent. However, the essence of AHP / FAHP still relies on single, definitive evaluation values ​​(such as precise scores) given by experts to construct the judgment matrix. This approach ignores potential disagreements and cognitive uncertainties within the expert group, failing to express genuine group hesitation such as "some experts believe the risk is high, while others believe it is moderate," thus losing valuable decision-making information and raising questions about the stability and reliability of the assessment results.

[0004] To further address uncertainty, fuzzy comprehensive evaluation and matter-element extension methods based on fuzzy mathematics theory have been introduced. These methods transform qualitative descriptions into quantitative calculations through membership functions, improving the granularity of the evaluation. Grey system theory has demonstrated its applicability to the problem of "small sample size and limited information," for example, by combining it with the CRITIC objective weighting method to reduce subjective arbitrariness. Nevertheless, the information input source for these methods is still mostly individual expert ratings (whether exact or interval scores), and their fundamental flaw—the inability to characterize the probability distribution of expert opinions—remains unresolved.

[0005] To address the aforementioned issues, this application proposes a risk assessment method for deep foundation pit construction in subway stations based on bilateral probabilistic language. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by proposing a risk assessment method for deep foundation pit construction in subway stations based on bilateral probabilistic language. This method introduces a bilateral probabilistic language term set (DPLTS) to fully characterize the distribution of expert opinions and combines the LCM objective standardization method with a fuzzy entropy-cross entropy-BWM combined weighting model to construct a risk assessment system that is information-complete, scientifically weighted, and robust to decision-making. This effectively compensates for the deficiencies of existing technologies in expressing complex uncertainties and integrating subjective and objective information, and significantly improves the reliability, discriminative power, and practical value of risk assessment results.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A risk assessment method for deep foundation pit construction in subway stations based on bilateral probabilistic language includes the following steps:

[0009] Step 1: Construct an evaluation set in the form of a bilateral probabilistic linguistic terminology set: Systematically convert the individual scores of experts for secondary indicators into a bilateral probabilistic linguistic terminology set; specifically, this includes: determining the linguistic terminology set and its numerical mapping relationship; statistically analyzing the frequency of each linguistic term in the expert scores as a probability to generate a membership set M(a) representing the opinion of "supporting high risk"; based on the complementarity principle, deriving and generating a non-membership set N(b) representing the opinion of "supporting low risk"; and finally constructing a complete bilateral probabilistic linguistic element for each secondary indicator.

[0010] Step 2: Objective standardization of evaluation information: To address the issue of inconsistent lengths between membership and non-membership sets in different DPLTSs, a standardization method based on the least common multiple is adopted. The least common multiple of the lengths of the DPLTS sets to be compared is calculated, and all DPLTSs are extended to a uniform length by repeating elements and distributing their probabilities equally. This method strictly preserves the expected value and variance of the original information, providing an objective and consistent mathematical basis for subsequent calculations.

[0011] Step 3: Determine the combined weights of subjective and objective information: Establish a weight determination model that integrates subjective and objective information. For objective weights, fuzzy entropy and cross-entropy are used comprehensively: fuzzy entropy measures the fuzziness of the evaluation information itself; the smaller the entropy value, the greater the weight. Cross-entropy measures the difference between the evaluation information and the ideal state; the greater the difference, the greater the weight. For subjective weights, the best-worst method is used to determine the weights of the primary indicators, reducing the number of judgments and improving consistency through structured comparison. Finally, the subjective and objective weights are integrated through a balance coefficient to form a combined weight.

[0012] Step 4: Layered information aggregation based on weighted average operator: Layered information fusion is performed using a bilateral probabilistic language weighted average operator. First, the objective combination weights of the secondary indicators are used to aggregate their standardized evaluation values ​​to the corresponding primary indicators to obtain the comprehensive evaluation value of the primary indicators. Then, the subjective weights of the primary indicators are used to further aggregate the comprehensive evaluation values ​​of all primary indicators, and finally, bilateral probabilistic language elements representing the overall risk level of the project are obtained.

[0013] Step 5: Risk Quantification and Level Determination: Calculate the expected value and variance of the overall risk assessment value. Based on the magnitude of the expected value, compare it with the preset risk level classification standard to determine the final risk level of the project. The variance is used to measure the degree of disagreement among the expert group's evaluation. The smaller the variance, the higher the consensus and the more reliable the assessment results.

[0014] Preferably, step 1 includes the following method:

[0015] Step 1.1: To facilitate calculation, the linguistic terms need to be converted into numerical values. Using the linear symmetric mapping method, a five-granularity linguistic term set T = {t1, t2, t3, t4, t5} is defined.

[0016] In DPLTS, when the same linguistic term t3 (value 0.50) appears in both the membership set and the non-membership set, its semantics are determined by the context:

[0017] In the membership set M(a), t3(0.50) indicates "moderate support for its high risk";

[0018] In the non-membership set N(b), t3(0.50) indicates "moderate support for its low risk"; Step 1.2: Generate membership PLTS M(a)

[0019] For any specific secondary indicator c i(k) Let there be y experts participating in the evaluation, and their score set be X = {x1, x2, ..., x...} y}, where x q ∈[1,5],q∈[1,y] represents the single-value score of the q-th expert;

[0020] (1) Terminology mapping: Map each expert's score x q Round to the nearest integer and map to the corresponding language term t. k ∈T, the mapping rule is:

[0021] k = round(x q (1.1)

[0022] Where, round(·) is the rounding function, and k is the language term index, which is obtained by rounding the expert scores and has a value of 1-5;

[0023] (2) Probability calculation: Statistical analysis of each term t k The number of times n appears in m expert evaluations k Calculate its frequency of occurrence as the probability:

[0024]

[0025] And satisfy a (k) Let n be the probability of the k-th language term, m be the total number of expert evaluations for a certain indicator, and n be the probability of the k-th language term. k For each term t k The number of times it appears in m expert evaluations.

[0026] (3) Constructing the membership set: Term(s) with a probability of zero are removed, forming the membership set (PLTS) of the indicator:

[0027] M(a)={t k (a k )|(a k )>0}

[0028] M(a) represents the distribution of the expert group’s collective opinion that “the indicator is of high risk”;

[0029] Step 1.3: Generate non-membership PLTS N(b)

[0030] The non-membership degree represents the distribution of the expert group's collective opinion that "the indicator has low risk." Based on the complementary nature of "high risk" and "low risk" in risk assessment, the non-membership degree set is derived through the following transformation rule:

[0031] Through numerical mapping, the strength of an evaluation supporting "low risk" should be 1 minus the strength of that evaluation supporting "high risk". However, this results in a new value, which needs to be mapped back to the most recent language term. Then, based on the term mapping and probability calculation in step 1.2 above, the non-membership set is obtained:

[0032] N(b)={t k (b k )|(b k )>0}

[0033] N(b) represents the distribution of the expert group’s collective opinion that “the risk of this indicator is low”;

[0034] Step 1.4: Construct Bilateral Probabilistic Language Elements (DPLE)

[0035] Combining the generated membership set with the non-membership set yields the complete DPLE representing the group evaluation of this secondary indicator:

[0036] P i(k) =<M(a),N(b)>

[0037] This P i(k) This will serve as the basis for all subsequent calculations.

[0038] Preferably, step 2 includes the following method:

[0039] Suppose there exist two bilateral probabilistic linguistic elements P1 to be compared or aggregated.<M1(a),N1(b)> and P2 =<M2(a),N2(b)> ,in:

[0040]

[0041] M1(a) represents the membership set of the bilateral probability linguistic element P1, characterizing the distribution of the expert group's collective opinion that "the corresponding risk factor is high risk"; M(i)1 represents the i-th linguistic term in M1(a), belonging to the predefined linguistic term set T; a(i)1 represents the probability corresponding to the linguistic term M(i)1, reflecting the proportion of this term in the expert group's evaluation, satisfying a(i)1≥0; i is the membership set M 1 (a) Index of the linguistic terms (starting from 1); #M1(a) represents the number of non-zero probability linguistic terms in the membership set M1(a); This means that the sum of the probabilities of all language terms in M1(a) does not exceed 1 (hesitation information is allowed, and the part without assigned probability reflects hesitation).

[0042] N1(b) represents the set of non-membership degrees of the bilateral probability linguistic element P1, characterizing the distribution of the expert group's collective opinion that "the corresponding risk factor is low risk"; the j-th linguistic term in N1(b) belongs to the predefined linguistic term set T; b(j)1 represents the probability corresponding to the linguistic term b(j)1, reflecting the proportion of this term in the expert group's evaluation, satisfying b(j)1≥0; j is the set of non-membership degrees of N. 1 (b) Index of the linguistic terms (starting from 1); #N1(b) represents the number of non-zero probability linguistic terms in the non-membership set N1(b); This means that the sum of the probabilities of all language terms in N1(b) does not exceed 1 (hesitation information is allowed, and the part without assigned probability reflects hesitation).

[0043] M2(a) and N2(b) are the second bilateral probabilistic linguistic elements, with each parameter defined similarly to M1(a) and N1(b).

[0044] Step 2.1: Calculate the length of the least common multiple.

[0045] First, calculate the least common multiple of the lengths of the membership set and the non-membership set respectively:

[0046] m h =lcm(#M1(a), #M2(b)) (1.3)

[0047] m g =lcm(#N1(a), #N2(b)) (1.4)

[0048] Where, m h m is the least common multiple of the lengths of the two membership sets. g The least common multiple of the length of the non-membership set is denoted by lcm(e,f), which represents the least common multiple of integers e and f, where e and f represent the numerical lengths of the membership set or non-membership set in two bilateral probabilistic linguistic elements to be compared or aggregated.

[0049] Step 2.2: Construct the extended DPLTS

[0050] By repeating the elements in the original set and distributing their probabilities equally, each DPLTS is expanded to a uniform length. For the membership set M1(a) of M1, its expanded set... Defined as:

[0051]

[0052] The element and its adjusted probability are:

[0053]

[0054] Here, κ is the element index of the expanded membership set, and the correspondence between the superscript i and κ is as follows:

[0055] i = ((κ-1)mod#M1(a))+1, which means that each element in the original set M1(a) will be repeated m times. h / #M1(a) times, and its original probability Distributed equally among all these repeating elements, becoming

[0056] Similarly, the non-membership set N1(b) of P1 is extended as follows:

[0057]

[0058] γ is the element index of the expanded non-membership set, and the original probability of the non-membership set. After expansion, it becomes Perform the exact same operation on step 2 to obtain the expanded version.

[0059] Preferably, step 3 includes the following method:

[0060] Step 3.1: Determining Objective Weights

[0061] When constructing an objective weight determination model, it is necessary to accurately measure the degree of uncertainty and discriminative ability of the information carried by the DPLTS. Fuzzy entropy is used to measure the fuzziness or uncertainty of a single DPLTS itself, while cross entropy is used to measure the degree of difference between two DPLTSs.

[0062] Distance measure is the basis for calculating distance-based cross entropy. After standardizing DPLTS using the LCM extension method, the distance between them can be precisely defined.

[0063] Definition (Two-sided probabilistic linguistic distance measure): Let... and For two DPLTS extended by the LCM method, their generalized normalized distance is defined as:

[0064]

[0065] Where λ is the distance metric parameter, λ>0, when λ=1, it is the normalized Hamming distance; when λ=2, it is the normalized Euclidean distance, and φ(·) is the linear symmetric mapping function;

[0066] Step 3.11: For any secondary indicator c i(k) The fuzzy entropy of all DPLTS scores given by experts was calculated using a formula based on Shannon entropy:

[0067]

[0068] Where, μ (i) =φ(M (i) (Numerical mapping of membership degree set terminology), v (j) =φ(N (j) (Numerical mapping of non-membership degree set terminology);

[0069] Step 3.12: Calculate the index c. i(k) The total entropy value below:

[0070]

[0071] r ij(k) This refers to the actual DPLTS evaluation information for the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator.

[0072] Step 3.13: Calculate the weights based on fuzzy entropy. The smaller the entropy value, the clearer the information, and the larger the weight.

[0073]

[0074] #c i(k) Let be the number of all secondary indicators corresponding to the i-th primary indicator.

[0075] Step 3.14: Define an ideal reference r for this indicator. i0(k) (The ideal reference DPLTS evaluation information for the kth secondary indicator under the ith primary indicator), whose DPLTS can be set as <{t1(1)}, {t5(1)}>. For different secondary indicators, the distance is extended to the same length using the LCM method (using Hamming distance, λ=1).

[0076] Step 3.15: Calculate r for each evaluation unit. ij(k) (The actual DPLTS evaluation information of the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator) and the ideal reference r i0(k) Cross-entropy:

[0077]

[0078] Where φ(·) is a linear symmetric mapping function that converts linguistic terms into numerical values.

[0079] These represent the membership set and non-membership set (containing language terms and their corresponding probabilities) of the expanded DPLTS, respectively. p > 0 is an adjustment parameter, typically set to the cardinality of the language term set minus one, ensuring sufficient discriminative power of the evaluation information on the computational scale. T = (1+p)ln(1+p) - (2+p)(ln(2+p) - ln2) is a normalization factor, ensuring... And when At that time, XE = 0;

[0080] Step 3.16: Calculate the index c. i(k) The total cross-entropy value below:

[0081]

[0082] Step 3.17: Calculate the weights based on cross-entropy. The larger the cross-entropy, the stronger the discriminative power of the indicator, and the larger the weight should be.

[0083]

[0084] Step 3.18: Combine the two using a balance coefficient β∈[0,1] to obtain the comprehensive objective weight of the secondary indicator:

[0085]

[0086] Step 3.2: Determining Subjective Weights

[0087] The best-worst method greatly reduces the number of comparisons and significantly improves the consistency of judgments through a structured comparison process. Therefore, it is particularly suitable for dealing with problems such as deep foundation pit risk assessment, which have a large number of criteria and require efficient and reliable acquisition of expert subjective weights.

[0088] Suppose there are n primary indicators whose weights need to be determined, denoted as C = {c1, c2, ..., cn}. n};

[0089] Step 3.21: Determine the most important and least important indicators.

[0090] From the set of indicators C, determine the most important one (denoted as c). B The indicators and a least important one (denoted as c) W The indicators;

[0091] Step 3.22: Construct the optimal comparison vector and the worst comparison vector.

[0092] Using the 1-9 scale, experts first conduct a preliminary evaluation of all primary indicators and calculate the average expert score for each primary indicator. Based on the average score, the indicator with the highest average score is selected as the most important indicator (c). B The lowest average value is considered the least important indicator, c. W The scale means: 1 = equally important, 3 = slightly important, 5 = significantly important, 7 = strongly important, 9 = absolutely important, and 2 / 4 / 6 / 8 are intermediate values. Two groups of comparisons are conducted separately:

[0093] Optimal comparison vector: The most important indicator c B By comparing with all other metrics, a vector is obtained:

[0094] V B =(υ B1 ,υ B2 ,…,υ Bn )

[0095] Among them, υ Bi Indicates the most important indicator c B Relative to index c i The importance of V is obvious. BB =1;

[0096] Worst Comparison Vector: Compares all other metrics with the least important metric c. W By comparing, we obtain the vector:

[0097] V W =(υ1W υ 2W , …, υ nW )

[0098] Among them, v iW Indicator c i Compared to the least important indicator c W The importance of V. Clearly, V WW =1;

[0099] Step 3.23: Construct the optimization model and solve for the weights.

[0100] BWM finds an optimal set of weights θ = (θ1, θ2, ..., θ3) by constructing an optimization model. n This allows the weights to satisfy the preference relationship reflected by both the best and worst comparisons to the greatest extent possible.

[0101]

[0102] min max{...} is the objective function, which means "minimize the maximum deviation", that is, to minimize the deviation between the weight and the importance of the expert judgment (to ensure consistency). The deviation between the weighting ratio and expert judgment (θ) B / θ i It should be as close as possible to υ Bi (The smaller the deviation, the better the consistency). The deviation (θ) between another set of weighting ratios and expert judgment i / θ W (It should be as close as possible). `st` contains two constraints: the sum of the weights of all first-level indicators is 1 (weight normalization), and the weights are non-negative (weights cannot be negative).

[0103] Model (M-1) is transformed into the following linear programming model (M-2) for solution:

[0104] minξ

[0105]

[0106] Solving model (M-2) yields the optimal subjective weight vector for the primary indicators.

[0107] And the consistency index ξ. ξ is the consistency deviation variable (the variable to be solved), which represents the upper limit of all deviations. The goal is to minimize ξ (the closer it is to 0, the better the consistency of expert judgment).

[0108] Preferably, step 4 includes the following method:

[0109] After determining the weights of indicators at all levels and standardizing the evaluation information, the evaluations of the underlying indicators are integrated into an overall risk value, and risk ranking is performed accordingly. Based on the bilateral probability language weighted average (DPLWA) operator, a hierarchical information aggregation model is constructed, and the expected value-variance criterion is introduced for the final ranking.

[0110] Step 4.1: Aggregate the evaluation values ​​of secondary indicators to primary indicators.

[0111] For the i-th primary index c i Its comprehensive evaluation value P i By aggregating all its secondary indicators c i(k) Standardized evaluation value and its objective weight θ i(k) The calculation was performed using the bilateral probabilistic language weighted average operator (DPLWA):

[0112]

[0113] in, ⊙ and ⊙ represent DPLTS addition and scalar multiplication operations, respectively. This step integrates the evaluations of multiple specific risk factors belonging to the same dimension into a holistic evaluation P for that dimension. i ;

[0114] Step 4.2: Aggregate the evaluation values ​​of primary indicators into the overall risk.

[0115] Overall construction risk assessment value P of the project 总 By aggregating the comprehensive evaluation value P of all n primary indicators i and its subjective weight θ i The calculation also uses the DPLWA operator:

[0116]

[0117] At this point, the evaluation information of all underlying indicators has been aggregated into a final two-sided probabilistic language element P, representing the overall risk level of the project. 总 .

[0118] Preferably, step 5 includes the following method:

[0119] Step 5.1, Overall Risk Expectation e(P) 总 The calculation is based on its DPLTS form, calculating the weighted average of the membership and non-membership parts separately:

[0120]

[0121] in:

[0122]

[0123] is the weighted mean of the membership set M(a), reflecting the overall strength of "supporting high risk".

[0124] is the weighted mean of the non-membership set N(b), reflecting the overall strength of "supporting low risk".

[0125] After expansion, for the membership set, the numerator becomes:

[0126]

[0127] The denominator becomes:

[0128]

[0129] Step 5.2: The overall risk variance is used to measure the degree of disagreement in expert evaluations. The calculation formula is as follows:

[0130]

[0131] Step 5.3: Based on the calculated overall risk expectation value e(P) 总 The final risk level of the project is determined by comparing it with the preset risk level classification standards;

[0132] Step 5.4: When comparing the risk levels of multiple projects or options, the primary criterion is based on the expected value e(P). 总 Sort the data in descending order; the higher the expected value, the greater the risk. If the expected values ​​are the same or very close, use the variance σ. 2 (P) is used as a supplementary criterion, with objects having smaller variance being ranked first because they have less uncertainty.

[0133] Compared with the prior art, the present invention has the following beneficial effects:

[0134] 1. This invention uses a bilateral probabilistic language terminology set (DPLTS) to characterize the probability distribution information of expert group opinions, avoiding information loss from the source of information compared to traditional single-value scoring methods. Case analysis of deep foundation pits in subway stations shows that the DPLTS-based evaluation model can accurately identify key risk indicators such as "unreasonable excavation speed" and "inappropriate design parameters," with a significantly higher expected risk value of 0.5 than other indicators. Compared to traditional methods, it demonstrates higher sensitivity and discriminative power in identifying high-risk factors.

[0135] 2. This invention integrates fuzzy entropy and cross-entropy into an objective weighting model, effectively overcoming the shortcomings of traditional methods (such as AHP) which have uniform weight distribution and difficulty in distinguishing key indicators. Through comparison, this method significantly assigns higher weights to key secondary indicators such as "over-excavation" and "under-excavation" and "inappropriate design parameters" than AHP and CRITIC methods, improving the distinguishability of the weight distribution by approximately 30%, ensuring that risk management resources are accurately allocated to the most critical areas.

[0136] 3. The LCM standardization method used in this invention strictly maintains the mathematical characteristics of the original information. Combined with DPLTS's complete expression of hesitant information, the model naturally accommodates expert opinions of differing nature. Sensitivity analysis shows that, using different combinations of fuzzy entropy measures and cross-entropy, the fluctuation range of the overall risk expectation is less than ±0.011, and the risk level determination results remain consistent (all are Level III, moderate risk), proving that the model has excellent stability in the face of information fuzziness.

[0137] 4. This invention introduces variance as a quantitative indicator of expert consensus in deep foundation pit risk assessment. In this case, the overall risk variance is 0.0527, only 20.8% of the theoretical maximum variance of disagreement, indicating a high degree of consensus among the expert group and reliable assessment results. Simultaneously, this method can accurately locate high-variance risk points (such as "unreasonable excavation speed," with a variance of 0.089), providing clear guidance for decision-makers to focus on uncertainties and conduct targeted reassessments.

[0138] 5. This invention ultimately outputs an intuitive risk level and a clear ranking. The assessment result in this case is Level III, moderate risk, with "excavation of the foundation pit" being the most critical risk dimension. This conclusion is highly consistent with the actual engineering situation, providing a direct and reliable decision-making basis for formulating precise risk prevention and control measures. It avoids the misjudgments that may be caused by the simplification of information in traditional methods, and has high engineering application value. Attached Figure Description

[0139] Figure 1 This is a stratigraphic profile of an engineering example of the present invention;

[0140] Figure 2 This is the evaluation index system for engineering cases of this invention;

[0141] Figure 3 A comparison chart of the weights of secondary and primary indicators for three risk assessment methods;

[0142] Figure 4 This is a comparison chart of the expected values ​​of the secondary and primary indicators for three risk assessment methods. Detailed Implementation

[0143] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0144] Example:

[0145] This invention addresses the challenges of numerous uncertainties and difficulty in quantifying risks during the risk assessment of deep foundation pits in subway stations. It involves systematic engineering data collection and on-site investigation. Key tasks include: collecting the station's design drawings, construction organization design, engineering geological survey report, and surrounding environmental investigation report; comprehensively analyzing the distribution and water-bearing capacity of perched water, Quaternary pore water, and clastic rock fissure water within the site; monitoring and recording in real-time the displacement of the foundation pit support structure, surface settlement, and groundwater level changes through on-site monitoring and manual inspection; and establishing a two-tiered indicator system based on the "Code for Risk Management of Underground Engineering Construction in Urban Rail Transit" (GB50652-2011) and related literature, combined with expert opinions. This system encompasses 8 primary indicators and 25 secondary indicators, covering the key factors affecting the safety of deep foundation pit construction.

[0146] Through the above systematic work, complete basic data for the risk assessment of deep foundation pit construction in subway stations were obtained. Senior experts were invited to independently score each risk indicator according to clear scoring criteria, forming the original dataset of expert scores for model validation.

[0147] A risk assessment method for deep foundation pit construction in subway stations based on bilateral probabilistic language includes the following steps:

[0148] Step 1: Construct an evaluation set in the form of a bilateral probabilistic linguistic terminology set: Systematically convert the individual scores of experts for secondary indicators into a bilateral probabilistic linguistic terminology set; specifically, this includes: determining the linguistic terminology set and its numerical mapping relationship; statistically analyzing the frequency of each linguistic term in the expert scores as a probability to generate a membership set M(a) representing the opinion of "supporting high risk"; based on the complementarity principle, deriving and generating a non-membership set N(b) representing the opinion of "supporting low risk"; and finally constructing a complete bilateral probabilistic linguistic element for each secondary indicator.

[0149] Step 2: Objective standardization of evaluation information: To address the issue of inconsistent lengths between membership and non-membership sets in different DPLTSs, a standardization method based on the least common multiple is adopted. The least common multiple of the lengths of the DPLTS sets to be compared is calculated, and all DPLTSs are extended to a uniform length by repeating elements and distributing their probabilities equally. This method strictly preserves the expected value and variance of the original information, providing an objective and consistent mathematical basis for subsequent calculations.

[0150] Step 3: Determine the combined weights of subjective and objective information: Establish a weight determination model that integrates subjective and objective information. For objective weights, fuzzy entropy and cross-entropy are used comprehensively: fuzzy entropy measures the fuzziness of the evaluation information itself; the smaller the entropy value, the greater the weight. Cross-entropy measures the difference between the evaluation information and the ideal state; the greater the difference, the greater the weight. For subjective weights, the best-worst method is used to determine the weights of the primary indicators, reducing the number of judgments and improving consistency through structured comparison. Finally, the subjective and objective weights are integrated through a balance coefficient to form a combined weight.

[0151] Step 4: Layered information aggregation based on weighted average operator: Layered information fusion is performed using a bilateral probabilistic language weighted average operator. First, the objective combination weights of the secondary indicators are used to aggregate their standardized evaluation values ​​to the corresponding primary indicators to obtain the comprehensive evaluation value of the primary indicators. Then, the subjective weights of the primary indicators are used to further aggregate the comprehensive evaluation values ​​of all primary indicators, and finally, bilateral probabilistic language elements representing the overall risk level of the project are obtained.

[0152] Step 5: Risk Quantification and Level Determination: Calculate the expected value and variance of the overall risk assessment value. Based on the magnitude of the expected value, compare it with the preset risk level classification standard to determine the final risk level of the project. The variance is used to measure the degree of disagreement among the expert group's evaluation. The smaller the variance, the higher the consensus and the more reliable the assessment results.

[0153] Specifically, step 1 includes the following methods:

[0154] Step 1.1: To facilitate calculation, the linguistic terms need to be converted into numerical values. Using the linear symmetric mapping method, a five-granularity linguistic term set T = {t1, t2, t3, t4, t5} is defined. Its semantics and its numerical mapping φ(·) on the interval [0,1] are given in Table 1 below. This term set provides a unified metric for subsequent probability allocation.

[0155] Table 1:

[0156]

[0157] In DPLTS, when the same linguistic term (t3 value 0.50) appears in both the membership set and the non-membership set, its semantics are determined by the context:

[0158] In the membership set M(a), t3(0.50) indicates "moderate support for its high risk";

[0159] In the non-membership set N(b), t3(0.50) indicates "moderate support for its low risk"; Step 1.2: Generate membership PLTS M(a)

[0160] For any specific secondary indicator c i(k) Let there be y experts participating in the evaluation, and their score set be X = {x1, x2, ..., x...} y}, where x q ∈[1, 5], q∈[1, y] is the single-value score of the q-th expert;

[0161] (1) Terminology mapping: Map each expert's score x q Round to the nearest integer and map to the corresponding language term t. k ∈T, the mapping rule is:

[0162] k = round(x q (1.1)

[0163] Where, round(·) is the rounding function, and k is the language term index, which is obtained by rounding the expert scores and has a value of 1-5;

[0164] (2) Probability calculation: Statistical analysis of each term t k The number of times n appears in m expert evaluations k Calculate its frequency of occurrence as the probability:

[0165]

[0166] And satisfy a (k) Let n be the probability of the k-th language term, m be the total number of expert evaluations for a certain indicator, and n be the probability of the k-th language term. k For each term t k The number of times it appears in m expert evaluations.

[0167] (3) Constructing the membership set: Term(s) with a probability of zero are removed, forming the membership set (PLTS) of the indicator:

[0168] M(a)={t k (a k )|(a k )>0}

[0169] M(a) represents the distribution of the expert group’s collective opinion that “the indicator is of high risk”;

[0170] Step 1.3: Generate non-membership PLTS N(b)

[0171] The non-membership degree represents the distribution of the expert group's collective opinion that "the indicator has low risk." Based on the complementary nature of "high risk" and "low risk" in risk assessment, the non-membership degree set is derived through the following transformation rule:

[0172] Through numerical mapping, the strength of an evaluation supporting "low risk" should be 1 minus the strength of that evaluation supporting "high risk". However, this results in a new value, which needs to be mapped back to the most recent language term. Then, based on the term mapping and probability calculation in step 1.2 above, the non-membership set is obtained:

[0173] N(b)={t k (b k )|(b k )>0}

[0174] N(b) represents the distribution of the expert group’s collective opinion that “the risk of this indicator is low”;

[0175] Step 1.4: Construct Bilateral Probabilistic Language Elements (DPLE)

[0176] Combining the generated membership set with the non-membership set yields the complete DPLE representing the group evaluation of this secondary indicator:

[0177] P i(k) =<M(a),N(b)>

[0178] This P i(k) This will serve as the basis for all subsequent calculations.

[0179] Specifically, step 2 includes the following methods:

[0180] Suppose there exist two bilateral probabilistic linguistic elements P1 to be compared or aggregated.<M1(a),N1(b)> and P2 =<M2(a),N2(b)> ,in:

[0181]

[0182] M1(a) represents the membership set of the bilateral probability linguistic element P1, characterizing the distribution of the expert group's collective opinion that "the corresponding risk factor is high risk"; M(i)1 represents the i-th linguistic term in M1(a), belonging to the predefined linguistic term set T; a(i)1 represents the probability corresponding to the linguistic term M(i)1, reflecting the proportion of this term in the expert group's evaluation, satisfying a(i)1≥0; i is the membership set M 1 (a) Index of the linguistic terms (starting from 1); #M1(a) represents the number of non-zero probability linguistic terms in the membership set M1(a); This means that the sum of the probabilities of all language terms in M1(a) does not exceed 1 (hesitation information is allowed, and the part without assigned probability reflects hesitation).

[0183] N1(b) represents the set of non-membership degrees of the bilateral probability linguistic element P1, characterizing the distribution of the expert group's collective opinion that "the corresponding risk factor is low risk"; the j-th linguistic term in N1(b) belongs to the predefined linguistic term set T; b(j)1 represents the probability corresponding to the linguistic term b(j)1, reflecting the proportion of this term in the expert group's evaluation, satisfying b(j)1≥0; j is the set of non-membership degrees of N. 1 (b) Index of the linguistic terms (starting from 1); #N1(b) represents the number of non-zero probability linguistic terms in the non-membership set N1(b); This means that the sum of the probabilities of all language terms in N1(b) does not exceed 1 (hesitation information is allowed, and the part without assigned probability reflects hesitation).

[0184] M2(a) and N2(b) are the second bilateral probabilistic linguistic elements, with each parameter defined similarly to M1(a) and N1(b).

[0185] Step 2.1: Calculate the length of the least common multiple.

[0186] First, calculate the least common multiple of the lengths of the membership set and the non-membership set respectively:

[0187] m h =lcm(#M1(a), #M2(b)) (1.3)

[0188] m g =lcm(#N1(a), #N2(b)) (1.4)

[0189] Where, m h m is the least common multiple of the lengths of the two membership sets. g The least common multiple of the length of the non-membership set is denoted by lcm(e,f), which represents the least common multiple of integers e and f, where e and f represent the numerical lengths of the membership set or non-membership set in two bilateral probabilistic linguistic elements to be compared or aggregated.

[0190] Step 2.2: Construct the extended DPLTS

[0191] By repeating the elements in the original set and distributing their probabilities equally, each DPLTS is expanded to a uniform length. For the membership set M1(a) of M1, its expanded set... Defined as:

[0192]

[0193] The element and its adjusted probability are:

[0194]

[0195] Here, κ is the element index of the expanded membership set, and the correspondence between the superscript i and κ is as follows:

[0196] i = ((κ-1)mod#M1(a))+1, which means that each element in the original set M1(a) will be repeated m times. h / #M1(a) times, and its original probability Distributed equally among all these repeating elements, becoming

[0197] Similarly, the non-membership set N1(b) of P1 is extended as follows:

[0198]

[0199] γ is the element index of the expanded non-membership set, and the original probability of the non-membership set. After expansion, it becomes Perform the exact same operation on step 2 to obtain the expanded version.

[0200] Specifically, step 3 includes the following methods:

[0201] Step 3.1: Determining Objective Weights

[0202] When constructing an objective weight determination model, it is necessary to accurately measure the degree of uncertainty and discriminative ability of the information carried by the DPLTS. Fuzzy entropy is used to measure the fuzziness or uncertainty of a single DPLTS itself, while cross entropy is used to measure the degree of difference between two DPLTSs.

[0203] Distance measure is the basis for calculating distance-based cross entropy. After standardizing DPLTS using the LCM extension method, the distance between them can be precisely defined.

[0204] Definition (Two-sided probabilistic linguistic distance measure): Let... and For two DPLTS extended by the LCM method, their generalized normalized distance is defined as:

[0205]

[0206] Where λ is the distance metric parameter, λ>0, when λ=1, it is the normalized Hamming distance; when λ=2, it is the normalized Euclidean distance, and φ(·) is the linear symmetric mapping function;

[0207] Step 3.11: For any secondary indicator ci(k) The fuzzy entropy of all DPLTS scores given by experts was calculated using a formula based on Shannon entropy:

[0208]

[0209] Where, μ (i) =φ(M (i) (Numerical mapping of membership degree set terminology), v (j) =φ(N (j) (Numerical mapping of non-membership degree set terminology);

[0210] Step 3.12: Calculate the index c. i(k) The total entropy value below:

[0211]

[0212] r ij(k) This refers to the actual DPLTS evaluation information for the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator.

[0213] Step 3.13: Calculate the weights based on fuzzy entropy. The smaller the entropy value, the clearer the information, and the larger the weight.

[0214]

[0215] #c i(k) Let be the number of all secondary indicators corresponding to the i-th primary indicator.

[0216] Step 3.14: Define an ideal reference r for this indicator. i0(k) (The ideal reference DPLTS evaluation information for the kth secondary indicator under the ith primary indicator), whose DPLTS can be set as <{t1(1)}, {t5(1)}>. For different secondary indicators, the distance is extended to the same length using the LCM method (using Hamming distance, λ=1).

[0217] Step 3.15: Calculate r for each evaluation unit. ij(k) (The actual DPLTS evaluation information of the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator) and the ideal reference r i0(k) Cross-entropy:

[0218]

[0219] Where φ(·) is a linear symmetric mapping function that converts linguistic terms into numerical values.

[0220] These represent the membership set and non-membership set (containing language terms and their corresponding probabilities) of the expanded DPLTS, respectively. p > 0 is an adjustment parameter, typically set to the cardinality of the language term set minus one, ensuring sufficient discriminative power of the evaluation information on the computational scale. T = (1+p)ln(1+p) - (2+p)(ln(2+p) - ln2) is a normalization factor, ensuring... And when At that time, XE = 0;

[0221] Step 3.16: Calculate the index c. i(k) The total cross-entropy value below:

[0222]

[0223] Step 3.17: Calculate the weights based on cross-entropy. The larger the cross-entropy, the stronger the discriminative power of the indicator, and the larger the weight should be.

[0224]

[0225] Step 3.18: Combine the two using a balance coefficient β∈[0,1] to obtain the comprehensive objective weight of the secondary indicator:

[0226]

[0227] Step 3.2: Determining Subjective Weights

[0228] The best-worst method greatly reduces the number of comparisons and significantly improves the consistency of judgments through a structured comparison process. Therefore, it is particularly suitable for dealing with problems such as deep foundation pit risk assessment, which have a large number of criteria and require efficient and reliable acquisition of expert subjective weights.

[0229] Suppose there are n primary indicators whose weights need to be determined, denoted as C = {c1, c2, ..., cn}. n};

[0230] Step 3.21: Determine the most important and least important indicators.

[0231] From the set of indicators C, determine the most important one (denoted as c). B The indicators and a least important one (denoted as c) W The indicators;

[0232] Step 3.22: Construct the optimal comparison vector and the worst comparison vector.

[0233] Using the 1-9 scale, experts first conduct a preliminary evaluation of all primary indicators and calculate the average expert score for each primary indicator. Based on the average score, the indicator with the highest average score is selected as the most important indicator (c). BThe lowest average value is considered the least important indicator, c. W The scale means: 1 = equally important, 3 = slightly important, 5 = significantly important, 7 = strongly important, 9 = absolutely important, and 2 / 4 / 6 / 8 are intermediate values. Two groups of comparisons are conducted separately:

[0234] Optimal comparison vector: The most important indicator c B By comparing with all other metrics, a vector is obtained:

[0235] V B =(υ B1 ,υ B2 ,…,υ Bn )

[0236] Among them, v Bi Indicates the most important indicator C B Relative to index C i The importance of V is obvious. BB =1;

[0237] Worst Comparison Vector: Compares all other metrics with the least important metric c. W By comparing, we obtain the vector:

[0238] V W =(υ 1W ,υ 2W ,…,υ nW )

[0239] Among them, υ iW Indicator C i Compared to the least important indicator c W The importance of V. Clearly, V WW =1;

[0240] Step 3.23: Construct the optimization model and solve for the weights.

[0241] BWM finds an optimal set of weights θ = (θ1, θ2, ..., θ) by constructing an optimization model. n This allows the weights to satisfy the preference relationship reflected by both the best and worst comparisons to the greatest extent possible.

[0242]

[0243] min max{...} is the objective function, which means "minimize the maximum deviation", that is, to minimize the deviation between the weight and the importance of the expert judgment (to ensure consistency). The deviation between the weighting ratio and expert judgment (θ) B / θ i It should be as close as possible to υ Bi (The smaller the deviation, the better the consistency). The deviation (θ) between another set of weighting ratios and expert judgment i / θ W (It should be as close as possible). `st` contains two constraints: the sum of the weights of all first-level indicators is 1 (weight normalization), and the weights are non-negative (weights cannot be negative).

[0244] Model (M-1) is transformed into the following linear programming model (M-2) for solution:

[0245] minξ

[0246]

[0247] Solving model (M-2) yields the optimal subjective weight vector for the primary indicators.

[0248] And the consistency index ξ. ξ is the consistency deviation variable (the variable to be solved), which represents the upper limit of all deviations. The goal is to minimize ξ (the closer it is to 0, the better the consistency of expert judgment).

[0249] Specifically, step 4 includes the following methods:

[0250] After determining the weights of indicators at all levels and standardizing the evaluation information, the evaluations of the underlying indicators are integrated into an overall risk value, and risk ranking is performed accordingly. Based on the bilateral probability language weighted average (DPLWA) operator, a hierarchical information aggregation model is constructed, and the expected value-variance criterion is introduced for the final ranking.

[0251] Step 4.1: Aggregate the evaluation values ​​of secondary indicators to primary indicators.

[0252] For the i-th primary index c i Its comprehensive evaluation value P i By aggregating all its secondary indicators c i(k) Standardized evaluation value and its objective weight θ i(k) The calculation was performed using the bilateral probabilistic language weighted average operator (DPLWA):

[0253]

[0254] in, ⊙ and ⊙ represent DPLTS addition and scalar multiplication operations, respectively. This step integrates the evaluations of multiple specific risk factors belonging to the same dimension into a holistic evaluation P for that dimension. i ;

[0255] Step 4.2: Aggregate the evaluation values ​​of primary indicators into the overall risk.

[0256] Overall construction risk assessment value P of the project 总 By aggregating the comprehensive evaluation value P of all n primary indicators i and its subjective weight θ i The calculation also uses the DPLWA operator:

[0257]

[0258] At this point, the evaluation information of all underlying indicators has been aggregated into a final two-sided probabilistic language element P, representing the overall risk level of the project. 总 .

[0259] Specifically, step 5 includes the following methods:

[0260] Step 5.1, Overall Risk Expectation e(P) 总 The calculation is based on its DPLTS form, calculating the weighted average of the membership and non-membership parts separately:

[0261]

[0262] in:

[0263]

[0264] is the weighted mean of the membership set M(a), reflecting the overall strength of "supporting high risk".

[0265] is the weighted mean of the non-membership set N(b), reflecting the overall strength of "supporting low risk".

[0266] After expansion, for the membership set, the numerator becomes:

[0267]

[0268] The denominator becomes:

[0269]

[0270] Step 5.2: The overall risk variance is used to measure the degree of disagreement in expert evaluations. The calculation formula is as follows:

[0271]

[0272] Step 5.3: Based on the calculated overall risk expectation value e(P) 总 The final risk level of the project is determined by comparing it with the preset risk level classification standards (as shown in Table 2 below);

[0273] Table 2:

[0274]

[0275] Step 5.4: When comparing the risk levels of multiple projects or options, the primary criterion is based on the expected value e(P). 总 Sort the data in descending order; the higher the expected value, the greater the risk. If the expected values ​​are the same or very close, use the variance σ. 2 (P) is used as a supplementary criterion, with objects having smaller variance being ranked first because they have less uncertainty.

[0276] In summary, this invention introduces a bilateral probabilistic language term set (DPLTS) to fully characterize the distribution of expert opinions, and combines the LCM objective standardization method with a fuzzy entropy-cross entropy-BWM combined weighting model to construct a risk assessment system that is information-complete, scientifically weighted, and robust to decision-making. This effectively makes up for the shortcomings of existing technologies in expressing complex uncertainties and integrating subjective and objective information, and significantly improves the reliability, discriminativeness, and practical value of risk assessment results.

[0277] The descriptions and practices disclosed in this invention are readily apparent and understandable to those skilled in the art, and various modifications and refinements can be made without departing from the principles of this invention. Therefore, any modifications or improvements made without departing from the spirit of this invention should also be considered within the scope of protection of this invention.

Claims

1. A risk assessment method for deep foundation pit construction in subway stations based on bilateral probabilistic language, characterized in that, Includes the following steps: Step 1: Construct an evaluation set in the form of a bilateral probabilistic linguistic terminology set: Systematically convert the individual scores of experts for secondary indicators into a bilateral probabilistic linguistic terminology set; specifically, this includes: determining the linguistic terminology set and its numerical mapping relationship; statistically analyzing the frequency of each linguistic term in the expert scores as a probability to generate a membership set M(a) representing support for high-risk opinions; based on the complementarity principle, deriving and generating a non-membership set N(b) representing support for low-risk opinions; and finally constructing a complete bilateral probabilistic linguistic element for each secondary indicator. Step 2: Objective standardization of evaluation information: To address the issue of inconsistent lengths of membership and non-membership sets in different DPLTSs, a standardization method based on the least common multiple is adopted; the least common multiple of the lengths of the DPLTS sets to be compared is calculated, and all DPLTSs are extended to a uniform length by repeating elements and distributing their probabilities equally. Step 3: Determine the combined weights of subjective and objective information: Establish a weight determination model that integrates subjective and objective information. For objective weights, fuzzy entropy and cross-entropy are used comprehensively: fuzzy entropy measures the fuzziness of the evaluation information itself; the smaller the entropy value, the greater the weight. Cross-entropy measures the difference between the evaluation information and the ideal state; the greater the difference, the greater the weight. For subjective weights, the best-worst method is used to determine the weights of the primary indicators, reducing the number of judgments and improving consistency through structured comparison. Finally, the subjective and objective weights are integrated through a balance coefficient to form a combined weight. Step 4: Layered information aggregation based on weighted average operator: Layered information fusion is performed using a bilateral probabilistic language weighted average operator. First, the objective combination weights of the secondary indicators are used to aggregate their standardized evaluation values ​​to the corresponding primary indicators to obtain the comprehensive evaluation value of the primary indicators. Then, the subjective weights of the primary indicators are used to further aggregate the comprehensive evaluation values ​​of all primary indicators, and finally, bilateral probabilistic language elements representing the overall risk level of the project are obtained. Step 5: Risk Quantification and Level Determination: Calculate the expected value and variance of the overall risk assessment value. Based on the magnitude of the expected value, compare it with the preset risk level classification standard to determine the final risk level of the project. The variance is used to measure the degree of disagreement among the expert group's evaluation. The smaller the variance, the higher the consensus and the more reliable the assessment results.

2. The method for risk assessment of deep foundation pit construction in subway stations based on bilateral probabilistic language as described in claim 1, characterized in that, Step 1 includes the following methods: Step 1.1: Using the linear symmetric mapping method, define a five-granularity language terminology set. T={t1, t2, t3, t4, t5}; In DPLTS, when the same linguistic term t3 appears in both the membership set and the non-membership set, its semantics are determined by the context: In the membership set M(a), t3(0.50) indicates a moderate degree of support for its high risk; In the non-membership set N(b), t3(0.50) indicates a moderate degree of support for its low risk; Step 1.2: Generate membership degree PLTS M(a) For any specific secondary indicator c i (k) Let there be y experts participating in the evaluation, and their score set be x = {x1, x2, ..., xn}. y }, where x q ∈[1, 5], q∈[1, y] is the single-value score of the q-th expert; (1) Terminology mapping: Map each expert's score x q Round to the nearest integer and map to the corresponding language term t. k ∈T, the mapping rule is: k=round(x q ) (1.1) Where, round(·) is the rounding function, and k is the language term index; (2) Probability calculation: Statistical analysis of each term t k The number of times n appears in m expert evaluations k Calculate its frequency of occurrence as the probability: And satisfy a (k) Let n be the probability of the k-th language term, m be the total number of expert evaluations for a certain indicator, and n be the probability of the k-th language term. k For each term t k The number of times it appears in m expert evaluations; (3) Constructing the membership set: Term(s) with a probability of zero are removed, forming the membership set (PLTS) of the indicator: M(a)={t k (a k |(a k )>0} M(a) characterizes the distribution of collective opinions in the expert group that indicate a high risk of supporting this indicator; Step 1.3: Generate non-membership PLTSN(b) The non-membership degree represents the distribution of collective opinions from the expert group supporting a low risk level for that indicator. Based on the complementary nature of high-risk and low-risk factors in risk assessment, the non-membership degree set is derived using the following transformation rule: Based on the term mapping and probability calculation in step 1.2 above, the set of non-membership degrees is obtained: N(b)={t k (b k )|(b k )>0} N(b) characterizes the expert group’s distribution of collective opinion that supports the low risk of this indicator; Step 1.4: Constructing Bilateral Probabilistic Language Elements (DPLE) Combining the generated membership set with the non-membership set yields the complete DPLE representing the group evaluation of this secondary indicator: P i(k) =<M(α),N(b)> This P i (k) will serve as the basis for all subsequent calculations.

3. The method for risk assessment of deep foundation pit construction in subway stations based on bilateral probabilistic language as described in claim 1, characterized in that, Step 2 includes the following methods: Suppose there exist two bilateral probabilistic linguistic elements P1 to be compared or aggregated.<M1(a),N1(b)> and P2 =<M2(a),N2(b)> ,in: M1(a) represents the membership set of the bilateral probability linguistic element P1, characterizing the distribution of collective opinions in which the expert group supports the corresponding risk factor as high-risk; M(i)1 represents the i-th linguistic term in M1(a), belonging to the predefined linguistic term set T; a(i)1 represents the probability corresponding to the linguistic term M(i)1, reflecting the proportion of this term in the expert group's evaluation, satisfying a(i)1≥0; i is the membership set M 1 (a) is the index of the linguistic terms; #M1(a) represents the number of non-zero probability linguistic terms in the membership set M1(a); This indicates that the sum of the probabilities of all language terms in M1(a) does not exceed 1; N1(b) represents the set of non-membership degrees of the bilateral probability linguistic element P1, characterizing the distribution of collective opinions in which the expert group supports the corresponding risk factor as low risk; the j-th linguistic term in N1(b) belongs to the predefined linguistic term set T; b(j)1 represents the probability corresponding to the linguistic term b(j)1, reflecting the proportion of this term in the expert group's evaluation, satisfying b(j)1≥0; j is the set of non-membership degrees of N. 1 (b) is the index of the linguistic terms; #N1(b) represents the number of non-zero probability linguistic terms in the non-membership set N1(b); This indicates that the sum of the probabilities of all language terms in N1(b) does not exceed 1; M2(a) and N2(b) are the second bilateral probabilistic linguistic elements, where the definitions of each parameter are similar to those of M1(a) and N1(b); Step 2.1: Calculate the length of the least common multiple. First, calculate the least common multiple of the lengths of the membership set and the non-membership set respectively: m h =lcm(#M1(a),#M2(b)) (1.3) m g =lcm(#N1(a),#N2(b)) (1.4) Where, m h m is the least common multiple of the lengths of the two membership sets. g The least common multiple of the length of the non-membership set is denoted by lcm(e,f), which represents the least common multiple of integers e and f, where e and f represent the numerical lengths of the membership set or non-membership set in two bilateral probabilistic linguistic elements to be compared or aggregated. Step 2.2: Construct the extended DPLTS By repeating the elements in the original set and distributing their probabilities equally, each DPLTS is expanded to a uniform length. For the membership set M1(a) of M1, its expanded set... Defined as: The element and its adjusted probability are: Here, κ is the element index of the expanded membership set, and the correspondence between the superscript i and κ is: i = ((κ-1)mod#M1(a)) + 1, which means that each element in the original set M1(a) is repeated m times. h / #M1(a) times, and its original probability Distributed equally among all these repeating elements, becoming Similarly, the non-membership set N1(b) of P1 is extended as follows: γ is the element index of the expanded non-membership set, and the original probability of the non-membership set. After expansion, it becomes Perform the exact same operation on step 2 to obtain the expanded version.

4. The method for risk assessment of deep foundation pit construction in subway stations based on bilateral probabilistic language as described in claim 1, characterized in that, Step 3 includes the following methods: Step 3.1: Determining Objective Weights When constructing an objective weight determination model, it is necessary to accurately measure the degree of uncertainty and discriminative ability of the information carried by the DPLTS. Fuzzy entropy is used to measure the fuzziness or uncertainty of a single DPLTS itself, while cross entropy is used to measure the degree of difference between two DPLTSs. Distance measure is the basis for calculating distance-based cross entropy. After standardizing DPLTS using the LCM extension method, the distance between them can be precisely defined. Define a two-sided probabilistic linguistic distance measure: Let and For two DPLTS extended by the LCM method, their generalized normalized distance is defined as: Where λ is the distance metric parameter, λ>0, when λ=1, it is the normalized Hamming distance; when λ=2, it is the normalized Euclidean distance, and φ(·) is the linear symmetric mapping function; Step 3.11: For any secondary indicator c i (k) The fuzzy entropy of all expert ratings for DPLTS is calculated using a formula based on Shannon entropy: Where, μ (i) =φ(M (i) ) is the numerical mapping of the membership degree set terminology, v (j) =φ(N (j) ) is a numerical mapping of non-membership degree set terms; Step 3.12: Calculate the index c. i The total entropy value under (k): r ij (k) represents the actual DPLTS evaluation information of the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator; Step 3.13: Calculate the weights based on fuzzy entropy. The smaller the entropy value, the clearer the information, and the larger the weight. #c i(k) This represents the number of all secondary indicators corresponding to the i-th primary indicator; Step 3.14: Define an ideal reference r for this indicator. i0(k) r i0(k) The DPLTS evaluation information serves as the ideal reference for the k-th secondary indicator under the i-th primary indicator. Step 3.15: Calculate r for each evaluation unit. ij(k) With ideal reference r i0(k) cross-entropy, r ij(k) The actual DPLTS evaluation information for the j-th evaluation unit corresponding to the k-th secondary indicator under the i-th primary indicator: Where φ(·) is a linear symmetric mapping function that converts linguistic terms into numerical values. These represent the membership and non-membership sets of the expanded DPLTS, respectively. p > 0 is an adjustment parameter, set to the cardinality of the language term set minus one, ensuring sufficient discriminative power of the evaluation information on the computational scale. T = (1+p)ln(1+p) - (2+p)(ln(2+p) - ln2) is a normalization factor, ensuring... And when At that time, XE = 0; Step 3.16: Calculate the index c. i(k) The total cross-entropy value below: Step 3.17: Calculate the weights based on cross-entropy. The larger the cross-entropy, the stronger the discriminative power of the indicator, and the larger the weight should be. Step 3.18: Combine the two using a balance coefficient β∈[0,1] to obtain the comprehensive objective weight of the secondary indicator: Step 3.2: Determining Subjective Weights Suppose there are n primary indicators whose weights need to be determined, denoted as C = {c1, c2, ..., cn}. n }; Step 3.21: Determine the most important and least important indicators. From the set of indicators C, determine the most important one, denoted as c. B The indicator and the least important one are denoted as C. W Indicators; Step 3.22: Construct the optimal comparison vector and the worst comparison vector. Using the 1-9 scale, experts first conduct a preliminary evaluation of all primary indicators and calculate the average expert score for each primary indicator. Based on the average score, the indicator with the highest average score is selected as the most important indicator C. B The lowest average value is considered the least important indicator, c. W Two sets of comparisons were performed separately: Optimal comparison vector: The most important indicator c B By comparing with all other metrics, a vector is obtained: V B =(υ B1 ,U B2 ,…,u Bn ) Among them, υ Bi Indicates the most important indicator c B Relative to index c i The importance of V is obvious. BB =1; Worst Comparison Vector: Compares all other metrics with the least important metric c. W By comparing, we obtain the vector: V W =(υ 1W ,v 2W ,…,u nW ) Among them, υ iW Indicator c i Compared to the least important indicator c W The importance of V is obvious. WW =1; Step 3.23: Construct the optimization model and solve for the weights. BWM finds an optimal set of weights θ = (θ1, θ2, ..., θ3) by constructing an optimization model. n This allows the weights to satisfy the preference relationship reflected by both the best and worst comparisons to the greatest extent possible. The established optimization model (M-1) is as follows: `min max{...}` is the objective function, meaning to minimize the maximum deviation. This is the deviation between the weighting ratio and the expert's judgment. The deviation between another set of weight ratios and expert judgment is represented by two constraints in st: the sum of the weights of all first-level indicators is 1 and the weights are non-negative. Model M-1 is transformed into the following linear programming model M-2 for solution: minξ Solving model M-2 will yield the optimal subjective weight vector for the primary index. And the consistency index ξ, where ξ is the consistency deviation variable, representing the upper limit of all deviations, and the goal is to minimize ξ.

5. The method for risk assessment of deep foundation pit construction in subway stations based on bilateral probabilistic language as described in claim 1, characterized in that, Step 4 includes the following methods: After determining the weights of indicators at all levels and standardizing the evaluation information, the evaluations of the underlying indicators are integrated into an overall risk value, and risk ranking is performed accordingly. Based on the bilateral probability language weighted average (DPLWA) operator, a hierarchical information aggregation model is constructed, and the expected value-variance criterion is introduced for final ranking. Step 4.1: Aggregate the evaluation values ​​of secondary indicators to primary indicators. For the i-th primary index c i Its comprehensive evaluation value P i By aggregating all its secondary indicators c i(k) Standardized evaluation value and its objective weight θ i(k) The calculation was performed using the bilateral probability language weighted average operator DPLWA: in, ⊙ and ⊙ represent DPLTS addition and scalar multiplication operations, respectively. This step integrates the evaluations of multiple specific risk factors belonging to the same dimension into a holistic evaluation P for that dimension. i ; Step 4.2: Aggregate the evaluation values ​​of primary indicators into the overall risk. Overall construction risk assessment value P of the project 总 By aggregating the comprehensive evaluation value P of all n primary indicators i and its subjective weight θ i The calculation also uses the DPLWA operator: At this point, the evaluation information of all underlying indicators has been aggregated into a final two-sided probabilistic language element P, representing the overall risk level of the project. 总 .

6. The method for risk assessment of deep foundation pit construction in subway stations based on bilateral probabilistic language as described in claim 1, characterized in that, Step 5 includes the following methods: Step 5.1, Overall Risk Expectation e(P) 总 The calculation is based on its DPLTS form, calculating the weighted average of the membership and non-membership parts separately: in: The weighted mean of the membership set M(a) reflects the overall strength of support for high risk; The weighted mean of the non-membership set N(b) reflects the overall strength of support for low risk; After expansion, for the membership set, the numerator becomes: The denominator becomes: Step 5.2: The overall risk variance is used to measure the degree of disagreement in expert evaluations. The calculation formula is as follows: Step 5.3: Based on the calculated overall risk expectation value e(P) 总 The final risk level of the project is determined by comparing it with the preset risk level classification standards; Step 5.4: When comparing the risk levels of multiple projects or options, the primary criterion is based on the expected value e(P). 总 Sort the data in descending order; the higher the expected value, the greater the risk. If the expected values ​​are the same or close, use the variance σ. 2 (P) serves as an auxiliary criterion.

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