Joint probability distribution model of tunnel construction potential safety hazard frequency and application

Abstract

The invention provides a joint probability distribution model of tunnel construction potential safety hazard frequency and application. The joint probability distribution model is constructed and obtained according to the following steps of 1, potential hazard data statistical analysis, 2, construction of a joint probability density function, and 3, determination of the most probable interval and the extreme value of potential hazard symptom. The risk prediction application method based on the model comprises the following steps: step 4, dividing into five grades based on different surpassing probabilities according to all weekly or monthly frequency distribution of a project preorder, and giving a final risk grade by adopting a most probable result predicted by a joint probability distribution model; after a potential safety hazard frequency result is obtained, different potential safety hazard frequency levels are divided according to the potential safety hazard frequency distribution characteristics of all sections, and early warning is made for the field safety management level. According to the method, the distribution rule of future hidden dangers can be scientifically predicted from the perspective of conditional probability and hidden danger statistical analysis, and theoretical reference is provided for hidden danger prevention and risk control of future major engineering.

Description

Technical Field

[0001] The present invention relates to the field of engineering hidden danger prediction and risk control, and in particular to a joint probability distribution model of the frequency of safety hidden dangers in tunnel construction and its application. Background Art

[0002] Accurate safety hazard prediction can eliminate all kinds of safety accidents in the bud, transform post-event disposal into pre-event prevention, and ensure that the construction party has the initiative before a major safety accident occurs. Therefore, in order to deeply explore the evolution characteristics of the frequency of safety hazards at the tunnel construction site, reveal its inherent change laws, and provide scientific safety control measures for on-site construction management personnel, it is necessary to conduct an in-depth analysis of the changing characteristics of the frequency of safety hazards at the tunnel construction site and achieve effective prediction.

[0003] The invention application of CN114565184B relates to a method, system, storage device and terminal for predicting safety hazards in smart mines. The method comprises: S10, establishing a database of safety hazard factors in coal mines, the database comprising: safety hazard names, regional locations corresponding to the safety hazard names, and evaluation indicators of the hazard factors; wherein each safety hazard name corresponds to at least one regional location, and each regional location corresponds to at least one evaluation indicator of the hazard factor; and the evaluation indicator of each hazard factor corresponds to a data value of the hazard factor; S20, obtaining the data value of the hazard factor existing in the coal mine to be predicted and writing it into the database; S30, determining the weight information corresponding to the evaluation indicator of the hazard factor in each regional location; S40, calculating the safety hazard score based on the weight information and the data value of the hazard factor to obtain the safety hazard prediction result; the present invention has the beneficial effect of reliable data calculation and is suitable for the field of smart mine safety.

[0004] The invention application of CN117172561B relates to a method and system for predicting geological disaster risk hazards based on an intelligent model algorithm, which obtains geological acquisition data to be predicted for geological disaster risk hazards, and generates a geological detection characterization vector for each geological detection source data through deep feature extraction. According to the geological detection characterization vector, feature correlation estimation is performed on each geological detection source data, and feature correlation estimation results are generated, which helps to reveal the inherent correlation between data and further improve the accuracy of geological disaster risk prediction. Afterwards, the geological disaster risk hazard data matching each disassembled geological acquisition data is searched in the geological disaster risk hazard database to determine the risk hazard node, so as to predict the geological disaster risk hazard according to the risk hazard node, which helps to achieve accurate and efficient geological disaster risk assessment, thereby providing an important basis for preventing geological disasters.

[0005] The invention application of CN116469056A relates to a method and system for predicting hidden dangers in a smart factory based on image processing, which combines the image descriptors of each suspected abnormal state image block in the running state image block queue to determine the queue description vector of the running state image block queue, and the state-related features of each suspected abnormal state image block before and after to determine the state trend variable of the running state image block queue, so as to accurately and comprehensively mine the details used for risk hidden danger characterization in the running state image of the smart factory. Combining the queue description vector and state trend variable of the running state image of the smart factory, as well as the multi-dimensional details of the sample set of the running state image of the smart factory under different risk hidden danger types, and determining the risk hidden danger type matched by the running state image of the smart factory through an AI classifier, it is possible to accurately and comprehensively analyze the risk hidden danger types, so as to improve the accuracy and credibility of the risk hidden danger type prediction analysis of the running state image of the smart factory.

[0006] Although some studies have conducted preliminary research on the prediction of safety hazard frequency, the main problems currently exist are: (1) the changing characteristics of the safety hazard frequency at tunnel construction sites have not yet been revealed; and (2) the prediction and classification of safety hazard frequency still need to be discussed in detail. Summary of the invention

[0007] The present invention establishes a hidden danger prediction model based on hidden danger statistical analysis data and conditional probability distribution, and gives detailed conditional probability distribution analysis steps, and gives the most likely value and distribution interval of the prediction result in combination with the confidence interval, and finally gives a hidden danger level classification method. The invention can scientifically predict the distribution law of future hidden dangers from the perspective of conditional probability and hidden danger statistical analysis, and provide a theoretical reference for the prevention of hidden dangers and risk control of major projects in the future.

[0008] Technical solution of the present invention:

[0009] A joint probability distribution model of the frequency of safety hazards in tunnel construction is constructed by following the steps below:

[0010] Step 1: Statistical analysis of hidden danger data:

[0011] First, determine the basic parameters of the research object, prediction frequency, and hidden danger type, among which:

[0012] The research object is for the entire project or for different bidding sections;

[0013] Whether the forecast frequency is for weekly or monthly hidden danger statistics;

[0014] The hidden danger type is a safety hidden danger or other type of hidden danger;

[0015] Then statistically analyze the corresponding hidden danger frequency;

[0016] The frequency of hidden dangers Xi in this bidding section of the research object project this week (this month) and the frequency of hidden dangers Yi in other bidding sections last week (last month) will be statistically analyzed;

[0017] Step 2: Construct the joint probability density function f X,Y (x,y):

[0018] First, select the Copula function that is suitable for the joint distribution characteristics of Xi and Yi;

[0019] Then estimate the marginal distribution F of Xi and Yi x (x i ) and F Y (y i ), and convert it into the inverse cumulative distribution function U and V of the standard normal distribution, and calculate the correlation coefficient ρ between U and V;

[0020] Finally, based on the Copula function, the joint probability density function f of the hidden danger data of this section this week (this month) and the hidden danger data of other sections last week (last month) is determined. X,Y (x,y);

[0021] Step 3: Determine the most likely range and maximum value of hidden danger symptoms:

[0022] Obtain the probability density function f of the number of hidden dangers in this section this week (this month) under the condition of hidden danger data B of other sections last week (last month) X|Y (x|B), and the cumulative distribution function (CDF) of the conditional probability density function F X|Y (x|B), and then obtain the most likely interval and the most likely value of the hidden danger symptom.

[0023] The model-based risk prediction application method includes step 4:

[0024] Step 4: Based on the weekly (monthly) frequency distribution of all engineering predecessors, they are divided into five levels based on different exceedance probabilities, and the most likely result predicted by the joint probability distribution model is used to give the final risk level.

[0025] After obtaining the safety hazard frequency results, the present invention will divide different safety hazard frequency levels according to the hazard frequency distribution characteristics of each bidding section, and make early warnings for the on-site safety management level. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Implementation process of the present invention.

[0027] Figure 2 The cumulative probability density distribution of hidden danger frequency of the present invention.

[0028] Figure 3 Copula joint probability density diagram of each section in the engineering example.

[0029] Figure 4 Engineering example model training results.

[0030] Figure 5 Example software display. DETAILED DESCRIPTION

[0031] The process of the present invention is described in detail below. Figure 1 , the steps are as follows:

[0032] 1. Statistical analysis and research on the frequency of safety hazards in the project every week

[0033] Collect and analyze weekly safety hazard frequency data, compile a statistical list of the frequency of hidden dangers in this bidding section this week, and a statistical list of the frequency of hidden dangers in other bidding sections last week, to provide basic data for subsequent modeling and prediction (divided into: 80% for model building + 20% for prediction).

[0034] 2. Copula function establishment

[0035] The weekly safety hazard frequencies Xi of each bidding section and the weekly safety hazard frequencies Yi of other bidding sections are counted, and a method for modeling the short-term safety hazard frequencies using Gaussian Copula function is established to obtain the joint probability density function and joint cumulative distribution function of Xi and Yi.

[0036] (1) Copula function selection

[0037] After selecting the Copula function, it is necessary to estimate the parameters of the Copula. This method uses maximum likelihood estimation (MLE).

[0038] After estimating the parameters, the goodness of fit of the model needs to be tested. Commonly used methods include AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion). By comparing the AIC and BIC values ​​of different Copula models, the Copula function that best describes the data dependency structure can be selected. Generally, the smaller the AIC and BIC values, the better the model fit.

[0039] In this method, it is considered that the frequency law of safety hazards is most suitable for the Gaussian Copula model.

[0040] (2) Calculation of marginal distribution

[0041] It is necessary to estimate the marginal distribution of Xi and Yi. According to a large number of existing studies, Xi and Yi obey the distribution function F x (x i ) and F Y (yi ).

[0042]

[0043]

[0044] Where Φ represents the cumulative distribution function of the standard normal distribution; X i represents the i-th sample data point X, which represents the frequency data of safety hazards in a certain section over the past week; Y i represents the i-th sample data point Y, which represents the frequency data of safety hazards in other sections over the past week; n represents the number of samples, that is, the total number of X and Y data points; h represents the bandwidth parameter, which is used for kernel density estimation; x i represents the specific value of the variable x used to calculate the marginal distribution function; y i Represents the specific value of the variable y used to calculate the marginal distribution function.

[0045] (3) Map the marginal distribution to the standard normal distribution

[0046] Since the construction of Gaussian Copula requires mapping the marginal distribution to the standard normal distribution, the inverse normal distribution function is used to map the marginal distribution value to the standard normal distribution.

[0047] u i ′=Φ -1 (u i )

[0048] v i ′=Φ -1 (v i )

[0049] Among them, Φ -1 is the inverse function of Φ.

[0050] (4) Constructing Gaussian Copula function

[0051]

[0052] Among them, ρ is the correlation coefficient between standard normal distribution, φ is the probability density function of standard normal distribution, φ(u′) and φ(v′) are Φ -1 (u i ) and Φ -1 (v i )’s probability density value.

[0053] (5) Calculation of joint probability density function

[0054] f X,Y (x,y)=c(F x (x),F Y(y);ρ)·f X (x)·f Y (y)

[0055] Among them, f X (x) and f Y (y) are the marginal probability density functions of X and Y respectively.

[0056] 80% of the data of each bid section is used to build the model and obtain the joint probability density of each bid section.

[0057] 3. Establish a hidden danger symptom prediction model based on conditional probability distribution

[0058] The most likely range of hidden danger symptoms:

[0059] In order to calculate the most likely interval of Xi when Yi = B (e.g., 70% confidence interval), we need to obtain f X|Y (x|B):

[0060] f X|Y (x|B)=c(F x (x),F Y (B);ρ)·f x (A)

[0061] And calculate the cumulative distribution function (CDF) of the conditional probability density function F X|Y (x|B):

[0062]

[0063] To determine a 70% confidence interval, find a lower limit M and an upper limit N such that the following conditions hold:

[0064] F X|Y (M|B)-F X|Y (N|B)=0.7

[0065] After obtaining the lower limit M and upper limit N, the interval [N,M] is the required 70% confidence interval.

[0066] Most likely value of hidden danger symptom:

[0067] In order to calculate the conditional probability of Xi when Yi = B, we need to use the formula f X|Y (x|B):

[0068] f X|Y (x|B)=c(F x (x),F Y (B);ρ)·f x (A)

[0069] When Xi=A, there exists f X|YIf (x|B) reaches a maximum value, the A value at that time is considered to be the most likely value for this section this week.

[0070] Model verification: After constructing the hidden danger symptom prediction model, take the remaining 20% ​​of the data from each section for prediction, verify and adjust the model, that is, use historical data for backtesting to test the prediction ability of this model.

[0071] 4. Frequency classification of safety hazards

[0072] Select the historical frequency of safety hazards in this section, calculate the mean and standard deviation, and draw a probability density curve of the normal distribution, such as Figure 2 , respectively obtain the safety hazard frequencies when the cumulative probabilities are 0.4, 0.7, 0.99, and 0.999, and then obtain the hazard frequency classification table, as shown in Table 1.

[0073] Table 1 Hidden danger frequency level table

[0074] grade Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Frequency of hidden dangers ＞40 (27,40] (17,27] (7,17] ≤7

[0075] Engineering application examples

[0076] Statistics were collected on the frequency of various safety hazards reported on the digital construction platform of TJ-03 and TJ-04 sections since the start of construction of Qingdao Second Tunnel until May 29, 2024. The Gaussian Copula model was used to explore the potential nonlinear correlation between the frequency of hidden dangers at the construction site and the frequency of historical hidden dangers, and then the level of tunnel construction management was evaluated and early warning was issued.

[0077] 80% of the data of each section from the start of construction to the end of May is used to build the model, and the joint probability density diagram of each section can be obtained as follows: Figure 3 shown.

[0078] 20% of the data from the start of construction to the end of May for each section is used to verify the model effect, and the predicted most likely value and 70% confidence interval of each section can be obtained as follows: Figure 4 shown.

[0079] The results show that the predicted results are basically consistent with the actual results, and the actual data can basically fall within the prediction range. Because the frequency of hidden dangers is affected by many factors, such as centralized safety inspections, shutdowns, holidays, and patrol habits of inspectors during the week, the current model is difficult to achieve accurate predictions.

[0080] Take May 26, 2024 to June 1, 2024 as an example. During this period, TJ-03 had 46 hidden dangers and TJ-04 had 12 hidden dangers. Based on the frequency of safety hazards in each section this week, the frequency of safety hazards in this section next week is predicted. According to the prediction:

[0081] Next week, the frequency of potential hidden dangers in the TJ-03 section is 21 times, with a 70% probability of falling within the interval [0,26], and the hidden danger frequency level is Level IV.

[0082] The developed software application is shown in the figure Figure 5 As shown, it will be promoted and applied in the safety hazard module of Qingdao Second Tunnel Construction Safety Risk Management Platform.

Claims

1. A joint probability distribution model for the frequency of safety hazards in tunnel construction, characterized in that: Follow the steps below to build: Step 1: Statistical analysis of hidden danger data: First, determine the basic parameters of the research object, prediction frequency, and hidden danger type, among which: The research object is for the entire project or for different bidding sections; Whether the forecast frequency is for weekly or monthly hidden danger statistics; The hidden danger type is a safety hidden danger or other type of hidden danger; Then statistically analyze the corresponding hidden danger frequency; The frequency of hidden dangers Xi in this bidding section of the research object project this week (this month) and the frequency of hidden dangers Yi in other bidding sections last week (last month) will be statistically analyzed; Step 2: Construct the joint probability density function f X,Y (x,y): First, select the Copula function that is suitable for the joint distribution characteristics of Xi and Yi; Then estimate the marginal distribution F of Xi and Yi x (x i ) and F Y (y i ), and convert it into the inverse cumulative distribution function U and V of the standard normal distribution, and calculate the correlation coefficient ρ between U and V; Finally, based on the Copula function, the joint probability density function f of the hidden danger data of this section this week (this month) and the hidden danger data of other sections last week (last month) is determined. X,Y (x,y); Step 3: Determine the most likely range and maximum value of hidden danger symptoms: Obtain the probability density function f of the number of hidden dangers in this section this week (this month) under the condition of hidden danger data B of other sections last week (last month) X|Y (x|B), and the cumulative distribution function (CDF) of the conditional probability density function F X|Y (x|B), and then obtain the most likely interval and the most likely value of the hidden danger symptom.

2. The risk prediction application method based on the joint probability distribution model of the frequency of tunnel construction safety hazards in claim 1 is characterized by: Includes step 4: Step 4: Based on the weekly (monthly) frequency distribution of all engineering predecessors, they are divided into five levels based on different exceedance probabilities, and the most likely result predicted by the joint probability distribution model is used to give the final risk level.

Images