CN115510566B - Subway station earthquake damage early warning method and system based on improved logistic regression - Google Patents
Subway station earthquake damage early warning method and system based on improved logistic regression Download PDFInfo
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Abstract
The invention provides a subway station earthquake damage early warning method and system based on improved logistic regression, which comprises the following steps: step 1: establishing a finite element model for a target working condition; and 2, step: establishing an input parameter sample set and a corresponding finite element model; and step 3: defining a damage state, and endowing a label value for the finite element model; and 4, step 4: establishing a logistic regression function related to each damage state, wherein the cross entropy coefficient in the Loss of the logistic regression function is A, and the regularization term coefficient is B; and 5: obtaining optimal values of A and B for each damage state using a Gaussian regression process; and 6: obtaining a logistic regression function of each damage state based on the optimal value in the step 5; and 7: and outputting the damage state of the most serious subway station as alarm information, and if not, quitting. The method considers parameter variability, adopts improved logistic regression advanced early warning on the earthquake damage state of the subway station, and guarantees the operation safety of the subway station.
Description
Technical Field
The invention relates to the field of subway station safety, in particular to a subway station earthquake damage early warning method and system based on improved logistic regression.
Background
Underground engineering is a favorable means for promoting urbanization development and relieving land tension. At present, subway stations become important components of city lifelines. When an earthquake disaster occurs, damage and destruction of a subway station may cause serious economic loss and even casualties. Therefore, how to early warn the damage degree of the subway station under the earthquake so as to take emergency measures in time becomes a problem to be solved urgently in the safety field of the subway station.
The subway station and the surrounding soil body have interaction, so that a plurality of parameters influencing the damage degree of the subway station under the earthquake exist, and the plurality of parameters have uncertainty. The traditional theoretical analysis method has lower precision, and the Monte Carlo sampling method has overlarge time consumption. Therefore, an improved logistic regression-based subway station earthquake damage early warning method and system are urgently needed.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method solves the problems that the precision is low and the time consumption is too large when the damage degree of the subway station under the earthquake is predicted in the prior art.
The technical solution of the invention is as follows: the subway station earthquake damage early warning method based on improved logistic regression comprises the following steps:
step 1: and establishing a subway station finite element model based on the parameter standard value for the target working condition.
Step 2: according to the subway station parameters, the load parameters and the seismic parameter standard values and the respective distribution, monte Carlo sampling is adopted to establish an input parameter sample set of the subway station parameters, the load parameters and the seismic parameters, and a corresponding finite element model is established for each input parameter sample.
And 3, step 3: defining four damage states according to the damage severity of the subway station and setting a damage threshold value for each damage state, judging that the subway station reaches the damage state and giving a Label value Label =1 when the damage index of the subway station exceeds the damage threshold value set by the damage state under the earthquake for each damage state, and judging that the subway station does not reach the damage state and giving the Label value Label =0 if the damage index does not exceed the damage threshold value set by the damage state.
And 4, step 4: for each damage state, python is adopted to establish a logistic regression function g (z) related to the damage state, the Loss of the logistic regression function adopts cross entropy and introduces a regularization term, and the calculation formula of the Loss is as follows:
in the formula, N represents the number of finite element model samples of the subway station,
representing the tag value of the subway station in the ith finite element model about the damage state, wherein m represents the number of input parameters, and the number of the input parameters is greater than or equal to>
The weight value of the jth input parameter is represented, A represents the coefficient of the cross entropy, and B represents the coefficient of the regularization term. g (z) i ) The logistic regression function corresponding to the input parameter sample in the ith finite element model is represented by the following formula: />
In the formula x ij Representing the value of the jth input parameter in the ith finite element model.
And 5: k points are uniformly selected in the defined domain of A and B to form K multiplied by K coefficient combination points, any p coefficient combination points are taken as observation points, the Loss corresponding to the p coefficient combination points is calculated, and the random value Loss of the other K multiplied by K-p coefficient combination points is generated by adopting Gaussian process regression s Repeating the Gaussian regression process q times to generate q lost points for K multiplied by K-p coefficient combination points s Record the Loss of each Gaussian regression process s The coefficient combination point corresponding to the minimum value of (2) is counted, and the Loss is obtained by counting K multiplied by K-p coefficient combination points s And selecting the coefficient combination point with the maximum frequency as a newly added observation point, and calculating the corresponding Loss.
Step 6: and repeating the step 5 to continuously add new observation points until the number of the observation points reaches the specified number, stopping adding the observation points, and selecting A and B corresponding to the Loss minimum value in the known observation points as the optimal values of A and B related to the damage state.
And 7: based on the optimal values of a and B for each damage state in step 6, an optimal weight combination for each damage state is calculated:
in the formula
The weight value vector representing the corresponding input parameter at the optimum value of A and B, when Loss takes the minimum value, will be ^ based on the injury status>
And substituting the logistic regression function to obtain the logistic regression function of each damage state.
And 8: when an earthquake occurs, inputting corresponding earthquake parameters into the logistic regression function of each damage state, calculating the probability that the subway station reaches each damage state, if the probability exceeds a set probability threshold value, judging that the subway station reaches the damage state, outputting the damage state of the most serious degree reached by the subway station as alarm information, and otherwise, quitting.
Further, the subway station parameters in the step 2 include subway station structure material parameters and subway station surrounding soil parameters.
Further, in the step 2, according to the subway station parameters, the load parameters, the seismic parameter standard values and the respective distribution: subway station parameters obey logarithmic normal distribution, load parameters obey normal distribution, and earthquake parameters obey uniform distribution.
Further, the four damage states in step 3 include: mild injury, moderate injury, severe injury, and disfigurement injury.
Further, in the step 3, the damage index of the subway station under the earthquake is determined by adopting a two-parameter damage model.
Further, the random value Loss of the other K multiplied by K-p coefficient combination points in the step 5 s The acquisition mode is as follows:
calculating a covariance matrix of the observation points, wherein elements in the covariance matrix are calculated by adopting a Gaussian kernel function;
loss of the remaining K-p coefficient combination points s Obeying a Gaussian distribution for K x K-pCalculating covariance vectors of the point and the observation point by adopting a Gaussian kernel function at any point in the coefficient combination points, and calculating a Gaussian distribution parameter of the point based on the covariance matrix of the observation point and the covariance vectors of the point and the observation point;
loss based on K x K-p coefficient combination points by adopting Monte Carlo method s Obtaining the random value Loss of K multiplied by K-p sample points by the obeyed Gaussian distribution s 。
The subway station earthquake damage early warning system based on improved logistic regression comprises an information acquisition module, a processing module and an early warning module;
the information acquisition module is used for acquiring subway station parameters, load parameters and earthquake parameters;
the processing module is used for acquiring an input parameter sample set according to the distribution of the subway station parameters, the load parameters and the seismic parameters acquired by the information acquisition module, establishing a corresponding finite element model and calculating a label value related to each damage state; taking the input parameter sample set and the label value related to each damage state as a data set to train a logistic regression function of each damage state; adopting a Gaussian process to regress and optimize coefficients of cross entropy and regularization items in loss of a logistic regression function; and calculating the probability of the subway station reaching each damage state under the earthquake based on the logistic regression function of each damage state.
The early warning module is used for judging whether the probability that the underground railway station reaches each damage state exceeds a set probability threshold value or not, if so, judging that the underground railway station reaches the damage state, outputting the damage state of the maximum severity degree reached by the underground railway station as alarm information, and otherwise, quitting.
Compared with the prior art, the invention has the advantages that:
according to the scheme provided by the embodiment of the invention, the parameter uncertainty and the interaction between the subway station and the soil body are considered, and a finite element method, a logistic regression method and a Gaussian process regression method are combined; irrelevant parameters in a plurality of input parameters are removed efficiently, the model training efficiency and effect are effectively improved, and then an improved logistic regression model of the damage of the subway station under the earthquakes of different grades related to various damage states is established. The method provides powerful means for earthquake damage early warning of the subway station; the analysis method is clear and has strong reliability.
Drawings
Fig. 1 is a schematic flow chart of a subway station earthquake damage early warning method based on improved logistic regression according to an embodiment of the present invention.
Detailed Description
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the subway station earthquake damage early warning method based on improved logistic regression provided by the embodiment of the invention is shown, and includes the following steps:
s101: and establishing a subway station finite element model based on the parameter standard value for the target working condition.
S102: and adopting Monte Carlo sampling to establish an input parameter sample set of subway station parameters, load parameters and seismic parameters, and establishing a corresponding finite element model for each input parameter sample. The subway station parameters comprise station structure material parameters and soil body parameters around the station. Subway station parameters obey lognormal distribution, load parameters obey normal distribution, and earthquake parameters obey uniform distribution.
S103: the damage index D of the subway station under the earthquake is determined by adopting a two-parameter damage model, and the formula of the D is as follows:
in the formula y 1 For maximum elastic deformation of the member under the action of an earthquake, y 2 Is the ultimate deformation of the member, and epsilon is the action of the member in the earthquakeCumulative hysteresis energy consumption, epsilon, under use u And the energy is consumed for the component at the utmost. Defining four damage states of a light damage, a medium damage, a severe damage and a damaged damage for the subway station according to the damage severity, setting a damage threshold value for each damage state, judging that the subway station reaches the damage state and endowing a Label value Label =1 when the damage index of the subway station under the earthquake exceeds the damage threshold value set by the damage state for each damage state, and judging that the subway station does not reach the damage state and endowing the Label value Label =0 if the damage index does not exceed the damage threshold value set by the damage state.
S104: for each damage state, python is adopted to establish a logistic regression function g (z) related to the damage state, the Loss of the logistic regression function adopts cross entropy and introduces a regularization term, and the calculation formula of the Loss is as follows:
in the formula, N represents the number of finite element model samples of the subway station,
representing the tag value of the subway station in the ith finite element model about the damage state, wherein m represents the number of input parameters, and the number of the input parameters is greater than or equal to>
Represents the weight value of the jth input parameter, a represents the coefficient of the cross entropy, and B represents the coefficient of the regularization term. g (z) i ) The logistic regression function corresponding to the input parameter sample in the ith finite element model is represented by the following formula:
in the formula x ij Representing the value of the jth input parameter in the ith finite element model.
S105: the optimal values of A and B are obtained by adopting Gaussian process regression, and the process is as follows:
(1) k points are uniformly selected in the definition domain of A and B to form K multiplied by K coefficient combination points, p coefficient combination points are randomly selected as observation points, the Loss corresponding to the p coefficient combination points is calculated, and elements in a covariance matrix C of the observation points are calculated by adopting a Gaussian kernel function;
(2) loss for the remaining K-p coefficient combination points s Loss of the K multiplied by K-p coefficient combination points obtained by adopting Monte Carlo sampling s And (3) obeying Gaussian distribution, wherein for any point (A, B) in the K multiplied by K-p coefficient combination points, the parameters of the Gaussian distribution are mu and sigma:
in the formula
For covariance vectors between (A, B) points and observation points, a Gaussian kernel function is used to calculate->
Middle element, L is the Loss vector of the observation point, and is based on the value of the line>
The autocorrelation coefficient takes a value of 1;
(3) repeating the step (2) to generate the Loss of K multiplied by K-p coefficient combination points s Gaussian distribution parameter of (2). Loss based on K x K-p coefficient combination points by adopting Monte Carlo method s Obtaining the random value Loss of K multiplied by K-p sample points by the obeyed Gaussian distribution s And recording Loss in the sampling result s A coefficient combination point corresponding to the minimum value of (a);
(4) repeating the step (3) for q times by adopting Monte Carlo sampling, and counting K multiplied by K-p coefficient combination points to obtain Loss s Selecting a coefficient combination point with the maximum frequency as a newly increased observation point, and calculating the corresponding Loss;
(5) and (4) repeating the steps (2) to (4) to continuously increase the observation points, stopping increasing the observation points when the number of the observation points reaches the specified number, and selecting A and B corresponding to the Loss minimum value in the known observation points as the optimal values of A and B related to the damage state.
S106: based on the optimal values of a and B for each damage state in S105, an optimal weight combination for each damage state is calculated:
in the formula
The weight value vector representing the corresponding input parameter at the optimum value of A and B, when Loss takes the minimum value, will be ^ based on the injury status>
And substituting the logistic regression function to obtain the logistic regression function of each damage state.
S107: when an earthquake occurs, inputting corresponding earthquake parameters into the logistic regression function of each damage state, calculating the probability that the subway station reaches each damage state, if the probability exceeds a set probability threshold value, judging that the subway station reaches the damage state, outputting the damage state of the most serious degree reached by the subway station as alarm information, and otherwise, quitting.
According to the scheme provided by the embodiment of the invention, the parameter uncertainty and the interaction between the subway station and the soil body are considered, and the finite element method, the logistic regression and the Gaussian process regression are combined, so that the damage state of the subway station under the earthquake is efficiently and accurately predicted in advance, the early deployment of emergency measures by related managers according to the damage state of the subway station is facilitated, and the loss of the subway station under the earthquake load is reduced.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a component of' 8230; \8230;" does not exclude the presence of another like element in a process, method, article, or apparatus that comprises the element.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (7)
1. The subway station earthquake damage early warning method based on improved logistic regression is characterized by comprising the following steps of:
step 1: establishing a subway station finite element model based on a parameter standard value for a target working condition;
and 2, step: according to the subway station parameters, the load parameters and the seismic parameter standard values and the respective distribution, adopting Monte Carlo sampling to establish an input parameter sample set of the subway station parameters, the load parameters and the seismic parameters, and establishing a corresponding finite element model for each input parameter sample;
and step 3: defining four damage states according to the damage severity degree for the subway station and setting a damage threshold value for each damage state, judging that the subway station reaches the damage state and endowing a Label value Label =1 when the damage index of the subway station exceeds the damage threshold value set by the damage state under the earthquake for each damage state, and judging that the subway station does not reach the damage state and endowing the Label value Label =0 if the damage index does not exceed the damage threshold value set by the damage state;
and 4, step 4: for each damage state, python is adopted to establish a logistic regression function g (z) related to the damage state, the Loss of the logistic regression function adopts cross entropy and introduces a regularization term, and the calculation formula of the Loss is as follows:
in the formula, N represents the number of finite element model samples of the subway station,
a tag value representing the damage state of the subway station in the ith finite element model is shown, m represents the number of input parameters, and the number of the input parameters is greater than or equal to>
Weight value representing jth input parameter, A represents coefficient of cross entropy, B represents coefficient of regularization term, g (z) i ) The formula of the logistic regression function corresponding to the input parameter sample in the ith finite element model is as follows:
in the formula x ij Representing the value of the jth input parameter in the ith finite element model;
and 5: k points are uniformly selected in the defined domain of A and B to form K multiplied by K coefficient combination points, any p coefficient combination points are taken as observation points, the Loss corresponding to the p coefficient combination points is calculated, and the random value Loss of the other K multiplied by K-p coefficient combination points is generated by adopting Gaussian process regression s Repeating the Gaussian regression process q times to generate q lost points for K multiplied by K-p coefficient combination points s Record the Loss of each Gaussian regression process s The coefficient combination point corresponding to the minimum value of (2) is counted, and the Loss is obtained by counting K multiplied by K-p coefficient combination points s Selecting a coefficient combination point with the maximum frequency as a newly added observation point, and calculating the corresponding Loss;
step 6: repeating the step 5 to continuously add new observation points until the number of the observation points reaches the specified number, stopping adding the new observation points, and selecting A and B corresponding to the Loss minimum value in the known observation points as the optimal values of A and B related to the damage state;
and 7: based on the optimal values of a and B for each damage state in step 6, an optimal weight combination for each damage state is calculated:
in the formula
The weight value vector representing the corresponding input parameter at the optimum value of A and B, when Loss takes the minimum value, will be ^ based on the injury status>
Introducing a logistic regression function to obtain the logistic regression function of each damage state;
and step 8: when an earthquake occurs, inputting corresponding earthquake parameters into the logistic regression function of each damage state, calculating the probability that the subway station reaches each damage state, if the probability exceeds a set probability threshold value, judging that the subway station reaches the damage state, outputting the damage state of the most serious degree reached by the subway station as alarm information, and otherwise, quitting.
2. A subway station earthquake damage early warning method based on improved logistic regression as claimed in claim 1, wherein said subway station parameters in step 2 include subway station structure material parameters and subway station surrounding soil parameters.
3. A subway station earthquake damage early warning method based on improved logistic regression as claimed in claim 1, wherein in said step 2 according to subway station parameters, load parameters, earthquake parameter standard values and their respective distribution: subway station parameters obey logarithmic normal distribution, load parameters obey normal distribution, and earthquake parameters obey uniform distribution.
4. A subway station earthquake damage early warning method based on improved logistic regression as claimed in claim 1, wherein said four damage states in step 3 include: mild injury, moderate injury, severe injury, and disfigurement injury.
5. The improved logistic regression-based subway station earthquake damage early warning method as claimed in claim 1, wherein in said step 3, the damage index of the subway station under earthquake is determined by using a two-parameter damage model.
6. The improved logistic regression-based earthquake damage early warning method for subway station as claimed in claim 1, wherein said step 5 is characterized in that said random value Loss of the other K x K-p coefficient combination points s The acquisition mode is as follows:
calculating a covariance matrix of the observation points, wherein elements in the covariance matrix are calculated by adopting a Gaussian kernel function;
loss of the other K x K-p coefficient combination points s Obeying Gaussian distribution, calculating a covariance vector of any point in the K multiplied by K-p coefficient combination points and an observation point by adopting a Gaussian kernel function, and calculating a Gaussian distribution parameter of the point based on a covariance matrix of the observation point and the covariance vector of the point and the observation point;
loss based on K x K-p coefficient combination points by adopting Monte Carlo method s Obtaining the random value Loss of K multiplied by K-p sample points by the obeyed Gaussian distribution s 。
7. The system formed by the subway station earthquake damage early warning method based on the improved logistic regression is characterized by comprising an information acquisition module, a processing module and an early warning module;
the information acquisition module is used for acquiring subway station parameters, load parameters and earthquake parameters;
the processing module is used for acquiring an input parameter sample set according to the distribution of the subway station parameters, the load parameters and the seismic parameters acquired by the information acquisition module, establishing a corresponding finite element model and calculating a label value related to each damage state; training a logistic regression function of each damage state by taking the input parameter sample set and the label value related to each damage state as a data set; adopting a Gaussian process to regress and optimize coefficients of cross entropy and regularization items in loss of a logistic regression function; calculating the probability of the subway station reaching each damage state under the earthquake based on the logistic regression function of each damage state;
the early warning module is used for judging whether the probability that the underground railway station reaches each damage state exceeds a set probability threshold value or not, if so, judging that the underground railway station reaches the damage state, outputting the damage state of the maximum severity degree reached by the underground railway station as alarm information, and otherwise, quitting.
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| CN114021236A (en) * | 2021-11-04 | 2022-02-08 | 哈尔滨工业大学 | Urban subway underground station anti-seismic toughness assessment method and equipment considering subsystem association |
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| CN114966832A (en) * | 2022-04-07 | 2022-08-30 | 西南交通大学 | Train earthquake disposal mode calculation method, device and equipment and readable storage medium |
| CN115099114A (en) * | 2022-07-18 | 2022-09-23 | 大连海事大学 | Underground structure fuzzy earthquake vulnerability calculation method based on multiple failure criteria |
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| CN114021236A (en) * | 2021-11-04 | 2022-02-08 | 哈尔滨工业大学 | Urban subway underground station anti-seismic toughness assessment method and equipment considering subsystem association |
| CN114065534A (en) * | 2021-11-22 | 2022-02-18 | 哈尔滨工业大学 | Method for determining post-earthquake restoration scheme of subway underground station |
| CN114491765A (en) * | 2022-02-15 | 2022-05-13 | 大连海事大学 | Earthquake risk analysis method for underground structure of subway station |
| CN114966832A (en) * | 2022-04-07 | 2022-08-30 | 西南交通大学 | Train earthquake disposal mode calculation method, device and equipment and readable storage medium |
| CN115099114A (en) * | 2022-07-18 | 2022-09-23 | 大连海事大学 | Underground structure fuzzy earthquake vulnerability calculation method based on multiple failure criteria |
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