A bridge scouring risk calculation formula optimization method, device and medium considering parameter value randomness

Abstract

The application discloses a bridge scour risk calculation formula optimization method and device considering parameter value randomness, equipment and medium, containing a scour data set, determining the distribution characteristics of scour calculation parameters; a scour calculation basic formula is constructed, a correction item training target is constructed; the expression of the candidate correction item is selected by symbolic regression, the to-be-optimized parameters are defined as random parameters, and a candidate scour model is established; a posterior scour calculation formula corresponding to the optimal model is obtained; a model correction factor distribution is determined, joint random samples of input parameters, posterior random parameters and model correction factors are generated, and scour safety margin and scour failure probability are calculated; a corresponding relationship between a risk safety coefficient and a failure probability is established, a target risk safety coefficient is determined, and a bridge scour risk calculation formula is formed. The application simultaneously considers input parameter randomness, model parameter posterior uncertainty and model correction factor uncertainty, and improves the applicability and risk control capability of the bridge scour calculation formula.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering and water conservancy technology, and particularly relates to an optimization method, equipment and medium for calculating bridge scour risk considering the randomness of parameter values. Background Technology

[0002] Bridge scour is one of the main causes of bridge failure. Currently, the prediction of bridge scour depth mainly relies on empirical formulas. However, these traditional calculation methods have the following problems: existing scour calculation formulas are mostly based on regression fitting under specific experimental conditions, which are limited by the amount of research data and the formula shape-finding method, and have limited adaptability to different geographical conditions and bridge site characteristics.

[0003] Furthermore, existing methods typically use deterministic parameters for calculation, ignoring the randomness and uncertainty of hydrological and hydraulic parameters, leading to deviations between predicted results and actual conditions; the determination of the scour safety factor lacks scientific quantitative basis and usually relies on engineering experience for estimation, making it difficult to accurately assess the true risk level of bridge scour; existing conventional methods are unable to make targeted optimizations and adjustments to the calculation formula based on the actual risk tolerance level of different bridge sites. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide an optimization method, device, and medium for bridge scour risk calculation formula that considers the randomness of parameter values. This invention can simultaneously consider the randomness of input parameters, the posterior uncertainty of model parameters, and the uncertainty of model correction factors, thereby improving the applicability and risk control capability of bridge scour calculation formula.

[0005] Technical Solution: To achieve the above objectives, this invention discloses an optimization method for calculating bridge scour risk that considers the randomness of parameter values, comprising the following steps: S1. Determine the required scour calculation parameters and denot them as the scour calculation parameter set; then construct a scour dataset consisting of multiple scour samples, each of which includes the measured scour depth and the scour calculation parameter set. S2. Construct the basic formula for scour calculation to be optimized; S3. Taking the basic formula for scour calculation to be optimized as the object to be corrected, construct a set of dimensionless variables from the set of scour calculation parameters, construct the training target of the correction term, and use symbolic regression to conduct a preliminary selection of the correction term expression to generate a set of candidate expressions. S4. Convert the candidate expressions in the candidate expression set into an acyclic computation graph consisting of operation nodes, variable nodes, and constant nodes to be optimized, and define the constant to be optimized in the acyclic computation graph as a random parameter; establish the corresponding prior distribution based on the initial value of the constant to be optimized. S5. The sequential Monte Carlo method is used to perform Bayesian inference and model optimization on the random parameters of each candidate expression, determine the optimal correction term and its posterior distribution of random parameters, and form the optimal scour model as the posterior scour calculation formula. S6. Based on the optimal scour model and scour dataset, determine the distribution of the model correction factor, the distribution of scour calculation parameters, the posterior distribution of the random parameters of the optimal correction term, and the corresponding cumulative distribution function. S7. Select the risk safety factor, generate a joint random sample consisting of the model correction factor, random scour calculation parameters and the random parameters of the optimal correction term, calculate the scour safety margin through random sampling, and obtain the set of scour failure probabilities under different candidate risk safety factors. S8. Establish the correspondence between risk safety factor and failure probability based on the set of scour failure probabilities under different candidate risk safety factors, determine the target risk safety factor based on the target allowable failure probability, and combine the target risk safety factor with the optimal scour model to establish a bridge scour risk calculation formula.

[0006] Optionally, step S2 specifically includes the following steps: The basic formula for scour calculation to be optimized is denoted as: Used to describe the predicted scour depth and pier width Upstream water depth Upstream flow velocity Gravitational acceleration HEC-18 correction factor And Freud The fundamental physical relationship between them, and the basic formula for scour calculation to be optimized. The expression is: , , Basic formula for scour calculation to be optimized The output value is the predicted scour depth.

[0007] Optionally, step S3 specifically includes the following steps: Based on the set of scour calculation parameters ,in The median particle size of the sediment is... Given the projected width of the bridge pier; construct a set of dimensionless variables. and will the The set of scour calculation parameters and the set of dimensionless variables corresponding to each scour sample are denoted as follows: and ; with the first Measured scour depth of a single scour sample Basic formula for scour calculation The ratio of the output values ​​is used as the first Training objective for the correction term corresponding to each flushing sample The expression is: , The training objective is to modify the correction terms of each flushing sample. and the set of dimensionless variables Constitutes the sample pair set And define this set of sample pairs as the training dataset for the correction term. ; train the dataset with the correction term Input a symbolic regression model; in the symbolic regression model, first define an expression search space, which consists of dimensionless variables, constants to be optimized, addition, subtraction, multiplication, division, and logarithmic operations; perform iterative optimization within the expression search space, and each symbolic regression run outputs the optimal candidate expression sequence arranged from low to high complexity, where the complexity is the sum of the number of dimensionless variables, constants to be optimized, and operators in the expression; Repeatedly run using different random seeds Secondary symbolic regression forms a candidate expression set. ,in, Indicates the first The function structure of candidate expressions, For the first The constant vector to be optimized for the candidate expression includes the constant vector to be optimized for the . Initial values ​​for all constants to be optimized in the candidate expressions; candidate expressions are used to express the training objective of the correction term. and the set of dimensionless variables The functional relationship.

[0008] Optionally, step S4 specifically includes the following steps: Candidate expressions Transform into an acyclic computation graph consisting of computation nodes, variable nodes, and constant nodes to be optimized. In this context, the operation nodes correspond to addition, subtraction, multiplication, division, or logarithmic operations, while the variable nodes correspond to a set of dimensionless variables. The dimensionless variables in the expression, and the constant nodes to be optimized, correspond to the constants to be optimized in the candidate expressions. Acyclic computation graph The Middle The constant nodes to be optimized are defined as random parameters. To obtain a random parameter vector ,in, For the first The number of constants to be optimized in each candidate expression; The obtained first Initial values ​​of the constants to be optimized Centered on random parameters We set a uniform prior distribution, where... The constant vector to be optimized The Middle Initial values ​​for the constants to be optimized: , in, Indicates the interval Evenly distributed on top; Therefore, the acyclic computation graph The corresponding candidate expression is ,in, For the first All random parameters in the candidate expressions.

[0009] Optionally, step S5 specifically includes the following steps: Assuming the training objective of the correction term With the candidate expressions Satisfy the following expression: , , in, For the first The candidate expression for the _th The error of each flushed sample, This indicates that the mean is 0 and the variance is 0. Normal distribution; standard deviation of error Defined as a positive random variable, with error standard deviation The prior distribution is: ; For the 10 candidate expressions, used as the training dataset for the correction term. For the observation data, the sequential Monte Carlo method is used to analyze the random parameters. and standard deviation of error Perform Bayesian inference to obtain random parameters. posterior distribution Error standard deviation posterior distribution and model marginal likelihood ; Repeat the Bayesian inference process for all candidate expressions, and select the candidate expression number with the highest marginal likelihood of the model according to the following formula: , Number The random parameter vector in the corresponding candidate expression is denoted as and candidate expressions The optimal correction term is determined, where the random parameter vector is... Follows the posterior distribution ; Based on the scour calculation formula to be optimized and the optimal correction term A posterior scour calculation formula is derived, which constitutes the optimal scour model. : , in, This indicates that the optimal scour model The calculated scour depth was obtained.

[0010] Optionally, step S6 specifically includes the following steps: Based on the optimal scouring model obtained in step S5 Determine the distribution of the model correction factor: For flushing datasets The Middle A flushing sample, with a random parameter vector posterior mean vector Substitute into the optimal scour model Calculate the predicted value of scour depth : , The first is determined according to the ratio of the measured scour depth to the predicted scour depth. Model correction factor samples corresponding to each flushing sample : , Based on the sample set of model correction factors Estimate the mean and coefficient of variation of the model correction factor, and determine the cumulative distribution function of the model correction factor using a pre-defined parameterized distribution. The cumulative distribution function represents the probability that a variable takes a value less than or equal to a certain value; the model correction factor... It follows a normal distribution, and its mean is denoted as . The coefficient of variation is The standard deviation is Model correction factor The cumulative distribution function is: , in, The cumulative distribution function of the standard normal distribution. The model correction factor is set to a value for the probability to be calculated; According to the scour dataset Determine the set of scour calculation parameters Distribution of various scour calculation parameters in the middle: The sample mean and sample standard deviation of each random scour calculation parameter were statistically analyzed, and the coefficient of variation was calculated by the ratio of the sample standard deviation to the sample mean; among which, the pier width pier projection width and gravitational acceleration For deterministic variables, the upstream water depth Following a normal distribution, the upstream flow velocity and median particle size of sediment It follows a log-normal distribution; for the th Let there be a random scouring calculation parameter, and its mean be denoted as . The coefficient of variation is Standard deviation is ; If the parameters for calculating random erosion follow a normal distribution, then its cumulative distribution function... for: , If the random scouring calculation parameters follow a log-normal distribution, then first set the mean... and coefficient of variation Parameters converted to logarithmic space and : , , Its cumulative distribution function for: , In step S5, the sequential Monte Carlo inference has given random parameters. posterior distribution ,set up For random parameter vectors The first in Let be random parameters, and let the posterior sample output by the sequential Monte Carlo method be denoted as . hour, Corresponding cumulative distribution function It can be represented as the following function: , in, For random parameter vectors The number of any parameter component in the equation. For the first step used to calculate the cumulative probability The values ​​of each random parameter, Indicates the first The random parameters are less than or equal to The posterior probability; This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. This represents the total number of posterior samples.

[0011] Optionally, step S7 specifically includes the following steps: Select a set of candidate risk safety coefficients ,in, The number of candidate risk safety factors; the set of scour calculation parameters for the bridge site to be designed is denoted as... ,Depend on Construct a set of dimensionless variables ; Optimal scour model adopted posterior mean vector Calculate the representative value of the scour depth at the bridge site to be designed. The expression is: , For the Each candidate risk safety coefficient The corresponding candidate risk control scouring depth Defined as: , The inverse transform method is used to generate samples of each random variable. The inverse transform method refers to first generating... arrive A uniformly random number between these points is used, which is then considered as the cumulative probability position on the target distribution. The variable value corresponding to this probability position is then found through the inverse function of the cumulative distribution function. For the cumulative distribution function... Its inverse function is The expression is: , in, Represents the cumulative probability of random generation. Represents the candidate values ​​of the target random variable; This indicates that the cumulative probability in the target distribution reaches The corresponding variable value; symbol Indicates that all conditions are met. Candidate values Select the minimum value from the cumulative distribution curve, that is, find the first value on the cumulative distribution curve that makes the cumulative probability not less than 1. The variable value; In specific sampling... These correspond to the values ​​of the model correction factors. , No. The values ​​of the random scouring calculation parameters are as follows: or the Each random parameter value ; to proceed with the first During the random sampling, each random flushing calculation parameter is numbered. and each random parameter number Generate independent uniform random numbers respectively and And generate uniform random numbers for the model correction factor. The inverse transform method is used to generate the model correction factor, random input parameters, and random parameter samples respectively: , , , in, For the first The random scouring calculation parameters are in the first... The value taken from the second sample. For the first The random parameter at the th in the th The value taken from the second sample. For the first The model correction factor obtained from the second sampling; composed of the sampled values ​​of the random flushing calculation parameters and the designed values ​​of the deterministic input parameters. Set of parameters for flushing calculation in the sub-sampling , by random parameter vector The sampling results of each parameter component constitute the first... Random parameter vector sample from the second sampling and according to the first Set of parameters for flushing calculation in the sub-sampling Construct a set of dimensionless variables Calculate the first The scour depth corresponding to the next sampling: , In the In the random sampling, calculate the... Safety margin samples corresponding to candidate risk safety coefficients : , For the Repeat the above random sampling for each candidate risk safety factor. Next, we obtain the safety margin sample set. Based on whether the safety margin sample is less than or equal to zero, the statistics are calculated for the first... The probability of scouring failure corresponding to each candidate risk safety factor: , in, For the first The probability of scouring failure corresponding to each candidate risk safety factor For indicator functions, For the number of random samples; when Time to determine the first The second sampling resulted in scour failure; the above process was repeated for all candidate risk safety factors to obtain the set of scour failure probabilities under different candidate risk safety factors. .

[0012] Optionally, step S8 specifically includes the following steps: Based on the set of scour failure probabilities under different candidate risk safety coefficients The relationship between the risk safety factor and the probability of scour failure is established by fitting a polynomial in the following form: , in, Let be the order of the polynomial. The first is obtained by fitting the set of scour failure probabilities under different candidate risk safety factors. Polynomial coefficients of order 1 Representation of failure probability The corresponding risk safety factor; when the allowable failure probability of the target is At that time, the target risk safety factor is set. ; target risk safety factor Substituting into the posterior scour calculation formula, we obtain the formula for calculating bridge scour risk: , in, Indicates the probability of failure of the target. Risk control scour depth determined under constraints.

[0013] This invention discloses an electronic device, including a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0014] The present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0015] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) This invention uses the HEC-18 pier local scour formula as the basic framework and constructs uncertainty correction terms through dimensionless variables, so that the optimized scour calculation formula has both basic physical relationship and data correction capability, avoiding insufficient applicability caused by relying entirely on empirical fitting. (2) The present invention uses symbolic regression to select candidate correction terms in the expression space composed of dimensionless variables and basic operations, which can form candidate correction terms with large structural differences, reduce the subjectivity brought about by manually pre-setting the form of correction terms, and convert the candidate expressions into acyclic computation graphs for random parameter modeling. While retaining the explicit mathematical structure, it incorporates parameter uncertainty and observation error into the model inference, so that the correction term structure has interpretability and uncertainty propagation capability. (3) The present invention uses the sequential Monte Carlo method to perform Bayesian inference and model selection on candidate scour models, which can obtain the posterior scour calculation formula when there is uncertainty in the model parameters, and uses the marginal likelihood of the model as the basis for candidate model selection, thereby improving the objectivity of the model selection process. (4) This invention incorporates the randomness of input parameters, the posterior uncertainty of model parameters, and model error into the calculation of scour safety margin and failure probability through model correction factor, inverse transformation random sampling, and Monte Carlo simulation, making the bridge scour risk assessment results more consistent with actual uncertainty conditions; the risk safety coefficient is determined according to the target allowable failure probability, and a bridge scour risk calculation formula is established, which can provide a quantitative basis for determining the scour depth of bridge foundations under different risk control requirements, and improve the reliability of scour protection design and safety assessment.

[0016] (5) This invention can reduce engineering costs caused by over-design while ensuring the safety of bridge foundations by calibrating the bridge scour risk calculation formula with high precision, quantifying the uncertainty of input parameters, and optimizing the safety factor to match the engineering risk level. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the process of converting candidate formulas into acyclic graphs and optimizing the selection in this invention; Figure 3 This is a schematic diagram illustrating the relationship between failure probability and safety factor in this invention. Detailed Implementation

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0019] like Figure 1 As shown, this invention discloses an optimization method for calculating bridge scour risk considering the randomness of parameter values, comprising the following steps: S1. Determine the required scour calculation parameters, including the pier width. pier projection width Upstream water depth Upstream flow velocity Gravitational acceleration and median particle size of sediment All scour calculation parameters are denoted as the scour calculation parameter set. , ; Reconstruct by The scour dataset consists of scour samples. Each scour sample includes the measured scour depth. and scour calculation parameter set , flushing the dataset Recorded as , For the first One scouring sample, The number of samples to be flushed. .

[0020] S2. Based on the HEC-18 pier local scour formula, construct the basic formula for scour calculation to be optimized.

[0021] Step S2 specifically includes the following steps: The basic formula for scour calculation to be optimized is denoted as: Used to describe the predicted scour depth and pier width Upstream water depth Upstream flow velocity Gravitational acceleration HEC-18 correction factor And Freud The fundamental physical relationship between them, and the basic formula for scour calculation to be optimized. The expression is: , , Basic formula for scour calculation to be optimized The output value is the predicted scour depth.

[0022] S3, the basic formula for scour calculation to be optimized. The object to be corrected is determined by the set of scour calculation parameters. Construct a set of dimensionless variables A training objective for the correction term is constructed, and symbolic regression is used to perform a preliminary screening of the correction term expression to generate a candidate expression set. .

[0023] Step S3 specifically includes the following steps: Based on the set of scour calculation parameters ,in The median particle size of the sediment is... Given the projected width of the bridge pier; construct a set of dimensionless variables. and will the The set of scour calculation parameters and the set of dimensionless variables corresponding to each scour sample are denoted as follows: and ; with the first Measured scour depth of a single scour sample Basic formula for scour calculation The ratio of the output values ​​is used as the first Training objective for the correction term corresponding to each flushing sample The expression is: , The training objective is to modify the correction terms of each flushing sample. and the set of dimensionless variables Constitutes the sample pair set And define this set of sample pairs as the training dataset for the correction term. ; train the dataset with the correction term Input a symbolic regression model; in the symbolic regression model, first define an expression search space, which consists of dimensionless variables, constants to be optimized, addition, subtraction, multiplication, division, and logarithmic operations; perform iterative optimization within the expression search space, and each symbolic regression run outputs the optimal candidate expression sequence arranged from low to high complexity, where the complexity is the sum of the number of dimensionless variables, constants to be optimized, and operators in the expression; Repeatedly run using different random seeds Secondary symbolic regression forms a candidate expression set. ,in, Indicates the first The function structure of candidate expressions, For the first The constant vector to be optimized for the candidate expression includes the constant vector to be optimized for the . Initial values ​​for all constants to be optimized in the candidate expressions; candidate expressions are used to express the training objective of the correction term. and the set of dimensionless variables The functional relationship.

[0024] S4. Set the candidate expressions The first in candidate expressions Transform it into an acyclic computation graph consisting of computation nodes, variable nodes, and constant nodes to be optimized. The constant to be optimized in the acyclic computation graph is defined as a random parameter. ; Establish the corresponding prior distribution based on the initial value of the constant to be optimized.

[0025] like Figure 2 As shown, step S4 specifically includes the following steps: Candidate expressions Transform into an acyclic computation graph consisting of computation nodes, variable nodes, and constant nodes to be optimized. In this context, the operation nodes correspond to addition, subtraction, multiplication, division, or logarithmic operations, while the variable nodes correspond to a set of dimensionless variables. The dimensionless variables in the expression, and the constant nodes to be optimized, correspond to the constants to be optimized in the candidate expressions. Acyclic computation graph The Middle The constant nodes to be optimized are defined as random parameters. To obtain a random parameter vector ,in, For the first The number of constants to be optimized in each candidate expression; The obtained first Initial values ​​of the constants to be optimized Centered on random parameters We set a uniform prior distribution, where... The constant vector to be optimized The Middle Initial values ​​for the constants to be optimized: , in, Indicates the interval Evenly distributed on top; Therefore, the acyclic computation graph The corresponding candidate expression is ,in, For the first All random parameters in the candidate expressions.

[0026] S5. Using the sequential Monte Carlo method, Bayesian inference and model optimization are performed on the random parameters of each candidate expression to determine the optimal correction term and its posterior distribution of random parameters, thus forming the optimal scour model as the posterior scour calculation formula. .

[0027] like Figure 2 As shown, step S5 specifically includes the following steps: Assuming the training objective of the correction term With the candidate expressions Satisfy the following expression: , , in, For the first The candidate expression for the _th The error of each flushed sample, This indicates that the mean is 0 and the variance is 0. Normal distribution; standard deviation of error Defined as a positive random variable, with error standard deviation The prior distribution is: ; For the 10 candidate expressions, used as the training dataset for the correction term. For the observation data, the sequential Monte Carlo method is used to analyze the random parameters. and standard deviation of error Perform Bayesian inference to obtain random parameters. posterior distribution Error standard deviation posterior distribution and model marginal likelihood ; Repeat the Bayesian inference process for all candidate expressions, and select the candidate expression number with the highest marginal likelihood of the model according to the following formula: , Number The random parameter vector in the corresponding candidate expression is denoted as and candidate expressions The optimal correction term is determined, where the random parameter vector is... Follows the posterior distribution ; Based on the scour calculation formula to be optimized and the optimal correction term A posterior scour calculation formula is derived, which constitutes the optimal scour model. : , in, This indicates that the optimal scour model The calculated scour depth was obtained.

[0028] S6, Based on the optimal scouring model and flushing dataset The distributions of the model correction factor, the scour calculation parameters, the posterior distribution of the random parameters of the optimal correction term, and the corresponding cumulative distribution function are determined.

[0029] Step S6 specifically includes the following steps: Based on the optimal scouring model obtained in step S5 Determine the distribution of the model correction factor: For flushing datasets The Middle A flushing sample, with a random parameter vector posterior mean vector Substitute into the optimal scour model Calculate the predicted value of scour depth : , The first is determined according to the ratio of the measured scour depth to the predicted scour depth. Model correction factor samples corresponding to each flushing sample : , Based on the sample set of model correction factors Estimate the mean and coefficient of variation of the model correction factor, and determine the cumulative distribution function of the model correction factor using a pre-defined parameterized distribution. The cumulative distribution function represents the probability that a variable takes a value less than or equal to a certain value; the model correction factor... It follows a normal distribution, and its mean is denoted as . The coefficient of variation is The standard deviation is Model correction factor The cumulative distribution function is: , in, The cumulative distribution function of the standard normal distribution. The model correction factor is set to a value for the probability to be calculated; According to the scour dataset Determine the set of scour calculation parameters Distribution of various scour calculation parameters in the middle: The sample mean and sample standard deviation of each random scour calculation parameter were statistically analyzed, and the coefficient of variation was calculated by the ratio of the sample standard deviation to the sample mean; among which, the pier width pier projection width and gravitational acceleration For deterministic variables, the upstream water depth Following a normal distribution, the upstream flow velocity and median particle size of sediment It follows a log-normal distribution; for the th Let there be a random scouring calculation parameter, and its mean be denoted as . The coefficient of variation is Standard deviation is ; If the parameters for calculating random erosion follow a normal distribution, then its cumulative distribution function... for: , If the random scouring calculation parameters follow a log-normal distribution, then first set the mean... and coefficient of variation Parameters converted to logarithmic space and : , , Its cumulative distribution function for: , In step S5, the sequential Monte Carlo inference has given random parameters. posterior distribution ,set up For random parameter vectors The first in Let be random parameters, and let the posterior sample output by the sequential Monte Carlo method be denoted as . hour, Corresponding cumulative distribution function It can be represented as the following function: , in, For random parameter vectors The number of any parameter component in the equation. For the first step used to calculate the cumulative probability The values ​​of each random parameter, Indicates the first The random parameters are less than or equal to The posterior probability; This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. This represents the total number of posterior samples.

[0030] S7. Select the risk safety factor, and use the inverse transformation method to generate a joint random sample consisting of the model correction factor, random scour calculation parameters and the random parameters of the optimal correction term. Calculate the scour safety margin through random sampling to obtain the scour failure probability under different candidate risk safety factors.

[0031] Step S7 specifically includes the following steps: Select a set of candidate risk safety coefficients ,in, The number of candidate risk safety factors; the set of scour calculation parameters for the bridge site to be designed is denoted as... ,Depend on Construct a set of dimensionless variables ; Optimal scour model adopted posterior mean vector Calculate the representative value of the scour depth at the bridge site to be designed. The expression is: , For the Each candidate risk safety coefficient The corresponding candidate risk control scouring depth Defined as: , The inverse transform method is used to generate samples of each random variable. The inverse transform method refers to first generating... arrive A uniformly random number between these points is used, which is then considered as the cumulative probability position on the target distribution. The variable value corresponding to this probability position is then found through the inverse function of the cumulative distribution function. For the cumulative distribution function... Its inverse function is The expression is: , in, Represents the cumulative probability of random generation. Represents the candidate values ​​of the target random variable; This indicates that the cumulative probability in the target distribution reaches The corresponding variable value; symbol Indicates that all conditions are met. Candidate values Select the minimum value from the cumulative distribution curve, that is, find the first value on the cumulative distribution curve that makes the cumulative probability not less than 1. The variable value; In specific sampling... These correspond to the values ​​of the model correction factors. , No. The values ​​of the random scouring calculation parameters are as follows: or the Each random parameter value ; to proceed with the first During the random sampling, each random flushing calculation parameter is numbered. and each random parameter number Generate independent uniform random numbers respectively and And generate uniform random numbers for the model correction factor. The inverse transform method is used to generate the model correction factor, random input parameters, and random parameter samples respectively: , , , in, For the first The random scouring calculation parameters are in the first... The value taken from the second sample. For the first The random parameter at the th in the th The value taken from the second sample. For the first The model correction factor obtained from the second sampling; composed of the sampled values ​​of the random flushing calculation parameters and the designed values ​​of the deterministic input parameters. Set of parameters for flushing calculation in the sub-sampling , by random parameter vector The sampling results of each parameter component constitute the first... Random parameter vector sample from the second sampling and according to the first Set of parameters for flushing calculation in the sub-sampling Construct a set of dimensionless variables Calculate the first The scour depth corresponding to the next sampling: , In the In the random sampling, calculate the... Safety margin samples corresponding to candidate risk safety coefficients : , For the Repeat the above random sampling for each candidate risk safety factor. Next, we obtain the safety margin sample set. Based on whether the safety margin sample is less than or equal to zero, the statistics are calculated for the first... The probability of scouring failure corresponding to each candidate risk safety factor: , in, For the first The probability of scouring failure corresponding to each candidate risk safety factor For indicator functions, For the number of random samples; when Time to determine the first The second sampling resulted in scour failure; the above process was repeated for all candidate risk safety factors to obtain the set of scour failure probabilities under different candidate risk safety factors. .

[0032] S8. Establish the correspondence between risk safety factors and failure probabilities based on the set of scour failure probabilities under different candidate risk safety factors, and determine the target allowable failure probability. Determine the target risk safety factor and the target risk safety factor With the optimal scour model Based on this, a formula for calculating bridge scour risk was established.

[0033] Step S8 specifically includes the following steps: Based on the set of scour failure probabilities under different candidate risk safety coefficients Establish the correspondence between the risk safety factor and the probability of scour failure, such as Figure 3 As shown, the probability of scouring failure and risk safety factor All are dimensionless coefficients.

[0034] The following polynomial form is used for fitting: , in, Let be the order of the polynomial. The first is obtained by fitting the set of scour failure probabilities under different candidate risk safety factors. Polynomial coefficients of order 1 Representation of failure probability The corresponding risk safety factor; when the allowable failure probability of the target is At that time, the target risk safety factor is set. ; target risk safety factor Substituting into the posterior scour calculation formula, we obtain the formula for calculating bridge scour risk: , in, Indicates the probability of failure of the target. Risk control scour depth determined under constraints.

[0035] The bridge scour risk calculation formula is used to directly calculate the scour depth for risk control, taking into account parameter randomness, posterior uncertainty of model parameters, and uncertainty of model correction factors.

[0036] To select a set of dimensionless variables middle As a dimensionless variable, the specific calculation formulas are optimized to obtain the optimal scour model. , , When the project requires a failure probability of 10 -3 The corresponding safety factor is 2.6. The formula for calculating the scour risk under this failure probability is: .

[0037] Example 2: This invention discloses an electronic device, including a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0038] Example 3: The present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

Claims

1. An optimization method for calculating bridge scour risk considering the randomness of parameter values, characterized in that, Includes the following steps: S1. Determine the required scour calculation parameters and record them as the scour calculation parameter set; Then, a scour dataset consisting of multiple scour samples is constructed, with each scour sample including the measured scour depth and a set of scour calculation parameters; S2. Construct the basic formula for scour calculation to be optimized; S3. Taking the basic formula for scour calculation to be optimized as the object to be corrected, construct a set of dimensionless variables from the set of scour calculation parameters, construct the training target of the correction term, and use symbolic regression to conduct a preliminary selection of the correction term expression to generate a set of candidate expressions. S4. Convert the candidate expressions in the candidate expression set into an acyclic computation graph consisting of operation nodes, variable nodes, and constant nodes to be optimized, and define the constant to be optimized in the acyclic computation graph as a random parameter; establish the corresponding prior distribution based on the initial value of the constant to be optimized. S5. The sequential Monte Carlo method is used to perform Bayesian inference and model optimization on the random parameters of each candidate expression, determine the optimal correction term and its posterior distribution of random parameters, and form the optimal scour model as the posterior scour calculation formula. S6. Based on the optimal scour model and scour dataset, determine the distribution of the model correction factor, the distribution of scour calculation parameters, the posterior distribution of the random parameters of the optimal correction term, and the corresponding cumulative distribution function. S7. Select the risk safety factor, generate a joint random sample consisting of the model correction factor, random scour calculation parameters and the random parameters of the optimal correction term, calculate the scour safety margin through random sampling, and obtain the set of scour failure probabilities under different candidate risk safety factors. S8. Establish the correspondence between risk safety factor and failure probability based on the set of scour failure probabilities under different candidate risk safety factors, determine the target risk safety factor based on the target allowable failure probability, and combine the target risk safety factor with the optimal scour model to establish a bridge scour risk calculation formula.

2. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​as described in claim 1, characterized in that, Step S2 specifically includes the following steps: The basic formula for scour calculation to be optimized is denoted as: Used to describe the predicted scour depth and pier width Upstream water depth Upstream flow velocity Gravitational acceleration HEC-18 correction factor And Freud The fundamental physical relationship between them, and the basic formula for scour calculation to be optimized. The expression is: ， ， Basic formula for scour calculation to be optimized The output value is the predicted scour depth.

3. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​according to claim 2, characterized in that, Step S3 specifically includes the following steps: Based on the set of scour calculation parameters ,in The median particle size of the sediment is... This refers to the projected width of the bridge pier. Construct a set of dimensionless variables and will the The set of scour calculation parameters and the set of dimensionless variables corresponding to each scour sample are denoted as follows: and ; with the first Measured scour depth of a single scour sample Basic formula for scour calculation The ratio of the output values ​​is used as the first Training objective for the correction term corresponding to each flushing sample The expression is: ， The training objective is to modify the correction terms of each flushing sample. and the set of dimensionless variables Constitutes the sample pair set And define this set of sample pairs as the training dataset for the correction term. ; train the dataset with the correction term Input a symbolic regression model; in the symbolic regression model, first define an expression search space, which consists of dimensionless variables, constants to be optimized, addition, subtraction, multiplication, division, and logarithmic operations; perform iterative optimization within the expression search space, and each symbolic regression run outputs the optimal candidate expression sequence arranged from low to high complexity, where the complexity is the sum of the number of dimensionless variables, constants to be optimized, and operators in the expression; Repeatedly run using different random seeds Secondary symbolic regression forms a candidate expression set. ,in, Indicates the first The function structure of candidate expressions, For the first The constant vector to be optimized for the candidate expression includes the constant vector to be optimized for the . Initial values ​​for all constants to be optimized in the candidate expressions; candidate expressions are used to express the training objective of the correction term. and the set of dimensionless variables The functional relationship.

4. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​according to claim 3, characterized in that, Step S4 specifically includes the following steps: Candidate expressions Transform into an acyclic computation graph consisting of computation nodes, variable nodes, and constant nodes to be optimized. In this context, the operation nodes correspond to addition, subtraction, multiplication, division, or logarithmic operations, while the variable nodes correspond to a set of dimensionless variables. The dimensionless variables in the expression, and the constant nodes to be optimized, correspond to the constants to be optimized in the candidate expressions. Acyclic computation graph The Middle The constant nodes to be optimized are defined as random parameters. To obtain a random parameter vector ,in, For the first The number of constants to be optimized in each candidate expression; The obtained first Initial values ​​of the constants to be optimized Centered on random parameters We set a uniform prior distribution, where... The constant vector to be optimized The Middle Initial values ​​for the constants to be optimized: ， in, Indicates the interval Evenly distributed on top; Therefore, the acyclic computation graph The corresponding candidate expression is ,in, For the first All random parameters in the candidate expressions.

5. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​according to claim 4, characterized in that, Step S5 specifically includes the following steps: Assuming the training objective of the correction term With the candidate expressions Satisfy the following expression: ， ， in, For the first The candidate expression for the _th The error of each flushed sample, This indicates that the mean is 0 and the variance is 0. Normal distribution; standard deviation of error Defined as a positive random variable, with error standard deviation The prior distribution is: ; For the 10 candidate expressions, used as the training dataset for the correction term. For the observation data, the sequential Monte Carlo method is used to analyze the random parameters. and standard deviation of error Perform Bayesian inference to obtain random parameters. posterior distribution Error standard deviation posterior distribution and model marginal likelihood ; Repeat the Bayesian inference process for all candidate expressions, and select the candidate expression number with the highest marginal likelihood of the model according to the following formula: ， Number The random parameter vector in the corresponding candidate expression is denoted as and candidate expressions The optimal correction term is determined, where the random parameter vector is... Follows the posterior distribution ; Based on the scour calculation formula to be optimized and the optimal correction term A posterior scour calculation formula is derived, which constitutes the optimal scour model. : ， in, This indicates that the optimal scour model The calculated scour depth was obtained.

6. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​according to claim 5, characterized in that: Step S6 specifically includes the following steps: Based on the optimal scouring model obtained in step S5 Determine the distribution of the model correction factor: For flushing datasets The Middle A flushing sample, with a random parameter vector posterior mean vector Substitute into the optimal scour model Calculate the predicted value of scour depth : ， The first is determined according to the ratio of the measured scour depth to the predicted scour depth. Model correction factor samples corresponding to each flushing sample : ， Based on the sample set of model correction factors Estimate the mean and coefficient of variation of the model correction factor, and determine the cumulative distribution function of the model correction factor using a pre-defined parameterized distribution. The cumulative distribution function represents the probability that a variable takes a value less than or equal to a certain value; the model correction factor... It follows a normal distribution, and its mean is denoted as . The coefficient of variation is The standard deviation is Model correction factor The cumulative distribution function is: ， in, The cumulative distribution function of the standard normal distribution. The model correction factor is set to a value for the probability to be calculated; According to the scour dataset Determine the set of scour calculation parameters Distribution of various scour calculation parameters in the middle: The sample mean and sample standard deviation of each random scour calculation parameter were statistically analyzed, and the coefficient of variation was calculated by the ratio of the sample standard deviation to the sample mean; among which, the pier width pier projection width and gravitational acceleration For deterministic variables, the upstream water depth Following a normal distribution, the upstream flow velocity and median particle size of sediment It follows a log-normal distribution; for the th Let there be a random scouring calculation parameter, and its mean be denoted as . The coefficient of variation is Standard deviation is ; If the parameters for calculating random erosion follow a normal distribution, then its cumulative distribution function... for: ， If the random scouring calculation parameters follow a log-normal distribution, then first set the mean... and coefficient of variation Parameters converted to logarithmic space and : ， ， Its cumulative distribution function for: ， In step S5, the sequential Monte Carlo inference has given random parameters. posterior distribution ,set up For random parameter vectors The first in Let be random parameters, and let the posterior sample output by the sequential Monte Carlo method be denoted as . hour, Corresponding cumulative distribution function It can be represented as the following function: ， in, For random parameter vectors The number of any parameter component in the equation. For the first step used to calculate the cumulative probability The values ​​of each random parameter, Indicates the first The random parameters are less than or equal to The posterior probability; This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. This represents the total number of posterior samples.

7. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​as described in claim 6, characterized in that: Step S7 specifically includes the following steps: Select a set of candidate risk safety coefficients ,in, The number of candidate risk safety factors; the set of scour calculation parameters for the bridge site to be designed is denoted as... ,Depend on Construct a set of dimensionless variables ; Optimal scour model adopted posterior mean vector Calculate the representative value of the scour depth at the bridge site to be designed. The expression is: ， For the Each candidate risk safety coefficient The corresponding candidate risk control scouring depth Defined as: ， The inverse transform method is used to generate samples of each random variable. The inverse transform method refers to first generating... arrive A uniformly random number between these points is used, which is then considered as the cumulative probability position on the target distribution. The variable value corresponding to this probability position is then found through the inverse function of the cumulative distribution function. For the cumulative distribution function... Its inverse function is The expression is: ， in, Represents the cumulative probability of random generation. Represents the candidate values ​​of the target random variable; This indicates that the cumulative probability in the target distribution reaches The corresponding variable value; symbol Indicates that all conditions are met. Candidate values Select the minimum value from the cumulative distribution curve, that is, find the first value on the cumulative distribution curve that makes the cumulative probability not less than 1. The variable value; In specific sampling... These correspond to the values ​​of the model correction factors. , No. The values ​​of the random scouring calculation parameters are as follows: or the Each random parameter value ; to proceed with the first During the random sampling, each random flushing calculation parameter is numbered. and each random parameter number Generate independent uniform random numbers respectively and And generate uniform random numbers for the model correction factor. The inverse transform method is used to generate the model correction factor, random input parameters, and random parameter samples respectively: ， ， ， in, For the first The random scouring calculation parameters are in the first... The value taken from the second sample. For the first The random parameter at the th in the th The value taken from the second sample. For the first The model correction factor obtained from the second sampling; composed of the sampled values ​​of the random flushing calculation parameters and the designed values ​​of the deterministic input parameters. Set of parameters for flushing calculation in the sub-sampling , by random parameter vector The sampling results of each parameter component constitute the first... Random parameter vector sample from the second sampling and according to the first Set of parameters for flushing calculation in the sub-sampling Construct a set of dimensionless variables Calculate the first The scour depth corresponding to the next sampling: ， In the In the random sampling, calculate the... Safety margin samples corresponding to candidate risk safety coefficients : ， For the Repeat the above random sampling for each candidate risk safety factor. Next, we obtain the safety margin sample set. Based on whether the safety margin sample is less than or equal to zero, the statistics are calculated for the first... The probability of scouring failure corresponding to each candidate risk safety factor: ， in, For the first The probability of scouring failure corresponding to each candidate risk safety factor For indicator functions, For the number of random samples; when Time to determine the first The second sampling resulted in scour failure; the above process was repeated for all candidate risk safety factors to obtain the set of scour failure probabilities under different candidate risk safety factors. .

8. The method for optimizing the bridge scour risk calculation formula considering the randomness of parameter values ​​according to claim 7, characterized in that: Step S8 specifically includes the following steps: Based on the set of scour failure probabilities under different candidate risk safety coefficients The relationship between the risk safety factor and the probability of scour failure is established by fitting a polynomial in the following form: ， in, Let be the order of the polynomial. The first is obtained by fitting the set of scour failure probabilities under different candidate risk safety factors. Polynomial coefficients of order 1 Representation of failure probability The corresponding risk safety factor; when the allowable failure probability of the target is At that time, the target risk safety factor is set. ; target risk safety factor Substituting into the posterior scour calculation formula, we obtain the formula for calculating bridge scour risk: ， in, Indicates the probability of failure of the target. Risk control scour depth determined under constraints.

9. An electronic device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 8.

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