Deviation correction Bayesian model averaging-based flood flow prediction method and system

Abstract

The invention discloses a flood flow prediction method and system based on deviation correction Bayesian model averaging, and the method comprises the steps: constructing a hydrodynamic model through employing the obtained river section data, hydrodynamic model parameter data, historical flow data or hydrological model output flow data, and constructing a model set through employing the hydrodynamic model, outputting a flow prediction result of the model set; for K candidate models in the model set in the step 1, averaging and post-processing Bayesian models based on correction coefficients according to a total probability formula, and constructing a log-likelihood function; maximizing a log-likelihood function by using an SCE-UA algorithm, and calculating an average optimal parameter of a Bayesian model; and calculating a final predicted value and a confidence interval according to the calculated average optimal parameter estimation result of the Bayesian model. According to the method, the accuracy of flood flow prediction can be improved.

Description

Technical Field

[0001] The invention relates to a flood flow prediction method based on bias-corrected Bayesian model averaging, and belongs to the field of flood risk analysis. Background Art

[0002] In flood risk analysis, numerical simulation technology is a key means to predict flood flow and analyze flood propagation characteristics. By simulating the dynamic flow process of floods, the spatiotemporal distribution characteristics of floods in a specific basin can be revealed, providing important scientific support for flood warning systems. Based on the results of numerical simulation, flood warning systems can release flood risk information to the public in real time, providing a basis for decision-making to effectively reduce flood disasters.

[0003] However, due to the uncertainty of model input, structural simplification and parameter estimation errors, there are often certain deviations in the numerical simulation results, which affects the accuracy and stability of flood flow prediction. In order to further improve the reliability of simulation results, prediction methods based on integrated models have gradually attracted attention. By integrating the prediction results of multiple single models, the integrated model can not only reduce the limitations of single model prediction, but also effectively reduce errors and improve the accuracy and robustness of flood flow prediction. However, it cannot reduce the systematic errors of a single model in the model set, resulting in the accuracy improvement effect of the final prediction result being limited, and the uncertainty of the final estimated confidence interval is too large. At the same time, the traditional Bayesian model averaging method usually uses the EM algorithm to solve the Bayesian model average parameters, but the EM algorithm can only guarantee convergence to the local optimal point, and cannot guarantee that the parameters are the global optimal parameters.

[0004] Combining bias correction with Bayesian model averaging can reduce the systematic errors of individual models in the model set and further optimize the prediction performance of the integrated model. Bias-corrected Bayesian model averaging corrects the systematic errors between model output and observed data, making the prediction results of a single model closer to the actual situation, and integrates the corrected multi-model results through probability distribution to generate more reliable comprehensive predictions, reduce and quantify the uncertainty of the prediction. The global optimal algorithm SCE-UA is used to improve the performance of approximating the global optimal parameter estimation. This method combining the SCE-UA algorithm and bias-corrected Bayesian model averaging provides a high-precision and high-reliability technical path for flood risk analysis. Summary of the invention

[0005] The technical problem to be solved by the present invention is that in the process of ensemble forecast post-processing using ordinary Bayesian model averaging, the model cannot be adjusted to improve the performance of a single model when there are systematic errors in the model, which ultimately leads to insufficient prediction accuracy and excessive uncertainty.

[0006] In order to solve the above technical problems, the present invention proposes a flood flow prediction method based on bias-corrected Bayesian model averaging, comprising the following steps:

[0007] Step 1, constructing a hydrodynamic model by acquiring river section data, hydrodynamic model parameter data, historical flow data or hydrological model output flow data, and then constructing a model set by using the hydrodynamic model;

[0008] Step 2, for the candidate models in the model set in step 1, post-process the Bayesian model average based on the correction coefficient according to the total probability formula to construct a log-likelihood function;

[0009] Step 3, using the SCE-UA algorithm to maximize the log-likelihood function and calculate the average optimal parameters of the Bayesian model;

[0010] Step 4: Calculate the final prediction value and confidence interval based on the average optimal parameter estimation results of the Bayesian model calculated in step 3.

[0011] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step 1:

[0012] (11) Collect river section information, obtain historical flow data recorded by hydrological stations in the basin, or output flow data through hydrological models as upstream basic flow data , based on basic traffic data Constructing hydrodynamic models;

[0013] (12) According to the riverbed type and water flow characteristics, select the corresponding foundation roughness coefficient ;

[0014] (13) Using the acquired flow data, a model ensemble is constructed using a hydrodynamic model.

[0015] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step (13):

[0016] (131) Based on the basic flow determined in step (11) and the basic roughness coefficient determined in step (12) Setting the traffic scaling factor and the roughness scaling factor ; Traffic scaling factor Contains a, roughness scaling factor Contains b items;

[0017] (132) The flow input data and the initially set roughness data are scaled and combined to become K = a × b candidate models, forming a model set.

[0018] In the aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging, in step (132), the hydrodynamic model includes a flow file, a geometry file and an operation plan file. The flow file is processed according to the flow scaling factor to obtain a flow files. The roughness in the geometry file is modified to obtain b geometry files. By combining the flow file and the geometry file, a total of K = a × b plan files are obtained. K model outputs are obtained by running the K plan files to construct a model set.

[0019] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step 2:

[0020] (21) Using the K candidate models in step 1, establish the predicted posterior distribution of the predicted variable y based on the total probability formula

[0021] (1)

[0022] in, is the probability density function of the average probability prediction of the Bayesian model; Given observation data Under the condition of The posterior probability of ; Given the k-th model output and observational data Under the condition that The conditional probability distribution of ;

[0023] (22) Substituting the conditional probability distribution in equation (1) Set it as Gaussian probability density, get the corresponding log-likelihood function, and correct the Bayesian model output through the correction coefficient.

[0024] (2)

[0025] in, is the log-likelihood function, is the flow data length, t is the time step, is the number of candidate models, is the model output value at time step t of the kth model, is the average parameter of the Bayesian model to be estimated, , including the weights of each model , the standard deviation of the probability density of each model , the correction coefficient for each model , Correction factor 2 ;

[0026] (23) Maximizing formula (2) is equivalent to maximizing the likelihood function, thereby obtaining the average parameter estimate of the Bayesian model. The calculation formula is as follows:

[0027] (3)

[0028] in is the parameter estimate after maximizing the likelihood function.

[0029] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging, in step (3), includes the following steps:

[0030] (31) Initialize the number of complexes , the number of interior points of the complex , sample size , the maximum number of iterations of the algorithm rep;

[0031] (32) Randomly sample in the initial parameter space samples, calculate the negative log-likelihood function value;

[0032] (33) Arrange the negative log-likelihood function values ​​calculated in step (32) in ascending order Sample points are stored in the buffer D;

[0033] (34) Divide the points in buffer D into complexes, each of which contains points;

[0034] (35) Perform CCE evolution calculation on each complex;

[0035] (36) Arrange the points in the complex in ascending order in the buffer zone D;

[0036] (37) If the convergence condition is met, the process ends and the optimal average parameter of the Bayesian model is output. If the convergence condition is not met, the process returns to step (34) until the convergence condition is met or the maximum number of iterations of the algorithm, rep, is reached. At this time, the operation is stopped and the optimal average parameter estimation result is output.

[0037] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step (35):

[0038] (351) Initialize CCE evolution, determine the number of internal points q of the subcomplex, the number of subcomplex iterations α, and the number of complex evolutions β, with the constraints of 2≤q≤m, α≥1, β≥1;

[0039] (352) According to the linear probability distribution, calculate the selection probability of each point in the complex , the calculation formula is:

[0040] (4)

[0041] is the index of the point, arranged from low to high according to the negative log-likelihood function value, is the number of interior points of the complex; is the normalization factor, that is, the sum of the selection possibilities of all points, ensuring the selection probability The sum is 1;

[0042] (353) Based on the selection probability calculated in step (352), randomly draw points without replacement in the complex, select q points in total, store them in the buffer B, and the q points together constitute a sub-complex. Record the position information L at this time;

[0043] (354) Generate the next iteration group and obtain the final buffer B;

[0044] (355) Replace the subcomplex in the original complex, i.e., position L, with the final buffer B, and arrange the complexes in ascending order according to the negative log-likelihood function value;

[0045] (356) Repeat steps (352) to (355) β times.

[0046] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step (354):

[0047] (01). Sort buffer B by objective function value from small to large, and find the worst estimated point in B. The centroid of the remaining q-1 points is recorded as ;

[0048] (02). Calculate the reflection point of the worst point , if the reflection point If the parameter is within the feasible space, go to step (04), otherwise go to step (03);

[0049] (03). Randomly generate points , replace the reflection point , go to step (04);

[0050] (04). Calculate the reflection point The negative log-likelihood function of The negative log-likelihood function is less than the original worst point , then the reflection point Replace the worst estimate point , otherwise go to step (05);

[0051] (05). Calculation , if point The negative log-likelihood function is less than the original worst estimate point , then point Replace the worst estimate point , otherwise randomly generate points , replace the worst estimate point ;

[0052] (06) Repeat steps (01) to (05) α times to obtain the final buffer B.

[0053] The aforementioned flood flow prediction method based on bias-corrected Bayesian model averaging includes, in step 4:

[0054] (41) Based on the average parameters of the Bayesian model and the Bayesian model output obtained in step (3), calculate the final prediction value:

[0055] (5)

[0056] Here is the expected final prediction value, , , is the optimal parameter value estimated in step (3), is the output of the kth model in the model set;

[0057] (42) Based on the obtained Bayesian model average parameters and model output, the Bayesian model average variance is calculated, and then the confidence interval of the Bayesian model average final prediction value is obtained.

[0058] (6)

[0059] is the average variance of the Bayesian model, is the output of the kth model in the model set; the weight of each model , the standard deviation of the probability density of each model , the correction coefficient for each model , Correction factor 2 are the optimal parameter values ​​estimated in step 3;

[0060] (7)

[0061] is the confidence interval of the Bayesian model's average final prediction value, Corresponding confidence level The critical value of the standard normal distribution.

[0062] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0063] Beneficial effects achieved by the present invention: The method of the present invention adopts the Bayesian model averaging method based on the correction coefficient, which can integrate the outputs of multiple corrected models on the basis of reducing the systematic error of a single model in the model set, thereby improving the accuracy of the prediction. At the same time, because it is under the framework of Bayesian model averaging, the confidence interval of the prediction result can also be obtained to reflect the uncertainty of the prediction result. At the same time, the SCE-UA algorithm is a global optimization algorithm that avoids convergence to a local optimal solution through complex evolution and random search, solving the problem that the Bayesian model average parameter solution may converge to a local optimal solution in a high-dimensional complex problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of a flood flow prediction method based on bias-corrected Bayesian model averaging in Example 1 of the present invention;

[0065] Figure 2 The geometric model of the hydrodynamic model established in Example 1 of the present invention and the corresponding basic flow data and model parameter diagram;

[0066] Figure 3 This is a diagram of parameter estimation results obtained according to the SCE-UA algorithm in Example 1 of the present invention;

[0067] Figure 4 This is a performance comparison diagram of a single model before and after correction in Example 1 of the present invention;

[0068] Figure 5 This is a comparison chart of the final prediction result and its confidence interval obtained by averaging the SCE-UA algorithm and the bias-corrected Bayesian model in Example 1 of the present invention, and the prediction results of a single model and without correction. DETAILED DESCRIPTION

[0069] The method of the present invention is described in detail below with reference to the accompanying drawings.

[0070] Example 1

[0071] like Figure 1 As shown, this example provides a flood flow prediction method based on bias-corrected Bayesian model averaging, including the following steps:

[0072] Step 1: construct a hydrodynamic model using river section data, hydrodynamic model parameter data, historical flow data or hydrological model output flow data, then construct a model set using the hydrodynamic model, and output the flow prediction results of the model set, including:

[0073] (1.1) Collect river section information through field measurements or high-resolution digital elevation models, obtain historical flow data recorded by hydrological stations in the basin, or output flow data through hydrological models as upstream basic flow data , based on basic traffic data Constructing hydrodynamic models;

[0074] (1.2) According to the riverbed type and water flow characteristics, select the corresponding foundation roughness coefficient ;

[0075] (1.3) Using the acquired flow data, a model set is constructed using a hydrodynamic model, including:

[0076] (1.3.1) Based on the base flow determined in step (1.1) and the basic roughness coefficient determined in step (1.2) Setting the traffic scaling factor and the roughness scaling factor ; Traffic scaling factor Contains a, roughness scaling factor Contains b items;

[0077] (1.3.2) Scaling and combining the flow input data and the initially set roughness data to form K = a × b candidate models, forming a model set;

[0078] In step (1.3.2), the hydrodynamic model includes a flow file, a geometry file, and an operation plan file. The flow file is processed according to the flow scaling factor to obtain a flow file. The roughness in the geometry file is modified to obtain b geometry files. Through the combination of the flow file and the geometry file, a total of K = a × b plan files are obtained. By running K plan files, K model outputs are obtained to construct a model set. Using the model set for subsequent predictions can reduce uncertainty and improve the accuracy and robustness of the hydrodynamic model.

[0079] In this embodiment, the error is calculated as 20%, that is, = =[0.8,1.0,1.2] is the coefficient scaling combination, then there are 3×3=9 models in total, such as Figure 2 As shown, the geometric model of the established hydrodynamic model and the corresponding basic flow data and basic model parameters;

[0080] Step 2: For the K candidate models in the model set in step 1, the Bayesian model average based on the correction coefficient is post-processed according to the total probability formula to construct a log-likelihood function; the outputs of multiple candidate models are integrated to improve the reliability and accuracy of the prediction, including:

[0081] (2.1) Using the K candidate models in step 1, establish the predicted posterior distribution of the predicted variable y based on the total probability formula

[0082] (1)

[0083] in, is the probability density function of the average probability prediction of the Bayesian model; Given the observation data Under the condition of The posterior probability of ; Given the k-th model output and observational data Under the condition that The conditional probability distribution of ;

[0084] (2.2) The conditional probability distribution in equation (1) Set it as Gaussian probability density, get the corresponding log-likelihood function, and correct the Bayesian model output through the correction coefficient.

[0085] (2)

[0086] in, is the log-likelihood function, is the flow data length, t is the time step, is the number of candidate models, is the model output value at time step t of the kth model, is the average parameter of the Bayesian model to be estimated, , including the weights of each model , the standard deviation of the probability density of each model , the correction coefficient for each model , Correction factor 2 ;

[0087] (2.3) Maximizing formula (2) is equivalent to maximizing the likelihood function, thereby obtaining the average parameter estimate of the Bayesian model. The calculation formula is as follows:

[0088] (3)

[0089] in is the parameter estimate after maximizing the likelihood function;

[0090] Step 3, using the SCE-UA algorithm to maximize the log-likelihood function and calculate the average optimal parameters of the Bayesian model; the SCE-UA algorithm is a method for minimizing the objective function, and maximizing the log-likelihood function is equivalent to minimizing the negative log-likelihood function, including the following steps:

[0091] (3.1) Initialize the number of complexes , the number of interior points of the complex , sample size , the maximum number of iterations of the algorithm rep;

[0092] (3.2) Randomly sample in the initial parameter space samples, calculate the negative log-likelihood function value;

[0093] (3.3) Arrange the negative log-likelihood function values ​​calculated in step (3.2) in ascending order Sample points are stored in the buffer D;

[0094] (3.4) Divide the points in the buffer zone D into complexes, each of which contains points;

[0095] (3.5) Perform CCE evolution calculation on each complex, including:

[0096] (3.5.1) Initialize CCE evolution, determine the number of internal points q of the subcomplex, the number of subcomplex iterations α, and the number of complex evolutions β, with the constraints of 2≤q≤m, α≥1, β≥1;

[0097] (3.5.2) Calculate the selection probability of each point in the complex according to the linear probability distribution , the calculation formula is:

[0098] (4)

[0099] is the index of the point, arranged from low to high according to the negative log-likelihood function value, is the number of interior points of the complex; is the normalization factor, that is, the sum of the selection possibilities of all points, ensuring the selection probability The sum is 1;

[0100] (3.5.3) Based on the selection probability calculated in step (3.5.2), randomly draw points without replacement in the complex, select q points in total, store them in the buffer B, and the q points together form a subcomplex. Record the position information L at this time;

[0101] (3.5.4) Generate the next iteration group and obtain the final buffer B, including:

[0102] (01) Sort buffer B in ascending order according to the objective function value and find the worst estimated point in B. The centroid of the remaining q-1 points is recorded as ;

[0103] (02). Calculate the reflection point of the worst point , if the reflection point If the parameter is within the feasible space, go to step (04), otherwise go to step (03);

[0104] (03). Randomly generate points , replace the reflection point , go to step (04);

[0105] (04). Calculate the reflection point The negative log-likelihood function of The negative log-likelihood function is less than the original worst point , then the reflection point Replace the worst estimate point , otherwise go to step (05);

[0106] (05)Calculation , if point The negative log-likelihood function is less than the original worst estimate point , then point Replace the worst estimate point , otherwise randomly generate points , replace the worst estimate point ;

[0107] (06) Repeat steps (01) to (05) α times to obtain the final buffer B.

[0108] (3.5.5) Replace the subcomplex in the original complex, i.e., position L, with the final buffer B, and sort the complexes in ascending order of the negative log-likelihood function value;

[0109] (3.5.6) Repeat steps (3.5.2) to (3.5.5) β times;

[0110] (3.6) Arrange the points in the complex in ascending order in the buffer D;

[0111] (3.7) If the convergence condition is met, the operation ends and the optimal average parameter of the Bayesian model is output. If the convergence condition is not met, return to step 3.4 until the convergence condition is met or the maximum number of iterations of the algorithm rep is reached. At this time, the operation stops and the optimal average parameter estimation result is output.

[0112] like Figure 3 The figure shows the average parameter estimate of the Bayesian model after rep=50w iterations reach convergence. Figure 3 (a) shows the relationship between the weight and standard deviation estimates calculated by arranging the weights from large to small and the RMSE after model correction. It can be seen that the model with lower standard deviation and RMSE is given a higher weight. Figure 3 (b) in the middle represents the estimated bias correction parameter value at this time.

[0113] Step 4: Calculate the final prediction value and confidence interval based on the average optimal parameter estimation results of the Bayesian model calculated in step 3:

[0114] (4.1) According to the average parameters of the Bayesian model and the Bayesian model output obtained in step 3, calculate the final prediction value:

[0115] (5)

[0116] Here is the expected final prediction value, , , is the optimal parameter value estimated in step 3, is the output of the kth model in the model set;

[0117] (4.2) Based on the obtained Bayesian model average parameters and model output, the Bayesian model average variance is calculated, and then the confidence interval of the Bayesian model average final prediction value is obtained.

[0118] (6)

[0119] is the average variance of the Bayesian model, is the output of the kth model in the model set; the weight of each model , the standard deviation of the probability density of each model , the correction coefficients for each model , Correction factor 2 are the optimal parameter values ​​estimated in step 3;

[0120] (7)

[0121] is the confidence interval of the Bayesian model's average final prediction value, Corresponding confidence level The critical value of the standard normal distribution.

[0122] Figure 4The changes in the RMSE of individual models before and after correction (arranged from large to small according to model weight) and the average RMSE of the Bayesian model without bias correction are shown. It can be seen that after bias correction, the bias of the model has decreased significantly, and in the final integrated prediction, the bias-corrected Bayesian model has a lower RMSE on average.

[0123] Figure 5 The predicted values ​​and confidence intervals of the Bayesian model average without bias correction (a) and the Bayesian model average after bias correction (b). It can be seen that the bias-corrected Bayesian model average significantly reduces the size of the confidence interval, indicating that it significantly reduces the uncertainty of the final prediction results of the integrated model.

[0124] Example 2

[0125] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0126] Example 3

[0127] A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that the computer program / instruction implements the steps of the above method when executed by a processor.

[0128] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0129] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0130] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0131] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A flood flow prediction method based on bias-corrected Bayesian model averaging, characterized in that: The following steps are involved: Step 1, constructing a hydrodynamic model by acquiring river section data, hydrodynamic model parameter data, historical flow data or hydrological model output flow data, and then constructing a model set by using the hydrodynamic model; Step 2, for the candidate models in the model set in step 1, post-process the Bayesian model average based on the correction coefficient according to the total probability formula to construct a log-likelihood function; Step 3, using the SCE-UA algorithm to maximize the log-likelihood function and calculate the average optimal parameters of the Bayesian model; Step 4: Calculate the final prediction value and confidence interval based on the average optimal parameter estimation results of the Bayesian model calculated in step 3.

2. A flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 1, characterized in that: In step 1, include: (11) Collect river section information, obtain historical flow data recorded by hydrological stations in the basin, or output flow data through hydrological models as upstream basic flow data , based on basic traffic data Constructing hydrodynamic models; (12) According to the riverbed type and water flow characteristics, select the corresponding foundation roughness coefficient ; (13) Using the acquired flow data, a model ensemble is constructed using a hydrodynamic model.

3. A flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 2, characterized in that: In step (13), it includes: (131) Based on the basic flow determined in step (11) and the basic roughness coefficient determined in step (12) Setting the flow scaling factor and the roughness scaling factor ; Traffic scaling factor Contains a, roughness scaling factor Contains b items; (132) The flow input data and the initially set roughness data are scaled and combined to become K = a × b candidate models, forming a model set.

4. A flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 3, characterized in that: In step (132), the hydrodynamic model includes a flow file, a geometry file and an operation plan file. The flow file is processed according to the flow scaling factor to obtain a flow files. The roughness in the geometry file is modified to obtain b geometry files. By combining the flow file and the geometry file, a total of K = a × b plan files are obtained. By running K plan files, K model outputs are obtained to construct a model set.

5. The flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 1 is characterized in that: In step 2, include: (21) Using the K candidate models in step 1, establish the predicted posterior distribution of the predicted variable y based on the total probability formula (1) in, is the probability density function of the average probability prediction of the Bayesian model; Given observation data Under the condition of The posterior probability of ; Given the k-th model output and observational data Under the condition that The conditional probability distribution of ; (22) Substituting the conditional probability distribution in equation (1) Set it as Gaussian probability density, get the corresponding log-likelihood function, and correct the Bayesian model output through the correction coefficient. (2) in, is the log-likelihood function, is the flow data length, t is the time step, is the number of candidate models, is the model output value at time step t of the kth model, is the average parameter of the Bayesian model to be estimated, , including the weights of each model , the standard deviation of the probability density of each model , the correction coefficient for each model , Correction factor 2 ; (23) Maximizing formula (2) is equivalent to maximizing the likelihood function, thereby obtaining the average parameter estimate of the Bayesian model. The calculation formula is as follows: (3) in is the parameter estimate after maximizing the likelihood function.

6. The flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 1 is characterized in that: In step 3, the following steps are included: (31) Initialize the number of complexes , the number of interior points of the complex , sample size , the maximum number of iterations of the algorithm rep; (32) Randomly sample in the initial parameter space samples, calculate the negative log-likelihood function value; (33) Arrange the negative log-likelihood function values ​​calculated in step (32) in ascending order Sample points are stored in the buffer D; (34) Divide the points in buffer D into complexes, each of which contains points; (35) Perform CCE evolution calculation on each complex; (36) Arrange the points in the complex in ascending order in the buffer zone D; (37) If the convergence condition is met, the process ends and the optimal average parameter of the Bayesian model is output. If the convergence condition is not met, the process returns to step (34) until the convergence condition is met or the maximum number of iterations of the algorithm, rep, is reached. At this time, the operation is stopped and the optimal average parameter estimation result is output.

7. A flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 6, characterized in that: In step (35), it includes: (351) Initialize CCE evolution, determine the number of internal points q of the subcomplex, the number of subcomplex iterations α, and the number of complex evolutions β, with the constraints of 2≤q≤m, α≥1, β≥1; (352) According to the linear probability distribution, calculate the selection probability of each point in the complex , the calculation formula is: (4) is the index of the point, arranged from low to high according to the negative log-likelihood function value, is the number of interior points of the complex; is the normalization factor, that is, the sum of the selection possibilities of all points, ensuring the selection probability The sum is 1; (353) Based on the selection probability calculated in step (352), randomly draw points without replacement in the complex, select q points in total, store them in the buffer B, and the q points together constitute a sub-complex. Record the position information L at this time; (354) Generate the next iteration group and obtain the final buffer B; (355) Replace the subcomplex in the original complex, i.e., position L, with the final buffer B, and arrange the complexes in ascending order according to the negative log-likelihood function value; (356) Repeat steps (352) to (355) β times.

8. The flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 7 is characterized in that: In step 354), it includes: (01) Sort buffer B in ascending order according to the objective function value and find the worst estimated point in B. The centroid of the remaining q-1 points is recorded as ; (02). Calculate the reflection point of the worst point , if the reflection point If the parameter is within the feasible space, go to step (04), otherwise go to step (03); (03). Randomly generate points , replace the reflection point , go to step (04); (04). Calculate the reflection point The negative log-likelihood function of The negative log-likelihood function is less than the original worst point , then the reflection point Replace the worst estimate point , otherwise go to step (05); (05)Calculation , if point The negative log-likelihood function is less than the original worst estimate point , then take the point Replace the worst estimate point , otherwise randomly generate points , replace the worst estimate point ; (06) Repeat steps (01) to (05) α times to obtain the final buffer B.

9. The flood flow prediction method based on bias-corrected Bayesian model averaging according to claim 1 is characterized in that: In step 4, include: (41) Based on the average parameters of the Bayesian model and the Bayesian model output obtained in step 3, calculate the final prediction value: (5) Here is the expected final prediction value, , , is the optimal parameter value estimated in step 3, is the output of the kth model in the model set; (42) Based on the obtained Bayesian model average parameters and model output, the Bayesian model average variance is calculated, and then the confidence interval of the Bayesian model average final prediction value is obtained. (6) is the average variance of the Bayesian model, is the output of the kth model in the model set; the weight of each model , the standard deviation of the probability density of each model , the correction coefficient for each model , Correction factor 2 are the optimal parameter values ​​estimated in step 3; (7) is the confidence interval of the Bayesian model's average final prediction value, Corresponding confidence level The critical value of the standard normal distribution.

10. A computer device / equipment / system, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 9.

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