CN117273200A - Runoff interval forecasting method based on convolution optimization algorithm and Pyraformer neural network - Google Patents

Runoff interval forecasting method based on convolution optimization algorithm and Pyraformer neural network Download PDF

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CN117273200A
CN117273200A CN202311112445.4A CN202311112445A CN117273200A CN 117273200 A CN117273200 A CN 117273200A CN 202311112445 A CN202311112445 A CN 202311112445A CN 117273200 A CN117273200 A CN 117273200A
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王政
彭甜
葛宜达
陈杰
张楚
陈帅
张新荣
陈佳雷
王熠炜
张学东
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Abstract

The invention discloses a runoff interval forecasting method based on a convolution optimization algorithm and a Pyraformer neural network, which comprises the steps of collecting data, and optimizing a Pyraformer neural network model by using the convolution optimization algorithm as a prediction model of the runoff interval; the coverage rate index PICP, the average width index PINAW and the symmetry index PIS are utilized to define a composite objective function CSWC of a convolution optimization algorithm as an adaptability function of the model, and the parameters of the prediction model are optimized in a parameter feasible domain range; predicting the upper boundary and the lower boundary of the runoff interval value by using a prediction model; meanwhile, the accuracy of the upper boundary and the lower boundary is evaluated and corrected by using a coverage rate index PICP, an average width index PINAW and a symmetry index PIS; obtaining a prediction result of error data by using the upper and lower boundary errors; and sending the predicted result into a designed error correction strategy to obtain a final interval predicted result. The method solves the problem that the runoff interval forecast by the local optimization algorithm is inaccurate in the prior art.

Description

Runoff interval forecasting method based on convolution optimization algorithm and Pyraformer neural network
Technical Field
The invention relates to the technical field of runoff interval forecasting, in particular to a runoff interval forecasting method based on a convolution optimization algorithm and a Pyraformer neural network.
Background
Under the common influence of global climate change and human activities, extreme weather events frequently occur, the air moisture content of the global near-surface and troposphere rises, and strong precipitation in the range of human activity areas is also exacerbated, which increases the flood risk year by year. Meanwhile, the characteristics of the river basin are changed, and the phenomenon of runoff fragmentation is increasingly serious, so that hydrologic elements such as river runoff are obviously changed.
The runoff prediction model is a mathematical model for predicting river runoff, is a simplified representation of a real hydrologic system, and predicts the change condition of the river flow path flow in a future period according to the hydrologic characteristics, meteorological conditions, topography and other information of a river basin, and is usually composed of an upper boundary and a lower boundary of runoff prediction. In the radial flow interval prediction, besides a complete radial flow interval prediction model, model parameters also determine the key of prediction accuracy, and the parameter problem of the radial flow interval prediction model is mainly a manual trial and error method, so that researchers are required to have higher experience knowledge, but the efficiency is low, and the result is difficult to reach the optimum.
Along with the development of modern computer technology and the coming of big data age, more abundant data resources are easy to obtain, and the local optimization algorithm is used for carrying out parameter optimization on a runoff interval forecast model, such as a Rosenblock method, a Powell method and a Simplex method, the local optimization algorithm provides convenience for the parameter rate of the runoff interval forecast model to a certain extent, but because of the nonlinearity of the runoff interval forecast model, the local optimization algorithm is easy to sink into the local optimization, and the global optimal calibration result is difficult to capture, so the global optimization algorithm is proposed, such as a particle swarm algorithm, a differential evolution algorithm, a simulated annealing algorithm and the like, has higher robustness, and the interference of local extremum can be effectively avoided. However, in the actual prediction of the runoff interval, there are often requirements on multiple indexes such as flow, flow process, etc., and these indexes are mutually restricted, so that the optimization cannot be achieved at the same time. There is therefore a need for a more accurate method of forecasting radial intervals to provide more comprehensive forecast information.
Disclosure of Invention
The invention aims to: the invention aims to provide a runoff interval forecasting method based on a convolution optimization algorithm and a Pyraformer neural network, which is used for accurately and rapidly forecasting upper and lower boundary intervals of runoff.
The technical scheme is as follows: in order to achieve the above purpose, the runoff interval forecasting method based on a convolution optimization algorithm and a Pyraformer neural network comprises the following steps:
step 1: collecting data, including a geographic potential dependent sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological sequence of a runoff region;
step 2: defining a coverage index PICP, an average width index PINAW and a symmetry index PIS;
step 3: optimizing a Pyraformer neural network model by adopting a convolution optimization algorithm to serve as a prediction model of a runoff interval;
step 4: operating the radial flow interval prediction model obtained in the step 3 by using the data in the step 1 to obtain a parameter feasible region of the model; defining a composite objective function CSWC of a convolution optimization algorithm by using the index in the step 2 as an adaptability function of the model, and optimizing predicted model parameters of a runoff interval in a parameter feasible domain range;
step 5: inputting the data set in the step 1 into the runoff interval prediction model after optimizing parameters in the step 4, extracting time-space dimension characteristics of the data, and predicting upper and lower boundaries of the runoff interval value by combining with the fully-connected prediction output layer; performing accuracy evaluation and correction on the upper and lower boundaries of the predicted runoff interval by using the indexes in the step 2;
step 6: calculating the upper and lower boundary errors of the predicted runoff interval to obtain error data, and sending the error data into a prediction model of the runoff interval after optimizing parameters to obtain a prediction result of the error data;
step 7: and designing an error correction strategy, and sending the prediction result of the error data into the error correction strategy to obtain a final interval prediction result.
The data described in step 1 is the entire basin containing |v|=n sub-basins, and the set of sub-basin control sites is defined as v= { V 1 ,...,v n ,...,v N N represents the nth sub-watershed site; the dependency matrix between the sub-watershed control sites is l= { L geo ,L rel }, wherein L geo Is a geographic adjacency matrix L rel An adjacency matrix for potential spatial dependencies;
for any two different sub-watershed i and j, its geographic adjacency matrix and latent dependency matrix distribution are expressed as:
wherein CEPMI (v) i ,v j ) Copula entropy bias mutual information between the sub-watershed i and j is represented; l (L) rel =1, meaning that the partial mutual information of sub-watershed i and j is greater than a given threshold δ;
according to the distribution of the geographical adjacency matrix and the potential dependency matrix of any two different sub-watersheds i and j, a subscript T is intercepted along a time axis g The time sequence is a geographic potential dependency sequence
Analyzing the time dependence of the basin runoff process on periodicity and adjacent moments, and respectively intercepting subscripts T along a time axis h 、T p And T m The time sequence segment is the input of the model at the adjacent time, the periodical repeated time and the historical meteorological sequence component, t 0 The time sequence sets are respectively expressed as
Is provided withRepresenting the runoff value at time t in the sub-basin n, then +.>The method comprises the steps of collecting runoff values of all sub-watershed at t time, namely a target value;
construction of sample set (x t ,Y t ) T=1, 2,., N, N represents the number of sub-watershed, i.e. the number of sample points, where x t ＝[L,K,P,T] T For the input data set, data information of a geographic potential dependency sequence L, a nearby sequence K, a periodic repeated sequence P and a historical meteorological sequence T is contained.
The indexes in the step 2 are respectively as follows:
coverage index PICP:
when the target value is covered by the forecast interval Shi Buer function c i The value of (2) is 1, otherwise 0;
average width index PINAW:
symmetry index PIS:
wherein N represents the size of the sample set, R is the value range of the target vector, i is the sample point, y i Representing the measured value of the i-th sample point; LB (LB) i And UB i Respectively represent y i Lower and upper limits of (2).
The optimization method in the step 3 is as follows: introducing a convolution optimization algorithm MCOA to optimize parameters of the Pyraformer neural network model including learning rate, hidden layer number and number of detail points so as to improve the convergence rate of the model, wherein the specific optimization process is as follows: inputting the number of the initialized population, the dimension of the individual position, the maximum iteration times, the convolution kernel parameters and the fitness function; performing a location update strategy; updating the global optimal solution and the position thereof; and outputting the parameters of the optimal solution assigned to the Pyraformer neural network model.
The method for obtaining the parameter feasible region of the runoff interval prediction model in the step 4 is as follows: initializing parameters of a runoff interval prediction model, inputting data, obtaining an optimal parameter set theta of the runoff interval prediction model, slightly perturbing the set theta, obtaining a parameter feasible region F, wherein the feasible region F is expressed as:
F＝[θ-ω≤θ≤θ+ω]。
the formula of the composite objective function CSWC in the step 4 is as follows:
wherein a, b and c are weight values of indexes, and the smaller CSWC is, the higher the coverage rate of the forecast interval is, the smaller the width is, and the higher the symmetry is;
in the CSWC function, PIARW is used as a main measurement index, a is set to be a larger value to ensure that the coverage rate of a forecast interval is better, and then a more ideal forecast interval is obtained, and the sum form among PICP, PIARW and index PIS in the CSWC function is used to avoid the extreme condition that PIARW is 0 in the product form, namely the upper boundary and the lower boundary of the forecast interval are overlapped, and the forecast width is 0.
And 5, predicting the upper and lower boundaries of the runoff interval value, wherein the specific process is as follows:
constructing a large matrix data set by using a geographic potential dependency sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological element sequence, and sending the large matrix data set into a prediction model of a runoff interval, and constructing a multi-resolution C element tree by using a coarse scale construction module CSCM, wherein the coarse scale nodes summarize information of corresponding fine scale C nodes; the pyramid attention module PAM is introduced to further capture time-space dependencies of different ranges, and the attention mechanism in the pyramid diagram is utilized to transmit messages; the output of the fully connected network is directly used as the prediction of the upper and lower boundaries of the interval prediction;
wherein the pyramid attention module PAM comprises a scale time connection and a scale space connection, the scale time connection forming a C-ary tree, wherein each parent node has C child nodes; using the finest scale of the pyramid graph to correlate with the hourly observations of the original time series, the nodes on the coarse scale are considered as time-of-day, week, and month features of the time series; connecting adjacent nodes through a scale space, and capturing a remote dependency relationship in a coarse scale;
in the attention mechanism, X and Y represent input and output of single attention, respectively, and X is first linearly transformed into three different matrices, i.e. query q=xw Q Key k=xw K Value v=xw V WhereinW Q ,W K ,W V Respectively a weight matrix of inquiry, a weight matrix of key, a Q of ith row in Q i Is any row in K, i.e. a key, the output of the attention mechanism is:
wherein,transpose of line I in K, D K Representing the dimension of the key; i is the sample point, y i The measured value of the i-th sample point is shown.
And carrying out single-step prediction on the historical sequence, after the sequence is subjected to PAM coding of a pyramid attention module, assembling the features of the last node in the pyramid graph on all scales, inputting the spliced features into a fully-connected layer for prediction, outputting two predicted values, wherein a larger value is used as the upper boundary of a prediction interval at the moment, and a smaller value is used as the lower boundary of the prediction interval at the moment.
The evaluation method in the step 5 comprises the following steps:
when the value of the coverage rate index PICP is close to 1, the more actual measurement values are covered by the prediction interval, the better the effect of the prediction model of the runoff interval is; the average width index PINAW is as narrow as possible in an effective forecasting interval under the condition of higher coverage rate, so that the forecasting interval contains effective information;
when the forecast interval covers the actual measurement value, the symmetry index PIS takes the value between 0 and 0.5; when the actual measurement is in the center of the prediction interval, namely the optimal symmetry condition, the symmetry index PIS takes a value of 0; when the symmetry index PIS is close to 0, the symmetry of the prediction interval about the measured value is better; when the measured value is smaller than the lower boundary of the predicted interval and larger than the upper boundary of the predicted interval, the value of the symmetry index PIS is larger than 0.5, and the degree of asymmetry of the predicted interval to the measured value is high;
the correction method comprises the following steps: calculating the evaluation results of a coverage index PICP, an average width index PINAW and a symmetry index PIS according to the upper boundary and the lower boundary of the prediction interval, and giving a confidence probability of 100 (1-alpha)%, and correcting the prediction of the prediction interval which cannot meet the index by the following formula:
wherein,forecasting the upper and lower boundaries of the runoff interval value, wherein alpha is the significance level, and the forecasting interval is expressed as +.>The target vector is located in the forecast interval +.>The probability of (2) is expressed as
The error data in step 6 is expressed as:
in the formula, UB_Err i 、And UB con Respectively representing an upper boundary error, a forecast upper boundary and a set upper boundary; LB_Err i 、/>And LB con Respectively representing a lower boundary error, a forecast lower boundary and a set lower boundary; wherein forecast boundary->Andis the value of the predicted result of the runoff interval prediction model and corrected by the result of the three indexes;
the method for obtaining the prediction result of the error data comprises the following steps: the UB_Err is used for i And LB_Err i The error data is input into a prediction model of the runoff interval to obtain prediction results of the error data, wherein the prediction results are respectively upper boundary prediction results UB_Err pre And lower boundary prediction result LB_Err pre 。
The design process of the error correction strategy described in the step 7 is as follows:
according to the prediction result of the runoff interval prediction model after optimizing the parametersAnd->Calculating a coverage rate index PICP value;
if the coverage index PICP value is higher than the set confidence level, the adjustment strategy is as follows: the reduction of the average width index PINAW and the symmetry index PIS is more important than the increase of the coverage index PICP to improve the quality of the forecast interval;
when the upper boundary error UB_Err pre In the positive direction, the upper boundary prediction result UB is represented pre Greater than the set upper boundary UB con Then the upper boundary prediction result UB pre Subtracting the upper boundary error UB_Err pre To reduce the width of the forecast interval;
when the upper boundary error UB_Err pre When negative, the upper boundary prediction result UB is represented pre Less than the set upper boundary UB con Upper boundary error UB _ Err pre Switching to zero to avoid increasing the forecast interval width; LB (LB) pre Is to adjust policy and UB pre Conversely;
if the coverage index PICP value is lower than the set confidence level, it is more important to increase PICP than to decrease PINAW and PIS, so the strategy is adjusted as follows: upper boundary error ub_err pre And lower boundary error LB_Err pre Remain unchanged to ensure that the boundary of the forecast interval approaches the set interval edgeA boundary; when the coverage rate index PICP is increased, the quality of the forecast interval is improved;
the final interval prediction result obtained through the difference correction strategy is expressed as:
wherein UB is cal And LB cal Representing the correction upper and correction lower boundaries, respectively.
The beneficial effects are that: the invention has the following advantages: 1. the prediction model of the runoff interval constructed by the method can better process time sequence data and capture the long-term dependence relationship between the data, and outputs the predicted upper and lower boundaries by combining with the fully-connected prediction layer to form a complete prediction interval, so that more comprehensive prediction information is provided; 2. the accuracy of the upper boundary and the lower boundary of the predicted runoff interval is evaluated and corrected by using a coverage rate index PICP, an average width index PINAW and a symmetry index PIS, so that a more accurate predicted runoff interval is obtained; 3. and an error correction strategy is provided for adjusting the upper boundary and the lower boundary of the forecast interval, so that possible deviation of the forecast interval is corrected in time, and a more reliable forecast result is provided.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
fig. 2 is a flowchart of a Pyraformer neural network model.
Detailed Description
The technical scheme of the present invention will be described in detail with reference to the following examples and the accompanying drawings.
As shown in fig. 1, a runoff interval forecasting method based on a convolution optimization algorithm and a Pyraformer neural network comprises the following steps:
step 1: collecting data, including a geographic potential dependent sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological sequence of a runoff region;
step 2: defining a coverage index PICP, an average width index PINAW and a symmetry index PIS;
step 3: optimizing a Pyraformer neural network model by adopting a convolution optimization algorithm to serve as a prediction model of a runoff interval;
step 4: using the data in the step 1 to run a prediction model of the runoff interval to obtain a parameter feasible region of the model; defining a composite objective function CSWC of a convolution optimization algorithm by using a coverage rate index PICP, an average width index PINAW and a symmetry index PIS as an adaptability function of the model, and optimizing prediction model parameters of a runoff interval in a parameter feasible domain range;
step 5: the data set in the step 1 is input into a prediction model of the runoff interval after the optimization parameters to extract the time dimension and the space dimension characteristics of the data, and the upper boundary and the lower boundary of the value of the runoff interval are predicted by combining with a fully-connected prediction output layer; evaluating and correcting the accuracy of the upper and lower boundaries of the predicted runoff interval by using a coverage rate index PICP, an average width index PINAW and a symmetry index PIS;
step 6: calculating the upper and lower boundary errors of the predicted runoff interval to obtain error data, and sending the error data into a prediction model of the runoff interval after optimizing parameters to obtain a prediction result of the error data;
step 7: and designing an error correction strategy, and sending the prediction result of the error data into the error correction strategy to obtain a final interval prediction result.
The data described in step 1 is the entire basin containing |v|=n sub-basins, and the set of sub-basin control sites is defined as v= { V 1 ,...,v n ,...,v N N represents the nth sub-watershed site; the dependency matrix between the sub-watershed control sites is l= { L geo ,L rel }, wherein L geo Is a geographic adjacency matrix L rel An adjacency matrix for potential spatial dependencies;
for any two different sub-watershed i and j, its geographic adjacency matrix and latent dependency matrix distribution are expressed as:
wherein CEPMI (v) i ,v j ) Copula entropy bias mutual information between the sub-watershed i and j is represented; l (L) rel =1, meaning that the partial mutual information of sub-watershed i and j is greater than a given threshold δ;
according to the distribution of the geographical adjacency matrix and the potential dependency matrix of any two different sub-watersheds i and j, a subscript T is intercepted along a time axis g The time sequence is a geographic potential dependency sequence
Analyzing the time dependence of the basin runoff process on periodicity and adjacent moments, and respectively intercepting subscripts T along a time axis h 、T p And T m The time sequence segment is the input of the model at the adjacent time, the periodical repeated time and the historical meteorological sequence component, t 0 The time sequence sets are respectively expressed as
Is provided withRepresenting the runoff value at time t in the sub-basin n, then +.>The method comprises the steps of collecting runoff values of all sub-watershed at t time, namely a target value;
construction of sample set (x t ,Y t ) T=1, 2,., N, N represents the number of sub-watershed, i.e. the number of sample points, where x t ＝[L,K,P,T] T For the input data set, data information of a geographic potential dependency sequence L, a nearby sequence K, a periodic repeated sequence P and a historical meteorological sequence T is contained.
The indexes in the step 2 are respectively as follows:
coverage index PICP:
when the target value is covered by the forecast interval Shi Buer function c i The value of (2) is 1, otherwise 0;
average width index PINAW:
symmetry index PIS:
wherein N represents the size of the sample set, R is the value range of the target vector, i is the sample point, y i Representing the measured value of the i-th sample point; LB (LB) i And UB i Respectively represent y i Lower and upper limits of (2).
The optimization method in the step 3 is as follows: introducing a convolution optimization algorithm MCOA to optimize parameters of the Pyraformer neural network model including learning rate, hidden layer number and number of detail points so as to improve the convergence rate of the model, wherein the specific optimization process is as follows: inputting the number of the initialized population, the dimension of the individual position, the maximum iteration times, the convolution kernel parameters and the fitness function; performing a location update strategy; updating the global optimal solution and the position thereof; and outputting the parameters of the optimal solution assigned to the Pyraformer neural network model, as shown in fig. 2.
The method for obtaining the parameter feasible region of the runoff interval prediction model in the step 4 is as follows: initializing parameters of a runoff interval prediction model, inputting data, obtaining an optimal parameter set theta of the runoff interval prediction model, slightly perturbing the set theta, obtaining a parameter feasible region F, wherein the feasible region F is expressed as:
F＝[θ-ω≤θ≤θ+ω]。
the formula of the composite objective function CSWC in the step 4 is as follows:
wherein a, b and c are weight values of indexes, and the smaller CSWC is, the higher the coverage rate of the forecast interval is, the smaller the width is, and the higher the symmetry is;
in the CSWC function, PIARW is used as a main measurement index, a is set to be a larger value to ensure that the coverage rate of a forecast interval is better, and then a more ideal forecast interval is obtained, and the sum form among PICP, PIARW and index PIS in the CSWC function is used to avoid the extreme condition that PIARW is 0 in the product form, namely the upper boundary and the lower boundary of the forecast interval are overlapped, and the forecast width is 0.
And 5, predicting the upper and lower boundaries of the runoff interval value, wherein the specific process is as follows:
constructing a large matrix data set by using a geographic potential dependency sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological element sequence, and sending the large matrix data set into a prediction model of a runoff interval, and constructing a multi-resolution C element tree by using a coarse scale construction module CSCM, wherein the coarse scale nodes summarize information of corresponding fine scale C nodes; the pyramid attention module PAM is introduced to further capture time-space dependencies of different ranges, and the attention mechanism in the pyramid diagram is utilized to transmit messages; the output of the fully connected network is directly used as the prediction of the upper and lower boundaries of the interval prediction;
wherein the pyramid attention module PAM comprises a scale time connection and a scale space connection, the scale time connection forming a C-ary tree, wherein each parent node has C child nodes; using the finest scale of the pyramid graph to correlate with the hourly observations of the original time series, the nodes on the coarse scale are considered as time-of-day, week, and month features of the time series; connecting adjacent nodes through a scale space, and capturing a remote dependency relationship in a coarse scale;
in the attention mechanism, X and Y represent input and output of single attention respectively, and X is first linearly transformed into three different matrices, i.e. query q=xW Q Key k=xw K Value v=xw V WhereinW Q ,W K ,W V Respectively a weight matrix of inquiry, a weight matrix of key, a Q of ith row in Q i Is any row in K, i.e. a key, the output of the attention mechanism is:
wherein,transpose of line I in K, D K Representing the dimension of the key; i is the sample point, y i The measured value of the i-th sample point is shown.
And carrying out single-step prediction on the historical sequence, after the sequence is subjected to PAM coding of a pyramid attention module, assembling the features of the last node in the pyramid graph on all scales, inputting the spliced features into a fully-connected layer for prediction, outputting two predicted values, wherein a larger value is used as the upper boundary of a prediction interval at the moment, and a smaller value is used as the lower boundary of the prediction interval at the moment.
The evaluation method in the step 5 comprises the following steps:
when the value of the coverage rate index PICP is close to 1, the more actual measurement values are covered by the prediction interval, the better the effect of the prediction model of the runoff interval is; the average width index PINAW is as narrow as possible in an effective forecasting interval under the condition of higher coverage rate, so that the forecasting interval contains effective information;
when the forecast interval covers the actual measurement value, the symmetry index PIS takes the value between 0 and 0.5; when the actual measurement is in the center of the prediction interval, namely the optimal symmetry condition, the symmetry index PIS takes a value of 0; when the symmetry index PIS is close to 0, the symmetry of the prediction interval about the measured value is better; when the measured value is smaller than the lower boundary of the predicted interval and larger than the upper boundary of the predicted interval, the value of the symmetry index PIS is larger than 0.5, and the degree of asymmetry of the predicted interval to the measured value is high;
the correction method comprises the following steps: calculating the evaluation results of a coverage index PICP, an average width index PINAW and a symmetry index PIS according to the upper boundary and the lower boundary of the prediction interval, and giving a confidence probability of 100 (1-alpha)%, and correcting the prediction of the prediction interval which cannot meet the index by the following formula:
wherein,forecasting the upper and lower boundaries of the runoff interval value, wherein alpha is the significance level, and the forecasting interval is expressed as +.>The target vector is located in the forecast interval +.>The probability of (2) is expressed as
The error data in step 6 is expressed as:
in the formula, UB_Err i 、And UB con Respectively representing an upper boundary error, a forecast upper boundary and a set upper boundary; LB_Err i 、/>And LB con Respectively representing a lower boundary error, a forecast lower boundary and a set lower boundary; wherein forecast boundary->Andis the value of the predicted result of the runoff interval prediction model and corrected by the result of the three indexes;
the method for obtaining the prediction result of the error data comprises the following steps: the UB_Err is used for i And LB_Err i The error data is input into a prediction model of the runoff interval to obtain prediction results of the error data, wherein the prediction results are respectively upper boundary prediction results UB_Err pre And lower boundary prediction result LB_Err pre 。
The design process of the error correction strategy described in the step 7 is as follows:
according to the prediction result of the runoff interval prediction model after optimizing the parametersAnd->Calculating a coverage rate index PICP value;
if the coverage index PICP value is higher than the set confidence level, the adjustment strategy is as follows: the reduction of the average width index PINAW and the symmetry index PIS is more important than the increase of the coverage index PICP to improve the quality of the forecast interval;
when the upper boundary error UB_Err pre In the positive direction, the upper boundary prediction result UB is represented pre Greater than the set upper boundary UB con Then the upper boundary prediction result UB pre Subtracting the upper boundary error UB_Err pre To reduce the width of the forecast interval;
when the upper boundary error UB_Err pre When negative, the upper boundary prediction result UB is represented pre Less than the set upper boundary UB con Upper boundary error UB _ Err pre Switching to zero to avoid increasing the forecast interval width; LB (LB) pre Is to adjust policy and UB pre Conversely;
if the coverage index PICP value is lower than the set confidence level, it is more important to increase PICP than to decrease PINAW and PIS, so the strategy is adjusted as follows: upper boundary error ub_err pre And lower boundary error LB_Err pre Keeping unchanged to ensure that the forecast interval boundary approaches the set interval boundary; when the coverage rate index PICP is increased, the quality of the forecast interval is improved;
the final interval prediction result obtained through the difference correction strategy is expressed as:
wherein UB is cal And LB cal Representing the correction upper and correction lower boundaries, respectively.

Claims (10)

1. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network is characterized by comprising the following steps of:
step 1: collecting data, including a geographic potential dependent sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological sequence of a runoff region;
step 2: defining a coverage index PICP, an average width index PINAW and a symmetry index PIS;
step 3: optimizing a Pyraformer neural network model by adopting a convolution optimization algorithm to serve as a prediction model of a runoff interval;
step 4: operating the radial flow interval prediction model obtained in the step 3 by using the data in the step 1 to obtain a parameter feasible region of the model; defining a composite objective function CSWC of a convolution optimization algorithm by using the index in the step 2 as an adaptability function of the model, and optimizing predicted model parameters of a runoff interval in a parameter feasible domain range;
step 5: inputting the data set in the step 1 into the runoff interval prediction model after optimizing parameters in the step 4, extracting time-space dimension characteristics of the data, and predicting upper and lower boundaries of the runoff interval value by combining with the fully-connected prediction output layer; performing accuracy evaluation and correction on the upper and lower boundaries of the predicted runoff interval by using the indexes in the step 2;
step 6: calculating the upper and lower boundary errors of the predicted runoff interval to obtain error data, and sending the error data into a prediction model of the runoff interval after optimizing parameters to obtain a prediction result of the error data;
step 7: and designing an error correction strategy, and sending the prediction result of the error data into the error correction strategy to obtain a final interval prediction result.
2. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the data in the step 1 is an entire drainage basin including |v|=n sub-drainage basins, and the set of sub-drainage basin control sites is defined as v= { V 1 ,...,v n ,...,v N N represents the nth sub-watershed site; the dependency matrix between the sub-watershed control sites is l= { L geo ,L rel }, wherein L geo Is a geographic adjacency matrix L rel An adjacency matrix for potential spatial dependencies;
for any two different sub-watershed i and j, its geographic adjacency matrix and latent dependency matrix distribution are expressed as:
wherein CEPMI (v) i ,v j ) Copula entropy bias mutual information between the sub-watershed i and j is represented; l (L) rel =1, meaning that the partial mutual information of sub-watershed i and j is greater than a given threshold δ;
according to the distribution of the geographical adjacency matrix and the potential dependency matrix of any two different sub-watersheds i and j, a subscript T is intercepted along a time axis g The time sequence is a geographic potential dependency sequence
Analyzing the time dependence of the basin runoff process on periodicity and near moments,cut off subscripts T along time axis h 、T p And T m The time sequence segment is the input of the model at the adjacent time, the periodical repeated time and the historical meteorological sequence component, t 0 The time sequence sets are respectively expressed as
Is provided withRepresenting the runoff value at time t in the sub-basin n, then +.>The method comprises the steps of collecting runoff values of all sub-watershed at t time, namely a target value;
construction of sample set (x t ,Y t ) T=1, 2,., N, N represents the number of sub-watershed, i.e. the number of sample points, where x t ＝[L,K,P,T] T For the input data set, data information of a geographic potential dependency sequence L, a nearby sequence K, a periodic repeated sequence P and a historical meteorological sequence T is contained.
3. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the indexes in the step 2 are respectively as follows:
coverage index PICP:
when the target value is forecastedInter-overlay Shi Buer function c i The value of (2) is 1, otherwise 0;
average width index PINAW:
symmetry index PIS:
wherein N represents the size of the sample set, R is the value range of the target vector, i is the sample point, y i Representing the measured value of the i-th sample point; LB (LB) i And UB i Respectively represent y i Lower and upper limits of (2).
4. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the optimization method in the step 3 is as follows: introducing a convolution optimization algorithm MCOA to optimize parameters of the Pyraformer neural network model including learning rate, hidden layer number and number of detail points so as to improve the convergence rate of the model, wherein the specific optimization process is as follows: inputting the number of the initialized population, the dimension of the individual position, the maximum iteration times, the convolution kernel parameters and the fitness function; performing a location update strategy; updating the global optimal solution and the position thereof; and outputting the parameters of the optimal solution assigned to the Pyraformer neural network model.
5. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the method for obtaining the parameter feasible region of the runoff interval forecasting model in step 4 is as follows: initializing parameters of a runoff interval prediction model, inputting data, obtaining an optimal parameter set theta of the runoff interval prediction model, slightly perturbing the set theta, obtaining a parameter feasible region F, wherein the feasible region F is expressed as:
F＝[θ-ω≤θ≤θ+ω]。
6. the runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the complex objective function CSWC formula in the step 4 is as follows:
wherein a, b and c are weight values of indexes, and the smaller CSWC is, the higher the coverage rate of the forecast interval is, the smaller the width is, and the higher the symmetry is;
in the CSWC function, PIARW is used as a main measurement index, a is set to be a larger value to ensure that the coverage rate of a forecast interval is better, and then a more ideal forecast interval is obtained, and the sum form among PICP, PIARW and index PIS in the CSWC function is used to avoid the extreme condition that PIARW is 0 in the product form, namely the upper boundary and the lower boundary of the forecast interval are overlapped, and the forecast width is 0.
7. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the forecasting of the upper and lower boundaries of the runoff interval value in the step 5 comprises the following specific processes:
constructing a large matrix data set by using a geographic potential dependency sequence, a proximity sequence, a periodic repeated sequence and a historical meteorological element sequence, and sending the large matrix data set into a prediction model of a runoff interval, and constructing a multi-resolution C element tree by using a coarse scale construction module CSCM, wherein the coarse scale nodes summarize information of corresponding fine scale C nodes; the pyramid attention module PAM is introduced to further capture time-space dependencies of different ranges, and the attention mechanism in the pyramid diagram is utilized to transmit messages; the output of the fully-connected network is directly used as the prediction of the upper and lower boundaries of the interval prediction, the larger value is used as the upper boundary of the time prediction interval, and the smaller value is used as the lower boundary of the time prediction interval.
8. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the evaluating method in the step 5 is as follows:
when the value of the coverage rate index PICP is close to 1, the more actual measurement values are covered by the prediction interval, the better the effect of the prediction model of the runoff interval is; the average width index PINAW is as narrow as possible in an effective forecasting interval under the condition of higher coverage rate, so that the forecasting interval contains effective information;
when the forecast interval covers the actual measurement value, the symmetry index PIS takes the value between 0 and 0.5; when the actual measurement is in the center of the prediction interval, namely the optimal symmetry condition, the symmetry index PIS takes a value of 0; when the symmetry index PIS is close to 0, the symmetry of the prediction interval about the measured value is better; when the measured value is smaller than the lower boundary of the predicted interval and larger than the upper boundary of the predicted interval, the value of the symmetry index PIS is larger than 0.5, and the degree of asymmetry of the predicted interval to the measured value is high;
the correction method comprises the following steps: calculating the evaluation results of a coverage index PICP, an average width index PINAW and a symmetry index PIS according to the upper boundary and the lower boundary of the prediction interval, and giving a confidence probability of 100 (1-alpha)%, and correcting the prediction of the prediction interval which cannot meet the index by the following formula:
wherein,forecasting the upper and lower boundaries of the runoff interval value, wherein alpha is the significance level, and the forecasting interval is expressed as +.>The target vector is located in the forecast interval +.>The probability of (2) is expressed as
9. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the error data in step 6 is expressed as:
in the formula, UB_Err i 、And UB con Respectively representing an upper boundary error, a forecast upper boundary and a set upper boundary; LB_Err i 、/>And LB con Respectively representing a lower boundary error, a forecast lower boundary and a set lower boundary; wherein forecast boundary->Andis the value of the predicted result of the runoff interval prediction model and corrected by the result of the three indexes;
the method for obtaining the prediction result of the error data comprises the following steps: the UB_Err is used for i And LB_Err i The error data is input into a prediction model of the runoff interval to obtain prediction results of the error data, wherein the prediction results are respectively upper boundary prediction results UB_Err pre And lower boundary prediction result LB_Err pre 。
10. The runoff interval forecasting method based on the convolution optimization algorithm and the Pyraformer neural network according to claim 1, wherein the error correction strategy design process in the step 7 is as follows:
according to the prediction result of the runoff interval prediction model after optimizing the parametersAnd->Calculating a coverage rate index PICP value;
if the coverage index PICP value is higher than the set confidence level, the adjustment strategy is as follows:
when the upper boundary error UB_Err pre In the positive direction, the upper boundary prediction result UB is represented pre Greater than the set upper boundary UB con Then the upper boundary prediction result UB pre Subtracting the upper boundary error UB_Err pre To reduce the width of the forecast interval;
when the upper boundary error UB_Err pre When negative, the upper boundary prediction result UB is represented pre Less than the set upper boundary UB con Upper boundary error UB _ Err pre Switching to zero to avoid increasing the forecast interval width; LB (LB) pre Is to adjust policy and UB pre Conversely;
if the coverage index PICP value is lower than the set confidence level, the adjustment strategy is as follows: upper boundary error ub_err pre And lower boundary error LB_Err pre Keeping unchanged to ensure that the forecast interval boundary approaches the set interval boundary; when the coverage rate index PICP is increased, the quality of the forecast interval is improved;
the final interval prediction result obtained through the difference correction strategy is expressed as:
wherein UB is cal And LB cal Representing the correction upper and correction lower boundaries, respectively.
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