CN117077543B - Hydrologic model parameter calibration method based on gradient search shuffling complex evolutionary algorithm - Google Patents
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Abstract
The invention provides a hydrological model parameter calibration method based on a gradient search shuffling complex evolution algorithm, which comprises the following steps of data collection: performing complex division; extracting simplex; performing a falling search of the simplex; positioning a gradient descent fine search strategy; executing the gradient descent fine search strategy; complex cyclic competition evolution; mixing all the complex sample points to shuffle again after the complex circulation competition evolution is completed, and repeatedly executing the steps until convergence conditions are met; and outputting the optimal parameter set of the hydrologic model. According to the hydrological model parameter calibration method based on the gradient search shuffling complex evolution algorithm, the simplex downhill search is carried out by introducing the local optimal information in the complex competition evolution process, the introduction proportion of the local optimal information is adjusted in a heuristic mode according to the search effect, the simplex downhill search direction is optimized, and the deep search capability of the algorithm is enhanced.
Description
Technical Field
The invention relates to the technical field of drainage basin hydrologic models, in particular to a hydrologic model parameter calibration method based on a gradient search shuffling complex evolutionary algorithm.
Background
The shuffling complex evolutionary algorithm is a global optimization search algorithm, and is coupled with a plurality of methods such as random search, population competition evolutionary, simplex descent search, shuffling algorithm and the like. Compared with other global optimization algorithms (such as genetic algorithm, particle swarm optimization algorithm and the like), the shuffling complex evolution algorithm has obvious advantages in the effectiveness and robustness of global search, and is widely applied to the field of hydrological model parameter calibration.
The error response surface of the hydrologic model is very complex, and has the characteristics of high nonlinearity, discontinuous and non-guiding, and the like, and the global optimizing algorithm has a single concept of a depth searching scheme and a poor optimizing effect although the breadth searching capability is strong. The advanced search scheme adopted by the shuffling complex evolutionary algorithm is a complex competitive evolutionary algorithm, and the advanced search capability of the advanced search scheme has certain advantages compared with other global algorithms, but the optimizing effect is still poor when facing certain extremely complex error response surfaces. In recent years, although some scholars propose improvement on the complex competition evolution algorithm, the improvement of the optimizing effect of the algorithm is limited.
Therefore, the complex competition evolution algorithm still has great room for improvement, and can introduce a gradient descent fine search strategy combining an objective function and a spatial derivative, strengthen the depth search capability of the algorithm and improve the optimizing effect of hydrologic model parameter calibration.
The invention patent application with the application publication number of CN106709181A discloses a distributed hydrological model calibrating method based on parallel programming and a modular method, which comprises the following steps: 1) Based on the parallel programming environment constructed by MPICH, coupling an open source distributed hydrological model source program and a multi-objective optimization algorithm; 2) Calibrating a hydrologic model according to the daily runoff sequence and the peak value sequence respectively, and establishing a corresponding model frame; 3) And combining the runoff output of the model by using a module method to form a recombined simulated runoff result. The method has the disadvantage that the calculation speed of the algorithm is improved, the mechanism of the algorithm is not improved, and the quality of the solution is not improved.
The invention patent application with the application publication number of CN113255206A discloses a hydrological forecast model parameter calibration method based on deep reinforcement learning, which comprises the following steps: selecting a proper hydrological forecasting model according to the characteristics of the river basin, and determining parameters and parameter value ranges of model rating; establishing a reinforcement learning model with hydrologic prediction model parameter calibration, and determining three elements of reinforcement learning, namely a state space, an action space and a reward function; and optimizing the rating parameters of the hydrologic forecasting model by applying a deep reinforcement learning method DQN. The method has the defects of low calculation efficiency, long time consumption and special GPU hardware support; the method is easy to fall into a local optimal point and has poor global property; the AI training results are poor in stability, and the reliability of the multiple training results is required to be improved.
Disclosure of Invention
In order to solve the technical problems, the hydrological model parameter calibration method based on the gradient search shuffling complex evolution algorithm introduces a gradient descent fine search strategy in the complex competition evolution process, positions the search point position of successful simplex downhill search, and executes the gradient descent fine search strategy by taking the successful simplex downhill search point as an initial point, thereby greatly enhancing the depth search capability of the algorithm.
The invention aims to provide a hydrological model parameter calibration method based on a gradient search shuffling complex evolution algorithm, which comprises the following steps of data collection:
step 1: performing complex division;
step 2: extracting simplex;
step 3: performing a falling search of the simplex;
step 4: positioning a gradient descent fine search strategy;
step 5: executing the gradient descent fine search strategy;
step 6: complex cyclic competition evolution;
step 7: mixing all the complex sample points to re-shuffle after the complex circulation competition evolution is completed, and repeatedly executing the steps 1-6 until convergence conditions are met;
step 8: and outputting the optimal parameter set of the hydrologic model.
Preferably, the data collection includes:
1) Selecting a data stream domain and a proper hydrological model;
2) Collecting rainfall sequence and evaporation capacity sequence data of a data watershed as input variables of a hydrological model;
3) Determining reasonable upper and lower limits of various parameters of the hydrologic model for allowing variation, and determining a feasible space generated by a sample and a constraint domain of fine search;
4) Collecting the actual measurement runoff sequence data as a comparison sequence required by calculating the objective function evaluation value of each sample point;
5) And generating an ideal runoff sequence by using the manually set parameter set as a comparison sequence required for calculating the objective function evaluation value of each sample point.
In any of the above schemes, preferably, the step 1 includes the following substeps:
step 11: randomly generating a total sample in a parameter feasible space;
step 12: ascending order according to the evaluation value of each sample objective function;
step 13: extracting sample filling complex shape with complex shape number as interval number interval;
step 14: and finishing the complex division until all complex forms are filled.
In any of the above embodiments, it is preferable that the total number of samplessIs complex in numbermAnd the number of samples in complex formnIn the feasible space of the parameters, generating 0-1 uniformly distributed random numbers by a Meissn rotation algorithm, and randomly generating total samples by combining the absolute value of the difference between the allowable variation upper limit and the allowable variation lower limit of each parameter dimension and the lower limit value determined by each parameter dimensionD = {x i , i = 1, ...,sAnd } wherein,x i is the firstiAnd a number of sample points.
In any of the above embodiments, preferably, the step 12 includes the step of determining, based on each sample pointx i Substituting the simulated runoff sequence generated by the hydrologic model and the actually measured or ideal runoff sequence into the objective function to calculate the objective function evaluation valuef i And for the total samples d= {x i , f i I=1,..s } is sorted in ascending order according to the objective function evaluation value.
In any of the above embodiments, preferably, the step 13 includes, for the complex shapeA k From the ordered sample pointsx k In complex formmExtraction as interval numbernMultiple sample point filling complex shapeA k Wherein, the method comprises the steps of, wherein,k=1,…,m。
in any of the above embodiments, preferably, the step 13 further includes mixing the total sampleDDivided intomThe number of the complex-shape is that,D = {A k , k = 1, ..., mcomplex division is expressed as
，
Wherein,for the total sample, ++>Complex 1>In the form of a complex shape 2,is complex-shapedm。
In any of the above schemes, preferably, the step 2 includes the following substeps:
step 21: non-repeatedly extracting a complex sample point filling simplex according to the linear probability distribution;
step 22: the sample points in the simplex are sorted in ascending order according to the objective function evaluation value;
step 23: centroid points of the best point and the worst point in the simplex and other points except the worst point are recorded.
In any of the above embodiments, preferably, the step 21 includes setting a simplex sample numberqIs complex and has the number of inner samplesnIs non-repeatedly extracted according to a linear probability distributionnSerial numbers of the complex samples according tonExtracting complex sample points from the serial numbers of the complex samples, and filling the complex sample points into a simplex sample space X= {x i , f i , i = 1, ..., q}。
In any of the above schemes, it is preferable that the formula for extracting the sequence number using the linear probability distribution is as follows
，
Wherein,posin order to extract the serial number of the sample,npgin order to multiplex the number of members to be formed,genrand_real1 is a random number generator uniformly distributed by a Meissen rotation algorithm 0-1,to round down the symbol.
In any of the above schemes, preferably, the step 3 includes that the simplex worst point reflects or contracts with the simplex centroid point as a reference point, and linearly deviates from the simplex best point by a certain proportion, so as to generate a preliminary simplex search point: reflection pointX ref_ini Shrinkage pointX con_ini The formula is
X ref_ini= X w +2(X ce －X w )
，
Wherein,X w as the worst point of the simplex,X ce is a simplex centroid point.
In any of the above schemes, preferably, the step 3 further includes the following sub-steps:
step 31: simplex worst pointX w By simplex centroid pointsX ce Reflecting for a reference point;
step 32: initialization offlag =0, if the reflection pointX ref In the domain, then with reflection pointsX ref As a reflection step search point; if the reflection point isX ref Outside the domain, randomly generating sample points in the parameter feasible domain as reflection step search points and changingflag = 1；
Step 33: if the reflection step search point is a reflection pointX ref And the objective function evaluation valuef ref Less than simplex modeDifference pointX worst Is an objective function evaluation value of (a)f worst The simplex reflection search is considered to be successful to reflect the pointX ref As the final simplex search point;
step 34: if the reflection step search point is a random point and the objective function evaluation value f ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Taking the reflection step random point as a final simplex search point; if the reflection step searches the evaluation value of the point objective functionf ref Greater than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Step 35 is performed;
step 35: if the search point is contractedX con The objective function evaluation value is smaller than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Then the simplex search is considered successful to shrink the step search pointsX con As the final simplex search point; if the search point is contractedX con The objective function evaluation value is larger than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Randomly generating sample points in the parameter feasible domainX random As the final simplex search point.
In any of the above schemes, preferably, the step 4 includes marking the point as a gradient descent fine search strategy initiation point when the simplex search is successful, i.e., the reflection search is successful or the contraction search is successful.
In any of the above schemes, preferably, the step 4 further includes not marking any random points generated when the simplex search fails.
In any of the above schemes, preferably, after the simplex falling search is finished in the step 5, if the marking is executed in the step 4, the success point of the simplex falling search according to the marking is used as the initial solution variable of the gradient falling fine search strategyθPerforming gradient descent fine searchStrategyFSS。
In any of the above schemes, it is preferable that the gradient descent fine search strategyFSSComprises the following substeps:
step 51: initial sampling step sizehTaking half of the feasible range of each dimension parameter, and initializing the iteration timesit = 1；
Step 52: in sampling stepshEstimating solution variablesθIs of the residual vector of (2)rAnd Jacobian matrixJCalculating solution variablesθIs a gradient vector and hessian matrix;
step 53: evaluating the condition of an active set mark of each dimension parameter; constructing a gradient vector without non-free parameters according to the condition of the active set marks of the parameters of each dimensiongHehessian matrixH；
Step 54: gradient vector according to the removed non-free parametersgAnd the hessian matrixHSolving the search step using truncated SVD decomposition algorithmδAdjusting the search stepδTo avoid jumping out of the reasonable range of parameters;
step 55: from new search pointsθ+δSolving for a new solutionf t Performing line search policy calculationsf ls Updating according to the line search comparison strategyf t Andf ls ；
step 56: from gradient search resultsf t And the space point information BSP stored when evaluating the objective function each time, by searching the result with the linef ls To decide whether to increase or decrease the sampling step: gradient search resultsf t Or (b)BSPWhen the space point information is better, the sampling step length is increasedhThe method comprises the steps of carrying out a first treatment on the surface of the Line search resultsf ls Preferably, the sampling step length is reducedh；
Step 57: and (3) circularly iterating until convergence conditions of the gradient descent fine search strategy are met, and finally outputting a fine search solution vectorθAs an improvement point for simplex search success points.
In any of the above embodiments, preferably, the step 57 includes a simplex searchSuccess point isX ref Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX ref_fss The method comprises the steps of carrying out a first treatment on the surface of the If the simplex search success point isX con Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX con_fss 。
In any of the above embodiments, preferably, the step 6 includes replacing the simplex worst point if the simplex search is successfulX worst Fine search strategy for the gradient descentFSSImprovement of (2)X ref_fss Or (b)X con_fss The simplex sample points are re-embedded into the complex shape according to the original positions, and the sample points in the complex shape are ordered according to the ascending order of the objective function evaluation value.
In any of the above embodiments, preferably, the step 6 further includes when the number of complex competition evolutions reaches a set numberβAnd stopping the competition evolution of the multiplexing cycle.
In any of the above schemes, preferably, the convergence condition is that the change value of the objective function evaluation value of the optimal point in the total sample under a certain algebraic condition is smaller than a set threshold value
In any of the above schemes, preferably, the step 8 includes selecting a sample with the smallest evaluation value of the objective function among the total samples as the set of the optimal parameters of the hydrological model.
The invention provides a hydrological model parameter calibration method based on a gradient search shuffling complex evolution algorithm, which marks a search success point as an initial point of a gradient descent fine search strategy when a simplex is used for downhill search; the simplex random points are not marked, and the breadth searching capability of the algorithm is not weakened.
Drawings
FIG. 1 is a flow chart of a preferred embodiment of a hydrological model parameter calibration method based on a gradient search shuffle complex evolution algorithm in accordance with the present invention.
Fig. 2 is a flow chart of another preferred embodiment of a hydrological model parameter calibration method based on a gradient search shuffle complex evolution algorithm according to the present invention.
FIG. 3 is a flow chart of one embodiment of a gradient search-based complex competition evolutionary algorithm for a hydrological model parameter calibration method based on a gradient search shuffle complex evolutionary algorithm in accordance with the present invention.
FIG. 4 is a flow chart of one embodiment of a gradient descent refinement search strategy for a hydrological model parameter calibration method based on a gradient search shuffle complex evolution algorithm in accordance with the present invention.
Detailed Description
The invention is further illustrated by the following figures and specific examples.
Example 1
As shown in fig. 1, step 100 is performed to perform data collection, including:
1) Selecting a data stream domain and a proper hydrological model;
2) Collecting rainfall sequence and evaporation capacity sequence data of a data watershed as input variables of a hydrological model;
3) Determining reasonable upper and lower limits of various parameters of the hydrologic model for allowing variation, and determining a feasible space generated by a sample and a constraint domain of fine search;
4) Collecting the actual measurement runoff sequence data as a comparison sequence required by calculating the objective function evaluation value of each sample point;
5) And generating an ideal runoff sequence by using the manually set parameter set as a comparison sequence required for calculating the objective function evaluation value of each sample point.
Step 110 is performed to perform complex division, including the sub-steps of:
step 111 is executed to randomly generate total samples in the parameter feasible space, and the total sample numbersIs complex in numbermAnd the number of samples in complex formnIn the feasible space of the parameters, generating 0-1 uniformly distributed random numbers by a Meissn rotation algorithm, and randomly generating total samples by combining the absolute value of the difference between the allowable variation upper limit and the allowable variation lower limit of each parameter dimension and the lower limit value determined by each parameter dimensionD = {x i , i = 1, ..., sAnd } wherein,x i is the firstiAnd a number of sample points.
Step 112 is executed to sort according to the ascending order of the objective function evaluation values of the samples, and according to the sample pointsx i Substituting the simulated runoff sequence generated by the hydrologic model and the actually measured or ideal runoff sequence into the objective function to calculate the objective function evaluation valuef i And for the total samples d= {x i , f i I=1,..s } is sorted in ascending order according to the objective function evaluation value.
Step 113 is executed to extract sample filling complex shape with complex shape number as interval number interval, for complex shapeA k From the ordered sample pointsx k In complex formmExtraction as interval numbernMultiple sample point filling complex shapeA k Wherein, the method comprises the steps of, wherein,k=1,…,m. Total sample is takenDDivided intomThe number of the complex-shape is that,D = {A k , k = 1, ..., mcomplex division is expressed as
，
Wherein,for the total sample, ++>Complex 1>In the form of a complex shape 2,is complex-shapedm。
Step 114 is performed until all the complex shapes are filled, and the complex shape division is completed.
Step 120 is performed to extract the simplex, comprising the sub-steps of:
step 121 is executed to set the number of simplex samples by non-repeatedly extracting the complex sample point-filling simplex according to the linear probability distributionqIs complex internal sampleNumber of principal pointsnIs non-repeatedly extracted according to a linear probability distributionnSerial numbers of the complex samples according tonExtracting complex sample points from the serial numbers of the complex samples, and filling the complex sample points into a simplex sample space X= {x i , f i , i = 1, ..., q}. The formula for extracting the serial number by adopting the linear probability distribution is as follows
，
Wherein,posin order to extract the serial number of the sample,npgin order to multiplex the number of members to be formed,genrand_real1 is a random number generator uniformly distributed by a Meissen rotation algorithm 0-1,to round down the symbol.
Step 122 is executed, wherein the sample points in the simplex are sorted according to the ascending order of the objective function evaluation value;
step 123 is performed to record centroid points of the best point and the worst point in the simplex and points other than the worst point.
Step 130 is executed to perform the descent search of the simplex, where the worst simplex point reflects or contracts with the simplex centroid point as a reference point, and linearly deviates from the simplex centroid point by a certain proportion, so as to generate a preliminary simplex search point: reflection pointX ref_ini Shrinkage pointX con_ini The formula is
X ref_ini= X w +2(X ce －X w )
，
Wherein,X w as the worst point of the simplex,X ce is a simplex centroid point.
Step 130 includes the sub-steps of:
step 131, simplex worst pointX w By simplex centroid pointsX ce Reflecting for a reference point;
step 132, initializingflag =0, if the reflection pointX ref In the domain, then with reflection pointsX ref As a reflection step search point; if the reflection point isX ref Outside the domain, randomly generating sample points in the parameter feasible domain as reflection step search points and changingflag = 1；
Step 133, if the reflection step search point is a reflection pointX ref And the objective function evaluation valuef ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst The simplex reflection search is considered to be successful to reflect the pointX ref As the final simplex search point;
step 134, if the reflection step search point is a random point and the objective function evaluation value f ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Taking the reflection step random point as a final simplex search point; if the reflection step searches the evaluation value of the point objective functionf ref Greater than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Step 135 is performed;
step 135, if the step search points are contractedX con The objective function evaluation value is smaller than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Then the simplex search is considered successful to shrink the step search pointsX con As the final simplex search point; if the search point is contractedX con The objective function evaluation value is larger than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Randomly generating sample points in the parameter feasible domainX random As the final simplex search point.
Step 140 is performed to locate the gradient descent fine search strategy, and when the simplex search is successful, i.e., the reflection search is successful or the contraction search is successful, the point is marked as the gradient descent fine search strategy initiation point. The random points generated when the simplex search fails are not marked.
Executing step 150, wherein after the gradient descent fine search strategy is executed and the simplex descent search is finished, if the step 140 executes the marking, the success point of the marked simplex search is used as the initial solution variable of the gradient descent fine search strategyθPerforming gradient descent fine search strategyFSS。
The gradient descent fine search strategyFSSComprises the following substeps:
step 151 is executed to initially sample the step sizehTaking half of the feasible range of each dimension parameter, and initializing the iteration timesit = 1；
Step 152 is performed to sample the step sizehEstimating solution variablesθIs of the residual vector of (2)rAnd Jacobian matrixJCalculating solution variablesθIs a gradient vector and hessian matrix;
executing step 153, and evaluating the condition of the active set marks of the dimension parameters; constructing a gradient vector without non-free parameters according to the condition of the active set marks of the parameters of each dimensiongHehessian matrixH；
Step 154 is executed according to the gradient vector without the non-free parametersgAnd the hessian matrixHSolving the search step using truncated SVD decomposition algorithmδAdjusting the search stepδTo avoid jumping out of the reasonable range of parameters;
step 155 is performed according to the new search pointsθ+δSolving for a new solutionf t Performing line search policy calculationsf ls Updating according to the line search comparison strategyf t Andf ls ；
step 156 is performed based on the gradient search resultsf t Each time an objective function is evaluatedStored spatial point information BSP, by and line search resultsf ls To decide whether to increase or decrease the sampling step: gradient search resultsf t Or (b)BSPWhen the space point information is better, the sampling step length is increasedhThe method comprises the steps of carrying out a first treatment on the surface of the Line search resultsf ls Preferably, the sampling step length is reducedh；
Executing step 157, iterating circularly until the convergence condition of the gradient descent fine search strategy is met, and finally outputting the fine search solution vectorθAs the improvement point of the simplex search success point, if the simplex search success point isX ref Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX ref_fss The method comprises the steps of carrying out a first treatment on the surface of the If the simplex search success point isX con Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX con_fss 。
Step 160 is executed to perform the complex loop competition evolution to replace the worst point of the simplex if the simplex search is successfulX worst Fine search strategy for the gradient descentFSSImprovement of (2)X ref_fss Or (b)X con_fss The simplex sample points are re-embedded into the complex shape according to the original positions, and the sample points in the complex shape are ordered according to the ascending order of the objective function evaluation value. When the number of complex competition evolutions reaches the set numberβAnd stopping the competition evolution of the multiplexing cycle.
After all of the complex loop race evolutions are completed, all of the complex sample points are mixed and reshuffled, step 170 is performed.
Step 180 is executed to determine whether a convergence condition is satisfied, where the convergence condition is that a change value of an objective function evaluation value of an optimal point in the total sample under a certain algebra is smaller than a set threshold. If the convergence condition is not satisfied, re-executing step 110; if the convergence condition is satisfied, step 190 is executed to output a set of optimal parameters of the hydrological model, and a sample with the smallest evaluation value of the objective function is selected from the total samples as the set of optimal parameters of the hydrological model obtained by calibration.
Example 2
The invention provides a hydrological model parameter calibration method based on a gradient search shuffling complex evolution algorithm, which introduces a gradient descent fine search strategy in the complex competition evolution process, positions the search point position of successful simplex downhill search, executes the gradient descent fine search strategy by taking the successful simplex downhill search point as an initial point, and then completes optimization search work through the complex circulation competition evolution and total sample shuffling to strengthen the deep search capability of the algorithm. In order to solve the technical problems, the invention adopts the following scheme:
a hydrological model parameter calibration method based on a gradient search shuffling complex evolution algorithm comprises the following steps:
step 1, data preparation: the method comprises a specific hydrologic model, wherein the hydrologic model is applicable to rainfall data and evaporation data of a data river basin, and the rainfall data and the evaporation data are actually measured runoff sequence data or ideal runoff sequence data generated by a manual parameter group, and the river basin related parameters are needed by the hydrologic model;
in step 1, ideal runoff sequence data is obtained by combining rainfall and evaporation sequence data through a set of parameter sets manually set in a reasonable parameter range and inputting the rainfall and evaporation sequence data into a hydrological model.
Step 2, complex division: randomly generating a total sample in a parameter feasible space; ascending order according to the evaluation value of each sample objective function; extracting sample filling complex shape with complex shape number as interval number interval; and finishing the complex division until all complex forms are filled.
In step 2, randomly generating a total sample in a parameter feasible space through a Meissen rotation algorithm; calculating an objective function evaluation value according to the simulated runoff sequence and the actual measurement or ideal runoff sequence generated by substituting each sample into the hydrologic model, and sequencing the total samples in ascending order; extracting sample points at intervals of complex number as interval number to fill a complex shape; until all complex forms are filled.
Step 3, simplex extraction: non-repeatedly extracting a complex sample point filling simplex according to the linear probability distribution; the sample points in the simplex are sorted in ascending order according to the objective function evaluation value; centroid points of the best point and the worst point in the simplex and other points except the worst point are recorded.
In step 3, setting the simplex sample size to be half of the complex sample size; non-repeatedly extracting a complex sample point filling simplex according to the linear probability distribution; the sample points in the simplex are sorted in ascending order according to the objective function evaluation value; record centroid points of worst points (last position after ascending) and other points except the worst points in the simplex.
Step 4, simplex descent search: the simplex worst point uses the simplex centroid point as the reference point to reflect or shrink, and generates the simplex search point.
In step 4, the core of the complex competition evolution is simplex downhill search: the worst point of the simplex is reflected by taking the centroid point of the simplex as a reference point. If the reflection point is in the domain, taking the reflection point as a reflection step searching point; if the reflection point is outside the domain, randomly generating sample points in the parameter feasible domain as reflection step search points. If the reflection step search point is a reflection point and the objective function evaluation value is smaller than the simplex worst point, the simplex reflection search is considered to be successful, and the reflection point is taken as a final simplex search point; if the reflection step searching point is a random point and the objective function evaluation value is smaller than the simplex worst point, the reflection step random point is used as a final simplex searching point; if the evaluation value of the object function of the searching point of the reflection step is larger than the worst point of the simplex, the step is shifted to a contraction step. If the target function evaluation value of the contracted step search point is smaller than the worst point of the simplex, the contracted step search point is regarded as successful in the simplex contracted search, and the contracted step search point is taken as the final simplex search point; if the object function evaluation value of the contracted searching point is larger than the worst point of the simplex, the sample point is randomly generated in the parameter feasible domain as the final simplex searching point (the point is not evaluated to be compared with the worst point object function evaluation value of the simplex).
Step 5, positioning a gradient descent fine search strategy: marking the successful point of simplex descent search, and taking the point as the initial point of gradient descent fine search strategy.
In step 5, when the simplex search is successful (reflection search is successful or contraction search is successful), the point is marked as the initial point of the gradient descent fine search strategy.
Step 6, executing a gradient descent fine search strategy: and executing a gradient descent fine search strategy on the simplex search success points, and outputting a fine search solution vector and a fine search solution as improvement points of the simplex search success points.
In step 6, after the simplex descent search is finished, if the marking is executed in step 5, the gradient descent fine search strategy is executed according to the marked simplex search success point as the gradient descent fine search strategy initial point. Based on the gradient vector and the hessian matrix, the search step length is solved, the real-time correction is assisted by a line search scheme, and the loop iteration finally outputs a fine search solution vector and a fine search solution as improvement points of simplex search success points.
Step 7, complex form circulation competition evolution: replacing the worst point of the simplex as a simplex search point, re-embedding the simplex sample point into the complex according to the original position, and sequencing the complex according to the ascending order of the objective function evaluation value; repeating the steps 3-7 until the complex competition evolution times reach the set times.
In step 7, replacing the worst point of the simplex as the final simplex search point, re-embedding the simplex sample points into the complex form according to the original position, and sorting the sample points in the complex form according to the ascending order of the objective function evaluation value; repeating the steps 3-7 to circularly evolve the complex until the complex competition evolution times reach the set times (generally twice the parameter dimension).
Step 8, total sample shuffling: mixing all the complex sample points for reshuffling after the complex cyclic competition evolution is completed; and (5) repeating the steps 2-8 until the convergence condition is met.
In step 8, after all the complex-shaped cyclic competition evolution is completed, mixing all the complex-shaped sample points for reshuffling; step 2-step 8 (the total samples are not randomly generated when step 2 is repeated) is repeated until convergence conditions are met (the optimal objective function evaluation value can be formulated from the objective function evaluation times with the maximum limit, the constant angle tends to be formed in n generations).
Step 9, outputting the optimal parameter set of the hydrologic model: stopping running after the algorithm meets the convergence condition, and outputting an optimal target parameter set;
in step 9, the algorithm stops running after meeting the convergence condition, and a sample with the minimum evaluation value of the objective function is selected from the total samples as the optimal parameter set of the hydrological model obtained by calibration.
The hydrological model parameter calibration method based on the gradient search shuffling complex evolution algorithm has the following beneficial effects:
on the basis of a shuffling complex competition algorithm, marking a successful searching point as an initial point of a gradient descent fine searching strategy when a simplex is used for downhill searching; the simplex random points are not marked, and the breadth searching capability of the algorithm is not weakened.
When the simplex downhill search is performed, the simplex downhill search success point is marked as an initial point of a gradient descent fine search strategy, the search step length is solved based on the gradient vector and the hessian matrix, the line search scheme is assisted for real-time correction, the fine search solution vector and the fine search solution are finally output through loop iteration and serve as improved points of the simplex search success point, and the depth search capability of an algorithm is greatly enhanced.
Example 3
As shown in fig. 2 and 3, the present invention is based on a shuffling complex evolution algorithm, and the specific implementation modes are as follows:
1. data preparation (as shown in FIG. 2)
A data basin and a proper hydrologic model are selected. Collecting rainfall sequence and evaporation capacity sequence data of a data watershed as input variables of a hydrological model; determining reasonable upper and lower limits of various parameters of the hydrologic model for allowing variation, and determining a feasible space generated by a sample and a constraint domain of fine search; when the method is actually applied, the actual measurement runoff sequence data is collected and used as a comparison sequence required by calculating the objective function evaluation value of each sample point; when the performance of the algorithm is evaluated, an ideal runoff sequence is generated by a manually set parameter set and is used as a comparison sequence required for calculating the evaluation value of the objective function of each sample point.
2. Complex division (as shown in figure 2)
Total number of samplessIs fixed to complex numbermAnd the number of samples in complex formnProduct of (2). In a parameter feasible space, generating 0-1 uniformly distributed random numbers through a Meissen rotation algorithm, and randomly generating a total sample by combining an absolute value of a difference between upper and lower allowable change limits of each parameter dimension and a lower limit value determined by each parameter dimensionD = {x i , i = 1, ..., s-a }; according to each sample pointx i Substituting the simulated runoff sequence generated by the hydrologic model and the actually measured or ideal runoff sequence into the objective function to calculate the objective function evaluation valuef i And for the total sampleD = {x i , f i , i = 1, ..., sAscending order according to the evaluation value of the objective function; for complex shapeA 1 From the ordered sample points x 1 Starting with a complex number ofmExtraction as interval numbernMultiple sample point filling complex shapeA 1 Repeating the steps to obtain a total sampleDDivided intomThe number of the complex-shape is that,D = {A k , k = 1, ..., m}。
the specific scheme of complex division is as follows:
3. simplex extraction (as shown in fig. 3)
Setting the number of simplex samplesqIs half of complex sample number, and is extracted non-repeatedly according to linear probability distributionnSerial numbers of the complex samples according tonExtracting complex sample points from the serial numbers of the complex samples, and filling the complex sample points into a simplex sample spaceX = {x i , f i , i = 1, ..., q-a }; the calculation formula for extracting the serial number by the linear probability distribution is shown in formula (1). The sample points in the simplex are sorted according to the ascending order of the evaluation value of the objective function, and the optimal points in the simplex are recordedX best (first digit after ascending order)X 1 ) And the worst pointX worst (last position after ascending order)X q ) Centroid point of other points except the worst pointX ce，
(1)
Wherein:posin order to extract the serial number of the sample,npgto multiplex the number of formants (number of samples),genrand_real1 is a random number generator uniformly distributed by a Meissen rotation algorithm 0-1.To round down the symbol.
4. Simplex descent search (as shown in fig. 3)
The core of complex competition evolution is simplex downhill search; the simplex worst point uses the simplex centroid point as a reference point to reflect or shrink, and a preliminary simplex search point is generated. Generating preliminary search points-reflection pointsX ref Shrinkage pointX con The formula of (2) is as follows:
X ref_ini= X w +2(X ce －X w ) (2)
(3)
simplex worst pointX w First, the centroid point of simplex is usedX ce Reflecting for the reference point. Initialization offlag=0, if the reflection pointX ref In the domain, then with reflection pointsX ref As a reflection step search point; if the reflection point isX ref Outside the domain, randomly generating sample points in the parameter feasible domain as reflection step search points and changingflag =1. If the reflection step search point is a reflection pointX ref And the objective function evaluation valuef ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst It is regarded as simpleSuccessful form reflection search to reflect the pointX ref As the final simplex search point; if the reflection step search point is a random point and the objective function evaluation valuef ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Taking the reflection step random point as a final simplex search point; if the reflection step searches the evaluation value of the point objective functionf ref Greater than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Then go to the shrink step. If the search point is contractedX con The objective function evaluation value is smaller than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Then the simplex search is considered successful to shrink the step search pointsX con As the final simplex search point; if the search point is contractedX con The evaluation value of the objective function is larger than the worst point X of the simplex worst Is an objective function evaluation value of (a)f worst Randomly generating sample points in the parameter feasible domainX random As the final simplex search point (the point is no longer evaluated for its merits as compared to the simplex worst point objective function evaluation value).
5. Localization of gradient descent fine search strategy (as shown in FIG. 3)
According to step 4, when the simplex search is successful, i.e. the reflection search is successful or the contraction search is successful, the point is marked as the initial point of the gradient descent fine search strategy. In addition, any mark is not made on the random points generated when the simplex search fails, so that the breadth search capability of the algorithm is prevented from being weakened.
6. Execution of gradient descent fine search strategy (as shown in FIG. 4)
After simplex descent search is finished, if the step 5 executes marking, the success point of simplex search according to the marking is used as the initial solution variable of the gradient descent fine search strategyθPerforming gradient descent fine search strategyFSS。
(1) Initial sampling stepTaking the length h as half of the feasible range of each dimension parameter, and initializing the iteration timesit = 1；
(2) In sampling stepshEstimating solution variablesθIs of the residual vector of (2)rAnd Jacobian matrixJCalculating a solution variableθIs a gradient vector and hessian matrix;
(3) Evaluating the condition of an active set mark of each dimension parameter; constructing a gradient vector without non-free parameters according to the condition of the active set marks of the parameters of each dimensiongHehessian matrixH；
(4) Gradient vector based on removal of non-free parametersgHehessian matrixHSolving the search step using truncated SVD decomposition algorithmδAdjusting the search stepδTo avoid jumping out of the reasonable range of parameters;
(5) From new search pointsθ+δSolving for a new solutionf t Performing line search policy calculationsf ls Updating according to the line search comparison strategyf t Andf ls ；
(6) From the gradient search results f t And the information of the space point stored when evaluating the objective function each timeBSP) Search results by and linef ls To decide whether to increase or decrease the sampling step: gradient search resultsf t Or (b)BSPBetter, increase sampling stephThe method comprises the steps of carrying out a first treatment on the surface of the Line search resultsf ls Preferably, the sampling step length is reducedh；
(7) And (3) circularly iterating until convergence conditions of the gradient descent fine search strategy are met, and finally outputting a fine search solution vectorθImproved points as simplex search success points (if simplex search success points areX ref Then viaFSSThe improvement points of (1) are thatX ref_fss The method comprises the steps of carrying out a first treatment on the surface of the If the simplex search success point isX con Then viaFSSThe improvement points of (1) are thatX con_fss ）。
7. Complex cyclic competition evolution (as shown in figure 3)
If it is singlySuccessful simplex search, replacing the worst point of simplexX worst The method is characterized in that the method is an improved simplex search pointX ref_fss Or (b)X con_fss ) Re-embedding the simplex sample points into the complex shape according to the original position, and sorting the sample points in the complex shape according to the ascending order of the objective function evaluation value; repeating the steps 3-7 to circularly evolve the complex until the complex competition evolution times reach the set timesβ(typically set to twice the parameter dimension).
8. Total sample shuffling (as shown in figure 2)
Mixing all the complex sample points for reshuffling after the complex cyclic competition evolution is completed; step 2-step 8 (the total samples are not randomly generated when step 2 is repeated) is repeated until convergence conditions are met (the optimal objective function evaluation value can be formulated from the objective function evaluation times with the maximum limit, the constant angle tends to be formed in n generations).
9. Output hydrologic model optimal parameter set (as shown in figure 2)
And stopping running after the algorithm meets the convergence condition, and selecting a sample with the minimum target function evaluation value from the total samples as an optimal parameter set of the hydrological model obtained by calibration.
The foregoing description of the invention has been presented for purposes of illustration and description, but is not intended to be limiting. Any simple modification of the above embodiments according to the technical substance of the present invention still falls within the scope of the technical solution of the present invention. In this specification, each embodiment is mainly described in the specification as a difference from other embodiments, and the same or similar parts between the embodiments need to be referred to each other. For system embodiments, the description is relatively simple as it essentially corresponds to method embodiments, and reference should be made to the description of method embodiments for relevant points.
Claims (6)
1. The hydrological model parameter calibration method based on the gradient search shuffling complex evolution algorithm comprises the steps of data collection and is characterized by further comprising the following steps:
step 1: performing complex division;
step 2: extracting simplex;
step 3: performing a falling search of the simplex, comprising the sub-steps of:
step 31: simplex worst pointX w By simplex centroid pointsX ce Reflecting for a reference point;
step 32: initialization offlag =0, if the reflection pointX ref In the domain, then with reflection pointsX ref As a reflection step search point; if the reflection point isX ref Outside the domain, randomly generating sample points in the parameter feasible domain as reflection step search points and changingflag = 1；
Step 33: if the reflection step search point is a reflection pointX ref And the objective function evaluation valuef ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst The simplex reflection search is considered to be successful to reflect the pointX ref As the final simplex search point;
step 34: if the reflection step search point is a random point and the objective function evaluation value f ref Less than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Taking the reflection step random point as a final simplex search point; if the reflection step searches the evaluation value of the point objective functionf ref Greater than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Step 35 is performed;
step 35: if the search point is contractedX con The objective function evaluation value is smaller than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Then the simplex search is considered successful to shrink the step search pointsX con As the final simplex search point; if the search point is contractedX con The objective function evaluation value is larger than the simplex worst pointX worst Is an objective function evaluation value of (a)f worst Randomly generating sample points in the parameter feasible domainX random As the final simplex search point;
step 4: a localization gradient descent fine search strategy comprising: when simplex searching is successful, namely reflection searching is successful or shrinkage searching is successful, marking the point as an initial point of a gradient descent fine searching strategy, and not marking any random point generated when simplex searching fails;
step 5: executing the gradient descent fine search strategy, wherein the step 5 comprises the step of taking the successful point of the simplex search marked as the initial solution variable of the gradient descent fine search strategy if the step 4 executes the marking after the simplex descent search is finishedθPerforming gradient descent fine search strategyFSSThe gradient descent fine search strategyFSSComprises the following substeps:
step 51: initial sampling step sizehTaking half of the feasible range of each dimension parameter, and initializing the iteration timesit = 1；
Step 52: in sampling stepshEstimating solution variablesθIs of the residual vector of (2)rAnd Jacobian matrixJCalculating solution variablesθIs a gradient vector and hessian matrix;
step 53: evaluating the condition of an active set mark of each dimension parameter; constructing a gradient vector without non-free parameters according to the condition of the active set marks of the parameters of each dimensiongHehessian matrixH；
Step 54: gradient vector according to the removed non-free parametersgAnd the hessian matrixHSolving the search step using truncated SVD decomposition algorithmδAdjusting the search stepδTo avoid jumping out of the reasonable range of parameters;
step 55: from new search pointsθ+δSolving for a new solutionf t Performing line search policy calculationsf ls Updating according to the line search comparison strategyf t Andf ls ；
step 56: from gradient search resultsf t And the space point information BSP stored when evaluating the objective function each time, by searching the result with the linef ls To decide whether to increase or decrease the sampling step: gradient search resultsf t Or (b)BSPWhen the space point information is better, the sampling step length is increasedhThe method comprises the steps of carrying out a first treatment on the surface of the Line search resultsf ls Preferably, the sampling step length is reducedh；
Step 57: and (3) circularly iterating until convergence conditions of the gradient descent fine search strategy are met, and finally outputting a fine search solution vectorθAs an improvement point of simplex search success points;
step 6: complex cyclic competition evolution;
step 7: mixing all the complex sample points to re-shuffle after the complex circulation competition evolution is completed, and repeatedly executing the steps 1-6 until convergence conditions are met;
step 8: and outputting the optimal parameter set of the hydrologic model.
2. The hydrographic model parameter calibration method based on the gradient search shuffle complex evolutionary algorithm of claim 1, wherein said data collection comprises:
1) Selecting a data watershed and a hydrological model;
2) Collecting rainfall sequence and evaporation capacity sequence data of a data watershed as input variables of a hydrological model;
3) Determining reasonable upper and lower limits of various parameters of the hydrologic model for allowing variation, and determining a feasible space generated by a sample and a constraint domain of fine search;
4) Collecting the actual measurement runoff sequence data as a comparison sequence required by calculating the objective function evaluation value of each sample point;
5) And generating an ideal runoff sequence by using the manually set parameter set as a comparison sequence required for calculating the objective function evaluation value of each sample point.
3. The method for calibrating hydrological model parameters based on gradient search shuffle complex evolution algorithm according to claim 2, wherein said step 1 comprises the following sub-steps:
step 11: randomly generating a total sample in a parameter feasible space;
step 12: ascending order according to the evaluation value of each sample objective function;
step 13: extracting sample filling complex shape with complex shape number as interval number interval;
step 14: and finishing the complex division until all complex forms are filled.
4. The method for calibrating hydrological model parameters based on gradient search shuffle complex evolution algorithm according to claim 3, wherein said step 2 comprises the sub-steps of:
step 21: non-repeatedly extracting a complex sample point filling simplex according to the linear probability distribution;
step 22: the sample points in the simplex are sorted in ascending order according to the objective function evaluation value;
step 23: centroid points of the best point and the worst point in the simplex and other points except the worst point are recorded.
5. The method for calibrating hydrological model parameters based on gradient search shuffle complex evolution algorithm according to claim 4, wherein the step 3 comprises the steps of reflecting or shrinking the worst simplex point by taking the simplex centroid point as a reference point and linearly shifting the best simplex point in a certain proportion to generate a preliminary simplex search point: reflection pointX ref_ini Shrinkage pointX con_ini The formula is
X ref_ini= X w +2(X ce －X w )
，
Wherein,X w as the worst point of the simplex,X ce is a simplex centroid point.
6. The method for calibrating hydrological model parameters based on gradient search shuffle complex evolutionary algorithm according to claim 5, wherein said step 57 comprises if simplex search success points areX ref Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX ref_fss The method comprises the steps of carrying out a first treatment on the surface of the If the simplex search success point isX con Fine search strategy is then dropped via the gradientFSSThe improvement points of (1) are thatX con_fss 。
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