CN108920737B - Particle filtering assimilation method and device of hydrodynamic model and computing equipment - Google Patents

Particle filtering assimilation method and device of hydrodynamic model and computing equipment Download PDF

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CN108920737B
CN108920737B CN201810372803.8A CN201810372803A CN108920737B CN 108920737 B CN108920737 B CN 108920737B CN 201810372803 A CN201810372803 A CN 201810372803A CN 108920737 B CN108920737 B CN 108920737B
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冶运涛
曹引
梁犁丽
蒋云钟
顾晶晶
方海泉
龚家国
赵红莉
张双虎
杜军凯
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China Institute of Water Resources and Hydropower Research
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Abstract

The invention provides a particle filter assimilation method, a particle filter assimilation device and a particle filter assimilation computing device of a hydrodynamic model, which are specifically used for collecting computing parameters of a research area and setting the size of a grid of the research area and boundary conditions of inflow and outflow; generating a plurality of equally weighted particles according to the parameters at the current moment; respectively utilizing the water flow state and model roughness coefficient contained in each particle, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the update of the hydrodynamic model output from the current moment to the next moment; calculating the likelihood function value of each particle at the next moment, and updating the weight of the particle; and calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient. Due to the fact that the time-space variability of the roughness coefficient is considered in the scheme, the accuracy and the reliability of the output result of the hydrodynamic model are high, the optimal estimation values of the state variables and the roughness coefficients at different spaces can be accurately obtained, and the accuracy and the reliability of the output result of the hydrodynamic model are improved.

Description

Particle filtering assimilation method and device of hydrodynamic model and computing equipment
Technical Field
The invention relates to the technical field of water conservancy, in particular to a particle filter assimilation method and device of a hydrodynamic model and computing equipment.
Background
The hydrodynamic model is an important tool for simulating the motion state of water bodies in water areas such as lakes, rivers, seacoasts and the like, can effectively support management decisions, and is widely applied to the fields of dam-break water flow simulation, flood forecasting, water quality simulation prediction and the like. In practice, the data such as water terrain, inflow and outflow flow and the like required by hydrodynamic model modeling are often difficult to accurately measure, and in addition, because important parameter roughness coefficients for representing roughness in the hydrodynamic model cannot be directly measured, and errors caused by grid dispersion, model structure and the like, the output result of the hydrodynamic model is full of uncertainty, and the accuracy and reliability of the output result of the hydrodynamic model are reduced.
The inventor of the application finds in practice that observation data can be reasonably fused into a hydrodynamic model by using a data assimilation technology, and system states and parameters are continuously updated in the process of simulating by using the hydrodynamic model, so that model uncertainty can be reduced, and the simulation or prediction precision of a physical process can be finally improved. The particle filter algorithm is used as a sequential Bayes filter data assimilation algorithm, can approximately obtain mathematical expectation of any function form taking state variables and parameters as independent variables, utilizes a certain number of random particles to represent posterior probability density distribution of the state variables and the parameters in the model, and can be applied to any nonlinear random model.
The roughness coefficient is influenced by factors such as the roughness of a riverbed and a quay wall, the water flow state, aquatic plants and the submerging state of the aquatic plants, has obvious space-time variability, and cannot capture the influence of the space variability on a model simulation result only by a data assimilation method considering the time variability of the roughness coefficient, so that the optimal estimation values of state variables and the roughness coefficient at different spaces are difficult to accurately obtain, and the accuracy and the reliability of the output result of the hydrodynamic model are poor.
Disclosure of Invention
In view of this, the present invention provides a particle filtering assimilation method, device and computing apparatus for a hydrodynamic model, so as to solve the problem of poor accuracy and reliability of the output result of the current hydrodynamic model.
In order to solve the above problems, the present invention discloses a particle filter assimilation method of a hydrodynamic model, which comprises the following steps:
collecting calculation parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all the grids at the current moment to obtain a particle set;
respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the update of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
judging whether a water level observation value exists in the simulated water level at the current moment, and if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value;
calculating an optimal estimated value of the simulated water level, the simulated flow and a preset roughness coefficient;
performing polynomial resampling on the particles to obtain a new particle set;
and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. Optionally, the calculated parameters include part or all of a bottom elevation, a boundary inflow flow, an initial water level, and an initial flow of the study area.
Optionally, the preset roughness coefficient is a roughness coefficient prior value.
Optionally, the performing polynomial resampling on the particle includes:
randomly generating a plurality of random numbers from the [0,1] uniform distribution;
and sampling the particles corresponding to the random numbers meeting the preset conditions in the plurality of random numbers as new sample points to obtain a new particle set.
There is also provided a particle filter assimilation device for hydrodynamic modeling, comprising:
the parameter acquisition module is used for acquiring calculation parameters of a research area and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
the first particle sampling module is used for generating a plurality of particles with equal weight according to the water levels and the flow of all the grids at the current moment and a preset roughness coefficient to obtain a particle set;
the model output module is used for respectively utilizing the water flow state and the model roughness coefficient contained in each particle in the particle set and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model so as to realize the update of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
the condition judgment module is used for judging whether a water level observation value exists in the simulated water level at the current moment or not, and if the water level observation value does not exist, directly executing the simulation of outputting the simulated water level and the simulated flow by the hydrodynamic model;
a first calculating module, configured to calculate a likelihood function value of each particle at the next time if the water level observation value exists, and update a weight of the particle with the likelihood function value;
the second calculation module is used for calculating the optimal estimated value of the simulated water level, the simulated flow and the preset roughness coefficient;
the second particle sampling module is used for performing polynomial resampling on the particles to obtain a new particle set;
and a particle set replacement module, configured to replace the particle set with the new particle set, and perform the step of outputting the simulated water level and the simulated flow rate by using the next time as the current time.
Optionally, the calculated parameters include part or all of a bottom elevation, a boundary inflow flow, an initial water level, and an initial flow of the study area.
Optionally, the preset roughness coefficient is a roughness coefficient prior value.
Optionally, the second particle sampling module includes:
a random number generation unit for randomly generating a plurality of random numbers from [0,1] uniform distribution;
and the sampling execution unit is used for sampling the particles corresponding to the random numbers meeting the preset conditions in the plurality of random numbers as new sample points to obtain the new particle set.
In addition, the computing equipment is provided with the particle filter assimilation device.
There is also provided another computing device comprising at least one processor, a memory for storing computer programs or instructions, and a data bus for signal connection of the at least one processor with the memory, the processor being configured to execute the computer programs or instructions to implement the steps of:
collecting calculation parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all the grids at the current moment to obtain a particle set;
respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the update of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
judging whether a water level observation value exists in the simulated water level at the current moment; if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value;
calculating an optimal estimated value of the simulated water level, the simulated flow and a preset roughness coefficient;
performing polynomial resampling on the particles to obtain a new particle set;
and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. According to the technical scheme, the invention provides a particle filtering assimilation method, a particle filtering assimilation device and a particle filtering assimilation computing device of a hydrodynamic model, and particularly comprises the steps of collecting computing parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow; generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all grids at the current moment to obtain a particle set; respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment; judging whether a water level observation value exists in the simulated water level at the current moment; if the water level observation value does not exist, directly executing the implementation of outputting a simulated water level and a simulated flow by the hydrodynamic model; if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value; calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient; performing polynomial resampling on the particles to obtain a new particle set; and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. The time-space variability of the roughness coefficient is considered in the scheme, namely the time-space variability is considered, and the space variability is also considered, so that the accuracy and the reliability of the output result of the hydrodynamic model are higher, the optimal estimation values of the state variables and the roughness coefficients in different spaces can be accurately obtained, and the problem of poorer accuracy and reliability of the output result of the hydrodynamic model is solved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart illustrating steps of a particle filter assimilation method for a hydrodynamic model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the terrain and observation point positions of a Toce river physical model according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the change of inflow rate of a Toce river physical model with time according to an embodiment of the present invention;
FIG. 4 is a water level assimilation root mean square error diagram of the Toce river physical model at 10 observation points provided by the embodiment of the invention;
FIG. 5 is a comparison graph of assimilation water level and simulated water level at observation points of the Toce river physical models P1, S6D, P8 and P21 provided by the embodiment of the invention;
FIG. 6 is a chart of a Manning roughness coefficient assimilation result at 10 observation points of the Toce river physical model provided by the embodiment of the present invention;
fig. 7 is a block diagram illustrating a structure of a particle filter assimilation device of a hydrodynamic model according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example one
Fig. 1 is a flowchart illustrating steps of a particle filter assimilation method for a hydrodynamic model according to an embodiment of the present invention.
Referring to fig. 1, the particle filter assimilation method provided in this embodiment is used for optimizing a hydrodynamic model, and specifically includes the following steps:
and S1, acquiring calculation parameters of the research area, and setting the size of the grid of the research area and the boundary conditions of inflow and outflow.
The calculated parameters include the bottom elevation of the research area, the boundary inflow flow, the initial water level, the initial flow and the like.
Take the tose river dynamic model as an example. The Toce river dynamic model is a hydrodynamic model which is established in a range of about 5km upstream of the Toce river in Milan Italy according to a scale of 1:100 and is used as a standard model to be commonly used for testing the precision and the stability of various dam break mathematical models. The hydrodynamic model was about 50m long and about 11m wide. The spatial resolution of the elevation of the model is 5cm, and the real terrain of the Toce river is accurately described.
The topography and observation point locations of the tose river dynamics model are shown in fig. 2. There is an empty reservoir in the river, which has an opening on the side near the river, but the gate is closed. Due to the blocking effect of the bank, the water level of the flood can be enabled to be high when the dam is broken, and the flood can enter the reservoir through the dam as the water level rises. The tose river dynamic model simulates the dam break inflow process by using the sudden increase of the water level of the top pool, and the change of the boundary inflow flow with time is shown in fig. 3. The initial water depth of the model is 0m, and the outlet of the model is set with a free outflow boundary. The size of the model simulation grid is 0.1m multiplied by 0.1m, and the roughness is 0.0162s/m recommended by ENEL1/3。
And S2, generating a plurality of equally weighted particles according to the water levels, the flow rates and the preset roughness coefficients of all the grids at the current moment to obtain a particle set.
Or respectively and randomly generating N particles with equal weight according to the prior distribution of the water level z and the roughness coefficient N of all grids at the initial moment of the Toce river dynamic model, thereby obtaining the particle set.
Figure BDA0001638992970000071
Figure BDA0001638992970000072
In the formula:
Figure BDA0001638992970000073
and
Figure BDA0001638992970000074
respectively representing the simulation water level, flow and roughness coefficient of the ith particle at the jth grid at the time t, wherein i is the particle number, and j is the grid unit number; ncell represents the total number of calculation grids.
The influence of the initial conditions on the assimilation effect is small, and the water depth and the flow speed of the Toce river dynamic model at the initial moment are both 0, so that when the particles are initialized, the water levels of all the particles are set to be 0, and only the Manning roughness coefficient is initialized. The number of particles N is set to 100, and the interval [0.062, 0.0262 ] from the Manning coefficient of roughness is set]s/m1/3Wherein 100 Manning roughness coefficients are respectively generated at all the grids randomly according to uniform distribution.
And S3, respectively using the water flow state represented by each particle and the model roughness coefficient as initial conditions, and sequentially driving the hydrodynamic model by using the inflow and outflow boundary conditions to update the simulated water level output by the hydrodynamic model from the current moment to the next moment.
The hydrodynamic model describes water flow motion by two-dimensional shallow water control equations (9) to (11) based on water depth average, discretizes the equations based on a structural grid, calculates grid interface flux by using an approximate Riemann solution in an HLLC format, and continuously integrates forwards by using an MUSCL-Hancock method to ensure that the model has second-order precision in space and time; performing discrete processing on the source item to ensure the stability of the model; the model simultaneously introduces an effective dry-wet boundary and an irregular terrain boundary processing method based on a B-spline method, accurately simulates the water flow characteristics on the dynamic alternation and complex boundary of the dry-wet unit, and realizes the recursion of all grid simulation water levels from t to t + 1.
Figure BDA0001638992970000075
Figure BDA0001638992970000076
Figure BDA0001638992970000077
Wherein ζ is the relative height of the free water surface; h (═ ζ + h)s) The total water depth; h issThe reference water depth is set; u and v represent flow rates in the x and y directions; g is the acceleration of gravity; rho is water density; tau isbxAnd τbyThe friction stress of the bed surface in the x and y directions.
And S4, judging whether the water level observed value exists in the simulated water level at the current moment.
The water level observed value here refers to a water level value actually observed in the actual operation of the model. If not, directly executing the step of realizing the output of the simulated water level and the simulated flow of the hydrodynamic model.
And S5, if yes, calculating the likelihood function value of each particle at the next time, and updating the weight of the particle.
That is, if the water level observed value exists in the simulated water level, the likelihood function value of each particle at time t +1 (time next to the current time) is calculated by equations (12) to (13)
Figure BDA0001638992970000081
And updating the particle weight using the likelihood function value
Figure BDA0001638992970000082
Figure BDA0001638992970000083
Figure BDA0001638992970000084
In the formula (I), the compound is shown in the specification,
Figure BDA0001638992970000085
and
Figure BDA0001638992970000086
respectively the water level analog value of the ith particle at the jth grid at the moment of t +1 and the observed value of the water level at the jth grid,
Figure BDA0001638992970000087
the standard deviation of the observed water level at the jth grid.
Selecting water level observation values at 10 observation points (fig. 2), calculating likelihood function values of grid particles where the 10 observation points are located at the time t +1, and updating the particle weight. Since the inflow was substantially 0 before 20s, assimilation was started from 20 s. Error of observation
Figure BDA0001638992970000089
Is a key parameter affecting the effect of particle filtering,
Figure BDA00016389929700000810
if the setting is too large, the particle weight is not sensitive to the observed value, the assimilation effect of the observed value on the analog value is reduced,
Figure BDA00016389929700000811
if the particle weight is too small, the particle weight is too sensitive to an observed value, so that the particles close to an observed water level obtain a weight close to 1, and the particles after resampling are seriously depleted, thereby affecting the filtering effect. Taking into account, setting
Figure BDA00016389929700000812
And S6, calculating the optimal estimation values of the simulated water level, the simulated flow and the prediction roughness coefficient of the hydrodynamic model.
The specific calculation formula is as follows:
Figure BDA0001638992970000088
and S7, performing polynomial resampling on all the particles to obtain a new particle set.
And if the simulated water level does not have a corresponding water level observation value, performing polynomial resampling on the particles to obtain a new particle set with the same weight.
One of the main drawbacks of particle filtering is that as the number of iterations increases, the weights of many particles become smaller, only a few particles get larger weights, a particle degradation phenomenon occurs, and a large amount of computing resources are used to update the particles with weights close to 0. The main approach to solving the particle degradation at present is to resample the particles. The currently widely used resampling method mainly comprises: polynomial resampling, layered resampling, system resampling and residual resampling, wherein the polynomial resampling is the basis of other three resampling methods and can basically solve the problem of particle degradation in the resampling process. The concrete measures are as follows:
first, from [0,1]]Randomly generating N random numbers u in uniform distributioni。
Then, if a certain random number u thereiniAnd if the condition (14) is met, copying the m-th particle as a new sample point, and sampling the new sample point to obtain the new particle set.
Figure BDA0001638992970000091
Although resampling can solve the problem of particle degradation, copying particles with large weight can cause a large number of particles to be completely consistent, thereby causing 'particle depletion', and for the 'particle depletion' problem, the most direct method is to increase white noise by parameters, but as the number of iterations increases, the variance of the prior distribution of the parameters will increase continuously, and the kernel smoothing method (equation (15)) can avoid the problem, so that the kernel smoothing method is adopted to realize the recursion of the particle parameters from t to t + 1.
Figure BDA0001638992970000092
In the formula (I), the compound is shown in the specification,
Figure BDA0001638992970000093
the Manning roughness coefficient for the ith particle at the jth grid,
Figure BDA0001638992970000094
the mean value of the Manning roughness coefficients represented by the N particles at the jth grid, h is the kernel smoothing parameter, VtThe variance is perturbed for the roughness coefficient. The kernel smoothing parameter h takes the value 0.2, VtTaking the value 3X 10-4。
And S8, taking the new particle set as the original particle set, and taking the next moment as the current moment to execute the operation of outputting the simulated water level and the simulated flow rate by the hydrodynamic model.
That is, let t be t +1, the process returns to step S3 to perform loop iteration until the operation is completed at all times. The root mean square error (RMSE, equation (16), fig. 4) of the assimilation water level and the simulated water level at 10 observation points are calculated respectively, and the assimilation water level and the simulated water level pair are shown in fig. 5 (taking P1, S6D, P8 and P21 as examples), so that the water level after being assimilated by the particle filter is closer to the observation water level, and the root mean square error at each observation point is obviously reduced. Since the hydrodynamic model has no measured flow value at each observation point, the result of flow equalization is not verified. Furthermore, the Manning coefficient update results are shown in fig. 6, and as can be seen from fig. 6, significant spatio-temporal variability exists in the Manning coefficient. It should be noted that the estimated Manning roughness coefficient does not represent the actual roughness. Because only parameter uncertainties are considered in the assimilation system, the estimation result of the Manning roughness coefficient contains uncertainties caused by terrains, boundary conditions, grid dispersion, model structures and the like. For example, the estimated value of the Manning coefficient at observation point S6D gradually increases, and the Manning coefficient gradually increasesMaximum value greater than 0.1s/m1/3Significantly greater than the recommended 0.0162s/m1/3. Errors caused by other uncertainty sources to the model simulated water level can be balanced by the parameters. The assimilation method considers the time-space variability of the roughness coefficient, and can accurately estimate the simulated water levels at different positions by automatically adjusting the roughness coefficients at different positions.
Figure BDA0001638992970000101
Wherein, RMSEkThe root mean square error of the assimilation or simulated water level at the k-th observation point, T is the total simulation time, T is 180,
Figure BDA0001638992970000102
is the observed value of the water level at the kth observation point at the time t,
Figure BDA0001638992970000103
and (4) the water level assimilation value or the analog value at the time t of the kth observation point.
It can be seen from the foregoing technical solutions that, the present embodiment provides a particle filter assimilation method for a hydrodynamic model, specifically, a method for collecting calculation parameters of a research area, and setting a size of a grid of the research area and boundary conditions of inflow and outflow; generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all grids at the current moment to obtain a particle set; respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment; judging whether a water level observation value exists in the simulated water level at the current moment; if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value; calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient; if the water level observation value does not exist, performing polynomial resampling on the particles to obtain a new particle set; and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. The time-space variability of the roughness coefficient is considered in the scheme, namely the time-space variability is considered, and the space variability is also considered, so that the accuracy and the reliability of the output result of the hydrodynamic model are higher, the optimal estimation values of the state variables and the roughness coefficients in different spaces can be accurately obtained, and the problem of poorer accuracy and reliability of the output result of the hydrodynamic model is solved.
It should be noted that, for simplicity of description, the method embodiments are described as a series of acts or combination of acts, but those skilled in the art will recognize that the present invention is not limited by the illustrated order of acts, as some steps may occur in other orders or concurrently in accordance with the embodiments of the present invention. Further, those skilled in the art will appreciate that the embodiments described in the specification are presently preferred and that no particular act is required to implement the invention.
Example two
Fig. 7 is a block diagram illustrating a structure of a particle filter assimilation device of a hydrodynamic model according to an embodiment of the present invention.
Referring to fig. 7, the particle filter assimilation device provided in this embodiment is used to optimize a hydrodynamic model, and specifically includes a parameter acquisition module 10, a first particle sampling module 20, a model output module 30, a condition determination module 40, a first calculation module 50, a second calculation module 60, a second particle sampling module 70, and a particle set replacement module 80.
The parameter acquisition module is used for acquiring calculation parameters of the research area and setting the size of a grid of the research area and the boundary conditions of inflow and outflow.
The calculated parameters include the bottom elevation of the research area, the boundary inflow flow, the initial water level, the initial flow and the like.
Take the tose hydrodynamic model as an example. The Toce river dynamic model is a hydrodynamic model which is established in a range of about 5km upstream of the Toce river in Milan Italy according to a scale of 1:100 and is used as a standard model to be commonly used for testing the precision and the stability of various dam break mathematical models. The hydrodynamic model was about 50m long and about 11m wide. The spatial resolution of the elevation of the model is 5cm, and the real terrain of the Toce river is accurately described.
The topography and observation point locations of the tose river dynamics model are shown in fig. 2. An empty reservoir is arranged in the middle of the river, an opening is formed in one side, close to the river, of the reservoir, due to the blocking effect of the bank, the water level of flood can be enabled to be high at the beginning of dam breaking, and the flood can enter the reservoir through the flood bank along with the rising of the water level. The tose hydrodynamic model simulates the dam break inflow process with a sudden increase in the top pool water level, and the change of the boundary inflow flow with time is shown in fig. 3. The initial water depth of the model is 0m, and the outlet of the model is set with a free outflow boundary. The size of the model simulation grid is 0.1m multiplied by 0.1m, and the roughness is 0.0162s/m recommended by ENEL1/3。
The first particle sampling module is used for generating a plurality of equally weighted particles according to the water levels, the flow rates and the preset roughness coefficients of all the grids at the current moment to obtain a particle set.
Or respectively and randomly generating N particles with equal weight according to the prior distribution values of the water level z and the roughness coefficient N of all grids at the initial moment of the Toce river dynamic model, thereby obtaining the particle set.
Figure BDA0001638992970000121
Figure BDA0001638992970000122
In the formula:
Figure BDA0001638992970000123
and
Figure BDA0001638992970000124
respectively representing the simulation water level, flow and roughness coefficient of the ith particle at the jth grid at the time t, wherein i is the particle number, and j is the grid unit number; ncell denotes the total number of calculation grids.
The influence of the initial conditions on the assimilation effect is small, and the water depth and the flow speed of the Toce river dynamic model at the initial moment are both 0, so that when the particles are initialized, the water levels of all the particles are set to be 0, and only the Manning roughness coefficient is initialized. The number of particles N is set to 100, and the coefficient interval [0.062, 0.0262 ] is set from the Manning roughness table]s/m1/3And respectively generating 100 Manning roughness table coefficients at all grids randomly according to uniform distribution in the interval.
The model output module is used for respectively utilizing the water flow state represented by each particle and the model roughness coefficient as initial conditions, sequentially driving the hydrodynamic model by utilizing the inflow and outflow boundary conditions, and realizing the updating of the simulated water level output by the hydrodynamic model from the current moment to the next moment.
The hydrodynamic model describes water flow motion by two-dimensional shallow water control equations (9) to (11) based on water depth average, discretizes the equations based on a structural grid, calculates grid interface flux by using an approximate Riemann solution in an HLLC format, and continuously integrates forwards by using an MUSCL-Hancock method to ensure that the model has second-order precision in space and time; performing discrete processing on the source item to ensure the stability of the model; the model simultaneously introduces an effective dry-wet boundary and an irregular terrain boundary processing method based on a B-spline method, accurately simulates the water flow characteristics on the dynamic alternation and complex boundary of the dry-wet unit, and realizes the recursion of all grid simulation water levels from t to t + 1.
Figure BDA0001638992970000125
Figure BDA0001638992970000126
Figure BDA0001638992970000127
Wherein ζ is the relative height of the free water surface; h (═ ζ + h)s) The total water depth; h issThe reference water depth is set; u and v represent flow rates in the x and y directions; g is the acceleration of gravity; rho is water density; tau isbxAnd τbyThe friction stress of the bed surface in the x and y directions.
The condition judgment module is used for judging whether a water level observation value exists in the simulated water level at the current moment.
The water level observed value here refers to a water level value actually observed in the actual operation of the model. If not, directly executing the implementation of outputting the simulated water level and the simulated flow by the hydrodynamic model.
The first calculation module is used for calculating the likelihood function value of each particle at the next moment and updating the weight of the particle if the water level observation value exists.
That is, if the water level observed value exists in the simulated water level, the likelihood function value of each particle at time t +1 (time next to the current time) is calculated by equations (12) to (13)
Figure BDA0001638992970000131
And updating the particle weight using the likelihood function value
Figure BDA0001638992970000132
Figure BDA0001638992970000133
Figure BDA0001638992970000134
In the formula (I), the compound is shown in the specification,
Figure BDA0001638992970000135
and
Figure BDA0001638992970000136
respectively the water level analog value of the ith particle at the jth grid at the moment of t +1 and the observed value of the water level at the jth grid,
Figure BDA0001638992970000137
the standard deviation of the observed water level at the jth grid.
Selecting water level observation values at 10 observation points (fig. 2), calculating likelihood function values of grid particles where the 10 observation points are located at the time t +1, and updating the particle weight. Since the inflow was substantially 0 before 20s, assimilation was started from 20 s. Error of observation
Figure BDA0001638992970000138
Is a key parameter affecting the effect of particle filtering,
Figure BDA0001638992970000139
if the setting is too large, the particle weight is not sensitive to the observed value, the assimilation effect of the observed value on the analog value is reduced,
Figure BDA00016389929700001310
if the particle weight is too small, the particle weight is too sensitive to an observed value, so that the particles close to an observed water level obtain a weight close to 1, and the particles after resampling are seriously depleted, thereby affecting the filtering effect. Taking into account, setting
Figure BDA00016389929700001311
The second calculation module is used for calculating the optimal estimation values of the simulated water level, the simulated flow and the prediction roughness coefficient of the hydrodynamic model.
The specific calculation formula is as follows:
Figure BDA00016389929700001312
and the second particle sampling module is used for performing polynomial resampling on all particles to obtain a new particle set.
I.e. the updated particles are polynomial resampled to obtain a new set of particles with the same weight.
One of the main drawbacks of particle filtering is that as the number of iterations increases, the weights of many particles become smaller, only a few particles get larger weights, a particle degradation phenomenon occurs, and a large amount of computing resources are used to update the particles with weights close to 0. The main approach to solving the particle degradation at present is to resample the particles. The currently widely used resampling method mainly comprises: polynomial resampling, layered resampling, system resampling and residual resampling, wherein the polynomial resampling is the basis of other three resampling methods and can basically solve the problem of particle degradation in the resampling process. The second particle sampling module specifically comprises a random number generation unit and a sampling execution unit.
A random number generation unit for generating a random number from [0,1]Randomly generating N random numbers u in uniform distributioni。
The sampling execution unit is used for judging if a certain random number u is contained in the sampling execution unitiAnd if the condition (14) is met, copying the m-th particle as a new sample point, and sampling the new sample point to obtain the new particle set.
Figure BDA0001638992970000141
Although resampling can solve the problem of particle degradation, copying particles with large weight can cause a large number of particles to be completely consistent, thereby causing 'particle depletion', and for the 'particle depletion' problem, the most direct method is to add white noise to parameters, but as the number of iterations increases, the variance of the prior distribution of the parameters will increase continuously, and the kernel smoothing method (equation (15)) can avoid the problem, so the kernel smoothing method is adopted to realize the recursion of particle parameters from t to t + 1.
Figure BDA0001638992970000142
In the formula (I), the compound is shown in the specification,
Figure BDA0001638992970000143
the Manning roughness coefficient for the ith particle at the jth grid,
Figure BDA0001638992970000144
the mean value of the Manning roughness coefficients represented by the N particles at the jth grid, and h is the kernel smoothing parameter，VtThe variance is perturbed for the roughness coefficient. The kernel smoothing parameter h takes the value 0.2, VtTaking the value 3X 10-4。
And the particle set replacement module is used for taking the new particle set as the original particle set and simultaneously taking the next moment as the current moment to execute the operation of outputting the simulation water level and the simulation flow rate by the hydrodynamic model.
That is, let t be t +1, the process returns to step S3 to perform loop iteration until the operation is completed at all times. The root mean square error (RMSE, equation (16), fig. 4) of the assimilation water level and the simulated water level at 10 observation points are calculated respectively, and the assimilation water level and the simulated water level pair are shown in fig. 5 (taking P1, S6D, P8 and P21 as examples), so that the water level after being assimilated by the particle filter is closer to the observation water level, and the root mean square error at each observation point is obviously reduced. Since the hydrodynamic model has no measured flow value at each observation point, the result of flow equalization is not verified. Furthermore, the Manning coefficient update results are shown in fig. 6, and as can be seen from fig. 6, significant spatio-temporal variability exists in the Manning coefficient. It should be noted that the estimated Manning roughness coefficient does not represent the actual roughness. Because only parameter uncertainties are considered in the assimilation system, the estimation result of the Manning roughness coefficient contains uncertainties caused by terrains, boundary conditions, grid dispersion, model structures and the like. For example, the estimated value of the Manning coefficient at the observation point S6D gradually increases, and the maximum value of the Manning coefficient is more than 0.1S/m1/3Significantly greater than the recommended 0.0162s/m1/3. Errors caused by other uncertainty sources to the model simulated water level can be balanced by the parameters. The assimilation method considers the time-space variability of the roughness coefficient, and can accurately estimate the simulated water levels at different positions by automatically adjusting the roughness coefficients at different positions.
Figure BDA0001638992970000151
Wherein, RMSEkThe root mean square error of the assimilation or simulated water level at the k-th observation point, T is the total simulation time, T is 180,
Figure BDA0001638992970000152
is the observed value of the water level at the kth observation point at the time t,
Figure BDA0001638992970000153
and (4) the water level assimilation value or the analog value at the time t of the kth observation point.
It can be seen from the foregoing technical solutions that, the present embodiment provides a particle filtering assimilation device for a hydrodynamic model, specifically, a method for collecting calculation parameters of a research area, and setting the size of a grid of the research area and boundary conditions of inflow and outflow; generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all grids at the current moment to obtain a particle set; respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment; judging whether a water level observation value exists in the simulated water level at the current moment; if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model; if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value; calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient; performing polynomial resampling on the particles to obtain a new particle set; and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. The time-space variability of the roughness coefficient is considered in the scheme, namely the time-space variability is considered, and the space variability is also considered, so that the accuracy and the reliability of the output result of the hydrodynamic model are higher, the optimal estimation values of the state variables and the roughness coefficients in different spaces can be accurately obtained, and the problem of poorer accuracy and reliability of the output result of the hydrodynamic model is solved.
EXAMPLE III
The embodiment provides a computing device, which is provided with the particle filter assimilation device provided in the previous embodiment, wherein the device is used for collecting computing parameters of a research area and setting the size of a grid of the research area and the boundary conditions of inflow and outflow; generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all grids at the current moment to obtain a particle set; respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment; judging whether a water level observation value exists in the simulated water level at the current moment; if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model; if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value; calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient; performing polynomial resampling on the particles to obtain a new particle set; and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment. According to the particle filtering assimilation device of the computing equipment, the time-space variability of the roughness coefficient is considered, namely the time-space variability and the space variability are considered, so that the accuracy and the reliability of the output result of the hydrodynamic model are high, the optimal estimation values of the state variable and the roughness coefficient in different spaces can be accurately obtained, and the problem that the accuracy and the reliability of the output result of the hydrodynamic model are poor is solved.
Example four
The present embodiments provide a computing device comprising at least one processor and a memory, the processor and the memory being connected by a data bus.
The memory is used for storing computer programs or instructions, and the processor is used for executing the computer programs or instructions, so that the computing device realizes the following operations:
collecting calculation parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
generating a plurality of particles with equal weight according to the water levels, the flow rates and the preset roughness coefficient of all grids at the current moment to obtain a particle set;
respectively utilizing the water flow state and model roughness coefficient contained in each particle in the particle set, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
judging whether a water level observation value exists in the simulated water level at the current moment;
if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
if the water level observation value exists, calculating a likelihood function value of each particle at the next moment, and updating the weight of the particle by using the likelihood function value;
calculating the optimal estimated values of the simulated water level, the simulated flow and the preset roughness coefficient;
performing polynomial resampling on the particles to obtain a new particle set;
and replacing the particle set by the new particle set, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model by taking the next moment as the current moment.
In the scheme, the time-space variability of the roughness coefficient is specifically considered, namely the time-space variability is considered, and the space variability is also considered, so that the accuracy and the reliability of the output result of the hydrodynamic model are higher, the optimal estimation values of the state variables and the roughness coefficients in different spaces can be accurately obtained, and the problem of poor accuracy and reliability of the output result of the hydrodynamic model is solved.
For the device embodiment, since it is basically similar to the method embodiment, the description is simple, and for the relevant points, refer to the partial description of the method embodiment.
The embodiments in the present specification are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing terminal to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing terminal to cause a series of operational steps to be performed on the computer or other programmable terminal to produce a computer implemented process such that the instructions which execute on the computer or other programmable terminal provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications of these embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the embodiments of the invention.
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or terminal that comprises the element.
The technical solutions provided by the present invention are described in detail above, and the principle and the implementation of the present invention are explained in this document by applying specific examples, and the descriptions of the above examples are only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (10)

1. A particle filter assimilation method for hydrodynamic modeling, comprising:
collecting calculation parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
respectively generating a plurality of particles with equal weight in each grid according to the water level, the flow and the preset roughness coefficient of all the grids at the current moment to obtain a particle set of all the grids, wherein the water level, the flow and the preset roughness coefficient of each grid in all the grids are represented by a group of particles, and the serial numbers of the particles are 1,2, ·, and N;
respectively utilizing water flow states and model roughness coefficients contained in particles with the same number in all the grids, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
judging whether a water level observation value exists in the simulated water level at the current moment, and if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
if the water level observation value exists, calculating a likelihood function value of each particle under the next moment of the grid where the water level observation is located, and updating the weight of each particle in the grid by using the likelihood function value;
calculating the optimal estimated values of the grid simulation water level, the grid simulation flow and the roughness coefficient;
performing polynomial resampling on the grid particles to obtain a new particle set of the grid;
replacing the grid particle set by the new grid particle set, keeping the rest grid particles unchanged, and simultaneously taking the next moment as the current moment to execute the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
the hydrodynamic model describes water flow motion by adopting a two-dimensional shallow water control equation based on water depth average;
according to the particle filter assimilation method, the time-space variability of the roughness coefficient is considered, the roughness coefficients of different positions are automatically adjusted, and the simulated water levels of different positions are accurately estimated.
2. The particle filter assimilation method of claim 1 wherein the calculated parameters include some or all of the floor elevation, boundary inflow flow, initial water level, and initial flow of the study area.
3. The particle filter assimilation method of claim 1, wherein the predetermined roughness factor is a roughness factor prior value.
4. The particle filter assimilation method of claim 1 wherein said polynomial resampling of said particles comprises:
randomly generating a plurality of random numbers from the [0,1] uniform distribution;
and sampling the particles corresponding to the random numbers meeting the preset conditions in the plurality of random numbers as new sample points to obtain a new particle set.
5. A particle filter assimilation device for hydrodynamic modeling, comprising:
the parameter acquisition module is used for acquiring calculation parameters of a research area and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
the first particle sampling module is used for respectively generating a plurality of particles with equal weight in each grid according to the water level, the flow and the preset roughness coefficient of all the grids at the current moment to obtain a particle set of all the grids, wherein the water level, the flow and the preset roughness coefficient of each grid in all the grids are all represented by a group of particles, and the particle numbers are all represented by 1,2, ·, and N;
the model output module is used for respectively utilizing the water flow states and the model roughness coefficients contained in the particles with the same number in all the grids and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model so as to realize the update of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
the condition judgment module is used for judging whether a water level observation value exists in the simulated water level at the current moment;
a first calculating module, configured to calculate a likelihood function value of each particle at a next time of a grid where the water level observation is located if the water level observation value exists, and update a weight of each particle in the grid using the likelihood function value;
the second calculation module is used for calculating the optimal estimated values of the grid simulation water level, the grid simulation flow and a preset roughness coefficient;
the second particle sampling module is used for performing polynomial resampling on the grid particles to obtain a new particle set of the grid;
a particle set replacement module, configured to replace the new grid particle set with the grid particle set, keep the rest of the grid particles unchanged, and perform the step of implementing the hydrodynamic model to output the simulated water level and the simulated flow rate by using the next time as the current time;
the hydrodynamic model describes water flow motion by adopting a two-dimensional shallow water control equation based on water depth average;
the particle filtering assimilation device considers the time-space variability of the roughness coefficient, automatically adjusts the roughness coefficients of different positions and accurately estimates the simulated water levels of the different positions.
6. The particle filter assimilation device of claim 5 wherein the calculated parameters include some or all of the bottom elevation, boundary inflow flow, initial water level, and initial flow of the study area.
7. The particle filter assimilation device of claim 5 wherein the predetermined roughness factor is a roughness factor a priori.
8. The particle filter assimilation device of claim 5 wherein the second particle sampling module comprises:
a random number generation unit for randomly generating a plurality of random numbers from [0,1] uniform distribution;
and the sampling execution unit is used for sampling the particles corresponding to the random numbers meeting the preset conditions in the plurality of random numbers as new sample points to obtain the new particle set.
9. A computing device provided with a particle filter assimilation device as claimed in any one of claims 5 to 8.
10. A computing device comprising at least one processor, a memory for storing computer programs or instructions, and a data bus for signal connection of the at least one processor with the memory, the processor being configured to execute the computer programs or instructions to implement the steps of:
collecting calculation parameters of a research area, and setting the size of a grid of the research area and the boundary conditions of inflow and outflow;
respectively generating a plurality of particles with equal weight in each grid according to the water level, the flow and the preset roughness coefficient of all the grids at the current moment to obtain a particle set of all the grids, wherein the water level, the flow and the preset roughness coefficient of each grid in all the grids are represented by a group of particles, and the serial numbers of the particles are 1,2, ·, and N;
respectively utilizing water flow states and model roughness coefficients contained in particles with the same number in all the grids, and simultaneously utilizing the inflow and outflow boundary conditions to sequentially drive the hydrodynamic model, so as to realize the updating of the simulated water level and the simulated flow output by the hydrodynamic model from the current moment to the next moment;
judging whether a water level observation value exists in the simulated water level at the current moment;
if the water level observation value does not exist, directly executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model;
if the water level observation value exists, calculating a likelihood function value of each particle under the next moment of the grid where the water level observation is located, and updating the weight of each particle in the grid by using the likelihood function value;
calculating the optimal estimated values of the grid simulation water level, the grid simulation flow and a preset roughness coefficient;
performing polynomial resampling on the grid particles to obtain a grid new particle set;
and replacing the grid particle set by the new grid particle set, taking the next moment as the current moment, keeping the rest grid particles unchanged, and executing the step of outputting the simulated water level and the simulated flow by the hydrodynamic model.
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