CN115902142A - Water body point source tracing method based on improved ensemble Kalman filtering algorithm - Google Patents
Water body point source tracing method based on improved ensemble Kalman filtering algorithm Download PDFInfo
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Abstract
The invention discloses a water point source tracing method based on an improved ensemble Kalman filtering algorithm, which comprises the following steps: investigating the background of pollutants in a research area where leakage accidents may occur; arranging pollutant concentration monitoring points according to the field conditions of the research area; according to the terrain and hydrological data of a research area, constructing a hydrodynamic model and a substance transport model of the area; improving an ensemble Kalman filtering algorithm, coupling and nesting the algorithm and a substance transportation model, and constructing a pollution source parameter assimilation model based on the coupling algorithm; according to the pollutant concentration data of the monitoring points transmitted back remotely in real time, carrying out assimilation calculation on pollution source parameters by adopting an assimilation model; and correcting the pollution source information according to the assimilation result, determining the assimilation value of the pollution source parameter when the parameter assimilation result tends to be stable, and predicting the pollutant propagation path in real time by using the assimilated pollution source parameter. The method can more quickly and accurately capture the position of the pollution source and identify the initial release time and release amount of the pollution source.
Description
Technical Field
The invention relates to the technical field of surface water pollution source parameter optimization identification, in particular to a water point source tracing method based on an improved ensemble Kalman filtering algorithm.
Background
When an environmental pollution accident occurs suddenly, pollution source information such as the position, release time and release amount of the pollution source is rapidly and accurately obtained, which is very critical for the management, control, risk assessment and remediation of the accident. Because the timeliness and the urgency are very important to solve the problem of tracing the source of the pollutants, the efficiency and the precision of the method in identifying the parameters of the pollution source need to be concerned when the tracing method is applied. The traditional tracing method needs to distribute a large number of monitoring points on site and survey and research on the spot, has huge consumption on manpower and material resources, is lower in source searching efficiency, and cannot take remedial measures to the source in time. With the continuous upgrading of monitoring equipment, the remote transmission of monitoring data is popularized, and meanwhile, an optimization algorithm is matched, so that the pollution source can be quickly captured and identified under the condition of fewer monitoring points.
Disclosure of Invention
The invention aims to solve the technical problem of providing a water body point source tracing method based on an improved integrated Kalman filtering algorithm, which can more quickly and accurately capture the position of a pollution source and identify the initial release time and release amount of the pollution source, and provides technical support for the treatment work of the pollution source.
In order to solve the technical problem, the invention provides a water point source tracing method based on an improved ensemble Kalman filtering algorithm, which comprises the following steps:
and 6, dynamically correcting the pollution source information according to each synchronization result, determining the assimilation value of the pollution source parameter when the parameter assimilation result tends to be stable, and predicting the pollutant propagation path in real time by using the assimilated pollution source parameter.
Preferably, in step 1, the background of the pollutants in the investigation region, where a leakage accident may occur, is a potential pollutant type and risk hazard near the investigation region, so that a corresponding pollution monitoring device can be selected conveniently.
Preferably, in the step 2, pollutant concentration monitoring points including the arrangement positions and the number of the monitoring points are reasonably arranged according to the field conditions of the research area, if the flow field of the research area is unidirectional flow, only one or two monitoring points need to be arranged at the downstream, if the flow field of the research area is reciprocating flow, a plurality of monitoring points are arranged in the research area, and specifically, the monitoring points can be arranged near the potential pollution source area according to investigation or at equal intervals in the longitudinal direction or the transverse direction, so that the comprehensiveness of data acquisition is ensured.
Preferably, in step 3, the hydrodynamic model is constructed according to the terrain and water depth of the research area, the model is a planar two-dimensional model, the model calculation adopts an ELCIRC open source program based on Fortran language, the model grid adopts an unstructured grid, the grid dimension can be generally set to 10m-50m, and the local area can be encrypted according to the actual situation.
Preferably, in step 3, the material transport model is a planar two-dimensional model, and the control equation is represented by formula (1):
in the formula: c is the concentration of the substance; t is time; u, v are the flow velocity components in the x, y directions, respectively; h is water depth; k is an x, y spatial two-dimensional diffusion tensor whose value is represented by the following equation (2):
K xx ＝K L cos 2 (θ)+K T sin 2 (θ)(2a)
K xy ＝K xy ＝(K L -K T )cos(θ)sin(θ)(2b)
K yy ＝K L sin 2 9θ)+K T cos 2 (θ) (2 c) wherein: theta is an included angle between the flow direction and the x axis; k L 、K T Longitudinal and transverse diffusion coefficients, respectively, which are expressed in relation to the flow velocity by the following equation (3)
In the formula: c is the metabolization capacity coefficient; alpha and beta are respectively constant coefficients; g is the acceleration of gravity;
separating the convection term and the diffusion term in the formula (1) into two parts by an operator splitting method,
and (4) respectively carrying out differential solution on the formula by adopting a finite volume method, and finally obtaining the concentration of the released substances in the research area.
Preferably, in step 3, the mesh of the material transport model is the same as that of the hydrodynamic model, and the flow field of the material transport model is provided by calculation of the hydrodynamic model and used for driving material transport.
Preferably, in step 4, the assimilated parameters of the pollution source in the pollution source parameter assimilation model are respectively a pollution source position, an initial release time of the pollution source and a total release amount of the pollution source.
Preferably, in step 4, the improved ensemble kalman filtering algorithm is constructed by integrating correlation coefficients based on a standard ensemble kalman filtering algorithm, and the construction steps are as follows:
(1) Generating an initial set; respectively generating sets containing Nr members aiming at four pollution source parameters, randomly selecting initial values of the set members from independent uniform distribution, determining the upper limit and the lower limit of the uniform distribution by the acquired prior information, and representing a pollution source parameter vector by the following formula:
in the formula:
representing a pollution source parameter vector, wherein i is a number realized by a set, a superscript T represents a matrix transposition, and X, Y, T and M in the vector are respectively a horizontal coordinate, a vertical coordinate, initial release time and release amount of a pollution source space plane position;
(2) Predicting; putting the latest pollution source parameter value obtained at an observation time t-1 into a material transportation model, starting calculation from an initial time 0, stopping calculation until the observation time t, obtaining a simulation state of the observation time t at the moment, and updating the state from the time 0 to the time t-1, wherein the simulation state parameter refers to the pollutant concentration, and the prediction of the state variable is as follows:
in the formula: c 0 Is a state initial concentration profile; superscripts a and f represent predicted values and updated values, respectively; psi is a state transition operator, referred to herein as a material transport model;
for equation (6), a correlation coefficient R between the predicted concentration and the observed concentration in the observed time series is introduced as a state variable instead of the contaminant concentration, the correlation coefficient R being represented by the following equation:
in the formula: subscript j is a time series number; superscripts s and ob represent concentration analog and observed values respectively,
and &>
Are respectively C s And C ob Average value of (d);
therefore, the state prediction of equation (6) is represented by the following equation:
in the formula: f is a
Switch over to->
The conversion operator of (3);
due to the introduction of the correlation coefficient R, according to the migration characteristic of the pollutants, when the position and the release time of the pollution source are determined, if other situations remain unchanged, the pollutant release amount has no influence on the magnitude of the correlation coefficient, and the pollutant release amount M is separated from the pollution source parameter to be identified; pollution source parameter vector to be assimilated
Only two parameters of the contamination source position and the initial release time are included;
(3) Updating; before updating, normal score conversion is carried out on parameters, the parameters are selected from uniform distribution, the optimal parameter can be achieved by the Kalman filtering method when the parameters obey Gaussian distribution, the normal score conversion equation needs to be recalculated after each prediction step, and the conversion of system parameters is shown as the following formula:
in the formula: phi (phi) of t A conversion form of normal score at time t, the conversion being related to the cumulative distribution function; the upper line indicates the parameters after conversion of the normal score.
Then, updating the parameters; assuming that the number of observation points is Nob, each realization in the set is updated by the following equation;
in the formula:
and &>
Respectively updating parameters and predicting vectors after the conversion of the normal score at the moment t; r is t The autocorrelation coefficient of the observed pollutant concentration from time 0 to t; e.g. of the type t Is r t The error vector of (2); g t Is a Kalman gain matrix, and the expression is as follows:
in the formula: r ′ t Is an error vector e t The covariance matrix of (a);
is contaminated byDye source parameter vector>
And predicted correlation coefficient>
The covariance of (a); />
Is the relevant coefficient->
An auto-covariance;
updated transformation source parameters
Requires a reverse conversion into ∑ in the prediction of step (2)>
By means of a conversion inverse function related to the cumulative distribution inverse function->
The assimilation vector at time t->
The parameters that contain the following final updates:
preferably, in the step 5, the assimilation calculation of the pollution source parameters comprises two parts, wherein one part is the assimilation calculation of the pollution source parameters including the position and the initial release time of the pollution source, and the other part is the parameter optimization calculation of the total release amount of the separated pollutants; assimilating calculation is carried out on the pollution source parameters including the position of the pollution source and the initial release time according to an expression (5) -an expression (13), and the optimization of the pollutant release total quantity parameters is calculated according to the following expression:
in the formula: RMSE is the average error between the process of simulating concentration and the process of observing concentration, i is the step length of observation time,
and &>
Respectively an observed concentration and a simulated concentration at an observation time step i, and n is a concentration time process data volume.
Preferably, in step 6, dynamically correcting the pollution source information is performed based on the data of each observation step, the corrected pollution source information is the position of the pollution source and the initial release time, the optimization calculation is performed according to the formula (14) when the assimilation results of the two parameters tend to be stable, and finally the optimized pollution source parameters are obtained to perform the real-time prediction of the pollutant propagation path.
The invention has the beneficial effects that: the invention provides a tracing method suitable for the point source of the surface water body on the basis of the transportation rule of pollutants released by the point source in the surface water body, by introducing relevant coefficient factors into an ensemble Kalman filtering method and coupling an improved ensemble Kalman filtering algorithm with a surface water substance transportation model.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a schematic flow chart of a method of an improved ensemble Kalman filtering algorithm of the present invention.
Fig. 3 is a schematic diagram of a source tracing and assimilating result based on an improved ensemble kalman filtering algorithm.
Fig. 4 is a schematic diagram of a source tracing and assimilating result based on an improved ensemble kalman filtering algorithm.
Fig. 5 is a schematic view of a traceability homogenization result based on an improved ensemble kalman filter algorithm according to the present invention.
Fig. 6 is a schematic view of a traceability homogenization result based on an improved ensemble kalman filter algorithm according to the present invention.
Detailed Description
As shown in fig. 1, a water point source tracing method based on an improved ensemble kalman filtering algorithm includes the following steps:
and 6, dynamically correcting the pollution source information according to each synchronization result, determining the assimilation value of the pollution source parameter when the parameter assimilation result tends to be stable, and predicting the pollutant propagation path in real time by using the assimilated pollution source parameter.
Example (b):
the water point source tracing method based on the improved ensemble Kalman filtering algorithm comprises the following steps:
step 1: the background of pollutants in a possible leakage accident in a research area is investigated, the research area is a square area of 500m by 500m in the embodiment, the real position of a pollution source is (250 ), the initial release time is 100s, the total pollutant release amount is 10kg, and the pollutant index is COD.
And 2, step: pollutant concentration monitoring points are reasonably arranged according to the field conditions of the research area, in the embodiment, 3 monitoring points are arranged, the positions are (290, 260), (300, 255) and (330, 270), the pollutant concentration data of the observation points contain 20% of random errors, the observation time is 130 s-300 s, and the observation interval is 1s.
And step 3: and constructing a hydrodynamic model and a substance transportation model of the region according to the terrain and hydrological data of the research region. The hydrodynamic model provides a hydrodynamic field for the material transport model.
And 4, step 4: and improving an ensemble Kalman filtering algorithm, coupling and nesting the algorithm and a substance transport model, and constructing a pollution source parameter assimilation model based on the coupling algorithm.
And 5: and carrying out assimilation calculation on the pollution source parameters by adopting an assimilation model according to the pollutant concentration data of the monitoring point transmitted back in real time in a remote mode. As shown in the box diagrams of fig. 3 to 5, assimilation data of two parameters, i.e., the source position (abscissa and ordinate points) and the initial release time of the contamination source at the calculation time steps of 11 th, 20 th, 40 th, 60 th, 80 th, 100 th, 120 th, 140 th, and 160 th, respectively, are selected, and the central horizontal line of the box in the diagrams is the median of the set, it can be seen that the assimilation parameters tend to converge stably at the calculation time step of 100 th, and the assimilation results can maintain accuracy even when the contamination concentration data contains a random error of 20%.
And 6: and dynamically correcting the pollution source information according to each synchronization result, determining the assimilation value of the pollution source parameter when the parameter assimilation result tends to be stable, and performing real-time prediction on the pollutant propagation path by using the assimilated pollution source parameter. And selecting the position (horizontal and vertical coordinates) of the pollution source at the 100 th calculation time step and the assimilation set average value of the initial release time of the pollution source as an assimilation result, optimizing the parameter of the total pollutant release amount based on the result, wherein fig. 6 shows the optimization result of the total pollutant release amount, and the release value corresponding to the lowest RMSE value is selected as the final optimization value of the parameter. And performing forward simulation by using a material transport model according to the optimized pollution source parameters, and predicting a subsequent pollutant propagation path in real time.
Claims (10)
1. A water point source tracing method based on an improved ensemble Kalman filtering algorithm is characterized by comprising the following steps:
step 1, investigating a pollutant background of a possible leakage accident in a research area;
step 2, reasonably arranging pollutant concentration monitoring points according to the field conditions of the research area;
step 3, constructing a regional hydrodynamic model and a substance transportation model according to the terrain and hydrological data of the research region;
step 4, improving an ensemble Kalman filtering algorithm, coupling and nesting the algorithm and a substance transport model, and constructing a pollution source parameter assimilation model based on the coupling algorithm;
step 5, carrying out assimilation calculation on pollution source parameters by adopting an assimilation model according to the pollutant concentration data of the monitoring point transmitted back in real time in a remote mode;
and 6, dynamically correcting the pollution source information according to each synchronization result, determining the assimilation value of the pollution source parameter when the parameter assimilation result tends to be stable, and predicting the pollutant propagation path in real time by using the assimilated pollution source parameter.
2. The water body point source tracing method based on the improved ensemble Kalman filtering algorithm according to claim 1, wherein in step 1, the background of the pollutants possibly causing leakage accidents in the investigation research area is potential pollutant types and risk hazards near the investigation research area, and corresponding pollution monitoring equipment is convenient to select.
3. The water body point source tracing method based on the improved ensemble Kalman filtering algorithm according to claim 1, characterized in that in step 2, pollutant concentration monitoring points are reasonably arranged according to field conditions of a research area, including the arrangement positions and the number of the monitoring points, if the flow field of the research area is unidirectional flow, only one or two monitoring points are arranged at downstream, if the flow field of the research area is reciprocating flow, a plurality of monitoring points are arranged in the research area, and the comprehensiveness of acquired data is ensured according to the arrangement near a potential pollution source area or according to longitudinal or transverse equidistance.
4. The water body point source tracing method based on the improved ensemble Kalman filtering algorithm according to claim 1, characterized in that in step 3, the hydrodynamic model is constructed according to the terrain and water depth of the research area, and is a planar two-dimensional model, the model calculation adopts an ELCIRC source opening program based on Fortran language, the model mesh adopts an unstructured mesh, the mesh size is set to 10m-50m, and the local area is encrypted according to the actual situation.
5. The water body point source tracing method based on the improved ensemble Kalman filtering algorithm according to claim 1, wherein in step 3, the material transport model is a planar two-dimensional model, and the control equation is expressed by formula (1):
in the formula: c is the concentration of the substance; t is time; u and v are flow velocity components in the x and y directions respectively; h is water depth; k is an x, y spatial two-dimensional diffusion tensor whose value is represented by the following equation (2):
K xx ＝K L cos 2 (θ)+K T sin 2 (θ)(2a)K xy ＝K xy ＝(K L -K T )cos(θ)sin(θ)(2b)K yy ＝K L sin 2 (θ)+K T cos 2 (θ) (2 c) wherein: theta is an included angle between the flow direction and the x axis; k L 、K T Longitudinal and transverse diffusion coefficients, respectively, which are expressed in relation to the flow velocity by the following equation (3)
In the formula: c is the metabolization capacity coefficient; α, α) are constant coefficients, respectively;
separating the convection term and the diffusion term in the formula (1) into two parts by an operator splitting method,
and (4) respectively carrying out differential solution on the formula by adopting a finite volume method, and finally obtaining the concentration of the released substances in the research area.
6. The improved ensemble kalman filter algorithm-based water point source tracing method according to claim 1, wherein in step 3, the mesh of the material transport model is the same as that of the hydrodynamic model, and the flow field of the material transport model is provided by calculation of the hydrodynamic model and used for driving material transport.
7. The method for tracing the source of the water body point based on the improved ensemble kalman filter algorithm according to claim 1, wherein in step 4, the assimilated parameters of the pollution source in the pollution source parameter assimilation model are the position of the pollution source, the initial release time of the pollution source and the total release amount of the pollution source, respectively.
8. The water body point source tracing method based on the improved Kalman filtering algorithm of claim 1, wherein in the step 4, the improved Kalman filtering algorithm is constructed by integrating correlation coefficients based on a standard Kalman filtering algorithm, and the construction steps are as follows:
(1) Generating an initial set; respectively generating sets containing Nr members aiming at three pollution source parameters, randomly selecting initial values of the set members from independent uniform distribution, determining the upper limit and the lower limit of the uniform distribution by the acquired prior information, and expressing a pollution source parameter vector by the following formula:
in the formula:
representing a pollution source parameter vector, wherein i is a number realized by a set, and superscript T represents matrix transposition;
(2) Predicting; putting the latest pollution source parameter value obtained at an observation time t-1 into a material transportation model, starting calculation from an initial time 0, stopping calculation until the observation time t, obtaining a simulation state of the observation time t at the moment, and updating the state from the time 0 to the time t-1, wherein the simulation state parameter refers to the pollutant concentration, and the prediction of the state variable is as follows:
in the formula: c 0 Is a state initial concentration profile; superscripts a and f represent predicted values and updated values, respectively; psi is a state transition operator, here a material transport model;
for equation (6), a correlation coefficient R between the predicted concentration and the observed concentration in the observed time series is introduced as a state variable instead of the contaminant concentration, the correlation coefficient R being represented by the following equation:
in the formula: subscript j is a time series number; superscripts s and ob represent the simulated and observed values respectively,
and &>
Are respectively C s And C ob Average value of (d);
therefore, the state prediction of equation (6) is represented by the following equation:
in the formula: f is a
Switch over to->
The conversion operator of (3);
due to the introduction of the correlation coefficient R, according to the migration characteristic of the pollutants, after the position and the release time of the pollution source are determined, if other situations remain unchanged, the pollutant release amount has no influence on the magnitude of the correlation coefficient, and the pollutant release amount M is separated from the parameters of the pollution source to be identified independently; pollution source parameter vector to be assimilated
Only two parameters of the position of the pollution source and the initial release time are included; />
(3) Updating; before updating, normal score conversion is carried out on parameters, the parameters are selected from uniform distribution, the optimal parameter can be achieved by the Kalman filtering method when the parameters obey Gaussian distribution, the normal score conversion equation needs to be recalculated after each prediction step, and the conversion of system parameters is shown as the following formula:
in the formula: phi t A conversion form of normal score at time t, the conversion being related to the cumulative distribution function;
then, updating the parameters; assuming that the number of observation points is Nob, each realization in the set is updated by the following equation;
in the formula:
and &>
Respectively updating parameters and predicting vectors after normal score conversion at the time t; r is t Is the observed contaminant concentration autocorrelation coefficient from time 0 to t; e.g. of the type t Is r t The error vector of (2); g t Is a Kalman gain matrix, and the expression is as follows:
in the formula: r ′ t Is an error vector e t The covariance matrix of (a);
for the contamination source parameter vector->
And predicted correlation coefficient R f The covariance of (a); />
Is a correlation coefficient R f An auto-covariance;
updated translation source parameters
Requires a reverse conversion into &'s in step (2) prediction>
By means of a conversion inverse function related to the cumulative distribution inverse function->
Assimilation vector at time t>
The parameters that contain the following final updates:
9. the water body point source tracing method based on the improved ensemble Kalman filtering algorithm according to claim 1, characterized in that in step 5, the pollution source parameter assimilation calculation includes two parts, one part is the pollution source parameter assimilation calculation including the pollution source position and the initial release time, and the other part is the parameter optimization calculation of the total release amount of the separated pollutants; assimilating calculation is carried out on the pollution source parameters including the position of the pollution source and the initial release time according to an expression (5) -an expression (13), and the optimization of the pollutant release total quantity parameters is calculated according to the following expression:
in the formula: i is the observation time step size,
and &>
Respectively, an observed concentration and a simulated concentration at an observation time step i.
10. The water body point source tracing method based on the improved ensemble kalman filter algorithm as claimed in claim 1, wherein in step 6, the dynamic correction of the pollution source information is performed based on the data of each observation step, the corrected pollution source information is the position of the pollution source and the initial release time, the total amount of the pollution source release is optimized and calculated according to the formula (14) when the assimilation results of the two parameters tend to be stable, and finally the optimized pollution source parameters are obtained for the real-time prediction of the pollutant propagation path.
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| CN116739386B (en) * | 2023-08-10 | 2024-03-08 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Multi-index fusion pollution tracing method, equipment and readable storage medium |
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