CN114692471A - Karst groundwater system flow network simulation method - Google Patents
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Abstract
The invention discloses a karst groundwater system flow network simulation method, which comprises the following steps: step one, establishing a conceptual model; step two, selecting a mathematical model; step three, carrying out numeralization on the mathematical model; step four, correcting the model; optimizing the flow network information of the karst underground water system through a chaotic optimization algorithm model, and realizing water quantity; fifthly, correcting sensitivity analysis; step six, model verification; the invention realizes the simulation of the flow network of the karst underground water system by a laboratory image simulation method, and greatly improves the analysis capability, the application capability and the further research capability of the karst underground water system by simulating, simulating and analyzing according to the flow network image data.
Description
Technical Field
The invention relates to the technical field of flow network simulation control and adjustment, in particular to a flow network simulation method for a karst underground water system.
Background
The karst water-containing system is a watershed range of a certain karst underground water system with a uniform supply boundary and a uniform underground runoff field. Karst is a general term for geological actions of water on soluble rocks (carbonate rock, gypsum, rock salt, etc.) mainly by chemical erosion action and by mechanical actions of flowing water such as erosion, undermining and collapse, and for phenomena resulting from these actions. Such as the landforms caused by karst effects, known as karst landforms (karst landforms). Karst water systems are also known as "karst waters", when large karst springs are the primary drainage ports, also known as "karst spring zones". The essence of the method is a general name of a karst underground water collection body which has a definite boundary, a continuous karst aquifer, a unified karst underground water flow field and relatively independent circulation. The collection range not only comprises the supply range of karst groundwater resources, but also comprises other types of controllable collection areas of groundwater and surface water which are closely related to the karst groundwater.
The Flow Net (Flow Net) refers to a grid in the seepage field, which is formed by intersecting a set of Flow lines with a set of equipotential lines (a set of equal head lines when the volume weight is unchanged). An orthogonal network is formed for the isotropic medium. Streamlines (streamlines) are curves tangent to the seepage velocity vector everywhere within the seepage field. A net consisting of two groups of mutually orthogonal flow lines and equipotential lines reflecting factors such as the movement direction, the flow speed and the like of the underground water in the seepage field on a plan view or a section view; or in the case of planar flow, when the fluid point has no angular velocity, the group of flow lines and the group of equipotential lines form an orthogonal grid. The flow velocity profile, and thus the pressure profile and flow, can be calculated using the flow network. Flow nets are the most useful and comprehensive pattern for studying the problem of two-dimensional planar seepage; with the flow net, the whole field problem is solved. The network diagram is formed by interweaving flow lines and equal water head lines in a seepage field, intuitively summarizes water conservancy factors and characteristics in the seepage field, can obtain water heads, hydraulic slopes, seepage speeds, seepage pressures, seepage flows passing through each subarea or an overflowing section and the like required by related estimation of seepage field characteristics and engineering seepage control design from a flow network, and can know and judge seepage paths, courses, water quantity complementary relations among all subareas in the field, relative water permeability of the subareas, potential seepage deformation areas and the like according to the change characteristics, the flow lines and the change forms of the equal water head lines of the flow network.
Because the karst underground water system is a huge system, when the karst underground water system is researched, a plurality of adverse factors exist in actual operation, and how to simulate the flow network state of the karst underground water system in a laboratory environment, so that the karst underground water system can provide theoretical research and technical reference for water conservancy construction.
Disclosure of Invention
Aiming at the technical problems, the invention discloses a flow network simulation method of a karst underground water system, which realizes the flow network simulation of the karst underground water system by a laboratory image simulation method, and greatly improves the analysis capability, the application capability and the further research capability of the karst underground water system by simulating, simulating and analyzing according to flow network image data.
In order to realize the technical effects, the invention adopts the following technical scheme:
a flow network simulation method for a karst groundwater system comprises the following steps:
step one, establishing a conceptual model;
determining the size of a simulated area, the number of aquifer layers, the information dimension of karst underground water, the water flow state, the medium condition, the boundary condition and the initial condition by acquiring the landform, the geology, the hydrogeology, the tectonic geology, the hydrogeochemistry, the rock minerals, the hydrology, the meteorology or the industrial and agricultural conditions and the like;
step two, selecting a mathematical model;
constructing a water quality and water ecology multi-target coupling model, adding a differential evolution algorithm into the water quality and water ecology multi-target coupling model, realizing water balance in a karst underground water system flow network simulation process through the water quality and water ecology multi-target coupling model, and realizing optimal configuration of the water balance through the differential evolution algorithm;
step three, carrying out numeralization on the mathematical model;
realizing karst underground water system flow network simulation through a finite element algorithm, and carrying out numerical representation on a water quantity, water quality and water ecological multi-target coupling model;
step four, correcting the model;
the optimization of the flow network information of the karst underground water system is realized through a chaotic optimization algorithm model, the optimization of a water quantity, quality and water ecology multi-target coupling model is realized, and the simulation capacity of the water quantity, quality and water ecology multi-target coupling model is improved;
step five, correcting sensitivity analysis;
the sensitivity analysis of the water quantity, water quality and water ecology multi-target coupling model is realized by adjusting the parameter data information of the chaos optimization algorithm model;
step six, model verification;
and the evaluation and verification of the simulation result of the flow network of the karst underground water system are realized through an improved Schmidt orthogonal control algorithm.
As a further technical scheme of the invention, the method for constructing the water quality and quantity ecological multi-target coupling model comprises the following steps:
in the water quantity, quality and water ecology multi-target coupling model, the water balance equation of the flow network of the karst underground water system is as follows:
in the formula (1), W represents the natural rainfall in cm, ET represents the evapotranspiration in cm, and P1Represents inflow of surface water in cm, P2The effluent amount of surface water is expressed in cm, G1Represents the inflow of groundwater in cm, G2The flow rate of underground water is expressed in cm, M represents the amount of karst, the unit is cm, the karst depth wiring method is used for determining the daily karst depth of the karst surface, and the water storage depth except the various dissolved amounts is expressed by the following formula:
in the formula (2), the subscript d represents the water storage date, H represents the water storage depth in cm, IW represents irrigation quantity in cm, F represents infiltration quantity in cm, and P represents surface drainage quantity in cm. The formula of the surface water displacement is as follows:
in the formula (3), Oh represents the height of the water storage ditch on the surface of the stream net, and the unit is cm.
As a further technical scheme of the invention, the method for constructing the differential evolution algorithm comprises the following steps:
Wherein each link of the karst underground water system is individually recorded as Xj=[xj,1，xj,2，···，xjD]Indicating an optimization therein;
j is a non-zero natural number, and D is the information dimension of each link of the karst groundwater system;
in the formula (4), W represents a variant individual vector, y represents a scaling factor, and the formula (4) represents that the g +1 generation variant individual vector consists of a g generation base vector and a variant difference vector;
and 3, performing cross operation on all the variant individuals, and performing cross variant individual to obtain filial generation individuals:
in the formula (5), w represents the crossed offspring individuals, rand () represents a randomly generated natural number, CR represents the cross probability, and the initial formula about CR is:
in the formula (6), R0Representing an initial cross-probability value;
and 4, after obtaining the offspring individuals, selecting the optimal solution, comparing the W individuals with the x individuals by taking the minimum adaptive value as a representative optimal solution, wherein the comparison formula is as follows:
in the formula (7), f represents an adaptive function, a solution of the optimal value of the function, and the optimal state of the karst groundwater system for maintaining water balance.
As a further technical scheme of the invention, the method for constructing the differential evolution algorithm comprises the following steps: the method for realizing the flow network simulation of the karst underground water system by the finite element method is to divide the karst underground water system to be analyzed into finite modules to solve the flow network performance problem and then divide the karst underground water system into finite modules for analysis, wherein the method for constructing the finite element algorithm model comprises the following steps:
in the formula (8), the reaction mixture is,
1is the magnetic vector position of the earth magnetic field,
1is the density of the terrain and the geology,
1representing the electromotive force induced by the earth forming magnetic fields,
1the number of the types of the geological properties of the structure where the karst groundwater system is located is represented,
1is a duty cycle that is a function of,
respectively the content of the hydrological geochemical substances,
is the solubility of the rock mineral, and the solubility of the rock mineral,
is the influence factor of the karst underground water system flow network by external data information,
1the number of equal lines divided for the stream network;
the flow net finite element simulation formula (9) shows:
in the formula (9), the reaction mixture is,
2to the streamlineThe vector deviation to the earth's magnetic field,
2is the density of the equipotential lines and,
2indicating the electromotive force of the equipotential lines induced by the earth's gravity,
1represents the virtual number of turns of the equipotential lines,
2is a duty cycle that is a function of,
respectively, are the seepage velocity vector values,
is the equivalent water leakage amount of each point in the seepage zone in the water flow direction,
0is the pressure distribution of the streamlines under the force of gravity of the earth,
2for the load in the seepage velocity process, then discretizing the two formulas to obtain a flow net finite element equation shown in (10):
in the formula (10), the compound represented by the formula (10),
the streamline vector magnetic potential comprehensive value of the earth magnetic field is obtained;
permeability of a karst groundwater system;
influence factors of the flow network of the karst underground water system by external data information are defined;
the density of equipotential lines is affected to varying degrees by the topography.
As a further technical scheme of the invention, the method for realizing the simulation of the flow network condition of the karst underground water system by the finite element algorithm model comprises the following steps:
firstly, setting an initial value, defining a flow network area of a karst underground water system and a marked acquisition point, and setting parameter information such as topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock minerals, hydrological or meteorological data information characteristics which reflect the flow network condition of the karst underground water system, wherein the parameter information is based on finite elements; simulating a flow network flow field, simulating the flow network condition and characteristics in a simulated karst underground water system, calculating vector deviation formed by the flow line under the action of the earth magnetic field, density of equipotential lines, electromotive force of the potential lines for inducing the earth attraction, virtual turn number of the equipotential lines, seepage velocity vector value or pressure distribution data information of the flow line under the action of the earth attraction by using a finite element algorithm model, calculating the whole potential line distribution by using a flow network weighted finite element, outputting a calculation result when a set threshold value is less than 0.4, and returning to an initial value for calculation when the set threshold value is more than or equal to 0.4.
As a further technical scheme of the invention, the working method of the chaos optimization algorithm model is as follows:
and (2) setting a parameter information function f (x) of any topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock mineral, hydrological or meteorological data information characteristics, wherein x and y are two random variables of the objective function. There is a tightness metric space M such that
And meets the following conditions:
in equation (11), n >0, z represents the initial value sensitivity, z >0, and there are any two open sets A, B on the metric space M such that:
where k >0, the values of the function f, derived from equation (12), are dense in the measurement space M, with f (x): m → M, and f is defined as the chaos in the measurement space M, and the chaos mathematical model is as follows:
in formula (13), u represents a chaotic parameter, different chaotic time sequences are mapped through different chaotic parameter values, and when u =4, the method has no definite chaotic time sequence, so that the interval [0,1 [ ]]Performing internal mapping to obtain the optimal chaotic characteristic expression, assuming that the dimension is D, setting the parameter information population scale of the topographic and geomorphic, geological, hydrogeological, tectonic, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristic in the karst underground water system to be NP, and setting the original time sequence B = { B } through chaos1，B2，···，BNPPerforming dimensionality extension to obtain an initial time sequence matrix as follows:
in equation (14), the time series calculation in the initial time series matrix in the karst groundwater system is shown as equation (15):
in formula (15), Xa,dRepresenting the d-dimensional initial optimal solution of the individual samples of the parameter information of the topographic and geomorphic, geological, hydrogeological, tectonic geological, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristics in the a-th karst underground water system, wherein the matrix of the initial optimal solution is as follows:
in equation (16), whether the optimized solution of the new individual is the optimal solution is selected by means of dynamic probability, as shown in (17):
as a further technical scheme of the invention, the working method of the chaos optimization algorithm model comprises the following steps: the method for adjusting the parameter data information of the chaos optimization algorithm model comprises the steps of carrying out parallel calculation on a differential evolution algorithm process, dividing a parameter information population individual with topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrographic data or meteorological data information characteristics in a karst underground water system into more than 20 data attributes, carrying out variation, intersection and optimal solution selection through different attributes, repeatedly carrying out iterative settlement, setting the iteration frequency to be more than 100 times, and outputting an adjustment parameter until the iteration frequency reaches the maximum value.
As a further technical scheme of the invention, the working method of the chaos optimization algorithm model comprises the following steps: the Schmidt orthogonal control algorithm demonstrates the parameter information of the topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrology or meteorological data information characteristics in the karst underground water system in a three-dimensional space through FPGA control, and further realizes the control of flow network information.
The method has the advantages that the simulation of the flow network of the karst underground water system is realized by a laboratory image simulation method, the simulation of the flow network of the karst underground water system is realized by a finite element algorithm, and the water quantity, water quality and water ecological multi-target coupling model is numerically expressed; optimizing the flow network information of the karst underground water system through the chaotic optimization algorithm model, optimizing the water quality and water ecology multi-target coupling model, and improving the simulation capacity of the water quality and water ecology multi-target coupling model; by simulating, simulating and analyzing according to the flow network image data, the analysis capability, the application capability and the further research capability of the karst underground water system are greatly improved.
Drawings
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 other drawings can be obtained by those skilled in the art without inventive exercise, wherein:
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a water quantity-quality water ecology multi-target coupling model in the invention;
FIG. 3 is a schematic flow chart of the difference algorithm of the present invention;
FIG. 4 is a schematic flow chart of a finite element algorithm according to the present invention;
FIG. 5 is a schematic exploded view of a finite element algorithm according to the present invention;
FIG. 6 is a schematic diagram of a finite element algorithm simulation process according to the present invention;
FIG. 7 is a schematic diagram of a finite element algorithm simulation result in the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, and it should be understood that the embodiments described herein are merely for the purpose of illustrating and explaining the present invention and are not intended to limit the present invention.
As shown in fig. 1, a flow network simulation method for a karst groundwater system includes the following steps:
establishing a conceptual model, and determining the size of a simulated area, the number of aquifer layers, the information dimension of karst underground water, the water flow state (stable flow and unstable flow, saturated flow and unsaturated flow in specific embodiments), the medium condition (homogeneous and heterogeneous, isotropic and anisotropic, pores, fissures and double media and density difference of fluid in specific embodiments), the boundary condition and the initial condition by acquiring topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrogeology, meteorological or industrial and agricultural conditions. In a specific embodiment, a series of laboratory tests and field tests are performed as necessary to obtain relevant parameters, such as permeability coefficient, diffusion coefficient, partition coefficient, reaction rate constant, etc.
Selecting a mathematical model, constructing a water quality and water ecological multi-target coupling model, adding a differential evolution algorithm into the water quality and water ecological multi-target coupling model, realizing water balance in a karst underground water system flow network simulation process through the water quality and water ecological multi-target coupling model, and realizing optimal configuration of the water balance through the differential evolution algorithm;
in the specific embodiment, the differential evolution algorithm is a brand-new heuristic group random optimization method, direct search is performed through the difference between groups, and the method is widely accepted by many researchers due to the advantage of simple and rapid calculation. The basic principle of the differential evolution algorithm is that an original population is used for carrying out variation to generate variation individuals, the variation individuals are crossed to obtain filial generation individuals, filial generation with the optimal solution is selected, and iteration is carried out.
The selection is made according to a conceptual model. Such as one-dimensional, two-dimensional, and three-dimensional mathematical models, water flow models, solute transport models, reaction models, hydrodynamic-water coupling models, hydrodynamic-reaction coupling models, and hydrodynamic-dispersion-reaction coupling models.
Step three, carrying out numeralization on the mathematical model
Most mathematical models are not analytically solvable. The numeralization is to convert a mathematical model into a solvable numerical model. Realizing karst underground water system flow network simulation through a finite element algorithm, and carrying out numerical representation on a water quantity, water quality and water ecological multi-target coupling model;
step four, correcting the model
Optimizing the flow network information of the karst underground water system through the chaotic optimization algorithm model, optimizing the water quality and water ecology multi-target coupling model, and improving the simulation capacity of the water quality and water ecology multi-target coupling model;
and comparing the simulation result with the actual measurement result, and adjusting parameters to make the simulation result coincide with the actual measurement result within a given error range. The parameter adjusting process is a complicated and hard work, and the adjusted parameters must meet the specific conditions of the simulation area. Fortunately, automatic parameter adjusting programs (such as PEST) have been developed and researched very vigorously abroad recently, and the work efficiency of simulators is greatly improved.
Step five, correcting sensitivity analysis
The sensitivity analysis of the water yield, quality and water ecology multi-target coupling model is realized by adjusting the parameter data information of the chaotic optimization algorithm model;
the corrected model is influenced by the uncertainty of the spatial-temporal distribution of the parameter values, the boundary conditions, the water flow state and the like. The sensitivity analysis is to determine how much the uncertainty affects the calibration model.
Step six, model verification
Evaluating and verifying the simulation result of the flow network of the karst underground water system by an improved Schmidt orthogonal control algorithm;
the model verification is to further adjust parameters on the basis of model correction to enable the simulation result to be matched with the second actual measurement result so as to further improve the confidence coefficient of the model.
In the second step, the method for constructing the water quality and water ecology multi-target coupling model comprises the following steps:
as shown in fig. 2, in the water quality and water ecology multi-target coupling model, the water balance equation of the flow network of the karst groundwater system is as follows:
in the formula (1), W represents the natural rainfall in cm, ET represents the evapotranspiration in cm, and P1Represents inflow of surface water in cm, P2The effluent amount of surface water is expressed in cm, G1Represents the inflow of groundwater in cm, G2The flow rate of underground water is expressed in cm, M represents the amount of karst, the unit is cm, the karst depth wiring method is used for determining the daily karst depth of the karst surface, and the water storage depth except the various dissolved amounts is expressed by the following formula:
in the formula (2), the subscript d represents the water storage date, H represents the water storage depth in cm, IW represents irrigation quantity in cm, F represents infiltration quantity in cm, and P represents surface drainage quantity in cm. The formula of the surface water displacement is as follows:
in the formula (3), Oh represents the height of the water storage ditch on the earth surface of the flow net, and the unit is cm.
In the specific embodiment, the water storage depth is an important management parameter for maintaining the optimal circulation state of the flow network. When the upper layer of the karst groundwater system is saturated, soil water will permeate to the lower layer. In the karst groundwater system, surface soil is covered by water, even if deeper soil moisture is considered to be saturated, a differential evolution algorithm is added in the water quality water ecological multi-target coupling model, the water balance in the simulation process of the flow network of the karst groundwater system is realized through the water quality water ecological multi-target coupling model, and the optimal configuration of the water balance is realized through the differential evolution algorithm.
In the second step, the method for constructing the differential evolution algorithm comprises the following steps:
as shown in fig. 3, the differential evolution algorithm is a completely new heuristic random population optimization method, and performs direct search through the difference between populations, and is widely recognized by many researchers due to the advantage of simple and fast calculation. The basic principle of the differential evolution algorithm is that an original population is used for carrying out variation to generate variation individuals, the variation individuals are crossed to obtain filial generation individuals, filial generation with the optimal solution is selected, and iteration is carried out. The algorithm comprises the following specific processes:
Wherein each link of the karst underground water system is individually recorded as Xj=[xj,1，xj,2，···，xjD]A solution to the optimization method is shown. Wherein j is a non-zero natural number, and D is the information dimension of each link of the karst groundwater system;
in the formula (4), W represents a variant individual vector, y represents a scaling factor, and the formula (4) represents that the g +1 generation variant individual vector consists of a g generation base vector and a variant difference vector;
and 3, performing cross operation on all the variant individuals, and performing cross variant individual to obtain filial generation individuals:
in the formula (5), w represents the crossed offspring individuals, rand () represents a randomly generated natural number, CR represents the cross probability, and the initial formula about CR is:
in the formula (6), R0Representing an initial cross-probability value;
and 4, after obtaining the offspring individuals, selecting an optimal solution, comparing the W individuals with the x individuals by taking the minimum adaptive value as a representative optimal solution, wherein the comparison formula is as follows:
in the formula (7), f represents an adaptive function, a solution of the optimal value of the function, and an optimal state of water balance of the karst groundwater system,
in a specific embodiment, the topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrology and meteorology of the karst groundwater system satisfying these conditions are the optimal solutions obtained by the differential evolution algorithm. And is also the best state value for achieving the optimal configuration of water balance.
In the third step, the method for realizing the flow network simulation of the karst underground water system by the finite element method comprises the following steps:
dividing the karst underground water system to be analyzed into limited modules to solve the problem of the flow network performance, then dividing the karst underground water system into the limited modules to analyze, and constructing a finite element algorithm model by the method comprising the following steps:
calculating the information characteristics of topographic, geomorphic, hydrogeological, tectonic, hydrogeochemistry, rock mineral, hydrological or meteorological data of the karst groundwater system, wherein the formula (1) shows that:
in the formula (8), the reaction mixture is,
1is the magnetic vector position of the earth magnetic field,
1is the density of the terrain and the geology,
1representing the electromotive force induced by the earth forming magnetic fields,
1the number of the types of the geological properties of the structure where the karst groundwater system is located is represented,
1is a duty cycle that is a function of,
respectively the content of the hydrological geochemical substances,
is the solubility of the rock mineral, and the solubility of the rock mineral,
is the influence factor of the karst underground water system flow network by external data information,
1the number of equal lines divided for the stream network;
the flow net finite element simulation formula (9) shows:
in the formula (9), the reaction mixture is,
2the streamlines are subjected to vector deviations formed by the earth's magnetic field,
2is the density of the equipotential lines and,
2electromotive force representing equipotential lines induced by earth's gravity，
1Represents the virtual number of turns of the equipotential lines,
2is a duty cycle that is a function of,
respectively, are the vector values of the seepage velocity,
is the equivalent water leakage amount of each point in the seepage zone in the water flow direction,
0is the pressure distribution of the streamlines under the force of gravity of the earth,
2for the load in the seepage velocity process, then discretizing the two formulas to obtain a flow net finite element equation shown in (10):
in the formula (10), the compound represented by the formula (10),
the streamline vector magnetic potential comprehensive value of the earth magnetic field is obtained;
permeability of a karst groundwater system;
influence factors of the flow network of the karst underground water system by external data information are defined;
the density of equipotential lines is affected to varying degrees by the topography.
As shown in fig. 4 and 5, in step three, the method for realizing the simulation of the flow network condition of the karst groundwater system by using the finite element algorithm model comprises the following steps:
firstly, setting initial values, delimiting a flow network area of a karst underground water system and a marked acquisition point, setting parameter information such as topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrology or meteorological data information characteristics which reflect the flow network condition of the karst underground water system, and setting the parameter information based on finite elements; simulating a flow network flow field, simulating the flow network condition and characteristics in a simulated karst underground water system, calculating vector deviation formed by the flow line under the action of the earth magnetic field, density of equipotential lines, electromotive force of the potential lines for inducing the earth attraction, virtual turn number of the equipotential lines, seepage velocity vector value or pressure distribution data information of the flow line under the action of the earth attraction by using a finite element algorithm model, calculating the whole potential line distribution by using a flow network weighted finite element, outputting a calculation result when a set threshold value is less than 0.4, and returning to an initial value for calculation when the set threshold value is more than or equal to 0.4.
As shown in fig. 6 and 7, simulation of the flow network condition of the karst groundwater system is achieved by using the streamline weighting finite element method, the electric potential lines of the flow network of the karst groundwater system can sense the parameter information set by the finite element algorithm model, different data information is output through the introduced formula, and then eddy current is generated.
In the fourth step, the working method of the chaos optimization algorithm model is as follows:
and (2) setting a parameter information function f (x) of any topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock mineral, hydrological or meteorological data information characteristics, wherein x and y are two random variables of the objective function. There is a tightness metric space M such that
And meets the following conditions:
in equation (11), n >0, z represents the initial value sensitivity, z >0, and there are any two open sets A, B on the metric space M such that:
where k >0, the values of the function f derived from equation (12) are dense in the metric space M, and there is f (x): m → M, and f is defined as the chaos in the measurement space M, and the chaos mathematical model is as follows:
in formula (13), u represents a chaotic parameter, different chaotic time sequences are mapped through different chaotic parameter values, and when u =4, the method has no definite chaotic time sequence, so that the interval [0,1 [ ]]Performing internal mapping to obtain the optimal chaotic characteristic expression, assuming that the dimension is D, setting the parameter information population scale of the topographic and geomorphic, geological, hydrogeological, tectonic, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristic in the karst underground water system to be NP, and setting the original time sequence B = { B } through chaos1，B2，···，BNPPerforming dimensionality extension to obtain an initial time sequence matrix as follows:
in the formula (14), by calculating the time series in the initial time series matrix in the karst groundwater system as shown in the formula (15),
in formula (15), Xa,dRepresenting the d-dimensional initial optimal solution of the individual samples of the parameter information of the topographic and geomorphic, geological, hydrogeological, tectonic geological, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristics in the a-th karst underground water system, wherein the matrix of the initial optimal solution is as follows:
in equation (16), whether the optimized solution of the new individual is the optimal solution is selected by means of dynamic probability, as shown in (17):
in the fifth step, the method for adjusting the parameter data information of the chaos optimization algorithm model is to perform parallel calculation on the differential evolution algorithm process, divide the parameter information population individuals of the topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristics in the karst underground water system into more than 20 data attributes, perform variation, intersection and optimal solution selection through different attributes, repeatedly perform iterative settlement, set the iteration times to be more than 100 times, and output the adjustment parameters until the iteration times reaches the maximum value.
Step six model verification
The Schmidt orthogonal control algorithm demonstrates the parameter information of the topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrology or meteorological data information characteristics in the karst underground water system in a three-dimensional space through FPGA control, and further realizes the control of flow network information.
In a specific implementation, Schmidt orthogonalization (Schmidt orthogonalization) is a method for finding the euclidean space orthogonal basis. Vector set alpha free of linear independence from Euclidean space1，α2，…，αmStarting from the vector, a set of orthogonal vectors β is obtained1，β2，…，βmFrom α to α1，α2，…，αmAnd vector set beta1，β2，…，βmEquivalently, each vector in the orthogonal vector group is unitized to obtain a standard orthogonal vector group, and the method is called Schmitt orthogonalization.
Although specific embodiments of the present invention have been described above, it will be understood by those skilled in the art that these specific embodiments are merely illustrative and that various omissions, substitutions and changes in the form of the detail of the methods and systems described above may be made by those skilled in the art without departing from the spirit and scope of the invention. For example, it is within the scope of the present invention to combine the steps of the above-described methods to perform substantially the same function in substantially the same way to achieve substantially the same result. Accordingly, the scope of the invention is to be limited only by the following claims.
Claims (8)
1. A karst groundwater system flow network simulation method is characterized in that: the method comprises the following steps:
step one, establishing a conceptual model;
determining the size of a simulated area, the number of aquifer layers, the information dimension of karst underground water, the water flow state, the medium condition, the boundary condition and the initial condition by acquiring the landform, the geology, the hydrogeology, the tectonic geology, the hydrogeochemistry, the rock minerals, the hydrology, the meteorology or the industrial and agricultural conditions and the like;
step two, selecting a mathematical model;
constructing a water quality and water ecology multi-target coupling model, adding a differential evolution algorithm into the water quality and water ecology multi-target coupling model, realizing water balance in a karst underground water system flow network simulation process through the water quality and water ecology multi-target coupling model, and realizing optimal configuration of the water balance through the differential evolution algorithm;
step three, carrying out numeralization on the mathematical model;
realizing flow network simulation of a karst underground water system through a finite element algorithm, and carrying out numerical expression on a water quantity, quality and water ecological multi-target coupling model;
step four, correcting the model;
optimizing the flow network information of the karst underground water system through the chaotic optimization algorithm model, optimizing the water quality and water ecology multi-target coupling model, and improving the simulation capacity of the water quality and water ecology multi-target coupling model;
step five, correcting sensitivity analysis;
the sensitivity analysis of the water quantity, water quality and water ecology multi-target coupling model is realized by adjusting the parameter data information of the chaos optimization algorithm model;
step six, model verification;
and the evaluation and verification of the simulation result of the flow network of the karst underground water system are realized through an improved Schmidt orthogonal control algorithm.
2. The karst groundwater system flow network simulation method according to claim 1, wherein: the method for constructing the water quantity, water quality and water ecology multi-target coupling model comprises the following steps:
in the water quantity, quality and water ecology multi-target coupling model, the water balance equation of the flow network of the karst underground water system is as follows:
in the formula (1), W represents the natural rainfall in cm, ET represents the evapotranspiration in cm, and P1Represents inflow of surface water in cm, P2The effluent amount of surface water is expressed in cm, G1Represents the inflow of groundwater in cm, G2The flow rate of underground water is expressed in cm, M represents the amount of karst, the unit is cm, the karst depth wiring method is used for determining the daily karst depth of the karst surface, and the water storage depth except the various dissolved amounts is expressed by the following formula:
in formula (2), subscript d represents the water storage date, H represents the water storage depth in cm, IW represents the irrigation volume in cm, F represents the infiltration volume in cm, P represents the surface drainage volume in cm;
the formula of the surface water displacement is as follows:
in the formula (3), Oh represents the height of the water storage ditch on the surface of the stream net, and the unit is cm.
3. The karst groundwater system flow network simulation method according to claim 1, wherein: the method for constructing the differential evolution algorithm comprises the following steps:
step 1, setting the water population scale of a karst groundwater system to be NPOriginal population X = [ X ]1，X2，···，XNP]；
Wherein each link of the karst underground water system is individually recorded as Xj=[xj,1，xj,2，···，xjD]Represents an optimization therein;
j is a non-zero natural number, and D is the information dimension of each link of the karst groundwater system;
step 2, assuming that g is a population algebra, carrying out mutation operation on a certain individual in an original population in each link of the karst underground water system to generate a variant individual:
in the formula (4), W represents a variant individual vector, y represents a scaling factor, and the formula (4) represents that the g +1 generation variant individual vector consists of a g generation base vector and a variant difference vector;
and 3, performing cross operation on all the variant individuals, and performing cross variant individual to obtain filial generation individuals:
in the formula (5), w represents the crossed offspring individuals, rand () represents a randomly generated natural number, CR represents the cross probability, and the initial formula about CR is:
in the formula (6), R0Representing an initial cross probability value;
and 4, after obtaining the offspring individuals, selecting an optimal solution, comparing the W individuals with the x individuals by taking the minimum adaptive value as a representative optimal solution, wherein the comparison formula is as follows:
in equation (7), f represents the adaptive function, the solution of the optimal value of the function, and the optimal state of the karst groundwater system for maintaining water balance.
4. The karst groundwater system flow network simulation method according to claim 1, wherein: the method for constructing the differential evolution algorithm comprises the following steps: the method for realizing the flow network simulation of the karst underground water system by the finite element method is to divide the karst underground water system to be analyzed into finite modules to solve the performance problem of the flow network, and then divide the karst underground water system into the finite modules for analysis, wherein the method for constructing the finite element algorithm model comprises the following steps:
in the formula (8), the reaction mixture is,
1is the magnetic vector position of the earth magnetic field,
1is the density of the terrain and the geology,
1representing the electromotive force induced by the earth forming magnetic fields,
1the number of the types of the geological properties of the structure where the karst groundwater system is located is represented,
1is a duty cycle that is a function of,
respectively the content of the hydrological geochemical substances,
is the solubility of the rock mineral, and the solubility of the rock mineral,
is the influence factor of the karst underground water system flow network by external data information,
1the number of equal lines divided for the stream network;
the flow net finite element simulation formula (9) shows:
in the formula (9), the reaction mixture is,
2the streamlines are subjected to vector deviations formed by the earth's magnetic field,
2is the density of the equipotential lines and,
2representing the electromotive force of the equipotential lines induced by the earth's gravitational force,
1represents the virtual number of turns of the equipotential lines,
2is a duty cycle of the electric power,
respectively, are the seepage velocity vector values,
is the equivalent water leakage amount of each point in the seepage zone in the water flow direction,
0is the pressure distribution of the streamlines under the force of gravity of the earth,
2for the load in the seepage velocity process, then discretizing the two formulas to obtain a flow net finite element equation shown in (10):
in the formula (10), the compound represented by the formula (10),
is the streamline vector magnetic potential comprehensive value of the earth magnetic field;
permeability of a karst groundwater system;
influence factors of the karst underground water system flow network from external data information are obtained;
the density of equipotential lines is affected to varying degrees by the topography.
5. The karst groundwater system flow network simulation method according to claim 1, wherein: the method for realizing the simulation of the flow network condition of the karst underground water system through the finite element algorithm model comprises the following steps:
firstly, setting an initial value, defining a flow network area of a karst underground water system and a marked acquisition point, and setting parameter information such as topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock minerals, hydrological or meteorological data information characteristics which reflect the flow network condition of the karst underground water system, wherein the parameter information is based on finite elements; simulating a flow network flow field, simulating the flow network condition and characteristics in a simulated karst underground water system, calculating vector deviation formed by the flow line under the action of the earth magnetic field, density of equipotential lines, electromotive force of the potential lines for inducing earth attraction, virtual turn number of the equipotential lines, seepage velocity vector value or pressure distribution data information of the flow line under the action of the earth attraction by using a finite element algorithm model, calculating the overall potential line distribution through a flow network weighted finite element, outputting a calculation result when a set threshold value is less than 0.4, and returning to an initial value for calculation when the set threshold value is more than or equal to 0.4.
6. The karst groundwater system flow network simulation method according to claim 1, wherein: the working method of the chaos optimization algorithm model is as follows:
setting parameter information functions f (x) of any topographic and geomorphic, geological, hydrogeological, tectonic geology, hydrogeochemistry, rock mineral, hydrological or meteorological data information characteristics, wherein x and y are two random variables of a target function;
there is a tightness metric space M such that
And meets the following conditions:
in equation (11), n >0, z represents the initial value sensitivity, z >0, and there are any two open sets A, B on the metric space M such that:
where k >0, the values of the function f derived from equation (12) are dense in the metric space M, and there is f (x): m → M, and f is defined as the chaos in the measurement space M, and the chaos mathematical model is as follows:
in formula (13), u represents a chaotic parameter, different chaotic time sequences are mapped through different chaotic parameter values, and when u =4, the method has no definite chaotic time sequence, so that the interval [0,1 ] is]Performing internal mapping to obtain the optimal chaotic characteristic expression, assuming that the dimension is D, setting the parameter information population scale of the topographic and geomorphic, geological, hydrogeological, tectonic, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristic in the karst underground water system to be NP, and setting the original time sequence B = { B } through chaos1，B2，···，BNPPerforming dimensionality extension to obtain an initial time sequence matrix as follows:
in equation (14), the time series calculation in the initial time series matrix in the karst groundwater system is shown as equation (15):
in formula (15), Xa,dRepresenting the d-dimensional initial optimal solution of the individual samples of the parameter information of the topographic and geomorphic, geological, hydrogeological, tectonic geological, hydrogeochemistry, rock mineral, hydrographic or meteorological data information characteristics in the a-th karst underground water system, wherein the matrix of the initial optimal solution is as follows:
in equation (16), whether the optimized solution of the new individual is the optimal solution is selected by means of dynamic probability, as shown in (17):
7. the karst groundwater system flow network simulation method according to claim 1, wherein: the working method of the chaos optimization algorithm model comprises the following steps: the method for adjusting the parameter data information of the chaos optimization algorithm model comprises the steps of carrying out parallel calculation on a differential evolution algorithm process, dividing a parameter information population individual with topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrographic data or meteorological data information characteristics in a karst underground water system into more than 20 data attributes, carrying out variation, intersection and optimal solution selection through different attributes, repeatedly carrying out iterative settlement, setting the iteration frequency to be more than 100 times, and outputting an adjustment parameter until the iteration frequency reaches the maximum value.
8. The karst groundwater system flow network simulation method according to claim 1, wherein: the working method of the chaos optimization algorithm model comprises the following steps: the Schmidt orthogonal control algorithm demonstrates the parameter information of the topographic features, geology, hydrogeology, tectonic geology, hydrogeochemistry, rock minerals, hydrology or meteorological data information characteristics in the karst underground water system in a three-dimensional space through FPGA control, and further realizes the control of flow network information.
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