CN112131751A - Parameter prediction method based on HYDROUS-1D - Google Patents

Parameter prediction method based on HYDROUS-1D Download PDF

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CN112131751A
CN112131751A CN202011045917.5A CN202011045917A CN112131751A CN 112131751 A CN112131751 A CN 112131751A CN 202011045917 A CN202011045917 A CN 202011045917A CN 112131751 A CN112131751 A CN 112131751A
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赵鹏
赵玉炜
崔丽敏
赵伟高
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Abstract

The invention discloses a parameter prediction method based on HYDROUS-1D, which comprises the following steps: simulating a migration penetration curve of the pollutant with known concentration by using HYDROUS-1D, and adjusting parameters to the optimal fitting degree; establishing a linear and nonlinear regression equation for each adjusted parameter and the pollutant concentration by adopting curve estimation, and selecting a parameter which is optimal to fit with a concentration variable as a control parameter; combining the rest parameters and the control parameters into new variable parameters, and establishing a linear or nonlinear regression equation between the new variable parameters and the concentration; and (4) performing input parameter prediction on the migration of the pollutants with other concentrations to be simulated by using a regression equation. The invention can effectively predict the input parameters of the simulated pollutants, so that the simulation and parameter optimization are more efficient and accurate.

Description

Parameter prediction method based on HYDROUS-1D
Technical Field
The invention relates to the field of pollutant migration simulation in sand filtration media, in particular to a parameter prediction method based on HYDROUS-1D.
Background
The migration of pollutants in porous media is usually simulated and parameter inverse solution by using HYDROUS-1D software, and an estimated initial value is required to be input in the parameter inverse solution process, and iteration is performed based on the initial value. At present, a two-point dynamic adsorption model in the HYDROUS-1D is commonly used for simulating the migration of a single pollutant, and the research for simulating the migration process of each pollutant under the condition of existence of double pollutants by using the model is less. Therefore, the initial values of the input parameters in the presence of dual contaminants cannot be well predicted due to insufficient relevant reference data.
In the software running process, the initial value of the input parameter is directly related to the iterative process of parameter inverse solution, when the input initial value is greatly deviated from the true value, the requirement on a computer is high, the software running is retarded or even wrong due to the calculation pressure, and further, the simulation and optimization results are inaccurate.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a parameter prediction method based on the HYDROUS-1D, which can better predict parameters required by pollutant migration simulation to a certain extent, can reduce the operating pressure of a computer by using the predicted values as initial values to carry out parameter optimization, and obtains good optimization and simulation effects.
The purpose of the invention is realized by the following technical scheme.
The parameter prediction method based on the HYDROUS-1D comprises the following processes:
the first step is as follows: simulating a migration penetration curve of the pollutant with known concentration by using HYDROUS-1D, and adjusting parameters to the optimal fitting degree;
the second step is that: establishing a linear and nonlinear regression equation for each parameter and pollutant concentration adjusted in the first step by adopting curve estimation, and selecting a parameter which is optimal to fit with a concentration variable as a control parameter;
the third step: combining the rest parameters and the control parameters into new variable parameters, and establishing a linear or nonlinear regression equation between the new variable parameters and the concentration;
the fourth step: and (4) predicting the input parameters of the migration of the pollutants with other concentrations to be simulated by using the regression equation established in the third step.
The simulations described in the first step are applicable to a two-point kinetic adsorption model, and the parameters include Smax, katt2, kdet2, katt1, kdet 1; wherein Smax represents the maximum solid phase adsorption concentration, katt2 and kdet2 represent the first order attachment coefficient and the first order desorption coefficient of kinetic site 2, and katt1 and kdet1 represent the first order attachment coefficient and the first order desorption coefficient of kinetic site 1, respectively.
The optimum degree of fit stated in the first step is R2>0.98。
In the second step, the curve estimation adopts a curve estimation module of SPSS software, and the selected curve estimation model is a linear or nonlinear model and comprises a linear model of a unitary element, a quadratic function, a cubic function, an exponential function and a power function.
In the second step, the goodness of fit R of the regression fit of the control parameters2Greater than 0.98.
And the new variable parameter in the third step is obtained by algebraically dividing other parameters and the control parameter.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
the invention selects the control parameter and combines with other parameters by carrying out regression analysis on the optimal parameter data obtained by simulation and the corresponding concentration condition thereof, finds out the internal rule thereof and predicts the initial value of the input parameter under other concentration conditions. The method can provide data reference for the HYDROUS-1D simulation and inverse solution parameters, the parameters are further optimized based on the predicted values, the simulation is more efficient, the obtained parameter values are closer to the real values, and meanwhile, the operation pressure of the computer can be relieved to a certain extent. The invention provides reference for the simulation of pollutant migration, so that the parameter optimization is carried out more efficiently and accurately.
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FIG. 1 is a flow chart of a HYDROUS-1D-based parameter prediction method of the present invention;
FIG. 2 is a comparison of the transmission curves of contaminants (4.5 μm polystyrene microspheres) modeled using predicted and optimized values in the examples of the present invention.
Detailed Description
In order to make the purpose and technical solution of the present invention clearer, the present invention is further described in detail below with reference to the accompanying drawings in combination with specific embodiments.
The parameter prediction method based on the HYDROUS-1D is based on the condition that two pollutants in a sand filter medium are cooperatively migrated by adopting a two-point dynamic adsorption model. As shown in fig. 1, the specific implementation process is as follows:
the first step is as follows: and (5) simulating a migration penetration curve of the pollutant with known concentration by using the HYDROUS-1D, and adjusting parameters to the optimal fitting degree.
Wherein the parameters include Smax, katt2, kdet2, katt1, kdet 1. Smax represents the maximum solid phase adsorption concentration, katt2, kdet2 represent the first order attachment coefficient and first order desorption coefficient, respectively, for kinetic site 2, and katt1, kdet1 represent the first order attachment coefficient and first order desorption coefficient, respectively, for kinetic site 1. Goodness of fit determination coefficient R2And (4) measuring, wherein the calculation formula is as follows:
R2＝SSR/SST＝1-SSE/SST (1)
wherein SSR stands for regression sum of squares, SSE for residual sum of squares, and SST for total sum of squares.
The optimal degree of fit described herein is R2>0.98, the model fitting is good in this case, and the model fitting can be used as a reliable basis for subsequent verification.
The second step is that: and (3) establishing a linear and nonlinear regression equation for each parameter and pollutant concentration after adjustment in the first step by adopting curve estimation, selecting a parameter which can be optimally fitted with a concentration variable as a control parameter, and using a function model as an estimation function of the control parameter.
Wherein the goodness of fit R of the regression fit2Greater than 0.98. The curve estimation adopts a curve estimation module of SPSS software, and when the curve estimation is adopted for function model selection, linear or nonlinear models such as unitary linear, quadratic function, cubic function, exponential function, power function and the like are selected for regression analysis according to the trend of a data scatter diagram, for example:
the cubic function model formula is:
y＝b0+b1x+b2x2+b3x3 (2)
the exponential function model formula is:
Figure BDA0002707955370000031
wherein x is independent variable (referring to pollutant concentration in the invention), y is dependent variable (referring to each parameter to be solved in the invention), b0Is a constant number, b1、b2、b3Are regression coefficients.
According to goodness of fit (R)2) The test, the F test and the significance value (sig) converted by the test select the best regression equation, significance sig.<0.05 represents significant results after the F test.
The third step: for other parameters with weak significance of regression analysis, algebraic division is carried out between the parameters and control parameters to combine the parameters and the control parameters into new variable parameters, so that the effect of amplifying the relation between the original parameters and the independent variable is achieved. A linear or non-linear regression equation is established between the new variable parameters and the concentrations.
The regression equation model may be examined and evaluated for back-substitution errors, where the error E of the predicted value is calculated using equation (4) below, i.e., the difference between the predicted value and the exact value.
Figure BDA0002707955370000041
The mean absolute percentage error MAPE calculation formula is calculated as following equation (5) and ranges from 0, infinity.
Figure BDA0002707955370000042
Wherein n represents the sample size, i.e. the number of data sets; a MAPE of 0% represents a perfect model, and a MAPE greater than 100% represents a poor model.
The fourth step: and (4) performing input parameter prediction on the migration of the pollutants with other concentrations to be simulated by using the regression equation established in the third step, wherein the obtained result is a prediction result, and further accurate optimization can be performed on the basis of the result when the HYDROUS-1D simulation is adopted.
The specific embodiment is as follows:
the parameter prediction method based on the HYDROUS-1D comprises the following steps:
(1) 2 × 10 times of Humic Acid (HA) with different concentrations in KCl background salt solution of 100mM and at the flow rate of 5mL/min, measured by a simulation experiment of HYDROUS-1D software6The penetration curve of 4.5 mu m polystyrene microspheres in each ml in a quartz sand column is adjusted by parameters so that the goodness of fit R of each curve2Are all greater than 0.98, and the optimum parameter values at each concentration are shown in table 1.
TABLE 1 optimum parameter values for fitting at different HA concentrations
Figure BDA0002707955370000043
(2) Linear and nonlinear regression analysis is established on the optimal parameters and the HA concentration by using a curve estimation module of SPSS software, data at concentrations of 0.1ppm, 0.5ppm, 2ppm, 10ppm, 20ppm and 30ppm are selected for regression, the HA concentration is used as an independent variable, the optimal parameters are used as dependent variables, and the obtained optimal regression parameter values of the parameters and the corresponding concentrations are shown in table 2.
TABLE 2 optimal regression analysis results for each parameter
Figure BDA0002707955370000051
According to R2And significance results it can be seen that the variable that can establish the best fit with the HA concentration values is katt1 and is therefore determined to be the control parameter. The regression equation is:
y0＝1.274e-0.056x (6)
wherein, y0Represents katt1 in min-1(ii) a x represents the HA concentration in ppm.
(3) For other parameters that are not significant for regression analysis, they are combined with the control parameters into new variable parameters. Here, the quotient of each parameter and the control parameter is taken as a new variable parameter, which is Smax/katt1, katt2/katt1, kdet2/katt1 and kdet1/katt1, respectively. The new parameters were fitted to the corresponding concentration values by regression using a cubic function, and the fitting results are shown in Table 3 below.
TABLE 3 results of regression analysis of each of the new parameters
Figure BDA0002707955370000052
According to R2And the significance result shows that the regression goodness of fit of the new parameters and the corresponding HA concentration values is obviously improved compared with the original parameters, the goodness of fit is high, and the model is good. The regression equation corresponding to each new parameter is as follows:
y1＝1.112+0.701x-0.097x2+0.003x3 (7)
y2＝14.110+0.972x+0.096x2-0.002x3 (8)
y3＝31.978+5.093x-0.297x2+0.010x3 (9)
y4＝0.001+0.004x+0.00000895x3 (10)
wherein y is1、y2、y3、y4Respectively, Smax/katt1, katt2/katt1, kdet2/katt1 and kdet1/katt1, and x represents the HA concentration in ppm.
(4) The original data are back substituted to obtain the parameter values under each concentration, see table 4:
TABLE 4 data back substitution results
Figure BDA0002707955370000061
The mean error rate MAPE of each parameter is obtained from the back substitution results as shown in table 5:
TABLE 5 mean error Rate results for each parameter
Figure BDA0002707955370000062
MAPE values of katt2, kdet2 and katt1 are all less than 10%, and the model is perfect; the MAPE value of Smax2 is relatively large, and the model fitting accuracy is medium; because the kdet1 value is very small and the regression coefficient is also very small, the contribution of the value to model fitting is not large according to experience, and the predicted value can be selected from 0-0.1.
(5) The fitting equation above was used to predict the various input parameters for an HA concentration of 1ppm, and the results are shown in Table 6:
TABLE 6 predicted and optimized values of the respective parameters at an HA concentration of 1ppm
Figure BDA0002707955370000071
The predicted value is input into HYDROUS-1D to carry out simulation under the condition of 1ppm HA concentration, and the penetration curve of the obtained polystyrene microspheres with the diameter of 4.5 mu m is shown as a graph in figure 2 (a). Wherein the goodness of fit is R2The mean absolute error is 0.014, with a better fit, when it is 0.988.
On the basis, the parameters are optimized, and the penetration curve of the optimized 4.5-micron polystyrene microspheres is shown in FIG. 2 (b). Wherein the goodness of fit is R2The average absolute error is 0.989, the difference with the fitting result obtained by the predicted value is not large, the operation process is fast, only 8.08s is needed, and the pressure to the computer is small. And the time required for optimizing by blindly guessing the input initial value under the condition of no prediction basis is different within the range of 5-30 s.
While the present invention has been described in terms of its functions and operations with reference to the accompanying drawings, it is to be understood that the invention is not limited to the precise functions and operations described above, and that the above-described embodiments are illustrative rather than restrictive, and that various changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention as defined by the appended claims.

Claims (6)

1. A parameter prediction method based on the HYDROUS-1D is characterized by comprising the following processes:
the first step is as follows: simulating a migration penetration curve of the pollutant with known concentration by using HYDROUS-1D, and adjusting parameters to the optimal fitting degree;
the second step is that: establishing a linear and nonlinear regression equation for each parameter and pollutant concentration adjusted in the first step by adopting curve estimation, and selecting a parameter which is optimal to fit with a concentration variable as a control parameter;
the third step: combining the rest parameters and the control parameters into new variable parameters, and establishing a linear or nonlinear regression equation between the new variable parameters and the concentration;
the fourth step: and (4) predicting the input parameters of the migration of the pollutants with other concentrations to be simulated by using the regression equation established in the third step.
2. The method of claim 1, wherein the simulation in the first step is adapted to a two-point kinetic adsorption model, and the parameters include Smax, katt2, kdet2, katt1, kdet 1; wherein Smax represents the maximum solid phase adsorption concentration, katt2 and kdet2 represent the first order attachment coefficient and the first order desorption coefficient of kinetic site 2, and katt1 and kdet1 represent the first order attachment coefficient and the first order desorption coefficient of kinetic site 1, respectively.
3. The method of claim 1, wherein the optimal degree of fit in the first step is R2>0.98。
4. The hydrous-1D based parameter prediction method of claim 1, wherein the curve estimation in the second step uses a curve estimation module of SPSS software, and the selected curve estimation model is a linear or non-linear model including a univariate linear, quadratic, cubic, exponential, or power linear model.
5. The method of claim 1, wherein the second step comprises controlling the goodness-of-fit R of the parameter, regression fit thereof2Greater than 0.98.
6. The method of claim 1, wherein the new variable parameters in the third step are obtained by algebraically dividing the other parameters by the control parameters.
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CN105260514A (en) * 2015-09-24 2016-01-20 中国环境科学研究院 Strong quantitative evaluation method for underground water pollution source
CN111489015A (en) * 2020-03-20 2020-08-04 天津大学 Atmosphere O based on multiple model comparison and optimization3Concentration prediction method
CN111351762A (en) * 2020-04-22 2020-06-30 青岛理工大学 Ultraviolet-visible light full-wavelength scanning sewage quality on-line rapid detection method and application

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