A water quality model parameter calibration method based on equivalent pollution source idea

Abstract

This invention discloses a water quality model parameter calibration method based on the concept of equivalent pollution sources. The method fully utilizes real-time water quality monitoring data, employing curve fitting and integration to equate the upstream section's pollutant concentration sequence to a known total pollutant amount. Simultaneously and instantaneously released pollution sources within a certain spatial range are considered as pollution sources for the downstream section. The method simulates and calculates the downstream section's pollutant concentration sequence, determines the range and step size of the parameters to be calibrated using empirical formulas, and performs a comprehensive combination. The final calibration result is determined by comparing the error between the simulated and measured pollutant concentration sequences at the downstream section. By designing a water pollution scenario, the parameter calibration under upstream discharge conditions is calculated and analyzed, verifying the feasibility and accuracy of this method. This invention proposes a water quality model parameter calibration method based on the concept of equivalent pollution sources, characterized by its comprehensive integration of river measured data, resulting in reasonable, accurate, and diverse calibration results.

Description

Technical Field

[0001] This invention relates to the field of water pollution source tracing, and in particular to a method for calibrating water quality model parameters based on the concept of equivalent pollution sources. Background Technology

[0002] In recent years, rapid economic development has led to the emergence of many water pollution problems. At the same time, the possibility of sudden water pollution incidents and the intensity of pollution have gradually increased. Tracing the source of water pollution accidents, locating the pollution source, and determining the discharge volume and time are crucial for timely cutting off the pollution source or taking relevant measures to prevent and control water pollution.

[0003] There are many methods for tracing the source of water pollution. Among them, the pure mathematical model simulation method mainly solves the problem by mathematical inverse method, but the relevant data is not easy to obtain and the feasibility is poor. The method that relies solely on real-time monitoring can detect anomalies in a timely manner, but the source tracing efficiency is low. The source tracing method based on deterministic theory mainly establishes an optimization problem that minimizes the error between the simulated value of the water quality model and the measured value of the monitoring station. It has a certain timeliness and high efficiency, but because the water quality model parameters are affected by the conditions of different rivers, the accuracy requirements of the water quality model parameters are high.

[0004] Water quality model parameters generally need to be determined through theoretical formulas, tracer experiments, or empirical formulas, or obtained through model parameter calibration. Since different rivers have different characteristics, theoretical formulas and empirical formulas have certain uncertainties, while tracer experiments and subsequent model parameter calibration lack timeliness and are not applicable in tracing the source of sudden water pollution.

[0005] By reviewing relevant literature and patents on water quality model parameter calibration, the following patents were found: "Method for Identifying Water Quality Model Parameters Based on Adaptive Strategy Differential Evolution" (Applicant: Jiangxi University of Science and Technology, Publication No.: CN108304675A). This method focuses on the steps of using adaptive strategy differential evolution but does not elaborate on the source of measured water quality data. Another patent, "An Improved Hybrid Genetic Algorithm for Optimizing Water Quality Model Parameters" (Applicant: Nanjing University, Publication No.: CN1900956A), discloses a method for calibrating water quality model parameters based on an improved hybrid genetic algorithm. This method focuses on the improvement and implementation of the genetic algorithm but does not consider the timeliness of parameter calibration. Summary of the Invention

[0006] The purpose of this invention is to utilize water quality data obtained from real-time online water quality monitoring equipment, and to achieve online calibration of water quality model parameters by processing upstream and downstream cross-sectional data, thereby improving the accuracy of the water quality model and, consequently, the source tracing accuracy of the source tracing method based on deterministic theory.

[0007] A method for calibrating water quality model parameters based on the concept of equivalent pollution sources, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0008] Step 1: Obtain basic data of the river area to be calibrated, model it using a two-dimensional river pollutant convection and diffusion model, and determine the calibration parameters.

[0009] Step 2: Deploy online monitoring equipment at equal intervals within the river channel to be calibrated to monitor water quality in real time.

[0010] Step 3: When pollution occurs, data is acquired using water quality anomaly equipment and the nearest downstream equipment to obtain two sets of pollutant concentration value sequences.

[0011] Step 4: Using the concept of integration, the pollutant concentration value sequence of the upstream section is equivalent to the total amount of known pollutants, and the distribution sources that are released instantaneously at the same time within a certain spatial range are taken as the pollution sources of the downstream section. By superimposing the countless instantaneous distribution sources that are equivalent to this through integration, the pollutant concentration value sequence of the downstream section is simulated and calculated.

[0012] Step 5: Determine k and D using empirical formulas. y The values ​​are selected to determine the range and step size, and each parameter is iterated and combined within the range of values.

[0013] Step 6: Establish an objective function that minimizes the error between the simulated and measured values ​​of the downstream section.

[0014] Step 7: Traverse the parameter combinations within the range of parameters to be calibrated, perform numerical simulations, and calculate the objective function value.

[0015] Step 8: Sort the objective function values, and finally determine a set of parameter combinations as the calibration result based on the objective function values ​​and the river conditions.

[0016] Furthermore, the water quality model parameter calibration method based on the concept of equivalent pollution sources is applicable to river channels with a depth / width of less than or equal to 1 / 30.

[0017] Furthermore, the basic data required for modeling the two-dimensional river pollutant convection and diffusion model proposed in step 1 include river depth h, river width b, and parallel bank flow velocity u. x Vertical riverbank flow velocity u y The available data, the parameter to be calibrated is the transverse dispersion coefficient D x Vertical dispersion coefficient D y And the degradation coefficient k.

[0018] Furthermore, in step 2, the online monitoring equipment deployment should have an interval of less than or equal to 200m, and the monitoring frequency should be less than or equal to the interval distance / parallel riverbank flow velocity.

[0019] Furthermore, the water quality data acquisition proposed in step 3 is judged when pollution occurs if three consecutive monitoring data are all greater than the previous monitoring value by 20%, that is, when there is an upward trend.

[0020] Furthermore, in step 3, the water quality data acquisition involves two sets of devices sampling within the same sampling time period. The sampling time period begins when the upstream device's three consecutive monitoring data are all greater than the previous monitoring value by 20%, and ends when the downstream device's three consecutive monitoring data are all less than the previous monitoring value by 20%.

[0021] Furthermore, the pollution source equivalence proposed in step 4 includes the following steps:

[0022] Step 4.1: Convert the time series measured by the emergency monitoring equipment into a spatial series. The calculation formula is as follows:

[0023] n = t n ×u x (1)

[0024] n i =t i ×u x (2)

[0025] In formula (1), n ​​is the total length of space, and t n To monitor the total duration, u x For the parallel riverbank velocity; in formula (2), n i t represents the spatial sequence spacing; i For monitoring frequency; u x The velocity is parallel to the riverbank.

[0026] Step 4.2: Use MATLAB to fit the converted sequence graph with common curves to determine the relationship function between concentration and distance as f(x).

[0027] Step 4.3: Calculate the simulated pollutant concentration sequence at the downstream section by superimposing several instantaneous concentrated sources using an integral form. The formula for calculating the superimposed concentration at a specified time x is:

[0028]

[0029] In formula (3), C(x,t) is the pollutant concentration at x at time t, in mg / L; f(x) is the function relating concentration and distance; n is the total spatial length of the upstream section; x is the distance from the river point to the instantaneous point source in the direction parallel to the river flow, in meters (here, it should be the interval distance between the two devices); y is the distance from the river point to the instantaneous point source in the direction perpendicular to the river flow, in meters; t is the time from the occurrence of the instantaneous pollution, in seconds (here, it should be the time node to be calculated); h is the river depth, in meters; D x D y These are the dispersion coefficients in the x and y directions, respectively, in meters. 2 / s;u x The velocity of the river flow parallel to the bank is expressed in m / s; u y ρ is the vertical flow velocity along the riverbank, in m / s; k is the degradation coefficient, in 1 / d.

[0030] Furthermore, the determination of the calibration parameter range and step size proposed in step 5 is based on the following empirical formulas:

[0031] k=(lnC1-lnC2)*u x / L (4)

[0032]

[0033]

[0034] In formula (4), C1 and C2 are the pollutant concentrations at the upstream and downstream sections of the river, respectively, in mg / L; x The velocity of the parallel riverbank is m / s; L is the distance between the two cross-sections, m.

[0035] In formulas (5) and (6), u x denoted as ρ = ρ_i, where ρ is the velocity of the parallel riverbank (m / s); b is the river width (m); h is the water depth (m); i is the hydraulic gradient; and g is the acceleration due to gravity (9.8 m / s).

[0036] Furthermore, the calibration parameter range and step size proposed in step 5 determine that the values ​​of Dy and k are within the range of [0.1D]. y * 10D y * [0.1k*, 10k*], D x Take the empirical value range [10, 20], D y * and k* are the calculated values ​​of the actual data determined by empirical formulas, where D x The step size is 0.1, D y The step size is 0.01, and the k-step size is 0.001.

[0037] Furthermore, the objective function proposed in step 6 is established. The objective function is the sum of the deviations between the downstream section pollutant concentration value sequence calculated using the pollution diffusion model and the actual observed pollutant concentration value sequence. The objective function is as follows:

[0038]

[0039] In formula (7), f(y,y*) is the objective function; y is the theoretical calculated value of pollutant concentration; y* is the observed concentration value; and m is the number of observed values.

[0040] Compared with existing technologies, this invention makes full use of real-time monitoring data to calibrate pollutant diffusion model parameters online. It treats the upstream section as an equivalent pollution source for the downstream section, and determines the value range of each parameter by combining empirical formulas with relevant actual parameters. Within a reasonable range, it simulates and calculates the pollutant concentration value sequence of the downstream section through a traversal method, calculates the objective function value, sorts the values, and determines the optimal solution by combining the sorting results with the actual situation, while retaining the suboptimal solution results, thus improving the accuracy of parameter calibration.

[0041] This invention proposes a method for calibrating water quality model parameters based on the concept of equivalent pollution sources, which features rapid, efficient and accurate calibration.

[0042] The beneficial effects of this invention are as follows:

[0043] This invention proposes to use two sets of real-time monitoring data and employ a pollution source equivalence method for parameter calibration, ensuring the accuracy and timeliness of the data source.

[0044] This invention proposes to determine the range of parameters to be calibrated using empirical formulas and actual river data, which ensures the rationality of the range of parameters to be calibrated, while reducing the traversal range and saving calibration time.

[0045] This invention proposes to set a step size within a reasonable range and then use a traversal method to achieve random combinations of different parameters, which improves the accuracy of calibration. After calculating the objective function, the parameters are sorted, and the optimal solution is determined in combination with the actual situation, while other solutions are retained, thus avoiding the uniformity of the results. Attached Figure Description

[0046] Figure 1 This is a flowchart of a water quality model parameter calibration method based on the concept of equivalent pollution sources.

[0047] Figure 2 This is a sequence diagram of pollutant concentration values ​​at the upstream section.

[0048] Figure 3 This is a sequence diagram of pollutant concentration values ​​at the downstream section.

[0049] Figure 4This is a conversion diagram of the time series and distance series of the upstream section.

[0050] Figure 5 This is a fitting graph of the pollution source function at the upstream section. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of the present invention.

[0052] A method for calibrating water quality model parameters based on the concept of equivalent pollution sources, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0053] Step 1: Obtain basic data for the river channel area to be calibrated, including river depth h = 0.5m, river width b = 15m, and parallel riverbank flow velocity u. x The vertical flow velocity u is 0.5 m / s. y The velocity is 0.01 m / s, and the parameter to be calibrated is the transverse dispersion coefficient D. x Vertical dispersion coefficient D y And the degradation coefficient k.

[0054] Step 2: In this embodiment, two emergency monitoring sections are set up, with a distance of 200 meters between the two sections and a monitoring time interval of 10 seconds.

[0055] Step 3: After the pollution occurred, obtain two sets of pollutant concentration value sequences, such as... Figure 2 , Figure 3 As shown.

[0056] Step 4: Convert the upstream section concentration value sequence into the downstream section pollution source through time series and spatial series conversion and integral calculation.

[0057] Step 5: Based on the actual situation of the river, through D y The values ​​of each parameter are calculated using relevant empirical formulas, and the range of the parameter to be calibrated is determined to be [0.1D]. y *, 10D y *],[0.1k*,10k*],D y * and k* are the calculated values ​​of the actual data determined by empirical formulas, and Dx is determined to be within the range of [10, 20] based on experience.

[0058] Step 6: Based on the sampling frequency and the number of pollutant concentration value series monitoring values, establish the objective function that minimizes the error between the simulated and measured sequences of the downstream section:

[0059]

[0060] Where m = 109, y i* y is the measured value. i These are simulated values.

[0061] Step 7: Perform numerical simulations using an integral form of the water quality model under different parameter combinations and calculate the objective function value.

[0062] Step 8: Sort the objective function values, and determine the parameter combination as the calibration result based on the sorting results and the river conditions.

[0063] Furthermore, the pollution source equivalence proposed in step 4 includes the following steps:

[0064] Step 4.1: Convert the time series data obtained from the emergency monitoring equipment into a spatial series:

[0065] n = 1090 × 0.5 = 545m

[0066] n i =10 × 0.5 = 5m

[0067] The transformed sequence is as follows Figure 4 As shown.

[0068] Step 4.2: Use MATLAB to fit the converted spatial sequence graph to common curves to determine the relationship function between concentration and distance as f(x), R. 2 The value is 0.9946, and the fitted graph is as follows: Figure 5 As shown, f(x) is as follows:

[0069] f(x) = -1.017e -19 x 10 +2.928e -16 x 9 -3.602e -13 x 8 +2.466e -10 x 7 -1.024e -7 x 6 +2.626e - 5 x 5 -0.004044x 4 +0.3427x 3 -13.3x 2 +198.5x-778.8

[0070] Step 4.3: Calculate the simulated pollutant concentration sequence at the downstream section by superimposing an equivalent set of countless instantaneous concentrated sources using an integral form. The formula for calculating the superimposed concentration at a specified time x is:

[0071]

[0072] The calibration parameter is D x D y , k, where t is a time series of 10, 20, ..., 1090.

[0073] Furthermore, the calibration parameter range and step size proposed in step 5 are used to determine D in conjunction with relevant parameters and empirical formulas. y * and k* are respectively:

[0074] k * =(ln24.00208202-ln1.84365E-13)*0.5 / 200=0.08125

[0075]

[0076]

[0077] Furthermore, the calibration parameter range and step size proposed in step 5, D y 、k、D x The value range is [0.0138, 1.38], [0.008125, 0.8125], [10, 20] where D x The step size is 0.1, D y The step size is 0.01, and the k-step size is 0.001.

[0078] The calibration result D was obtained through calculation. x It is 18.3, D y The value is 0.12, and k is 0.080.

[0079] The above description is only the most effective embodiment of the present invention. It should be noted that for those skilled in the art, appropriate improvements and modifications can be made without departing from the working principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calibrating water quality model parameters based on the concept of equivalent pollution sources, characterized in that: The method includes the following steps: Step 1: Obtain basic data of the river area to be calibrated, model it using a two-dimensional river pollutant convection and diffusion model, and determine the parameters to be calibrated; Step 2: Deploy online monitoring devices at equal intervals within the river channel area to be calibrated to monitor water quality in real time; Step 3: When the monitoring data of a certain online monitoring device is greater than the previous monitoring value by 20% for three consecutive times, it is determined that pollution has occurred, and the online monitoring device is identified as a water quality abnormal device. At the same time, data is acquired from the water quality abnormal device and the nearest downstream device to obtain two sets of pollutant concentration value sequences. Step 4: Using the concept of integration, the pollutant concentration sequence at the upstream section is equivalent to a distribution source with a known total amount of pollutants, released instantaneously within a certain spatial range. This source is then used as the pollution source at the downstream section. By superimposing these countless equivalent instantaneous distribution sources through integration, the pollutant concentration sequence at the downstream section is simulated and calculated. The steps for equating the pollutant concentration sequence at the upstream section to the pollution source at the downstream section are as follows: Step 4.1: Convert the time series into a spatial series according to the relationship between time and flow velocity. The calculation formula is as follows: n=t n ×u x (1) n i =t i ×u x (2) In formula (1), n Let t be the total length of the space. n To monitor the total duration, u x The velocity is parallel to the riverbank; in formula (2), n i Spatial sequence spacing, t i For monitoring frequency; Step 4.2: Fit the converted sequence graph to the curve to determine the relationship function between concentration and distance; Step 4.3: Calculate the simulated pollutant concentration sequence at the downstream section by superimposing countless equivalent instantaneous concentrated sources in an integral form, at a specified time. x The formula for calculating the superimposed concentration is: In formula (3), C ( x , t )for t time x Pollutant concentration at the location, in mg / L; f(x) This is a function relating concentration and distance. n The total spatial length of the upstream section; x The distance from the river point to the instantaneous point source in the direction parallel to the river flow is expressed in meters (m). Here, it represents the distance between the two devices. y The distance from the instantaneous point source to the river point in the direction perpendicular to the river flow direction, expressed in meters (m). t This represents the time elapsed since the instantaneous pollution occurred, in seconds; this is the time point to be calculated. h River depth, in meters (m). D x , D y They are respectively x and y Dispersion coefficient in direction, in meters 2 / s; u x The velocity of the river flow parallel to the bank is expressed in m / s. u y The velocity is perpendicular to the riverbank, in m / s; k The degradation coefficient is expressed in units of 1 / d. Step 5: Determine the range and step size of the parameters to be calibrated using empirical formulas, and iterate through the combinations of each parameter within the range of values; Step 6: Establish an objective function that minimizes the error between the simulated and measured pollutant concentration sequences at the downstream section; Step 7: Traverse the parameter combinations within the range of parameters to be calibrated, perform numerical simulations, and calculate the objective function value; Step 8: Sort the objective function values, and finally determine a set of parameter combinations as the calibration result based on the objective function values ​​and the river conditions.

2. The parameter calibration method according to claim 1, characterized in that: The channel depth / width to be calibrated is less than or equal to 1 / 30.

3. The parameter calibration method according to claim 1, characterized in that: In step 1, the basic data for the river channel area to be calibrated includes river depth. h River width b Parallel riverbank flow velocity u x Vertical riverbank flow velocity u y The parameter to be calibrated is the transverse dispersion coefficient. D x Vertical dispersion coefficient D y and degradation coefficient k .

4. The parameter calibration method according to claim 1, characterized in that: In step 2, online monitoring equipment is deployed along the direction parallel to the riverbank. The interval between the deployed online monitoring equipment is less than or equal to 200m, and the monitoring frequency is less than or equal to the interval distance / parallel riverbank flow velocity.

5. The parameter calibration method according to claim 1, characterized in that: In step 3, data from the same sampling time period of two real-time online water quality monitoring devices are used for parameter calibration. The sampling time period starts when the upstream device's three consecutive monitoring data are all greater than the previous monitoring value by 20%, and ends when the downstream device's three consecutive monitoring data are all less than the previous monitoring value by 20%.

6. The parameter calibration method according to claim 1, characterized in that: In step 5, calculations are performed using empirical formulas and the actual conditions of the river. D y , k ,Sure D y , k The value range is [0.1]. D y * 10 D y * ],[ 0.1 k* 10 k* ], D y * 、k* These are calculated values ​​determined from actual data using empirical formulas. D x Take the empirical value range [10, 20].

7. The parameter calibration method according to claim 1, characterized in that: In step 6, the objective function is the sum of the deviations between the simulated pollutant concentration sequence and the measured pollutant concentration sequence at the downstream section calculated using the pollution diffusion model. The objective function is as follows: In formula (4), f(y,y * ) The objective function is... y These are theoretically calculated values ​​for pollutant concentrations. y * is the concentration observation value; m is the number of observation values.

8. The parameter calibration method according to claim 7, characterized in that: In step 8, the objective function values ​​are sorted in ascending order to determine the parameter combination order, and the final parameter combination is determined in combination with the actual situation of the river channel to be calibrated.

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