Water ecology in-situ monitoring method based on artificial intelligence

Through artificial intelligence, identify biological species in water microscopic images, calculate species diversity index, and build a water quality parameter evaluation model, which solves the problem that the existing technology cannot classify algae at the genus and species level, and achieves efficient water ecological monitoring and Early warning.

CN119290875APending Publication Date: 2025-01-10JIANGSU HONGZHONG BAIDE BIOTECHNOLOGY CO LTD
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Patent Information

Application Number
CN202411416913.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-11
Publication Date
2025-01-10

AI Technical Summary

Technical Problem

The existing water ecological monitoring methods cannot classify algae at the genus and species level, resulting in low monitoring and early warning and subsequent treatment efficiency of cyanobacteria blooms, and cannot form an effective water ecological monitoring and early warning mechanism.

Method used

Using artificial intelligence-based in-situ monitoring method, we can obtain water quality samples and microscopic images of water body monitoring points, identify biological species, calculate species diversity index, and build an evaluation system model of water quality parameters and species diversity index to achieve automatic Identify and count to form water ecological assessment.

Benefits of technology

A refined monitoring and early warning of water ecology has been achieved, detection efficiency and timeliness have been improved, and an effective water ecology monitoring and early warning mechanism has been formed.

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Abstract

The invention discloses a water ecology in-situ monitoring method based on artificial intelligence, and relates to the technical field of water ecology monitoring. The method comprises the following steps: acquiring a water quality sample at a water body monitoring point, acquiring water quality parameter information of the water quality sample, enriching phytoplankton and zooplankton in the water quality sample into a detection area through a suction filtration effect, acquiring a microscopic image of the detection area, and identifying all biological species contained in the microscopic image of the detection area. Acquiring biomass parameter information at the monitoring point, calculating and acquiring a species diversity index according to the acquired biomass parameter information, and constructing an evaluation system model of the to-be-detected area by taking the water quality parameter and the species diversity index as evaluation indexes, and calculating an evaluation value of the obtained water quality parameter and the species diversity index in the evaluation system model, and evaluating the water ecology of the to-be-detected area through the evaluation value.
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Description

Technical Field

[0001] The present invention relates to the technical field of water ecology monitoring, and in particular to an artificial intelligence-based water ecology in-situ monitoring method. Background Art

[0002] At present, in-situ monitoring of water ecology mostly relies on common buoy-type algae in-situ monitoring equipment, which are mostly algae classification products based on fluorescence spectroscopy. By capturing the fluorescence of living algae, algae classification is achieved, and then chlorophyll and algae density information in the water body is obtained. However, this method is limited to the analysis of algae classification at the phylum level, and it is impossible to obtain classification information at the genus and species level, which makes it difficult to provide refined support for cyanobacteria bloom monitoring, early warning and subsequent treatment. If you want to obtain more detailed algae information in the water body, you need to take water samples and conduct further tests in the laboratory, which reduces the detection efficiency and the timeliness of supervision, and cannot form an effective water ecology monitoring and early warning mechanism. To this end, we propose an in-situ monitoring method of water ecology based on artificial intelligence. Summary of the invention

[0003] The main purpose of the present invention is to provide an artificial intelligence-based water ecology in-situ monitoring method, which can effectively solve the problems in the background technology.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] The artificial intelligence-based in-situ water ecology monitoring method includes:

[0006] Obtaining water quality samples at water body monitoring points, and collecting water quality parameter information of the water quality samples, wherein the water quality parameter types include at least one of water temperature, pH, dissolved oxygen, dissolved oxygen saturation, conductivity, turbidity, chlorophyll a concentration, and blue-green algae density;

[0007] Enriching phytoplankton and zooplankton in the water sample into the detection area by filtration, and obtaining a microscopic image of the detection area;

[0008] Identify all biological species contained in the microscopic image of the detection area, obtain biomass parameter information at the monitoring point, and calculate the species diversity index based on the obtained biomass parameter information, wherein the biomass parameter information includes species type, number of individuals of the species, and total number of individuals of all species; the species diversity index includes:

[0009] The species information index is used to indicate the richness of species and the uniformity of the composition of each species. The larger the value, the greater the species diversity.

[0010] The species richness index is used to describe the species richness contained in the community. The larger the value, the higher the species richness.

[0011] The species dominance index is used to measure the evenness of species distribution in a community. The larger the value, the more uneven the distribution of species in the community and the more prominent the position of the dominant species.

[0012] The species evenness index is used to measure the evenness of the distribution of each species in the community. The closer its value is to 1, the more even the species distribution is.

[0013] The calculation formulas for each index are:

[0014]

[0015] Where H is the species information index; n i is the number of individuals of the i-th species; N is the total number of individuals of all species,

[0016]

[0017] In the formula, d is the species richness index; s represents the total number of species; N represents the total number of individuals of all species;

[0018]

[0019] Where, E is the species evenness index; H max It is expressed as the maximum value of species diversity index;

[0020]

[0021] Where D is the species dominance index; p i It is represented by the relative frequency of the i-th species in the community; S is represented by the total number of species in the community;

[0022] The biomass parameter information acquisition process includes the following steps:

[0023] Acquire microscopic images of all biological species that may be contained in the detection area as comparison images;

[0024] Extracting all characteristic parameters of the i-th species in the comparison image to construct a comparison characteristic parameter set;

[0025] The acquired microscopic image of the detection area is preprocessed, and the preprocessing process includes the following steps:

[0026] Extract the color information in the microscopic image. Suppose the sum of the b channel in the r, g, and b channels of the current image is B, and the sum of the r channel is R;

[0027] Microscopic images are divided into three types according to color information: one-type images, two-type images, and three-type images. The principle of image division is:

[0028] When B≤10 5 When , the image is a type of image;

[0029] When B≤3×10 4 , and R≤2×10 4 When , the image is a second-class image;

[0030] When B≤10 4 , or B≤3×10 4 , and R>2×10 4 When , the images are of three types;

[0031] When the microscopic image is a type of image, no processing is performed on the original microscopic image;

[0032] When the microscopic image is a second-class image, the original microscopic image is converted into a grayscale image, and a Gaussian low-pass filter is performed to eliminate high-frequency noise in the image;

[0033] When the microscopic image is a third-class image, the original microscopic image is converted into a grayscale image and subjected to Gaussian high-pass filtering;

[0034] Performing image segmentation on the preprocessed microscopic image of the detection area to obtain a region of interest in the image;

[0035] After adjusting the acquired region of interest to a uniform size of ε×ε, grayscale processing is performed in sequence. The processing formula is: s=c×r γ , where r is the grayscale image input value; s is the grayscale output value after gamma transformation; c is the grayscale scaling coefficient; γ is the gamma value;

[0036] Extract the characteristic parameters of the region of interest after grayscale processing as identification characteristic parameters;

[0037] The obtained identification feature parameters are matched with the comparison feature parameters, and the biological species category in the region of interest is determined according to the matching results, where the expression of the matching model is:

[0038]

[0039] In the formula, It is expressed as the matching degree between the kth region of interest and the contrast feature parameter; It is represented as the qth identification feature parameter of the kth region of interest; t dq It is expressed as the qth contrast feature parameter; Q is the feature type, And when The closer it is to 0, the higher the matching degree between the kth region of interest and the contrast feature parameter;

[0040] Count the identified biological species and obtain biomass parameter information

[0041] Using the water quality parameters and the species diversity index as evaluation indicators, an evaluation system model for the area to be tested is constructed, and the construction process includes the following steps:

[0042] The evaluation index types of water quality parameters and species diversity index are divided into four categories: positive index, negative index, intermediate index and interval index.

[0043] Among them, for positive indicators, the larger the index value, the better the water ecological environment;

[0044] For the reverse index, the smaller the index value is, the better the water ecological environment is;

[0045] For intermediate indicators, the closer the indicator value is to a certain fixed value, the better the water ecological environment is;

[0046] For interval indicators, when the indicator value falls within a certain interval, the water ecological environment is better;

[0047] According to the above classification principles, the indicator types of various water quality parameters and species diversity index can be determined;

[0048] Obtaining the minimum threshold of the positive indicator, the maximum threshold of the negative indicator, the optimal threshold of the intermediate indicator, and the optimal interval threshold of the interval indicator;

[0049] The evaluation model is constructed according to the set indicator threshold, where the expression of the model is:

[0050]

[0051] In the formula, ge is the evaluation value; c u is the sampling value of the u-th positive indicator; c umin is the minimum threshold of the u-th positive indicator; U is the type of positive indicator; f v is the sampling value of the vth reverse indicator; f vmax is the maximum threshold of the vth reverse indicator; V is the type of reverse indicator; z w is the sampling value of the w-th intermediate indicator; z wb is the optimal threshold of the wth intermediate indicator; W is the type of intermediate indicator; q y is the sampling value of the yth interval indicator; q ya is the lower limit of the optimal interval of the yth interval indicator; q ybis the upper limit of the optimal interval of the yth interval-type indicator; Y is the type of interval-type indicator; α is the state parameter, where α=0 or 1; ya ,q yb > indicates taking q ya ,q yb Any value in .

[0052] The principle for selecting the value of the state parameter α is:

[0053] When y <q ya or q y >q yb When α=1;

[0054] When ya ≤q y ≤q yb , α=0.

[0055] ya ,q yb The value principle of > is:

[0056] When y <q ya hour, ya ,q yb > Take q ya ;

[0057] When y >q yb hour, ya ,q yb > Get q yb ;

[0058] When ya ≤q y ≤q yb hour, ya ,q yb > Get q ya or q yb .

[0059] The present invention has the following beneficial effects:

[0060] ​​​​​Compared with the prior art, the method obtains water quality samples at water body monitoring points, collects water quality parameter information of water quality samples, enriches phytoplankton and zooplankton in water quality samples into a detection area through filtration, obtains a microscopic image of the detection area, identifies all biological species contained in the microscopic image of the detection area, obtains biomass parameter information at the monitoring point, and calculates the species diversity index based on the obtained biomass parameter information. An evaluation system model of the area to be detected is constructed using the water quality parameters and the species diversity index as evaluation indicators. Evaluation values ​​of the obtained water quality parameters and species diversity index in the evaluation system model are calculated. The water ecology of the area to be detected is evaluated through the evaluation values. Computer imaging and artificial intelligence algorithms are used to automatically identify and count species in water quality samples, and a water ecology evaluation model is constructed, thereby forming an effective water ecology monitoring and early warning mechanism and realizing in situ monitoring of the water environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 The present invention is a flow chart of the artificial intelligence-based in-situ water ecology monitoring method. DETAILED DESCRIPTION

[0062] The present invention will be further described below in conjunction with specific implementation methods, wherein the accompanying drawings are only used for exemplary descriptions and represent only schematic diagrams rather than actual drawings, and should not be understood as limiting the present invention. In order to better illustrate the specific implementation methods of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product.

[0063] The implementation process of the technical solution of the present invention includes the following steps:

[0064] Step 1: Obtain water quality samples at water body monitoring points and collect water quality parameter information of the water quality samples, wherein the water quality parameter types include at least one of water temperature, pH, dissolved oxygen, dissolved oxygen saturation, conductivity, turbidity, chlorophyll a concentration, and blue-green algae density;

[0065] Step 2: Enrich the phytoplankton and zooplankton in the water sample into the detection area through filtration, and obtain a microscopic image of the detection area;

[0066] Step 3: Identify all biological species contained in the microscopic image of the detection area, obtain biomass parameter information at the monitoring point, and calculate the species diversity index based on the obtained biomass parameter information, where the biomass parameter information includes species type, number of individuals of the species, and total number of individuals of all species; the species diversity index includes:

[0067] The species information index is used to indicate the richness of species and the uniformity of the composition of each species. The larger the value, the greater the species diversity.

[0068] The species richness index is used to describe the species richness contained in the community. The larger the value, the higher the species richness.

[0069] The species dominance index is used to measure the evenness of species distribution in a community. The larger the value, the more uneven the distribution of species in the community and the more prominent the position of the dominant species.

[0070] The species evenness index is used to measure the evenness of the distribution of each species in the community. The closer its value is to 1, the more even the species distribution is.

[0071] The calculation formulas for each index are:

[0072]

[0073] Where H is the species information index; n i is the number of individuals of the i-th species; N is the total number of individuals of all species,

[0074]

[0075] In the formula, d is the species richness index; s represents the total number of species; N represents the total number of individuals of all species;

[0076]

[0077] Where, E is the species evenness index; H max It is expressed as the maximum value of species diversity index;

[0078]

[0079] Where D is the species dominance index; p i It is represented by the relative frequency of the i-th species in the community; S is represented by the total number of species in the community;

[0080] The biomass parameter information acquisition process includes the following steps:

[0081] Step 31: Obtaining microscopic images of all possible biological species in the detection area as comparison images;

[0082] Step 32: extract all characteristic parameters of the i-th species in the comparison image and construct a comparison characteristic parameter set;

[0083] Step 33: Preprocess the acquired microscopic image of the detection area. The preprocessing process includes the following steps:

[0084] Step 34: extract color information from the microscopic image, assuming that the sum of the b channel in the r, g, and b channels of the current image is B, and the sum of the r channel is R;

[0085] Step 35: Classify the microscopic images into three types: first-class images, second-class images, and third-class images according to color information, wherein the image classification principle is:

[0086] When B≤10 5 When , the image is a type of image;

[0087] When B≤3×10 4 , and R≤2×10 4 When , the image is a second-class image;

[0088] When B≤10 4 , or B≤3×10 4 , and R>2×10 4 When , the images are of three types;

[0089] Step 36: When the microscopic image is a type of image, no processing is performed on the original microscopic image;

[0090] When the microscopic image is a second-class image, the original microscopic image is converted into a grayscale image, and a Gaussian low-pass filter is performed to eliminate high-frequency noise in the image;

[0091] When the microscopic image is a third-class image, the original microscopic image is converted into a grayscale image and subjected to Gaussian high-pass filtering;

[0092] Step 37: performing image segmentation on the pre-processed microscopic image of the detection area to obtain a region of interest in the image;

[0093] Step 38: After adjusting the acquired region of interest to a uniform size of ε×ε, grayscale processing is performed in sequence. The processing formula is: s=c×r γ , where r is the grayscale image input value; s is the grayscale output value after gamma transformation; c is the grayscale scaling coefficient; γ is the gamma value;

[0094] Step 39: extracting characteristic parameters of the region of interest after grayscale processing as identification characteristic parameters;

[0095] Step 310: Match the acquired identification feature parameters with the comparison feature parameters, and determine the biological species category in the region of interest according to the matching results, wherein the expression of the matching model is:

[0096]

[0097] In the formula, It is expressed as the matching degree between the kth region of interest and the contrast feature parameter; It is represented as the qth identification feature parameter of the kth region of interest; t dq It is expressed as the qth contrast feature parameter; Q is the feature type, And when The closer it is to 0, the higher the matching degree between the kth region of interest and the contrast feature parameter;

[0098] Step 311: Count the identified biological species and obtain biomass parameter information

[0099] Step 4: Using water quality parameters and species diversity index as evaluation indicators, construct an evaluation system model for the area to be tested. The construction process includes the following steps:

[0100] Step 41: Divide the evaluation index types of water quality parameters and species diversity index into four categories: positive index, negative index, intermediate index and interval index;

[0101] Among them, for positive indicators, the larger the index value, the better the water ecological environment;

[0102] For the reverse index, the smaller the index value is, the better the water ecological environment is;

[0103] For intermediate indicators, the closer the indicator value is to a certain fixed value, the better the water ecological environment is;

[0104] For interval indicators, when the indicator value falls within a certain interval, the water ecological environment is better;

[0105] According to the above classification principles, the indicator types of various water quality parameters and species diversity index can be determined;

[0106] For the species diversity index:

[0107] The larger the value of the species information index is, the greater the species diversity is and the better the water ecological environment is, so it is a positive indicator;

[0108] The larger the species richness index value, the higher the species richness and the better the water ecological environment, which is a positive indicator;

[0109] The species dominance index, the larger its value, the more uneven the species distribution in the community, the more prominent the position of the dominant species, and it is a reverse indicator;

[0110] The closer the value of species evenness index is to 1, the more even the species distribution is and the better the water ecological environment is, so it is an intermediate indicator;

[0111] According to the above principles, water quality parameters are divided into indicator types:

[0112] Among them, positive indicators include dissolved oxygen saturation and dissolved oxygen;

[0113] Reverse indicators include blue-green algae density, conductivity, and turbidity;

[0114] Interval indicators include chlorophyll a concentration, water temperature, and pH;

[0115] Step 42: Obtain the minimum threshold of the positive indicator, the maximum threshold of the reverse indicator, the optimal threshold of the intermediate indicator, and the optimal interval threshold of the interval indicator;

[0116] Step 43: Construct an evaluation model based on the set indicator threshold, where the model expression is:

[0117]

[0118] In the formula, ge is the evaluation value; c u is the sampling value of the u-th positive indicator; c umin is the minimum threshold of the u-th positive indicator; U is the type of positive indicator; f v is the sampling value of the vth reverse indicator; f vmax is the maximum threshold of the vth reverse indicator; V is the type of reverse indicator; z w is the sampling value of the w-th intermediate indicator; z wb is the optimal threshold of the wth intermediate indicator; W is the type of intermediate indicator; q y is the sampling value of the yth interval indicator; q ya is the lower limit of the optimal interval of the yth interval indicator; q yb is the upper limit of the optimal interval of the yth interval-type indicator; Y is the type of interval-type indicator; α is the state parameter, where α=0 or 1; ya ,q yb > indicates taking q ya ,q yb Any value in .

[0119] The principle for selecting the value of the state parameter α is:

[0120] When y <q ya or q y >q yb When α=1;

[0121] When ya ≤q y ≤q yb , α=0.

[0122] <q​ya ,q yb The value principle of > is:

[0123] When y <q ya hour, ya ,q yb > Get q ya ;

[0124] When y >q yb hour, ya ,q yb > Get q yb ;

[0125] When ya ≤q y ≤q yb hour, ya ,q yb > Get q ya or q yb .

[0126] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.​​​

Claims

1. The water ecology in-situ monitoring method based on artificial intelligence is characterized by: include: Obtain water quality samples at water body monitoring points and collect water quality parameter information of water quality samples; Enriching phytoplankton and zooplankton in the water sample into the detection area by filtration, and obtaining a microscopic image of the detection area; Identifying all biological species contained in the microscopic image of the detection area, obtaining biomass parameter information at the monitoring point, and calculating the species diversity index based on the obtained biomass parameter information; Using the water quality parameters and the species diversity index as evaluation indicators, constructing an evaluation system model for the area to be tested; The evaluation values ​​of the acquired water quality parameters and species diversity index in the evaluation system model are calculated, and the water ecology of the area to be tested is evaluated by the evaluation values.

2. The artificial intelligence-based water ecology in-situ monitoring method according to claim 1 is characterized in that: The water quality parameter types include at least one of water temperature, pH, dissolved oxygen, dissolved oxygen saturation, conductivity, turbidity, chlorophyll a concentration, and blue-green algae density.

3. The artificial intelligence-based water ecology in-situ monitoring method according to claim 1 is characterized in that: The biomass parameter information includes species, number of individuals of the species, and total number of individuals of all species; the species diversity index includes: The species information index is used to indicate the richness of species and the uniformity of the composition of each species. The larger the value, the greater the species diversity. The species richness index is used to describe the species richness contained in the community. The larger the value, the higher the species richness. The species dominance index is used to measure the evenness of species distribution in a community. The larger the value, the more uneven the distribution of species in the community and the more prominent the position of the dominant species. The species evenness index is used to measure the evenness of the distribution of each species in the community. The closer its value is to 1, the more even the species distribution is. The calculation formulas for each index are: Where H is the species information index; n i is the number of individuals of the i-th species; N is the total number of individuals of all species, In the formula, d is the species richness index; s represents the total number of species; N represents the total number of individuals of all species; Where, E is the species evenness index; H max It is expressed as the maximum value of species diversity index; Where D is the species dominance index; p i It is represented by the relative frequency of the i-th species in the community; S is represented by the total number of species in the community.

4. The artificial intelligence-based water ecology in-situ monitoring method according to claim 1 is characterized in that: The biomass parameter information acquisition process includes the following steps: Acquire microscopic images of all biological species that may be contained in the detection area as comparison images; Extracting all characteristic parameters of the i-th species in the comparison image to construct a comparison characteristic parameter set; Preprocessing the acquired microscopic image of the detection area; Performing image segmentation on the preprocessed microscopic image of the detection area to obtain a region of interest in the image; After adjusting the acquired region of interest to a uniform size of ε×ε, grayscale processing is performed in sequence. The processing formula is: s=c×r γ , where r is the grayscale image input value; s is the grayscale output value after gamma transformation; c is the grayscale scaling coefficient; γ is the gamma value; Extract the characteristic parameters of the region of interest after grayscale processing as identification characteristic parameters; The obtained identification feature parameters are matched with the comparison feature parameters, and the biological species category in the region of interest is determined according to the matching results, where the expression of the matching model is: In the formula, It is expressed as the matching degree between the kth region of interest and the contrast feature parameter; It is represented as the qth identification feature parameter of the kth region of interest; t dq It is expressed as the qth contrast feature parameter; Q is the feature type; Count the identified biological species and obtain biomass parameter information.

5. The artificial intelligence-based water ecology in-situ monitoring method according to claim 4 is characterized in that: And when The closer it is to 0, the higher the matching degree between the kth region of interest and the contrast feature parameter.

6. The artificial intelligence-based water ecology in-situ monitoring method according to claim 4 is characterized in that: The microscopic image preprocessing process includes the following steps: Extract the color information in the microscopic image. Suppose the sum of the b channel in the r, g, and b channels of the current image is B, and the sum of the r channel is R; Microscopic images are divided into three types according to color information: one-type images, two-type images, and three-type images. The principle of image division is: When B≤10 5 When , the image is a type of image; When B≤3×10 4 , and R≤2×10 4 When , the image is a second-class image; When B≤10 4 , or B≤3×10 4 , and R>2×10 4 When , the images are of three types; When the microscopic image is a type of image, no processing is performed on the original microscopic image; When the microscopic image is a second-class image, the original microscopic image is converted into a grayscale image, and a Gaussian low-pass filter is performed to eliminate high-frequency noise in the image; When the microscopic image is a third-class image, the original microscopic image is converted into a grayscale image and subjected to Gaussian high-pass filtering.

7. The artificial intelligence-based water ecology in-situ monitoring method according to claim 1 is characterized in that: The construction process of the evaluation system model for the area to be inspected includes the following steps: The evaluation index types of water quality parameters and species diversity index are divided into four categories: positive index, negative index, intermediate index and interval index. Obtaining the minimum threshold of the positive indicator, the maximum threshold of the negative indicator, the optimal threshold of the intermediate indicator, and the optimal interval threshold of the interval indicator; The evaluation model is constructed according to the set indicator threshold, where the expression of the model is: In the formula, ge is the evaluation value; c u is the sampling value of the u-th positive indicator; c umin is the minimum threshold of the u-th positive indicator; U is the type of positive indicator; f v is the sampling value of the vth reverse indicator; f vmax is the maximum threshold of the vth reverse indicator; V is the type of reverse indicator; z w is the sampling value of the w-th intermediate indicator; z wb is the optimal threshold of the wth intermediate indicator; W is the type of intermediate indicator; q y is the sampling value of the yth interval indicator; q ya is the lower limit of the optimal interval of the yth interval indicator; q yb is the upper limit of the optimal interval of the yth interval-type indicator; Y is the type of interval-type indicator; α is the state parameter, where α=0 or 1; ya ,q yb > indicates taking q ya ,q yb Any value in .​ 8. The artificial intelligence-based in-situ water ecology monitoring method according to claim 7 is characterized in that: The principle for selecting the value of the state parameter α is: When y <q ya or q y >q yb When α=1; When ya ≤q y ≤q yb , α=0.

9. The artificial intelligence-based water ecology in-situ monitoring method according to claim 7 is characterized in that: ηq ya ,q yb The value principle of > is: When y <q ya hour, ya ,q yb > Take q ya ;​ When y >q yb hour, ya ,q yb > Take q yb ;​ When ya ≤q y ≤q yb hour, ya ,q yb > Take q ya or q yb .​

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