A crayfish breeding system based on internet of things

By using an IoT-based crayfish farming system, a dynamic oxygenation control strategy is generated by constructing a relationship between dissolved oxygen levels and data acquisition and neural network models. This solves the problems of poor PID control parameter settings and high energy consumption of manual oxygenation, achieving efficient and energy-saving oxygenation and stable control of dissolved oxygen levels.

CN118318778BActive Publication Date: 2025-11-25FRESHWATER FISHERIES RES INSITUTE OF JIANGSUPROVINCE
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Patent Information

Application Number
CN202410456804.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-04-16
Publication Date
2025-11-25
Estimated Expiration
2044-04-16

AI Technical Summary

Technical Problem

In existing crayfish farming, setting the control parameters of PID-controlled aerators to moderate values ​​makes it difficult to achieve ideal control results. Furthermore, manually controlling aerators consumes a lot of energy, making it difficult to achieve efficient and energy-saving aeration.

Method used

An IoT-based crayfish farming system is adopted. Environmental and ecological parameters are acquired through a data acquisition module, and a neural network model is used to construct the relationship between dissolved oxygen influencing factors. A dynamic oxygenation control strategy is generated, and the dissolved oxygen level in the farming area is adjusted through an oxygenation command execution module.

Benefits of technology

It achieves dynamic adjustment based on real-time changes in dissolved oxygen levels, saving energy and ensuring that the dissolved oxygen level in the water is maintained near the standard value, which is beneficial to the growth of crayfish.

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Abstract

The application discloses a crayfish breeding system based on Internet of Things and relates to the crayfish breeding field. The application scheme performs correlation analysis on the environmental parameters, the breeding parameters, the ecological parameters and the dissolved oxygen content data in the oxygenation state and the non-oxygenation state of the test points in the breeding area, screens the dissolved oxygen content influencing factors, obtains the first neural network model and the second neural network model, obtains the first relationship between the dissolved oxygen content influencing parameters in the oxygenation state and the dissolved oxygen content and the second relationship between the dissolved oxygen content influencing factors in the non-oxygenation state and the dissolved oxygen content, sets the dissolved oxygen content standard value at the test points, formulates the oxygenation control strategy according to the obtained first relationship and second relationship, generates the control instruction for adjusting the dissolved oxygen content in the breeding area according to the obtained oxygenation control strategy, and the oxygenation instruction execution module adjusts the dissolved oxygen content in the breeding area in response to the control instruction generated by the oxygenation control strategy generation module.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of crayfish culture, and particularly relates to a crayfish culture system based on the Internet of Things. BACKGROUND

[0002] With the development of crayfish industry in China, large-scale culture is becoming more and more widespread. With the continuous development of Internet of Things technology, such as advanced intelligent detection, wireless sensor network, GPRS wireless communication and other technologies are more and more applied to crayfish culture. Through real-time monitoring of the temperature, pH value, dissolved oxygen and light of the culture water, appropriate measures are taken according to the influencing factors to ensure the best environment for large-scale crayfish culture, and the real-time control of the adverse environment is realized, so as to realize the high safety, high yield and high quality of large-scale crayfish culture.

[0003] In the process of crayfish culture, the oxygen content of the culture water is required to be high. When the dissolved oxygen content of the water body is maintained at 3 mg / L or more, the crayfish can grow normally. In order to ensure the dissolved oxygen content in the culture water, the commonly used method is to use manual control to make the oxygen increasing machine work intermittently at a fixed frequency for aeration oxygenation. Although this method can ensure the sufficiency of water dissolved oxygen, it needs manual control and the energy saving effect is poor. With the continuous development of automatic control technology, using PI-PID frequency conversion control oxygen increasing machine can well solve the problem of large energy consumption. However, three main parameters need to be set in the PID control instruction: proportional gain, integral time and differential time. Since the water dissolved oxygen content is a variable affected by many factors, it has great uncertainty and hysteresis. In order to ensure the control effect, the control parameters are usually set to moderate value, which makes it difficult to achieve the ideal state. Therefore, we propose a crayfish culture system based on the Internet of Things. SUMMARY

[0004] The main purpose of the present application is to provide a crayfish culture system based on the Internet of Things, which can effectively solve the problems in the background art.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is,

[0006] A crayfish culture system based on the Internet of Things, comprising: a dissolved oxygen content influencing factor determination module, a data acquisition module, a first neural network model construction module, a second neural network model construction module, an oxygen increasing control strategy generation module, and an oxygen increasing instruction execution module.

[0007] The data acquisition module is used for collecting environmental parameters, breeding parameters, ecological parameters and dissolved oxygen data in an oxygenation state and a non-oxygenation state of a test point in a breeding area, wherein the environmental parameters include air temperature, air pressure, light intensity, wind speed, breeding area area, water flow rate and average water depth of the breeding area; the breeding parameters include breeding density, feeding frequency and feeding amount; and the ecological parameters include water grass area and growth density of the breeding area.

[0008] The dissolved oxygen influencing factor determination module is connected with the data acquisition module, and is used for performing correlation analysis on the obtained environmental parameters, breeding parameters, ecological parameters and dissolved oxygen data, and screening a factor type with strong correlation with the dissolved oxygen as a dissolved oxygen influencing factor, wherein the factor type with strong correlation with the dissolved oxygen is specifically an influencing factor with an absolute value of a correlation coefficient between the factor type and the dissolved oxygen greater than 0.7, and a calculation formula of the correlation coefficient is: ; in the formula, is a correlation coefficient between the i-th type factor and the dissolved oxygen; is the j-th collected data of the i-th type factor; is a mean value of the collected data of the i-th type factor; is the j-th collected data of the dissolved oxygen; is a mean value of the collected data of the dissolved oxygen; and m is a total number of the collected data.

[0009] The first neural network model construction module is used for training, taking the dissolved oxygen influencing factor data in the oxygenation state as input and corresponding dissolved oxygen as output, to obtain a first neural network model, and outputting a first relationship between the dissolved oxygen influencing parameters in the oxygenation state and the dissolved oxygen according to the obtained first neural network model: , in the formula, represents an n-th dissolved oxygen influencing parameter value in the oxygenation state, represents dissolved oxygen of the test point in the breeding area at moment t in the oxygenation state, represents a k-th oxygenation parameter.

[0010] The second neural network model construction module is used for training, taking the dissolved oxygen influencing factor data in the non-oxygenation state as input and corresponding dissolved oxygen as output, to obtain a second neural network model, and outputting a second relationship between the dissolved oxygen influencing factors in the non-oxygenation state and the dissolved oxygen according to the obtained second neural network model: , in the formula, represents an n-th dissolved oxygen influencing parameter value in the non-oxygenation state, represents dissolved oxygen of the test point in the breeding area at moment t in the non-oxygenation state.

[0011] The oxygenation control strategy generation module is used to set the standard value of dissolved oxygen at the test point, and formulate an oxygenation control strategy based on the obtained first and second relational expressions. The obtained oxygenation control strategy generates control instructions to adjust the dissolved oxygen level in the aquaculture area. The steps for obtaining the control instructions are as follows:

[0012] Step s01, set the standard value of dissolved oxygen at the test point to be... ;

[0013] Step s02: Using T as the sampling period, the real-time dissolved oxygen value at the test point is acquired in real time. ;

[0014] Step s03: Compare real-time dissolved oxygen values Compared with the standard value of dissolved oxygen Size;

[0015] Step s04, if there is This indicates that the dissolved oxygen level in the aquaculture area is low, generating a control command that requires oxygenation, and based on the first relational formula: After determining the various oxygenation parameters, return to step s02;

[0016] Step s05, if there is If the result is positive, it indicates that the dissolved oxygen level in the aquaculture area is at a normal level. After generating a control command that does not require oxygenation, return to step s02.

[0017] The method for determining the sampling period T in step s02 is as follows:

[0018] when When T ≤ 1 second;

[0019] when At that time, according to the second relation: The dissolved oxygen level changes at test points within the aquaculture area, under current influencing factors and without oxygenation, are determined as the standard dissolved oxygen value. The required time T0 is taken as T≤T0 / 2;

[0020] The oxygenation command execution module is connected to the oxygenation control strategy generation module. In response to the control command generated by the oxygenation control strategy generation module, the oxygenation command execution module adjusts the dissolved oxygen level in the aquaculture area.

[0021] The present invention has the following beneficial effects:

[0022] Compared with existing technologies, the technical solution of this invention collects environmental parameters, aquaculture parameters, ecological parameters, and dissolved oxygen data under both aeration and non-aeration conditions at test points within the aquaculture area. Correlation analysis is performed on the acquired data, and factors strongly correlated with dissolved oxygen are selected as influencing factors. Using the dissolved oxygen influencing factor data under aeration conditions as input and the corresponding dissolved oxygen levels as output, a first neural network model is trained to obtain the model. Based on the obtained first neural network model, a first relationship between the dissolved oxygen influencing parameters under aeration conditions and the dissolved oxygen level is output: Using data on factors influencing dissolved oxygen levels under non-oxygenated conditions as input and the corresponding dissolved oxygen levels as output, a second neural network model is trained to obtain the model. Based on the obtained second neural network model, a second relationship between the factors influencing dissolved oxygen levels under non-oxygenated conditions is output: The system sets a standard value for dissolved oxygen at the test point and formulates an oxygenation control strategy based on the obtained first and second relationships. The obtained oxygenation control strategy generates control instructions to adjust the dissolved oxygen in the aquaculture area. In response to the control instructions generated by the oxygenation control strategy generation module, the oxygenation instruction execution module adjusts the dissolved oxygen in the aquaculture area. It can dynamically adjust the dissolved oxygen according to various influencing parameters in the aquaculture area, which can not only effectively save energy in the oxygenation process, but also ensure that the dissolved oxygen in the water in the aquaculture area is maintained near the standard value, which is conducive to the growth of crayfish. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the workflow of an IoT-based crayfish farming system according to the present invention.

[0024] Figure 2 This is a structural block diagram of an Internet of Things-based crayfish farming system according to the present invention;

[0025] Figure 3 A flowchart for the method of obtaining control instructions;

[0026] Figure 4 A diagram showing the location of the test points. Detailed Implementation

[0027] The present invention will be further described below with reference to specific embodiments. The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the present invention. In order to better illustrate the specific embodiments of the present invention, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the actual product size. Example

[0028] like Figures 1-4As shown, an IoT-based crayfish farming system includes: a module for determining factors affecting dissolved oxygen, a data acquisition module, a first neural network model construction module, a second neural network model construction module, an oxygenation control strategy generation module, and an oxygenation command execution module.

[0029] The data acquisition module is used to collect environmental parameters, aquaculture parameters, ecological parameters, and dissolved oxygen data at test points within the aquaculture area under both aeration and non-aeration conditions.

[0030] The module for determining factors affecting dissolved oxygen is connected to the data acquisition module. It is used to perform correlation analysis on the acquired environmental parameters, aquaculture parameters, ecological parameters and dissolved oxygen data, and to screen the types of factors that are strongly correlated with dissolved oxygen as factors affecting dissolved oxygen.

[0031] The first neural network model construction module is used to train and obtain the first neural network model by taking the data of dissolved oxygen influencing factors under aeration conditions as input and the corresponding dissolved oxygen as output. Based on the obtained first neural network model, the module outputs the first relationship between the dissolved oxygen influencing parameters and the dissolved oxygen under aeration conditions: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under oxygenation conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under aeration conditions. Represented as the k-th oxygenation parameter;

[0032] The second neural network model construction module takes the data on factors influencing dissolved oxygen under non-oxygenated conditions as input and the corresponding dissolved oxygen levels as output to train and obtain a second neural network model. Based on the obtained second neural network model, it outputs a second relationship between the factors influencing dissolved oxygen under non-oxygenated conditions and the dissolved oxygen levels: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under non-oxygenated conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under non-oxygenated conditions.

[0033] The oxygenation control strategy generation module is used to set the standard value of dissolved oxygen at the test point and formulate an oxygenation control strategy based on the obtained first and second relational formulas. The obtained oxygenation control strategy generates control instructions to adjust the dissolved oxygen in the aquaculture area.

[0034] The oxygenation command execution module is connected to the oxygenation control strategy generation module. In response to the control commands generated by the oxygenation control strategy generation module, the oxygenation command execution module adjusts the dissolved oxygen level in the aquaculture area.

[0035] The specific implementation process of the technical solution of this invention includes the following steps:

[0036] Step 1: Collect environmental parameters, aquaculture parameters, ecological parameters, and dissolved oxygen data under both aeration and non-aeration conditions at test points within the aquaculture area using the data acquisition module. Environmental parameters include air temperature, air pressure, light intensity, wind speed, aquaculture area area, water flow velocity, and average water depth. Aquaculture parameters include stocking density, feeding frequency, and feeding amount. Ecological parameters include the area and density of aquatic plants within the aquaculture area.

[0037] It should be noted that, in this embodiment, the test point and the aerator placement point within the aquaculture area should maintain a certain distance, ideally within a water area that represents the average dissolved oxygen level of the aquaculture area. Generally, when the aerator is placed at the center of the aquaculture area, the test point is preferably located at the center of the connection between the aerator and the shoreline. The specific location should be determined based on the area and water depth distribution of the aquaculture area. For example, if the aquaculture area is circular... Figure 4 As shown in diagram a, the aerator is generally placed at the center of the circle, and the test point can be set at any point on the dotted line in the diagram. Taking the breeding area as a rectangle as an example, ... Figure 4 As shown in b, the aerator is generally set at the center of the rectangle, and the test point can be set at any point on the dashed line A or B;

[0038] Step 2: Using the dissolved oxygen influencing factor determination module, perform correlation analysis on the acquired environmental parameters, aquaculture parameters, ecological parameters, and dissolved oxygen data, and screen out factors with a strong correlation to dissolved oxygen as influencing factors. Specifically, factors with a strong correlation to dissolved oxygen are those with an absolute value of the correlation coefficient greater than 0.7. The formula for calculating the correlation coefficient is: ;

[0039] In the formula, Let be the correlation coefficient between the i-th type factor and dissolved oxygen level; This is the j-th collected data point for the i-th type factor; The mean of the data collected for the i-th type factor; This is the j-th data point collected for dissolved oxygen. is the mean of the dissolved oxygen data collected; m is the total number of data collected.

[0040] Step 3: After obtaining the factors influencing dissolved oxygen, the first neural network model is trained using the data on these factors under aeration conditions as input and the corresponding dissolved oxygen level as output. In this embodiment, a recurrent neural network can be selected to process sequential data. The specific construction steps are as follows:

[0041] Define the model structure: determine the size of the input layer, hidden layer, and output layer, as well as the type of activation function. In this embodiment, the input layer is the data on factors affecting dissolved oxygen under oxygenation conditions, and the output layer is the corresponding dissolved oxygen level.

[0042] Initialize parameters: Randomly initialize the network's weights and biases;

[0043] Forward propagation: Perform forward propagation step by step, calculating the hidden state and output at each time step;

[0044] Calculate the loss: Using an appropriate loss function, such as cross-entropy loss, calculate the difference between the model output and the true label;

[0045] Backpropagation: Perform BPTT to compute the gradient of the loss with respect to each parameter;

[0046] Parameter update: Update the network's weights and biases using gradient descent or other optimization algorithms;

[0047] Iterative training: Repeat the above steps until the model performance reaches a satisfactory level;

[0048] By constructing a first neural network model, dissolved oxygen data corresponding to different dissolved oxygen influencing factors can be output, thereby establishing a mapping relationship between dissolved oxygen influencing factors and dissolved oxygen, and obtaining the first relationship between dissolved oxygen influencing parameters and dissolved oxygen under oxygenation conditions: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under oxygenation conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under aeration conditions. Represented as the k-th oxygenation parameter;

[0049] Step 4: Similar to Step 3, the second neural network model is trained using the data on factors influencing dissolved oxygen levels under non-oxygenated conditions as input and the corresponding dissolved oxygen levels as output through the second neural network model construction module. Based on the obtained second neural network model, the second relationship between the factors influencing dissolved oxygen levels under non-oxygenated conditions and the dissolved oxygen levels is output: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under non-oxygenated conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under non-oxygenated conditions.

[0050] Step 5: After obtaining the first relationship between dissolved oxygen influencing parameters and dissolved oxygen under aeration conditions and the second relationship between dissolved oxygen influencing factors and dissolved oxygen under non-aeration conditions, an aeration control strategy can be formulated based on the real-time collected data. Before this, it is necessary to pre-set the standard value of dissolved oxygen at the test point. The specific steps include:

[0051] Step s51, set the standard value of dissolved oxygen at the test point to be... ;

[0052] Step s52: The real-time dissolved oxygen value at the test point is acquired for the first time through the data acquisition module. ;

[0053] Step s53: Compare real-time dissolved oxygen values Compared with the standard value of dissolved oxygen Size;

[0054] Step s54, if there is This indicates that the dissolved oxygen level in the aquaculture area is low, generating a control command that requires oxygenation, and based on the first relational formula: The oxygenation parameters are determined, including the working time and frequency of the aerator. The specific parameters should be determined based on the type of aerator and the signal used in the breeding area. Once the selected aerator is determined, the corresponding operating parameters, namely the oxygenation parameters, can be obtained according to the first relational formula. This embodiment will not be described in detail. The obtained oxygenation parameters are sent to the oxygenation command execution module. In response to the control command generated by the oxygenation control strategy generation module, the oxygenation command execution module adjusts the dissolved oxygen level in the breeding area, that is, the aerator operates according to the oxygenation parameters received at this time.

[0055] It should be noted that, since the factors affecting dissolved oxygen are irregular variables that change in real time, the oxygenation parameters obtained at this time reflect the state of these influencing factors within this specific time period. Therefore, after obtaining the oxygenation parameters for this period, it is necessary to return to step s02 to collect real-time dissolved oxygen data again. The sampling period T ≤ 1 second is taken, and then the oxygenation parameters for the next sampling period are obtained according to the first relationship. It should be noted that when entering the next period, the data acquisition module needs to collect the dissolved oxygen influencing factors data again while collecting the real-time dissolved oxygen data at the test point.

[0056] Step s55, if there is This indicates that the dissolved oxygen level in the aquaculture area is at a normal level. After generating a control command that does not require additional oxygenation, and based on the second relationship: The dissolved oxygen level changes at test points within the aquaculture area, under current influencing factors and without oxygenation, are determined as the standard dissolved oxygen value. The required time T0 indicates that, under the influence of factors affecting dissolved oxygen during this period, it takes time T0 for the dissolved oxygen level at the test point to drop to the standard dissolved oxygen value. At this point, return to step s02, taking the sampling period T ≤ T0 / 2. It should be noted that when entering the next period, the data acquisition module, while collecting real-time dissolved oxygen data at the test point, also needs to collect data on factors affecting dissolved oxygen again, and then, according to the second relationship: The dissolved oxygen level changes at test points within the aquaculture area, under current influencing factors and without oxygenation, are determined as the standard dissolved oxygen value. The required time is used to determine the sampling period again, and this process is repeated until... The acquired oxygenation parameters are sent to the oxygenation command execution module. In response to the control command generated by the oxygenation control strategy generation module, the oxygenation command execution module adjusts the dissolved oxygen level in the aquaculture area. At this time, the aerator is in standby mode.

[0057] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A crayfish farming system based on the Internet of Things, characterized in that, include: The system includes modules for determining factors affecting dissolved oxygen, data acquisition, constructing a first neural network model, constructing a second neural network model, generating oxygenation control strategies, and executing oxygenation commands. The data acquisition module is used to collect environmental parameters, aquaculture parameters, ecological parameters, and dissolved oxygen data at test points within the aquaculture area under both aeration and non-aeration conditions. The dissolved oxygen influencing factor determination module is connected to the data acquisition module and is used to perform correlation analysis on the acquired environmental parameters, aquaculture parameters, ecological parameters and dissolved oxygen data, and to screen the factor types that are strongly correlated with dissolved oxygen as dissolved oxygen influencing factors. The first neural network model construction module is used to train and obtain a first neural network model by taking the data of dissolved oxygen influencing factors under aeration conditions as input and the corresponding dissolved oxygen as output. Based on the obtained first neural network model, it outputs a first relationship between the dissolved oxygen influencing parameters under aeration conditions and the dissolved oxygen: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under oxygenation conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under aeration conditions. Represented as the k-th oxygenation parameter; The second neural network model construction module takes the data on factors affecting dissolved oxygen under non-oxygenated conditions as input and the corresponding dissolved oxygen level as output to train and obtain the second neural network model. Based on the obtained second neural network model, it outputs a second relationship between the factors affecting dissolved oxygen under non-oxygenated conditions and the dissolved oxygen level: In the formula, This represents the value of the nth parameter affecting dissolved oxygen under non-oxygenated conditions. This represents the dissolved oxygen level at the test point within the aquaculture area at time t under non-oxygenated conditions. The oxygenation control strategy generation module is used to set the standard value of dissolved oxygen at the test point, and formulate an oxygenation control strategy based on the obtained first and second relational formulas, so as to generate control instructions to adjust the dissolved oxygen in the aquaculture area based on the obtained oxygenation control strategy. The oxygenation command execution module is connected to the oxygenation control strategy generation module. In response to the control command generated by the oxygenation control strategy generation module, the oxygenation command execution module adjusts the dissolved oxygen level in the aquaculture area.

2. The crayfish farming system based on the Internet of Things according to claim 1, characterized in that, Factors strongly correlated with dissolved oxygen are those with an absolute value of the correlation coefficient greater than 0.

7.

3. The crayfish farming system based on the Internet of Things according to claim 2, characterized in that, The formula for calculating the correlation coefficient is: ; In the formula, Let be the correlation coefficient between the i-th type factor and dissolved oxygen level; This is the j-th collected data point for the i-th type factor; The mean of the data collected for the i-th type factor; This is the j-th data point collected for dissolved oxygen. This represents the average value of the dissolved oxygen data collected. m represents the total number of data collected.

4. The crayfish farming system based on the Internet of Things according to claim 1, characterized in that, The environmental parameters include air temperature, air pressure, light intensity, wind speed, aquaculture area, water flow velocity, and average water depth of the aquaculture area. The breeding parameters include breeding density, feeding frequency, and feeding amount; The ecological parameters include the area and growth density of aquatic plants in the aquaculture area.

5. The crayfish farming system based on the Internet of Things according to claim 1, characterized in that, The steps for obtaining control commands are as follows: Step s01, set the standard value of dissolved oxygen at the test point to be... ; Step s02: Using T as the sampling period, the real-time dissolved oxygen value at the test point is acquired in real time. ; Step s03: Compare real-time dissolved oxygen values Compared with the standard value of dissolved oxygen Size; Step s04, if there is < This indicates that the dissolved oxygen level in the aquaculture area is low, generating a control command that requires oxygenation, and based on the first relational formula: After determining the various oxygenation parameters, return to step s02; Step s05, if there is If the result is positive, it indicates that the dissolved oxygen level in the aquaculture area is at a normal level. After generating a control command that does not require oxygenation, the process returns to step s02.

6. The crayfish farming system based on the Internet of Things according to claim 5, characterized in that, The method for determining the sampling period T in step s02 is as follows: when When T ≤ 1 second; when At that time, according to the second relation: The dissolved oxygen level changes at test points within the aquaculture area, under current influencing factors and without oxygenation, are determined as the standard dissolved oxygen value. The required time is T0, and we take T≤T0 / 2.

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