An optimization method for the layout of water quality monitoring stations in a bay

By establishing a water quality model in the bay water quality monitoring and adjusting the station using optimization algorithms, the problem of improper layout of the bay water quality monitoring stations is solved, efficient water quality monitoring and resource optimization are achieved, and changes in different conditions are adapted to the changes in different conditions.

CN119477010BActive Publication Date: 2025-07-29SECOND INST OF OCEANOGRAPHY MNR

Patent Information

Application Number
CN202510053635.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-01-14
Publication Date
2025-07-29
Estimated Expiration
2045-01-14

AI Technical Summary

Technical Problem

In the bay area, it is difficult for existing technology to scientifically and reasonably determine the number and location of water quality monitoring stations under limited time and funding conditions, resulting in low data value and ineffectively reflecting the spatial and temporal changes of water quality, affecting environmental management and pollution control.

Method used

By collecting historical water quality data, conducting comprehensive analysis, establishing a water quality model, dynamically adjusting the number and position of stations in combination with optimization algorithms, optimizing layout using trust domain methods and particle swarm optimization algorithms, determining key monitoring areas, and improving monitoring efficiency and data representativeness.

Benefits of technology

It has achieved rapid finding an approximate optimal position layout plan in bay water quality monitoring, improved monitoring efficiency and benefits, ensured the representativeness and comprehensiveness of the data, and adapted to changes in different monitoring goals and conditions.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN119477010B_ABST
    Figure CN119477010B_ABST
Patent Text Reader

Abstract

The present invention discloses an optimization method for the layout of water quality monitoring stations in a bay. The method includes: dividing the research area into grids to obtain data points; determining the initial range of algorithm search according to the characteristic values of the data points; determining the optimal step size for updating the data points by calculating the gradient and curvature information of the objective function, and updating the positions of the data points based on the comparison result of the actual decrease and the predicted decrease of the objective function, and iterating cyclically until the preset convergence condition is reached. The finally obtained positions of the data points are the positions of the water quality monitoring stations in the bay. Based on the trust region mapping method, the particle swarm optimization algorithm is used to quickly solve the problem of the location layout of the water quality monitoring stations in the bay. When the number of monitoring stations is not restricted, it can give the appropriate number of stations according to the requirements, with high calculation rationality and high application value.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention mainly relates to the technical field of water quality monitoring station layout, and particularly to an optimization method for the layout of water quality monitoring stations in a bay. Background Art

[0002] A bay is a well-defined spatial area, which is a collection of various environmental elements such as the ocean, rivers flowing into the sea, soil, and vegetation, and is even more an aggregation area of human activities. As the ultimate receptor of various factor inputs, the seawater body is affected by multiple factors in different spatial ranges, and its water quality usually has obvious temporal and spatial variability. Obviously, on the premise of limited funds and time, fully grasping the temporal and spatial changes of water quality status is the basis and prerequisite for carrying out research and application work such as development, protection, and restoration in the bay. This requires research on the layout of water quality monitoring stations, and the key point is to scientifically and reasonably determine the number and spatial positions of stations in a repeatable manner. However, this is a long-term challenge in any region, and no unified technical standards or processes have been established yet. If the layout of monitoring stations is improper, it is very likely that the water quality data collected will be almost worthless, resulting in significant financial or time losses.

[0003] Generally, the fundamental purpose of the layout of seawater monitoring stations in a limited area is to find a certain minimum cost under various constraints to optimize the overall or average performance. Currently, there are mainly two challenges in solving such problems: one is how to achieve layout optimization analysis within a limited time; the other is how to obtain a global optimal solution. Based on these two challenges, the present application proposes an optimization method for the layout of water quality monitoring stations in a bay. Summary of the Invention

[0004] Technical Objectives

[0005] To solve at least one of the technical problems mentioned in the above background art, the objective of the present invention is to provide an optimization method for the layout of water quality monitoring stations in a bay. By collecting historical water quality data in the bay area, comprehensively analyzing environmental elements such as the hydrology, meteorology, topography, and geomorphology of the bay, and extracting key factors affecting water quality through data mining technology, a corresponding water quality model is established. On this basis, an optimization algorithm is further used to optimize the layout of monitoring stations, and the number and positions of stations are dynamically adjusted according to the water quality model and actual monitoring requirements to achieve the best balance between monitoring efficiency and cost. This solution can not only effectively reflect the temporal and spatial variation characteristics of the water quality in the bay, but also adapt to the changes of different monitoring objectives and conditions, providing strong technical support for the environmental management, pollution control, and ecological restoration of the bay.

[0006] Technical Solution

[0007] An optimization method for the layout of water quality monitoring stations in a bay includes:

[0008] S1. Divide the research area into grids to obtain data points; the characteristic values of the data points include the change trend of future water quality predicted based on the historical monitoring data of existing monitoring stations.

[0009] S2. Determine the initial range of algorithm search according to the characteristic values of the data points.

[0010] S3. Determine the optimal step size for updating the data points by calculating the gradient and curvature information of the objective function, and update the data point positions based on the comparison result of the actual descent amount and the predicted descent amount of the objective function, and perform iterative loops.

[0011] S4. When the preset convergence condition is reached, the finally obtained data point positions are the positions of the bay water quality monitoring stations.

[0012] Furthermore, in step S1, the following factors need to be considered for the characteristic values of the data points:

[0013] ① The interaction between the bay ecosystem and seawater quality;

[0014] ② The promoting effect of the water body exchange rate on the improvement of seawater quality;

[0015] ③ The human activity sewage discharge points that have a greater negative impact on water quality.

[0016] Furthermore, build a decision tree to determine the key characteristics that have the greatest impact on water quality changes in the historical monitoring data of existing monitoring stations, and predict the change trend of future water quality based on the spatial distribution information in the grid division, specifically including: collecting the historical monitoring data of existing monitoring stations, and processing the missing values and outliers in the data; extracting characteristic data according to factors such as the bay ecosystem and water body exchange rate, and determining the key characteristics that have the greatest impact on the prediction results; building a decision tree through the random forest algorithm, and adjusting the number of trees, the depth of the trees, etc.

[0017] Furthermore, the feature importance in the random forest is calculated by the average decrease in impurity, and the calculation formula is as follows:

[0018]

[0019] where, is the number of trees; is the impurity before feature splitting; is the impurity after feature splitting.

[0020] Furthermore, build a water quality model according to the change trend of future water quality, couple the water quality model and the hydrodynamic model to simulate the promoting effect of the water body exchange rate on the improvement of seawater quality, and the hydrodynamic model equations are expressed as equations (1) and (2):

[0021] (1);

[0022] (2);

[0023] In formulas (1) and (2), is the water depth; is the time; is the velocity vector; is the gradient of the velocity vector; is the potential energy of the fluid; is the gradient of the fluid potential energy; is the density of water; is the kinematic viscosity coefficient; is the Coriolis force.

[0024] By simulating the promoting effect of the water body exchange rate on the improvement of seawater quality, the water quality monitoring stations can be determined more scientifically, ensuring the representativeness and comprehensiveness of the monitoring data, helping to identify key monitoring areas, optimizing the allocation of monitoring resources, and improving the efficiency and effectiveness of water quality monitoring.

[0025] Furthermore, in step S3, by finding an optimal step size near the current data point to minimize the objective function while keeping the step size within the trust region radius, the optimal step size solution formula is expressed as formula (3):

[0026] (3);

[0027] In formula (3), represents finding a step size to minimize the model function under the constraint of the trust region radius; is the objective function value at the current point; is the gradient at the current point; is the transpose; is the step size vector; is the Hessian matrix; is the norm; is the trust region adjustment factor for adjusting the size of the trust region; is the trust region radius.

[0028] Furthermore, the size of the trust region radius is determined according to the actual decrease of the objective function.

[0029] The application of the trust region mapping method enables the particle swarm optimization algorithm to perform a more refined search when approaching the optimal solution, improving the search accuracy of the algorithm. By dynamically adjusting the size of the trust region, the algorithm can balance the needs of global search and local search, thus accelerating the convergence speed and improving the convergence stability.

[0030] Further, in step S3, the data point position and velocity update formulas are expressed as in Eqs. (4) and (5):

[0031] (4);

[0032] (5);

[0033] In Eqs. (4) and (5), is the velocity of data point in the -th iteration on the -th dimension; is the velocity of data point in the -th iteration on the -th dimension; is the position of data point in the -th iteration on the -th dimension; is the position of the historical best position of data point in the -th iteration on the -th dimension; is the position of data point in the -th iteration on the -th dimension; is the position of the global best position in the -th iteration on the -th dimension; is the inertia weight; is the first acceleration constant; is the second acceleration constant; and are random numbers between 0 and 1; is the scaling factor used to control the intensity of chaotic perturbation; is the chaotic function used to introduce non-linearity and randomness in velocity update; and are different from the velocity concept in physics, but an abstract concept in the search space, representing the change in the position of the data point during the iteration process.

[0034] It is simple and easy to implement, with a fast convergence speed. During the optimization process of the bay water quality monitoring station layout, it can quickly find an approximate optimal monitoring station layout plan, combining the local search characteristics of the trust region method and the global search ability of the particle swarm optimization algorithm, improving the efficiency and quality of the optimization process.

[0035] Further, if the actual decrease and the predicted decrease of the objective function are close, and the step size is within the trust region radius, then update the position of the data point.

[0036] Further, in step S4, the preset convergence condition is that the change in the position of the data point is less than a certain threshold, the maximum number of iterations has been reached, or the norm of the gradient is small enough.

[0037] A computer-readable storage medium stores a computer program executable by a processor. When the computer program is executed by the processor, at least one step in the aforementioned bay water quality monitoring station layout optimization method is run.

[0038] A computer device includes a memory, a processor, a communication interface, and a communication bus. Among them,

[0039] The memory, the processor, and the communication interface communicate with each other through the communication bus;

[0040] The memory is used to store a computer program;

[0041] The processor is used to execute the computer program stored on the memory. When the processor executes the computer program, at least one step in the aforementioned bay water quality monitoring station layout optimization method is implemented.

[0042] Beneficial effects

[0043] By implementing the bay water quality monitoring station layout optimization method provided by the present invention above, the following technical effects are achieved:

[0044] This application collects historical water quality data in the bay area, comprehensively analyzes environmental factors such as the hydrology, meteorology, and topography of the bay, extracts key factors affecting water quality through data mining techniques, and establishes a corresponding water quality model. On this basis, an optimization algorithm is further used to optimize the layout of monitoring stations, dynamically adjusting the number and location of stations according to the water quality model and actual monitoring requirements to achieve the best balance between monitoring efficiency and cost. By simulating the promoting effect of water body exchange rate on the improvement of seawater quality, this application can more scientifically determine the water quality monitoring stations, ensuring the representativeness and comprehensiveness of monitoring data, helping to identify key monitoring areas, optimize the allocation of monitoring resources, and improve the efficiency and effectiveness of water quality monitoring. Its algorithm is simple and easy to implement, with a fast convergence speed. During the process of optimizing the layout of water quality monitoring stations in the bay, it can quickly find an approximate optimal monitoring station layout scheme, combining the local search characteristics of the trust region method and the global search ability of the particle swarm optimization algorithm, improving the efficiency and solution quality of the optimization process. This indirectly shows that the calculation results of this application are relatively stable and have high rationality, and the research results can be well applied in other bays and even open sea areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] To make the above-mentioned method for optimizing the layout of water quality monitoring stations in the bay of the present invention more clearly understandable, the drawings required for the specific implementation manners of the present invention will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative efforts.

[0046] Figure 1 It shows a schematic diagram of the method for optimizing the layout of water quality monitoring stations in the bay;

[0047] Figure 2 It shows a schematic diagram of the data point iteration process;

[0048] Figure 3 It shows a structural block diagram of a computer-readable storage medium. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] Those skilled in the art can draw on the content of this article and implement it by appropriately replacing and / or modifying process parameters. However, it should be particularly noted that all such similar replacements and / or modifications are obvious to those skilled in the art, and they are all considered to be included in the present invention. The products and preparation methods described in the present invention have been described through preferred examples, and those skilled in the art can obviously make changes or appropriate alterations and combinations to the products and preparation methods described in this article without departing from the content, spirit, and scope of the present invention to implement and apply the technology of the present invention.

[0050] Unless otherwise defined, the technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art to which this invention belongs. This invention uses the methods and materials described herein; however, other suitable methods and materials known in the art may also be used. The materials, methods, and examples described herein are illustrative only and not intended to be limiting. All publications, patent applications, patents, provisional applications, database entries, and other references mentioned herein are incorporated herein by reference in their entirety. In case of conflict, the present specification, including definitions, shall prevail.

[0051] Unless otherwise specified, the materials, methods, and examples described herein are exemplary and not restrictive. Although methods and materials similar or equivalent to those described herein may be used in the practice or testing of this invention, suitable methods and materials are still described herein.

[0052] The present invention is described in detail below.

[0053] Example 1:

[0054] In this example, a method for optimizing the layout of water quality monitoring stations in a bay is provided with a certain lagoon as the research area. The method for optimizing the layout of water quality monitoring stations in the bay is as Figure 1 shown. This lagoon is a typical tropical coastal lagoon with a water area of about 10 square kilometers and has many typical ecosystems. According to relevant research, there are many human activities around the lagoon, including shallow sea cage aquaculture, coastal fishery aquaculture, direct discharge of urban sewage, farmland planting, livestock farming, and tourist destinations.

[0055] Considering the calculation requirements, the spatial map is projected onto the Gauss-Kruger plane coordinates. Combining with the data accuracy, the research area is divided into 200m×200m using the fishnet function in ArcGIS 10.2, so that 250 grids, that is, 250 data points, can be obtained. These data points are assigned as .

[0056] To determine suitable seawater monitoring stations in the lagoon area, the following factors need to be considered:

[0057] ① The interaction between the bay ecosystem and seawater quality;

[0058] ② The promoting effect of the water body exchange rate on the improvement of seawater quality;

[0059] ③ Pollutant discharge points of human activities that have a greater negative impact on water quality.

[0060] By building a decision tree, identify the key features in the historical monitoring data of existing monitoring stations that have the greatest impact on water quality changes, and predict the future water quality change trend based on the spatial distribution information in the grid division. Specifically, it includes: collecting the historical monitoring data of existing monitoring stations and processing the missing values and outliers in the data; extracting feature data according to factors such as the bay ecosystem and water exchange rate, and determining the key features that have the greatest impact on the prediction results; building a decision tree through the random forest algorithm and adjusting the number of trees, the depth of the tree, etc.

[0061] The feature importance in the random forest is calculated by the average decrease in impurity. The calculation formula is as follows:

[0062]

[0063] Where, is the number of trees; is the impurity before feature splitting; is the impurity after feature splitting.

[0064] Suppose there are 100 trees, and the average decrease in impurity value of each feature in all trees includes temperature 2.5, dissolved oxygen 3.0, pH value 2.0, turbidity 1.5, and vegetation coverage rate 4.0;

[0065] The total average decrease in impurity value is: 2.5 + 3.0 + 2.0 + 1.5 + 4.0 = 13.0;

[0066] Among them, the importance of temperature is , the importance of dissolved oxygen is , the importance of pH value is , the importance of turbidity is , and the importance of vegetation coverage rate is ;

[0067] According to the above calculation results, the vegetation coverage rate has the highest importance, followed by dissolved oxygen.

[0068] Build a water quality model according to the future water quality change trend, couple the water quality model and the hydrodynamic model to simulate the promotion effect of the water exchange rate on the improvement of seawater quality. The hydrodynamic model equations are expressed as equations (1) and (2):

[0069] (1);

[0070] (2);

[0071] In equations (1) and (2), is the water depth; is the time; is the flow velocity vector; is the gradient of the flow velocity vector; is the potential energy of the fluid; is the gradient of the fluid potential energy; is the density of water; is the kinematic viscosity coefficient; is the Coriolis force.

[0072] Example 2:

[0073] Based on the foregoing example, by finding an optimal step size near the current data point to minimize the objective function while keeping the step size within the trust region radius, the optimal step size solution formula is expressed as in Equation (3):

[0074] (3);

[0075] In Equation (3), represents finding a step size to minimize the model function under the constraint of the trust region radius; is the objective function value at the current point; is the gradient at the current point; is the transpose; is the step size vector; is the Hessian matrix; is the norm; is the trust region adjustment factor used to adjust the size of the trust region; is the trust region radius.

[0076] Determine the size of the trust region radius according to the actual decrease of the objective function.

[0077] The data point position and velocity update formulas are expressed as in Equations (4) and (5):

[0078] (4);

[0079] (5);

[0080] In Equations (4) and (5), is the velocity of the data point at the th iteration in the dimension; is the velocity of the data point at the th iteration in the dimension; is the position of the data point at the th iteration in the dimension; is the Data points in the $i$-th iteration The historical optimal position at the dimension; Let be the data points in the $i$-th iteration at the dimension; Let be the global optimal position at the dimension in the $i$-th iteration; Let be the first acceleration constant; Let and be random numbers between 0 and 1; Let be the scaling factor used to control the intensity of chaotic perturbation; and is different from the concept of velocity in physics and is an abstract concept in the search space, representing the change in the position of data points during the iteration process.

[0081] For example, assume is , the objective function is , the size of the data points is 2, the number of iterations is 5, the inertia weight is 0.7, the first acceleration constant is 2, the second acceleration constant is 2, the scaling factor is 0.5, and the position of the initial data points is is 0, 6.

[0082] In the first iteration, , , the historical optimal , , the global optimal ;

[0083] For data point 1:

[0084] ;

[0085] For data point 2:

[0086] ;

[0087] Update the position, for data point 1: , for data point 2: ;

[0088] Go through 5 iterations in sequence to find the value that minimizes the objective function.

[0089] If the actual decrease and the predicted decrease of the objective function are close, and the step size is within the trust region radius, then update the position of the data point. The data point iteration process is as Figure 2 shown. The particle swarm optimization algorithm can effectively maintain a balance between global search and local search, and at the same time use the chaotic perturbation term to increase the randomness of the search, so as to find a better solution in the optimization problem of the layout of the water quality monitoring stations in the bay. This optimization method can not only improve the quality of the solution, but also shorten the time of the optimization process and improve the efficiency of the optimization process.

[0090] Figure 2 In [reference], as the number of iterations increases, the number of data point representative points also slowly decreases. However, the 15 most stable data point representative points obtained after 110 iterations all appear within the range of the better representative points screened out in the previous iterations, indicating that as the number of iterations increases, there are still some data point representative points remaining unchanged, indicating that the algorithm scheme and algorithm results of this application are very stable, there will be no sudden jumps in the screened positions, and the rationality is relatively high, and it can be well adapted to other lagoons, bays, sea areas, etc.

[0091] The preset convergence conditions are: the change in the position of the data point is less than a certain threshold, the maximum number of iterations has been reached, or the norm of the gradient is small enough.

[0092] Example 3:

[0093] A computer-readable storage medium, as Figure 3 shown, stores a computer program executable by a processor. When the computer program is executed by the processor, it runs each step in the aforementioned method for optimizing the layout of the water quality monitoring stations in the bay, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here.

[0094] Example 4:

[0095] A computer device includes a memory, a processor, a communication interface, and a communication bus; wherein, the memory, the processor, and the communication interface communicate with each other through the communication bus; the memory is used to store a computer program; the processor is used to execute the computer program stored on the memory. When the processor executes the computer program, it can implement each step in the aforementioned method for optimizing the layout of the water quality monitoring stations in the bay, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here.

[0096] A computer-readable medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information accessible by a computing device. As defined herein, a computer-readable medium does not include transitory computer-readable media, such as modulated data signals and carrier waves.

[0097] The conventional technologies in the above embodiments are the prior arts known to those skilled in the art, so they will not be described in detail herein.

[0098] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains may use similar ways to replace the described specific embodiments, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

[0099] Although a detailed description of the present invention has been made and some specific embodiments have been cited, it is obvious that various changes or modifications can be made by those skilled in the art without departing from the spirit and scope of the present invention.

[0100] Although the above specific embodiments have shown, described, and pointed out the novel features applicable to various embodiments, it should be understood that various omissions, substitutions, and changes in the form and details of the described apparatus or method can be made without departing from the spirit of the present disclosure. Additionally, the above various features and methods can be used independently of each other or can be combined in various ways. All possible combinations and sub-combinations are intended to fall within the scope of the present disclosure. Many of the above embodiments include similar components, and therefore, these similar components can be interchanged in different embodiments. Although the present invention has been disclosed in the context of certain embodiments and examples, those skilled in the art should understand that the present invention can extend beyond the specifically disclosed embodiments to other alternative embodiments and / or applications and equivalents. Therefore, the present invention is not intended to be limited by the specific disclosure of the preferred embodiments herein.

[0101] Matters not covered by the present invention are all well-known technologies.

Claims

1. An optimization method for the layout of water quality monitoring stations in a bay, characterized in that: Including: S1. Grid-divide the research area to obtain data points, predict the future water quality change trend based on the spatial distribution information in the grid division, and determine the key features that have the greatest impact on the water quality change in the historical monitoring data of the existing monitoring stations through the random forest algorithm. Specifically, it includes: collecting the historical monitoring data of the existing monitoring stations and processing the missing values and outliers in the data; extracting feature data according to the factors of the bay ecosystem and the water body exchange rate, and determining the key features that have the greatest impact on the prediction results; the feature values of the data points include the future water quality change trend predicted based on the historical monitoring data of the existing monitoring stations, and the interaction between the bay ecosystem and the seawater quality, the promotion effect of the water body exchange rate on the improvement of the seawater quality, and the human activity sewage discharge points that have a greater negative impact on the water quality also need to be considered; Construct a water quality model based on the changing trend of the future water quality, couple the water quality model with the hydrodynamic model to simulate the promoting effect of the water body exchange rate on the improvement of seawater quality. The hydrodynamic model equation is as follows: ; ; In the formula, is the water depth; is the time; is the velocity vector; is the gradient of the velocity vector; is the potential energy of the fluid; is the gradient of the fluid potential energy; is the density of water; is the kinematic viscosity coefficient; is the Coriolis force; S2. Determine the initial range searched by the optimization algorithm through the GIS spatial analysis according to the feature values of the data points; S3. Determine the optimal step size for updating the data points by calculating the gradient and curvature information of the objective function, and update the data point position based on the comparison result of the actual descent amount and the predicted descent amount of the objective function, and perform iterative loops; use the optimization algorithm to optimize the layout of the monitoring stations, dynamically adjust the number and position of the stations according to the water quality model and the actual monitoring requirements, so as to achieve the best balance between the monitoring efficiency and the cost. The optimization algorithm can effectively maintain the balance between the global search and the local search, and at the same time use the chaotic perturbation term to increase the randomness of the search, so as to find a better solution in the problem of optimizing the layout of the bay water quality monitoring stations; S4. When the preset convergence condition is reached, the finally obtained data point position is the site of the bay water quality monitoring station.

2. The method for optimizing the layout of the bay water quality monitoring stations according to claim 1, characterized in that: The feature importance in the random forest algorithm is calculated by the average impurity reduction, and the formula is: In the formula, is the number of trees; is the impurity before feature splitting; is the impurity after feature splitting.

3. The method for optimizing the layout of the bay water quality monitoring stations according to claim 1, characterized in that: In step S3, by finding an optimal step size near the current data point to minimize the objective function while keeping the step size within the trust region radius, the formula for solving the optimal step size is: wherein, represents finding a step size to minimize the model function under the constraint of the trust region radius; is the objective function value at the current point; is the gradient at the current point; is the transpose; is the step size vector; is the Hessian matrix; is the norm; is the trust region adjustment factor for adjusting the size of the trust region; is the trust region radius.

4. The method for optimizing the layout of the bay water quality monitoring stations according to claim 3, characterized in that: Determine the size of the trust region radius according to the actual descent amount of the objective function.

5. The method for optimizing the layout of the bay water quality monitoring stations according to claim 4, characterized in that: The formulas for updating the data point position and velocity are: In the formula, is the velocity of the data point at the -th iteration in the dimension; is the velocity of the data point at the -th iteration in the dimension; is the position of the data point at the -th iteration in the dimension; is the position of the historical best position of the data point at the -th iteration in the dimension; is the position of the data point at the -th iteration in the dimension; is the position of the global best position at the -th iteration in the dimension; is the inertia weight; is the first acceleration constant; is the second acceleration constant; and are random numbers between 0 and 1; is the scaling factor used to control the intensity of chaotic perturbation; is the chaotic function used to introduce nonlinearity and randomness in velocity update; and are different from the concept of velocity in physics, but an abstract concept in the search space, representing the change amount of the position of the data point during the iteration process.

6. The method for optimizing the layout of the bay water quality monitoring stations according to claim 1, characterized in that: If the actual descent amount and the predicted descent amount of the objective function are close, and the step size is within the trust region radius, then update the position of the data point.

7. A computer-readable storage medium storing a computer program executable by a processor, characterized in that: The computer program, when executed by a processor, runs at least one step in the method according to any one of claims 1-6.

8. A computer device, the computer device comprising a memory, a processor, a communication interface, and a communication bus; wherein, The memory, the processor, and the communication interface communicate with each other through the communication bus; the memory is used for storing a computer program; the processor is used for executing the computer program stored on the memory, and is characterized in that when the processor executes the computer program, at least one step in the method according to any one of claims 1-6 is implemented.

Citation Information

Patent Citations

  • Pre-selected water quality monitoring network multi-objective optimized deployment method for some monitoring points

    CN107908889A

  • Optimized layout determination method for bay water quality monitoring stations

    CN116644832A

Cited By

  • Water quality monitoring data analysis method and system

    CN120632369A

  • A method and system for analyzing water quality monitoring data

    CN120632369B