A method and apparatus for obtaining the average equivalent diameter of floc particles based on maximum correlation entropy.

Abstract

This invention discloses a method and apparatus for obtaining the average equivalent diameter of floc particles based on maximum correlation entropy, specifically including the following steps: S1, acquiring images of floc particles from an industrial camera; S2, obtaining the characteristic parameters of the floc particles and the corresponding number of floc particles, wherein the characteristic parameters of the floc particles include the area, perimeter, central empty area, and aspect ratio of the floc particles; S3, calculating the equivalent diameter of the corresponding floc particle based on the area, perimeter, central empty area, and aspect ratio of each floc particle; S4, obtaining the average equivalent diameter of the floc particles; S5, determining the turbidity of the effluent. This invention optimizes the solution for the average equivalent diameter of floc particles through the MCC algorithm, eliminating or reducing the influence of invalid abnormal equivalent diameters on the overall sedimentation of floc particles under actual conditions, providing an effective data processing reference method for water treatment fields such as tap water treatment and sewage treatment.

Description

Technical Field

[0001] This invention relates to the field of water treatment technology, specifically to a method and apparatus for obtaining the average equivalent diameter of floc particles based on maximum correlation entropy. Background Technology

[0002] In actual water treatment processes at water plants, coagulation is a crucial step in removing minerals and organic particles from raw water, exhibiting typical time delays and nonlinearities. The coagulation effect directly impacts the effluent turbidity. Based on the strong correlation between the average equivalent diameter of floc particles and effluent turbidity, image processing methods are used to preprocess floc images and quantitatively analyze floc particle parameters to obtain the average equivalent diameter of floc particles, which can serve as one basis for controlling coagulant dosage. However, factors such as microbial influences, excessive or insufficient dosage, equipment leaks, and temperature fluctuations can all lead to abnormal aggregation and sedimentation of floc particles. This results in some invalid outliers in the calculated equivalent diameter of floc particles, preventing the captured floc particle images from reflecting the true state of the sedimentation tank. Regardless of environmental interference, the equivalent diameter of floc particles calculated from floc particle images always contains a few invalid outliers, thus preventing the subsequent calculation of the average equivalent diameter using traditional least squares methods from accurately characterizing the coagulation effect.

[0003] Based on the above theory, in industry, the average equivalent diameter of floc particles is often used to determine water turbidity (coagulation effect) and is fed back to the coagulant dosing control system to control the dosage of coagulant in real time during the coagulation process. However, the traditional method for calculating the average equivalent diameter of floc particles requires first obtaining the equivalent diameter of each floc particle, and then averaging the results to obtain the average equivalent diameter. Because this traditional method for calculating the average equivalent diameter of floc particles does not consider invalid outliers, the obtained average equivalent diameter deviates significantly from the effective average equivalent diameter of the floc particles, making it impossible to accurately evaluate the current coagulation effect. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for obtaining the average equivalent diameter of floc particles based on the maximum correlation entropy, so as to reduce the negative impact of the ineffective and abnormal equivalent diameter of floc particles on the average equivalent diameter, more accurately determine whether the current coagulation effect is good, provide important reference data for the precise dosing control of coagulants, and verify the feasibility of the theoretical results through multiple numerical experiments.

[0005] The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy specifically includes the following steps:

[0006] S1. Acquire images of floc particles taken by an industrial camera during the coagulation process. The floc particle images include samples of multiple floc particles.

[0007] S2. Obtain the characteristic parameters of the flocculent particles and the corresponding number of flocculent particles based on the flocculent particle image. The characteristic parameters of the flocculent particles include the area, perimeter, central empty area, and aspect ratio of the flocculent particles.

[0008] S3. Calculate the equivalent diameter of the flocculent particles based on their area, perimeter, central void area, and aspect ratio.

[0009] S4. Input the equivalent diameter of all floc particles calibrated in the above steps, and the corresponding number of floc particles, into the equivalent diameter model to obtain the average equivalent diameter after removing invalid outliers. The equivalent diameter model is established based on the maximum correlation entropy criterion.

[0010] Furthermore, the equivalent diameter model specifically includes the following steps:

[0011] Based on the equivalent diameter φ of the flocculent particles i And the number of floc particles n with the corresponding equivalent diameter. i Establish a cost function based on the maximum correlation entropy criterion:

[0012]

[0013] Where N represents the number of types of equivalent diameters of flocculent particles, φ i n represents the i-th equivalent diameter of the flocculent particles. i The equivalent diameter is represented by φ i The number of flocculent particles, where Φ represents the average equivalent diameter of the flocculent particles, and σ represents the kernel width of the Gaussian kernel function;

[0014] Based on the semi-quadratic optimization strategy, the cost function is solved to obtain the average equivalent diameter of the flocculent particles:

[0015]

[0016] Furthermore, the equivalent diameter model specifically includes the following steps:

[0017] Based on the equivalent diameter φ of the flocculent particles i And the number of floc particles n with the corresponding equivalent diameter. i Establish a cost function based on the maximum correlation entropy criterion:

[0018]

[0019] Where N represents the number of types of equivalent diameters of flocculent particles, φ i n represents the i-th equivalent diameter of the flocculent particles. i The equivalent diameter is represented by φ iThe number of flocculent particles, where Φ represents the average equivalent diameter of the flocculent particles, and σ represents the kernel width of the Gaussian kernel function;

[0020] Based on the semi-quadratic optimization strategy, the cost function is solved to obtain the recursive equation;

[0021] Based on the recursive equation, the equivalent diameter model is repeatedly executed until the iteration number k or the mean square error value converges to the steady-state error, and the average equivalent diameter of the flocculent particles is output:

[0022]

[0023] Furthermore, the φ i It is calculated using the following formula:

[0024]

[0025] Where, φ i It is the i-th equivalent diameter of the flocculent particles, s i It is the area of ​​the i-th type of equivalent diameter flocculent particle, l i It is the perimeter of the i-th type of equivalent diameter flocculent particle, s i0 It is the hollow area of ​​the i-th type of equivalent diameter flocculent particle, m i It is the aspect ratio of the i-th type of equivalent diameter flocculent particles, where k1, k2, and k3 are the perimeters l i Aspect Ratio (m) i and hollow area s i0 The coefficients, k1, k2, and k3, are decimals from 0 to 1.

[0026] Furthermore, the recursive equation includes:

[0027]

[0028]

[0029]

[0030] Where, ρ i It is an auxiliary variable.

[0031] Furthermore, the cost function is solved according to a semi-quadratic optimization strategy, including the following steps:

[0032] Introducing auxiliary variable ρ i The cost function is rewritten as:

[0033]

[0034] in,

[0035] A device for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy includes:

[0036] One or more processors;

[0037] A storage unit is used to store one or more programs that, when executed by one or more processors, enable the one or more processors to implement the method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy.

[0038] The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy specifically includes the following steps:

[0039] S1. Acquire images of floc particles taken by an industrial camera during the coagulation process. The floc particle images include samples of multiple floc particles.

[0040] S2. Obtain the characteristic parameters of the flocculent particles and the corresponding number of flocculent particles based on the flocculent particle image. The characteristic parameters of the flocculent particles include the area, perimeter, central empty area, and aspect ratio of the flocculent particles.

[0041] S3. Calculate the equivalent diameter of the flocculent particles based on their area, perimeter, central void area, and aspect ratio.

[0042] S4. Input the equivalent diameter of all floc particles calibrated in the above steps, and the corresponding number of floc particles into the equivalent diameter model to obtain the average equivalent diameter after removing invalid outliers. The equivalent diameter model is established based on the maximum correlation entropy criterion.

[0043] S5. The turbidity of the effluent is determined based on the average equivalent diameter of the floc particles.

[0044] The beneficial effects of this invention are as follows:

[0045] Even without interference from the objective environment, the calculated equivalent diameter of floc particles may contain a small number of invalid outliers, regardless of the coagulation effect. These invalid outliers cause a significant deviation between the average equivalent diameter obtained by the traditional least squares method and the average effective equivalent diameter of the floc particles, making it impossible to accurately evaluate the current coagulation effect. Furthermore, in actual water plant operation, invalid outliers will appear in the equivalent diameter of floc particles regardless of the coagulation effect. To avoid the deviation between the average equivalent diameter and the average effective equivalent diameter caused by invalid outlier equivalent diameters of floc particles, this paper introduces the MCC (Maximum Correlation Entropy Criterion) algorithm. The MCC algorithm optimizes the solution for the average equivalent diameter of floc particles, eliminating or reducing the impact of invalid outlier equivalent diameters on the overall settling of floc particles under actual conditions, providing an effective data processing reference method for water treatment fields such as tap water treatment and wastewater treatment. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of Gaussian kernel functions with different kernel widths according to the present invention;

[0047] Figure 2 This is a schematic diagram of the MSE in the joint space of variables A and B in this invention;

[0048] Figure 3 This is a schematic diagram of the correlation entropy in the joint space of variables A and B in this invention;

[0049] Figure 4 This is a schematic diagram of the three sample means of the first 90 floc particles with Gaussian distribution and effective equivalent diameters in the range of 0.3mm-2.6mm, and the last 10 floc particles with invalid abnormal equivalent diameters in the range of 5.6mm-6.8mm.

[0050] Figure 5 This is a schematic diagram of the three sample means of the first 90 inner points with Gaussian distribution and effective equivalent diameter in the range of 4.6mm-7.7mm, and the last 10 outlier points with invalid and abnormal equivalent equivalent diameter in the range of 0.8-2mm.

[0051] Figure 6 This is a schematic diagram of the average values ​​of three samples from the present invention, including 90 randomly distributed inner points with effective equivalent diameters in the range of 0.3 mm to 2.3 mm and 10 invalid abnormal points with equivalent equivalent diameters in the range of 5.5 mm to 7 mm.

[0052] Figure 7 This is a schematic diagram of the three sample means of the present invention, which includes 90 randomly distributed in-cell points with effective equivalent diameters in the range of 4.3 mm to 7.5 mm and 10 out-of-cell points with invalid and abnormal equivalent diameters in the range of 0.3 mm to 2.2 mm.

[0053] Figure 8 This is a schematic diagram of the process for calculating the equivalent diameter of MCC floc particles according to the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0056] At the same time, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn according to actual scale.

[0057] Furthermore, for clarity and brevity, descriptions of well-known structures, functions, and configurations may have been omitted. Those skilled in the art will recognize that various changes and modifications can be made to the examples described herein without departing from the spirit and scope of this disclosure.

[0058] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0059] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0060] Example 1

[0061] This application investigated the intrinsic relationship between geometric parameters such as the equivalent diameter of floc particles and the dosage of coagulant, and also explored the intrinsic relationship between other parameters of floc particles and the dosage of coagulant, thus alleviating the lag and nonlinearity of water quality indicators in water treatment to some extent. However, in the application of precise control of coagulant dosage, the accurate calculation of relevant parameters such as the average equivalent diameter of floc particles remains an urgent problem to be solved. In actual water treatment processes at water plants, the coagulation effect is greatly affected by the actual environment. Factors such as microorganisms, abnormal coagulant dosage, equipment leakage, and air temperature can all lead to abnormal settling of floc particles after coagulation. For example, in hot weather, microorganisms in sludge decompose and produce gas, thereby generating microbubbles in the sludge. Equipment leakage can lead to excessively high gas content in the water, and excessively low temperatures can affect the reaction rate of the coagulant. These objective factors affect the effect of floc particle aggregation and settling, causing the captured floc particle images to not reflect the actual situation of the sedimentation tank, and the equivalent diameter of floc particles calculated based on these floc particle images will have a small number of invalid outliers. Furthermore, even without interference from the objective environment, the calculated equivalent diameter of floc particles may contain a small number of invalid outliers, regardless of the coagulation effect. These invalid outliers cause a significant deviation between the average equivalent diameter obtained by the traditional least squares method and the actual average effective equivalent diameter of the floc particles, making it impossible to accurately evaluate the current coagulation effect. Therefore, researching a new optimization method for processing the average equivalent diameter of floc particles is of great significance for eliminating the negative impact of a small number of invalid outliers on the average equivalent diameter of the flocs.

[0062] To address the issue of invalid and anomaly-prone equivalent diameter values ​​for some floc particles calculated during coagulation, this paper introduces the Maximum Relevant Entropy Criterion (MCC) and presents an optimal calculation method—a method for calculating the average equivalent diameter of floc particles based on MCC. This method optimizes the process of solving for the average equivalent diameter of floc particles, reduces calculation errors caused by invalid and anomaly-prone equivalent diameters, and achieves the goal of accurately calculating the average equivalent diameter of floc particles. This provides important reference data for the subsequent precise control of coagulant dosing.

[0063] The equivalent diameter refers to the diameter of a sphere used to represent the diameter of a flocculent particle when the flocculent particles have the same or similar physical properties as spherical particles. In water treatment, the settling characteristics of flocculent particles are complex. During settling, flocculent particles are in a discrete state; their mass, size, and properties do not change, and their settling velocity remains undisturbed.

[0064] Stokes' theorem, commonly used, is the mathematical expression for particle sedimentation motion:

[0065]

[0066] Where v is the settling velocity of the flocs, ρ is the floc density, ρ0 is the density of water, g is the acceleration due to gravity, μ is the viscosity coefficient of water, and d s It is the diameter of the flocculent particles.

[0067] Further research shows that the density of the flocs changes as the particle size changes:

[0068]

[0069] Where, k p is a coefficient, typically ranging from 1.2 to 1.5, depending on the coagulant filling rate and the quality of the raw water. By integrating equations (1) and (2), the following conclusion can be drawn: the relationship between floc particle size and settling velocity is:

[0070]

[0071] The above analysis is based on the assumption that flocculent particles are spherical. However, we know that actual flocculents are irregular in shape, and their settling velocity should indeed be slower than that of spherical flocculents of the same volume. Images of flocculent particles captured by industrial cameras can effectively reflect the size and shape of the particles, with each floc region in the image reflecting the motion of the particles during the agglomeration process. Flocculent particle images can be characterized by four parameters: particle area (related to size); particle perimeter (related to shape); area of ​​open space in the middle of the particles (related to looseness); and aspect ratio. These characteristics represent the properties of the flocculent particles. The above four parameters can be converted to φ using the following formula. i :

[0072]

[0073] Where, φ i It is the i-th equivalent diameter of the flocculent particles, s i It is the area of ​​the i-th type of equivalent diameter flocculent particle, l i It is the perimeter of the i-th type of equivalent diameter flocculent particle, s i0 It is the hollow area of ​​the i-th type of equivalent diameter flocculent particle, m i It is the aspect ratio of the i-th type of equivalent diameter flocculent particle, where k1, k2, and k3 are the perimeters l i Aspect Ratio (m) i and hollow area s i0 The coefficients, k1, k2, and k3, are decimals from 0 to 1.

[0074] Through the above analysis and calculations, the equivalent diameter of floc particles can be extracted from the floc image. The equivalent diameter of floc particles is an important characteristic parameter of floc particles and has a strong correlation with water turbidity. It not only reflects the quality of coagulation but also relates to whether the turbidity of the subsequent effluent meets the water supply requirements. Using it as a target value to control the dosage of coagulant can achieve excellent control results. As shown in the above formula, the larger the equivalent diameter, the faster the settling speed, meaning better floc formation integrity, more complete sedimentation, and lower turbidity of the settled water. Changes in the equivalent diameter value not only reflect the quality of coagulation but also relate to whether the utilization rate of the coagulant reaches its maximum benefit.

[0075] However, the i-th equivalent diameter φ of the flocculent particles i It is still impossible to characterize the overall flocculation effect. In practical applications, the equivalent diameter of each floc particle is calculated according to equation (4), and then the average equivalent diameter Φ, which is the key parameter for controlling the dosage of coagulant, is calculated in real time based on the equivalent diameter of the floc particles obtained within a certain time range. The average equivalent diameter Φ is expressed as follows:

[0076]

[0077] Where N represents the number of types of equivalent diameters of flocculent particles, φ i n represents the i-th equivalent diameter of the flocculent particles. i The equivalent diameter is represented by φ i The number of flocculent particles.

[0078] Based on the above analysis, we can display the real-time acquired images of floc particles on a computer and calculate the s of the floc particles with the equivalent diameter of type i in formula (4) through image preprocessing, image segmentation, and other image processing techniques. i l i m i and s i0 Thus obtaining φ i Finally, φ i and n i Substituting into equation (5) yields the average equivalent diameter Φ of the flocculent particles.

[0079] In actual water treatment processes at water plants, factors such as the influence of microorganisms, excessive or insufficient dosage of chemicals, equipment leaks, and temperature can all lead to abnormal aggregation and sedimentation of floc particles. This results in captured floc particle images failing to reflect the true state of the sedimentation tank, and the calculated equivalent diameter of the floc particles containing some invalid values. However, regardless of whether the coagulation effect is affected by environmental interference, the equivalent diameter of the floc particles calculated from the floc particle images always contains a few invalid values. Therefore, the average equivalent diameter calculated using the subsequent least squares method cannot accurately characterize the coagulation effect. To eliminate or reduce the influence of invalid equivalent diameters of floc particles on the average equivalent diameter of floc particles, the maximum correlation entropy criterion is introduced to optimize the calculation process of the average equivalent diameter of floc particles, thereby accurately describing the actual coagulation effect of floc particles. Due to its good robustness, the maximum correlation entropy criterion (MCC) is widely used in many fields, such as computer vision, feature extraction, and signal processing. It is mainly used to handle non-Gaussian noise and outliers. MCC is based on entropy, which originates from information theory. Correlation entropy is used to measure the similarity between two variables, expressed as follows:

[0080] V σ (A, B) = E(k) σ (AB)), (6)

[0081] Where E(*) is the expected value of *, k σ (·) represents the Gaussian kernel function, and σ represents k. σ The kernel width (·). Correlation entropy uses a kernel function to nonlinearly map the original space to a higher-dimensional space. For a finite sample, the mathematical expectation can be estimated using the mean. Typically, the joint probability distribution between variables A and B is unknown, for variables A = (a1, a2, ... a...). N ) and B = (b1, b2, ... b N The relevant entropy estimate can also be expressed as:

[0082]

[0083] in,

[0084] It's important to note that Mean Squared Error (MSE) is a global metric that reflects the degree of difference between the estimator and the estimated value. In contrast, MCC is a local metric, its value primarily depending on the probability along the A=B direction, and its local extent depends on the kernel width σ. The convergence speed of the function varies with the kernel width. Kernel functions exhibit better robustness to jump errors or outliers. When the error is large, the kernel function displays a small value, even close to zero, thus avoiding the negative impact of outliers during computation and demonstrating good stability even when data anomalies are caused by disturbances. Figure 2 and Figure 3This illustrates the difference between mean squared error and correlation entropy. In this paper, an optimization model based on MCC is constructed to eliminate the adverse effects of invalid outliers (abnormal equivalent diameters of flocculent particles) on the average equivalent diameter of flocculent particles.

[0085] The traditional average equivalent diameter of flocculent particles can be expressed as the average equivalent diameter of flocculent particles in the least squares sense:

[0086]

[0087] This is an optimization problem, and its solution is:

[0088] Traditional calculation methods do not distinguish between invalid outliers and valid values. Considering that the equivalent diameter of floc particles may contain outliers, we introduce the maximum correlation entropy algorithm to mitigate the impact of invalid outliers on the average equivalent diameter of floc particles. Therefore, based on MCC, the optimization problem is formulated as:

[0089]

[0090] Assuming f(z) = z - zln(-z), we can obtain:

[0091] exp(-x)=sup z (zx-f(z)). (11)

[0092] pass We can find that when z = -exp(-x), we can obtain the maximum value of zx-f(z). This calculation process is called the semi-quadratic optimization strategy (HQ).

[0093] If let

[0094] z = ρ i (12)

[0095] and

[0096]

[0097] Therefore, using the HQ strategy, it is easy to obtain:

[0098]

[0099] and

[0100]

[0101] Where, ρ i It is an auxiliary variable.

[0102] If we take the partial derivative of Φ in (14), we can easily obtain:

[0103]

[0104]

[0105] And it's easy to obtain:

[0106]

[0107] In one embodiment, the problem is solved through iterative optimization (14).

[0108] First, when Φ is fixed, ρ i The solution is derived as follows:

[0109]

[0110] Where k≥0 is the number of iterations.

[0111] Secondly, when ρ i When Φ is fixed, the solution can be easily obtained as follows:

[0112]

[0113] Furthermore, after each iteration σ 2 Update according to the following formula:

[0114]

[0115] The update rule consists of the three steps described above, which are repeated until the convergence condition is met. This process is summarized in Algorithm 1.

[0116] Algorithm 1: Average equivalent diameter Φ based on MCC MCC =MCC-Mean(φ i n i (1≤i≤N).

[0117] 1: Input: Equivalent diameter φ i and equivalent diameter φ i The number of floc particles n i .

[0118] 2: Output: Average equivalent diameter Φ based on MCC MCC .

[0119] 3: Initialization: Φ(0)=Φ c , k = 0.

[0120] 4: When convergence fails, execute...

[0121] 5: Update (σ)(k+1) ) 2 ←(20).

[0122] 6: Update p i (k+1) ←(18).

[0123] 7: Update Φ (k+1) ←(19).

[0124] 8: k←k+1.

[0125] 9: End

[0126] 10: Φ MCC =Φ (k) As the average equivalent diameter based on MCC.

[0127] Four sets of simulation data were generated to verify the effectiveness of Algorithm 1, and for ease of simulation, n was set to n. i (1≤i≤N) is always equal to 1.

[0128] 1. To verify the effectiveness of Algorithm 1, the first set of simulation data was generated. Ninety points representing the effective equivalent diameter of 90 flocculent particles were randomly generated in one-dimensional space. These points represent the average diameter Φ. inlier =1.3mm, covariance σ inlier The distribution follows a Gaussian distribution with a mean of 0.2. Additionally, 10 points representing the equivalent diameters of 10 flocculent particles with ineffective anomalies are randomly generated; these points exhibit a mean of Φ. outlier =6mm, covariance σ outlier =0.3 Gaussian distribution. Using the generated data, the mean Φc of the traditional sample is calculated by formula (9), and the mean Φ of the MCC-based sample is calculated by algorithm 1. MCC And after removing invalid abnormal equivalent diameters, the mean Φv of the effective samples is calculated using formula (9). Φc, Φ MCC And the positions of the three sample averages, Φv, as shown below. Figure 4 As shown. From Figure 4 It can be clearly seen that the sample mean Φ based on MCC... MCC The mean of the traditional sample Φc almost overlaps with the mean of the effective sample Φv, while the traditional sample mean Φc deviates significantly from the mean of the effective sample Φv due to the presence of 10 outliers.

[0129] 2. To verify the effectiveness of Algorithm 1, a second set of simulation data was generated. Ten points representing the ineffective anomaly equivalent diameters of ten flocculent particles were randomly generated in one-dimensional space. These points are represented by the mean Φ. outlier =1.3mm, covariance σ outlierThe distribution follows a Gaussian distribution with a mean of 0.2. Additionally, 90 points representing the effective equivalent diameter of 90 flocculent particles were randomly generated; these points exhibit a mean of Φ. inlier =6mm, covariance σ inlier =0.3 Gaussian distribution. Using the generated data, the mean Φc of the traditional sample is calculated by formula (9), and the mean Φ of the MCC-based sample is calculated by algorithm 1. MCC And after removing invalid abnormal equivalent diameters, the mean Φv of the effective samples is calculated using formula (9). Φc, Φ MCC And the positions of the three sample averages, Φv, as shown below. Figure 5 As shown. From Figure 5 It can be clearly seen that the sample mean Φ based on MCC... MCC The mean of the traditional sample Φc almost overlaps with the mean of the effective sample Φv, while the traditional sample mean Φc deviates significantly from the mean of the effective sample Φv due to the presence of 10 outliers.

[0130] 3. To verify the effectiveness of Algorithm 1, a third set of simulation data was generated. First, 90 points representing the effective equivalent diameter of 90 flocculent particles were randomly generated in one-dimensional space. These points represent the average diameter Φ. inlier =1.3mm, covariance σ inlier The distribution follows a Gaussian distribution with a mean of 0.2. Additionally, 10 points representing the equivalent diameters of 10 flocculent particles with ineffective anomalies are randomly generated; these points exhibit a mean of Φ. outlier =6mm, covariance σ outlier The distribution follows a Gaussian distribution with a value of 0.3. Secondly, these 100 points are randomly ordered. Finally, using the generated data, the mean Φc of the traditional sample is calculated using formula (9), and the mean Φ of the MCC-based sample is calculated using algorithm 1. MCC And after removing invalid abnormal equivalent diameters, the mean Φv of the effective samples is calculated using formula (9). Φc, Φ MCC And the positions of the three sample averages, Φv, as shown below. Figure 6 As shown. From Figure 6 It can be clearly seen that the sample mean Φ based on MCC... MCC The mean of the traditional sample Φc almost overlaps with the mean of the effective sample Φv, while the traditional sample mean Φc deviates significantly from the mean of the effective sample Φv due to the presence of 10 outliers.

[0131] 4. To verify the effectiveness of Algorithm 1, a fourth set of simulation data was generated. First, 10 points representing the equivalent diameters of 10 flocculent particles with invalid anomalies were randomly generated in one-dimensional space. These points are represented by the average value Φ. outlier =1.3mm, covariance σ outlierThe distribution follows a Gaussian distribution with a mean of 0.2. Additionally, 90 points representing the effective equivalent diameter of 90 flocculent particles were randomly generated; these points exhibit a mean of Φ. inlier =6mm, covariance σ inlier The distribution follows a Gaussian pattern of 0.3. Secondly, these 100 points are randomly ordered. Using this generated data, the mean Φc of the traditional sample is calculated using formula (9), and the mean Φ of the MCC-based sample is calculated using algorithm 1. MCC And after removing invalid abnormal equivalent diameters, the mean Φv of the effective samples is calculated using formula (9). Φc, Φ MCC And the positions of the three sample averages, Φv, as shown below. Figure 7 As shown. From Figure 7 It can be clearly seen that the sample mean Φ based on MCC... MCC The mean of the traditional sample Φc almost overlaps with the mean of the effective sample Φv, while the traditional sample mean Φc deviates significantly from the mean of the effective sample Φv due to the presence of 10 outliers.

[0132] If, within the normal range, the average equivalent diameter of the flocculent particles corresponding to the effluent turbidity is approximately 1mm-2mm, then... Figure 4 and Figure 6 It can be seen that the coagulation effect is good, indicating that the effluent turbidity is within the normal range; therefore, from Figure 5 and Figure 7 It can be seen that the coagulation effect is poor, indicating that the turbidity of the effluent is not within the normal range.

[0133] Figure 4 The criteria are: the first 90 floc particles with an effective equivalent diameter in the range of 0.3mm-2.6mm and the last 10 floc particles with an invalid or abnormal equivalent equivalent diameter in the range of 5.6mm-6.8mm, all exhibiting a Gaussian distribution. The traditional sample mean Φc, the effective sample mean Φv, and the MCC-based sample mean Φ... MCC .

[0134] Figure 5 The criteria are: the first 90 floc particles with an effective equivalent diameter in the range of 4.6mm-7.7mm and the last 10 floc particles with an invalid or abnormal equivalent diameter in the range of 0.8mm-2mm, all exhibiting a Gaussian distribution. The traditional sample mean Φc, the effective sample mean Φv, and the MCC-based sample mean Φ... MCC .

[0135] Figure 6 The sample contains 90 randomly distributed inliers with effective equivalent diameters ranging from 0.3 mm to 2.3 mm and 10 outliers with invalid equivalent equivalent diameters ranging from 5.5 mm to 7 mm. The traditional sample mean Φc, the effective sample mean Φv, and the MCC-based sample mean Φ are also included. MCC.

[0136] Figure 7 The sample contains 90 randomly distributed inliers with effective equivalent diameters ranging from 4.3 mm to 7.5 mm and 10 outliers with invalid equivalent equivalent diameters ranging from 0.3 mm to 2.2 mm. The traditional sample mean is Φc, the effective sample mean is Φv, and the MCC-based sample mean is Φ. MCC .

[0137] Table 1 presents several sets of average equivalent diameters calculated by the traditional method and the MCC-based optimization method, along with the calculation results and error rates. As can be seen from Table 1, the MCC algorithm reduces the error rate of the average equivalent diameter of the flocculent particles.

[0138] Table 1 Calculation of the average equivalent diameter of flocculent particles

[0139]

[0140] in conclusion:

[0141] Based on the close correlation between the average equivalent diameter of floc particles and effluent turbidity, image processing technology is used to process the acquired floc particle images to obtain important parameters such as the average equivalent diameter of floc particles, which are then automatically fed back to the coagulant dosing control system. This effectively improves the utilization rate of coagulants, frees up manpower, and reduces production costs. The average equivalent diameter of floc particles is a parameter describing the flocculation and sedimentation characteristics after flocculation in water treatment. In actual water plant operation, regardless of the coagulation effect, abnormal invalid values ​​will appear in the equivalent diameter of floc particles. To avoid the deviation between the real-time calculated average equivalent diameter and the actual average effective equivalent diameter caused by invalid and abnormal equivalent diameters of floc particles, the MCC algorithm is introduced. The solution for the average equivalent diameter of floc particles is optimized based on the MCC algorithm, eliminating or reducing the influence of invalid and abnormal equivalent diameters on the overall sedimentation of floc particles under actual conditions, providing an effective data processing reference method for water treatment fields such as tap water treatment and sewage treatment. Finally, numerical experiments verify the effectiveness of the theoretical results.

[0142] Example 2: A computer-readable storage medium storing a computer program thereon, which, when executed by a processor, enables the method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy.

[0143] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Based on the technical essence of the present invention, any simple modifications, equivalent substitutions, and improvements made to the above embodiments within the spirit and principles of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy, characterized in that, Specifically, the following steps are included: S1. Acquire images of floc particles taken by an industrial camera during the coagulation process. The floc particle images include samples of multiple floc particles. S2. Obtain the characteristic parameters of the flocculent particles and the corresponding number of flocculent particles based on the flocculent particle image. The characteristic parameters of the flocculent particles include the area, perimeter, central empty area, and aspect ratio of the flocculent particles. S3. Calculate the equivalent diameter of the flocculent particles based on their area, perimeter, central void area, and aspect ratio. S4. Input the equivalent diameter of all floc particles calibrated in the above steps and the corresponding number of floc particles into the equivalent diameter model to obtain the average equivalent diameter after removing invalid outliers. The equivalent diameter model is established based on the maximum correlation entropy criterion. The equivalent diameter model is as follows: Based on the equivalent diameter of floc particles And the number of floc particles with corresponding equivalent diameters. Establish a cost function based on the maximum correlation entropy criterion: ， in, The number of types representing the equivalent diameter of flocculent particles. The first representing flocculent particles Equivalent diameter, The equivalent diameter is The number of flocculent particles, Represents the average equivalent diameter of the flocculent particles. The kernel width represents the Gaussian kernel function; Based on the semi-quadratic optimization strategy, the cost function is solved to obtain the average equivalent diameter of the flocculent particles: ,in It is an auxiliary variable.

2. The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy according to claim 1, characterized in that, The cost function is solved by the following steps: Based on the semi-quadratic optimization strategy, the cost function is solved to obtain the recursive equation; Based on the recursive equation, the equivalent diameter model is repeatedly executed until the iteration number k or the mean square error value converges to the steady-state error, and the average equivalent diameter of the flocculent particles is output: 。 3. The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy according to claim 2, characterized in that, The It is calculated using the following formula: ， in, It is the first flocculent particle Equivalent diameter, It is the first The area of ​​flocculent particles with equivalent diameter. It is the first The perimeter of the equivalent diameter flocculent particles, It is the first Hollow area of ​​flocculent particles with equivalent diameter. It is the first The aspect ratio of the equivalent diameter flocculent particles , , Perimeter Aspect Ratio and hollow area coefficient, , , Decimals ranging from 0 to 1.

4. The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy according to claim 2, characterized in that, The recursive equations include: ； ； ； in, It is an auxiliary variable.

5. The method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy according to claim 2, characterized in that, The cost function is solved according to the semi-quadratic optimization strategy, including the following steps: Introducing auxiliary variables The cost function is rewritten as: , in, .

6. A device for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy, characterized in that, include: One or more processors; A storage unit for storing one or more programs that, when executed by one or more processors, enable the one or more processors to implement the method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy according to any one of claims 1 to 5.

7. A method for obtaining the average equivalent diameter of flocculent particles based on maximum correlation entropy, characterized in that, Specifically, the following steps are included: S1. Acquire images of floc particles taken by an industrial camera during the coagulation process. The floc particle images include samples of multiple floc particles. S2. Obtain the characteristic parameters of the flocculent particles and the corresponding number of flocculent particles based on the flocculent particle image. The characteristic parameters of the flocculent particles include the area, perimeter, central empty area, and aspect ratio of the flocculent particles. S3. Calculate the equivalent diameter of the flocculent particles based on their area, perimeter, central void area, and aspect ratio. S4. Input the equivalent diameter of all floc particles calibrated in the above steps, and the corresponding number of floc particles into the equivalent diameter model to obtain the average equivalent diameter after removing invalid outliers. The equivalent diameter model is established based on the maximum correlation entropy criterion. The equivalent diameter model is as follows: Based on the equivalent diameter of floc particles and the number of floc particles with corresponding equivalent diameters. Establish a cost function based on the maximum correlation entropy criterion: ， in, The number of types representing the equivalent diameter of flocculent particles. The first representing flocculent particles Equivalent diameter, The equivalent diameter is The number of flocculent particles, Represents the average equivalent diameter of the flocculent particles. The kernel width represents the Gaussian kernel function; Based on the semi-quadratic optimization strategy, the cost function is solved to obtain the average equivalent diameter of the flocculent particles: ； S5. The turbidity of the effluent is determined based on the average equivalent diameter of the floc particles.

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