Industrial wastewater treatment system data enhancement method and system based on physical anchoring and GAN algorithm

Abstract

The invention discloses an industrial wastewater treatment system data enhancement method and system based on physical anchoring and a GAN algorithm, and belongs to the application technology of the GAN algorithm in industrial wastewater treatment. According to the method, firstly, a key parameter set influencing system operation indexes is determined based on mechanism analysis and random forest feature importance sorting, and then an extension space of out-of-domain data is determined based on a data distribution condition of the key parameter set; key out-of-domain working condition data of the industrial wastewater treatment system are obtained in a mode of combining a single-factor gradient experiment and a multi-factor orthogonal experiment, and then a GAN model based on physical anchor point guidance, physical law and biochemical mechanism constraint is constructed to train the working condition data; through secondary amplification of industrial wastewater treatment data guided by anchor point data which does not exceed 1% of the data volume in an original domain, and in combination with a generative adversarial network and physical and biochemical constraints, efficient directional data enhancement of the industrial wastewater treatment data is realized.

Description

Technical Field

[0001] This invention relates to the field of industrial intelligent system control, specifically to a data augmentation method and system for an industrial wastewater treatment system based on physical anchoring and GAN algorithm. Background Technology

[0002] With the deep penetration of industrial intelligent systems, intelligent operation monitoring and optimized control of water treatment systems have become core components in ensuring industrial safety and environmental compliance. For actual industrial wastewater treatment systems, dynamic adjustments are needed based on upstream and downstream discharges within a specific industrial park or region. Pre-planning and design cannot meet all requirements, and their operational stability highly depends on the low-fluctuation characteristics of upstream water. Essentially, they passively rely on upstream water quality control (such as adjusting influent flow and pollutant concentration fluctuations) to mitigate influent shocks. This results in water treatment facilities operating under long-term steady-state conditions with low to medium loads and low disturbances to avoid pollution problems caused by inadequate wastewater purification. Further considering actual operating conditions, there are several challenges: first, it is impossible to simulate high-level system operation through sufficient experiments; second, extreme operating conditions occur infrequently in actual industrial scenarios, making it difficult to collect enough data; and third, simulating extreme operating conditions through experiments is costly and may cause irreversible damage to equipment. Existing data augmentation technologies face these difficulties.

[0003] To achieve intelligent control, existing industrial wastewater treatment systems have established various control systems, including the application of artificial intelligence algorithms. However, due to the significant limitations in engineering data acquisition and model training of current anaerobic water treatment facilities, the reliance on front-end influent control has led to skewed distribution and information gaps in engineering data. Conversely, if engineering facilities do not implement strict front-end water supply control, they will find it difficult to stand up to increasingly stringent environmental emission standards. As a result, the system's operational performance analysis is far from sufficient, and it can only be built to high standards with low-load operation as a safety guarantee.

[0004] Furthermore, existing technologies largely focus on optimizing control parameters under steady-state conditions or employ traditional data processing methods such as mathematical modeling, statistical analysis, and neural network training, which have significant limitations. Some studies address anomalous operating conditions, such as attention mechanisms (e.g., Attention-based LSTM), but their core focus is on mitigating the annihilation effect of small-sample anomalous operating condition data being overwhelmed by large-sample steady-state operating condition data, lacking an understanding of out-of-domain (OOD) data. Some studies attempt to use Generative Adversarial Networks (GANs) for data augmentation, which, while effective in filling in missing values, has not yet solved the out-of-domain generalization problem under extreme conditions. Under complex, highly volatile operating conditions, the model's generalization performance still exhibits significant deficiencies. Other data generation methods often lack consideration for physical laws and mechanisms, making it difficult to guarantee the accuracy and rationality of the generated data. This situation creates two major technical bottlenecks:

[0005] 1) Operating condition coverage bias: Compared with the complex and ever-changing water quality characteristics upstream of the industrial park (such as periodic high load shocks and sudden pollutant peaks), the system lacks effective understanding of high load and strong fluctuation extreme operating conditions. The actual data collected is seriously biased towards steady-state scenarios, resulting in "data blind spots".

[0006] 2) Deficiency in model generalization ability: Although the prediction model trained based on existing data has high fitting accuracy under steady-state conditions in the in-domain, when faced with out-of-domain (OOD) conditions, the lack of extreme scenario feature learning significantly weakens the out-of-domain generalization ability, making it difficult to support the system's proactive early warning and control of sudden shocks.

[0007] Therefore, how to improve the predictive robustness and generalization ability under unforeseen operating conditions has become a pressing technical challenge. Summary of the Invention

[0008] Purpose of the invention: This invention aims to provide a data augmentation method and system for industrial wastewater treatment systems based on physical anchoring and GAN algorithms. By combining physical anchoring and GAN algorithms, it addresses the problems of insufficient data and weak data generalization ability in the control analysis and model building of industrial wastewater systems mentioned in the background art.

[0009] Technical solution: A data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithms, comprising the following steps:

[0010] S1. Obtain the operating condition data of the industrial wastewater treatment system under steady-state operation, including a set of key parameters that affect the system's operating indicators based on mechanism analysis and random forest feature importance ranking. The key parameters include at least one of the following: microbial metabolism data, material transformation data, and water quality condition data.

[0011] S2. Observe the data distribution of key parameters. Calculate the mean μ and standard deviation σ of the key parameters using the historical operating data obtained in step S1. Define the extra-domain extension space as μ±kσ (k≥2), where k is dynamically adjusted according to the system fault tolerance threshold.

[0012] S3. A combination of single-factor gradient experiments and multi-factor orthogonal experiments was used to obtain off-site operating data for the industrial wastewater treatment system. Specifically:

[0013] In single-factor gradient experiments, only one key parameter is changed each time, while other parameters are kept at the steady-state level. By setting several gradient values, experiments are conducted to determine the key performance indicators of the industrial wastewater treatment system under different parameter values. Then, parameter-performance curves are plotted to determine the critical value of the parameter's impact on the system.

[0014] Multi-factor orthogonal experiments are conducted on at least two key performance indicators that have a relatively significant impact on the operation of industrial wastewater treatment systems. Three levels of these key performance indicators (low, medium, and high) are selected, and experiments are designed using orthogonal arrays to analyze the impact of the interaction of key performance indicators on the system's operating performance. The combination of key parameters is determined through analysis of variance.

[0015] The combination of key parameters that causes the system’s critical performance indicators to exceed the preset safety threshold will be used as the external data anchor point for the industrial wastewater treatment system.

[0016] In the single-factor gradient experiment, five gradient values ​​were set, with a difference of 0.5σ between adjacent gradients; in the multi-factor orthogonal experiment, the low, medium, and high levels corresponded to μ-1.5σ, μ, and μ+1.5σ, respectively.

[0017] S4. Construct a GAN model based on physical laws and biochemical mechanisms to train the working condition data. This includes labeling the determined anchor point data, encoding the labeled information using One-Hot encoding, and then passing the encoded labeled information as a conditional input to the generative adversarial network for training.

[0018] Physical law constraints refer to the mass conservation relationship in the treatment of this industrial wastewater;

[0019] Biochemical mechanism constraints use the Monod equation to describe microbial growth kinetics combined with a microbial metabolic model. The generated data is used as input to the biochemical mechanism model to simulate the microbial metabolic process, calculate the concentration of key intermediate products and the final performance indicators, and define the metabolic model loss accordingly.

[0020] S5. Augmentation of operating data of industrial wastewater treatment system: Using a trained GAN model and anchor points as guides, a large amount of data simulating extreme and potentially complex operating conditions is generated by adjusting the distribution of random noise vectors while meeting physical and biochemical constraints. Then, guided by anchor points, the distribution of random noise vectors is adjusted to generate simulated data. The data is evaluated and screened from three dimensions: statistical feature similarity, physical mechanism conformity, and model improvement effect, thus achieving secondary data augmentation.

[0021] Statistical feature similarity is assessed using a KL divergence ≤ 0.2; physical mechanism conformity requires a carbon balance residual ≤ 10%; and model improvement requires a predicted R0. 2 Increase ≥0.1.

[0022] Furthermore, the key parameters include the pH value, redox potential, chemical oxygen demand, volatile fatty acid concentration, alkalinity, temperature, carbon-nitrogen ratio, hydraulic retention time, influent flow rate, and total organic load of the industrial wastewater treatment system.

[0023] The mechanistic analysis includes anaerobic digestion mechanism and biological denitrification mechanism;

[0024] The system operation indicators include COD removal rate, effluent compliance rate and / or methane production rate.

[0025] Step S4 includes preprocessing the anchor data before labeling it. The preprocessing includes denoising using a Butterworth filter and standardization.

[0026] Furthermore, in step S4, the GAN model based on physical laws and biochemical mechanisms is a conditional generative adversarial network architecture, and the network structure includes a generator G and a discriminator D.

[0027] Generator G receives random noise vectors and encoded anchor information as inputs, and generates simulated data through multi-layer neural network mapping.

[0028] The discriminator receives real data, generated data, and corresponding anchor point information, and outputs the discrimination result to determine whether the data comes from the real data distribution or the generated data distribution.

[0029] This GAN model is based on traditional adversarial loss, but introduces anchor point constraint loss, physical law constraint loss, and biochemical mechanism model constraint loss to form a comprehensive loss function. The anchor point constraint loss calculates the Euclidean distance between the generated data and the anchor point data in the core parameter space. The physical law constraint loss calculates the sum of squared residuals after substituting the generated data into the mass conservation equation. The biochemical mechanism model constraint loss calculates the sum of squared errors between the measured and calculated values ​​of key performance indicators after substituting the generated data into the biochemical mechanism model.

[0030] Furthermore, the GAN model uses gradient descent to alternately train the generator and discriminator. During the training process, by minimizing the comprehensive loss function L, the data generated by the generator is forced to conform to the real data distribution and move closer to the anchor point, while satisfying the constraints of physical laws and biochemical mechanism models.

[0031] Furthermore, this GAN model, based on traditional adversarial loss, introduces anchor constraint loss L. anchor Physical law constraint loss L physics and biochemical mechanism model constraint loss L biology This forms the comprehensive loss function L:

[0032] L = L adv +λL anchor +γL physics +δL biology

[0033] Where λ, γ, and δ are the non-negative weight coefficients of each loss term determined through cross-validation;

[0034] L adv For traditional adversarial losses, Wasserstein distance is used for calculation:

[0035]

[0036] Anchor point constraint loss L anchor Defined as calculating the Euclidean distance between the generated data and the anchor data in the core parameter space:

[0037]

[0038] Physical law constraint loss L physics It is calculated based on the physical laws of industrial wastewater treatment, and is expressed as:

[0039] This refers to the physical quantities in the industrial wastewater treatment system that conform to the law of conservation of mass. These physical quantities include carbon, nitrogen, phosphorus, and sulfur.

[0040] Biochemical mechanism model constraint loss L biologyThe Monod equation was used to describe microbial growth kinetics, and a biochemical mechanism model was constructed by combining it with a substrate metabolism model.

[0041]

[0042] Where μ is the specific growth rate of microorganisms, μ max The maximum specific growth rate is given by S, where S is the substrate concentration and K is the K value. S K is the half-saturation constant, I is the inhibitor concentration; I This is the inhibition coefficient.

[0043] The generated data is then used as input to a biochemical mechanism model to simulate metabolic processes such as organic matter degradation and microbial growth during microbial treatment. The concentrations of key intermediate products and final performance indicators are calculated, and the metabolic model loss is defined as:

[0044] and The measured and model calculations for the substrate degradation rate / or intermediate product yield of the i-th group of experiments are respectively used.

[0045] The present invention also provides an industrial wastewater treatment data enhancement and intelligent analysis system based on physical anchor points. The system amplifies the system operation data through the above method, and realizes intelligent analysis and actual control of the operation of the industrial wastewater treatment system based on the amplified operation data.

[0046] Furthermore, the system includes:

[0047] The anchor data experimental design module is used to screen key parameters affecting the operating performance of industrial wastewater treatment systems, execute single-factor gradient experiments and multi-factor orthogonal experiments, and determine external data anchor points.

[0048] The data preprocessing module standardizes and One-Hot encodes the data obtained from the anchor data experiment, providing the GAN model with input data that meets the requirements.

[0049] Constrained GAN Model Module: Constructs a conditional generative adversarial network based on physical and biochemical constraints, including a generator and a discriminator. It receives random noise vectors and encoded anchor information, and is trained through a comprehensive loss function to generate simulated data that conforms to physical laws and biochemical mechanisms.

[0050] Data evaluation and screening module: The quality of generated data is evaluated from three dimensions: statistical feature similarity, physical mechanism conformity, and model improvement effect. High-quality generated data is screened out and data that does not meet the requirements is removed.

[0051] Control module: Used to coordinate the workflow of each module, and control the execution order and parameter settings of processes such as anchor point experimental design, data preprocessing, model training, data evaluation and screening.

[0052] This invention also provides a data augmentation method for an industrial wastewater treatment system based on physical anchoring and GAN algorithms. This method obtains out-of-domain operating data of the industrial wastewater treatment system by combining Sobol sequence quasi-Monte Carlo sampling with adaptive response surface guided experiments. Specifically:

[0053] (1) Obtain steady-state operating data of the industrial wastewater treatment system, and determine the key parameter set P = {p1, p2, ..., p} based on mechanism analysis and random forest feature importance ranking. d} and its extended scope R i =[μ i -kσ i ,μ i +kσ i Establish a mapping function from the unit hypercube to the parameter space:

[0054] φ(x) i =L i +x i ×(U i -L i )

[0055] in:

[0056] L i =μ i -kσ i

[0057] U i =μ i +kσ i

[0058] x i ∈[0,1]

[0059] x i Let μ be the unit hypercube coordinate component, and σ be the mean value of parameter P. i For parameter p i Standard deviation, L i U is the lower boundary of parameter P. i Let P be the upper boundary of parameter P, and k be the expansion coefficient;

[0060] (2) Initial sampling and anchor point experiment design: Sobol sequences were used in [0,1] d N low-discrepancy sample points S = {s1, s2, ..., s} are generated spatially. N}, and transform it to the parameter space through the mapping function φ:

[0061] P init ={φ(s1),φ(s2),…,φ(s)} N )}

[0062] For P init Experiments were conducted on sample points to obtain the key performance index Y = {y1,…,y} of the industrial wastewater treatment system. N}, and obtain the experimental dataset.

[0063] (3) Construct a Gaussian process regression model to apply the experimental dataset D obtained from the anchor point experiment in step 2). init Optimization is performed to generate a candidate point set C. The mathematical expression corresponding to the Gaussian process regression model is as follows:

[0064]

[0065] The kernel function is represented as:

[0066]

[0067] The hyperparameter θ = {σ} is optimized by maximizing the log-marginal likelihood. f ,l1,…,l d ,σ n};

[0068] In the formula, x is the input vector [x1, x2, ..., xn]. d ] T , representing the combination of key operating condition parameters, μ(x) is the mean function, taking μ(x) = 0 or a constant, representing the system performance baseline value; in the kernel function k(x,x′), The signal variance represents the system performance vibration amplitude, l i Using length as the scale, the table shows the relevant distances across each parameter dimension. For noise variance, δ represents measurement error and random disturbance; xx′ For Kronecker delta, the correlation between the data points in the table.

[0069] (4) Adaptively select the point set C and complete the anchor point positioning. The specific process is as follows:

[0070] (41) For generating the candidate point set C = {c1, ..., c...} M Calculate the expected improvement function:

[0071]

[0072] in g min =min{y1,…,y N}, where F(·) and φ(·) are the cumulative distribution function and probability density function of the standard normal distribution, respectively;

[0073] (42) Choose EI(c)>θ EI The candidate points were used to perform additional anchor point experiments;

[0074] (43) Mark sample points that meet any of the following conditions as physical anchor points:

[0075]

[0076] in Let H(x) be the response surface gradient, H(x) be the Hessian matrix, and α, β, τ and γ be preset thresholds.

[0077] (5) Output the physical anchor point dataset A = {(a i )∣i=1,…,M}.

[0078] In this invention, the combination of single-factor gradient experiments and multi-factor orthogonal experiments is suitable for low-dimensional parameters, while the Sobol sequence method is suitable for high-dimensional parameters. That is, the Sobol sequence quasi-Monte Carlo sampling and adaptive response surface guided experiment for obtaining out-of-domain data is suitable for out-of-domain data acquisition scenarios with high-dimensional parameters (d≥4). For scenarios with less than 4 dimensions, the data can be obtained through the above-mentioned single-factor gradient experiments and multi-factor orthogonal experiments.

[0079] Beneficial effects: Compared with existing technologies, this invention proposes a data-driven approach for the management and control of industrial wastewater treatment systems. It proposes secondary amplification of industrial wastewater treatment data based on a very small number of anchor points (not exceeding 1% of the original data volume), and combines generative adversarial networks and physical and biochemical constraints to achieve efficient and targeted amplification of industrial wastewater treatment data. This provides high-quality data support for the optimized operation and model training of industrial wastewater treatment systems, and solves the problem of data scarcity under extreme operating conditions.

[0080] The proposed data secondary amplification method and system based on a very small number of anchor points innovatively combines a very small amount of experimental data, generative adversarial networks and physical and biochemical constraints to form a complete technical system. It is not only applicable to the field of industrial wastewater treatment, but can also be extended to other similar industrial scenarios for data amplification needs, and has broad versatility and application prospects. Attached Figure Description

[0081] Figure 1 It is a comparison of the data distribution characteristics before and after data augmentation, where, Figure 1 (a) is a comparison diagram of the kernel density estimation distribution before and after the amplification of wastewater treatment data in the embodiments of the present invention; Figure 1(b) is a kernel density distribution diagram of the data after amplification by a generative adversarial network in an embodiment of the present invention;

[0082] Figure 2 This is a comparison chart of the prediction accuracy of system processing performance before and after data amplification for systems that have not encountered the operating conditions. Figure 2 (a) is a comparison chart of the mean absolute error (MAE) of model prediction before and after data amplification under three specific working conditions in the embodiments of the present invention. Figure 2 (b) is the R-value of the model prediction results before and after data amplification in the embodiments of the present invention. 2 Comparison chart; Figure 2 (c) is a comparison of the predicted results of the model on the stability of the system under the impact of the inhibitor before and after data amplification in the embodiments of the present invention with the actual values;

[0083] Figure 3 is a scatter plot of the distribution of physical anchor points in the five-dimensional parameter space in the embodiment of the present invention; wherein Figure 3(a) shows the distribution of the five physical anchor points in the five-dimensional parameter space consisting of sludge age, microbial specific growth rate, COD degradation rate constant, influent COD concentration, and influent pH value, and Figure 3(b) is a multi-dimensional parameter heat map of the physical anchor points.

[0084] Figure 4 The loss function change curves of the generator and discriminator during the training process of the adversarial network are shown in the embodiments of the present invention. Detailed Implementation

[0085] To provide a detailed description of the technical solution provided by this invention, the following further describes the process of acquiring anchor point data and designing anchor point experiments.

[0086] This invention, based on a physically anchored constraint-based Generative Adversarial Network (GAN), deeply integrates prior physical laws with generative machine learning to systematically supplement virtual data samples for extreme operating conditions. This approach overcomes the shortcomings of traditional methods in utilizing global information and breaks through the limitations of GAN technology in lacking physical constraints. It effectively improves the model's robustness against disturbances and its out-of-domain generalization performance across all operating conditions, providing an innovative solution for the intelligent upgrading of industrial wastewater treatment systems.

[0087] Example 1: The data augmentation method for an industrial wastewater treatment system based on physical anchoring and GAN algorithm provided by this invention mainly includes the following steps:

[0088] Step 1: For different industrial wastewater treatment systems, comprehensively consider the impact and interrelationship of parameters on system performance from the dimensions of microbial metabolism, material transformation, and hydraulic conditions, and screen out the key parameters that affect system operation, such as pH value, oxidation-reduction potential (ORP), chemical oxygen demand (COD), volatile fatty acid (VFA) concentration, alkalinity (Alk), temperature, carbon-nitrogen ratio (C / N), hydraulic retention time (HRT), sludge retention time (SRT), influent flow rate, and hydraulic load.

[0089] The importance score of the parameters is calculated using the random forest algorithm:

[0090]

[0091] Among them, Importance i Let N represent the importance score of the i-th feature, and N be the number of decision trees in the ensemble learning model. trees ∑ nodes (Gain i ×I(node)) represents traversing and summing all nodes of all decision trees in the ensemble model, Gain i I(node) represents the impurity of the parent node minus the sum of the impurities of the child nodes. I(node) is an indicator function. If the node is split using feature i, the function value is 1; otherwise, it is 0.

[0092] This step involves in-depth analysis of the system's historical operating data, calculation of the mean μ and standard deviation σ of each core parameter, and determination of the normal operating range as μ±2σ.

[0093] Specifically, this embodiment analyzes the system's historical operating data from the past two years, calculates the mean and standard deviation of each parameter, and determines the normal operating range. Referring to industry reports and expert opinions, the test ranges for extreme operating parameters are expanded to include, for example, COD concentration test range of 2000-18000 mg / L, and pH value test range of 4-10.

[0094] Step 2: Based on the IWA (International Water Association) technical survey report published in this field and the extreme operating condition parameter fluctuations of similar systems in the same industry, combined with the system equipment tolerance limits (such as reactor pressure resistance value, microbial survival temperature range) and microbial survival conditions (such as pH tolerance range), the normal operating condition range is reasonably expanded to determine the extreme operating condition parameter test range, that is, the extra-domain expansion space is defined as μ±kσ (k≥2), where k is dynamically adjusted according to the system fault tolerance threshold.

[0095] Step 3: Design anchor point experiments to obtain physical anchor point data. In this embodiment 1, a combination of single-factor gradient experiments and multi-factor orthogonal experiments is used. In the single-factor gradient experiment, only one core parameter is changed each time, while other parameters remain at normal operating conditions. Multiple gradient values ​​are set for the experiment, and key performance indicators of the system (such as methane yield, COD removal rate, VFA concentration, etc.) are measured under different parameter values. Parameter-performance curves are plotted to determine the critical value of the parameter's impact on the system. For the multi-factor orthogonal experiment, for multiple parameters with significant effects (such as COD, pH, and temperature), three levels (low, medium, and high) are selected for each parameter. An orthogonal array (such as L9(3)) is used to determine the impact. 3 Experimental combinations were arranged to comprehensively explore the impact of parameter interactions on system performance, and key parameter combinations were determined through analysis of variance. Parameter combinations that significantly worsened key system performance indicators (such as a methane yield decrease exceeding 30% and COD removal rate below 50%) were identified as "outside-domain data" anchor points. The model processed through analysis of variance can be expressed as follows:

[0096] y = μ + α i +β j +γ k +ε ijk

[0097] Where μ is the overall mean, α i β j γ k The effects of factors A, B, and C are respectively, ε ijk This is random error. The sum of squared deviations S for each factor is calculated. A S B S C and mean square MS A The significance of factors was determined using MSB and MSC. Then, the raw experimental data were standardized to eliminate the influence of different parameter dimensions.

[0098] Specifically, in single-factor gradient experiments, five temperature gradients of 20℃, 25℃, 30℃, 35℃, and 40℃ are set for the experiment; multi-factor orthogonal experiments are conducted for three key parameters: COD concentration, pH value, and temperature, using L9(3)2. 3 Nine sets of experiments were arranged using an orthogonal array. Twenty parameter combinations that significantly degraded system performance were identified as "outside-domain data" anchor points, with the amount of data in these 20 sets being far less than 1% of the original in-domain data. For example, one set of anchor point data was: COD = 15000 mg / L, pH = 5, temperature = 40℃, ORP = -300mV, VFA concentration = 1500 mg / L, C / N = 20, HRT = 24h, influent flow rate = 10 m³ / h. 3 / h, hydraulic load = 0.4m 3 / (m2 At this point, the system's methane yield drops to 40% of the normal level, and the COD removal rate drops to 45%.

[0099] Step 4: Construct and train a GAN model based on physical and biochemical constraints to augment the anchor data, including preprocessing and encoding the anchor data.

[0100] Data standardization: The raw anchor data obtained from the experiment were standardized using the Z-score standardization method, with the formula as follows: Where x is the original data, μ is the mean, and σ is the standard deviation, eliminating the influence of different parameter units and making the data comparable.

[0101] One-hot encoding: Defined anchor data is labeled, and the labeled information is transformed using one-hot encoding. Assuming a parameter has m levels, when the parameter is at the k-th level, the encoded vector v is: The encoded information is then passed as conditional input to the subsequent generative adversarial network.

[0102] For example, for three pH levels (5, 7, 9), if the pH value of a certain anchor point is 5, it is encoded as [1,0,0], and the encoded data is passed as a conditional input to the generator of the GAN.

[0103] GAN Model Architecture: The GAN employs a Conditional Generative Adversarial Network (cGAN) architecture, consisting of a generator G and a discriminator D. The generator receives a random noise vector z and encoded anchor information c as input, and generates simulated data through a multi-layer neural network. The discriminator receives real data x and generates data. And the corresponding anchor point information c, output the discrimination result, and determine whether the data comes from the real data distribution or the generated data distribution.

[0104] Loss function design: Based on the traditional GAN ​​adversarial loss, an anchor constraint loss L is introduced. anchor Physical law constraint loss L physics and biochemical mechanism model constraint loss L biology This forms the comprehensive loss function L:

[0105] L = L adv +λL anchor +γL physics +δL biology

[0106] Among them, L adv For traditional adversarial losses, Wasserstein distance is used for calculation:

[0107]

[0108] Anchor point constraint loss L anchor Defined as calculating the Euclidean distance between the generated data and the anchor data in the core parameter space:

[0109]

[0110] Physical law constraint loss L physics It is calculated based on the physical laws of industrial wastewater treatment, and is expressed as:

[0111] This represents the physical quantities that conform to the law of conservation of mass in this industrial wastewater treatment system. These physical quantities include carbon, nitrogen, phosphorus, and sulfur. Calculated based on physical laws in industrial wastewater treatment (such as the law of conservation of mass), taking the conservation of carbon as an example, the residual is:

[0112]

[0113] Biochemical mechanism model constraint loss L biology The Monod equation was used to describe microbial growth kinetics, and a biochemical mechanism model was constructed by combining it with a substrate metabolism model.

[0114]

[0115] Where μ is the specific growth rate of microorganisms, μ max The maximum specific growth rate is given by S, where S is the substrate concentration and K is the K value. S K is the half-saturation constant, I is the inhibitor concentration; I This is the inhibition coefficient.

[0116] The generated data is used as input to a biochemical mechanism model to simulate metabolic processes such as organic matter degradation, microbial growth, and methanogenesis during anaerobic treatment. The concentrations of key intermediate products (e.g., VFA, biomass) and final performance indicators are calculated, and the metabolic model loss is defined.

[0117]

[0118] in, and The measured methane yield and the model-calculated methane yield for the i-th experiment are respectively used. λ, γ, and δ are weighting coefficients. Using a comprehensive loss function and 5-fold cross-validation, with the objective of minimizing the validation set RMSE, a search is performed in the {0.1, 0.2, ..., 1.0} grid, ultimately determining λ = 0.5, γ = 0.3, and δ = 0.2. The generator and discriminator are trained alternately using gradient descent for a total of 10,000 rounds, generating 100 samples per round.

[0119] Carbon balance verification formula for industrial wastewater treatment systems:

[0120] COD 去除 ×η=24×V CH4

[0121] Model training: The generator and discriminator are trained alternately using gradient descent. During the training process, by minimizing the comprehensive loss function L, the data generated by the generator is forced to conform to the real data distribution and move closer to the anchor point, while also satisfying the constraints of physical laws and biochemical mechanism models.

[0122] Step 5: Filter the data obtained in Step 4, i.e., conduct a quality assessment to complete the secondary expansion of the operational data of the industrial wastewater treatment system.

[0123] By using a trained GAN model and anchor points as a guide, and by adjusting the distribution of the random noise vector z, a large amount of data simulating extreme and potentially complex working conditions can be generated under the premise of satisfying physical and biochemical constraints, thereby achieving secondary data augmentation.

[0124] In this embodiment, a trained GAN model is used as a guide to adjust the distribution of random noise vectors using 20 sets of anchor points, generating 10,000 sets of simulated extreme working condition data.

[0125] The quality of the generated data was evaluated from three dimensions: statistical feature similarity, physical mechanism conformity, and model improvement effect. Statistical feature similarity evaluation used metrics such as Kullback-Leibler (KL) divergence and Wasserstein distance to compare the probability distributions of the generated data with those of the real data. Physical mechanism conformity verification checked whether the generated data satisfied physical laws and biochemical mechanism model constraint equations (such as carbon balance relationships and Monod equations). Model improvement effect evaluation mixed the augmented data with the original real data to train industrial wastewater treatment models (such as LSTM and random forests), and compared the performance metrics (such as RMSE and R²) of models trained only with the original data and models trained with the augmented data on a test set. 2 To verify the effectiveness of the data augmentation, high-quality generated data were selected, and data that did not meet the requirements were removed.

[0126] In Example 1, 8500 sets of valid generated data were obtained after screening. Practical application verification showed that the model trained using the data generated by this invention improved the prediction accuracy for extreme operating conditions by 40%, increased the system's methane yield by 25%, and increased the COD removal rate by 20%, effectively improving the operating efficiency and stability of the industrial high-concentration organic wastewater anaerobic methane power generation system.

[0127] Figure 1This paper presents a comparison of the data distribution characteristics before and after augmentation of industrial wastewater treatment data based on the method of this invention. The left side shows the original data distribution under real-world operating conditions, while the right side shows the data distribution after augmentation using a Generative Adversarial Network (GAN) guided by physical anchor points. It is clearly visible that the augmented data, in terms of distribution range and structural characteristics, matches the actual operating conditions of the industrial wastewater treatment system. This demonstrates the advantages of this invention in achieving efficient augmentation with minimal data, combined with the powerful generative capabilities of GANs, to realize large-scale data augmentation, and also provides a foundation for subsequent model training.

[0128] Example 2: Compared with Example 1, this example provides a method for physical anchor point positioning and anchor point data acquisition based on a combination of Sobol sequence quasi-Monte Carlo sampling and adaptive response surface guided experiment.

[0129] S1. Obtain steady-state operating data of a typical industrial wastewater treatment system (treating chemical wastewater containing organic pollutants). Through mechanistic analysis, identify the parameter categories closely related to key performance indicators such as system COD removal rate, methane production, and system stability. Then, use the random forest algorithm to rank the parameters by feature importance, and finally determine the set of key parameters, which specifically includes:

[0130] Microbial metabolic parameters: sludge time (SRT), specific growth rate of microorganisms (μ) max )

[0131] Material transformation parameters: COD degradation rate constant (k COD )

[0132] Dynamic water quality parameters: Influent COD concentration (COD) in ), influent pH value (pH) in )

[0133] S2. Construction of key parameter probability distribution model and determination of extension space.

[0134] For each parameter in the key parameter set, a normal probability distribution model is constructed based on steady-state operating data. The mean μ and standard deviation σ of each parameter are calculated, and the results are shown in Table 1 below. The extra-domain extension space is set to μ±3σ (k is set to 3 according to the fault tolerance threshold of the chemical wastewater treatment system) to cover the range of possible extreme operating parameters.

[0135] Table 1. Mean and Standard Deviation of Key Parameters in the Probability Distribution Model

[0136] parameter mean μ Standard deviation σ Sludge age (d) 15 3 Microbial specific growth rate (d⁻¹) 0.6 0.1 COD degradation rate constant (d⁻¹) 0.8 0.2 Influent COD concentration (mg / L) 3000 500 Inlet water pH 7.0 0.5

[0137] S3. Experimental design and positioning of physical anchor points, including:

[0138] Adaptive response surface guided experiment: A Gaussian process regression model is constructed based on the initial samples. The expected improvement (EI) function is used to dynamically identify the parameter boundary regions that are sensitive to the impact on system performance, and experimental points are added in these regions. Then, the data points that cause the key performance indicators of the system to exceed the preset safety threshold are marked as physical anchor points.

[0139] This step uses quasi-Monte Carlo sampling and adaptive response surface methodology to precisely locate the physical anchor point, specifically:

[0140] S3.1 Parameter Space Definition and Mapping: Based on the key parameter set {SRT, μ max ,k COD COD in pH in} and its extended range (e.g., the sludge age extended range is [15-3×3, 15+3×3]=[6, 24) d (The remaining parameter ranges are calculated similarly), establishing a unit hypercube [0,1). 5 Mapping function to parameter space:

[0141] φ(x) i =L i +x i ×(U i -L i )

[0142] in:

[0143] L i =μ i -kσ i

[0144] U i =μ i +kσ i

[0145] x i ∈[0,1]

[0146] S3.2 Initial Sampling and Experiment Execution: Sobol sequences were used in [0,1] d N low-discrepancy sample points S = {s1, s2, ..., s} are generated spatially. N}, and transform it to the parameter space through the mapping function φ:

[0147] P init ={φ(s1),φ(s2),…,φ(s)} N )}

[0148] For P init Experiments were performed on the sample points in the dataset to obtain the initial experimental sample points {x1, x2, ..., x...}. 50Subsequently, experiments were conducted on industrial wastewater treatment systems based on these sample points, and key performance indicators (COD removal rate, system stability, etc.) of the system corresponding to each sample point were recorded.

[0149] S3.3 Based on Experimental Dataset Constructing a Gaussian process regression model:

[0150]

[0151] The kernel function used is:

[0152]

[0153] The hyperparameter θ = {σ} is optimized by maximizing the log-marginal likelihood. f ,l1,…,l d ,σ n}

[0154] The final optimized hyperparameters are:

[0155] θ length =2.34,θ variance =1.12,θ noise =0.05

[0156] S3.4 Adaptive Sampling and Anchor Point Localization:

[0157] (a) Generate candidate point set C = {c1, ..., c M And calculate the expected improvement function:

[0158]

[0159] in g min =min{y1,…,y N}, where F and φ are the cumulative distribution function and probability density function of the standard normal distribution, respectively;

[0160] Table 2. EI(c) calculation results for some candidate points

[0161] Candidate point number EI(c) 1 0.85 2 0.72 3 0.91 4 0.68 5 0.88

[0162] (b) Select EI(c)>θ EI Additional experiments were performed on the candidate point (numbered 3, EI(c)) to obtain the corresponding key performance indicators of the system.

[0163] (c) Sample points meeting any of the following conditions are marked as physical anchor points: the key performance indicators of the system corresponding to the sample point exceed the preset safety thresholds (COD removal rate safety threshold is 60%, system stability safety threshold is 70%); the sample point is located in a boundary region in the parameter space that is extremely sensitive to the impact on system performance. After screening, 5 physical anchor points were obtained, and their specific information is shown in Table 3 below. The distribution of each anchor point in the parameter space can be visually displayed in Figure 3 (scatter plot of physical anchor point parameter space distribution).

[0164] Table 3. Specific Information on Physical Anchor Points

[0165]

[0166] S3.5 Output Physical Anchoring Dataset: Output a physical anchoring dataset containing anchor point coordinates (specific values ​​of each key parameter) and risk level, as shown in Table 3 above.

[0167] S4. Constraint-based GAN model training

[0168] A generative adversarial network (GAN) model based on physical laws (such as the law of conservation of mass) and biochemical mechanisms (such as microbial metabolic pathways and pollutant degradation kinetics) was constructed for training on operational data. First, the five physical anchor points obtained in step S3 were labeled, with "high risk" labeled as [1,0] and "medium risk" labeled as [0,1]. Then, the labeled information was encoded using One-Hot encoding. This encoded information was then passed as conditional input to the GAN, enabling the model to follow physical laws and biochemical mechanisms during training and generate realistic operational data. During training, the loss function values ​​of the generator and discriminator changed as follows: Figure 4 As shown, after 20,000 training rounds, the loss function tends to stabilize, with the generator loss stabilizing at around 0.3 and the discriminator loss stabilizing at around 0.15, indicating that the model training effect is good.

[0169] S5. Secondary amplification and screening of operating condition data

[0170] Using a pre-trained GAN model and guided by physical anchor points, 2000 data points simulating extreme and potentially complex operating conditions were generated by adjusting the distribution of random noise vectors while satisfying physical and biochemical constraints. The generated data was then evaluated and filtered based on the following three dimensions:

[0171] Statistical Feature Similarity: This calculates the similarity (mean, variance, etc.) between the generated data and real extreme operating condition data (obtained through artificial simulation of extreme operating conditions, totaling 300 data points) on key parameters (such as influent COD concentration, sludge age, etc.) and system performance indicators (COD removal rate, system stability, etc.). The similarity calculation formula is as follows:

[0172] in To generate the mean and variance of the i-th statistical feature of the data, Let n be the mean and variance of the i-th statistical feature of the real data, and n be the number of statistical features. The statistical feature similarity between the generated data and the real data is calculated to be 0.88.

[0173] Physical mechanism compliance: Three experts in the field were organized to evaluate the physical mechanism compliance of the generated data. A 10-point scoring system was used, and the average score was taken. The final score was 8.5 points, indicating that the generated data is in good agreement with the physical laws and biochemical mechanisms of industrial wastewater treatment.

[0174] Model improvement effect: The original steady-state data (500 records) and the amplified data (original steady-state data + filtered data, a total of 1500 records) were used to train the BP neural network model to evaluate the model's predictive performance on COD removal rate and system stability under extreme conditions. The results are shown in Table 4.

[0175] Table 4. Performance evaluation results of the model for predicting COD removal rate and system stability under extreme conditions.

[0176] Data types <![CDATA[COD removal rate prediction R 2 > <![CDATA[Prediction of methane production capacity R 2 > <![CDATA[System stability prediction R 2 > raw steady-state data 0.470 0.499 0.509 Amplified data 0.986 0.963 0.831

[0177] After evaluation and screening through the above three dimensions, 1,000 high-quality augmented datasets were finally obtained, achieving secondary data augmentation.

[0178] Combination Figure 2 As shown, Figure 2 (a) The predictive performance of the model before and after data amplification was compared under three specific operating conditions: high load, inhibitor impact, and water quality fluctuation. Experimental results show that the mean absolute error of the model decreased by 62.4%, 67.2%, and 65.0% for the above three operating conditions, respectively, fully demonstrating the role of the data amplified by the method of this invention in improving the predictive performance of the model under specific operating conditions. Figure 2 (b) Presents the model prediction results before and after data augmentation (R 2 The comparison of data before and after amplification shows the predictive value of COD removal rate. 2 It increased from 0.470 to 0.986. Figure 2(c) Presents the dataset after data augmentation processing using the method of this invention in this experiment, showing the R-value of the model's prediction of the system's methane production capacity. 2 It increased from 0.499 to 0.963; at the same time, Figure 2 (d) shows that the system stability prediction capability is improved from 0.509 to 0.831 in the face of the suppressor impact. The prediction accuracy and system stability of the model are significantly improved, which further verifies the effectiveness of the method of the present invention.

[0179] Figure 3 shows a scatter plot of the spatial distribution of physical anchor point parameters. Figure 3(a) illustrates the projection distribution of the five physical anchor points in a two-dimensional space after dimensionality reduction by PCA principal component analysis of the five-dimensional parameters consisting of sludge age, microbial specific growth rate, COD degradation rate constant, influent COD concentration, and influent pH value. The risk levels of the anchor points are distinguished by color. Figure 3(b) is a heat map of the multidimensional parameters of the physical anchor points, clearly comparing the differences of different anchor points in various key parameters, presenting the characteristics of the anchor points and their potential relationships with other factors (such as risk level).

[0180] Figure 4 These are the loss function curves of the generator and discriminator during the training of the GAN model. The horizontal axis represents the number of training rounds, and the vertical axis represents the loss function value. The generator loss curve and the discriminator loss curve respectively show the loss changes of the two during the training process. Eventually, they tend to stabilize, indicating that the model training has converged.

[0181] This invention achieves large-scale data amplification of industrial wastewater treatment data by driving efficient expansion with minimal data and leveraging the powerful data generation capabilities of generative adversarial networks (GANs). This significantly reduces experimental costs and time, solving the challenge of acquiring data under extreme conditions. Secondly, this invention ensures data authenticity through dual constraints. During data generation, both physical laws and microbial metabolic mechanism models are introduced to provide dual constraints, ensuring that the generated data conforms to actual physical laws and biochemical processes. This effectively improves the engineering applicability and reliability of the data, providing high-quality data support for subsequent model training and system optimization. Thirdly, secondary data amplification guided by anchor points can generate effective data for specific operating conditions (especially extreme and potentially complex conditions), enhancing the data's relevance and effectiveness. This significantly improves the prediction accuracy of industrial wastewater treatment models for extreme conditions and the system's resilience, thereby increasing system operating efficiency and stability.

Claims

1. A data augmentation method for an industrial wastewater treatment system based on physical anchoring and GAN algorithm, characterized in that, Includes the following steps: S1. Obtain the operating condition data of the industrial wastewater treatment system under steady-state operation, including a set of key parameters that affect the system's operating indicators based on mechanism analysis and random forest feature importance ranking. The key parameters include at least one of the following: microbial metabolism data, material transformation data, and water quality condition data. S2. Observe the data distribution of key parameters. Calculate the mean μ and standard deviation σ of the key parameters using the historical operating data obtained in step S1. Define the extra-domain extension space as μ±kσ (k≥2), where k is dynamically adjusted according to the system fault tolerance threshold. The system fault tolerance threshold refers to the requirement that the biochemical reaction indicators of the industrial wastewater treatment meet safety requirements. S3. A combination of single-factor gradient experiments and multi-factor orthogonal experiments was used to obtain key out-of-domain operating condition data for the industrial wastewater treatment system. Specifically: In single-factor gradient experiments, only one key parameter is changed each time, while other parameters are kept at the steady-state level. By setting several gradient values, experiments are conducted to determine the key performance indicators of the industrial wastewater treatment system under different parameter values. Then, parameter-performance curves are plotted to determine the critical value of the parameter's impact on the system. Multi-factor orthogonal experiments are conducted on at least two key performance indicators that have a relatively significant impact on the operation of industrial wastewater treatment systems. Three levels of these key performance indicators (low, medium, and high) are selected, and experiments are designed using orthogonal arrays to analyze the impact of the interaction of key performance indicators on the system's operating performance. The combination of key parameters is determined through analysis of variance. The combination of key parameters that causes the system’s critical performance indicators to exceed the preset safety threshold will be used as the physical anchor point for the off-domain data of the industrial wastewater treatment system. S4. Construct a GAN model based on physical anchor point guidance and physical laws and biochemical mechanisms to train the working condition data. This includes labeling the determined anchor point data, encoding the labeled information using One-Hot encoding, and then passing the encoded labeled information as conditional input to the generative adversarial network for training. Physical law constraints refer to the mass conservation relationship in the treatment of this industrial wastewater; Biochemical mechanism constraints use the Monod equation to describe microbial growth kinetics, combined with a microbial metabolic model, and use the generated data as input to the biochemical mechanism model to simulate the microbial metabolic process, calculate the concentration of key intermediate products and the final performance indicators, and define the metabolic model loss accordingly. S5. Augmentation of operating data of industrial wastewater treatment system: Using a trained GAN model, guided by anchor points, a large amount of data simulating extreme and potentially complex operating conditions is generated by adjusting the distribution of random noise vectors while meeting physical and biochemical constraints. Then, guided by physical anchor points, the distribution of random noise vectors is adjusted to generate simulated data. The data is evaluated and screened from three dimensions: statistical feature similarity, physical mechanism conformity, and model improvement effect, thus achieving secondary data augmentation.

2. The data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithm according to claim 1, characterized in that, The key parameters mentioned include the pH value, oxidation-reduction potential, chemical oxygen demand, volatile fatty acid concentration, alkalinity, temperature, carbon-nitrogen ratio, hydraulic retention time, influent flow rate, and total organic load of the industrial wastewater treatment system. The mechanistic analysis includes anaerobic digestion mechanism and biological denitrification mechanism; The system operation indicators include COD removal rate, effluent compliance rate and / or methane yield.

3. The data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithm according to claim 1, characterized in that, Step S4 includes preprocessing the anchor data before labeling it. The preprocessing includes noise reduction using a Butterworth filter and normalization.

4. The data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithm according to claim 1, characterized in that, Step S4 is based on a GAN model guided by physical anchor points and constrained by physical laws and biochemical mechanisms as a conditional generative adversarial network architecture. The network structure includes a generator G and a discriminator D. Generator G receives random noise vectors and encoded anchor information as inputs, and generates simulated data through multi-layer neural network mapping. Discriminator D receives real data, generated data, and corresponding anchor point information, and outputs the discrimination result to determine whether the data comes from the real data distribution or the generated data distribution. This GAN model is based on traditional adversarial loss, but introduces physical anchor point constraint loss, physical law constraint loss, and biochemical mechanism model constraint loss to construct a comprehensive loss function. The physical anchor point constraint loss calculates the Euclidean distance between the generated data and the anchor point data in the core parameter space; the physical law constraint loss calculates the sum of squared residuals after substituting the generated data into the mass conservation equation; and the biochemical mechanism model constraint loss calculates the sum of squared errors between the measured and calculated values ​​of key performance indicators after substituting the generated data into the biochemical mechanism model.

5. The data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithm according to claim 1 or 4, characterized in that, The GAN model uses gradient descent to train the generator and discriminator alternately. During the training process, by minimizing the comprehensive loss function L, the data generated by the generator is forced to conform to the real data distribution and move closer to the anchor point, while satisfying the constraints of physical laws and biochemical mechanism models.

6. The data augmentation method for industrial wastewater treatment systems based on physical anchoring and GAN algorithm according to claim 1 or 4, characterized in that, This GAN model is based on traditional adversarial loss and introduces anchor constraint loss L. anchor Physical law constraint loss L physics and biochemical mechanism model constraint loss L biology This forms the comprehensive loss function L: L=L adv +λL anchor +γL physics +δL biology Among them, L adv The traditional adversarial loss is calculated using Wasserstein distance, and the anchor point constraint loss L is... anchor Define the Euclidean distance between the generated data and the anchor data in the core parameter space; physical law constraint loss L physics It is based on the physical laws in industrial wastewater treatment and considers the physical quantities in the industrial wastewater treatment system that conform to the law of conservation of mass. These physical quantities include the input-output-biological transformation balance of carbon, nitrogen, phosphorus, and sulfur elements. Biochemical mechanism model constraint loss L biology The Monod equation is used to describe microbial growth kinetics, and a biochemical mechanism model is constructed by combining it with a microbial metabolic model. Its expression is as follows: Where μ is the specific growth rate of microorganisms, μ max The maximum specific growth rate is given by S, where S is the substrate concentration and K is the K value. S K is the half-saturation constant, I is the inhibitor concentration; I The inhibition coefficient; The generated data is then used as input to a biochemical mechanism model to simulate metabolic processes such as organic matter degradation and microbial growth during microbial treatment. The concentrations of key intermediate products and final performance indicators are calculated, and the metabolic model loss is defined as: in, and The measured and model-calculated substrate degradation rate / or intermediate product yield of the i-th experiment are respectively, and λ, γ, and δ are the non-negative weight coefficients of each loss term determined by cross-validation, and the optimal values ​​are determined by cross-validation.

7. A data augmentation and intelligent analysis system for industrial wastewater treatment based on physical anchor points, characterized in that, The system uses the method described in any one of claims 1-6 to amplify the system operating condition data, and uses the amplified operating condition data to achieve intelligent analysis and actual control of the operation of the industrial wastewater treatment system.

8. The data augmentation and intelligent analysis system for industrial wastewater treatment based on physical anchor points as described in claim 7, characterized in that, The system includes: The anchor data experimental design module is used to screen key parameters affecting the operating performance of industrial wastewater treatment systems, execute single-factor gradient experiments and multi-factor orthogonal experiments, and determine external data anchor points. The data preprocessing module standardizes and One-Hot encodes the data obtained from the anchor data experiment to provide the GAN model with input data that meets the requirements. Constrained GAN Model Module: Constructs a conditional generative adversarial network based on physical and biochemical constraints, including a generator and a discriminator. It receives random noise vectors and encoded anchor information, and is trained through a comprehensive loss function to generate simulated data that conforms to physical laws and biochemical mechanisms. Data evaluation and screening module: The quality of generated data is evaluated from three dimensions: statistical feature similarity, physical mechanism conformity, and model improvement effect. High-quality generated data is screened out and data that does not meet the requirements is removed. Control module: Used to coordinate the workflow of each module, and control the execution order and parameter settings of processes such as anchor point experimental design, data preprocessing, model training, data evaluation and screening.

9. A data augmentation method for an industrial wastewater treatment system based on physical anchoring and GAN algorithm, characterized in that, This method obtains out-of-domain operating data of the industrial wastewater treatment system by combining Sobol sequence quasi-Monte Carlo sampling with adaptive response surface guided experiments. Specifically: (1) Obtain steady-state operating data of the industrial wastewater treatment system, and determine the key parameter set P = {p1, p2, ..., p} based on mechanism analysis and random forest feature importance ranking. d } and extended range R i =[μ i -kσ i ,μ i +kσ i Establish a mapping function from the unit hypercube to the parameter space: φ(x) i =L i +x i ×(U i -L i ) in: L i =μ i -kσ i U i =μ i +kσ i x i ∈[0,1] x i Let μ be the unit hypercube coordinate component, and σ be the mean value of parameter P. i For parameter p i Standard deviation, L i U is the lower boundary of parameter P. i Let P be the upper boundary of parameter P, and k be the expansion coefficient; (2) Initial sampling and anchor point experiment design: Sobol sequences were used in [0,1] d N low-discrepancy sample points S = {s1, s2, ..., s} are generated spatially. N }, and transform it to the parameter space through the mapping function φ: P init ={φ(s1),φ(s2),…,φ(s N )} For P init Experiments were conducted on sample points to obtain the key performance index Y = {y1,…,y} of the industrial wastewater treatment system. N }, and obtain the experimental dataset. (3) Construct a Gaussian process regression model to apply the experimental dataset D obtained from the anchor point experiment in step 2). init Optimization is performed to generate a candidate point set C. The mathematical representation of the Gaussian process regression model is as follows: The kernel function is represented as: The hyperparameter θ = {σ} is optimized by maximizing the log-marginal likelihood. f ,l1,…,l d ,σ N }; In the formula, x is the input vector [x1, x2, ..., xn]. d ] T , representing the combination of key operating condition parameters, μ(x) is the mean function, taking μ(x) = 0 or a constant, representing the system performance baseline value; in the kernel function k(x,x′), The signal variance represents the system performance vibration amplitude, l i Using length as the scale, the table shows the relevant distances across each parameter dimension. For noise variance, δ represents measurement error and random disturbance; xx′ For Kronecker delta, the correlation between the data points in the table. (4) Adaptively select the candidate point set C and complete the anchor point location. The specific process is as follows: (41) For generating the candidate point set C = {c1, ..., c...} M Calculate the expected improvement function: in g min =min{y1,…,y N }, where F(·) and φ(·) are the cumulative distribution function and probability density function of the standard normal distribution, respectively; (42) Choose EI(C)>θ EI The candidate points were used to perform additional anchor point experiments; (43) Mark sample points that meet any of the following conditions as physical anchor points: in Let H(x) be the response surface gradient, H(x) be the Hessian matrix, and α, β, τ and γ be preset thresholds. (5) Output the physical anchor point dataset A = {(a i )∣i=1,…,M}.

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