A sewage dosing prediction method based on fisher information matrix residual compensation and block incremental deep SCN

Abstract

The present application relates to the field of sewage dosing prediction, and discloses a sewage dosing prediction method based on fisher information matrix residual compensation and block incremental deep SCN, obtains historical water quality data and reagent dosing quantity data of a sewage treatment plant, constructs a prediction model training set and a test set, constructs an initial deep random configuration network DeepSCN structure, and generates hidden layer nodes by using a block incremental deep modeling mechanism; the quality and redundancy of nodes are evaluated by using FIM, the output layer weight of the block incremental DeepSCN is solved, and the prediction residual between the output value of the main prediction model and the real reagent dosing quantity is calculated. A residual sensitivity matrix is constructed based on FIM, high information contribution features are screened to form a compensation feature matrix, the compensation weight is solved by using a generalized inverse, and the residual compensation output is obtained; the main model prediction value is obtained, the FIM residual linear compensation output is superimposed, and the final reagent dosing quantity prediction value is obtained. The present application realizes further fine dosing of drugs in the sewage treatment process.

Description

Technical Field

[0001] This invention relates to the field of wastewater dosing prediction, specifically to a wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN. Background Technology

[0002] In modern wastewater treatment, precise chemical dosing is crucial for ensuring effluent quality meets standards and controlling operating costs. Wastewater quality data is characterized by strong nonlinearity, high latency, multivariate coupling, and susceptibility to noise interference from sensor malfunctions and extreme weather. Traditional mechanistic models and linear regression methods struggle to achieve high-precision chemical dosage prediction. Currently, data-driven machine learning and neural network models are widely used for process parameter prediction and optimization. Deep stochastic allocation networks (DEEPSCNs), compared to traditional backpropagation networks, eliminate the need for cumbersome gradient updates, offering advantages such as faster modeling speed and less susceptibility to local optima. However, conventional DEEPSCNs, using a point-incremental approach, have limitations when applied to high-dimensional, massive, and nonlinear industrial water quality data. Furthermore, existing stochastic allocation mechanisms lack prior assessment of node quality, leading to redundant data and interference with prediction results. In wastewater treatment, errors caused by sensor drift, sudden water quality changes, process lags, and variable coupling cannot be completely eliminated by the nonlinear master model; residual linear components related to input features or hidden layer outputs may still exist in the residuals. Therefore, there is an urgent need for a neural network configuration that can adapt to the prediction of wastewater quality and drug dosage, so as to achieve further refined drug dosage in the wastewater treatment process. Summary of the Invention

[0003] Purpose of the invention: To address the problems mentioned in the background art, this invention discloses a wastewater chemical dosing prediction method based on Fisher Information Matrix Residual Compensation and Block Increment Depth (SCN). DeepBSCN is used as the master prediction model to learn the nonlinear mapping relationship between wastewater quality variables and PAC dosage. FIM is used to simultaneously complete candidate node information screening and master model residual sensitivity analysis, thereby achieving accurate wastewater chemical dosing prediction.

[0004] Technical solution:

[0005] This invention discloses a wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN. The method steps are as follows:

[0006] S1 acquires historical water quality data and reagent dosage data from the wastewater treatment plant, preprocesses the data, and constructs a training set and a test set for the prediction model.

[0007] S2 constructs an initial DeepSCN network structure with randomized depth configuration and uses a block incremental depth modeling mechanism to generate hidden layer nodes;

[0008] S3 uses FIM to evaluate node quality and redundancy, retains the best node with the largest FIM value and updates the node block, and performs convergence inequality constraint verification on the updated node block.

[0009] S4 solves the output layer weights of the block increment DeepSCN to obtain the master prediction model, and calculates the prediction residual between the output value of the master prediction model and the actual drug dosage.

[0010] S5 constructs a residual sensitivity matrix based on FIM, selects high-information-contribution features to form a compensation feature matrix, and uses the generalized inverse to solve the compensation weights to obtain the residual compensation output.

[0011] S6 inputs the real-time collected wastewater quality characteristics into the DeepBSCN master prediction model after equal preprocessing, obtains the master model prediction value, superimposes the FIM residual linear compensation output, and obtains the final reagent dosage prediction value. The output reagent dosage calibration term is then introduced to obtain the fused prediction value.

[0012] Furthermore, the S1 preprocessing steps are as follows:

[0013] A three-level wavelet reconstruction was performed on the original water quality data using a multi-resolution analysis wavelet thresholding denoising algorithm based on wavelet basis functions. The soft thresholding function processing mechanism decomposed the original signal into low-frequency approximation coefficients and high-frequency detail coefficients, calculated the optimal threshold, and set the wavelet coefficients to zero when the absolute value of the wavelet coefficients was less than the threshold; when the absolute value was greater than the threshold, the coefficients were contracted to zero. After preserving the signal abrupt change characteristics, an inverse transform was performed to reconstruct the pure signal. Pearson correlation analysis was used to calculate the correlation coefficients between each auxiliary indicator and the dosage of the reagents, and features with severe linearity and collinearity were removed. The core characteristic input variables of influent suspended solids, total influent instantaneous flow rate, influent total nitrogen, and effluent pH were retained.

[0014] Furthermore, the block incremental depth modeling mechanism described in S2 is specifically as follows:

[0015] In a single iteration, the system randomly generates a block of nodes containing multiple nodes in batches within a specified spanning space, and calculates the corresponding hidden layer output block and residual block.

[0016] No. During the nth iteration The output weight blocks of each hidden layer are :

[0017]

[0018] in, and They represent the first The corresponding hidden layer output block and residual block in the next iteration. Representing the Moore-Penrose generalized inverse matrix, the network increases the number of hidden layer nodes (node ​​blocks) in each iteration by adding hidden layer nodes in blocks. Each node is updated using a block update formula. Calculate the current residual.

[0019] Furthermore, S3 uses FIM to evaluate node quality and redundancy. The node evaluation rules are as follows:

[0020] For candidate nodes generated by the hidden layer, calculate their Fisher Information Matrix (FIM):

[0021]

[0022] By analyzing the model output for unknown parameters The differential response is used to calculate the information content of nodes. After configuring the node pool, the nodes with the highest sum of elements in the FIM are retained. In each iteration, the nodes in the node block are ensured to be the best hidden layer nodes. After the main prediction model is trained, the Fisher Information Matrix (FIM) is extended for the evaluation of prediction residual sensitivity. Let the training residual of the main model be... The candidate residual compensation feature matrix is Then the first The residual information score of each compensated feature is defined as:

[0023]

[0024] in, Indicates the first The compensation feature is in the first The values ​​taken on each sample This represents the master model prediction residual for the corresponding sample. The larger the value, the higher the sensitivity of the feature to the residuals of the master model, and the more suitable it is as a feature for linear compensation of residuals.

[0025] Furthermore, S3 performs convergence inequality constraint checks on the updated node blocks. The specific check criteria are as follows:

[0026] In the Hidden node blocks randomly configured within a hidden layer satisfy the following convergence inequality condition:

[0027]

[0028] in, Representing vectors and The inner product between For the first in the network The state vector of the layer, For the first The relevant vector of the layer, Represents a scalar constant. It is a scalar parameter.

[0029] Furthermore, S4 solves for the output layer weights and global network update of the fast incremental DeepBSCN, with the following specific rules:

[0030] After a node block is successfully incorporated into the network, the output layer weight vector under the new network structure is calculated. To minimize the approximation error, a one-step solution is used, combining the least squares method with the Moore-Penrose generalized inverse matrix, to minimize the approximation error objective function. The output weights are obtained by solving, where Output matrix of the current network hidden layer Moore-Penrose generalized inverse matrix, The target prediction vector; after obtaining the output layer weights, according to the formula... Update global network residuals Then, a termination condition is determined, namely, the current network residual norm is calculated and determined. Is it less than the set tolerance error? Or the current total number of hidden layers Has the maximum number of floors been reached? If satisfied or If any termination condition is met, training stops and the final DeepBSCN prediction model is output; if the above condition is not met, the process returns to S2 to continue iterating and randomly assigning parameters for the block incremental hidden layer.

[0031] Furthermore, S5 calculates the prediction residual vector on the training set; constructs a candidate compensation feature matrix containing core water quality variables, hidden layer node outputs, and operating condition characteristics; and uses the Fisher information matrix to evaluate the residual information contribution of each feature, eliminates low-contribution and redundant variables, and obtains the residual compensation feature matrix. Using the training residual of the DeepBSCN master prediction model as the fitting target, the compensation weights are solved by generalized inverse to obtain the residual compensation output.

[0032] Furthermore, S6 inputs the real-time collected wastewater quality characteristics into the trained DeepBSCN master prediction model after undergoing the same preprocessing to obtain the master model's predicted values. Then, the FIM residual compensation output is superimposed to obtain the final predicted value of the reagent dosage:

[0033]

[0034] Introduce an output calibration term based on the dosage of the agent at the previous sampling time, and assume that the predicted value after residual compensation is The PAC dosage at the previous sampling time was The fusion prediction value is:

[0035]

[0036] The linear calibration form is as follows:

[0037]

[0038] in, The historical continuous fusion coefficient is added, and its value is determined by the validation set.

[0039] Beneficial effects:

[0040] 1. Compared to traditional single-point incremental SCN, this invention employs deep block incremental technology, reducing the number of iterations from thousands to a fraction of the usual number. This reduces the time overhead caused by frequent pseudo-inverse calculations, further improving the online update and prediction efficiency of soft-sensor modeling for wastewater treatment.

[0041] 2. This invention, DeepSCN, combines the Fisher Information Matrix (FIM) selection mechanism to implement a merit-based selection process while generating block nodes. The model automatically filters out redundant neurons that contribute little to the reduction of prediction residuals, further curbing overfitting and the curse of dimensionality that deep networks are prone to fall into, and improving the model's generalization ability.

[0042] 3. This invention combines customized wavelet threshold denoising and feature variable dimensionality reduction to filter out instantaneous electromagnetic interference during sensor acquisition, retain key influencing factors with clear physical meaning, and purify input layer features. Compared with existing traditional methods such as the Model Tree Algorithm M5P, it significantly reduces the root mean square error (RMSE) of the dosing prediction output to below 0.066 and the mean absolute error (MAE) to around 0.043, further improving the reliability and error control accuracy of the prediction model in actual wastewater dosing prediction.

[0043] 4. After the DeepBSCN master prediction model completes nonlinear mapping learning, this invention further utilizes FIM (Fisher Information Modeling) to perform sensitivity analysis on the master model's prediction residuals, screening out high-contribution features in the residuals that still possess linear interpretability, and establishing a linear compensation term for the residuals. Compared to ordinary residual compensation, the FIM residual compensation of this invention uses the Fisher Information Matrix to calculate the sensitivity and information contribution of candidate residual compensation features to the master model residuals, and then screens high-contribution features to construct the compensation matrix. This corrects for systematic biases that are difficult for the master model to fit perfectly, improving the final prediction result from the master model output to the master model output plus residual compensation output, further reducing the prediction error of the reagent dosage, and improving the generalization ability and engineering stability under complex working conditions. Attached Figure Description

[0044] Figure 1This is a flowchart of the method of the present invention;

[0045] Figure 2 This is a graph showing the final prediction and fitting results of an embodiment of the present invention;

[0046] Figure 3 This is a comparison of the predicted residuals before and after FIM residual compensation in an embodiment of the present invention;

[0047] Figure 4 This is a comparison chart of the prediction performance of different prediction models for PAC agent dosage in embodiments of the present invention. Detailed Implementation

[0048] 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. 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.

[0049] like Figure 1 As shown, this invention discloses a wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN, the steps of which are as follows:

[0050] Step 1: Collect key water quality variables and reagent dosages during the wastewater treatment process using a sensor array to generate an initial sample set. To eliminate high-frequency noise and variable collinearity, the data is processed as follows:

[0051] (1) Outlier handling:

[0052] For the Calculate the sample mean from the observed data. with standard deviation ,use Criteria for removing outlier data:

[0053]

[0054] when When the error is large, the sample is considered to be abnormally large and is removed. The weighted average of the data at adjacent time points is then used for interpolation.

[0055] (2) Wavelet thresholding for noise reduction:

[0056] A multi-resolution analysis method is employed, utilizing wavelet basis functions to analyze time series data. Decompose the data and extract detail coefficients containing high-frequency noise. Introducing a universal threshold for VisuShrink Denoising is performed using a soft threshold shrinkage function:

[0057]

[0058]

[0059] (3) Feature dimensionality reduction:

[0060] For the preprocessed multidimensional feature set, the input features are calculated using the Pearson correlation coefficient. With the dosage of the agent Linear correlation between them:

[0061]

[0062] Select Variables with a correlation coefficient greater than a preset threshold are used as core input features, and redundant variables are removed.

[0063] Step 2: Initialize the DeepBSCN parameters for the block incremental depth randomization network.

[0064] Construct a multi-input, single-output prediction model. Given the input data processed in step 1... Group training samples ,in. , .

[0065] Set the initial network parameters, including: maximum number of hidden layers. , No. Maximum number of nodes in each hidden layer Target tolerance error The number of nodes contained in the newly added node block in each iteration That is, BlockSize, and the non-negative decreasing sequence of real numbers. Initialize the current network residual. Hidden index .

[0066] Step 3: Generation of hidden layer node matrix based on the evolution mechanism from single-point to block incremental DeepSCN to DeepBSCN

[0067] Compared to the traditional single-point incremental mode, this embodiment extends the node generation mechanism of the randomly configured network from a one-dimensional vector space to a multi-dimensional matrix spanned space, realizing deep block incremental modeling. The specific progression and derivation process is as follows.

[0068] (1) Mathematical limitations of the traditional DeepSCN single-point incremental mechanism: In the traditional DeepSCN, the network structure grows node by node. Assume the current network is at the... In the nth iteration, the residual vector is In generating the first When there are hidden layer nodes, the system randomly assigns a set of input weight vectors within a preset tensor interval. and bias Calculate its activation output To ensure network convergence, the single node must satisfy the strict point increment inner product inequality constraint:

[0069]

[0070] in, To control the convergence parameters, once a node satisfies the constraints, the output weight of that node is calculated separately using the pseudo-inverse matrix. The fatal flaw of this single-point incremental approach is that for massive industrial data, each additional node requires recalculating the global generalized inverse matrix Moore-Penrose Inverse, causing the computational complexity to explode exponentially with the number of nodes, and the contribution of a single point to the reduction of global error is extremely low in the later stages.

[0071] (2) Progression and Derivation of the DeepBSCN Incremental Mechanism: To overcome the aforementioned computational bottleneck, this embodiment extends the supervised optimization of one-dimensional nodes to the multi-dimensional matrix block space, proposing the DeepBSCN incremental mechanism. In a single iteration, the system no longer generates individual nodes, but rather nodes within a preset scale tensor interval. Within, a batch and parallel random generation of a set containing The parameter matrix of the nth node is the node block. Let the nth node be... The size of the newly added node block in the next iteration is The batch-generated input weight matrix is ​​then represented as: The bias vector is For the input training sample set The multidimensional activation output matrix corresponding to this node block for:

[0072]

[0073] in, The selected asymmetric Gaussian or Sigmoid activation function.

[0074] (3) Generalized convergence constraints of the block increment space, since the node representation is a vector leap to matrix Traditional single-point inner product inequalities are no longer applicable. This embodiment upgrades the convergence monitoring mechanism to block-level inequality constraints by introducing the Frobenius norm and trace operation. To ensure that the node blocks... The entire network is integrated and global residuals are ensured. For a node matrix to be strictly monotonically decreasing, it must satisfy the following generalized block convergence inequality within the spanned space:

[0075]

[0076] The equivalent expansion is in the form of the sum of squares of the inner products of all nodes within the block:

[0077]

[0078] Only when the entire candidate node block Only when the output span of the space satisfies the aforementioned expectation of multidimensional error reduction, is the block qualified to become the current hidden layer. This mechanism has been mathematically proven to be effective; adding neurons in the form of matrix blocks not only maintains the original universal approximation property of DeepSCN but also reduces the frequency of solving the pseudo-inverse matrix to a fraction of its original value. This allows for an order-of-magnitude leap in model training speed.

[0079] Step 4: Node swarm evaluation and optimal purification based on Fisher Information Matrix (FIM)

[0080] To eliminate information redundancy caused by batch node generation, this embodiment introduces the Fisher Information Matrix (FIM) theory to perform prior quality assessment on the nodes in the generated candidate node blocks. The Fisher Information Matrix measures the expected amount of information about unknown parameters carried by a random variable. In neural network modeling, if the network output is regarded as an estimate of the probability distribution of the target variable, then FIM can accurately evaluate the influence and sensitivity of hidden layer node parameters on the output distribution characteristics.

[0081] (1) Define the probability distribution model of the network output. ,in For node parameters. The Fisher information content corresponding to each node is defined as the expectation of the second moment of the log-likelihood gradient of that parameter:

[0082]

[0083] Equivalently, it can also be expressed as the negative expectation of the second derivative:

[0084]

[0085] (2) Considering the single-output regression prediction task in this embodiment, assume the network output is ,in The hidden layer output vector. These are the output layer weights. For the ... There are candidate nodes, and their output is: Within the framework of the mean squared error loss function, it can be approximately assumed that the model output follows a Gaussian distribution. At this point, the log-likelihood function is expressed as:

[0086]

[0087] Key parameters of this node Taking the partial derivative, we get:

[0088]

[0089] Therefore, the first The empirical Fisher information for each node is approximated as follows:

[0090]

[0091] In each iteration of the actual block increment construction, the constant term and residual sign are ignored, and the information score of the node on the training set is directly calculated. :

[0092]

[0093] in, For the first The node at the th Activation output on each sample This represents the prediction residual of the current network on the corresponding sample. The larger the value, the stronger the correlation between the node's output and the current residual. In other words, the smaller the perturbation of the node's parameters, the more significant the impact on the overall output distribution information, and the more information it carries that can effectively reduce prediction errors.

[0094] (3) All candidate blocks Nodes The values ​​are calculated and sorted in descending order, retaining only the top scores. Nodes This forms the simplified and optimized optimal hidden layer output submatrix. This operation utilizes strict information theory principles to eliminate redundant nodes, ensuring that each node block added in each iteration has the highest information contribution, thereby compressing the network size while maintaining information content. In this embodiment, FIM is not only used for information filtering of candidate nodes in the hidden layer, but also further used for residual sensitivity analysis after the master prediction model is trained. For residuals that the DeepBSCN master prediction model cannot explain... In this embodiment, a candidate residual compensation feature matrix is ​​constructed. The Fisher information contribution of each compensation feature is calculated using a residual squared weighted method:

[0095]

[0096] according to After sorting from largest to smallest, features contributing high residual information are retained, forming... This matrix is ​​used to characterize the remaining components of the main predictive model error that still have linear interpretability, rather than treating the FIM itself as a separate predictor.

[0097] Step 5: Inequality constraint verification of the block incremental supervision mechanism

[0098] For the purified node blocks Implement a monitoring mechanism. The selected node block must satisfy the convergence inequality condition that maximizes the decrease of the current prediction residual.

[0099] Define the current network residual as Introduce the inner product inequality in the spanned space:

[0100]

[0101] If the currently generated node block satisfies the above inequality, then the node block is allowed to be merged into the network's first node. If a hidden layer is not found, step 3 is repeated to generate new node blocks until a valid node block is found. This mechanism mathematically guarantees that as hidden layer node blocks are added, the network residual... It decreases monotonically and tends to 0.

[0102] Step 6: DeepBSCN Master Prediction Model Training and Master Model Residual Acquisition. After the node blocks are successfully incorporated into the network, the output layer weights are solved using the least squares method combined with the Moore-Penrose generalized inverse matrix to obtain the current network output:

[0103]

[0104] Calculate the training residuals of the main model:

[0105]

[0106] When the residual norm is less than the set tolerance error or the total number of hidden layers reaches the set maximum number of layers, the DeepBSCN main model training is stopped, and the main model parameters and training residuals are saved.

[0107] Step 7: Constructing the DeepBSCN master prediction model based on the Fisher information matrix residual sensitivity analysis and residual linear compensation. After training, the master model prediction output is first calculated using the training set samples:

[0108]

[0109] in, This represents the hidden layer output matrix formed after block increment and FIM node filtering. This represents the output layer weight matrix of the main prediction model. Subsequently, based on the actual drug dosage... Compared with the main model's predicted output The difference between them is used to calculate the residual vector of the master model:

[0110]

[0111] The residual This represents the prediction error that the DeepBSCN master model still cannot explain after completing the nonlinear mapping learning. Unlike ordinary residual compensation methods that simply fit the residual as a whole error sequence, this embodiment further utilizes the Fisher Information Matrix (FIM) to analyze the contribution of information contained within the residual, determining which parts of the residual still have stable correlations with input water quality variables, hidden layer node outputs, or operating condition changes. This transforms ordinary residuals into residual compensation objects with sensitivity ranking and information filtering capabilities. Specifically, a candidate residual compensation feature matrix is ​​constructed:

[0112]

[0113] in, Indicates the first The candidate residual compensation features include: pre-processed core water quality input variables, hidden layer node outputs after FIM screening, operating condition characteristics related to water volume fluctuations, sudden changes in water quality, sensor drift, and process lag, and residual sensitivity derived features obtained by combining the above variables. For the first... Candidate compensation features Calculate its contribution to the Fisher residual information of the master model residuals:

[0114]

[0115] in, The number of training samples. Indicates the first The compensation feature is in the first The values ​​taken on each sample Indicates the first The master model prediction residuals for each sample. The larger the value, the stronger the coupling between the compensation feature and the main model residuals, the higher its sensitivity to residual changes, and the more suitable it is for constructing residual compensation terms. Subsequently, for all candidate compensation features... The features are sorted in descending order, and variables with low residual information contribution, strong noise correlation, or high redundancy with other compensation features are removed. Only the top-ranked features with high residual information contribution are retained to form the FIM residual compensation feature matrix:

[0116]

[0117] in, , These are high-contribution compensation features obtained through FIM residual sensitivity screening. This screening process ensures that residual compensation no longer relies on all original variables or all hidden layer outputs, but only compensates for the most informative part of the unexplained error of the main model, thus avoiding noise amplification and overfitting problems that are prone to occur in ordinary residual compensation. Then, the residuals of the master model were used. To fit the target, the least squares method combined with the Moore-Penrose generalized inverse matrix is ​​used to solve for the residual linear compensation weights:

[0118]

[0119] in, The Moore-Penrose generalized inverse matrix represents the characteristic matrix of the FIM residual compensation. This represents the residual linear compensation weight. The FIM residual compensation output is obtained from this:

[0120]

[0121] Finally, the output of the DeepBSCN master prediction model is superimposed with the FIM residual compensation output to obtain the compensated drug dosage prediction result:

[0122]

[0123] Through the above process, this embodiment utilizes FIM to characterize the information content of the residuals, screen sensitive features, and extract linearly interpretable components, thus providing a clear information theory basis for residual compensation. This mechanism can effectively correct the systematic bias of the DeepBSCN master model, which is difficult to fully fit under complex wastewater conditions, and improve the accuracy, stability, and generalization ability of chemical dosing prediction.

[0124] Step 8: Input the real-time collected wastewater quality characteristics into the trained DeepBSCN master prediction model after equivalent preprocessing to obtain the master model's predicted values. Then, by superimposing the FIM residual linear compensation output, the final predicted value of the drug dosage is obtained:

[0125]

[0126] It also outputs the optimal PAC dosage required for the current wastewater treatment. Furthermore, to accommodate the temporal continuity of the wastewater treatment dosing process, after obtaining the FIM residual compensation predicted value, an output calibration term based on the PAC dosage at the previous sampling time can be introduced. Let the predicted value after residual compensation be... The PAC dosage at the previous sampling time was The fusion prediction value is:

[0127]

[0128] in, A continuous fusion coefficient is added to the historical data, and its value is determined by the validation set. Furthermore, a linear calibration method can be used:

[0129]

[0130] And adopt RMSE, MAE, Evaluation of model performance using indicators

[0131]

[0132]

[0133]

[0134] The technical solution of this invention will be further described in detail below, taking into account the PAC dosage scenario in a wastewater treatment plant. The steps are as follows:

[0135] Step 1: Wastewater process data acquisition and multi-stage pretreatment. The system collects influent water quality and biological treatment tank parameters through an industrial sensor array. Due to sudden changes in rainfall or sensor malfunctions, the raw data inevitably contains noise and anomalies.

[0136] (1) Handling missing and outlier values: Use the weighted average method to fill in the breakpoints, through... Guidelines Data with large deviations that exceed reasonable physical boundaries are removed.

[0137] (2) Multi-resolution wavelet denoising: The Symlets8 wavelet basis is used to perform three-level decomposition on high-frequency sequences with drastic fluctuations such as flow rate and redox potential. The optimal threshold is estimated by Bayesian method to filter high-frequency detail coefficients and then reconstruct the sequence to smooth out glitches.

[0138] (3) Dimensionality reduction of Pearson correlation features: Calculate the Pearson correlation coefficient for the preprocessed indexes. After calculation, the influent SS load, total influent instantaneous flow rate, biological tank influent flow rate, and multi-point dissolved oxygen index, which have the highest correlation, were selected as the core input matrix. The amount of PAC added is used as the target vector. .

[0139] Step 2: Initialize the hyperparameters of the DeepBSCN model and set the maximum number of hidden layers for the depth block incremental random configuration network. Maximum number of nodes that a single layer can accommodate Target tolerance error Define the block increment size parameter. This means that a parameter block of 10 nodes is generated simultaneously each time. At the same time, the set is initialized, and the residual of the iteration phase is set to the initial target vector.

[0140] Step 3: Perform random parameter allocation for the block incremental hidden layer, at the... During the construction of each hidden layer, within a preset range... Internally, the input weight matrix is ​​generated in random batches using a uniform distribution. and bias vector , forming a collection Candidate node blocks of each node The output matrix of the nodes in this batch is calculated using the activation function. At this stage, the model does not rush to compute the generalized inverse connection, but instead proceeds to the quality evaluation process.

[0141] Step 4: Implement node group purification and optimization based on the Fisher Information Matrix (FIM), targeting the node groups generated above that contain... The algorithm calculates the Fisher information content of each node in the predicted distribution for each candidate block of the given nodes.

[0142]

[0143] This indicator reflects the first The impact of minute perturbations in individual node parameters on the overall output distribution information content is analyzed. Nodes are sorted from largest to smallest according to their FIM values, and 50% or a predetermined threshold of high-information nodes are selected to form a simplified optimal candidate node block. This greatly eliminates redundant feature representations, allowing each remaining node to contribute to the maximum fitting capability.

[0144] Step 5: Supervision mechanism verification and output weight allocation for the purified optimal node block. Perform incremental supervision inequality constraint verification. To calculate the dot product between the current network residual and the output of the new node block, we must find the maximum constraint condition that makes the following expression true:

[0145]

[0146] in, Representing vectors and The inner product between For the first in the network The state vector of the layer, For the first The relevant vector of the layer, Represents a scalar constant. It is a scalar parameter.

[0147] Once the conditions are met, the block is officially incorporated into the network. The Moore-Penrose pseudo-inverse algorithm is used to solve for the output layer weight matrix corresponding to the node block in one step. Subsequently, the system updates the global residual using a block update formula:

[0148]

[0149] If the current residual If the target is not met and the current layer is not full, then stop training; if the target is not met and the current layer is not full, then continue to cycle through steps S3-S5; if the current layer is full, then create a new hidden layer to extend the network structure further.

[0150] Step 6: Master Model Residual Extraction and FIM Residual Compensation Training. After the DeepBSCN master model is trained, the master model output is calculated using the training set samples. And obtain the residual vector Construct candidate residual compensation feature matrices. This includes core input water quality variables, hidden layer node outputs after FIM screening, and operating condition characteristics sensitive to PAC dosage errors. The residual information scores for each candidate compensation feature are calculated. Retain the characteristics of those who rank highly and adopt Solve for the residual compensation weights to obtain the compensation model. .

[0151] Step 7: Online Soft Measurement and Engineering Validation. After the DeepBSCN master prediction model and FIM residual linear compensation module of this invention are trained, they are put into operation in a real water plant central control system. Real-time water quality characteristics, after equal preprocessing, are first output by the DeepBSCN master model as the master prediction value of PAC dosage, and then the FIM residual compensation module outputs the error correction value, ultimately forming the compensated PAC dosage prediction result. Through comparative verification on a test set, the compensated prediction curve better matches the actual dosage change trend and further reduces error indicators such as RMSE and MAE. The results are as follows: Figure 2 As shown. Comparison of prediction residuals before and after FIM residual compensation. Figure 3 As shown. A comparison of the prediction performance of different prediction models for PAC dosage is presented. Figure 4 As shown.

[0152] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN, characterized in that, The steps are as follows: S1 acquires historical water quality data and reagent dosage data from the wastewater treatment plant, preprocesses the data, and constructs a training set and a test set for the prediction model. S2 constructs an initial DeepSCN network structure with randomized depth configuration and uses a block incremental depth modeling mechanism to generate hidden layer nodes; S3 uses FIM to evaluate node quality and redundancy, retains the best node with the largest FIM value and updates the node block, and performs convergence inequality constraint verification on the updated node block. S4 Solve for the output layer weights of the block incremental DeepSCN to obtain the master prediction model, and calculate the prediction residual between the output value of the master prediction model and the actual dosage. S5 constructs a residual sensitivity matrix based on FIM, selects high-information-contribution features to form a compensation feature matrix, and uses the generalized inverse to solve the compensation weights to obtain the residual compensation output. S6 inputs the real-time collected wastewater quality characteristics into the DeepBSCN master prediction model after equal preprocessing, obtains the master model prediction value, superimposes the FIM residual linear compensation output, and obtains the final reagent dosage prediction value. The output reagent dosage calibration term is then introduced to obtain the fused prediction value.

2. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN as described in claim 1, characterized in that, The S1 preprocessing steps are as follows: A three-level wavelet reconstruction was performed on the original water quality data using a multi-resolution analysis wavelet thresholding denoising algorithm based on wavelet basis functions. The soft thresholding function processing mechanism decomposed the original signal into low-frequency approximation coefficients and high-frequency detail coefficients, calculated the optimal threshold, and set the wavelet coefficients to zero when the absolute value of the wavelet coefficients was less than the threshold; when the absolute value was greater than the threshold, the coefficients were contracted to zero. After preserving the signal abrupt change characteristics, an inverse transform was performed to reconstruct the pure signal. Pearson correlation analysis was used to calculate the correlation coefficients between each auxiliary indicator and the dosage of the reagents, and features with severe linearity and collinearity were removed. The core characteristic input variables of influent suspended solids, total influent instantaneous flow rate, influent total nitrogen, and effluent pH were retained.

3. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN as described in claim 1, characterized in that, The block incremental depth modeling mechanism described in S2 is as follows: In a single iteration, the system randomly generates a block of nodes containing multiple nodes in batches within a specified spanning space, and calculates the corresponding hidden layer output block and residual block. No. During the nth iteration The output weight blocks of each hidden layer are : ； in, and They represent the first The corresponding hidden layer output block and residual block in the next iteration. Representing the Moore-Penrose generalized inverse matrix, the network increases the number of hidden layer nodes (node ​​blocks) in each iteration by adding hidden layer nodes in blocks. Each node is updated using a block update formula. Calculate the current residual.

4. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN as described in claim 1, characterized in that, S3 uses FIM to evaluate node quality and redundancy. The node evaluation rules are as follows: For candidate nodes generated by the hidden layer, calculate their Fisher Information Matrix (FIM): ； By analyzing the model output for unknown parameters The differential response is used to calculate the information content of nodes. After configuring the node pool, the nodes with the highest sum of elements in the FIM are retained. In each iteration, the nodes in the node block are ensured to be the best hidden layer nodes. After the main prediction model is trained, the Fisher Information Matrix (FIM) is extended for the evaluation of prediction residual sensitivity. Let the training residual of the main model be... The candidate residual compensation feature matrix is Then the first The residual information score of each compensated feature is defined as: ； in, Indicates the first The compensation feature is in the first The values ​​taken on each sample This represents the master model prediction residual for the corresponding sample. The larger the value, the higher the sensitivity of the feature to the residuals of the master model, and the more suitable it is as a feature for linear compensation of residuals.

5. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN according to claim 4, characterized in that, S3 performs convergence inequality constraint checks on the updated node blocks. The specific check criteria are as follows: In the Hidden node blocks randomly configured within a hidden layer satisfy the following convergence inequality condition: ； in, Representing vectors and The inner product between For the first in the network The state vector of the layer, For the first The relevant vector of the layer, Represents a scalar constant. It is a scalar parameter.

6. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN according to claim 1, characterized in that, S4 solves for the output layer weights and global network update of Fast Incremental DeepBSCN, with the following specific rules: After a node block is successfully incorporated into the network, the output layer weight vector under the new network structure is calculated. To minimize the approximation error, a one-step solution is used, combining the least squares method with the Moore-Penrose generalized inverse matrix, to minimize the approximation error objective function. The output weights are obtained by solving, where Output matrix of the current network hidden layer Moore-Penrose generalized inverse matrix, The target prediction vector; after obtaining the output layer weights, according to the formula... Update global network residuals ; Then, a termination condition is determined, which involves calculating and judging the current network residual norm. Is it less than the set tolerance error? Or the current total number of hidden layers Has the maximum number of floors been reached? If satisfied or If any termination condition is met, training stops and the final DeepBSCN prediction model is output; if the above condition is not met, the process returns to S2 to continue iterating and randomly assigning parameters for the block incremental hidden layer.

7. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN as described in claim 1, characterized in that, S5 calculates the prediction residual vector on the training set; constructs a candidate compensation feature matrix containing core water quality variables, hidden layer node outputs and operating condition features, and uses the Fisher information matrix to evaluate the residual information contribution of each feature, removes low contribution and redundant variables, and obtains the residual compensation feature matrix. Using the training residual of the DeepBSCN master prediction model as the fitting target, the compensation weights are solved by generalized inverse to obtain the residual compensation output.

8. The wastewater dosing prediction method based on Fisher information matrix residual compensation and block increment depth SCN according to claim 1, characterized in that, S6 inputs the real-time collected wastewater quality characteristics into the trained DeepBSCN main prediction model after equivalent preprocessing to obtain the main model's predicted values. Then, the FIM residual compensation output is superimposed to obtain the final predicted value of the reagent dosage: ； Introduce an output calibration term based on the dosage of the agent at the previous sampling time, and assume that the predicted value after residual compensation is The PAC dosage at the previous sampling time was The fusion prediction value is: ； The linear calibration form is as follows: ； in, The historical continuous fusion coefficient is added, and its value is determined by the validation set.

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