Filter cake moisture soft measurement method based on double-regularization width learning system

Abstract

The invention discloses a filter cake moisture soft measurement method based on a double-regularization width learning system, and the method comprises the steps: obtaining key process parameter data in a filter cake forming process, and taking the key process parameter data as input characteristics; preprocessing the key process parameter data, removing the influence of an abnormal value by using an IQR quartile distance method, removing the influence of a missing value by using a dropna function, and removing the influence among different dimensions by using Z-score standardization to obtain a robust data set; training a double-regularization width learning system model by using the robust data set, performing constraint optimization on feature nodes of the double-regularization width learning system by combining a gradient descent algorithm and a cross validation method, and determining an optimal regularization parameter to obtain a prediction model; and inputting to-be-measured data into the prediction model to obtain a predicted value of the water content of the filter cake. According to the method, the moisture prediction precision can be improved, the calculation complexity is reduced, and rapid and stable online measurement is realized.

Description

Technical Field

[0001] The invention relates to the technical field of filter cake moisture measurement in a filter press process, and in particular to a filter cake moisture soft measurement method based on a double regularization width learning system. Background Art

[0002] Filter cake moisture content is a critical parameter in industrial filtration processes, impacting product quality, energy consumption, and production efficiency. Currently, filter cake moisture measurement relies primarily on offline physical testing, which presents challenges such as poor timeliness, high costs, and complex operations. To achieve real-time and accurate moisture measurement, researchers have developed a variety of soft sensing models. Among these, machine learning-based methods have garnered widespread attention due to their superior predictive capabilities.

[0003] In the actual production process of filter pressing, due to the long production cycle of the filter pressing process and the many factors affecting the moisture content of the final filter cake, the prediction of filter cake moisture has always been based on the judgment of on-site workers based on the amount of water output and years of work experience. This operation method is often subjective and arbitrary.

[0004] The Broad Learning System (BLS) is an efficient neural network modeling method with fast computational speed and a simple structure, making it suitable for real-time processing of large-scale data. However, the BLS model may suffer from feature redundancy and overfitting, which can affect prediction accuracy. Summary of the Invention

[0005] The present invention aims to address, at least to some extent, one of the technical problems in the related art. To this end, a first object of the present invention is to propose a filter cake moisture soft measurement method based on a dual-regularized width learning system. By performing constrained optimization on feature nodes, the method improves moisture prediction accuracy, reduces computational complexity, and enables fast and stable online measurement.

[0006] To achieve the above objectives, a first embodiment of the present invention proposes a filter cake moisture soft sensing method based on a dual regularized width learning system, the method comprising:

[0007] S1, obtaining key process parameter data in the filter cake formation process and using the key process parameter data as input features, the key process parameter data including feed concentration, feed flow rate, feed pressure, pressing pressure, feed time, pressing time and holding time;

[0008] S2, preprocessing the key process parameter data, using the IQR interquartile range method to remove the influence of outliers, using the dropna function to remove the influence of missing values, and using Z-score standardization to eliminate the influence between different dimensions, so as to obtain a robust data set;

[0009] S3, using the robust data set to train a dual-regularized width learning system model, and combining a gradient descent algorithm and a cross-validation method to perform constrained optimization on feature nodes of the dual-regularized width learning system to determine an optimal regularization parameter to obtain a prediction model;

[0010] S4, inputting the data to be measured into the prediction model to obtain a predicted value of the moisture content of the filter cake.

[0011] In addition, the filter cake moisture soft sensing method based on the dual regularized width learning system according to the above embodiment of the present invention may also have the following additional technical features:

[0012] According to one embodiment of the present invention, step S1 includes:

[0013] The key process parameter data is collected in real time by sensors, and the key process parameter data and the moisture content of the filter cake are combined into a data set, wherein the expression of the data set is:

[0014]

[0015] in, Input features are used to represent seven process parameters: feed concentration, feed flow, feed pressure, squeeze pressure, feed time, squeeze time and holding time; The output target represents the filter cake moisture content.

[0016] According to one embodiment of the present invention, step S2 includes:

[0017] If a key process parameter data is less than Q1-1.5×IQR or greater than Q3+1.5×IQR, the key process parameter data is an outlier and is removed, where Q1 is the first quartile of the data, Q3 is the third quartile of the data, and IQR is the interquartile range;

[0018] If there are missing values ​​in the key process parameter data corresponding to a row, the dropna function method is used to delete the key process parameter data corresponding to the row;

[0019] Use the following formula to perform Z-score standardization to eliminate the influence between different dimensions:

[0020]

[0021] Where μ is the mean of feature x, σ is the standard deviation, and x′ is the standardized feature value.

[0022] According to one embodiment of the present invention, step S3 includes:

[0023] S31, automatically generate weight W using random algorithm fi and bias b f , linearly change the input data, and map it into mapping features under the action of the activation function, store it in the mapping feature node, and record it as a feature mapping group, where the feature mapping group is expressed using the following formula:

[0024] H i =ζ(XW fi +b f ),i=1,2,...,m,

[0025] Among them, W fi is a randomly generated weight matrix; b f is the bias term; ζ(·) is the activation function; H i is the feature node after mapping; m is the number of feature mapping groups; c is the number of nodes in each feature mapping group;

[0026] The output matrix of the feature mapping layer is:

[0027] S32, the dual regularization width learning system is extended and enhanced to the enhancement layer based on the feature mapping layer, and the feature information is converted through the activation function to generate enhancement nodes, which are recorded as enhancement node groups. The expression of the enhancement node group is:

[0028] Z j =η(HW ej +b e ),j=1,2,...,n,

[0029] Among them, W ej is a random weight matrix; b e is the bias term; η(·) is the activation function; Z j is the output of the jth enhancement node; n is the number of enhancement groups; u is the number of nodes in each enhancement node group;

[0030] The output matrix of the enhancement layer is:

[0031] The output matrix of the feature mapping layer is merged with the output matrix of the enhancement layer to form the final feature representation:

[0032] S33, using gradient descent LASSO and elastic network to perform node reduction on the double regularized width learning system to reduce the feature map group from m groups to mk groups and the enhancement node group from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes;

[0033] S34, feature representation The output weight matrix is ​​calculated using the pseudo-inverse method (Moore-Penrose): in, is the generalized inverse matrix, Y is the output variable matrix, i.e. the moisture content of the filter cake, W o is the regression weight matrix;

[0034] Finally, the prediction value of the dual regularized width learning system is: in, is the predicted value of the filter cake moisture content.

[0035] According to one embodiment of the present invention, step S33 includes:

[0036] The gradient descent LASSO is used to constrain the model parameters through L1 regularization, where the LASSO objective function is expressed by the following formula:

[0037]

[0038] Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient corresponding to feature j; n is the number of samples; p is the number of features; λ is the weight of the L1 regularization term;

[0039] LASSO objective function is the least squares loss function, which represents the difference between the model's predicted value and the actual value; It is the L1 regularization term, which realizes feature selection by constraining the absolute value of the regression coefficient;

[0040] Each component β of the objective function is calculated by the following formula j Compute the subgradient:

[0041]

[0042] Where s is any value between [-1,1];

[0043] Using subgradient β (t+1) =β (t) -η·g (t) Update, where η is the learning rate, g (t) is the sub-gradient of the current iteration; at the same time, the soft threshold shrinkage method is combined to process the update of the LASSO of gradient descent:

[0044]

[0045] The soft threshold shrinkage operation is defined as:

[0046] S(β,λ)=sign(β)·max(0,|β|-λ)

[0047] The effect is as follows: if the absolute value of the regression coefficient is greater than the regularization strength parameter, the regularization strengthening parameter is reduced; otherwise, the regularization strengthening parameter is directly set to 0;

[0048] The elastic network objective function is expressed by the following formula:

[0049]

[0050] Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient; n is the number of samples; p is the number of features; λ1 is the weight of the L1 regularization term, λ2 is the weight of the L2 regularization term, is the L2 regularization term, which is used to control the sum of squares of the regression coefficients;

[0051] By combining the above steps, the feature map group is reduced from m groups to mk groups, and the enhancement node group is reduced from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes.

[0052] According to one embodiment of the present invention, the method further includes: after obtaining the predicted value of the filter cake moisture content, verifying the predicted value obtained by the prediction model with the actual value of the filter cake moisture content obtained by manual testing, wherein the verification index includes any one or more of the root mean square error, the mean absolute error and the determination coefficient.

[0053] Compared with the prior art, the filter cake moisture soft sensing method based on the dual regularization width learning system in the embodiment of the present invention has the following beneficial effects:

[0054] (1) The filter cake moisture soft-sensing method based on a dual-regularized width learning system in the present invention performs constrained optimization on feature nodes, automatically removing redundant and irrelevant feature nodes, and effectively reducing the dimensionality of the input features. This process not only reduces the computational burden but also avoids overfitting caused by redundant features, thereby significantly improving the accuracy of the filter cake moisture prediction model. In particular, it can address situations where traditional methods are difficult to achieve filter cake moisture measurement to meet the expected operating conditions.

[0055] (2) This paper uses a dual-regularized width learning system to map input features to a high-dimensional space through random mapping, capturing the complex nonlinear relationships between input features. Combining gradient descent LASSO with cross-validated elastic network optimization, this approach demonstrates enhanced nonlinear fitting capabilities for filter cake moisture soft measurement, effectively addressing complex data patterns in industrial environments.

[0056] (3) By optimizing feature node selection, the present invention significantly enhances the model's generalization capabilities, enabling it to maintain long-term stable prediction performance under different operating conditions. In particular, under conditions with small data volumes or large variations, the wide-band learning system model combined with dual regularization can adaptively adjust, improving the model's efficiency and robustness.

[0057] (4) Compared with traditional deep neural networks, wide learning has faster training speed and lower computational complexity by augmenting feature maps and calculating output weights using pseudo-inverse solutions. Combining gradient descent LASSO and cross-validated elastic network feature optimization, this invention achieves efficient modeling and fast online prediction, adapting to the real-time requirements of industrial production.

[0058] (5) The soft measurement method of the present invention is not only applicable to filter cake moisture prediction, but can also be extended to other industrial process monitoring and intelligent control, and has good versatility and scalability.

[0059] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Flowchart of a filter cake moisture soft sensing method based on a dual regularized width learning system according to an embodiment of the present invention;

[0061] Figure 2 2 is a flow chart of a filter cake moisture soft sensing method based on a dual regularized width learning system according to an embodiment of the present invention;

[0062] Figure 3 The figure is a comparison effect diagram of the predicted value and the true value according to one embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0064] The following describes a filter cake moisture soft sensing method based on a dual regularized width learning system proposed in an embodiment of the present invention with reference to the accompanying drawings.

[0065] like Figure 1 As shown, the filter cake moisture soft sensing method based on the dual regularization width learning system according to an embodiment of the present invention may include the following steps:

[0066] S1, obtaining key process parameter data in the filter cake formation process, and using the key process parameter data as input features, the key process parameter data including feed concentration, feed flow, feed pressure, pressing pressure, feed time, pressing time and holding time.

[0067] Specifically, in step S1, it is necessary to obtain key process parameter data during the filter cake formation process. This data forms the basis for subsequent modeling. Key process parameter data covers several important aspects of the filter cake formation process, including feed concentration, feed flow rate, feed pressure, pressing pressure, feed time, pressing time, and holding time. These parameters play a crucial role in the filter cake formation process, and their changes directly affect the final moisture content of the filter cake. For example, the higher the feed concentration, the higher the content of solid particles in the filter cake, which may lead to a lower moisture content in the filter cake; while the feed flow rate and feed time affect the thickness and uniformity of the filter cake, and thus the distribution and removal efficiency of the moisture. Pressing pressure, pressing time, and holding time are the most critical parameters in the pressing process, directly determining the degree of moisture squeezed out of the filter cake. The comprehensive collection of these key process parameter data can provide rich information for subsequent modeling and lay the foundation for accurately predicting the moisture content of the filter cake.

[0068] S2, preprocess the key process parameter data, use the IQR interquartile range method to remove the influence of outliers, use the dropna function to remove the influence of missing values, and use Z-score standardization to eliminate the influence between different dimensions to obtain a robust data set.

[0069] Specifically, data preprocessing is a crucial step in data science, improving data quality and thus model performance. First, the IQR interquartile range method is used to remove the impact of outliers. This method is based on data distribution and determines a reasonable data range by calculating the upper and lower quartiles. Data outside this range are considered outliers and removed. This method effectively prevents outliers from interfering with model training. For example, in feed pressure data, extremely high outliers may occur due to equipment failure or operational errors. If left unaddressed, these outliers can impair the model's fit to normal data. Second, the dropna function is used to remove the impact of missing values. In actual data collection, missing data may occur due to various reasons, such as sensor failure or data transmission errors. The dropna function can quickly remove records with missing values, ensuring data integrity. Finally, Z-score normalization is used to eliminate the influence of different dimensions. Key process parameter data may have different dimensions. For example, feed concentration may be expressed in percentages, while pressing pressure may be expressed in Pascals. Z-score normalization converts each data point to a multiple of its standard deviation relative to its mean, bringing data of different dimensions to the same order of magnitude and thus preventing the impact of dimensional differences on model training. After these preprocessing operations, a robust dataset is obtained, providing high-quality data support for subsequent model training.

[0070] S3 uses a robust data set to train the dual-regularization width learning system model, and combines the gradient descent algorithm and cross-validation method to perform constrained optimization on the feature nodes of the dual-regularization width learning system to determine the optimal regularization parameters to obtain a prediction model.

[0071] Specifically, the dual-regularized width learning system is an advanced machine learning model that introduces a dual regularization mechanism based on the width learning system, effectively improving the model's generalization and overfitting resistance. During training, the dual-regularized width learning system's feature nodes are constrainedly optimized using a combination of gradient descent and cross-validation. The gradient descent algorithm is a commonly used optimization algorithm that gradually adjusts model parameters to minimize the loss function by calculating the gradient of the loss function. Cross-validation is an effective means of evaluating model performance. By dividing the dataset into multiple subsets for training and validation, it can accurately evaluate the model's performance on different data subsets, thereby preventing the model from overfitting on specific datasets. By combining these two methods, the optimal regularization parameter can be determined, resulting in a high-performance prediction model. This prediction model can accurately predict the moisture content of the filter cake based on the input key process parameter data.

[0072] S4, inputting the data to be measured into the prediction model to obtain a predicted value of the moisture content of the filter cake.

[0073] Specifically, after previous training and optimization, the prediction model has acquired the ability to accurately predict filter cake moisture content. In practical applications, simply inputting key process parameter data from the filter cake formation process to the model will quickly output a predicted value for the filter cake moisture content. This method enables real-time monitoring and prediction of filter cake moisture content, providing strong support for quality control and process optimization in industrial production.

[0074] Therefore, the filter cake moisture soft sensing method based on the dual-regularized width learning system in the present embodiment significantly improves data quality and reliability from a data processing perspective by removing outliers through the IQR interquartile range method, removing missing values ​​using the dropna function, and eliminating dimensional differences through Z-score normalization. High-quality data is the foundation of model training. Only with accurate, complete, and consistent data can the model better learn the patterns and characteristics within the data, thereby improving prediction accuracy. Secondly, during model training, the dual-regularized width learning system combines a gradient descent algorithm and cross-validation methods to perform constrained optimization of feature nodes, effectively improving the model's generalization and overfitting resistance. This means that the model not only performs well on training data but also maintains high prediction accuracy on new, unseen data, which is of great significance for the complex and changing conditions in actual industrial production. Furthermore, this method enables rapid prediction of filter cake moisture content. In industrial production, timely and accurate information on filter cake moisture content is crucial for optimizing production processes, improving product quality, and reducing production costs. While traditional methods for measuring filter cake moisture content often require time and complex operations, this method rapidly generates predicted values ​​by simply inputting key process parameter data, significantly improving production efficiency. Finally, this method has broad applicability. The key process parameter data for filter cake formation are similar across many industrial sectors, making this method applicable to a wide range of industrial processes involving filter cake production, such as the chemical, pharmaceutical, and food industries, offering broad application prospects.

[0075] The following combination Figure 2 The specific details of each step of the filter cake moisture soft sensing method based on the dual regularization width learning system according to an embodiment of the present invention are described in detail.

[0076] According to one embodiment of the present invention, step S1 includes:

[0077] The key process parameter data are collected in real time by sensors, and the key process parameter data and the filter cake moisture content are combined into a data set, where the data set expression is:

[0078]

[0079] in, Input features are used to represent seven process parameters: feed concentration, feed flow, feed pressure, squeeze pressure, feed time, squeeze time and holding time; The output target represents the filter cake moisture content.

[0080] According to one embodiment of the present invention, step S2 includes:

[0081] First, check whether there are outliers or missing values ​​in the data, such as extreme values ​​(such as feed flow rate far above / below the reasonable range) or missing data in a row of input features;

[0082] If a key process parameter data is less than Q1-1.5×IQR or greater than Q3+1.5×IQR, the key process parameter data is an outlier and is removed, where Q1 is the first quartile of the data, Q3 is the third quartile of the data, and IQR is the interquartile range;

[0083] If there are missing values ​​in the key process parameter data corresponding to a row, the dropna function method is used to delete the key process parameter data corresponding to the row; this method means directly modifying the input features themselves and deleting all rows with missing values, rather than generating a new DataFrame; for most problems, deleting samples containing missing values ​​is the most direct method, thereby avoiding the estimation and interpolation of missing values ​​and reducing the possibility of introducing additional errors.

[0084] Use the following formula to perform Z-score standardization to eliminate the influence between different dimensions:

[0085]

[0086] Where μ is the mean of feature x, σ is the standard deviation, and x′ is the normalized feature value. This method is suitable for cases where the data distribution is relatively symmetrical and can transform the data into a standard normal distribution with a mean of 0 and a standard deviation of 1.

[0087] Through the above data collection and preprocessing steps, we can effectively balance the scales between different features, remove outliers and missing values, eliminate the influence between different dimensions, generate useful features, and obtain a robust dataset.

[0088] According to one embodiment of the present invention, step S3 includes:

[0089] S31, automatically generate weight W using random algorithm fi and bias b f , linearly change the input data, and map it into mapping features under the action of the activation function, store it in the mapping feature node, and record it as a feature mapping group, where the feature mapping group is expressed using the following formula:

[0090] H i =ζ(XW fi +b f ),i=1,2,...,m,

[0091] Among them, W fi is a randomly generated weight matrix; b f is the bias term; ζ(·) is the activation function; H i is the feature node after mapping; m is the number of feature mapping groups; c is the number of nodes in each feature mapping group;

[0092] The output matrix of the feature mapping layer is:

[0093] S32, the dual regularization width learning system is extended and enhanced to the enhancement layer based on the feature mapping layer, and the feature information is converted through the activation function to generate enhancement nodes, which are recorded as enhancement node groups. The expression of the enhancement node group is:

[0094] Z j =η(HW ej +b e ),j=1,2,...,n,

[0095] Among them, W ej is a random weight matrix; b e is the bias term; η(·) is the activation function; Z j is the output of the jth enhancement node; n is the number of enhancement groups; u is the number of nodes in each enhancement node group;

[0096] The output matrix of the enhancement layer is:

[0097] The output matrix of the feature mapping layer is merged with the output matrix of the enhancement layer to form the final feature representation:

[0098] S33 uses gradient descent LASSO and elastic network to perform node reduction on the double-regularized width learning system to reduce the feature map group from m groups to mk groups and the enhancement node group from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes.

[0099] According to one embodiment of the present invention, step S33 includes:

[0100] The gradient descent LASSO is used to constrain the model parameters through L1 regularization, where the LASSO objective function is expressed by the following formula:

[0101]

[0102] Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient corresponding to feature j; n is the number of samples; p is the number of features; λ is the weight of the L1 regularization term; gradient descent LASSO is selected as a regularization method for regression analysis. It constrains the model parameters through L1 regularization, forcing the coefficients of some features to become zero, thereby achieving feature selection.

[0103] LASSO objective function is the least squares loss function, which represents the difference between the model's predicted value and the actual value; It is the L1 regularization term, which realizes feature selection by constraining the absolute value of the regression coefficient. When it increases, more coefficients are shrunk to zero, thereby eliminating unimportant features.

[0104] Each component β of the objective function is calculated by the following formula j Compute the subgradient:

[0105]

[0106] Where s is any value between [-1,1];

[0107] Using subgradient β (t+1) =β (t) -η·g (t) Update, where η is the learning rate, g (t) is the sub-gradient of the current iteration; at the same time, the soft threshold shrinkage method is combined to process the update of the LASSO of gradient descent:

[0108]

[0109] The soft threshold shrinkage operation is defined as:

[0110] S(β,λ)=sign(β)·max(0,|β|-λ)

[0111] The effect is as follows: if the absolute value of the regression coefficient is greater than the regularization strength parameter, the regularization strengthening parameter is reduced; otherwise, the regularization strengthening parameter is directly set to 0 (that is, the variable is sparse);

[0112] The elastic network objective function is expressed by the following formula:

[0113]

[0114] Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient; n is the number of samples; p is the number of features; λ1 is the weight of the L1 regularization term, λ2 is the weight of the L2 regularization term, is the L2 regularization term, which is used to control the sum of squares of the regression coefficients and helps solve the problem of collinearity between features. L2 regularization tends to reduce the regression coefficients to smaller values, but does not compress them to zero. It should be noted that the Elastic Net combines the advantages of LASSO and Ridge Regression, uses L1 and L2 regularization for optimization, and can simultaneously handle feature selection and multicollinearity problems. The Elastic Net in this article uses a cross-validation version (Elastic Net CV), performs multiple cross-validations on the training data, tries different combinations of alpha and l1_ratio values, and selects the parameter combination that minimizes the cross-validation error as the final model parameters.

[0115] By combining the above steps, the feature map group is reduced from m groups to mk groups, and the enhancement node group is reduced from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes.

[0116] S34, feature representation The output weight matrix is ​​calculated using the pseudo-inverse method (Moore-Penrose): in, is the generalized inverse matrix, Y is the output variable matrix, i.e. the moisture content of the filter cake, W o is the regression weight matrix;

[0117] Finally, the prediction value of the dual regularized width learning system is: in, is the predicted value of the filter cake moisture content.

[0118] According to one embodiment of the present invention, the above method further includes: after obtaining the predicted value of the filter cake moisture content, verifying the predicted value obtained by the prediction model with the actual value of the filter cake moisture content obtained by manual testing, wherein the verification index includes any one or more of the root mean square error, the mean absolute error and the determination coefficient.

[0119] Specifically, the data to be tested is input into the prediction model to obtain the predicted value of the filter cake moisture content, which is then compared with the actual value obtained through manual testing. The following is the complete experimental plan:

[0120] Data partitioning involves randomly dividing the data set into training and test sets at a ratio of 7:3 during processing:

[0121] The following standards apply:

[0122] Root Mean Square Error (RMSE): It is the square root of the mean squared error (MSE). MSE measures the average squared error and can highlight the impact of larger errors. RMSE, on the other hand, has the same dimensions as the original data, making the errors more interpretable. It measures the mean squared error of the predictions; smaller is better.

[0123] Mean Absolute Error (MAE): Reflects the average deviation between the predicted value and the true value. The smaller the better.

[0124] Coefficient of determination (R 2 ): Reflects the goodness of fit of the model, the closer to 1 the better. i is the true value, is the predicted value, is the average of all true values, and N is the number of samples.

[0125] The three evaluation metrics above demonstrate that the proposed method performs well, reducing the impact of redundant features and improving computational efficiency. It also effectively learns nonlinear relationships, enhancing prediction accuracy and generalization. It is suitable for online soft sensing in complex industrial environments and provides an efficient and stable solution for intelligent prediction of filter cake moisture content.

[0126] In order to intuitively reflect the accuracy of the prediction method proposed in this paper, Figure 3 As shown in the figure, Matplotlib is used for visualization to show the comparison between the predicted value and the true value, and the data of three performance indicators are added.

[0127] In summary, the above methods demonstrate that combining gradient descent LASSO with cross-validated elastic nets for feature selection can effectively remove redundant feature nodes, reducing the computational complexity of the wide learning system while retaining relevant feature groups, avoiding information loss, and improving model stability and generalization. The wide learning system possesses efficient augmented feature mapping capabilities, while gradient descent LASSO and cross-validated elastic nets optimize input feature nodes, reduce overfitting, and improve prediction accuracy. This optimization strategy not only accelerates training but also enhances the long-term stability and adaptability of the wide learning system in filter cake moisture soft measurement tasks, making it more suitable for industrial environments with high dimensions, small sample sizes, and complex working conditions.

[0128] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0129] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0130] In the present invention, unless otherwise specified or limited, the terms "installed," "connected," "connect," "fixed," etc. should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integration; mechanical connection, electrical connection; direct connection, or indirect connection through an intermediate medium; internal communication between two components, or interaction between two components, unless otherwise specified. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0131] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A filter cake moisture soft sensing method based on a dual regularized width learning system, characterized in that: The method comprises: S1, obtaining key process parameter data in the filter cake formation process and using the key process parameter data as input features, the key process parameter data including feed concentration, feed flow rate, feed pressure, pressing pressure, feed time, pressing time and holding time; S2, preprocessing the key process parameter data, using the IQR interquartile range method to remove the influence of outliers, using the dropna function to remove the influence of missing values, and using Z-score standardization to eliminate the influence between different dimensions, so as to obtain a robust data set; S3, using the robust data set to train a dual-regularized width learning system model, and combining a gradient descent algorithm and a cross-validation method to perform constrained optimization on feature nodes of the dual-regularized width learning system to determine an optimal regularization parameter to obtain a prediction model; S4, inputting the data to be measured into the prediction model to obtain a predicted value of the moisture content of the filter cake.

2. The filter cake moisture soft sensing method based on the dual regularized width learning system according to claim 1 is characterized in that: Step S1 includes: The key process parameter data is collected in real time by sensors, and the key process parameter data and the moisture content of the filter cake are combined into a data set, wherein the expression of the data set is: in, Input features are used to represent seven process parameters: feed concentration, feed flow, feed pressure, squeeze pressure, feed time, squeeze time and holding time; The filter cake moisture content is expressed as an output target.

3. The filter cake moisture soft sensing method based on the dual regularized width learning system according to claim 1 is characterized in that: Step S2 includes: If a key process parameter data is less than Q1-1.5×IQR or greater than Q3+1.5×IQR, the key process parameter data is an outlier and is removed, where Q1 is the first quartile of the data, Q3 is the third quartile of the data, and IQR is the interquartile range; If there are missing values ​​in the key process parameter data corresponding to a row, the dropna function method is used to delete the key process parameter data corresponding to the row; Use the following formula to perform Z-score standardization to eliminate the influence between different dimensions: Where μ is the mean of feature x, σ is the standard deviation, and x′ is the standardized feature value.

4. The filter cake moisture soft sensing method based on the dual regularized width learning system according to claim 1 is characterized in that: Step S3 includes: S31, automatically generate weight W using random algorithm fi and bias b f , linearly change the input data, and map it into mapping features under the action of the activation function, store it in the mapping feature node, and record it as a feature mapping group, where the feature mapping group is expressed using the following formula: H i =ζ(XW fi +b f ),i=1,2,...,m, Among them, W fi is a randomly generated weight matrix; b f is the bias term; ζ(·) is the activation function; H i is the feature node after mapping; m is the number of feature mapping groups; c is the number of nodes in each feature mapping group; The output matrix of the feature mapping layer is: S32, the dual regularization width learning system is extended and enhanced to the enhancement layer based on the feature mapping layer, and the feature information is converted through the activation function to generate enhancement nodes, which are recorded as enhancement node groups. The expression of the enhancement node group is: Z j =η(HW ej +b e ),j=1,2,...,n, Among them, W ej is a random weight matrix; b e is the bias term; η(·) is the activation function; Z j is the output of the jth enhancement node; n is the number of enhancement groups; u is the number of nodes in each enhancement node group; The output matrix of the enhancement layer is: The output matrix of the feature mapping layer is merged with the output matrix of the enhancement layer to form the final feature representation: S33, using gradient descent LASSO and elastic network to perform node reduction on the double regularized width learning system to reduce the feature map group from m groups to mk groups and the enhancement node group from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes; S34, feature representation The output weight matrix is ​​calculated using the pseudo-inverse method (Moore-Penrose): in, is the generalized inverse matrix, Y is the output variable matrix, i.e. the moisture content of the filter cake, W o is the regression weight matrix; Finally, the prediction value of the dual regularized width learning system is: in, is the predicted value of the filter cake moisture content.

5. The filter cake moisture soft sensing method based on the dual regularized width learning system according to claim 4 is characterized in that: Step S33 includes: The gradient descent LASSO is used to constrain the model parameters through L1 regularization, where the LASSO objective function is expressed by the following formula: Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient corresponding to feature j; n is the number of samples; p is the number of features; λ is the weight of the L1 regularization term; LASSO objective function is the least squares loss function, which represents the difference between the model's predicted value and the actual value; It is the L1 regularization term, which realizes feature selection by constraining the absolute value of the regression coefficient; Each component β of the objective function is calculated by the following formula j Compute the subgradient: Where s is any value between [-1,1]; Using subgradient β (t+1) =β (t) -η·g (t) Update, where η is the learning rate, g (t) is the sub-gradient of the current iteration; at the same time, the soft threshold shrinkage method is combined to process the update of the LASSO of gradient descent: The soft threshold shrinkage operation is defined as: S(β,λ)=sign(β)·max(0,|β|-λ) The effect is as follows: if the absolute value of the regression coefficient is greater than the regularization strength parameter, the regularization strengthening parameter is reduced; otherwise, the regularization strengthening parameter is directly set to 0; The elastic network objective function is expressed by the following formula: Among them, y i is the target variable, i.e. the moisture content of the filter cake; X ij is the input feature; β j is the regression coefficient; n is the number of samples; p is the number of features; λ1 is the weight of the L1 regularization term, λ2 is the weight of the L2 regularization term, is the L2 regularization term, which is used to control the sum of squares of the regression coefficients; By combining the above steps, the feature map group is reduced from m groups to mk groups, and the enhancement node group is reduced from n groups to nt groups, thereby achieving node reduction and removing redundant or irrelevant nodes.

6. The filter cake moisture soft sensing method based on the dual regularized width learning system according to claim 1 is characterized in that: The method further comprises: After obtaining the predicted value of the filter cake moisture content, the actual value of the filter cake moisture content obtained by manual testing is used to verify the predicted value obtained by the prediction model, wherein the verification index includes any one or more of the root mean square error, the mean absolute error and the determination coefficient.

Images