A grinding granularity prediction method combining missing value completion and multi-model cooperation
By combining missing value completion with multi-model collaboration, a bi-branch grinding particle size prediction model was constructed, which solved the problems of insufficient data missingness and feature fusion in grinding particle size prediction models, achieved high-precision and interpretable particle size prediction, and improved the stability and adaptability of grinding operations.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGSHA RES INST OF MINING & METALLURGY CO LTD
- Filing Date
- 2026-01-27
- Publication Date
- 2026-06-12
AI Technical Summary
Existing grinding particle size prediction models suffer from high data loss rates in industrial settings, simple model structures, and insufficient feature fusion capabilities, resulting in low prediction robustness and accuracy. These limitations make it difficult to meet the high robustness, high accuracy, and interpretable prediction requirements of modern mineral processing plants.
A method combining missing value completion and multi-model collaboration is adopted. A completion module is constructed by using Gaussian mixture model and expectation-maximization algorithm. A two-branch grinding particle size prediction model is constructed by combining linear distribution regression and gradient boosting model. Feature extraction and completion are performed using multi-source operating data. By integrating the advantages of multiple models, high-precision and interpretable prediction of particle size distribution is achieved.
It improves the stability and generalization ability of grinding particle size prediction, enhances the adaptability and interpretability of the model under complex working conditions, and improves prediction accuracy and robustness, especially in environments where ore properties change rapidly and production disturbances are frequent.
Smart Images
Figure CN121579936B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mineral processing engineering technology, and in particular to intelligent monitoring and optimized control of grinding processes. Background Technology
[0002] Grinding is a crucial step in mineral processing, and its product particle size directly affects the performance indicators of subsequent separation operations and the final recovery rate. Achieving rapid and accurate prediction of grinding particle size is of great significance for optimizing grinding operations, stabilizing production indicators, and reducing energy consumption. Currently, the technical solutions in this field mainly suffer from the following shortcomings:
[0003] Data quality is highly dependent, and methods for handling missing values are crude. Existing predictive models heavily rely on complete, high-quality data. However, the harsh industrial environment and frequent sensor and communication link failures result in a large number of random missing data points in the collected multi-source data, such as mill current, vibration, and acoustic data. Traditional processing methods (such as directly deleting missing samples or simple mean imputation) introduce significant biases or lose a large amount of valuable information, severely limiting the usability and accuracy of the models in actual production.
[0004] The current model structure is too simplistic, making it difficult to balance accuracy and interpretability. Existing methods often employ a single model architecture, such as purely linear models or complex "black box" nonlinear models (like neural networks). While linear models offer strong interpretability, they struggle to capture the complex nonlinear dynamics of the grinding process, resulting in limited prediction accuracy. On the other hand, while nonlinear models can improve accuracy, their opaque decision-making logic makes them difficult for on-site process personnel to understand and trust, hindering their practical application and process optimization guidance.
[0005] The feature fusion capability is insufficient, failing to fully utilize multi-source information; grinding particle size is the result of the combined effects of multiple factors such as mill current, feed rate, vibration, and acoustics. Existing technologies often only utilize some parameters, failing to effectively fuse and uniformly represent these multimodal and multi-scale sensor data, thus failing to comprehensively characterize the internal operating state of the mill, limiting the robustness and generalization ability of the prediction model in the face of ore property fluctuations and complex operating conditions.
[0006] The aforementioned shortcomings indicate that existing technologies are insufficient to meet the urgent needs of modern mineral processing plants for robust, accurate, and interpretable predictions of grinding particle size. Therefore, a novel prediction method is urgently needed that can intelligently handle missing data, synergistically integrate the advantages of different models, and deeply mine the value of multi-source information. Summary of the Invention
[0007] This invention provides a grinding particle size prediction method that combines missing value completion and multi-model collaboration to solve the problems of low robustness, low accuracy and poor prediction effect of existing grinding prediction models.
[0008] To achieve the above objectives, the present invention employs the following technical solution:
[0009] This invention provides a grinding particle size prediction method that combines missing value completion and multi-model collaboration, comprising the following steps:
[0010] Step 1: Construct a completion module based on the Gaussian mixture model and the expectation-maximization algorithm framework, construct a linear distribution regression branch based on the linear regression model, construct a gradient boosting branch based on the gradient boosting model, and construct a two-branch grinding particle size prediction model based on the completion module, the linear distribution regression branch, and the gradient boosting branch.
[0011] Step 2: Collect multi-source operation data of the grinding process, preprocess the multi-source operation data to obtain missing features, input the missing features into the grinding particle size prediction model, the completion module uses a Gaussian mixture model based on the expectation-maximization algorithm to complete the missing features and obtain the completed features, the linear distribution regression branch and the gradient boosting branch respectively model the completed features, output the corresponding grinding particle size probability distribution prediction results, and fuse the grinding particle size probability distribution prediction results to obtain the final grinding particle size prediction distribution.
[0012] Furthermore, the multi-source operating data includes mill current, mill speed, feed rate, feed particle size distribution, feed moisture content, mill bearing temperature, vibration signal, and acoustic signal;
[0013] The preprocessing includes sequentially performing processes on the vibration signal and acoustic signal, such as removing DC components, filtering and denoising, normalization, segmentation, and extracting time-domain and frequency-domain features.
[0014] Furthermore, in step 2, after preprocessing, the time-domain and frequency-domain features of the extracted vibration signal and the time-domain and frequency-domain features of the acoustic signal are combined with the mean values of mill current, mill speed, feed moisture content, mill bearing temperature, feed rate, and feed particle size distribution to form missing features in vector form.
[0015] Furthermore, the time-domain features include: mean, variance, root mean square, peak value, skewness, and kurtosis;
[0016] The frequency domain features include: spectral centroid, bandwidth, roll-off point, spectral flatness, dominant frequency, and spectral entropy.
[0017] Based on the above design, a joint modeling approach is proposed that integrates multi-source operational data, including current, vibration, acoustics, feed rate, and classifier opening. This involves time-domain, frequency-domain, and time-frequency-domain feature extraction, and standardization and resampling to unify feature scales. The multi-source features are then concatenated into a unified feature vector, which is input into a collaborative optimization and completion model for dual-stream discrimination. This method fully leverages the complementarity of multi-source operational data, enhancing the model's ability to perceive fluctuations in particle size distribution under complex operating conditions. It effectively reduces the interference of single-parameter anomalies on prediction results, thereby improving prediction stability, robustness, and generalization ability. This approach is particularly effective in field environments characterized by rapid changes in ore properties and frequent production disturbances.
[0018] Furthermore, the grinding particle size prediction model constructs a joint loss function based on generation loss, first computational loss, second computational loss, and fusion loss combined with a regularization term;
[0019] The generation loss is constructed based on the negative log-likelihood of the completion features under a Gaussian mixture model;
[0020] By maximizing sample likelihood, the grinding particle size prediction model learns the parameters of a Gaussian mixture model that best represents the multimodal characteristic distribution of grinding operation. This ensures that the completed results are not only statistically reasonable but also consistent with the distribution structure of actual operating conditions. Since grinding data exhibits significant operating condition clusters and variable correlations (such as coupling between current, vibration, and acoustics), traditional mean or interpolation-based completion methods struggle to maintain variable relationships. For the Gaussian mixture model, combined with the expectation-maximization algorithm, the generated loss ensures that the completed features present the correct covariance structure within each Gaussian component, restoring the true correlation between missing variables. More importantly, this loss shares gradients with the subsequent discriminative model, causing the Gaussian mixture model to automatically favor more discriminative completion results for particle size prediction during the completion process. This significantly improves the robustness and reliability of predictions under high missing rate and high-noise environments.
[0021] The first calculated loss is constructed based on the distribution fitting criterion between the predicted particle size probability distribution calculated by the linear distribution regression branch and the actual grinding particle size distribution;
[0022] The first computational loss ensures that the grinding particle size prediction model accurately fits the trend of grinding particle size variation while maintaining interpretability. This loss, based on a distribution fitting criterion, allows the linear model to learn the "first-order linear influence law" between parameters and particle size distribution from the completed features. For the grinding process, this linear relationship is widely present in key process parameters such as feed rate, current, and bearing temperature. Therefore, the linear branch not only provides a stable and smooth prediction baseline but also directly explains the direction and intensity of a feature's influence on particle size through the weight matrix, helping engineers understand the model's decision-making basis. The introduction of the linear prediction loss enables the model to maintain good generalization even when industrial data exhibits fluctuations, abrupt changes, or noise, providing reliable and interpretable distribution prediction results.
[0023] The second calculated loss is constructed based on the distribution fitting error between the predicted particle size probability distribution calculated by the gradient boosting branch and the actual grinding particle size distribution;
[0024] The second computational loss term captures numerous high-order nonlinear mechanisms present during the grinding process. The tree model, by splitting the feature space, effectively expresses the nonlinear interactions between current, vibration, and acoustics, the piecewise characteristics caused by abrupt changes in operating conditions, and the complex response patterns resulting from variations in ore properties. A distribution fitting approach is employed to enhance the consistency between the particle size probability distribution output by the gradient boosting branch and the true label. Compared to the linear distribution regression branch, the gradient boosting branch can learn more conditional interactions, such as the complex pattern of "high feed rate + increased high-frequency vibration energy → coarser particle size," thus significantly improving overall prediction accuracy. This loss term ensures that the tree model can further refine its modeling for complex operating conditions after completing the data input, enabling the final system to cope with non-stationary, multi-disturbance industrial environments and achieve high-precision particle size distribution prediction.
[0025] The fusion loss is constructed based on the distribution difference between the output particle size probability distribution calculated by the fusion of linear distribution regression branch and gradient boosting branch and the actual grinding particle size distribution.
[0026] The fusion loss enables a synergistic balance between interpretability and nonlinear accuracy in the entire dual-flow system. The fusion module learns a weighted mapping between the two branches, allowing the model to adaptively select the more reliable prediction source under different operating conditions: for example, relying more on the linear branch when conditions are stable, and enhancing the contribution of the nonlinear branch when conditions change abruptly or ore properties change significantly. Through distribution-level supervision, the fusion loss ensures that the final output is as close as possible to the true granular distribution in its overall structure, while simultaneously constraining the output directions of the two branches to prevent conflict during training and instead promote complementary cooperation. The result is a comprehensive prediction model that combines robustness, interpretability, and high accuracy, providing more stable and reliable granular distribution predictions in complex industrial environments.
[0027] Furthermore, the training of the grinding particle size prediction model includes: acquiring multi-source operating data of the grinding process and the corresponding real grinding particle size distribution; preprocessing the multi-source operating data and inputting it into the grinding particle size prediction model in batches; iteratively updating the parameters of the linear distribution regression branch and the gradient boosting branch under the constraint of the joint loss function; and synchronously updating the parameters of the completion module until the predetermined number of rounds is reached.
[0028] Through the above design, this training method effectively utilizes computational resources and ensures that the model learns from the overall features of the batch data with each parameter update, thereby improving training efficiency and model stability. Through multiple iterations, the two branches of the grinding particle size prediction model can gradually achieve optimal collaborative prediction performance.
[0029] Furthermore, the grinding particle size prediction model uses a gradient boosting method to iteratively update the structural parameters and leaf node weights of each decision tree in the gradient boosting branch based on the loss value between the predicted particle size probability distribution of the gradient boosting branch and the actual grinding particle size distribution.
[0030] Furthermore, the grinding particle size prediction model updates the weight matrix and bias parameters of the linear distribution regression branch based on the loss value between the predicted particle size probability distribution and the actual grinding particle size distribution in the linear distribution regression branch using a gradient descent approach.
[0031] Furthermore, the grinding particle size prediction model is based on the joint loss function constraint, and uses gradient descent to iteratively update the parameters of the Gaussian mixture model according to the gradient information of the generated loss.
[0032] The parameters of the Gaussian mixture model include: the weights of each Gaussian component, the mean vector, and the covariance matrix.
[0033] Furthermore, the completion module uses a Gaussian mixture model based on the expectation-maximization algorithm to complete the missing features and obtain the completed features. This includes: calculating the posterior probability of each Gaussian component to which the missing feature belongs based on the observed features in the sample, and performing conditional expectation estimation on the missing feature according to the posterior probability to obtain the completed features.
[0034] Beneficial effects:
[0035] This invention provides a grinding particle size prediction method that combines missing value completion with multi-model collaboration. It employs a dual-stream discriminator architecture to balance prediction accuracy and interpretability, applying a linear regression branch and a gradient boosting branch in parallel for collaborative optimization and feature completion. The linear regression branch provides a clear explanation of the impact of operating parameters on particle size distribution, facilitating engineers' understanding of the model's decision-making basis. The gradient boosting branch captures higher-order nonlinear relationships between operating parameters, improving prediction accuracy. In the output stage, the results of the two branches are weighted and fused, ensuring that the final particle size distribution prediction inherits the interpretability of the linear model while possessing the high-performance modeling capabilities of gradient boosting. This increases operators' confidence in the model results and enhances the model's adaptability and generalization ability under different operating conditions and variations in ore properties.
[0036] Based on the expectation-maximization algorithm, discriminative feedback is introduced, and the generation loss, first computational loss, second computational loss, and fusion loss are constructed as a joint optimization objective. Gradient descent is used to directly optimize the parameters of the Gaussian mixture model, ensuring that missing value completion not only closely matches the true distribution of operating parameters but also improves the prediction performance of downstream grinding particle size. By using a discriminative feedback generation model to prioritize learning features that discriminate particle size distribution, the completed values become more distinguishable, thereby improving overall prediction accuracy and robustness. This method significantly improves the performance limitations of traditional completion methods, especially in the context of multi-source heterogeneous mining field data with high feature missing rates. Attached Figure Description
[0037] Figure 1 This is a data processing flowchart of a grinding particle size prediction method that combines missing value completion and multi-model collaboration according to an embodiment of the present invention. Detailed Implementation
[0038] The technical solution of the present invention will be clearly and completely described below. 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.
[0039] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.
[0040] Please see Figure 1 This application provides a grinding particle size prediction method that combines missing value completion and multi-model collaboration, including the following steps:
[0041] Step 1: Construct a completion module based on the Gaussian mixture model and the expectation-maximization algorithm framework, construct a linear distribution regression branch based on the linear regression model, construct a gradient boosting branch based on the gradient boosting model, and construct a two-branch grinding particle size prediction model based on the completion module, the linear distribution regression branch, and the gradient boosting branch.
[0042] In this application, the two prediction branches of the grinding particle size prediction model and the missing feature completion module can all be constructed using conventional models in the field. Specifically, the linear distribution regression branch can adopt a multi-output linear regression model, the gradient boosting branch can adopt a decision tree-based gradient boosting model (eXtreme Gradient Boosting, XGBoost), and the completion module can adopt a missing value completion model based on a Gaussian mixture model and the expectation-maximization algorithm. The technical focus of this application is to construct a dual-stream collaborative model structure that connects the completion module and the two prediction branches, and to achieve collaborative optimization of the generative model and the discriminative model through joint loss. The basic models themselves are all well-known technologies in the field, so their specific structures and implementation methods will not be described in detail.
[0043] The joint loss function for the grinding particle size prediction model, constructed based on the generation loss, the first computational loss, the second computational loss, and the fusion loss combined with a regularization term, is expressed by the following formula:
[0044] ;
[0045] in, Represents the joint loss function; Indicates the generation loss; Indicates the first calculated loss; Indicates the second calculated loss; Indicates fusion loss; Represents the regularization term; This represents the hyperparameter weights of each parameter, which are set to 1.0, 0.65, 0.35, 0.2, and [other values] respectively in this embodiment. .
[0046] The generation loss is constructed based on the negative log-likelihood of the completed features under the Gaussian mixture model, and is expressed by the following formula:
[0047] ;
[0048] in, Indicates the sample index; Indicates the number of samples in the current batch; Indicates the first One Gaussian component; Indicates the number of Gaussian components; Indicates the first Gaussian component mixing weights; Indicates sample In the Multi-source Gaussian probability density function values under Gaussian components; Indicates the first The completed feature sample vector is the feature that has been filled in; Indicates the first A vector of mean values of Gaussian components; Indicates the first The covariance matrix of Gaussian components.
[0049] The first calculated loss is constructed based on the distribution fitting criterion between the predicted particle size probability distribution calculated by the linear distribution regression branch and the actual grinding particle size distribution, and is expressed by the following formula:
[0050] ;
[0051] in, Indicates the granularity binning index; The number of bins indicating the particle size distribution of the grinding process; Indicates the first The sample at the th The true particle size distribution probability value on each particle size bin; This represents the predicted probability value of the linear regression branch for the corresponding sample in the corresponding grain size bin. The logarithmic operation here is used to calculate the log-likelihood of the predicted distribution under the constraints of the true distribution. The negative sign is used to transform the log-likelihood maximization problem into the loss minimization problem, thereby measuring the distribution level difference between the predicted results of the linear regression branch and the true grinding grain size distribution.
[0052] The second calculated loss is constructed based on the distribution fitting error between the predicted particle size probability distribution calculated by the gradient boosting branch and the actual grinding particle size distribution, and is expressed by the following formula:
[0053] ;
[0054] in, Indicates the gradient boosting branch for the first... The sample at the th The predicted probability value on each granularity bin is obtained by the ensemble output of multiple regression trees. The loss is measured by the cross-entropy between the true granularity distribution and the predicted distribution of the gradient boosting branch, which is used to constrain the gradient boosting model to learn the nonlinear mapping relationship between grinding condition parameters and granularity distribution.
[0055] The fusion loss is constructed based on the difference between the output particle size probability distribution calculated by fusing the linear regression branch and the gradient boosting branch and the actual grinding particle size distribution, and is expressed by the following formula:
[0056] ;
[0057] in, This represents the result obtained after combining the prediction results of the linear regression branch and the gradient boosting branch. The sample at the th The final predicted probability value on each grain size bin, the fusion loss is used to uniformly measure the distribution level error between the final predicted grain size distribution and the actual grain size distribution, and is used to coordinately constrain the prediction direction of the bi-branch model, so that the fusion output maintains stability and prediction accuracy under different grinding conditions.
[0058] For the training process of the grinding particle size prediction model, multi-source operation data of the grinding process and the corresponding real grinding particle size distribution are obtained. After the multi-source operation data is preprocessed, it is input into the grinding particle size prediction model in batches. Under the constraint of the joint loss function, the parameters of the linear distribution regression branch and the gradient boosting branch are iteratively updated, and the parameters of the completion module are updated synchronously until the predetermined round is reached.
[0059] Specifically, the grinding particle size prediction model uses the loss value between the predicted particle size probability distribution of the gradient boosting branch and the actual grinding particle size distribution to iteratively update the structural parameters and leaf node weights of each decision tree in the gradient boosting branch.
[0060] The grinding particle size prediction model is based on the loss value between the predicted particle size probability distribution and the actual grinding particle size distribution in the linear distribution regression branch. The weight matrix and bias parameters of the linear distribution regression branch are updated using gradient descent.
[0061] The grinding particle size prediction model is based on the joint loss function constraint. According to the gradient information of the generated loss, the parameters of the Gaussian mixture model are iteratively updated by gradient descent.
[0062] The parameters of a Gaussian mixture model include: the weights of each Gaussian component, the mean vector, and the covariance matrix.
[0063] In this embodiment, the training times are set to 1000 per batch and 5 training rounds.
[0064] Step 2: Collect multi-source operation data of the grinding process, preprocess the multi-source operation data to obtain missing features, input the missing features into the grinding particle size prediction model, the completion module uses a Gaussian mixture model based on the expectation-maximization algorithm to complete the missing features and obtain the completed features, the linear distribution regression branch and the gradient boosting branch respectively model the completed features, output the corresponding grinding particle size probability distribution prediction results, and fuse the grinding particle size probability distribution prediction results to obtain the final grinding particle size prediction distribution.
[0065] The collected multi-source operating data includes mill current, mill speed, feed rate, feed particle size distribution, feed moisture content, mill bearing temperature, vibration signal, and acoustic signal;
[0066] Among them, the sampling frequency of mill current, mill speed and mill bearing temperature is 1Hz, the feed moisture content is detected once every 2 seconds, the feed amount is the total amount of the detection cycle, the feed particle size distribution is detected once in the detection cycle, the sampling frequency of vibration signal is 1KHz, and the sampling frequency of acoustic signal is 8KHz.
[0067] After collecting multi-source operational data, the multi-source operational data is preprocessed. The preprocessing includes sequentially removing DC components, filtering and denoising, normalizing, segmenting, and extracting time-domain and frequency-domain features from the vibration and acoustic signals.
[0068] Among them, the filtering and noise reduction adopts the bandpass filter, and the filter design must satisfy the sampling theorem. Regarding the extraction of time domain features and frequency domain features, the extracted time domain features include: mean, variance, root mean square, peak value, skewness and kurtosis.
[0069] The extracted frequency domain features include: spectral centroid, bandwidth, roll-off point, spectral flatness, dominant frequency, and spectral entropy.
[0070] After preprocessing, the time-domain and frequency-domain features of the extracted vibration signal and the time-domain and frequency-domain features of the acoustic signal are combined with the mean values of mill current, mill speed, feed moisture content, mill bearing temperature, feed rate, and feed particle size distribution to form missing features in vector form. The missing features are then input into the grinding particle size prediction model for processing.
[0071] After being input into the grinding particle size prediction model, the completion module uses the expectation-maximization algorithm to complete the missing features. Based on the observed features in the sample, it calculates the posterior probability of each Gaussian component to which the missing feature belongs, and performs conditional expectation estimation on the missing feature according to the posterior probability to obtain the completed feature.
[0072] The linear distribution regression branch and the gradient boosting branch are modeled based on the completed features, and output the corresponding grinding particle size probability distribution prediction results. The grinding particle size prediction model integrates the grinding particle size probability distribution prediction results of each branch to obtain the final grinding particle size prediction distribution.
[0073] The final grinding particle size prediction distribution inherits the interpretability of the linear distribution regression branch and also possesses the high-performance modeling capability of the gradient boosting branch. This enhances the operator's confidence in the model results and strengthens the adaptability and generalization ability of the grinding particle size prediction model under different working conditions and ore property changes.
[0074] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.
Claims
1. A grinding particle size prediction method combining missing value completion and multi-model collaboration, characterized in that, Includes the following steps: Step 1: Construct a completion module based on the Gaussian mixture model and the expectation-maximization algorithm framework, construct a linear distribution regression branch based on the linear regression model, construct a gradient boosting branch based on the gradient boosting model, and construct a two-branch grinding particle size prediction model based on the completion module, the linear distribution regression branch, and the gradient boosting branch. The grinding particle size prediction model is based on the generation loss, the first computational loss, the second computational loss, and the fusion loss combined with a regularization term to construct a joint loss function; The generation loss is constructed based on the negative log-likelihood of the completion features under a Gaussian mixture model; The first calculated loss is constructed based on the distribution fitting criterion between the predicted particle size probability distribution calculated by the linear distribution regression branch and the actual grinding particle size distribution; The second calculated loss is constructed based on the distribution fitting error between the predicted particle size probability distribution calculated by the gradient boosting branch and the actual grinding particle size distribution; The fusion loss is constructed based on the distribution difference between the output particle size probability distribution calculated by the fusion of linear distribution regression branch and gradient boosting branch and the actual grinding particle size distribution; Step 2: Collect multi-source operation data of the grinding process, preprocess the multi-source operation data to obtain missing features, input the missing features into the grinding particle size prediction model, the completion module uses a Gaussian mixture model based on the expectation-maximization algorithm to complete the missing features and obtain the completed features, the linear distribution regression branch and the gradient boosting branch respectively model the completed features, output the corresponding grinding particle size probability distribution prediction results, and fuse the grinding particle size probability distribution prediction results to obtain the final grinding particle size prediction distribution.
2. The method according to claim 1, characterized in that, The multi-source operating data includes mill current, mill speed, feed rate, feed particle size distribution, feed moisture content, mill bearing temperature, vibration signal, and acoustic signal. The preprocessing includes sequentially performing processes on the vibration signal and acoustic signal, such as removing DC components, filtering and denoising, normalization, segmentation, and extracting time-domain and frequency-domain features.
3. The method according to claim 2, characterized in that, In step 2, after preprocessing, the time-domain and frequency-domain features of the extracted vibration signal and the time-domain and frequency-domain features of the acoustic signal are combined with the mean values of mill current, mill speed, feed moisture content, mill bearing temperature, feed rate, and feed particle size distribution to form missing features in vector form.
4. The grinding particle size prediction method combining missing value completion and multi-model collaboration as described in claim 3, characterized in that, The time-domain features include: mean, variance, root mean square, peak value, skewness, and kurtosis; The frequency domain features include: spectral centroid, bandwidth, roll-off point, spectral flatness, dominant frequency, and spectral entropy.
5. The grinding particle size prediction method combining missing value completion and multi-model collaboration according to claim 1, characterized in that, The training of the grinding particle size prediction model includes: acquiring multi-source operating data of the grinding process and the corresponding real grinding particle size distribution; preprocessing the multi-source operating data and inputting it into the grinding particle size prediction model in batches; iteratively updating the parameters of the linear distribution regression branch and the gradient boosting branch under the constraint of the joint loss function, and synchronously updating the parameters of the completion module until the predetermined number of rounds is reached.
6. The grinding particle size prediction method combining missing value completion and multi-model collaboration according to claim 5, characterized in that, The grinding particle size prediction model is based on the loss value between the predicted particle size probability distribution and the actual grinding particle size distribution of the gradient boosting branch. The model uses a gradient boosting method to iteratively update the structural parameters and leaf node weights of each decision tree in the gradient boosting branch.
7. The grinding particle size prediction method combining missing value completion and multi-model collaboration according to claim 5, characterized in that, The grinding particle size prediction model is based on the loss value between the predicted particle size probability distribution and the actual grinding particle size distribution in the linear distribution regression branch, and uses gradient descent to update the weight matrix and bias parameters of the linear distribution regression branch.
8. The grinding particle size prediction method combining missing value completion and multi-model collaboration according to claim 5, characterized in that, The grinding particle size prediction model is based on the joint loss function constraint, and uses gradient descent to iteratively update the parameters of the Gaussian mixture model according to the gradient information of the generated loss. The parameters of the Gaussian mixture model include: the weights of each Gaussian component, the mean vector, and the covariance matrix.
9. The grinding particle size prediction method combining missing value completion and multi-model collaboration according to claim 1, characterized in that, The completion module uses a Gaussian mixture model based on the expectation-maximization algorithm to complete missing features. The completion features are obtained by: calculating the posterior probability of each Gaussian component to which the missing feature belongs based on the observed features in the sample, and performing conditional expectation estimation on the missing feature according to the posterior probability to obtain the completion features.