A method, device, equipment and medium for missing data imputation in a grinding process

Abstract

The application provides a missing data imputation method, device, equipment and medium for a grinding process, wherein a candidate prediction model is obtained by training an initial prediction model by using a variable complete data set, and the variable complete data set contains complete data of a plurality of variables; missing data of each variable is obtained, and similar complete data of the missing data of each variable is determined from the complete data of each variable according to the missing data of each variable; candidate imputation values of the missing data of each variable are generated according to the similar complete data of the missing data of each variable; target imputation values of the missing data of each variable are determined by using the candidate prediction model according to the candidate imputation values of the missing data of each variable; and the missing data of each variable is imputed by using the target imputation values of the missing data of each variable to obtain imputed data of each variable. The above scheme is adopted to ensure the imputation effect of the missing data and improve the accuracy and reliability of data imputation.

Description

Technical Field

[0001] This invention relates to the field of data processing, and more specifically, to a method, apparatus, equipment, and medium for interpolating missing data in a grinding process. Background Technology

[0002] In copper ore processing, grinding particle size is a crucial factor directly affecting beneficiation efficiency and product quality; soft sensing technology has become a common solution for its effective detection. Soft sensing technology is a method for predicting variables that are not directly measurable or difficult to measure using easily measurable variables and mathematical models. Data such as throughput, ball mill power, and overflow concentration are collected in real time by sensors; soft sensing models can predict grinding particle size, providing decision support for operators. Despite the significant success of soft sensing technology in industrial applications, data loss remains one of the major challenges faced by soft sensing systems in practical operation. In real industrial environments, measuring devices may experience data loss due to wear, contamination, or malfunction; equipment downtime and manual intervention by operators can also lead to the inability to continuously and accurately collect and transmit some input variables. Furthermore, grinding particle size data is obtained through manual sampling and laboratory analysis, making this target variable particularly valuable. In such cases, the lack of partial input data in the soft sensing system directly affects the accuracy and stability of the model's predictions.

[0003] Currently, common methods for addressing missing data include direct deletion, mean imputation, and nearest neighbor imputation. While these methods can alleviate the problems caused by missing data to some extent, they have significant limitations when dealing with complex industrial scenarios. Traditional imputation methods typically assume independent data distribution and ignore the nonlinear relationships between input variables. Therefore, in practical applications, they struggle to accurately reproduce the true trend of missing data and lack flexibility and adaptability for specific scenarios, thus reducing the accuracy of data imputation and resulting in unsatisfactory imputation effects. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method, apparatus, equipment and medium for interpolating missing data in a grinding process, so as to ensure the interpolation effect of missing data and improve the accuracy and reliability of data interpolation.

[0005] In a first aspect, embodiments of this application provide a method for interpolating missing data in a grinding process, the method comprising:

[0006] Candidate prediction models are obtained by training an initial prediction model using a complete dataset of variables, wherein the complete dataset of variables contains complete data for several variables;

[0007] Obtain the missing data for each variable, and based on the missing data for each variable, determine the similar complete data for each variable from the complete data for each variable;

[0008] Generate candidate imputed values ​​for the missing data of each variable based on similar complete data for the missing data of each variable;

[0009] Based on the candidate imputation values ​​of the missing data for each variable, the target imputation values ​​of the missing data for each variable are determined using the candidate prediction model.

[0010] The missing data of each variable is imputed by using the target imputed values ​​of the missing data of each variable.

[0011] Optionally, the method further includes:

[0012] The interpolated data and the complete data of each variable are combined to obtain the model training data;

[0013] The target prediction model is obtained by training the candidate prediction model using the model training data.

[0014] Optionally, the method further includes:

[0015] The grinding particle size is predicted using the target prediction model.

[0016] Optionally, the step of determining similar complete data for each variable from the complete data of each variable based on the missing data of each variable includes:

[0017] Calculate the similarity between the complete data and the missing data for each variable;

[0018] Select the preset number of complete data points with the highest similarity to the missing data to determine the similar complete data points for each variable.

[0019] Alternatively, complete data whose similarity to the missing data exceeds a preset threshold can be identified as similar complete data to the missing data of each variable.

[0020] Optionally, generating candidate imputed values ​​for the missing data of each variable based on similar complete data of the missing data of each variable includes:

[0021] Construct similar datasets based on similar complete datasets with missing data for each variable;

[0022] Configure missing data imputation value ranges for missing data of each variable, and configure weights for each similar complete data in the similar dataset;

[0023] Based on the weights of each similar complete data set, candidate imputation values ​​for the missing data of each variable are generated within the imputation value range of the missing data of each variable using a random sampling method.

[0024] Optionally, configuring weights for each similar complete data point in the similar dataset includes:

[0025] The weights of similar complete data are determined based on the missing data and the complete data of each variable.

[0026] Optionally, determining the target imputed value for the missing data of each variable using the candidate prediction model based on the candidate imputed values ​​for the missing data of each variable includes:

[0027] The predicted value of each candidate interpolation value is determined using the candidate prediction model.

[0028] Calculate the error between the predicted value and the target value for each candidate interpolation value;

[0029] The candidate interpolation value with the smallest error between the predicted value and the target value among all candidate interpolation values ​​is determined as the target interpolation value.

[0030] Secondly, embodiments of this application provide a data interpolation device for missing data in a grinding process, the device comprising:

[0031] The candidate prediction model training module is used to train the initial prediction model using the complete variable dataset to obtain the candidate prediction model, wherein the complete variable dataset contains complete data of several variables.

[0032] The similar complete data determination module is used to obtain the missing data of each variable and determine the similar complete data of each variable from the complete data of each variable based on the missing data of each variable.

[0033] The candidate imputation value determination module is used to generate candidate imputation values ​​for the missing data of each variable based on similar complete data of the missing data of each variable;

[0034] The target imputation value determination module is used to determine the target imputation value of the missing data of each variable based on the candidate imputation values ​​of the missing data of each variable and using the candidate prediction model.

[0035] The imputation data generation module is used to impute the missing data of each variable by using the target imputation values ​​of the missing data of each variable to obtain the imputed data of each variable.

[0036] Optionally, the device further includes:

[0037] The training data generation module is used to merge the imputed data and the complete data of each variable to obtain the model training data;

[0038] The prediction model training module is used to train the candidate prediction model using the model training data to obtain the target prediction model.

[0039] Optionally, the device further includes:

[0040] The grinding particle size prediction module is used to predict the grinding particle size using the target prediction model.

[0041] Optionally, the step of determining similar complete data for each variable from the complete data of each variable based on the missing data of each variable includes:

[0042] Calculate the similarity between the complete data and the missing data for each variable;

[0043] Select the preset number of complete data points with the highest similarity to the missing data to determine the similar complete data points for each variable.

[0044] Alternatively, complete data whose similarity to the missing data exceeds a preset threshold can be identified as similar complete data to the missing data of each variable.

[0045] Optionally, generating candidate imputed values ​​for the missing data of each variable based on similar complete data of the missing data of each variable includes:

[0046] Construct similar datasets based on similar complete datasets with missing data for each variable;

[0047] Configure missing data imputation value ranges for missing data of each variable, and configure weights for each similar complete data in the similar dataset;

[0048] Based on the weights of each similar complete data set, candidate imputation values ​​for the missing data of each variable are generated within the imputation value range of the missing data of each variable using a random sampling method.

[0049] Optionally, configuring weights for each similar complete data point in the similar dataset includes:

[0050] The weights of similar complete data are determined based on the missing data and the complete data of each variable.

[0051] Optionally, determining the target imputed value for the missing data of each variable using the candidate prediction model based on the candidate imputed values ​​for the missing data of each variable includes:

[0052] The predicted value of each candidate interpolation value is determined using the candidate prediction model.

[0053] Calculate the error between the predicted value and the target value for each candidate interpolation value;

[0054] The candidate interpolation value with the smallest error between the predicted value and the target value among all candidate interpolation values ​​is determined as the target interpolation value.

[0055] Thirdly, embodiments of this application provide a computer device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, the steps of the grinding process missing data interpolation method described in any of the optional embodiments of the first aspect are performed.

[0056] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the grinding process missing data interpolation method described in any of the optional embodiments of the first aspect.

[0057] The technical solution provided in this application includes, but is not limited to, the following beneficial effects:

[0058] This application utilizes a complete dataset of variables to train an initial prediction model and obtain candidate prediction models. This ensures that the model can fully learn the correlations, trends, and potential rules between variables during training. Training with a complete, unmissing dataset allows the model to establish more accurate and robust predictive capabilities, providing a reliable basis for imputation in subsequent steps. Then, missing data for each variable is obtained, and similar complete data is identified from the complete dataset based on this missing data. This allows the model to infer the reasonable range or possible values ​​of missing values ​​using the similarity between data points, improving the accuracy and reasonableness of imputation. Next, candidate imputation values ​​are generated based on the similar complete data, providing multiple possible alternative values ​​for the missing data. This not only increases the flexibility of imputation but also provides a wealth of options for selecting the optimal imputation value using the prediction model in subsequent steps. Finally, the candidate prediction model is used to determine the target imputation value, which is then used to imput the missing data. The model can evaluate the reasonableness of each candidate value based on the inherent patterns and characteristics of the data, selecting the imputation value that best matches the overall trend and pattern of the data, thereby improving the accuracy and reliability of imputation. Finally, the selected target imputation values ​​are used to fill the missing parts in the original dataset, which not only makes the dataset more complete and usable, but also ensures that the imputed data maintains a similar distribution and characteristics to the original data, providing a reliable foundation for subsequent data analysis and modeling.

[0059] In summary, this application achieves effective processing of missing data by combining the advantages of data similarity and prediction models. This method not only improves the accuracy and reliability of imputation but also maintains the integrity and availability of the data, ensuring the effectiveness of data imputation.

[0060] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0061] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 The flowchart of a method for interpolating missing data in a grinding process provided in Embodiment 1 of the present invention is shown.

[0063] Figure 2 The flowchart of a target prediction model determination method provided in Embodiment 1 of the present invention is shown;

[0064] Figure 3 A schematic diagram of a soft measurement system for a copper ore grinding process provided in Embodiment 1 of the present invention is shown.

[0065] Figure 4 The flowchart of a method for determining similar complete data provided in Embodiment 1 of the present invention is shown;

[0066] Figure 5 The flowchart of a candidate interpolation value generation method provided in Embodiment 1 of the present invention is shown;

[0067] Figure 6 A flowchart of a target interpolation value determination method provided in Embodiment 1 of the present invention is shown;

[0068] Figure 7 A schematic diagram of a target variable fitting result provided in Embodiment 1 of the present invention is shown;

[0069] Figure 8 This diagram illustrates the structure of a data interpolation device for a grinding process provided in Embodiment 2 of the present invention.

[0070] Figure 9 A schematic diagram of the structure of a computer device provided in Embodiment 3 of the present invention is shown. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0072] Example 1

[0073] To facilitate understanding of this application, the following is combined with... Figure 1 The flowchart of the grinding process missing data interpolation method provided in Embodiment 1 of the present invention describes the contents of Embodiment 1 in detail.

[0074] See Figure 1 As shown, Figure 1 The flowchart illustrates a method for interpolating missing data in a grinding process according to Embodiment 1 of the present invention, wherein the method includes steps S101 to S105:

[0075] S101: Train the initial prediction model using the complete variable dataset to obtain a candidate prediction model, wherein the complete variable dataset contains complete data for several variables.

[0076] Specifically, obtain a complete dataset containing all variable data. This dataset is used to train an initial predictive model. This model can be any type of predictive model, such as linear regression, decision trees, neural networks, etc., depending on the characteristics of the data and the problem to be solved. The purpose of training is to allow the model to learn the relationships between variables, providing a predictive basis for the evaluation and selection of subsequent imputation data.

[0077] In the grinding process, the specific execution process of the missing data imputation method includes:

[0078] Get the complete dataset ,in , For the number of input variables, For the number of samples, This is the target output value corresponding to the sample, where Represents the set of real numbers. This represents a real matrix composed of input variables. Indicates the composition of the target variable A real matrix with 1 row and 1 column. All variable values ​​can be collected.

[0079] A stochastic configuration network (SCN) is selected as the base learner. Through a supervised mechanism, the input weights and biases of the hidden layer nodes are randomly configured, and the output of the initial prediction model is gradually optimized. The working mechanism of SCN is as follows: During the training process of SCN, the initial output... It is from the existing Output of each hidden layer node With corresponding weights Composed of:

[0080]

[0081] in, The formula is as follows:

[0082]

[0083] In the formula, Indicates the first The output of each hidden layer node , The hidden layer activation function is represented by the following formula:

[0084]

[0085] Among them, the The input weights and biases of each node are respectively and , , .

[0086] In each training iteration, SCN calculates the model residuals. To guide model updates:

[0087]

[0088] The target output is The current output is The residual is used to evaluate the training error of the current model when the following condition is met: or Stop adding new nodes, among which Indicates the allowable error. It represents the maximum number of hidden nodes.

[0089] If the above conditions are not met, then generate The nth node is the nth node in the hidden layer. The candidate nodes are selected through a supervision mechanism, and the best candidate node is chosen as the nth node. Each node is added to the hidden layer. Output of each node and constraint mechanisms As shown in the following formula:

[0090]

[0091]

[0092] in, and These are the random weights and biases of the new hidden layer nodes; (0,1); It is a sequence of non-negative real numbers and .satisfy The candidate node parameter with the maximum value ≥ 0 is used as the first 1 node The search radius is [value].

[0093] When a new node is added, SCN updates the weights of the output layer using the least squares method. The formula is as follows:

[0094]

[0095] in, yes The Moore-Penrose pseudo-inverse matrix.

[0096] Model trained on the complete dataset It can capture the nonlinear relationship between input variables and target variables and provide an evaluation basis for imputation of missing data.

[0097] S102: Obtain the missing data for each variable, and determine the similar complete data for each variable from the complete data of each variable based on the missing data for each variable.

[0098] Specifically, the first step is to determine which variables have missing data. Then, for each variable with missing data, find similar data points from the complete dataset—these are the similar complete data points. This can be achieved by calculating the similarity between the missing and complete data points, based on variable values, distance metrics, or other statistical methods. This step helps find a set of similar complete data points for each missing data point, which will be used to generate candidate imputed values ​​for the missing data.

[0099] In the grinding process, the specific execution process of the missing data imputation method also includes:

[0100] To obtain the missing dataset ,in, , For the number of input variables, This represents the number of missing samples. The target variable value corresponding to the missing sample. Indicates the composition of the target variable A real matrix with 1 row and 1 column. The values ​​of the target variables were all collected. To evaluate each missing data point... This step uses Euclidean distance to calculate similarity to the data in the complete dataset.

[0101] Given missing data and complete data Its Euclidean distance is defined as:

[0102]

[0103] in, and Missing data and complete data are respectively in the 1st and 2nd data. The values ​​that can be taken on each variable, if If missing, then This is the mean of the variable in the missing dataset.

[0104] All missing data Euclidean distance between smaller than radius Data Selected as a set of similar complete data .

[0105]

[0106] The search radius The settings were selected experimentally to ensure that similar datasets covered an appropriate amount of data, while maintaining... and High similarity.

[0107] In the selected set Then, further filtering was performed to select the data most similar to the missing data. This step ensures that the imputed data is generated based on highly similar data, thereby improving the reliability of the imputed data.

[0108]

[0109] in, express exist The most similar one selected from the previous ones Data items;

[0110] Represents a set of similar sets.

[0111] S103: Generate candidate imputation values ​​for the missing data of each variable based on similar complete data of the missing data of each variable.

[0112] Specifically, candidate imputation values ​​for the missing data are generated using the similar complete data points found in step S102. These imputation values ​​can be the mean, median, mode, or other statistics of the similar data points, or they can be linear interpolation, multinomial interpolation, or machine learning-based interpolation methods. This step generates one or more possible imputation values ​​for each missing data point, allowing subsequent steps to select the optimal imputation value.

[0113] In the grinding process, the specific execution process of the missing data imputation method also includes:

[0114] First, define the handling of missing values. ,exist Set upper and lower limits for the value of the variable. This is used to generate subsequent interpolation data.

[0115]

[0116] This interval represents the most similar intervals. In each data point, the minimum and maximum values ​​for each missing value within the variable are specified. This setting ensures that the generated imputed values ​​conform to the physical constraints of the actual data, preventing the generation of imputed data that exceeds a reasonable range.

[0117] Then, similarity weights are dynamically assigned to generate interpolated values, introducing weights. To quantify each missing data point With complete data The similarity is calculated using the following formula:

[0118]

[0119] in, This design ensures that highly similar samples play a greater role in the imputation process, thereby improving the reliability of imputation.

[0120] The weighting function for the interpolated values ​​proposed in this step Weighting similar data Taking all factors into account, the generated interpolated values ​​are more concentrated in the high similarity region:

[0121]

[0122] in, Based on similar data The normal distribution function centered at the center, The standard deviation is given. This method differs from traditional imputation techniques by assigning higher weights to highly similar data, thereby strengthening the influence of highly similar data on the imputed values ​​and generating more accurate imputation results.

[0123] This refers to the search radius. The maximum weight value of the candidate imputation value among the selected similar data points. The calculation formula is as follows:

[0124]

[0125] This parameter is the core of the interpolation algorithm in this application, ensuring the rationality and effectiveness of the rejection sampling process and overcoming the shortcomings of traditional methods that ignore the similarity between samples.

[0126] In the set interpolation interval Internally, generated based on the rejection sampling process candidate interpolation values ,in .

[0127] The specific rejection sampling process includes:

[0128] (1) For each candidate interpolation value Calculate its corresponding weight .

[0129] (2) Generate a random number .

[0130] (3) If Then accept the candidate interpolation value. Otherwise, reject the value and regenerate it.

[0131] Depend on The interpolation value constitutes the first... Candidate samples with missing variables are .

[0132] S104: Based on the candidate imputation values ​​of the missing data of each variable, the target imputation values ​​of the missing data of each variable are determined using the candidate prediction model.

[0133] Specifically, the generated candidate interpolation values ​​are input into the candidate prediction model to predict the interpolated data. The error between the predicted value and the target value of each interpolated data is calculated, and the interpolation value with the smallest prediction error is selected as the final target interpolation value.

[0134] In the grinding process, the specific execution process of the missing data imputation method also includes:

[0135] For each candidate sample ,Model Generate the corresponding prediction output .

[0136]

[0137] For each candidate sample It is necessary to calculate its prediction results. , and the corresponding true target value absolute error between :

[0138]

[0139] Based on the absolute error calculation results, select the option that maximizes the prediction error. The smallest sample is used as the final imputation result. .

[0140]

[0141] in, This represents the sample with the smallest prediction error corresponding to the missing value, which is also the target imputed value.

[0142] S105: Use the target imputation values ​​of the missing data of each variable to imput the missing data of each variable to obtain the imputation data of each variable.

[0143] Specifically, the missing data in the original data are replaced with the target imputation values ​​determined in step S104 to obtain an imputed dataset containing complete data for all variables. This imputed dataset can be used in subsequent data analysis, modeling, or prediction tasks.

[0144] In the grinding process, the specific execution process of the missing data imputation method also includes:

[0145] Using target interpolation values right Interpolation is performed to obtain interpolated data for each variable, forming the interpolated dataset. .

[0146] In an optional implementation, see Figure 2 As shown, Figure 2 The flowchart illustrates a target prediction model determination method provided in Embodiment 1 of the present invention, wherein the method further includes steps S201-S202:

[0147] S201: Combine the interpolated data of each variable with the complete data of each variable to obtain the model training data.

[0148] Specifically, the imputed data obtained in step S105 is merged with the complete data in the original data to form a new, more complete dataset, which now contains the values ​​of all variables, whether it is the original complete data or the imputed missing data.

[0149] Imputed dataset With the complete dataset Integrate them to form a new training dataset. .

[0150]

[0151] S202: Use the model training data to train the candidate prediction model to obtain the target prediction model.

[0152] Specifically, using a new training dataset For candidate prediction models Retraining is then performed. With the addition of imputed data, the model learns a more complete relationship between the input and target variables during training, thereby improving predictive ability. The new model can more effectively address the data gap problem that may occur in real-world industrial scenarios.

[0153] In an optional implementation, the method further includes:

[0154] The grinding particle size is predicted using the target prediction model.

[0155] Specifically, the target prediction model is applied to the soft measurement system of the copper ore grinding process. The model predicts the grinding particle size during the grinding process, inputting relevant variables into the model and outputting the predicted particle size value. The prediction results can be used to guide the grinding process, optimize grinding parameters, and improve grinding efficiency and product quality.

[0156] See Figure 3 As shown, Figure 3A schematic diagram of a soft measurement system for a copper ore grinding process provided in Embodiment 1 of the present invention is shown. In this system, the integration of a ball mill and a hydrocyclone enables effective pulverization and precise classification of the ore slurry. Copper ore, along with grinding media (such as steel balls), enters the ball mill, where it is pulverized and ground through impact and friction. Sensors monitoring key operating parameters (such as ball mill power) are highly susceptible to malfunction due to the harsh conditions of the grinding environment, leading to data loss. Subsequently, an appropriate amount of water is added to the system through the feed water and pump pool makeup water to adjust the ore slurry concentration; however, the sensors responsible for this adjustment are prone to clogging or corrosion due to the abrasiveness of the ore slurry, resulting in data loss. After being discharged from the ball mill, the ore slurry enters the pump pool and is then transported to the hydrocyclone by a slurry pump. The current and frequency of the slurry pump reflect the pump's operating status and conveying capacity. In the hydrocyclone, the slurry is classified by particle size under centrifugal force: fine particles, i.e., the proportion of slurry that passes through a 200-mesh standard sieve, are separated as overflow and used for subsequent flotation or processing stages, while coarse particles are returned to the ball mill as backwash for further grinding. By monitoring and adjusting these variables (such as feed water, pump pool makeup water, pump pool level, slurry pump current and frequency, etc.), the grinding and classification process can be optimized, improving overall efficiency and product quality.

[0157] In an optional implementation, see Figure 4 As shown, Figure 4 The flowchart illustrates a method for determining similar complete data according to Embodiment 1 of the present invention, wherein the step of determining similar complete data of each variable from the complete data of each variable based on the missing data of each variable includes steps S401 to S403:

[0158] S401: Calculate the similarity between the complete data and the missing data for each variable.

[0159] Specifically, similarity metrics include distance-based metrics (Euclidean distance, Manhattan distance, etc.) or feature-based relevance metrics. For each missing data point, it is compared with every data point in the complete dataset, and a similarity value is calculated between them. This similarity value reflects the degree of proximity or similarity between the two data points.

[0160] S402: Select the preset number of complete data that have the highest similarity to the missing data as the similar complete data for each variable.

[0161] Specifically, select several data points from the complete dataset that have the highest similarity to the missing data points as similar complete data.

[0162] S403: Alternatively, complete data whose similarity to the missing data exceeds a preset threshold shall be identified as similar complete data to the missing data of each variable.

[0163] Specifically, a similarity threshold is preset. If the similarity between a complete data point and a missing data point exceeds this threshold, then it is selected as a similar complete data point.

[0164] In an optional implementation, see Figure 5 As shown, Figure 5 The flowchart illustrates a method for generating candidate imputation values ​​according to Embodiment 1 of the present invention, wherein the step of generating candidate imputation values ​​for the missing data of each variable based on similar complete data of the missing data of each variable includes steps S501 to S503:

[0165] S501: Construct a similar dataset based on similar complete data with missing data for each variable.

[0166] Specifically, all complete data points similar to a missing data point are collected to form a similarity dataset. This dataset contains a series of data points similar to the missing data point, which will be used to generate candidate imputation values ​​for the missing data.

[0167] S502: Configure the missing data imputation value range for the missing data of each variable, and configure the weights for each similar complete data in the similar dataset.

[0168] Specifically, an imputation range is configured for the missing data of each variable, defining the range of possible values ​​for the missing data. Simultaneously, similarity weights are dynamically assigned to each similar complete data point in the similar dataset.

[0169] S503: Based on the weights of each similar complete data set, candidate imputation values ​​for the missing data of each variable are generated within the imputation value range of the missing data of each variable using a random sampling method.

[0170] Specifically, based on the weights of similar complete data, a value is randomly selected as a candidate imputation value within the imputation value range. Due to the influence of weights, data points with higher similarity are more likely to be selected, thus generating candidate imputation values ​​that are closer to the true value. This process can be repeated multiple times to generate multiple candidate imputation values ​​for each missing data point.

[0171] In an optional implementation, configuring weights for each similar complete data point in the similar dataset includes:

[0172] The weights of similar complete data are determined based on the missing data and the complete data of each variable.

[0173] Specifically, weights are introduced to quantify the similarity between each missing data point and the complete data, so as to ensure that highly similar samples play a greater role in the imputation process, thereby improving the reliability of imputation.

[0174] In an optional implementation, see Figure 6 As shown, Figure 6 The flowchart illustrates a method for determining target imputation values ​​according to Embodiment 1 of the present invention. The step of determining the target imputation values ​​for the missing data of each variable using the candidate prediction model based on the candidate imputation values ​​of the missing data of each variable includes steps S601-S603:

[0175] S601: The predicted value of each candidate interpolation value is determined using the candidate prediction model.

[0176] Specifically, each candidate interpolation value is substituted into the candidate prediction model to calculate the predicted value of the model under that interpolation value.

[0177] S602: Calculate the error between the predicted value and the target value of each candidate interpolation value.

[0178] Specifically, the target values ​​of each candidate imputation value are obtained by training with the complete dataset, and the error values ​​between these predicted values ​​and the target values ​​are calculated. This error value reflects the degree of difference between the predicted values ​​and the target values, and can be measured by indicators such as mean squared error (MSE), root mean square error (RMSE), and mean absolute error (MAE).

[0179] S603: The candidate interpolation value with the smallest error between the predicted value and the target value among all candidate interpolation values ​​is determined as the target interpolation value.

[0180] Specifically, after comparing the error values ​​of the predicted values ​​of all candidate imputation values ​​with the target value, the candidate imputation value with the smallest error is selected as the final imputation value for the missing data, i.e., the target imputation value.

[0181] The data interpolation method for missing grinding process provided in this application was applied to a soft measurement system for grinding particle size in a copper ore processing process to improve the prediction accuracy in the case of missing data. The data, consisting of 98 records (10 missing records), was collected manually and analyzed in the laboratory. Due to the limited data volume and complex acquisition process, this dataset is extremely valuable. The target variable is the overall yield of the product slurry passing through a 200-mesh standard sieve (i.e., the total proportion of particles smaller than 74 micrometers in the product). The input variables for the grinding process are shown in Table 1 below, which lists the serial number, name, and unit of each input variable.

[0182]

[0183] Table 1

[0184] The first 70% of the data was used as the training dataset, and the remaining 30% as the test dataset. The training dataset contained both complete and missing data, while the test dataset included input variables. To evaluate the performance of the proposed dynamic similarity weighting method for imputation of missing data, three commonly used imputation methods were compared: direct deletion, mean imputation, and K-nearest neighbors (KNN) imputation. Direct deletion simply removes data containing missing values; this method is simple and easy to implement. However, its drawback is the reduction in the amount of effective data, especially in industrial data-scarce scenarios where each data point is precious, and excessive data deletion severely impacts model training and prediction accuracy. Mean imputation fills in the missing values ​​using the mean of the variable containing the missing value, suitable for scenarios with relatively uniform data distribution, maintaining the overall trend of variables, but ignoring local correlations between variables. KNN imputation, based on the K-nearest neighbor algorithm (K=5), uses the values ​​of the five neighboring samples similar to the missing sample for imputation, maintaining data similarity, but its effectiveness may be limited when the data distribution is complex.

[0185] The experiment compared the effects of four interpolation methods, using correlation coefficient (COR), mean squared error (MSE), and mean absolute error (MAE) as performance evaluation criteria. The formulas are as follows:

[0186]

[0187] Where N represents the total number of samples in the test dataset. For the true value, For predicted values, The mean of the true values. This is the mean of the predicted values.

[0188] To ensure the robustness of the results, each performance metric was taken as the average of 10 experimental results. Simultaneously, the MSE and MAE values ​​corresponding to the optimal COR were recorded. Table 2 shows the experimental results of the four interpolation methods on the three performance metrics of COR, MSE, and MAE. The results show that the developed algorithm outperforms other comparative algorithms on all metrics, validating its high prediction accuracy in this industrial environment.

[0189]

[0190] Table 2

[0191] See Figure 7 As shown, Figure 7The figure shows a schematic diagram of the target variable fitting result provided in Embodiment 1 of the present invention, wherein COR=0.812. The figure shows that the prediction result can accurately follow the dynamic changes of the true value.

[0192] Example 2

[0193] Embodiment 2 of the present invention provides a data interpolation device for missing data in a grinding process, see [link to documentation]. Figure 8 As shown, Figure 8 The diagram shows a structural schematic of a data interpolation device for a grinding process provided in Embodiment 2 of the present invention, wherein the device includes:

[0194] The candidate prediction model training module 801 is used to train the initial prediction model using the complete variable dataset to obtain the candidate prediction model, wherein the complete variable dataset contains complete data of several variables.

[0195] The similar complete data determination module 802 is used to obtain the missing data of each variable and determine the similar complete data of each variable from the complete data of each variable based on the missing data of each variable.

[0196] The candidate imputation value determination module 803 is used to generate candidate imputation values ​​for the missing data of each variable based on similar complete data of the missing data of each variable;

[0197] The target interpolation value determination module 804 is used to determine the target interpolation value of the missing data of each variable based on the candidate interpolation values ​​of the missing data of each variable and using the candidate prediction model.

[0198] The imputation data generation module 805 is used to impute the missing data of each variable by using the target imputation values ​​of the missing data of each variable to obtain the imputed data of each variable.

[0199] In an optional implementation, the device further includes:

[0200] The training data generation module is used to merge the imputed data and the complete data of each variable to obtain the model training data;

[0201] The prediction model training module is used to train the candidate prediction model using the model training data to obtain the target prediction model.

[0202] Optionally, the device further includes:

[0203] The grinding particle size prediction module is used to predict the grinding particle size using the target prediction model.

[0204] Optionally, the step of determining similar complete data for each variable from the complete data of each variable based on the missing data of each variable includes:

[0205] Calculate the similarity between the complete data and the missing data for each variable;

[0206] Select the preset number of complete data points with the highest similarity to the missing data to determine the similar complete data points for each variable.

[0207] Alternatively, complete data whose similarity to the missing data exceeds a preset threshold can be identified as similar complete data to the missing data of each variable.

[0208] Optionally, generating candidate imputed values ​​for the missing data of each variable based on similar complete data of the missing data of each variable includes:

[0209] Construct similar datasets based on similar complete datasets with missing data for each variable;

[0210] Configure missing data imputation value ranges for missing data of each variable, and configure weights for each similar complete data in the similar dataset;

[0211] Based on the weights of each similar complete data set, candidate imputation values ​​for the missing data of each variable are generated within the imputation value range of the missing data of each variable using a random sampling method.

[0212] Optionally, configuring weights for each similar complete data point in the similar dataset includes:

[0213] The weights of similar complete data are determined based on the missing data and the complete data of each variable.

[0214] Optionally, determining the target imputed value for the missing data of each variable using the candidate prediction model based on the candidate imputed values ​​for the missing data of each variable includes:

[0215] The predicted value of each candidate interpolation value is determined using the candidate prediction model.

[0216] Calculate the error between the predicted value and the target value for each candidate interpolation value;

[0217] The candidate interpolation value with the smallest error between the predicted value and the target value among all candidate interpolation values ​​is determined as the target interpolation value.

[0218] Example 3

[0219] Based on the same application concept, see [link / reference] Figure 9 As shown, Figure 9 A schematic diagram of the structure of a computer device provided in Embodiment 3 of the present invention is shown, wherein, as Figure 9 As shown, the computer device 900 provided in Embodiment 3 of this application includes:

[0220] The computer device 900 includes a processor 901, a memory 902, and a bus 903. The memory 902 stores machine-readable instructions that can be executed by the processor 901. When the computer device 900 is running, the processor 901 communicates with the memory 902 through the bus 903. When the machine-readable instructions are executed by the processor 901, they perform the steps of the missing data interpolation method for the grinding process shown in Embodiment 1 above.

[0221] Example 4

[0222] Based on the same concept, this application also provides a computer-readable storage medium storing a computer program, which, when run by a processor, performs the steps of the grinding process missing data interpolation method described in any of the above embodiments.

[0223] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and apparatus described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0224] The computer program product for interpolating missing data in the grinding process provided in this embodiment of the invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation details, please refer to the method embodiments, which will not be repeated here.

[0225] The data interpolation device for missing grinding process data provided in this embodiment of the invention can be specific hardware on the equipment or software or firmware installed on the equipment. The implementation principle and technical effects of the device provided in this embodiment of the invention are the same as those in the foregoing method embodiments. For the sake of brevity, any parts not mentioned in the device embodiments can be referred to the corresponding content in the foregoing method embodiments. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can all be referred to the corresponding processes in the above method embodiments, and will not be repeated here.

[0226] In the embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the coupling or direct coupling or communication connection shown or discussed may be through some communication interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0227] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0228] In addition, the functional units in the embodiments provided by the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0229] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0230] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0231] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. All should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for interpolating missing data in a grinding process, characterized in that, The method includes: Candidate prediction models are obtained by training an initial prediction model using a complete dataset of variables. The initial prediction model is a randomly configured network. The complete dataset of variables contains complete data of several variables in the grinding process. The variables are key operating parameters, including throughput, ball mill power, overflow concentration, hydrocyclone pressure, slurry pump current and frequency. When a sensor used to monitor key operating parameters malfunctions, resulting in missing data for the key operating parameters, similar complete data reflecting the current load status of the grinding equipment can be determined from the complete data of each variable using Euclidean distance metric based on the missing data of each variable. Based on the similar complete data of the missing data of each variable, and combined with the data imputation value range pre-configured for each variable based on grinding process knowledge, candidate imputation values ​​for the missing data of each variable are generated. Based on the candidate imputation values ​​of the missing data of each variable, the target imputation values ​​of the missing data of each variable are determined using the candidate prediction model. Specifically, this includes: inputting each candidate imputation value into the candidate prediction model to obtain the predicted grinding particle size value, calculating the absolute error between the predicted value and the actual grinding particle size value collected at the current time corresponding to the missing data, and selecting the candidate imputation value with the smallest error as the target imputation value. The missing data of each variable is imputed by using the target imputed values ​​of the missing data of each variable; The interpolated data and the complete data of each variable are combined to obtain the model training data; The target prediction model is obtained by training the candidate prediction model using the model training data. The grinding particle size is predicted using the target prediction model.

2. The method according to claim 1, characterized in that, The process of determining similar complete data reflecting the current load status of the grinding equipment from the complete data of each variable based on the missing data of each variable using Euclidean distance metric includes: Calculate the similarity between the complete data and the missing data of each variable, wherein the similarity includes the Euclidean distance metric; Select the preset number of complete data points with the highest similarity to the missing data to determine the similar complete data points for each variable. Alternatively, complete data whose similarity to the missing data exceeds a preset threshold can be identified as similar complete data to the missing data of each variable.

3. The method according to claim 1, characterized in that, The process of generating candidate imputed values ​​for the missing data of each variable by combining similar complete data with pre-configured data imputed value ranges based on grinding process knowledge, including: Construct similar datasets based on similar complete datasets with missing data for each variable; Configure the missing data imputation range for the grinding process for the missing data of each variable, and configure the weights for each similar complete data in the similar dataset; Based on the weights of each similar complete data set, candidate imputation values ​​for the missing data of each variable are generated within the imputation value range of the missing data in the grinding process of each variable using a random sampling method.

4. The method according to claim 3, characterized in that, The step of configuring weights for each similar complete data point in the similar dataset includes: The weights of similar complete data are determined based on the missing data and the complete data of each variable.

5. The method according to claim 1, characterized in that, The step of determining the target imputation value for the missing data of each variable using the candidate prediction model based on the candidate imputation values ​​of the missing data of each variable includes: The predicted value of each candidate interpolation value is determined using the candidate prediction model. Calculate the error between the predicted value and the target value for each candidate interpolation value; The candidate interpolation value with the smallest error between the predicted value and the target value among all candidate interpolation values ​​is determined as the target interpolation value.

6. A data interpolation device for a grinding process, characterized in that, The device includes: The candidate prediction model training module is used to train the initial prediction model using the complete variable dataset to obtain candidate prediction models. The initial prediction model is a randomly configured network. The complete variable dataset contains complete data of several variables in the grinding process. The variables are key operating parameters, including throughput, ball mill power, overflow concentration, hydrocyclone pressure, slurry pump current and frequency. The similar complete data determination module is used to determine similar complete data reflecting the current load status of the grinding equipment from the complete data of each variable based on the missing data of each variable when the sensor used to monitor the key operating parameters fails, resulting in missing data of the key operating parameters. The candidate imputation value determination module is used to generate candidate imputation values ​​for the missing data of each variable based on similar complete data of the missing data of each variable, combined with the data imputation value range pre-configured for each variable based on grinding process knowledge. The target interpolation value determination module is used to determine the target interpolation value of the missing data of each variable based on the candidate interpolation values ​​of the missing data of each variable and the candidate prediction model. Specifically, it includes: inputting each candidate interpolation value into the candidate prediction model to obtain the predicted grinding particle size value, calculating the absolute error between the predicted value and the actual grinding particle size value collected at the current time corresponding to the missing data, and selecting the candidate interpolation value with the smallest error as the target interpolation value. The imputation data generation module is used to impute the missing data of each variable by using the target imputation values ​​of the missing data of each variable to obtain the imputed data of each variable. The training data generation module is used to merge the imputed data and the complete data of each variable to obtain the model training data; The prediction model training module is used to train the candidate prediction model using the model training data to obtain the target prediction model; The grinding particle size prediction module is used to predict the grinding particle size using the target prediction model.

7. A computer device, characterized in that, include: The system includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the missing data interpolation method for the grinding process as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the grinding process missing data interpolation method as described in any one of claims 1 to 5.

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