Method for detecting quality faults of a flotation process based on distributed dynamic graph embeddings

Abstract

This invention discloses a method for detecting quality faults in a flotation process based on distributed dynamic graph embedding. Step 1: Collect process variables such as concentration, pH value, ore fineness, froth layer thickness, and maximum allowable density during the flotation production process as input variables, and the concentrate grade of the flotation process as the output quality indicator. Step 2: Based on the mutual information method, establish a cross-correlation matrix MI between process variables and quality variables, calculate the average threshold, and select key variables. Step 3: Based on the production process and field experience of the flotation process, divide the key variables into Q quality-related sub-blocks and B quality-unrelated sub-blocks. Step 4: Use the key variable selection and sub-block decomposition results to establish a distributed dynamic graph model to achieve quality-related fault detection. Step 5: Use a Bayesian fusion network to fuse the monitoring results for decision-making. Step 6: Determine whether the fault is quality-related based on the monitoring results.

Description

Technical Field

[0001] This invention relates to a method for detecting quality faults in a flotation process based on distributed dynamic graph embedding. Background Technology

[0002] Flotation is a process for separating minerals, with grade serving as the final quality indicator. However, grade measurements during flotation are typically obtained through laboratory testing, which is time-consuming and lacks effective feedback to the production process. By establishing correlations between process and quality variables in the flotation process and monitoring them, production indicators can be adjusted in real-time based on the monitoring results to achieve optimal production.

[0003] Traditional monitoring methods use a single model to represent the entire process. However, with the development of modern industry, the scale of metallurgical production processes is increasing, characterized by large scale and multiple sub-processes. Using centralized fault detection methods can easily lead to the loss of localized information.

[0004] Therefore, it is necessary to design a new method for detecting quality defects in the flotation process. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for detecting quality faults in the flotation process based on distributed dynamic graph embedding, so as to solve the problem of low detection rate and high false alarm rate and false negative rate of quality-related faults in the current flotation production process.

[0006] The technical solution of the invention is as follows:

[0007] A method for detecting quality faults in a flotation process based on distributed dynamic graph embedding includes the following steps:

[0008] Step 1: Collect process variables from the flotation production process as input variables for the model, and use the concentrate grade from the flotation process as the quality index of the model output.

[0009] Process variables include: slurry concentration, pH value of the mixing tank, fineness of the ore feed, thickness of the foam layer, at most, and dosage of reagents;

[0010] Step 2: Based on the mutual information method, establish the cross-correlation matrix MI between process variables and quality indicators, calculate the average threshold, and select key variables;

[0011] Step 3: Based on the production process and field experience of the flotation process, the key variables are divided into Q quality-related sub-blocks and B quality-independent sub-blocks;

[0012] Step 4: Using the key variable selection and sub-block decomposition results, establish a distributed dynamic graph model to detect quality-related faults and obtain monitoring results;

[0013] The monitoring result of the distributed dynamic graph model is the statistic T. 2 and control limit T 2 lim ;

[0014] Step 5: Use a Bayesian fusion network to fuse the monitoring results of the distributed dynamic graph model for decision-making;

[0015] The reliability of the monitoring results is inferred, and a monitoring result BIC for fusion decision is given;

[0016] In this step, a Bayesian fusion network is used to integrate the statistics and control limits calculated from the Q quality-related sub-blocks and B quality-unrelated sub-blocks. Bayesian fusion considers the reliability and uncertainty of the statistics and control limits calculated from the sub-blocks, and uses a probabilistic model to weigh and integrate this information to obtain a more accurate and robust integrated result.

[0017] Step 6: Based on the BIC monitoring results of the fusion decision, faults with statistics exceeding the threshold are classified as quality-related faults. (Further analysis and judgment are performed on the flotation production process. For quality-related faults, a statistical value exceeding the threshold indicates a quality-related fault.)

[0018] In step 1, six process variables in the flotation production process are collected as input variables, and the concentrate grade in the flotation process is used as the output quality indicator.

[0019] The six process variables are concentration, pH value, ore fineness, foam layer thickness, maximum amount, and dosage.

[0020] Data samples are obtained by sampling the process variables at regular time intervals.

[0021] Each quantity is a feature, and the sample is the sampling interval. For example, if a sample is taken every 3 minutes, 960 samples are taken in 48 hours. The input data is 960*6, where 960 is the number of samples and 6 is the feature quantity: concentration, pH value, ore fineness, froth layer thickness, and reagent dosage during the flotation process.

[0022] The mutual information correlation matrix M and its average threshold M in step 2 threshold The calculation process is as follows:

[0023]

[0024]

[0025] Where M(xi,yi) is the cross-correlation coefficient between process variable x and quality variable y, M thresholdis the average threshold, and l is the total number of variables;

[0026] If M>M threshold If so, then this variable is the key variable.

[0027] Calculated average threshold M threshold Both M and M are specific values, such as M > M threshold If so, then this variable is a key variable;

[0028] For example: M threshold =0.6258

[0029] If M1 = 0.6934 and M2 = 0.5826, then M1 is the key variable, while M2 is not.

[0030] In step 3, based on the production process and field experience of the flotation process, the key variables are divided into Q quality-related sub-blocks and B quality-independent sub-blocks;

[0031] For example, the beneficiation process includes several steps such as crushing, grinding, flotation, and pressure filtration. Flotation itself includes roughing, cleaning, and scavenging processes. Therefore, this invention combines production processes and on-site experience, and mainly divides the flotation process into several sub-blocks based on experience. Based on the selection of key variables, these sub-blocks are further divided into quality-related and quality-independent sub-blocks.

[0032] In steps 4 and 5, the calculation of local detection metrics and global fusion results is as follows:

[0033]

[0034]

[0035] In the formula, X i Let X be the augmented matrix representing the input matrix X. The input is 6-dimensional, and using data augmentation, it is augmented to 16*6=96 dimensions. U represents the mass-dependent projection matrix, V represents the mass-independent projection matrix, and Λ represents X. i The diagonal matrix, v i The eigenvalues ​​of the elements on the diagonal (the eigenvalues ​​of the elements on the diagonal are the elements on the diagonal). Represents matrix X i The Frobenius norm is the square root of the sum of the squares of all elements in the matrix.

[0036] The mass-related projection matrix U is calculated as shown in equation (5):

[0037] U = X i (X i T X) -1 XT (5)

[0038] Since U and V are orthogonal matrices, therefore:

[0039] V = U T (6)

[0040] In the formula, the quality correlation matrix U is 6-dimensional, and the quality uncorrelation matrix V is also 6-dimensional;

[0041]

[0042]

[0043] In the formula, m represents the initial value of the sample, l represents the final value of the sample, and h represents the bandwidth parameter; in the monitoring of the flotation process, m = 960, l = 1, and h is calculated by formula (6). In formula (6), a is T i The mean of T, where v is T i The variance;

[0044]

[0045]

[0046]

[0047] Where T i 2 Q is a quality-related statistic. i This is a statistic that is irrelevant to quality. For quality-related monitoring and control limits, Q lim For quality-independent monitoring control limits, N and F represent normal and faulty, respectively; P(N) and P(F) represent the prior probabilities of normal and faulty samples, respectively, and P(T) represents the prior probabilities of faulty samples. b ) represents the statistical probability of the B-th quality-related sub-block, P(F / T) b ) represents the prior probability of a fault sample in the b-th quality-related sub-block;

[0048] P(F)=α (12)

[0049] P(N)=1-α (13)

[0050] P(T b |N)=exp(-T b / T b,lim )

[0051] In the formula, T b For T b 2 The square root of T b 2T represents the statistics of the b-th sub-block. b,lim 2 For T b,lim 2 The square root of T b,lim 2 These represent the control limits of the b-th sub-block. Their values ​​are calculated according to formulas (3) and (5).

[0052] P(T b |F)=exp(-T b,lim / T b (14)

[0053]

[0054] In the formula, BIC is the global index of Bayesian fusion, which is the monitoring result of fusion of multiple sub-blocks, where b represents the minimum value of the monitored sub-block and B is the maximum value of the monitored sub-block. In the flotation process monitoring, b = 1 and B = 3 are taken; the monitored T i 2 Q is a statistic related to the quality of the sub-blocks. i For statistics of quality-independent sub-blocks, Q is the monitoring and control limit for quality-related sub-blocks. lim For monitoring and control limits of quality-independent sub-blocks.

[0055] In step 6, determine whether the fault is quality-related according to the following formula:

[0056]

[0057] Beneficial effects:

[0058] This invention adopts the divide-and-conquer approach, dividing the entire flotation process monitoring model into several sub-blocks. Under the supervision of quality indicators, local information is enhanced by combining data time and neighborhood information, thus proposing a quality-related monitoring model for the flotation production process based on distributed dynamic graph embedding.

[0059] The flotation process quality fault detection method based on distributed dynamic graph embedding of the present invention has the following characteristics:

[0060] 1. This invention correlates process variables such as medium concentration, pH value, ore fineness, froth layer thickness, and at most with concentrate grade indicators during the flotation process, and performs quality-related fault detection in the flotation production process.

[0061] 2. This invention employs a dynamic graph embedding method to convert a one-dimensional time series into two-dimensional data containing time and spatial information, and performs dynamic feature enhancement in the form of a sliding window.

[0062] 3. This algorithm adopts a divide-and-conquer approach, combining mutual information methods and actual process operations. It selects key process variables and divides them into quality-related and quality-independent sub-blocks, establishes distributed dynamic graph embedding models for each, and finally uses a Bayesian network for global decision fusion. Attached Figure Description

[0063] Figure 1 The monitoring results are shown in the diagram, which divides the entire flotation process into three subspaces.

[0064] Figure 2 The diagram shows the effect of using five algorithms to monitor faults; (among them) Figure 2 af represents the fault-related curves, and the curves obtained using KPLS, TKPLS, MKPLS, DGE, and DDGE algorithms, respectively.

[0065] Figure 3 The diagram shows the effect of using five algorithms to monitor faults; (among them) Figure 3 af represents the fault-related curves, and the curves obtained using KPLS, TKPLS, MKPLS, DGE, and DDGE algorithms, respectively.

[0066] Figure 4 A graph showing the monitoring results after dividing uncorrelated variables into three subspaces;

[0067] Figure 5 The diagram shows the effect of using five algorithms to monitor faults; (among them) Figure 5 af represents the fault-related curves, and the curves obtained using KPLS, TKPLS, MKPLS, DGE, and DDGE algorithms, respectively.

[0068] Figure 6 The following is the implementation process of the present invention;

[0069] Figure 7 These are the specific steps of this algorithm. Detailed Implementation

[0070] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0071] Example 1: As Figures 6-7 Step 1: Collect process variables such as concentration, pH value, ore fineness, froth layer thickness, and maximum concentration during the flotation process as input variables X, and the concentrate grade during the flotation process as the output quality index Y, as shown in Table 1:

[0072] Table 1. Process Variables and Quality Variables

[0073]

[0074] Step 2: Data Preprocessing. Standardize and normalize the collected process variable X and quality variable Y.

[0075]

[0076]

[0077] In the formula, δ(x) represents the mean of each column of process variable X; δ(x) represents the variance of each column of process variable X. δ(y) represents the mean of each column of the quality variable Y; δ(y) represents the variance of each column of the quality variable Y.

[0078] Step 3: Calculate the mutual information coefficients between process variable X and quality variable Y, and construct the cross-correlation matrix M;

[0079]

[0080] N represents the sample size of the variables, l represents the feature dimension of the process variable X, and m represents the feature dimension of the quality variable Y. Their values ​​need to be determined based on the collected data. In the flotation data collected this time, N = 960, l = 33, and m = 1.

[0081] M(x i ,y j )=H(x i )+H(y j )-H(x i ,y j (4)

[0082] Where M(x) i ,y i H(x) is the mutual information coefficient. i Let H(y) be the information entropy of X, and H(y) be the information entropy of X. i H(x) is the information entropy of Y, and H(x) is the information entropy of Y. i ,y i Let X be the joint entropy of X and Y;

[0083]

[0084] Where M represents the mutual information matrix, M 1,1 M represents the mutual information coefficient between the first column X and Y. l,m This represents the mutual information coefficient between X and Y in the l-th row and m-th column.

[0085] Step 4: Calculate the mutual information threshold to select key variables;

[0086]

[0087] M represents the mutual information matrix, and M1 represents the sum of the mutual information coefficients in the first column, as detailed in formula (10). l This represents the sum of the mutual information coefficients in the l-th column, see formula (11) for details;

[0088] M1 = M 1,1 +M 1,2 +LM 1,m (7)

[0089] M l =M l,1 +M l,2 +LM l,m (8)

[0090] Among them, M threshold M1 is the mutual information threshold, M1 is the sum of the mutual information of the first column, M l Let l be the sum of the mutual information of the l-th column, and l be the total number of variables. When the mutual information coefficients of the variables are greater than the mutual information threshold M... threshold If so, then it is determined to be a key variable.

[0091] Step 5: Employing a hybrid knowledge- and data-driven approach, the selected key variables are divided into quality-related and quality-irrelevant sub-blocks. Specifically, in the first step, considering the physical location and operational processes of the process variables, the flotation process variables and their corresponding quality variables are divided into three sub-blocks—roughing, cleaning, and scavenging—according to the process sequence, driven by comprehensive industrial knowledge, corresponding to subspace 1, subspace 2, and subspace 3, respectively. Considering the coupling relationship between process variables during flotation, there are connecting variables between the first block and the next sub-block. In the second step, to avoid information redundancy and overwhelming caused by irrelevant process variables, variables from the first step that exceed the mutual information threshold are classified as quality-related sub-blocks, while those that are below the threshold are classified as quality-irrelevant sub-blocks. Note: Step 4 selects key variables, and Step 5 models these variables separately in different sub-blocks.

[0092] Step 6: Using the key variable selection and sub-block decomposition results, establish a distributed dynamic graph model to realize quality-related fault detection;

[0093]

[0094] In the formula, X i Let X represent the augmented matrix X, U represent the quality-dependent projection matrix, V represent the quality-independent projection matrix, and Λ represent X. i The covariance matrix, Represents matrix X i The Frobenius norm is the square root of the sum of the squares of all elements in the matrix.

[0095]

[0096]

[0097]

[0098] In the formula, a is T i The mean in a statistic, where v is T i Variance in statistics.

[0099]

[0100]

[0101] In the formula, T b This represents the statistics for the b-th sub-block.

[0102]

[0103] P(F)=α (16)

[0104] P(N)=1-α (17)

[0105] P(T b |N)=exp(-T b / T b,lim (18)

[0106] In the formula, T b,lim This represents the control limits for the b-th sub-block.

[0107] P(T b |F)=exp(-T b,lim / T b (19)

[0108]

[0109] Where T i 2 Q is a quality-related statistic. i This is a statistic that is irrelevant to quality. For quality-related monitoring and control limits, Q lim The control limits are for quality-independent monitoring, where N and F represent normal and faulty samples, respectively; P(N) and P(F) represent the prior probabilities of normal and faulty samples, respectively, with confidence levels of α and 1-α, respectively.

[0110] Step 7: Use a Bayesian fusion network to integrate the monitoring results and make decisions. Based on the monitoring results, determine whether the fault is quality-related.

[0111]

[0112] Among them, Ti 2 For statistical purposes, The monitoring and control limits are set, with the confidence level α ranging from (0,1). BIC is the global index of T2 and SPE after Bayesian fusion.

[0113] The effects of this invention can be obtained through the following simulation experiments, as detailed below:

[0114] To verify the feasibility of the algorithm proposed in this paper, simulation experiments were conducted using MATLAB software.

[0115] (1) Monitoring results of the quality-related subspace based on DDGE

[0116] First, based on the results of the block division, a DDGE model was established for each subspace for monitoring. The monitoring results are shown in Figure (1). As can be seen from the figure, the entire flotation process was divided into 3 subspaces, and quality-related faults in each space were monitored. The monitoring results show that the proposed algorithm has a high detection rate and no false alarm rate in all three subspaces.

[0117] (2) Monitoring results of different algorithms based on quality-related faults

[0118] To verify the superiority of the algorithm, it is compared with four typical fault detection algorithms: KPLS, TKPLS, MKPLS, and DGE. Figure 2 (a) shows quality-related faults (i.e. faults that have a significant impact on quality and whose quality variables cannot be self-recovered). The proposed algorithm DDGE is superior to other algorithms, with a high detection rate and no false alarm rate.

[0119] (3) Monitoring results of different algorithms based on semi-correlated quality faults

[0120] To verify the superiority of the algorithm, it is compared with four typical fault detection algorithms: KPLS, TKPLS, MKPLS, and DGE. Figure 3 (a) shows a quality semi-correlated fault (i.e., after a period of time, the system quality variables can recover after the fault occurs). The proposed algorithm DDGE is superior to other algorithms, and its false alarm rate is relatively lower than that of other algorithms.

[0121] (4) Monitoring results of mass-independent subspace based on DDGE

[0122] Based on the block partitioning results, the quality-independent variables were divided into three subspaces, and DDGE models were established for each subspace for monitoring. The monitoring results are as follows: Figure 4As shown in the figure, the entire flotation process is divided into three subspaces. Faults unrelated to quality are monitored in each subspace. The monitoring results show that the proposed algorithm has a low false alarm rate in all three subspaces.

[0123] (5) Monitoring results of different algorithms based on quality-irrelevant faults

[0124] To verify the superiority of the algorithm, it is compared with four typical fault detection algorithms: KPLS, TKPLS, MKPLS, and DGE. Figure 5 (a) shows a quality-irrelevant fault (i.e., a fault that is completely unrelated to quality and has no impact on quality). The proposed algorithm DDGE is superior to other algorithms, and its false alarm rate is relatively lower than that of other algorithms.

Claims

1. A method for detecting quality faults in a flotation process based on distributed dynamic graph embedding, characterized in that, Includes the following steps: Step 1: Collect process variables from the flotation production process as input variables for the model, and use the concentrate grade from the flotation process as the quality index of the model output. Process variables include: slurry concentration, pH value of the mixing tank, fineness of the ore feed, thickness of the foam layer, at most, and dosage of reagents; Step 2: Based on the mutual information method, establish the cross-correlation matrix MI between process variables and quality indicators, calculate the average threshold, and select key variables; Step 3: Based on the production process and field experience of the flotation process, the key variables are divided into Q quality-related sub-blocks and B quality-independent sub-blocks; Step 4: Using the key variable selection and sub-block decomposition results, establish a distributed dynamic graph model to detect quality-related faults and obtain monitoring results; The monitoring result of the distributed dynamic graph model is the statistic T. 2 and control limit T 2 lim ; Step 5: Use a Bayesian fusion network to fuse the monitoring results of the distributed dynamic graph model for decision-making; The reliability of the monitoring results is inferred, and a monitoring result BIC for fusion decision is given; Step 6: Based on the monitoring results BIC of the fusion decision, faults whose statistics exceed the threshold are judged as quality-related faults.

2. The method for detecting quality faults in the flotation process based on distributed dynamic graph embedding as described in claim 1, characterized in that... In step 1, six process variables in the flotation production process are collected as input variables, and the concentrate grade in the flotation process is used as the output quality indicator. The six process variables are concentration, pH value, ore fineness, foam layer thickness, maximum amount, and dosage. Data samples are obtained by sampling the process variables at regular time intervals.

3. The method for detecting quality faults in the flotation process based on distributed dynamic graph embedding as described in claim 1, characterized in that, The mutual information correlation matrix M and its average threshold M in step 2 threshold The calculation process is as follows: Where M(xi,yi) is the cross-correlation coefficient between process variable x and quality variable y, M threshold is the average threshold, and l is the total number of variables; If M>M threshold If so, then this variable is the key variable.

4. The method for detecting quality faults in the flotation process based on distributed dynamic graph embedding as described in claim 1, characterized in that, In step 3, based on the production process and on-site experience of the flotation process, the key variables are divided into Q quality-related sub-blocks and B quality-independent sub-blocks.

5. The method for detecting quality faults in the flotation process based on distributed dynamic graph embedding according to claim 1, characterized in that, In steps 4 and 5, the calculation of local detection metrics and global fusion results is as follows: In the formula, X i Let X represent the augmented matrix X, U represent the quality-dependent projection matrix, V represent the quality-independent projection matrix, and Λ represent X. i The diagonal matrix, v i The eigenvalues ​​of the elements on the diagonal. Represents matrix X i The Frobenius norm is the square root of the sum of the squares of all elements in the matrix. The mass-related projection matrix U is calculated as shown in equation (5): Since U and V are orthogonal matrices, therefore: V=U T (6) In the formula, the quality correlation matrix U is 6-dimensional, and the quality uncorrelation matrix V is also 6-dimensional; In the formula, m represents the initial value of the sample, l represents the final value of the sample, and h represents the bandwidth parameter; in the monitoring of the flotation process, m = 960, l = 1, and h is calculated by formula (6); where a in formula (6) is T i The mean of T, where v is T i The variance; Where T i 2 Q is a quality-related statistic. i This is a statistic that is irrelevant to quality. For quality-related monitoring and control limits, Q lim For quality-independent monitoring control limits, N and F represent normal and faulty, respectively; P(N) and P(F) represent the prior probabilities of normal and faulty samples, respectively, and P(T) represents the prior probabilities of faulty samples. b ) represents the statistical probability of the B-th quality-related sub-block, P(F / T) b ) represents the prior probability of a fault sample in the b-th quality-related sub-block; P(F)=α (12) P(N)=1-α (13) P(T b ∣N)=exp(-T b / T b,lim ) In the formula, T b For T b 2 The square root of T b 2 T represents the statistics of the b-th sub-block. b,lim For T b,lim 2 The square root of T b,lim 2 Represents the control limits of the b-th sub-block; P(T b ∣F)=exp(-T b,lim / T b ) (14) In the formula, BIC is the global index of Bayesian fusion, which is the monitoring result of fusion of multiple sub-blocks, where b represents the minimum value of the monitored sub-block and B is the maximum value of the monitored sub-block. In the flotation process monitoring, b = 1 and B = 3 are taken; the monitored T i 2 Q is a statistic related to the quality of the sub-blocks. i For statistics of quality-independent sub-blocks, Q is the monitoring and control limit for quality-related sub-blocks. lim For monitoring and control limits of quality-independent sub-blocks.

6. The monitoring result according to claim 5, characterized in that, In step 6, determine whether the fault is quality-related according to the following formula:

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