Soft measurement model construction method for Isa copper smelting process parameters

Abstract

The invention relates to the technical field of intelligent control of an Isa furnace smelting process, in particular to a soft measurement model construction method for Isa copper smelting process parameters, which comprises the following steps: carrying out data sampling on an Isa furnace; constructing a local linear embedding algorithm of kernel clustering, and processing sampling data; constructing an adaptive model based on generalized maximum entropy regression; a hidden Markov model is adopted to predict working conditions in the sampled data, and optimal parameters of the adaptive model based on generalized maximum entropy regression are obtained; and inputting the optimal value into the model, inputting a processed result into the model after the optimal value is obtained, and outputting a final prediction result. The prediction result is basically consistent with the actual production result, the prediction correctness and stability are good, and the method has reference value for optimization control of the actual production process.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent control of an Isa furnace smelting process, and in particular to a method for constructing a soft measurement model of Isa copper smelting process parameters. Background Art

[0002] Soft measurement technology is a kind of inference control theory. Its basic method is to collect auxiliary variables that are easy to measure in the industrial process and predict the dominant variables by constructing an estimation function. For example, in the ISA furnace smelting process, the three major parameters of matte temperature, matte grade, and iron-silicon ratio in slag are the dominant variables. It is difficult to measure them directly, but soft measurement technology can be used to model the easily measurable variables such as oxygen-enriched injection amount and furnace temperature, and then infer the value of the dominant variable. At present, soft measurement technology mainly includes two methods: mechanism-based soft measurement and neural network-based soft measurement.

[0003] However, in the existing soft measurement technology, the mechanism-based soft measurement method simulates the process parameters through physical and chemical principles and mathematical models. Although it has achieved certain results, it has the following problems: the model is complex and depends on the physical and chemical laws of the process, which makes it difficult to adapt to complex and changeable working conditions; the calculation accuracy is low, and the response to the fluctuation of complex working conditions is not sensitive, resulting in a significant increase in prediction errors; the model parameters are difficult to adjust in an industrial environment with high real-time requirements due to lack of adaptability. The neural network-based soft measurement method uses data mining technology to extract implicit information and parameter prediction models in industrial processes, but has poor generalization ability. Especially in the case of insufficient training data or uneven sample distribution, the stability and reliability of the prediction results are difficult to guarantee, the model structure is complex, the calculation cost is high, and it is difficult to meet the real-time requirements. The model is weak in interpretability, and there are obvious defects in the intuitiveness and industrial adaptability of the prediction results. In addition, although traditional dimensionality reduction technology (such as PCA) plays an important role in data processing, it mainly targets linear data when processing complex industrial data, and it is difficult to effectively process high-dimensional and nonlinear data in industry, resulting in low accuracy of feature extraction. After dimensionality reduction, some important information is lost, which limits the reliability of modeling and the accuracy of model prediction. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method for constructing a soft measurement model of Isa copper smelting process parameters.

[0005] To implement the above technical solution, the specific steps are as follows:

[0006] S1. Data sampling of Isa furnace;

[0007] The sampled data is represented by X, X = {x1,···,x n}, i∈n, n is the total number of sampled data, x i ∈Rd represents the sample space of Isa furnace smelting data, where d represents the feature dimension of the input data;

[0008] The sampled data include: matte temperature, matte grade and iron-silicon ratio in slag;

[0009] S2, construct a nonlinear dimensionality reduction algorithm (UMAP) model to reduce the dimensionality of the sampled data;

[0010] The processing steps are as follows:

[0011] S2.1. In high-dimensional data space, calculate the data set X = {x1, x2, ... x n The similarity weight w between the sample points in} ij , the expression is as follows:

[0012]

[0013] In the formula, x i represents sample point I, x j Represents sample point II, i, j∈n, i≠j; represents the key parameters in the model, By adjusting based on the k-nearest neighbor method, the expression is as follows:

[0014]

[0015] Where k is the number of neighborhood points, 5≤k≤10; x' ij Indicates the value of the i-th sample point on the j-th feature in high-dimensional data;

[0016] S2.2. Select the first n of each sample point neighbors neighbors, forming a local neighborhood graph G, where the weight of each edge is determined by w ij express;

[0017] S2.3, the data set X={x1,x2,...x n}Embed into data Y to construct low-dimensional data, optimize the representation of low-dimensional data by minimizing the Kullback-Leibler divergence between high-dimensional and low-dimensional data, so that the neighborhood relationship in high-dimensional space can be preserved in low-dimensional space;

[0018] Where Y = {y1,y2,...,y n}; m represents the target dimension after dimensionality reduction, which is reduced from d;

[0019] The Kullback-Leibler divergence expression is as follows:

[0020]

[0021] Where: w′ ij =(1+a||y i -y j || 2 ) -b , represents the similarity weight between sample points in low-dimensional space; a represents the adjustment parameter, which controls the sensitivity of low-dimensional distance to weight attenuation, b represents the power control parameter, which determines the degree of nonlinear change of weight, and y represents the i and j Respectively represent the low-dimensional data representation of sample point I and sample point II;

[0022] S3. Construct an adaptive (GMER+adaptive) model based on generalized maximum entropy regression, the expression is as follows:

[0023]

[0024] Where M GME is the soft measurement result of the soft measurement model based on generalized maximum entropy regression; M BE is the soft measurement result based on the mechanism model; μ and γ are the first and second importance evaluation indicators, defined as adaptive parameters; Y low is the final value of the measured parameter;

[0025] The construction steps are as follows:

[0026] S3.1. Construct a soft sensor model based on generalized maximum entropy regression. The steps are as follows:

[0027] S3.1.1. Construct a regression model; the expression is as follows:

[0028] Y low =X low β+ε

[0029] In the formula, β and ε represent the first parameter to be estimated and the second parameter to be estimated, where β T =[β1,β2,···,β m ] is input X low The weight vector, ε T =[ε1,ε2,···,ε n ] represents the adjustment fuzzy factor vector of the model;

[0030] S3.1.2. Parameter transformation of the regression model is as follows:

[0031] The β of the elements in β j (j=1,2,···,m) is defined as the following expression:

[0032]

[0033] In the formula, p js Is β j Support parameter Z js The corresponding probability, P js ∈[0,1], where S is generally taken as S≥2;

[0034] Subtract the ε of the elements in ε i (i=1,2,···,m) is defined as the following expression:

[0035]

[0036] In the formula, ε i represents the error term, which is obtained by the second parameter to be estimated; L represents the number of supported parameters; u il represents the error term ε i The probability corresponding to the support parameter; v il It is used to decompose the error ε i , describing the different dimensions or components of the error; u is represents the support parameter Z in the error decomposition s In the error decomposition term ε i The weight coefficient in is used to describe the distribution contribution relationship of each support parameter in the error term;

[0037] S3.1.3. Convert the estimated parameters β and ε into matrix form to represent the process of estimating the regression model parameters using the generalized maximum entropy method; the matrix form is as follows:

[0038]

[0039] In the formula, the matrix of β is obtained by a diagonal matrix I and a 1×m matrix I; the matrix of ε is obtained by a diagonal matrix II and a 1×m matrix II; Z'1...Z' m represents the elements in the diagonal matrix I; v'1...v' m represents the elements in the diagonal matrix II; p1...p m represents the elements in the 1×m matrix I; u1...u m Represents the elements in the 1×m matrix I; the m in the subscript represents the number of feature dimensions, which defines the complexity of the model. The higher the dimension, the larger the feature space that the model can fit, and the more complex data distribution it can handle; in the matrix representation, the size of β and ε is determined by m;

[0040] S3.1.4. Establish the first model through the matrix obtained in S3.1.3; the model expression is as follows:

[0041]

[0042] In the formula, pjs represents the support parameter Z in the j-th regression parameter error decomposition s The corresponding probability; p il represents the error term ε i The support parameter weight of x ij represents the value of the i-th sample point of the low-dimensional data on the j-th feature, with a range of i=1,2,...n and j=1,2,...m; Z js The basis component p of the regression coefficient js Weighting is performed to reflect the distribution of support parameters in different dimensions;

[0043] S3.1.5. Solve the first model using the Lagrange multiplier method; the details are as follows:

[0044] S3.1.5.1, establish the Lagrangian function;

[0045]

[0046] In the formula, λ i Represents the first parameter; represents the second parameter; θ i Indicates the third parameter;

[0047] S3.1.5.2. Take the partial derivatives of the first variable p, the second variable u, the first parameter λ, the second parameter ω and the third parameter θ in the Lagrangian function respectively and set them equal to zero, then solve the system of equations simultaneously; the expression of the system of equations is as follows:

[0048]

[0049] S3.1.5.3, by combining the KKT condition of the optimization theory with the equation group, find the first parameter to be estimated and the second parameter to be estimated β and ε in the regression equation;

[0050] The specific combination method is: construct the Lagrangian function to find the partial derivatives of each variable. The simultaneous equations can be solved simultaneously to find p js ,u il ,λ i ,ω j ,θ i By solving these variables, taking partial derivatives for each variable and setting them equal to 0, we get a set of KKT conditions to get the values ​​of β and ε:

[0051] By solving p js and Z js The value of each β can be directly calculated j ; where p js and Z js The value of is obtained by solving the above KKT conditions;

[0052] Furthermore, Z1′ and Z′ m Corresponding to Z in the following text js The weights of the regression parameters; p1 and p m P js Support parameters for the error term

[0053] ε i Defined as: By solving u il and v il The value of each ε can be directly calculated i ; where u il and v il The value of is also solved by the above KKT conditions;

[0054] Furthermore, u1 and u m Corresponding to u in the following text il Parameters of the error term; v1′ and v m ′ corresponds to v in the following text il ;

[0055] At this point, the generalized maximum entropy regression model can be used to perform soft measurement of the matte temperature, matte grade, and iron-silicon ratio in the slag during the Isa furnace copper smelting process;

[0056] S4. A prediction model (LSTM-HMM) based on a long short-term memory network (LSTM) is used to predict the working conditions in the sampled data, and the optimal parameters of the adaptive (GMER+adaptive) model based on generalized maximum entropy regression are obtained;

[0057] The predicted working conditions include: the sequence problem of working condition prediction and the training problem of working condition prediction;

[0058] The optimal parameters include: a third μ value to be estimated and a fourth γ value to be estimated;

[0059] Here are the steps:

[0060] S4.1. Use the LSTM-HMM model to analyze historical input data and predict the current working condition, as follows:

[0061] S4.1.1, LSTM-HMM model expression is as follows:

[0062] λ=(C,O,A,B,π)

[0063] Where C represents the state set of the working condition, which is defined as {normal, abnormal and abnormal, abnormal}, that is, C = {c1, c2, c3} three states; O represents the observation sequence, which is obtained from the input data, and the input data X = {x1, ···, x n} is converted into time series features H = {h1,h2,...h t}, each input variable has an observation symbol set, denoted by V, where V represents the observation symbol set, V = {v1,v2,···v m}; A represents the dynamic state transfer matrix, which is defined as a 3x3 matrix as shown in C; the expression is as follows:

[0064]

[0065] In the formula, any element a il Indicates the current time h t Located in state c i Transfer to the next step in state c l The probability of il The expression is: il (t) = softmax(W a ·h t +b a ), W a represents the weight of the dynamic state transfer matrix; b a Represents the bias term of the dynamic state transfer matrix;

[0066] B represents the dynamic observation probability matrix. Any element in B is represented by B(t). B(t) is defined as b ik (t) = P(v k |c i ,h t ), any element b ik The expression of (t) is: ik (t) = softmax(W b ·h t +b b ), where W b represents the weight of the dynamic observation probability matrix; b b Represents the bias term of the dynamic observation probability matrix;

[0067] The initial state distribution π is obtained through the prior distribution of the input variables;

[0068] S4.1.2, iteratively estimate the parameters in the LSTM-HMM model according to the Baum-Welch algorithm;

[0069] Specifically, the Baum-Welch algorithm is used to iteratively update the model parameters A, B, and π by maximizing the likelihood probability P(O|λ) of the observation sequence;

[0070] S4.1.3, use the Viterbi algorithm to decode the input observation sequence O in the optimal path and predict the current working state c t;

[0071] Specifically, the Viterbi algorithm is used to decode the input observation sequence O to generate the optimal state sequence Q. The optimal state sequence is used to calculate the current working condition c. t Classification is: C = {c1, c2, c3};

[0072] S4.2, based on the optimal operating condition, dynamically adjust the values ​​of μ and γ using linear interpolation;

[0073] The working conditions of the ISA furnace smelting process will fluctuate to a certain extent. Based on the generalized maximum entropy regression model, the measurement error is very small when the working conditions are good, but the performance is poor when the working conditions are bad, and the soft measurement accuracy is poor. However, through analysis, the effect obtained by the soft measurement based on the mechanism model is not affected by the change of working conditions. Therefore, it is necessary to combine the advantages of these two models to establish a soft measurement model that takes into account both error and stability.

[0074] The linear interpolation method dynamically adjusts the values ​​of μ and γ as follows:

[0075]

[0076] For the normal state (c1): the GMER model has the best performance, the μ value tends to 1, and the γ value tends to 0;

[0077] For abnormal state (c3): the mechanism model is more robust, the γ value tends to 1, and the μ value tends to 0;

[0078] For non-normal and abnormal conditions (c2): μ and γ values ​​are adjusted proportionally, the specific formula is:

[0079]

[0080] Where: N j Indicates the current state c t The number of samples; N is the total number of samples, N = n; α is the adjustment parameter to control the sensitivity of weight adjustment; historical data is used to verify the impact of different combinations of μ and γ on the model prediction performance; the optimal α parameter value is selected through cross-validation to ensure that the model has the best prediction performance under various working conditions;

[0081] The present invention extracts the features of time series data through LSTM, inputs these features into HMM, and dynamically adjusts the state transfer matrix and observation probability matrix of HMM, thereby improving the prediction accuracy of multiple working conditions; the LSTM-HMM model is not only applicable to the sequence problem of working condition prediction, but also can be optimized for the training problem of working condition prediction, and finally realizes the accurate prediction and monitoring of working condition status;

[0082] S4.3. Optimize the model obtained in S4.2; the details are as follows:

[0083] S4.3.1. Define the objective function of minimizing the prediction error so that the dynamic adjustment of weights μ and γ can accurately reflect the changes in working conditions. The expression is as follows:

[0084]

[0085] Where Y i Represents the true value, that is, the observed value of the working condition data; Indicates the working condition predicted by the LSTM-HMM model;

[0086] S4.3.2. Use the gradient descent method to optimize the objective function and update μ and γ; the expressions are as follows:

[0087]

[0088] In the formula, η represents the learning rate, which is used to control the step size of parameter adjustment in the gradient descent method;

[0089] S4.3.3, Iteration termination condition, when the objective function value When the rate of change is less than the set threshold, the iteration stops, or the iteration terminates when the maximum number of iterations is reached;

[0090] Threshold range: 10 -4 ~10 -6 ;

[0091] The maximum number of iterations is 2000;

[0092] S4.4. Use the Baum-Welch algorithm combined with LSTM back propagation to optimize the generated weight W a , bias b b and the weight W of B(t) b , bias b a ;

[0093] The parameter update formula is as follows:

[0094]

[0095] In the formula, λ1 represents the weight W a The coefficient of λ2 represents the weight W b The coefficients of ; λ1,λ2∈[0.01,0.1] select specific values ​​according to data characteristics and model complexity;

[0096] For the training problem of industrial detection, the LSTM-HMM model takes time series data as input, where the observation sequence O represents the time series input features sampled during the industrial detection process; the LSTM model extracts dynamic features h through time series analysis t The time step characteristics of each input variable are used to dynamically adjust the state transition probability and observation probability of LSTM-HMM. In the LSTM-HMM model, the elements of the state transition matrix A and the observation matrix B are dynamically generated by LSTM.

[0097] In the LSTM-HMM model, at time t, it is in state c i , and at time t+1 it transfers to state c l The probability is:

[0098]

[0099] In the formula, a t (i) Forward probability, indicating that the state is c at time t i The probability of t+1 (l) Backward probability, which represents the probability of observing the sequence starting from time t+1, a il (t) Dynamic state transition probability, b l (o t+1 ,t) dynamic observation probability; ξ t (i,l) is the core of parameter update in the Baum-Welch algorithm, which is used to estimate the dynamic state transition probability and dynamic observation probability. It describes the probabilistic relationship between the observation sequence O and the model state, which is the basis for model parameter optimization;

[0100] At time t, it is in state c i The probability of γ t (i) is expressed as:

[0101]

[0102] Therefore, the LSTM-HMM model λ w The parameters in can be estimated iteratively using the following formula.

[0103]

[0104] Where N represents the number of states of HMM;

[0105]

[0106] in

[0107] In the formula, T represents the number of time points of observation data; t represents the specific time point; Ok' Represents the k'th specific observation value in the observation data set;

[0108] S5, input the optimal value of S4 into the model of S3, and input the low-dimensional data processed by S2 and the process operation experience value into the model after obtaining the optimal value, and output the final prediction result;

[0109] The empirical values ​​of process operation include: oxygen enrichment injection amount, blast volume, concentrate volume, furnace top pressure, furnace temperature, slag-iron ratio, flue gas flow rate;

[0110] The low-dimensional data after S2 processing include: low-dimensional data of matte temperature, low-dimensional data of matte grade, and low-dimensional data of iron-silicon ratio in slag;

[0111] The LSTM-HMM model of S4 obtains prediction results based on 10 inputs;

[0112] The predicted results include: matte temperature, matte grade and iron-silicon ratio in slag.

[0113] Beneficial Effects of the Invention

[0114] The present invention proposes a soft sensor model construction method based on the combination of nonlinear dimensionality reduction technology UMAP and LSTM-HMM model. The method solves the difficulty of high-dimensional data dimensionality reduction through feature dimensionality reduction, time series feature extraction and dynamic model construction.

[0115] The present invention combines LSTM and HMM models to extract the time series characteristics of input variables using LSTM, dynamically adjusts the state transfer matrix and the observation probability matrix, and improves the real-time and adaptability of the working condition prediction. The Viterbi algorithm is used to optimize the working condition prediction path, and the Baum-Welch algorithm is used to adjust the model parameters to achieve accurate prediction of complex working conditions.

[0116] The present invention combines 10 input variables in the industrial process, including oxygen-enriched blast volume, blast volume, furnace top pressure, etc., combines time series characteristics with nonlinear characteristics, and comprehensively captures the characteristics of operating condition changes. The dynamically generated state transfer matrix and observation probability matrix effectively combine the characteristics of input data to achieve an accurate description of complex and variable operating conditions.

[0117] The soft sensor model constructed by the present invention through generalized maximum entropy regression (GMER) adopts multi-operating condition classification to dynamically adjust the model μ and γ, thereby improving the stability and adaptability of the model under multiple operating conditions. Combined with dynamic optimization technology and objective function minimization method, the training efficiency and prediction accuracy of the model are further improved, and the computational complexity is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1is a flow chart of the steps of the present invention;

[0119] Figure 2 It is the experimental flow chart of the present invention;

[0120] Figure 3 It is a comparison diagram of the working condition detection experimental results of the present invention; wherein, part (a) represents the result diagram of the segmented detection model based on historical data; part (b) represents the result diagram of the present invention;

[0121] Figure 4 This is a graph showing the temperature results of the copper matte of the present invention;

[0122] Figure 5 This is the matte temperature result diagram based on the GMER adaptive matte temperature soft-sensing model;

[0123] Figure 6 This is a graph showing the matte taste results of the present invention;

[0124] Figure 7 This is the matte taste result diagram based on the GMER adaptive matte temperature soft sensing model;

[0125] Figure 8 This is a result diagram of the iron-silicon ratio in the slag of the present invention;

[0126] Fig. 9 The result diagram of the iron-silicon ratio in slag based on the GMER adaptive soft-sensing model of matte temperature; DETAILED DESCRIPTION

[0127] The present invention is further described in detail below in conjunction with specific embodiments.

[0128] like Figure 1 and Figure 2 As shown, a method for constructing a soft sensor model of Isa copper smelting process parameters includes the following steps:

[0129] S1. Data sampling of Isa furnace;

[0130] The sampled data is represented by X, X = {x1,···,x n}, i∈n, n is the total number of sampled data, x i ∈R d represents the sample space of Isa furnace smelting data, where d represents the feature dimension of the input data, d=3;

[0131] The sampled data include: matte temperature, matte grade and iron-silicon ratio in slag;

[0132] In this embodiment, the total number of sampled data is determined by the experimental period and the sampling frequency of once every 2 hours; the experimental period is three days in total; the calculation expression of the total number of sampled data n is as follows:

[0133]

[0134] Therefore, in this embodiment, n=36 (times);

[0135] S2, construct a nonlinear dimensionality reduction algorithm (UMAP) model to reduce the dimensionality of the sampled data;

[0136] UMAP is used to reduce the dimensionality of multi-dimensional process parameter data (high-dimensional data) in the copper smelting process of the Isa furnace, solving the problem that the traditional dimensionality reduction method (PCA) cannot effectively process high-dimensional nonlinear industrial data; after dimensionality reduction, the data is mapped to a low-dimensional space; the feature data output by UMAP after dimensionality reduction will be used in the subsequent soft sensor model;

[0137] The processing steps are as follows:

[0138] S2.1. In high-dimensional data space, calculate the data set X = {x1, x2, ... x n The similarity weight w between the sample points in} ij , the expression is as follows:

[0139]

[0140] In the formula, x i represents sample point I, x j Represents sample point II, i, j∈n, i≠j; Represents the key parameters in the model, used to control the sample points, By adjusting based on the k-nearest neighbor method, the expression is as follows:

[0141]

[0142] Where k is the number of neighborhood points, 5≤k≤10; x' ij Indicates the value of the i-th sample point on the j-th feature in high-dimensional data;

[0143] S2.2. Select the first n of each sample point neighbors neighbors, forming a local neighborhood graph G, where the weight of each edge is determined by w ij express;

[0144] Number of neighbors n neighbors In this embodiment, it is 30, which indicates the size of the local neighborhood of each point;

[0145] S2.3, the data set X={x1,x2,...x n}Embed into data Y to construct low-dimensional data, optimize the representation of low-dimensional data by minimizing the Kullback-Leibler divergence between high-dimensional and low-dimensional data, so that the neighborhood relationship in high-dimensional space can be preserved in low-dimensional space;

[0146] Where Y = {y1,y2,...,y n}; m represents the target dimension after dimensionality reduction, which is reduced from d;

[0147] The Kullback-Leibler divergence expression is as follows:

[0148]

[0149] Where: w′ ij =(1+a||y i -y j || 2 ) -b , represents the similarity weight between sample points in low-dimensional space; a represents the adjustment parameter, which controls the sensitivity of low-dimensional distance to weight attenuation, b represents the power control parameter, which determines the degree of nonlinear change of weight, and y represents the i and j Respectively represent the low-dimensional data representation of sample point I and sample point II;

[0150] S3. Construct an adaptive (GMER+adaptive) model based on generalized maximum entropy regression, the expression is as follows:

[0151]

[0152] Where M GME is the soft measurement result of the soft measurement model based on generalized maximum entropy regression; M BE is the soft measurement result based on the mechanism model; μ and γ are the first and second importance evaluation indicators, defined as adaptive parameters; Y low is the final value of the measured parameter;

[0153] The construction steps are as follows:

[0154] S3.1. Construct a soft sensor model based on generalized maximum entropy regression. The steps are as follows:

[0155] S3.1.1. Construct a regression model; the expression is as follows:

[0156] Y low =X low β+ε

[0157] In the formula, β and ε represent the first parameter to be estimated and the second parameter to be estimated, where β T =[β1,β2,···,β m] is input X low The weight vector, ε T =[ε1,ε2,···,ε n ] represents the adjustment fuzzy factor vector of the model;

[0158] S3.1.2. Parameter transformation of the regression model is as follows:

[0159] The β of the elements in β j (j=1,2,···,m) is defined as the following expression:

[0160]

[0161] In the formula, p js Is β j Support parameter Z js The corresponding probability, P js ∈[0,1], where S is generally taken as S≥2. In this embodiment, S=2;

[0162] Subtract the ε of the elements in ε i (i=1,2,···,m) is defined as the following expression:

[0163]

[0164] In the formula, ε i represents the error term, which is obtained by the second estimated parameter; L represents the number of supported parameters, L = 2; u il represents the error term ε i The probability corresponding to the support parameter; v il It is used to decompose the error ε i , describing the different dimensions or components of the error; u is represents the support parameter Z in the error decomposition s In the error decomposition term ε i The weight coefficient in is used to describe the distribution contribution relationship of each support parameter in the error term;

[0165] S3.1.3. Convert the estimated parameters β and ε into matrix form to represent the process of estimating the regression model parameters using the generalized maximum entropy method; the matrix form is as follows:

[0166]

[0167] In the formula, the matrix of β is obtained by a diagonal matrix I and a 1×m matrix I; the matrix of ε is obtained by a diagonal matrix II and a 1×m matrix II; Z'1...Z' m represents the elements in the diagonal matrix I; v'1...v' m represents the elements in the diagonal matrix II; p1...pm represents the elements in the 1×m matrix I; u1...u m Represents the elements in the 1×m matrix I; the m in the subscript represents the number of feature dimensions, which defines the complexity of the model. The higher the dimension, the larger the feature space that the model can fit, and the more complex data distribution it can handle; in the matrix representation, the size of β and ε is determined by m;

[0168] S3.1.4. Establish the first model through the matrix obtained in S3.1.3; the model expression is as follows:

[0169]

[0170] In the formula, p js represents the support parameter Z in the j-th regression parameter error decomposition s The corresponding probability; p il represents the error term ε i The support parameter weight of x ij represents the value of the i-th sample point of the low-dimensional data on the j-th feature, with a range of i=1,2,...n and j=1,2,...m; Z js The basis component p of the regression coefficient js Weighting is performed to reflect the distribution of support parameters in different dimensions;

[0171] S3.1.5. Solve the first model using the Lagrange multiplier method; the details are as follows:

[0172] S3.1.5.1, establish the Lagrangian function;

[0173]

[0174] In the formula, λ i Represents the first parameter; represents the second parameter; θ i Indicates the third parameter;

[0175] S3.1.5.2. Take the partial derivatives of the first variable p, the second variable u, the first parameter λ, the second parameter ω and the third parameter θ in the Lagrangian function respectively and set them equal to zero, then solve the system of equations simultaneously; the expression of the system of equations is as follows:

[0176]

[0177] S3.1.5.3, by combining the KKT condition of the optimization theory with the equation group, find the first parameter to be estimated and the second parameter to be estimated β and ε in the regression equation;

[0178] The specific combination method is: construct the Lagrangian function to find the partial derivatives of each variable. The simultaneous equations can be solved simultaneously to find pjs ,u il ,λ i ,ω j ,θ i By solving these variables, taking partial derivatives for each variable and setting them equal to 0, we get a set of KKT conditions to get the values ​​of β and ε:

[0179] By solving p js and Z js The value of each β can be directly calculated j ; where p js and Z js The value of is obtained by solving the above KKT conditions;

[0180] Furthermore, Z1′ and Z′ m Corresponding to Z in the following text js The weights of the regression parameters; p1 and p m P js Support parameters for the error term

[0181] ε i Defined as: By solving u il and v il The value of each ε can be directly calculated i ; where u il and v il The value of is also solved by the above KKT conditions;

[0182] Furthermore, u1 and u m Corresponding to u in the following text il Parameters of the error term; v1′ and v m ′ corresponds to v in the following text il ;

[0183] At this point, the generalized maximum entropy regression model can be used to perform soft measurement of the matte temperature, matte grade, and iron-silicon ratio in the slag during the Isa furnace copper smelting process;

[0184] S4. A prediction model (LSTM-HMM) based on a long short-term memory network (LSTM) is used to predict the working conditions in the sampled data, and the optimal parameters of the adaptive (GMER+adaptive) model based on generalized maximum entropy regression are obtained;

[0185] The predicted working conditions include: the sequence problem of working condition prediction and the training problem of working condition prediction;

[0186] The optimal parameters include: a third μ value to be estimated and a fourth γ value to be estimated;

[0187] Here are the steps:

[0188] S4.1. Use the LSTM-HMM model to analyze historical input data and predict the current working condition, as follows:

[0189] S4.1.1, LSTM-HMM model expression is as follows:

[0190] λ=(C,O,A,B,π)

[0191] Where C represents the state set of the working condition, which is defined as {normal, abnormal and abnormal, abnormal}, that is, C = {c1, c2, c3} three states; O represents the observation sequence, which is obtained from the input data, and the input data X = {x1, ···, x n} is converted into time series features H = {h1,h2,...h t}, each input variable has an observation symbol set, denoted by V, where V represents the observation symbol set, V = {v1,v2,···v m}; A represents the dynamic state transfer matrix, which is defined as a 3x3 matrix as shown in C; the expression is as follows:

[0192]

[0193] In the formula, any element a il Indicates the current time h t Located in state c i Transfer to the next step in state c l The probability of il The expression is: il (t) = softmax(W a ·h t +b a ), W a represents the weight of the dynamic state transfer matrix; b a Represents the bias term of the dynamic state transfer matrix;

[0194] B represents the dynamic observation probability matrix. Any element in B is represented by B(t). B(t) is defined as b ik (t) = P(v k |c i ,h t ), any element b ik The expression of (t) is: ik (t) = softmax(W b ·h t +b b ), where W b represents the weight of the dynamic observation probability matrix; b b Represents the bias term of the dynamic observation probability matrix;

[0195] The initial state distribution π is obtained through the prior distribution of the input variables;

[0196] S4.1.2, iteratively estimate the parameters in the LSTM-HMM model according to the Baum-Welch algorithm;

[0197] Specifically, the Baum-Welch algorithm is used to iteratively update the model parameters A, B, and π by maximizing the likelihood probability P(O|λ) of the observation sequence;

[0198] S4.1.3, use the Viterbi algorithm to decode the input observation sequence O in the optimal path and predict the current working state c t ;

[0199] Specifically, the Viterbi algorithm is used to decode the input observation sequence O to generate the optimal state sequence Q. The optimal state sequence is used to calculate the current working condition c. t Classification is: C = {c1, c2, c3};

[0200] S4.2, based on the optimal operating condition, dynamically adjust the values ​​of μ and γ using linear interpolation;

[0201] The working conditions of the ISA furnace smelting process will fluctuate to a certain extent. Based on the generalized maximum entropy regression model, the measurement error is very small when the working conditions are good, but the performance is poor when the working conditions are bad, and the soft measurement accuracy is poor. However, through analysis, the effect obtained by the soft measurement based on the mechanism model is not affected by the change of working conditions. Therefore, it is necessary to combine the advantages of these two models to establish a soft measurement model that takes into account both error and stability.

[0202] The linear interpolation method dynamically adjusts the values ​​of μ and γ as follows:

[0203]

[0204] For the normal state (c1): the GMER model has the best performance, the μ value tends to 1, and the γ value tends to 0;

[0205] For abnormal state (c3): the mechanism model is more robust, the γ value tends to 1, and the μ value tends to 0;

[0206] For non-normal and abnormal conditions (c2): μ and γ values ​​are adjusted proportionally, the specific formula is:

[0207]

[0208] Where: N j Indicates the current state c tThe number of samples; N is the total number of samples, N = n; α is the adjustment parameter to control the sensitivity of weight adjustment; historical data is used to verify the impact of different combinations of μ and γ on the model prediction performance; the optimal α parameter value is selected through cross-validation to ensure that the model has the best prediction performance under various working conditions;

[0209] The present invention extracts the features of time series data through LSTM, inputs these features into HMM, and dynamically adjusts the state transfer matrix and observation probability matrix of HMM, thereby improving the prediction accuracy of multiple working conditions; the LSTM-HMM model is not only applicable to the sequence problem of working condition prediction, but also can be optimized for the training problem of working condition prediction, and finally realizes the accurate prediction and monitoring of working condition status;

[0210] S4.3. Optimize the model obtained in S4.2; the details are as follows:

[0211] S4.3.1. Define the objective function of minimizing the prediction error so that the dynamic adjustment of weights μ and γ can accurately reflect the changes in working conditions. The expression is as follows:

[0212]

[0213] Where Y i Represents the true value, that is, the observed value of the working condition data; Indicates the working condition predicted by the LSTM-HMM model;

[0214] S4.3.2. Use the gradient descent method to optimize the objective function and update μ and γ; the expressions are as follows:

[0215]

[0216] In the formula, η represents the learning rate, which is used to control the step size of parameter adjustment in the gradient descent method;

[0217] S4.3.3, Iteration termination condition, when the objective function value When the rate of change is less than the set threshold, the iteration stops, or the iteration terminates when the maximum number of iterations is reached;

[0218] Threshold range: 10 -4 ~10 -6 ;

[0219] The maximum number of iterations is 2000;

[0220] S4.4. Use the Baum-Welch algorithm combined with LSTM back propagation to optimize the generated weight W a , bias b b and the weight W of B(t) b , bias b a ;

[0221] The parameter update formula is as follows:

[0222]

[0223] In the formula, λ1 represents the weight W a The coefficient of λ2 represents the weight W b The coefficients of ; λ1,λ2∈[0.01,0.1] select specific values ​​according to data characteristics and model complexity;

[0224] For the training problem of industrial detection, the LSTM-HMM model takes time series data as input, where the observation sequence O represents the time series input features sampled during the industrial detection process; the LSTM model extracts dynamic features h through time series analysis t The time step features of each input variable are used to dynamically adjust the state transition probability and observation probability of LSTM-HMM. In the LSTM-HMM model, the elements of the state transition matrix A and the observation matrix B are dynamically generated by LSTM.

[0225] In the LSTM-HMM model, at time t, it is in state c i , and at time t+1 it transfers to state c l The probability is:

[0226]

[0227] In the formula, a t (i) Forward probability, indicating that the state is c at time t i The probability of t+1 (l) Backward probability, which represents the probability of observing the sequence starting from time t+1, a il (t) Dynamic state transition probability, b l (o t+1 ,t) dynamic observation probability; ξ t (i,l) is the core of parameter update in the Baum-Welch algorithm, which is used to estimate the dynamic state transition probability and dynamic observation probability. It describes the probabilistic relationship between the observation sequence O and the model state, which is the basis for model parameter optimization;

[0228] At time t, it is in state c i The probability of γ t (i) is expressed as:

[0229]

[0230] Therefore, the LSTM-HMM model λ w The parameters in can be estimated iteratively using the following formula.

[0231]

[0232] Wherein, N represents the number of states of HMM, which is 3 in this embodiment;

[0233]

[0234] in

[0235] In the formula, T represents the number of time points of observation data; t represents the specific time point; O k' Represents the k'th specific observation value in the observation data set;

[0236] S5, input the optimal value of S4 into the model of S3, and input the low-dimensional data processed by S2 and the process operation experience value into the model after obtaining the optimal value, and output the final prediction result;

[0237] The empirical values ​​of process operation include: oxygen enrichment injection amount, blast volume, concentrate volume, furnace top pressure, furnace temperature, slag-iron ratio, flue gas flow rate;

[0238] The low-dimensional data after S2 processing include: low-dimensional data of matte temperature, low-dimensional data of matte grade, and low-dimensional data of iron-silicon ratio in slag;

[0239] The LSTM-HMM model of S4 obtains prediction results based on 10 inputs;

[0240] The prediction results include: matte temperature, matte grade and iron-silicon ratio in slag;

[0241] In order to verify the effectiveness of the model, the present invention will experiment with the soft measurement based on the generalized maximum entropy regression (GMEG) model, the working condition detection performance based on LSTM-HMM, and the adaptive soft measurement model based on the generalized maximum entropy regression (GMEG); the experiment uses Matlab as a simulation experiment tool; the data in the experiment is obtained by sampling and measuring the copper smelting process of the Isa furnace every 2 hours, and then the data is reduced in dimension based on the kernel clustering local linear embedding algorithm to form an input vector;

[0242] Figure 3 It is a comparison chart of the working condition detection test results, such as Figure 3 As shown in part (a), the comparison method is based on the historical data segmentation detection model; Figure 3 As shown in part (b), the working condition detection method based on LSTM-HMM has improved the accuracy by 4.6% in 36 detections, reaching 86.1%, compared with the traditional working condition detection method based on historical data segmentation.

[0243] Figures 4 to 9It is the result of three consecutive days of prediction experiments on the three major process indicators. The "solid line with circle curve" in the figure represents the actual measurement value, and the "dashed line plus sign curve" represents the soft measurement prediction value. Figure 4 and Figure 5 It shows the comparison chart of matte temperature based on generalized maximum entropy regression model and GRME adaptive model; Figure 6 and Figure 7 A comparison chart of the matte taste based on the generalized maximum entropy regression model and the GRME adaptive model; Figure 8 and Fig. 9 The figure shows the comparison of the iron-silicon ratio in slag based on the generalized maximum entropy regression model and the GRME adaptive model. The experiment shows that the GMEG adaptive model has better experimental effect, and its predicted curve has smaller deviation than the actual curve.

[0244] Table 1 shows the error results of soft measurement of the three major process indicators. The experiment shows that the average relative error of soft measurement based on the generalized maximum entropy regression model is small, and the measurement error of the iron-silicon ratio in the slag is only 4.02%. However, the maximum relative error effect is poor, indicating that the stability of the model is not enough, especially under poor working conditions, the error is large. The GMEG adaptive model after adding working condition detection has better effect than the generalized maximum entropy regression model. The relative errors of the three major parameters are reduced by 30.4%, and the average error is reduced by 20.3%. Therefore, the stability and adaptability of the model are improved to a certain extent.

[0245] Table 1: Soft measurement error results of three major parameters

[0246]

Claims

1. A method for constructing a soft sensor model of Isa copper smelting process parameters, characterized in that: The following steps are involved: S1. Data sampling of Isa furnace; The sampled data include: matte temperature, matte grade and iron-silicon ratio in slag; S2, construct a nonlinear dimensionality reduction algorithm model to perform dimensionality reduction processing on the sampled data; S3, construct an adaptive model based on generalized maximum entropy regression; S4. Use a hidden Markov model based on a long short-term memory network to build a prediction model to predict the working conditions in the sampled data, and obtain the optimal parameters of the adaptive model based on generalized maximum entropy regression; S5, input the optimal value of S4 into the model of S3, and input the low-dimensional data processed by S2 and the process operation experience value into the model after obtaining the optimal value, and output the final prediction result; The empirical values ​​of process operation include: oxygen enrichment injection amount, blast volume, concentrate volume, furnace top pressure, furnace temperature, slag-iron ratio, flue gas flow rate; The low-dimensional data after S2 processing include: low-dimensional data of matte temperature, low-dimensional data of matte grade, and low-dimensional data of iron-silicon ratio in slag; The LSTM-HMM model of S4 obtains prediction results based on 10 inputs; The predicted results include: matte temperature, matte grade and iron-silicon ratio in slag.

2. The method for constructing a soft sensor model of Isa copper smelting process parameters according to claim 1, characterized in that: The steps of constructing a nonlinear dimensionality reduction algorithm model and performing dimensionality reduction processing on the sampled data are as follows: S2.

1. In high-dimensional data space, calculate the data set X = {x1, x2, ... x n The similarity weight w between the sample points in} ij , the expression is as follows: In the formula, x i represents sample point I, x j Represents sample point II, i, j∈n, i≠j; represents the key parameters in the model, By adjusting based on the k-nearest neighbor method, the expression is as follows: Where k is the number of neighborhood points, 5≤k≤10; x' ij Indicates the value of the i-th sample point on the j-th feature in high-dimensional data; S2.

2. Select the first n of each sample point neighbors neighbors, forming a local neighborhood graph G, where the weight of each edge is determined by w ij express; S2.3, the data set X={x1,x2,...x n }Embed into data Y to construct low-dimensional data, optimize the representation of low-dimensional data by minimizing the Kullback-Leibler divergence between high-dimensional and low-dimensional data, so that the neighborhood relationship in high-dimensional space can be preserved in low-dimensional space; Where Y = {y1,y2,...,y n }; m represents the target dimension after dimensionality reduction, which is reduced from d; The Kullback-Leibler divergence expression is as follows: Where: w′ ij =(1+a||y i -y j || 2 ) -b , represents the similarity weight between sample points in low-dimensional space; a represents the adjustment parameter; b represents the power control parameter; y i and j They represent the low-dimensional data of sample point I and sample point II respectively.

3. The method for constructing a soft sensor model of Isa copper smelting process parameters according to claim 1, characterized in that: The adaptive (GMER+adaptive) model based on generalized maximum entropy regression is expressed as follows: Where M GME is the soft measurement result of the soft measurement model based on generalized maximum entropy regression; M BE is the soft measurement result based on the mechanism model; μ and γ are the first and second importance evaluation indicators, defined as adaptive parameters; Y low is the final value of the measured parameter.

4. The method for constructing a soft sensor model of Isa copper smelting process parameters according to claim 1, characterized in that: The steps of constructing the adaptive (GMER+adaptive) model based on generalized maximum entropy regression are as follows: S3.

1. Construct a soft sensor model based on generalized maximum entropy regression. The steps are as follows: S3.1.

1. Construct a regression model; the expression is as follows: Y low =X low ·b+e In the formula, β and ε represent the first parameter to be estimated and the second parameter to be estimated, where β T =[β1,β2,···,β m ] is input X low The weight vector, ε T =[ε1,ε2,···,ε n ] represents the adjustment fuzzy factor vector of the model; S3.1.

2. Parameter transformation of the regression model is as follows: The β of the elements in β j (j=1,2,···,m) is defined as the following expression: In the formula, p js Is β j Support parameter Z js The corresponding probability, P js ∈[0,1], S ≥ 2; Subtract the ε of the elements in ε i (i=1,2,···,m) is defined as the following expression: In the formula, ε i represents the error term, which is obtained by the second parameter to be estimated; L represents the number of supported parameters; u il represents the error term ε i The probability corresponding to the support parameter; v il It is used to decompose the error ε i ;u is represents the support parameter Z in the error decomposition s In the error decomposition term ε i The weight coefficient in ; S3.1.

3. Convert the estimated parameters β and ε into matrix form to represent the process of estimating the regression model parameters using the generalized maximum entropy method; the matrix form is as follows: In the formula, the matrix of β is obtained by a diagonal matrix Ⅰ and a 1×m matrix Ⅰ; the matrix of ε is obtained by a diagonal matrix Ⅱ and a 1×m matrix Ⅱ; Z1'...Z' m represents the elements in the diagonal matrix I; v′1...v' m represents the elements in the diagonal matrix II; p1...p m represents the elements in the 1×m matrix I; u1...u m Represents the elements in the 1×m matrix I; the m in the subscript represents the number of feature dimensions; In the matrix representation, the size of β and ε is determined by m; S3.1.

4. Establish the first model through the matrix obtained in S3.1.3; the model expression is as follows: In the formula, p js represents the support parameter Z in the j-th regression parameter error decomposition s The corresponding probability; p il represents the error term ε i The support parameter weight of x ij represents the value of the i-th sample point of the low-dimensional data on the j-th feature, with a range of i=1,2,...n and j=1,2,...m; Z js The basis component p of the regression coefficient js weighting; S3.1.

5. Solve the first model using the Lagrange multiplier method; the details are as follows: S3.1.5.1, establish the Lagrangian function; In the formula, λ i Represents the first parameter; represents the second parameter; θ i Represents the third parameter; S3.1.5.

2. Take the partial derivatives of the first variable p, the second variable u, the first parameter λ, the second parameter ω and the third parameter θ in the Lagrangian function respectively and set them equal to zero, then solve the system of equations simultaneously; the expression of the system of equations is as follows: S3.1.5.

3. Use the KKT condition of optimization theory combined with the equation group to find the first and second estimated parameters β and ε in the regression equation.

5. The method for constructing a soft sensor model of Isa copper smelting process parameters according to claim 1, characterized in that: The prediction model is constructed by using a hidden Markov model based on a long short-term memory network to predict the working conditions in the sampled data, and the optimal parameters of the adaptive model based on generalized maximum entropy regression are obtained. The predicted working conditions include: the sequence problem of working condition prediction and the training problem of working condition prediction; The optimal parameters include: a third μ value to be estimated and a fourth γ value to be estimated; Here are the steps: S4.

1. Use the LSTM-HMM model to analyze historical input data and predict the current working condition, as follows: S4.1.1, LSTM-HMM model expression is as follows: λ=(C,O,A,B,π) In the formula, C represents the state set of the working condition, which is defined as {normal, non-normal and abnormal, abnormal}, that is, C = three states {c1, c2, c3}; O represents the observation sequence; A represents the dynamic state transfer matrix; B expresses the dynamic observation probability matrix; the initial state distribution π is obtained through the prior distribution of the input variable; S4.1.2, iteratively estimate the parameters in the LSTM-HMM model according to the Baum-Welch algorithm; Specifically, the Baum-Welch algorithm is used to iteratively update the model parameters A, B, and π by maximizing the likelihood probability P(O|λ) of the observation sequence; S4.1.3, use the Viterbi algorithm to decode the input observation sequence O in the optimal path and predict the current working state c t ; S4.2, based on the optimal operating condition, dynamically adjust the values ​​of μ and γ using linear interpolation; The linear interpolation method dynamically adjusts the values ​​of μ and γ as follows: For the normal state (c1): the GMER model has the best performance, the μ value tends to 1, and the γ value tends to 0; For abnormal state (c3): the mechanism model is more robust, the γ value tends to 1, and the μ value tends to 0; For non-normal and abnormal conditions (c2): μ and γ values ​​are adjusted proportionally, the specific formula is: Where: N j Indicates the current state c t The number of samples; N is the total number of samples, N = n; α is the adjustment parameter to control the sensitivity of weight adjustment; S4.

3. Optimize the model obtained in S4.2; the details are as follows: S4.3.

1. Define the objective function of minimizing the prediction error so that the dynamic adjustment of weights μ and γ can accurately reflect the changes in working conditions. The expression is as follows: Where Y i Represents the true value, that is, the observed value of the working condition data; Indicates the working condition predicted by the LSTM-HMM model; S4.3.

2. Use the gradient descent method to optimize the objective function and update μ and γ; the expressions are as follows: In the formula, η represents the learning rate, which is used to control the step size of parameter adjustment in the gradient descent method; S4.3.3, Iteration termination condition, when the objective function value When the rate of change is less than the set threshold, the iteration stops, or the iteration terminates when the maximum number of iterations is reached; Threshold range: 10 -4 ~10 -6 ; The maximum number of iterations is 2000; S4.

4. Use the Baum-Welch algorithm combined with LSTM back propagation to optimize the generated weight W a , bias b b and the weight W of B(t) b , bias b a ; The parameter update formula is as follows: Where λ1 represents the weight W of the dynamic state transfer matrix a The coefficient of λ2 represents the weight of the dynamic observation probability matrix W b The coefficients of ; λ1,λ2∈[0.01,0.1] select specific values ​​according to data characteristics and model complexity; In the LSTM-HMM model, at time t, it is in state c i , and at time t+1 it transfers to state c l The probability is: In the formula, a t (i) Forward probability, indicating that the state is c at time t i The probability of t+1 (l) Backward probability, which represents the probability of observing the sequence starting from time t+1, a il (t) Dynamic state transition probability, b l (o t+1 ,t) dynamic observation probability; ξ t (i,l) is used in the Baum-Welch algorithm to estimate the dynamic state transition probability and dynamic observation probability; At time t, it is in state c i The probability of γ t (i) is expressed as: Therefore, the LSTM-HMM model λ w The parameters in can be estimated iteratively by the following formula; Where N represents the number of states of HMM; in In the formula, T represents the number of time points of observation data; t represents the specific time point; O k' Represents the k'th specific observation value in the observation data set.

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