Clinker F-CaO content prediction method based on space-time spectrum clustering and block integration

Abstract

The invention discloses a clinker F-CaO content prediction method based on space-time spectral clustering and block integration. The method comprises the following steps: collecting cement production process data and carrying out time sequence alignment and outlier detection pretreatment; sample space distribution similarity is measured by using Jensen-Shannon divergence, time weight is calculated in combination with a hyperbolic secant function, and a historical sample subset most similar to a to-be-predicted sample is screened through spectral clustering; by constructing a comprehensive evaluation index fusing mutual information MI and conditional information gain CIG, dynamic sorting and self-adaptive blocking are carried out on the features; and training a GBDT sub-model for each feature block, calculating an integrated weight according to the JS divergence distance between the to-be-predicted sample and the centroid of each block, and carrying out weighted fusion to obtain an F-CaO predicted value. According to the method, the problem that time sequence information and characteristic dynamic changes are not fully utilized in a traditional method is solved, and continuous real-time prediction of the F-CaO content of the clinker can be achieved.

Description

Technical Field

[0001] This invention relates to the fields of machine learning and soft measurement application technology, specifically to a method for predicting the F-CaO content of clinker based on spatiotemporal spectral clustering and block integration. Background Technology

[0002] Cement, as a core material in modern infrastructure construction, is widely used in various fields, from residential buildings to major transportation projects. Its quality directly affects the safety and durability of construction projects. During the calcination process of cement clinker, the free calcium oxide (F-CaO) content is the most critical control indicator for evaluating clinker quality. Excessive F-CaO content leads to poor cement stability, causing volume expansion after setting and hardening, resulting in cracking of the concrete structure; while insufficient content means excessively high calcination temperature, which not only increases energy consumption but may also damage the kiln lining and shorten equipment lifespan.

[0003] Cement clinker calcination is a complex physicochemical reaction process involving multiple thermal devices such as preheaters, rotary kilns, and grate coolers. It is characterized by large time lags, strong coupling, nonlinearity, and time-varying properties. Therefore, achieving accurate and real-time detection of F-CaO content is of significant economic value and practical importance for optimizing combustion control, stabilizing clinker quality, reducing production energy consumption, and realizing intelligent manufacturing in the cement industry.

[0004] Currently, the commonly used method for detecting F-CaO content in industrial settings mainly relies on manual offline laboratory analysis. This method typically involves sampling every 1-2 hours, followed by complex chemical analysis procedures such as grinding and titration before results are obtained. This offline detection method suffers from a significant "lag effect." By the time the test results are relayed to the operators, production conditions have often changed, leading to untimely control adjustments and a high risk of producing large quantities of substandard clinker. Furthermore, this method is limited by the representativeness of the samples and the skill level of the laboratory personnel, making it difficult to meet the demands of modern cement industry for continuous, real-time, and precise control of the production process.

[0005] With the development of the Industrial Internet and big data technologies, data-driven soft measurement technologies (such as neural networks and support vector machines) have gradually become an effective way to solve the above problems. In particular, Just-In-Time Learning (JITL) strategies have shown certain advantages in handling time-varying processes because they can build local models by searching for historical similar samples online. However, existing soft measurement methods still have two limitations in cement F-CaO prediction: First, traditional sample selection methods mostly use simple Euclidean distance to measure similarity, ignoring the high-dimensional distribution characteristics and complex temporal dependencies of industrial process data, making it difficult to select truly representative "spatiotemporally similar" samples; second, existing feature selection methods (such as LASSO and mutual information) are usually static and global, unable to adapt to the dynamic changes in feature importance caused by equipment aging or operating condition drift, and often ignore the redundancy between features.

[0006] Therefore, in order to solve the above problems, this paper proposes a method for predicting the F-CaO content of clinker based on spatiotemporal spectral clustering and block integration. Summary of the Invention

[0007] The purpose of this invention is to provide a clinker F-CaO content prediction method based on spatiotemporal spectral clustering and block integration. This method can effectively and accurately predict the free calcium content of clinker by capturing the spatiotemporal distribution characteristics in cement production data and dynamically adjusting the feature weights, thus providing a reliable basis for the optimized control of cement calcination systems.

[0008] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: a method for predicting the F-CaO content of clinker based on spatiotemporal spectral clustering and block integration, characterized by comprising the following steps:

[0009] S1. Collect cement clinker production data to build a historical database, and collect and preprocess the samples to be predicted by noise reduction and alignment.

[0010] S2. Calculate the Jensen-Shannon divergence between the sample to be predicted and historical samples as the spatial distribution difference, use the hyperbolic secant function to calculate the time dimension difference, construct the spatiotemporal comprehensive similarity, and select the optimal sample subset through spectral clustering algorithm;

[0011] S3. On the preferred sample subset, the mutual information (MI) of the features is calculated as a correlation index and the conditional information gain (CIG) is calculated as a uniqueness index. Based on this, the features are sorted and dynamically divided into several feature sub-blocks.

[0012] S4. Train a sub-regression model for each feature sub-block, calculate the JS divergence distance between the sample to be predicted and the centroid of each feature sub-block, convert it into ensemble weights, and perform weighted ensemble of the results of each sub-model to obtain the final predicted value.

[0013] Furthermore, in S1, the preprocessing of acquiring, denoising, and aligning the samples to be predicted includes the following steps:

[0014] S1.1 The process parameters of the cement clinker production line are collected in real time through the distributed control system (DCS). The parameters include: raw meal feed rate, coal feed rate and decomposer outlet temperature in the preheater stage; kiln head hood temperature, kiln head negative pressure, kiln speed, coal-carrying air pressure and rotary kiln coal feed rate in the rotary kiln stage; tertiary air temperature and blower K11 pressure in the grate cooler stage; and F-CaO content test values ​​at the corresponding time are collected as target variables. The sampling frequency is 1 minute / time.

[0015] S1.2. Based on the residence time of materials in the three thermal equipment units of preheater, rotary kiln and grate cooler during the cement clinker production process, time offset alignment is performed on each process parameter.

[0016] S1.3. A robust statistical method based on median-standard deviation is used to detect outliers. For the time series X(j) of the j-th feature, the median M(j) and standard deviation σ(j) are calculated. The outlier determination boundaries of the median and standard deviation are shown in the following two equations:

[0017] L(j)=M(j)-k·σ(j)

[0018] U(j)=M(j)+k·σ(j)

[0019] In the formula, k = 7.0; for the detected outliers, a hierarchical correction strategy of bilateral interpolation, forward filling, backward filling or median substitution is adopted.

[0020] Furthermore, in S2, the construction of the spatiotemporal comprehensive similarity includes the following steps:

[0021] S2.1, Employ a batch calculation strategy to improve the computational efficiency of JS divergence; for test sample X test With training sample set The batch computation process is as follows: First, the training samples are divided according to the batch size (batch_size). For each batch:

[0022]

[0023] Calculate the mixed distribution:

[0024]

[0025] To avoid numerical instability, a smoothing parameter ∈ = 10 is introduced. -10 Sample X to be predicted test Regarding the mixed distribution M (i) The stable formula for calculating the Kullback-Leibler divergence is:

[0026]

[0027] Similarly, calculating historical samples Regarding the mixed distribution M (i) The formula for the stability calculation of the Kullback-Leibler divergence is:

[0028]

[0029] In the formula, j represents the j-th dimension of the feature vector;

[0030] Combining the two KL divergences mentioned above, we obtain the symmetric JS divergence value. The expression is as follows:

[0031]

[0032] In the formula, X test For testing purposes; For the training sample set;

[0033] The difference between the probability distribution of the sample to be predicted and the historical samples can be calculated using the above formula. The smaller the value, the closer the probability distribution pattern of the sample to be predicted is to that of historical samples.

[0034] S2.2 To improve computational efficiency on large-scale historical databases, a batch matrix operation strategy is adopted to calculate the divergence matrix between the sample to be predicted and all historical samples in one go, as follows:

[0035] ① The calculated JS divergence is converted into spatial similarity S by using a Gaussian kernel function for nonlinear mapping. spatial The expression is as follows:

[0036]

[0037] In the formula, σ is the kernel width parameter, which is used to adjust the sensitivity of similarity to distance changes;

[0038] ② Calculate the timestamp T of the sample to be predicted test Compared with historical sample timestamps The absolute time difference between them is expressed as follows:

[0039] time_diffi=∣T test -Ttraini |

[0040] ③ Perform logarithmic normalization on the time difference to obtain the normalized time difference. The expression is as follows:

[0041]

[0042] In the formula, 1.0 is to prevent the logarithmic operator input from being 0; max(log(Δt)) is the logarithmic value of the maximum time difference in the historical data; T max It is the time decay control parameter, T max =5;

[0043] ④ Use the hyperbolic secant function to calculate the time weight t w The expression is as follows:

[0044]

[0045] This function is in When the time difference is small, it provides a weight close to 1. As the time difference increases, its decay rate is more gradual than that of the Gaussian function, thus ensuring that even historical samples that are slightly older but have very similar operating conditions can obtain reasonable weights.

[0046] ⑤ To enhance the distinction between similar and dissimilar samples, i.e., to sharpen the similarity matrix, a temperature parameter F is introduced. s The spatial similarity S calculated above spatial and time weight t w By integrating the data, we can simultaneously utilize its distribution characteristics and temporal properties.

[0047] The enhanced distribution characteristics are calculated using the following expression:

[0048] eh s =exp(F s ×S spatial )

[0049] The enhanced time characteristics are calculated using the following expression:

[0050] eh t =exp(F s ×t w )

[0051] In the formula, the temperature parameter F s The value is 2;

[0052] The comprehensive spatiotemporal similarity Matrix_S between the final sample i and the sample to be predicted (i) For eh s and eh t The product of the two is expressed as follows:

[0053] Matrix_S (i) =eh s ×eh t

[0054] By traversing all historical samples, a complete spatiotemporal similarity vector is constructed, resulting in the final spatiotemporal similarity matrix.

[0055] Furthermore, in S2, the spectral clustering algorithm selects the optimal sample subset by employing... The approximation method for fast online data embedding involves the following steps:

[0056] ① During the offline training phase, a similarity matrix W is constructed for the historical dataset, and its normalized Laplacian matrix is ​​calculated as follows:

[0057] L sym =ID -1 / 2 WD -1 / 2

[0058] In the formula, D is the degree matrix, and its eigenvector matrix is ​​obtained by eigenvalue decomposition.

[0059] ② By traversing k∈[2,50], select the k value that maximizes the CMI index as the optimal number of clusters C;

[0060] ③ In the offline stage, the K-means algorithm is used to divide the projection of historical samples in the spectral space into C state clusters, and the cluster center c of each cluster is saved. k ;

[0061] ④ In the online prediction stage, for the sample x to be predicted new First, calculate its similarity vector s with historical samples. new Then use The formula calculates its embedding coordinates z in the low-dimensional spectral space. new The expression is as follows:

[0062]

[0063] ⑤ Calculate z new With all offline clustering centers c k The Euclidean distance is used to assign the sample to be predicted to the nearest Euclidean distance. A cluster; All historical samples are selected as the current "best modeling sample subset"; this subset contains historical data that is most consistent with the current operating conditions in terms of spatiotemporal distribution, and is used for subsequent feature engineering and modeling.

[0064] Furthermore, in S3, the mutual information (MI) of the combined calculated features is used as a correlation index, and the conditional information gain (CIG) is used as a uniqueness index. The steps are as follows:

[0065] S3.1 For the preferred sample subset, mutual information (MI) is used to measure each feature variable x. j The nonlinear dependence between MI and the target variable F-CaO content y; for ease of comparison, the MI value is Min-Max normalized and denoted as I. norm (x j );

[0066] S3.2 Introduce Conditional Information Gain (CIG) to measure the non-substitutability of features, as detailed below:

[0067] ① Use division by x j All features other than Ω\{x j}, construct a GBDT regression model;

[0068] ② Use this model to predict the target y and calculate the prediction residual, as shown in the following expression:

[0069]

[0070] ③ This residual represents information that cannot be explained by other features. Calculate feature x. j With the residual R (-j) The mutual information, which serves as an approximation of CIG, is expressed as follows:

[0071]

[0072] ④ The calculated approximate CIG value is also normalized using Min-Max, denoted as .

[0073] ⑤ Define a comprehensive evaluation index CM to balance the "high correlation" and "high uniqueness" of features. The expression is as follows:

[0074]

[0075] In the formula, β is the balance coefficient, β = 0.5, which means that relevance and uniqueness are equally valued.

[0076] Furthermore, in S3, the features are sorted and dynamically divided into several feature sub-blocks, as follows:

[0077] ① Based on the CM value, all candidate features are sorted in descending order and divided into K blocks, requiring that features within a block are not redundant and features between blocks are complementary;

[0078] ② Select the top K features with the highest CM values ​​and use them as the initial "seeds" or center features of the K feature blocks, with K=2 yielding the best results;

[0079] ③ For each of the remaining features x i Calculate its relationship with each current feature block. m The average correlation of existing features is used to measure the degree of correlation using the absolute value of the Pearson correlation coefficient (PCC), as shown in the following expression:

[0080]

[0081] ④ Use a greedy algorithm to select feature x i Assign the feature block with the smallest AvgCorr value; by traversing all features, finally form K feature subsets {Block1, ..., Block...} K}

[0082] Furthermore, in S4, a sub-regression model is trained for each feature sub-block, the JS divergence distance between the sample to be predicted and the centroid of each feature sub-block is calculated, and this distance is converted into ensemble weights. The results of each sub-model are then weighted and ensembled to obtain the final predicted value. The specific steps are as follows:

[0083] S4.1 Dynamically weight the data based on the distribution similarity between the sample to be predicted and the training data of the sub-model: For each feature block... m Gradient boosting decision tree (GBDT) is used as the base learner, and the training is performed using the projection data of the preferred sample subset on the feature block.

[0084] S4.2 For the m-th feature block, calculate the mean vector of all samples in the preferred sample subset in the feature space of that block, and define it as the "centroid" of that block. The expression is as follows:

[0085]

[0086] In the formula, Let represent the centroid vector of the m-th feature block, and N represent the total number of samples in the preferred historical sample subset. Let represent the projection vector of the i-th preferred historical sample onto the m-th feature block subspace; the centroid represents the typical state of the current preferred condition in this feature subspace.

[0087] S4.3 Calculate the sample x to be predicted test The projection vector and centroid on the m-th feature block The distribution differences between them; again, the aforementioned JS divergence formula is used to calculate...

[0088] S4.4. Use the Softmax function to convert the JS divergence of each block into normalized ensemble weights w. m The expression is as follows:

[0089]

[0090] In the formula, w m This represents the weight of the m-th feature block in the current prediction task. This represents the Jensen-Shannon divergence between the test sample and the mean of the m-th feature block;

[0091] S4.5 Summarize the prediction outputs of all K sub-models The final predicted value of F-CaO content in clinker was obtained. The expression is as follows:

[0092]

[0093] In the formula, w represents the predicted f-CaO content of the test sample by the Gradient Boosting Decision Tree (GBDT) model trained on the m-th feature block. m This represents the weight of the m-th feature block in the current prediction task. This is the final integrated prediction result.

[0094] The beneficial effects of this invention are:

[0095] This invention effectively addresses the failure of traditional Euclidean distance in high-dimensional industrial data by introducing JS divergence and time-weighted mechanisms, enabling precise capture of the spatiotemporal evolution of production conditions. Through comprehensive evaluation indicators and dynamic block partitioning strategies, it maximizes the diversity among feature subsets while ensuring feature correlation, thus resolving the problem of feature multicollinearity. Therefore, the method provided by this invention can effectively improve the prediction accuracy and robustness of the free calcium content in cement clinker while maintaining real-time performance. Attached Figure Description

[0096] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0097] Figure 1 This is a flowchart of the method for predicting the free calcium content in clinker according to Embodiment 1 of the present invention;

[0098] Figure 2 This is a system structure diagram of the converter final carbon content prediction method in Embodiment 1 of the present invention;

[0099] Figure 3 This invention provides a comparison of the clinker free calcium content prediction method of Example 1 with several mature and classic soft measurement methods in terms of the accuracy of clinker free calcium content prediction.

[0100] Figure 4 This is a curve showing the predicted free calcium content in clinker in Example 1 of the present invention. Detailed Implementation

[0101] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0102] Example 1

[0103] A method for predicting F-CaO content in clinker based on spatiotemporal spectral clustering and block integration includes the following steps:

[0104] Step 1: Cement Production Data Acquisition and Preprocessing

[0105] 1.1 Data Acquisition: Process parameters of the cement clinker production line are acquired in real time through a distributed control system (DCS), including: raw meal feed rate, coke feed rate, and coke outlet temperature in the preheater stage; kiln head hood temperature, kiln head negative pressure, kiln speed, coal-carrying air pressure, and rotary kiln feed rate in the rotary kiln stage; and tertiary air temperature and blower K11 pressure in the grate cooler stage. Simultaneously, the F-CaO content is collected as a target variable at corresponding times. The sampling frequency is 1 minute / time.

[0106] 1.2 Time Sequence Alignment: The cement clinker production process includes three thermal equipment units: preheater, rotary kiln, and grate cooler. The residence time of materials in each unit is approximately 30 seconds, 19-23 minutes, and 29 minutes, respectively. To ensure the time sequence consistency between input characteristics and F-CaO content, time offset alignment is performed on various process parameters. For example, tertiary air temperature, blower K11 pressure, and kiln outlet temperature correspond to 29 minutes before the F-CaO sampling time (T-29min); kiln outlet pressure and burner coal feeder speed correspond to T-49min; and decomposer top temperature and decomposer coal feed rate correspond to T-50min.

[0107] 1.3 Outlier Detection and Correction: A robust statistical method based on median-standard deviation is used to detect outliers. For the time series X(j) of the j-th feature, the median M(j) and standard deviation σ(j) are calculated, and the outlier judgment boundary is defined as shown in equations (1) and (2):

[0108] L(j)=M(j)-k·σ(j) (1)

[0109] U(j)=M(j)+k·σ(j) (2)

[0110] Where k = 7.0 (verified, this threshold only marks 0.92% of the samples as outliers, effectively avoiding misjudging normal operating condition fluctuations as anomalies). For detected outliers, a hierarchical correction strategy of bilateral interpolation, forward padding, backward padding, or median substitution is adopted.

[0111] Step 2: Construct a sample selection model based on spatiotemporal similarity (STSSC)

[0112] The cement clinker production process exhibits significant non-stationary characteristics, making it difficult for a single global model to adapt to varying operating conditions. Therefore, this invention first establishes a local sample optimization mechanism based on spatiotemporal similarity. The core of this mechanism lies in considering not only the numerical similarity of data in the feature space, but also their morphological similarity in probability distribution, as well as their dynamic evolution patterns over time.

[0113] 2.1 Distributed Spatial Similarity Measurement: Traditional Euclidean distance only measures the geometric distance between points, which is easily affected by the "curse of dimensionality" and becomes ineffective in high-dimensional and noisy cement production data. This embodiment uses Jensen-Shannon (JS) divergence to measure the difference in probability distribution between samples. JS divergence is symmetric and numerically bounded, making it more suitable for measuring distribution drift under non-stationary conditions.

[0114] Let X be the sample to be predicted at the current time. test The i-th training sample in the historical database is To calculate the JS divergence between the two, we first need to construct their mixture probability distribution M. (i) The calculation formula is shown in equation (3):

[0115]

[0116] When calculating the logarithmic term of the probability distribution, this embodiment introduces an extremely small smoothing parameter ∈ = 10 for the sake of standard deviation. -10 Based on this, the sample X to be predicted is calculated. test Regarding the mixed distribution M (i) The Kullback-Leibler (KL) divergence is shown in equation (4):

[0117]

[0118] In the formula, j represents the j-th dimension of the feature vector.

[0119] Similarly, calculate historical samples Regarding the mixed distribution M (i) The KL divergence is shown in the following formula:

[0120]

[0121] Combining the two KL divergences mentioned above, we obtain the symmetric JS divergence value. As shown in equation (6):

[0122]

[0123] The smaller the value, the closer the probability distribution pattern of the sample to be predicted is to that of historical samples.

[0124] To improve computational efficiency on large-scale historical databases (e.g., thousands of records), this embodiment adopts a batch matrix operation strategy, calculating the scatter matrix of the sample to be predicted and all historical samples at once, rather than calculating them one by one in a loop.

[0125] The calculated JS divergence is converted into spatial similarity S. spatial Here, a Gaussian kernel function is used for nonlinear mapping, as shown in equation (7):

[0126]

[0127] Where σ is the kernel width parameter, used to adjust the sensitivity of similarity to changes in distance.

[0128] 2.2 Long-Memory Time-Weighted Calculation: The cement rotary kiln system is a system with large inertia and large lag. The current F-CaO content depends not only on the current operating parameters, but also implicitly on recent historical trends. To capture this dynamic time-varying characteristic, this invention introduces a time-weighted mechanism.

[0129] First, calculate the timestamp T of the sample to be predicted. test Compared with historical sample timestamps The absolute time difference between them is shown in equation (8):

[0130]

[0131] Considering the potentially large time span, directly using the raw time difference would result in an excessively large numerical range; therefore, the time difference is logarithmically normalized to obtain the normalized time difference. As shown in equation (9):

[0132]

[0133] Here, 1.0 is to prevent the logarithmic operator input from being 0; max(log(Δt)) is the logarithmic value of the maximum time difference in the historical data; T max This is a time decay control parameter used to adjust the influence range of the time window. In this embodiment, T has been experimentally verified. max Setting it to 5 will yield the best results.

[0134] Existing techniques often use Gaussian functions to calculate weights, but Gaussian functions decay too quickly, easily neglecting the historical reference value in the medium to long term. This invention creatively uses the hyperbolic secant function to calculate the time weight t. w It utilizes its unique "heavy-tailed" characteristic to retain more historical information.

[0135] Time weight The specific calculation formula is shown in equation (10):

[0136]

[0137] This function is in When the time difference is small, it provides a weight close to 1. As the time difference increases, its decay rate is more gradual than that of the Gaussian function, thus ensuring that even historical samples that are slightly older but have very similar operating conditions can obtain reasonable weights.

[0138] 2.3 Spatiotemporal Similarity Fusion: In order to simultaneously utilize the distribution characteristics and temporal properties of the data, the spatial similarity S calculated above is fused together. spatial and time weight t w The fusion process is performed. To enhance the discriminative power between similar and dissimilar samples (i.e., sharpen the similarity matrix), this invention introduces a temperature parameter F. s .

[0139] The enhanced spatial and temporal terms are calculated separately as shown in equations (11) and (12):

[0140] eh s =exp(F s ×S spatial (11)

[0141] eh t =exp(F s ×t w (12)

[0142] Preferably, the temperature parameter F s The value is 2.

[0143] The comprehensive spatiotemporal similarity Matrix_S between the final sample i and the sample to be predicted (i)The product of the two is shown in equation (13):

[0144] Matrix_S (i) =eh s ×eh t (13)

[0145] By traversing all historical samples, a complete spatiotemporal similarity vector is constructed.

[0146] 2.4, based on Online spectral clustering method: For each new sample to be predicted, re-decomposing the full dataset using spectral clustering would be computationally too costly. This embodiment adopts... An approximation method is used for fast online data embedding.

[0147] During the offline training phase, a similarity matrix W has been constructed on the historical dataset, and its normalized Laplacian matrix has been calculated as shown in equation (14).

[0148] L sym =ID -1 / 2 WD -1 / 2 (14)

[0149] Where D is the degree matrix, and its eigenvalues ​​are decomposed to obtain the eigenvector matrix.

[0150] Determine the optimal number of clusters C. This embodiment proposes a clustering index (CMI) that comprehensively considers intra-cluster tightness and inter-cluster separation. By traversing k∈[2,50], the k value that maximizes the CMI index is selected as the optimal number of clusters C.

[0151] In the offline phase, the K-means algorithm is used to divide the projection of historical samples in the spectral space into C state clusters, and the cluster center c of each cluster is saved. k .

[0152] In the online prediction phase, for the sample x to be predicted new First, calculate its similarity vector s with historical samples. new (Corresponding to steps 2.1-2.3 above), then utilize The formula calculates its embedding coordinates z in the low-dimensional spectral space. new As shown in equation (15):

[0153]

[0154] Calculate z new With all offline clustering centers c kThe Euclidean distance is used to assign the sample to be predicted to the nearest Euclidean distance. Clusters. All historical samples are selected as the current "best modeling sample subset". This subset contains historical data that is most consistent with the current operating conditions in terms of spatiotemporal distribution, and is used for subsequent feature engineering and modeling.

[0155] Step 3: Perform feature engineering based on Dynamic Blocking (DFBE). Although the selected sample subset has similar operating conditions, cement production involves numerous variables (such as temperature, pressure, and flow rate), resulting in severe multicollinearity among features. Direct modeling would lead to model instability. This step uses dynamic blocking by calculating the comprehensive evaluation value of the features.

[0156] 3.1 Calculate feature relevance: For the preferred sample subset, mutual information (MI) is used to measure the relevance of each feature variable x. j The non-linear dependence between MI and the target variable y (F-CaO content). For ease of comparison, the MI value is Min-Max normalized and denoted as I. norm (x j ).

[0157] 3.2 Calculating Feature Uniqueness: Relying solely on correlation leads to the selection of multiple highly correlated redundant features (e.g., temperatures at different locations on the kiln head). This invention introduces Conditional Information Gain (CIG) to measure the non-substitutability of features. Its physical meaning is: given x... j In the case of all other features, feature x j How much additional information can it provide for predicting y?

[0158] To address the challenge of directly calculating conditional mutual information in high-dimensional spaces, this embodiment creatively proposes a calculation method based on "residual approximation": Step 1: Using division by x j All features other than Ω\{x j First, construct a GBDT regression model. Second, use this model to predict the target y and calculate the prediction residuals. Step 3: This residual represents information that other features cannot explain. Calculate feature x. j With the residual R (-j) The mutual information, which serves as an approximation of CIG, is shown in equation (16):

[0159]

[0160] The calculated approximate CIG value is also normalized using Min-Max, denoted as .

[0161] 3.3 Feature Comprehensive Evaluation Index (CM): Define the comprehensive evaluation index CM to balance the "high correlation" and "high uniqueness" of features, as shown in Equation (17).

[0162]

[0163] Wherein, β is the balance coefficient. After Bayesian optimization and 5-fold cross-validation, this embodiment sets β = 0.5, that is, to give equal importance to relevance and uniqueness.

[0164] 3.4 Dynamic Feature Blocking Strategy: All candidate features are sorted in descending order based on the CM value. To construct the sub-learners of the ensemble model, the features need to be divided into K blocks, requiring that features within each block are non-redundant and features between blocks are complementary.

[0165] Step 3.4.1: Select the top K features by CM value, and use them as the initial "seeds" or center features of the K feature blocks. In this embodiment, ablation experiments have verified that dividing the features into 2 blocks (i.e., K=2) yields the best results.

[0166] Step 3.4.2: For each remaining feature x i Calculate its relationship with each current feature block. m The average correlation of existing features; the degree of correlation is measured by the absolute value of the Pearson Correlation Coefficient (PCC) as shown in equation (18):

[0167]

[0168] Step 3.4.3: Use a greedy algorithm to select feature x. i Assign it to the feature block with the smallest AvgCorr value. Logical explanation: If a feature has low correlation with existing features within a block, it's considered "fresh" for that block, and adding it won't cause redundancy. By iterating through all features, K feature subsets are ultimately formed: {Block1, ..., Block...} K}

[0169] Step 4: Establish a mean JS divergence weighted ensemble prediction model: Unlike the traditional ensemble method that takes the average of all sub-models, this invention dynamically weights the models based on the distribution similarity between the sample to be predicted and the training data of the sub-models.

[0170] 4.1 Sub-model training: For each feature block... mGradient boosting decision tree (GBDT) is used as the base learner, and it is trained using the projection data of the preferred sample subset on the feature block.

[0171] 4.2 Centroid Feature Extraction: For the m-th feature block, calculate the mean vector of all samples in the preferred sample subset within the feature space of that block, and define it as the "centroid" of that block. As shown in equation (19).

[0172]

[0173] The centroid represents the typical state of the current preferred operating condition in this feature subspace.

[0174] 4.3 Dynamic Integration Weight Calculation: Calculate the weight of the sample to be predicted, x. test The projection vector and centroid on the m-th feature block The distribution differences between them. The aforementioned JS divergence formula is used again to calculate...

[0175] The Softmax function is used to convert the JS divergence of each block into normalized ensemble weights w. m As shown in equation (20):

[0176]

[0177] Physical meaning: If the distribution of the sample to be predicted is very close to the historical centroid (small JS divergence) in a certain feature block, it means that the sub-model is very familiar with the current sample, so it is given a larger prediction weight.

[0178] 4.4 Final Prediction Output: Summarize the prediction outputs of all K sub-models The final predicted value of F-CaO content in clinker was obtained. As shown in equation (21):

[0179]

[0180] Example 2

[0181] This embodiment experimentally verifies and analyzes the effect of a clinker F-CaO content prediction method based on spatiotemporal spectral clustering and block integration, as follows:

[0182] To verify the effectiveness of the method in this embodiment, actual DCS data from a clinker production line of a cement plant in China was used for testing.

[0183] Dataset Details: A total of 4105 samples were collected, arranged in chronological order. The first 3905 samples served as the historical training set, and the last 200 samples served as the test set to simulate the online prediction process. Input variables included key process parameters such as raw material feed rate, precalciner coal feed rate, precalciner outlet temperature, kiln head hood temperature, kiln head negative pressure, and tertiary air temperature.

[0184] The evaluation metrics used are: root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 ).

[0185] Experimental results data: Method of this invention (STSSC-DFBE): R 2 =0.7953, RMSE=0.2045, MAE=0.1202. Comparison method optimal value (MWUDA-CNN): R 2 =0.7251, RMSE=0.2197. Traditional BP neural network: R 2 = 0.5906. The results show that the method of this invention significantly outperforms existing technologies in prediction accuracy, R0 2 It increased by about 10% or more.

[0186] In summary, the present invention proposes a clinker F-CaO content prediction method based on spatiotemporal spectral clustering and block integration. It solves the sample matching problem under non-stationary conditions by using JS divergence and hyperbolic secant weights, solves the feature collinearity problem by using the CIG index with residual approximation and greedy block strategy, and achieves adaptive integration through centroid weighting mechanism.

[0187] This method not only improves prediction accuracy but also has good real-time performance, providing reliable data support for the refined control of the cement production process and has significant industrial application value.

Claims

1. A method for predicting F-CaO content in clinker based on spatiotemporal spectral clustering and block integration, characterized in that, Includes the following steps: S1. Collect cement clinker production data to build a historical database, and collect and preprocess the samples to be predicted by noise reduction and alignment. S2. Calculate the Jensen-Shannon divergence between the sample to be predicted and historical samples as the spatial distribution difference, use the hyperbolic secant function to calculate the time dimension difference, construct the spatiotemporal comprehensive similarity, and select the optimal sample subset through spectral clustering algorithm; S3. On the preferred sample subset, the mutual information (MI) of the features is calculated as a correlation index and the conditional information gain (CIG) is calculated as a uniqueness index. Based on this, the features are sorted and dynamically divided into several feature sub-blocks. S4. Train a sub-regression model for each feature sub-block, calculate the JS divergence distance between the sample to be predicted and the centroid of each feature sub-block, convert it into ensemble weights, and perform weighted ensemble of the results of each sub-model to obtain the final predicted value.

2. The method for predicting F-CaO content in clinker based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S1, the preprocessing for collecting, denoising, and aligning the samples to be predicted includes the following steps: S1.1 The process parameters of the cement clinker production line are collected in real time through the distributed control system (DCS). The parameters include: raw meal feed rate, coal feed rate and decomposer outlet temperature in the preheater stage; kiln head hood temperature, kiln head negative pressure, kiln speed, coal-carrying air pressure and rotary kiln coal feed rate in the rotary kiln stage; tertiary air temperature and blower K11 pressure in the grate cooler stage; and F-CaO content test values ​​at the corresponding time are collected as target variables. The sampling frequency is 1 minute / time. S1.

2. Based on the residence time of materials in the three thermal equipment units of preheater, rotary kiln and grate cooler during the cement clinker production process, time offset alignment is performed on each process parameter. S1.

3. A robust statistical method based on median-standard deviation is used to detect outliers. For the time series X(j) of the j-th feature, the median M(j) and standard deviation σ(j) are calculated. The outlier determination boundaries of the median and standard deviation are shown in the following two equations: L(j)=M(j)-k·σ(j) U(j)=M(j)+k·σ(j) In the formula, k = 7.0; for the detected outliers, a hierarchical correction strategy of bilateral interpolation, forward filling, backward filling or median substitution is adopted.

3. The method for predicting clinker F-CaO content based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S2, the construction of the spatiotemporal comprehensive similarity includes the following steps: S2.1, Employ a batch calculation strategy to improve the computational efficiency of JS divergence; for test sample X test With training sample set The batch computation process is as follows: First, the training samples are divided according to the batch size (batch_size). For each batch: Calculate the mixed distribution: To avoid numerical instability, a smoothing parameter ∈ = 10 is introduced. -10 Sample X to be predicted test Regarding the mixed distribution M (i) The stable formula for calculating the Kullback-Leibler divergence is: Similarly, calculating historical samples Regarding the mixed distribution M (i) The stable formula for calculating the Kullback-Leibler divergence is: In the formula, j represents the j-th dimension of the feature vector; Combining the two KL divergences mentioned above, we obtain the symmetric JS divergence value. The expression is as follows: In the formula, X test For testing purposes; For the training sample set; The difference between the probability distribution of the sample to be predicted and the historical samples can be calculated using the above formula. The smaller the value, the closer the probability distribution pattern of the sample to be predicted is to that of historical samples. S2.2 To improve computational efficiency on large-scale historical databases, a batch matrix operation strategy is adopted to calculate the divergence matrix between the sample to be predicted and all historical samples in one go, as follows: ① The calculated JS divergence is converted into spatial similarity S by using a Gaussian kernel function for nonlinear mapping. spatial The expression is as follows: In the formula, σ is the kernel width parameter, which is used to adjust the sensitivity of similarity to distance changes; ② Calculate the timestamp T of the sample to be predicted test Compared with historical sample timestamps The absolute time difference between them is expressed as follows: time_diff_ij=∣time_X i -time_X j ∣ ③ Perform logarithmic normalization on the time difference to obtain the normalized time difference. The expression is as follows: In the formula, the constant 1.0 is to prevent the logarithmic operator input from being 0; max(log(Δt)) is the logarithmic value of the maximum time difference in the historical data; T max It is the time decay control parameter, T max =5; ④ Use the hyperbolic secant function to calculate the time weight t w The expression is as follows: This function is When the time difference is small, it provides a weight close to 1. As the time difference increases, its decay rate is more gradual than that of the Gaussian function, thus ensuring that even historical samples that are slightly older but have very similar operating conditions can obtain reasonable weights. ⑤ To enhance the distinction between similar and dissimilar samples, i.e., to sharpen the similarity matrix, a temperature parameter F is introduced. s The spatial similarity S calculated above spatial and time weight t w By integrating the data, we can simultaneously utilize its distribution characteristics and temporal properties. The enhanced distribution characteristics are calculated using the following expression: eh s =exp(F s ×S spatial ) The enhanced time characteristics are calculated using the following expression: eh t =exp(F s ×t w ) In the formula, the temperature parameter F s The value is 2; The comprehensive spatiotemporal similarity Matrix_S between the final sample i and the sample to be predicted (i) For eh s and eh t The product of the two is expressed as follows: Matrix_S (i) =eh s ×eh t By traversing all historical samples, a complete spatiotemporal similarity vector is constructed, resulting in the final spatiotemporal similarity matrix.

4. The method for predicting clinker F-CaO content based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S2, the spectral clustering algorithm selects the optimal sample subset by employing The approximation method for fast online data embedding involves the following steps: ① During the offline training phase, a similarity matrix W is constructed for the historical dataset, and its normalized Laplacian matrix is ​​calculated as follows: L sym =I-D -1 / 2 WD -1 / 2 In the formula, D is the degree matrix, and its eigenvector matrix is ​​obtained by eigenvalue decomposition. ② By traversing k∈[2,50], select the k value that maximizes the CMI index as the optimal number of clusters C; ③ In the offline stage, the K-means algorithm is used to divide the projection of historical samples in the spectral space into C state clusters, and the cluster center c of each cluster is saved. k ; ④ In the online prediction stage, for the sample x to be predicted new First, calculate its similarity vector s with historical samples. new Then use The formula calculates its embedding coordinates z in the low-dimensional spectral space. new The expression is as follows: ⑤ Calculate z new With all offline clustering centers c k The Euclidean distance is used to assign the sample to be predicted to the nearest Euclidean distance. A cluster; All historical samples are selected as the current "best modeling sample subset"; this subset contains historical data that is most consistent with the current operating conditions in terms of spatiotemporal distribution, and is used for subsequent feature engineering and modeling.

5. The method for predicting clinker F-CaO content based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S3, the mutual information (MI) of the combined calculated features is used as the correlation index, and the conditional information gain (CIG) is used as the uniqueness index. The steps are as follows: S3.1 For the preferred sample subset, mutual information (MI) is used to measure each feature variable x. j The nonlinear dependence between MI and the target variable F-CaO content y; for ease of comparison, the MI value is Min-Max normalized and denoted as I. norm (x j ); S3.2 Introduce Conditional Information Gain (CIG) to measure the non-substitutability of features, as detailed below: ① Use division by x j All features other than Ω\{x j }, construct a GBDT regression model; ② Use this model to predict the target y and calculate the prediction residual, as shown in the following expression: ③ This residual represents information that cannot be explained by other features. Calculate feature x. j With the residual R (-j) The mutual information, which serves as an approximation of CIG, is expressed as follows: ④ The calculated approximate CIG value is also normalized using Min-Max, denoted as . ⑤ Define a comprehensive evaluation index CM to balance the "high correlation" and "high uniqueness" of features, as shown in the following expression: In the formula, β is the balance coefficient, β = 0.5, which means that relevance and uniqueness are equally valued.

6. The method for predicting clinker F-CaO content based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S3, the features are sorted and dynamically divided into several feature sub-blocks, as follows: ① Based on the CM value, all candidate features are sorted in descending order and divided into K blocks, requiring that features within a block are not redundant and features between blocks are complementary; ② Select the top K features with the highest CM values ​​and use them as the initial "seeds" or center features of the K feature blocks, with K=2 yielding the best results; ③ For each of the remaining features x i Calculate its relationship with each current feature block. m The average correlation of existing features is used to measure the degree of correlation using the absolute value of the Pearson correlation coefficient (PCC), as shown in the following expression: ④ Use a greedy algorithm to select feature x i Assign the feature block with the smallest AvgCorr value; by traversing all features, finally form K feature subsets {Block1,...,Block...} K } 7. The method for predicting clinker F-CaO content based on spatiotemporal spectral clustering and block integration according to claim 1, characterized in that, In S4, a sub-regression model is trained for each feature sub-block, the JS divergence distance between the sample to be predicted and the centroid of each feature sub-block is calculated, and this distance is converted into ensemble weights. The results of each sub-model are then weighted and ensembled to obtain the final predicted value. The specific steps are as follows: S4.1 Dynamically weight the data based on the distribution similarity between the sample to be predicted and the training data of the sub-model: For each feature block... m Gradient boosting decision tree (GBDT) is used as the base learner, and the training is performed using the projection data of the preferred sample subset on the feature block. S4.2 For the m-th feature block, calculate the mean vector of all samples in the preferred sample subset in the feature space of that block, and define it as the "centroid" of that block. The expression is as follows: In the formula, Let represent the centroid vector of the m-th feature block, and N represent the total number of samples in the preferred historical sample subset. Let represent the projection vector of the i-th preferred historical sample onto the m-th feature block subspace; the centroid represents the typical state of the current preferred condition in this feature subspace. S4.3 Calculate the sample x to be predicted test The projection vector and centroid on the m-th feature block The distribution differences between them; again, the aforementioned JS divergence formula is used to calculate... S4.

4. Use the Softmax function to convert the JS divergence of each block into normalized ensemble weights w. m The expression is as follows: In the formula, w m This represents the weight of the m-th feature block in the current prediction task. This represents the Jensen-Shannon divergence between the test sample and the mean of the m-th feature block; S4.5 Summarize the prediction outputs of all K sub-models The final predicted value of F-CaO content in clinker was obtained. The expression is as follows: In the formula, w represents the predicted f-CaO content of the test sample by the Gradient Boosting Decision Tree (GBDT) model trained on the m-th feature block. m This represents the weight of the m-th feature block in the current prediction task. This is the final integrated prediction result.

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