Raw meal homogenization store dynamic proportioning method based on ramanujan continued fraction

Abstract

The present application relates to cement production technical field, it provides raw meal homogenization storehouse dynamic proportioning method based on Ramanujan continued fraction, include: S1: obtain the continued fraction coefficient ak(0), bk(0) and the adjustment constant C of each material based on past 3-6 months production data is trained by Ramanujan continued fraction model;S2: real-time data acquisition and preprocessing, through laser composition analyzer continuously acquires material composition data Xi(t);S3: according to the latest Xi(t) and current coefficient, the Wi(t) of each material is calculated;Through PLC, continued fraction iterative calculation is carried out, k takes the first 8 items;Step S4: control signal output and execution, the weight Wi(t) calculated by PLC is converted, is sent to the frequency converter of belt scale, adjusts the discharge amount;S5: feedback optimization and self-learning, the standard deviation of raw meal CaCO3 is counted.The present application introduces Ramanujan continued fraction into cement raw meal proportioning field, constructs dynamic weight function, solves the deficiency of traditional control theory when dealing with complex industrial process nonlinear problem.

Description

Technical Field

[0001] This invention relates to the field of cement production technology, and in particular to a dynamic batching method for raw meal homogenization silos based on the Ramanujan continuous fractionation method. Background Technology

[0002] In dry-process cement production, raw meal homogenization is a crucial step in ensuring clinker quality. Traditional raw meal homogenization silos employ static batching or timed adjustment strategies, which result in a delayed response to fluctuations in raw material composition. When the coefficient of variation (R) of limestone CaCO3 exceeds 5%, the pre-homogenization effect becomes unstable, leading to fluctuations in clinker quality.

[0003] Although the cement industry, especially the new dry process production lines, has widely adopted automated equipment, its core control strategies still have significant shortcomings and are far from reaching the level of intelligence.

[0004] Limitations of Linear Programming Algorithms: Some advanced automated batching systems (such as the mentioned end-to-end multi-index batching method) have attempted to use linear programming algorithms to optimize multiple quality indicators (such as saturation ratio KH, silicate content SM, etc.). However, linear programming is essentially a static optimization tool. It relies on fixed raw material composition parameters for calculation and cannot effectively cope with nonlinear fluctuations caused by changes in mine raw material sources and seasonal changes. When the coefficient of variation R of limestone CaCO3 > 5%, the prediction accuracy of the model will drop sharply, leading to deviations between the batching scheme and actual needs.

[0005] The inherent flaws of the homogenization silo control mode: To compensate for potential deviations in a single batching, existing technologies have introduced a "homogenization silo control mode," which attempts to utilize the buffering capacity of the homogenization silo over multiple batching cycles to ensure the total raw material meets specifications. However, this mode heavily relies on precise control of the material quantity and composition within the homogenization silo, making it difficult to implement in practice. Essentially, it is a "post-event averaging" compensation mechanism rather than "pre-event predictive" precise control, and the response lag problem remains unresolved.

[0006] Insufficient data utilization and poor system synergy: Online laser component analyzers, belt scales, and other equipment on the production line generate massive amounts of real-time data, but traditional control algorithms fail to perform in-depth data mining and predictive applications. Control behavior still mainly relies on "snapshot" data from the previous detection cycle, lacking the ability to predict component trends. Furthermore, the control systems for the two key stages of "ingredient preparation" and "homogenization" often operate independently, failing to incorporate real-time inventory levels in the homogenization chamber and homogenization effects as dynamic variables into the ingredient preparation decision model, making it difficult to achieve the global optimization objective.

[0007] As China's cement industry moves towards high-quality and green development, new requirements have been placed on the accuracy and stability of raw material batching. According to the latest industry policies, the state continues to promote energy conservation and carbon reduction initiatives in key industries such as cement. This means that reducing energy consumption while ensuring clinker quality has become a mandatory target. The high electricity consumption in homogenization silos caused by traditional batching methods (accounting for 15-20% of the total energy consumption of the production line) directly impacts the carbon emissions and operating costs of enterprises.

[0008] The pursuit of stability in large-scale production has led to increasingly larger dry-process cement production lines (typically reaching 5,000 tons / day), employing distributed control systems (DCS) for full automation. In this context, any fluctuations in raw material composition that cannot be quickly mitigated will be amplified in large-scale production, resulting in substandard clinker quality and significant economic losses. Therefore, the industry urgently needs an intelligent batching algorithm capable of millisecond-level response and real-time adaptation.

[0009] Based on the above analysis, the existing technology lacks a dynamic predictive control method that can deeply integrate real-time sensor data, possess strong nonlinear processing capabilities, and achieve coordinated optimization of the entire batching-homogenization process. Summary of the Invention

[0010] The purpose of this invention is to provide a dynamic batching method for raw meal homogenization silos based on the Ramanujan continuous fractionation method, which solves the problems of unstable homogenization effect, slow response, and high energy consumption caused by fluctuations in raw material composition in the traditional cement raw meal batching process.

[0011] This invention provides the following technical solution:

[0012] The dynamic batching method for raw material homogenization bins based on the Ramanujan continuous fractionation method includes the following steps:

[0013] S1: Obtain the continuous fraction coefficients a based on production data from the past 3-6 months through training a Ramanujan continuous fraction model. k (0),b k (0), and the adjustment constant C for each material; the adjustment constant C is set according to the material characteristics;

[0014] The dynamic weight function of the Ramanujan continued fraction model is as follows:

[0015] (5)

[0016] In the formula, W i (t): The dynamic proportion weight of material i at time t, which is a real-time control variable; C: Material characteristic adjustment constant, which is set according to the material's natural properties, historical fluctuation range, and process requirements; a k ,b kThe Ramanujan continued fraction coefficients, obtained through training with a large amount of historical production data, determine the convergence characteristics and response speed of the weighting function; X i (t): Material composition data (such as CaCO3, SiO2, Fe2O3 content) collected in real time by the laser component analyzer, which is the direct input to the algorithm; t: Time variable;

[0017] S2: Real-time data acquisition and preprocessing

[0018] Material composition data is continuously collected using a laser component analyzer. i (t), the data is smoothed by a Kalman filter to remove noise and outliers;

[0019] S3: Dynamic Weight Calculation

[0020] With a period of 0.5 seconds, based on the latest X i (t) and the current coefficient, calculate W for each material. i (t); Calculate the continuous fraction iteratively using a PLC, with k taking the first 8 terms:

[0021] W i (t)=C·[1+a1 / (b1+t)+a2 / (b2+t)+...+a8 / (b8+t)]·Xi(t) (11)

[0022] Step S4: Control signal output and execution

[0023] The PLC will calculate the weight W. i (t) is converted into a 4-20mA analog signal or PROFIBUS P communication command and sent to the frequency converter of the belt scale to adjust the feeding amount;

[0024] S5: Feedback Optimization and Self-Learning

[0025] The standard deviation of CaCO3 in the raw material is calculated. If the deviation exceeds the threshold, 'a' is finely adjusted. k ,b k Then return to step S2 to execute, so that the Ramanujan continuous fraction model can continuously adapt to changes in raw materials.

[0026] Preferably, the training process of the Ramanujan continued fraction model in step S1 involves determining the continued fraction coefficients a using historical data. k ,b k To minimize the weighted predicted value W i The error between (t) and the actual optimal ratio is determined by the following steps:

[0027] S1.1 Data Preparation Stage

[0028] Data sources include raw material composition data and corresponding optimal ratio records extracted from the production line's historical database over the past 3-6 months; key data includes: real-time sensor data X i (t): includes limestone CaCO3 content, clay SiO2 content, iron powder Fe2O3 content, sampling frequency ≥ 2 times / second; and the actual optimal proportion weight W. actual (t): The historical best value derived from clinker quality, used as the training label;

[0029] Output objective: The training objective is to obtain the coefficient array a. k ,b k This makes the output of equation 11 and W actual Minimize the mean square error (MSE) of (t);

[0030] S1.2 Model Initialization and Parameter Setting

[0031] The first eight terms of the Ramanujan continuous fraction are used for truncation approximation, with coefficient a. k ,b k The initial values ​​are set based on the statistical characteristics of historical data; the error threshold ε = 0.001; the maximum number of iterations T. max =1000;

[0032] S1.3 Iterative Optimization Algorithm

[0033] Minimize the mean square error function using the gradient descent algorithm:

[0034] (8)

[0035] Where M represents the number of historical data points, the specific steps are as follows:

[0036] S1.3.1 Forward calculation: For each historical data point, substitute the current coefficient to calculate W. i (t);

[0037] S1.3.2 Error Backpropagation: Calculating the Gradient and By using the chain rule to differentiate term by term;

[0038] S1.3.3 Coefficient Update:

[0039] (9)

[0040] (10)

[0041] In the above formula, the learning rate η = 0.01;

[0042] S1.3.4 Convergence check, verified after each iteration. For k=1 to N, and the rate of change of MSE < 0.1%, if T is satisfied or reaches... max If so, then stop training;

[0043] S1.4. Training Validation and Convergence Check

[0044] To verify the generalization ability, use 20% of the retained historical data to test the generalization ability, requiring the MSE error to increase by less than 5% compared to the training set.

[0045] Preferably, in step S2, the real-time data acquisition stage, the raw data X collected by the laser component analyzer... i (t) contains high-frequency noise and occasional outliers. Before being fed into the continuous fraction algorithm, it is preprocessed using the Kalman filter algorithm. The preprocessing includes two stages: prediction and update.

[0046] In the prediction phase, based on the state estimate at time k-1, the state and covariance at time k are predicted:

[0047] (13)

[0048] In the above formula, x k∣k−1 The prior state estimation vector at time k represents the state predicted at time k based on data from k-1 and earlier; the state represents the true composition of the raw meal, expressed as a percentage (%).

[0049] x k−1∣k−1 : The posterior state estimation vector at time k-1, i.e., the state value after optimization in the previous filtering cycle;

[0050] A k : State transition matrix, describing the state evolution of the system from k-1 to k;

[0051] B k : Control input matrix, which maps the influence of control variables on the state;

[0052] u k : Control input vector;

[0053] State x corresponds to the true value of the raw material composition, observation y is the sensor reading, and the filtering objective is to approximate the true value through an algorithm and reduce noise;

[0054] (14)

[0055] P k∣k−1The prior estimation error covariance matrix represents the uncertainty of the predicted state. The diagonal elements are the variances, and the off-diagonal elements are the covariances.

[0056] P k−1∣k−1 The posterior estimation error covariance matrix at time k-1 reflects the estimation accuracy at the previous time step.

[0057] A k T : Transpose of the state transition matrix;

[0058] Q k The process noise covariance matrix represents the uncertainty of the system model.

[0059] Iteration of the P matrix ensures the algorithm's adaptation to model error, Q k The magnitude directly affects the filter's sensitivity to fluctuations;

[0060] During the update phase, the actual observed value y at time k is combined with... k Calculate the Kalman gain K k And update the state estimate and covariance estimate:

[0061] (15)

[0062] K k Kalman gain matrix: a weighted average of the confidence levels of predicted and observed values. A higher gain indicates greater confidence in the observations, while a lower gain indicates greater confidence in the predictions.

[0063] H k : Observation matrix, which maps the state space to the observation space; H k = 1 indicates a one-to-one correspondence between observation and state;

[0064] H k T : Transpose of the observation matrix;

[0065] R k The noise covariance matrix is ​​measured to represent the sensor noise level. Based on the accuracy of the laser component analyzer, let R... k It is a scalar;

[0066] Calibration: R k It needs to be set according to the sensor specifications. If the detection accuracy is ±0.05%, then the variance R k ≈(0.05)²=0.0025;

[0067] (16)

[0068] x k∣k The posterior state estimate vector at time k (dimension: n×1), i.e., the filtered optimal state value, output as smoothed data. Used for weight calculation;

[0069] y k The actual observation vector at time k (dimension: p×1) originates from the raw sensor data X. i (t), such as the CaCO3 content reading;

[0070] H k x k∣k−1 : Observational prediction, representing the expected observation based on the prior state;

[0071] y k -H k x k∣k−1 Residuals reflect the deviation between observations and predictions;

[0072] (17)

[0073] P k∣k : Posterior estimation error covariance matrix, updated uncertainty measure;

[0074] I: Identity matrix, compared with H k Dimension matching;

[0075] Convergence guarantee: This equation ensures that the P matrix decreases over time, reflecting the improvement in filtering performance.

[0076] Preferably, in step S4, the material feed rate is controlled by a dynamic weight W. i (t) is converted into specific control instructions via PLC; high-precision belt scales typically use frequency conversion speed regulation electronic belt scales, whose feed flow rate is proportional to the frequency of the frequency converter; the control model is:

[0077] (18)

[0078] Among them, F i (t) is the target feed rate of material i, in t / h, K. p It is the flow rate-frequency proportionality coefficient of the belt scale, F i,base This is the basic flow rate to ensure material flowability. This instruction is sent to the frequency converter of the belt scale through the analog output module of the PLC or PROFIBUS PEP communication.

[0079] Preferably, in step S5, the statistical object is the formula for calculating the standard deviation of calcium carbonate content in the raw material:

[0080] (12)

[0081] Where, x iThe CaCO3 content value for each test is expressed in %, μ is the mean, N is the number of data points within the statistical period, and the threshold is ±0.15%.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] This invention provides a dynamic batching method for raw meal homogenization silos based on Ramanujan's continuous fractions. It introduces Ramanujan's continuous fractions into the field of cement raw meal batching, constructs a dynamic weighting function, and mathematically addresses the shortcomings of traditional control theory in dealing with nonlinear problems in complex industrial processes. It can be implemented using a non-intrusive add-on design, integrating with existing DCS systems through standard interfaces (such as OPC and industrial Ethernet), achieving closed-loop control of "sensing-decision-execution," with convenient modification and low risk.

[0084] This invention achieves a leap from "passive response" to "active prediction" by deeply fusing real-time sensor data with historical training models. The algorithm not only reflects the current composition but also predicts changing trends through the memory characteristics of continued fractions.

[0085] This invention directly links proportion optimization with energy consumption management. By stabilizing the raw material composition, it significantly reduces the energy consumption of pneumatic stirring in the homogenization silo, while laying a solid foundation for energy conservation and consumption reduction in subsequent calcination processes, achieving a dual improvement in quality and energy efficiency. For example:

[0086] Improved stability of raw meal quality: The standard deviation of CaCO3 in raw meal can be stably controlled within ±0.1% from ±0.3%, which greatly improves the uniformity and consistency of clinker quality.

[0087] Significantly reduced energy consumption: Due to improved homogenization, the power consumption of pneumatic mixing in the homogenization silo is expected to decrease by more than 15%. For a cement production line with an annual output of 1 million tons, the estimated annual power savings could reach approximately 1.5 million kilowatt-hours.

[0088] Improved response speed: The response time to fluctuations in raw material composition has been reduced from minutes to seconds (algorithm cycle 0.5 seconds) in traditional methods, greatly enhancing the system's adaptability to raw material fluctuations.

[0089] Production cost and resource utilization optimization: Precise proportioning control reduces raw material waste and improves resource utilization. At the same time, increased automation reduces the intensity and frequency of manual intervention. Attached Figure Description

[0090] Figure 1 This is a schematic flowchart of a dynamic batching method for raw material homogenization bins based on Ramanujan continuous fractions, provided in an embodiment of the present invention. Detailed Implementation

[0091] Most improvements to existing dynamic batching methods focus on hardware upgrades or patching linear models, failing to innovate at the underlying mathematical model of control theory. The technical approach of this invention utilizes Ramanujan's continued fraction, a mathematical tool uniquely advantageous for handling convergence problems in complex, nonlinear systems.

[0092] Ramanujan's continued fractions possess strong convergence and the ability to approximate complex functions. Their basic mathematical form is:

[0093] (1)

[0094] To save vertical space, a compact notation is often used:

[0095] (2)

[0096] or

[0097] (3)

[0098] Where K is the special symbol for continued fractions (Kettenbruch). The meanings of the symbols in equations (1) to (3) are explained as follows:

[0099] The objective function represents the value defined by the continued fraction; it is a variable. The function.

[0100] The constant term, also known as the integer part of a continued fraction, determines the baseline level of the entire function.

[0101] ( The coefficients of the continued fraction determine its convergence and functional shape. These coefficients can be fixed constants or dependent on... The variables; in this application, they are core parameters obtained through training with historical data.

[0102] : Variables or parameters, which in specific applications can be related to time. Sensor readings Or related to other process parameters.

[0103] Ellipsis (...): indicates that the fractional structure theoretically continues indefinitely. In practical industrial applications, the first few terms (such as the first 8 or 10 terms) are usually truncated to meet accuracy requirements.

[0104] In real-time control systems, directly processing infinitely continuous fractions is impractical. This invention employs an engineering-oriented discretization process. First, the first N terms of the continuous fraction are taken (in practice, N=8 is sufficient to meet the accuracy requirements, because |a k / b k |Fast decay) is used for approximate calculation.

[0105] Secondly, coefficient a k ,b k The data is trained using historical data, and the training objective is to minimize the mean squared error between the predicted weights and the actual optimal weight distribution. The training process must satisfy the convergence condition: lim k→∞ |a k / b k |<ε (usually set ε=0.001) to ensure algorithm stability.

[0106] The dynamic weighting algorithm for raw material homogenization bins proposed in this invention application has the following dynamic weighting function as its mathematical model:

[0107] (4)

[0108] That is, expanded as:

[0109] (5)

[0110] In the formula:

[0111] W i (t): The dynamic proportion weight of material i (such as limestone, clay, iron powder) at time t, which is a real-time control variable;

[0112] C: Material property adjustment constant, set according to the material's natural properties, historical fluctuation range, and process requirements;

[0113] a k ,b k The Ramanujan continuous fraction coefficients, obtained through training with a large amount of historical production data, determine the convergence characteristics and response speed of the weighting function.

[0114] X i (t): Material composition data (such as CaCO3, SiO2, Fe2O3 content) collected in real time by the laser component analyzer is the direct input to the algorithm;

[0115] t: Time variable, reflecting the system's adaptive process.

[0116] Adaptability and Nonlinearity: The inherent structure of Ramanujan's continued fraction allows it to approximate complex nonlinear relationships with extreme efficiency. In the batching process, the fluctuations in raw material composition are nonlinear, which traditional linear PID controllers struggle to handle perfectly, while this continued fraction provides a strong mathematical foundation.

[0117] Coefficient training: Coefficient a k ,b k It is not arbitrarily set, but rather obtained through training and optimization using a large amount of historical production data (such as raw material composition data and optimal ratio data from the past 3-6 months), so that the function can best reflect the process characteristics of a specific production line. The training process must satisfy the convergence condition limk→∞∣a k / b k |<ϵ (for example, let ϵ=0.001) to ensure the stability of the algorithm.

[0118] Real-time prediction: combining time t and real-time sensor data X i Using (t) as input, this function can calculate the prediction of the component change trend in the short term from the current moment, thus achieving proactive adjustment rather than simply "remedial" based on the current deviation. The model uses an infinite series expansion of the Ramanujan continuous fraction to transform the coefficients (a) obtained from training with historical data. k ,b k ) and real-time sensor data (X i (t) Deep integration enables dynamic, nonlinear, and forward-looking adjustment of ingredient weights.

[0119] The present invention will now be described in detail with reference to embodiments and accompanying drawings. However, it should be understood that the embodiments and drawings are for illustrative purposes only and do not constitute any limitation on the scope of protection of the present invention. All reasonable modifications and combinations included within the inventive spirit of the present invention fall within the scope of protection of the present invention.

[0120] Example 1

[0121] The system adopts an external architecture, running in parallel with the cement plant's existing DCS system to ensure that the retrofit process does not affect production continuity. The system architecture is as follows: Figure 1 As shown, the equipment mainly includes three categories:

[0122] Composition detection equipment: An online laser composition analyzer (such as one based on neutron activation or X-ray fluorescence principle) is installed above the conveyor belt at the entrance of the raw material homogenization silo to detect the chemical composition of the raw materials entering the mill in real time, such as the content of CaCO3 in limestone, SiO2 in clay and Fe2O3 in iron powder. The data update frequency is ≥2 times / second and the detection accuracy is ±0.05%.

[0123] Data processing equipment: The core controller adopts a Siemens S7-1500 series PLC (configured as CPU: 1518-4PN / DP; memory: 4GB DDR3; communication: industrial Ethernet interface; algorithm cycle: 0.5 seconds). The PLC receives component data through industrial Ethernet, runs the Ramanujan continuous fraction algorithm, calculates the dynamic weight Wi(t), and outputs control signals.

[0124] Execution control equipment: including a high-precision belt scale (control accuracy ±0.1%, response time <0.5 seconds) and its frequency converter. The PLC is based on W... i (t) Adjust the speed of the belt scale motor in real time to accurately control the amount of each material fed.

[0125] The system exchanges data with the factory's upper-level information management system (such as MES and ERP) through the OPC (OLE for Process Control) interface to achieve visualized monitoring and data traceability of the entire batching process.

[0126] The dynamic batching method for raw material homogenization bins based on the Ramanujan continuous fractionation method provided in this embodiment includes the following steps:

[0127] Step S1: Obtain the continued fraction coefficients a based on production data from the past 3-6 months. k (0),b k (0), load the preset continued fraction coefficients a k (0),b k (0), and the adjustment constant C for each material.

[0128] During implementation, three months of raw material composition data were extracted from the historical database to train the initial coefficients: a1=0.85, b1=1.2; a2=0.63, b2=2.1; a3=0.42, b3=3.0;... a8=0.05, b8=8.7. The adjustment constant C was set according to the material characteristics: limestone C=1.2, clay C=0.8, iron powder C=1.0.

[0129] The training process does not directly use existing artificial intelligence models, but rather combines the mathematical tool of Ramanujan's continued fraction with the specificities of the cement production field, training the continued fraction coefficients (a) through a historical data-driven approach. k ,b k The core idea lies in applying Ramanujan's continued fraction to the dynamic weighting function of cement raw material batching. Traditionally used in pure mathematics, Ramanujan's continued fraction is engineered for the first time into a dynamic control algorithm. By training the coefficients with data, nonlinear predictive control is achieved. The training does not rely on any publicly available artificial intelligence models (such as neural networks or deep learning frameworks), but rather on custom-optimizing the continued fraction coefficients based on historical production data, ensuring close coupling with the cement process.

[0130] The training process aims to determine the continued fraction coefficients 'a' using historical data. k ,b k To minimize the weighted predicted value W i The error between (t) and the actual optimal ratio. The entire process is divided into four stages: data preparation, model initialization, iterative optimization, and validation. The specific steps are as follows:

[0131] S1.1 Data Preparation Stage

[0132] Data is extracted from the production line's historical database, containing raw material composition data and corresponding optimal ratio records for the past 3-6 months. Key data includes: real-time sensor data X. i (t): such as limestone CaCO3 content, clay SiO2 content, iron powder Fe2O3 content, sampling frequency ≥ 2 times / second; and the actual optimal proportion weight W. actual (t): The historical best value derived from clinker quality is used as the training label. The data needs to be smoothed using a Kalman filter to remove noise and outliers, ensuring input quality.

[0133] Output objective: The training objective is to obtain the coefficient array a. k ,b k This makes the output of the weighting function (Equation 4) equal to W. actual Minimize the mean squared error (MSE) of (t).

[0134] S1.2 Model Initialization and Parameter Setting

[0135] The Ramanujan continuous fraction is truncated using the first N terms (N=8 in practice), and its basic form is Equation 3, which is expressed as:

[0136] (6)

[0137] In this embodiment, the variable z is related to time t and sensor data X. i (t) correlation, the dynamic weight function expands to:

[0138] (7)

[0139] coefficient a k ,b k The initial values ​​are set based on the statistical characteristics of historical data. For example, linear regression can be used to initially estimate the trend before assigning values: a k (0) = rand(0,1) (small random number), b k(0) = k + offset (avoid division by zero). The adjustment constant C is preset according to the material characteristics: limestone C = 1.2, clay C = 0.8, iron powder C = 1.0.

[0140] Key hyperparameters: Error threshold ε = 0.001 (convergence condition); Maximum number of iterations T max =1000; learning rate η=0.01 (for gradient descent optimization).

[0141] S1.3 Iterative Optimization Algorithm

[0142] Optimization method: Minimize the mean squared error function using the gradient descent algorithm.

[0143] (8)

[0144] Where M represents the number of historical data points, the specific steps are as follows:

[0145] S1.3.1 Forward calculation: For each historical data point, substitute the current coefficient to calculate W. i (t).

[0146] S1.3.2 Error Backpropagation: Calculating the Gradient and The chain rule is used to differentiate each term.

[0147] S1.3.3 Coefficient Update:

[0148] (9)

[0149] (10)

[0150] S1.3.4 Convergence check, verified after each iteration. (For k=1 to N), and the rate of change of MSE < 0.1%. If T is satisfied or reached... max If the training stops, then training should be stopped.

[0151] Example training results: As shown in the example, the coefficients after training can be a1=0.85, b1=1.2; a2=0.63, b2=2.1; ...; a8=0.05, b8=8.7.

[0152] S1.4. Training Validation and Convergence Check

[0153] To verify generalization ability, use 20% of the retained historical data, requiring the MSE to increase by less than 5% compared to the training set error. For cement industry applications, the input and output are related as follows: Input X i (t) represents real-time component sensor data, output W. i (t) Directly control the material feeding amount of the belt scale to form a closed loop of "sensor → algorithm → actuator".

[0154] In terms of domain adaptability, process constraints are incorporated during coefficient training, such as the CaCO3 standard deviation threshold of ±0.15%, to ensure that the algorithm response is synchronized with the energy consumption optimization of homogenized gas stirring.

[0155] The training process drives the optimization of Ramanujan's continued fraction coefficients using historical data, achieving a leap from "static formulation" to "dynamic prediction".

[0156] Step S2: Real-time data acquisition and preprocessing.

[0157] Laser component analyzer continuously collects material composition data X i The data (t) is smoothed by a Kalman filter to remove noise and outliers.

[0158] Step 3: Dynamic weight calculation.

[0159] The PLC operates on a 0.5-second cycle, based on the latest X... i (t) and the current coefficient, calculate W for each material. i (t). This cycle matches the response time of the on-site belt scale and control mechanism (usually in the range of 0.1-1 seconds) to ensure real-time control.

[0160] In practice, continuous fractional iterative calculations are performed in the PLC, and the accuracy requirements are met by taking the first 8 terms.

[0161] W i (t)=C·[1+a1 / (b1+t)+a2 / (b2+t)+...+a8 / (b8+t)]·Xi(t) (11)

[0162] Step S4: Control signal output and execution.

[0163] The PLC will calculate the weight W. i (t) is converted into a 4-20mA analog signal or PROFIBUS P communication command and sent to the frequency converter of the belt scale to precisely adjust the feeding amount.

[0164] Step S5: Feedback optimization and self-learning.

[0165] The system automatically calculates the standard deviation of raw material CaCO3 every 24 hours. If the deviation exceeds the threshold (e.g., ±0.15%), then a is finely adjusted.k ,b k Then return to step S2 to execute, allowing the model to continuously adapt to changes in raw materials. The statistical object is the standard deviation of the calcium carbonate (CaCO3) content in the raw meal, which is a core indicator for measuring the uniformity of raw meal composition. The calculation formula is:

[0166] (12)

[0167] Where, x i The standard deviation (CCO3) represents the CaCO3 content value (%) for each test, μ is the mean, and N is the number of data points within the statistical period (e.g., N≈172,800 if sampling is performed twice per second within 24 hours). An example threshold of ±0.15% is used, set based on process requirements. When the standard deviation exceeds this threshold, it indicates that fluctuations in raw material composition have affected the homogenization effect, necessitating coefficient optimization. The standard deviation of CaCO3 is directly related to clinker quality. Traditional control methods achieve a deviation of ±0.3%, while this embodiment aims to control the deviation within ±0.1% to improve clinker consistency. This parameter is calculated by real-time data acquisition using an online laser component analyzer and a built-in algorithm, rather than by directly measuring "weight".

[0168] Furthermore, in step S2, the real-time data acquisition stage, the raw data X collected by the laser component analyzer... i (t) will contain high-frequency noise and occasional outliers. Before being fed into the continued fraction algorithm, a Kalman filter is used for preprocessing. This process includes two stages: prediction and update.

[0169] In the prediction phase, the state and covariance at time k are predicted based on the state estimate at time k-1.

[0170] (13)

[0171] x k∣k−1 : The prior state estimation vector at time k (dimension: n×1), representing the state predicted at time k based on data up to k-1. In this application, the state represents the actual composition value of the raw material (e.g., CaCO3 content), expressed as a percentage (%). For example, if only CaCO3 is being tracked, then n=1, x k∣k−1 It is a scalar.

[0172] x k−1∣k−1 : The posterior state estimation vector at time k-1 (dimension: n×1), which is the state value after optimization in the previous filtering cycle.

[0173] A kThe state transition matrix (dimension: n×n) describes the state evolution of the system from k-1 to k. In raw material batching, component changes are usually assumed to be linear or near-linear. If the component fluctuations are stable, A can be assumed to be linear. k =1 (identity matrix), indicating that there are no drastic changes in the state.

[0174] B k : Control input matrix (dimension: n×m), mapping the influence of control variables on the state. In this embodiment, there is no external control input, so Bk=0, and this term can be ignored.

[0175] u k : Control input vector (dimension: m×1), not used in this application, set to empty.

[0176] In the field of parameter correlation: the state x directly corresponds to the true value of the raw material composition, the observation y is the sensor reading, and the filtering goal is to approximate the true value through the algorithm and reduce noise.

[0177] (14)

[0178] P k | k−1 The prior estimation error covariance matrix (dimension: n×n) represents the uncertainty of the predicted state. The diagonal elements are the variances, and the off-diagonal elements are the covariances. In this application, if n=1, it degenerates into a scalar variance.

[0179] P k−1∣k−1 The posterior estimation error covariance matrix at time k-1 (dimension: n×n) reflects the estimation accuracy at the previous time step.

[0180] A k T : Transpose of the state transition matrix.

[0181] Q k The process noise covariance matrix (dimension: n×n) represents the uncertainty of the system model (such as nonlinear fluctuations in raw material composition). In cement production, it can be set based on historical data: if the composition fluctuations are stable, Q should be small (e.g., 0.01); if the fluctuations are large (coefficient of variation R>5%), Q needs to be increased (e.g., 0.1).

[0182] Iteration of the P matrix ensures the algorithm's adaptation to model error, Q k The magnitude directly affects the filter's sensitivity to fluctuations.

[0183] During the update phase, the actual observed value y at time k is combined with... k Calculate the Kalman gain K k And update the state estimate and covariance estimate.

[0184] (15)

[0185] K k Kalman gain matrix (dimension: n×p): Balances the confidence levels of predicted and observed values. A high gain indicates confidence in the observations, while a low gain indicates confidence in the predictions.

[0186] H k The observation matrix (dimension: p×n) maps the state space to the observation space. In this application, the sensor directly detects components, so H is usually the identity matrix (Hi). k = 1), indicating a one-to-one correspondence between observation and state.

[0187] H k T : Transpose of the observation matrix.

[0188] R k The noise covariance matrix (dimension: p×p) represents the sensor noise level. Based on the accuracy of the laser component analyzer (±0.05%), R can be set... k It is a scalar (e.g., 0.005²).

[0189] Calibration: R k It needs to be set according to the sensor specifications. For example, if the detection accuracy is ±0.05%, then the variance R... k ≈(0.05)²=0.0025.

[0190] (16)

[0191] x k∣k The posterior state estimate vector at time k (dimension: n×1), i.e., the filtered optimal state value, output as smoothed data. , used for weight calculation.

[0192] y k The actual observation vector at time k (dimension: p×1) originates from the raw sensor data X. i (t), such as the CaCO3 content reading.

[0193] H k x k∣k−1 : Observational prediction, representing the expected observation based on the prior state.

[0194] y k -H k x k∣k−1 The innovation item (residual) reflects the deviation between observation and prediction.

[0195] (17)

[0196] Pk∣k : Posterior estimation error covariance matrix (dimension: n×n), updated uncertainty measure.

[0197] I: Identity matrix (dimension: n×n), compared with H k Dimension matching.

[0198] Convergence Guarantee: This equation ensures that the P matrix decreases over time, reflecting the improvement in filtering performance.

[0199] Furthermore, in step S4, the material feed rate is controlled by a dynamic weight W. i (t) needs to be converted into specific control instructions via PLC. High-precision belt scales typically use variable frequency speed control electronic belt scales, where the feed flow rate is proportional to the frequency of the frequency converter. The control model can be simplified as follows:

[0200] (18)

[0201] Among them, F i (t) is the target feed rate of material i (unit: t / h), K p It is the flow rate-frequency proportionality coefficient of the belt scale (derived from calibration), F i,base This is the basic flow rate to ensure material flowability. This instruction is sent to the frequency converter of the belt scale via the PLC's analog output module or PROFIBUS DIP communication.

[0202] The dynamic batching method for raw material homogenization silos based on the Ramanujan continuous fractionation system, as described in this embodiment, was implemented on a 2500t / d production line of a cement company. The hardware installation and signal integration during implementation are as follows:

[0203] Installation of component analysis equipment: The online laser component analyzer is installed approximately 1.5 meters above the belt conveyor at the entrance of the homogenization silo, ensuring that the detection field of view covers the central area of ​​the material flow. To reduce belt vibration and dust interference, a shock-absorbing bracket and a dedicated purging system are required to protect the optical lens.

[0204] Control signal input: The S7-1500 PLC of this system connects to the factory's main DCS system via Industrial Ethernet (ProfiNet) or OPCUA interface. The calculated dynamic weight W... i (t) is sent as an analog signal (4-20mA) or directly as a setpoint message to the controller of the original batching scale to realize the "suggestion-execution" mode, without directly replacing the original control loop, thus ensuring production safety.

[0205] In terms of software programming and configuration:

[0206] Algorithm Function Block Development: Within the TIAPortal environment, the Ramanujan's continued fraction algorithm is encapsulated as an independent background data block (InstanceDB). The main input interfaces of this function block include: real-time component data X. i timestamp t, coefficient array a k [],b k []; The output interface is the dynamic weight W. i And weight status words. Human-Machine Interface (HMI) configuration: Add a monitoring screen to the operator station in the central control room to dynamically display the real-time weight W of each material. i (t), CaCO3 standard deviation trend curve, algorithm running status and alarm information (such as sensor failure, coefficient exceeding limits, etc.). Key parameters (such as target standard deviation threshold ±0.15%) should have modification permissions set.

[0207] The following table compares the algorithm provided in this embodiment with the traditional fixed-ratio approach:

[0208] Table 1 Comparison Table

[0209] Performance indicators Traditional fixed ratio control This embodiment describes a dynamic ingredient dispensing method. Increase <![CDATA[Standard deviation of raw material CaCO3 (%)]]> ±0.32% ±0.09% Reduced by 71.9% Unit power consumption of homogenization tank (kW·h / t) 18.5 15.7 Reduced by 15.1% Ingredient adjustment response time 3-5 minutes <1 second Improve by two orders of magnitude Standard deviation of clinker compressive strength at 28 days (MPa) 1.8 1.0 Significantly improved stability

[0210] The original batching system used a fixed ratio control, with a standard deviation of ±0.32% for CaCO3. After installing this system, the deviation was reduced to ±0.09%, and the power consumption of the homogenization silo decreased from 18.5 kW·h / t to 15.7 kW·h / t, resulting in annual power savings of approximately 450,000 yuan.

[0211] The above embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A dynamic batching method for raw material homogenization silos based on Ramanujan continuous fractionation, characterized in that: Includes the following steps: S1: Obtain the continuous fraction coefficients a based on historical production data trained using the Ramanujan continuous fraction model. k (0),b k (0), and the adjustment constant C for each material; the adjustment constant C is set according to the material characteristics; The dynamic weight function of the Ramanujan continued fraction model is as follows: （5） In the formula, W i (t): The dynamic proportion weight of material i at time t, which is a real-time control variable; C: Material characteristic adjustment constant, which is set according to the material's natural properties, historical fluctuation range, and process requirements; a k ,b k The Ramanujan continued fraction coefficients, obtained through training with a large amount of historical production data, determine the convergence characteristics and response speed of the weighting function; X i (t): Material composition data collected in real time by the laser composition analyzer; t: Time variable; S2: Real-time data acquisition and preprocessing Material composition data is continuously collected using a laser component analyzer. i (t), the data is smoothed by a Kalman filter to remove noise and outliers; S3: Dynamic Weight Calculation With a period of 0.5 seconds, based on the latest X i (t) and the current coefficient, calculate W for each material. i (t); Calculate the continuous fraction iteratively using a PLC, with k taking the first 8 terms: W i (t)=C·[1+a1 / (b1+t)+a2 / (b2+t)+...+a8 / (b8+t)]·X i (t) (11) Step S4: Control signal output and execution The PLC will calculate the weight W. i (t) is converted into a 4-20mA analog signal or PROFIBUS P communication command and sent to the frequency converter of the belt scale to adjust the feeding amount; S5: Feedback Optimization and Self-Learning The standard deviation of CaCO3 in the raw material is calculated. If the deviation exceeds the threshold, 'a' is finely adjusted. k ,b k Then return to step S2 to execute, so that the Ramanujan continuous fraction model can continuously adapt to changes in raw materials.

2. The dynamic batching method for raw material homogenization silos based on Ramanujan continuous fractionation as described in claim 1, characterized in that: The training process of the Ramanujan continued fraction model described in step S1 involves determining the continued fraction coefficients 'a' using historical data. k ,b k To minimize the weighted predicted value W i The error between (t) and the actual optimal ratio is determined by the following steps: S1.1 Data Preparation Stage Data sources include raw material composition data and corresponding optimal ratio records extracted from the production line's historical database over the past 3-6 months; key data includes: real-time sensor data X i (t): includes the CaCO3 content of limestone, the SiO2 content of clay, and the Fe2O3 content of iron powder, with a sampling frequency of ≥2 times / second; and the actual optimal proportion weight W. actual (t): The historical best value derived from clinker quality, used as the training label; Output objective: The training objective is to obtain the coefficient array a. k ,b k Make the output of equation 11 and W actual Minimize the mean square error (MSE) of (t); S1.2 Model Initialization and Parameter Setting The first eight terms of the Ramanujan continuous fraction are used for truncation approximation, with coefficient a. k ,b k The initial values ​​are set based on the statistical characteristics of historical data; the error threshold ε = 0.001; the maximum number of iterations T. max =1000; S1.3 Iterative Optimization Algorithm Minimize the mean square error function using the gradient descent algorithm: （8） Where M represents the number of historical data points, the specific steps are as follows: S1.3.1 Forward calculation: For each historical data point, substitute the current coefficient to calculate W. i (t); S1.3.2 Error Backpropagation: Calculating the Gradient and By using the chain rule to differentiate term by term; S1.3.3 Coefficient Update: (9) (10) In the above formula, the learning rate η = 0.01; S1.3.4 Convergence check, verified after each iteration. For k=1 to N, and the rate of change of MSE < 0.1%, if T is satisfied or reaches... max If so, then stop training; S1.

4. Training Validation and Convergence Check To verify the generalization ability, use 20% of the retained historical data to test the generalization ability, requiring the MSE error to increase by less than 5% compared to the training set.

3. The dynamic batching method for raw material homogenization silos based on Ramanujan continuous fractionation as described in claim 1, characterized in that: Step S2, real-time data acquisition stage, the raw data X collected by the laser component analyzer. i (t) contains high-frequency noise and occasional outliers. Before being fed into the continuous fraction algorithm, it is preprocessed using the Kalman filter algorithm. The preprocessing includes two stages: prediction and update. In the prediction phase, based on the state estimate at time k-1, the state and covariance at time k are predicted: （13） In the above formula, x k∣k−1 The prior state estimation vector at time k represents the state predicted at time k based on data from k-1 and earlier; the state represents the true composition of the raw meal, expressed as a percentage (%). x k−1∣k−1 : The posterior state estimation vector at time k-1, i.e., the state value after optimization in the previous filtering cycle; A k : State transition matrix, describing the state evolution of the system from k-1 to k; B k : Control input matrix, which maps the influence of control variables on the state; u k : Control input vector; State x corresponds to the true value of the raw material composition, observation y is the sensor reading, and the filtering objective is to approximate the true value through an algorithm and reduce noise; （14） P k | k−1 The prior estimation error covariance matrix represents the uncertainty of the predicted state. The diagonal elements are the variances, and the off-diagonal elements are the covariances. P k−1∣k−1 The posterior estimation error covariance matrix at time k-1 reflects the estimation accuracy at the previous time step. A k T : Transpose of the state transition matrix; Q k The process noise covariance matrix represents the uncertainty of the system model. Iteration of the P matrix ensures the algorithm's adaptation to model error, Q k The magnitude directly affects the filter's sensitivity to fluctuations; During the update phase, the actual observed value y at time k is combined with... k Calculate the Kalman gain K k And update the state estimate and covariance estimate: （15） K k Kalman gain matrix: a weighted average of the confidence levels of predicted and observed values. A higher gain indicates greater confidence in the observations, while a lower gain indicates greater confidence in the predictions. H k : Observation matrix, which maps the state space to the observation space; H k = 1 indicates a one-to-one correspondence between observation and state; H k T : Transpose of the observation matrix; R k The noise covariance matrix is ​​measured to represent the sensor noise level. Based on the accuracy of the laser component analyzer, let R... k It is a scalar; Calibration: R k It needs to be set according to the sensor specifications. If the detection accuracy is ±0.05%, then the variance R k ≈(0.05)²=0.0025; （16） x k∣k The posterior state estimate vector at time k (dimension: n×1), i.e., the filtered optimal state value, output as smoothed data. Used for weight calculation; y k The actual observation vector at time k (dimension: p×1) originates from the original sensor data X. i (t), such as the CaCO3 content reading; H k x k∣k−1 : Observational prediction, representing the expected observation based on the prior state; y k -H k x k∣k−1 Residuals reflect the deviation between observations and predictions; （17） P k∣k : Posterior estimation error covariance matrix, updated uncertainty measure; I: Identity matrix, compared with H k Dimension matching; Convergence guarantee: This equation ensures that the P matrix decreases over time, reflecting the improvement in filtering performance.

4. The dynamic batching method for raw material homogenization silos based on Ramanujan continuous fractionation as described in claim 1, characterized in that: Step S4: Material feed rate control, dynamic weight W i (t) is converted into specific control instructions via PLC; high-precision belt scales typically use frequency conversion speed regulation electronic belt scales, whose feed flow rate is proportional to the frequency of the frequency converter; the control model is: （18） Among them, F i (t) is the target feed rate of material i, in t / h, K. p It is the flow rate-frequency proportionality coefficient of the belt scale, F i,base This is the basic flow rate to ensure material flowability. This instruction is sent to the frequency converter of the belt scale through the analog output module of the PLC or PROFIBUS PEP communication.

5. The dynamic batching method for raw material homogenization silos based on Ramanujan continuous fractionation as described in claim 4, characterized in that: In step S5, the statistical object is the standard deviation of the calcium carbonate content in the raw material, calculated using the following formula: （12） Where, x i The CaCO3 content value for each test is expressed in %, μ is the mean, N is the number of data points within the statistical period, and the threshold is ±0.15%.

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