Modular function-based multi-objective optimization method for temperature field of a decomposition furnace

Abstract

The present application relates to the technical field of automatic control of cement production, and provides a kind of based on the decomposition furnace temperature field multi-objective optimization method of mode function, comprising: S1 multi-source temperature data fusion acquisition;S2: data preprocessing and feature extraction;S3: temperature field matching degree calculation based on mode function;Step 4: multi-objective particle swarm optimization solution optimal decision, set temperature uniformity index UI maximization and total coal consumption minimization goal;Improved particle swarm optimization algorithm is used to solve;S5: control instruction issue and execution;S6: feedback and adaptive adjustment.The present application realizes the accurate control of temperature field in decomposition furnace by establishing the nonlinear mapping model between temperature field and coal flow, reduces the temperature fluctuation range, improves the stability of raw material decomposition rate, reduces the coal consumption, accurately senses the three-dimensional temperature field, adapts to the change of working condition, and processes the decomposition furnace temperature control of multivariable strong coupling relationship, improves the stability, economy and environmental protection of cement production.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology in cement production, and in particular to a multi-objective optimization method for the temperature field of a decomposer furnace based on a modular function. Background Technology

[0002] In the new dry process cement production, the decomposer is a key piece of equipment for the decomposition of raw meal carbonates, and its temperature control stability directly affects the raw meal decomposition rate, clinker quality, and energy consumption. Current technologies mainly employ PID control and fuzzy control methods for decomposer temperature control, but these methods still have the following problems and shortcomings:

[0003] 1. Large temperature fluctuations and poor adaptability of the control model

[0004] Traditional control methods struggle to adapt to the complex, nonlinear, and time-delayed thermal processes within the decomposer. The decomposer is essentially a highly complex chemical reaction device; its internal gas-solid flow and chemical transformations constitute a dynamic and unpredictable system with significant nonlinear characteristics, multi-parameter interactions, and frequent uncertainties. PID controllers, relying on precise mathematical models, struggle to handle actual operating conditions such as coal quality fluctuations and feed rate variations, resulting in temperature fluctuations often exceeding ±50℃. This leads to unstable raw meal decomposition rates (deviating from the ideal range of 88%-95%), impacting the quality of subsequent clinker.

[0005] While advanced methods such as fuzzy control have reduced the reliance on precise mathematical models to some extent, the acquisition of control rules still largely depends on the experience of operators and experts, resulting in a high degree of subjectivity. When there are too many input variables or a large number of fuzzy subsets to be divided, relying on manual formulation of control rules is labor-intensive and prone to problems such as rule duplication and errors. Although some studies have attempted to mine control rules from data or use predictive control algorithms, their models often lack adaptability under varying operating conditions, making it difficult to achieve stable and reliable application in actual production.

[0006] 2. Challenges of incomplete pulverized coal combustion coupled with multiple factors

[0007] Controllers with fixed parameters cannot adjust the injection strategy in real time according to changes in coal quality. Fluctuations in indicators such as coal powder fineness, volatile matter content, and calorific value can significantly affect the combustion rate. For example, coal powder with high moisture content and coarse fineness cannot burn quickly in the furnace, easily causing "afterburning" and resulting in a higher outlet temperature; while coal powder with too low volatile matter content (such as as low as about 14%) has a high ignition temperature, poor reactivity, and a low burnout rate in the furnace, which will cause more serious incomplete combustion.

[0008] Furthermore, the decomposer outlet temperature is a complex control object characterized by pure time delay, high inertia, nonlinearity, and the coupling of multiple variables. Factors affecting temperature include not only the coal feed rate but also the raw material feed rate, tertiary air temperature and volume, kiln feed rate, and flue gas temperature. These factors are highly coupled; for example, increasing the kiln feed rate increases the heat required for material decomposition, leading to a decrease in the decomposer outlet temperature; conversely, increasing the tertiary air temperature will increase the decomposer outlet temperature. Traditional single-variable or simple control strategies struggle to coordinate these complex coupling relationships, resulting in low pulverized coal combustion efficiency, which not only increases coal consumption but also raises pollutant emission concentrations.

[0009] 3. Outdated detection methods and insufficient temperature field perception

[0010] Conventional thermocouple single-point temperature measurements are insufficient to reflect the true three-dimensional temperature field distribution within the decomposition furnace. The decomposition furnace has a large internal volume, and single-point measurements cannot capture the non-uniformity of the spatial temperature distribution; furthermore, localized high temperatures can lead to problems such as scaling and blockage. While infrared thermal imagers can provide two-dimensional temperature distribution information, the harsh environment of the decomposition furnace, with its high temperature and dust levels, makes its lenses susceptible to contamination and difficult to maintain stable operation over long periods, resulting in incomplete temperature field data acquisition.

[0011] Limited and potentially unreliable detection data further restricts the effectiveness of advanced control strategies. Control system decisions heavily rely on the accuracy and comprehensiveness of the detection data. When detection methods are outdated or data is incomplete, even highly sophisticated algorithms struggle to make precise adjustments, thus impacting the overall performance of the control system.

[0012] 4. Limitations of existing technological solutions

[0013] In the prior art, such as the Chinese patent with publication number CN110510894A, the disclosed "a preheating and pre-decomposition system for dry process cement production" adopts a dual-series preheater structure to extend the contact time between powder and high-temperature flue gas, but does not solve the problem of real-time optimization of the temperature field; while the Chinese patent with publication number CN114315191A, the disclosed "intelligent new dry process cement production line", improves the drying efficiency by improving the mixing mechanism, but does not involve the key link of decomposition furnace temperature control.

[0014] Some designs for RDF (waste-derived fuel), such as dual-loop fuzzy control, while considering the additional disturbances brought by waste fuel, are still based on the traditional fuzzy control architecture. Their stability and robustness in the face of drastic fluctuations caused by uncertain factors such as waste type, moisture content, and calorific value need improvement. Furthermore, some solutions focus on coal powder particle size pretreatment and feeding method optimization. These methods improve the physical state of materials and fuel to some extent, but fail to establish a precise and adaptive mapping relationship between the temperature field and the operating variables as a whole, thus limiting their optimization effect. Summary of the Invention

[0015] To overcome or alleviate the problems of insufficient accuracy in temperature field sensing, inability to adapt to changes in operating conditions, incomplete combustion of pulverized coal, and coupling with multiple factors, the present invention aims to provide a multi-objective optimization method for the temperature field of a decomposer based on a modular function. This optimization method establishes a nonlinear mapping model between the temperature field and the pulverized coal flow rate, thereby achieving precise control of the temperature field within the decomposer, reducing the temperature fluctuation range, improving the stability of raw material decomposition rate, and reducing pulverized coal consumption. This new decomposer temperature control method can accurately sense the three-dimensional temperature field, adapt to changes in operating conditions, and effectively handle strong coupling relationships among multiple variables, thereby improving the stability, economy, and environmental friendliness of cement production.

[0016] This invention provides the following technical solution:

[0017] A multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function includes the following steps:

[0018] S1, Multi-source temperature data fusion acquisition

[0019] An infrared thermal imager array is arranged in the upper, middle and lower parts of the decomposition furnace to synchronously collect three-dimensional temperature field data inside the furnace at a certain frequency; a thermocouple array is arranged at the four outlets of the four-channel adjustable pulverized coal injection pipe to monitor the local temperature in real time.

[0020] S2: Data Preprocessing and Feature Extraction

[0021] The controller first performs median filtering on the received raw temperature data to remove impulse noise, and then uses moving average filtering to suppress random fluctuations. The preprocessed temperature field data is then analyzed to extract key features, including the highest temperature, lowest temperature, average temperature, and temperature standard deviation, to obtain the actual temperature field data T. actual (x,y,z,t);

[0022] S3: Temperature field matching degree calculation based on modulus function

[0023] A temperature field model based on the modulus function is constructed, and the temperature field model is based on the following formula:

[0024] (1)

[0025] Where N=50, T opt Q is the optimal temperature field distribution function, in °C; τ(n) is the Ramanujan τ function; T0 is the ideal reference temperature of the decomposition furnace, ranging from 870-890 °C; Q m y is the real-time flow rate of pulverized coal, Q0 is the reference value of pulverized coal flow rate; (x,y,z,t) are the three-dimensional spatial and temporal parameters inside the decomposition furnace.

[0026] The ideal temperature field T is calculated. opt (x,y,z,t), the actual temperature field data T actual Substituting (x,y,z,t) into Equation 1, we can calculate the current temperature field and the ideal temperature field T predicted by the model. opt The matching degree of (x,y,z,t) is evaluated using mean squared error or a custom matching degree function.

[0027] S4: Solving Optimal Decisions in Multi-Objective Particle Swarm Optimization

[0028] Two optimization objectives are set: maximizing the temperature uniformity index (UI) and minimizing the total pulverized coal consumption. An improved particle swarm optimization (PSO) algorithm is used to solve these objectives, where each particle represents a possible pulverized coal flow allocation scheme. The PSO algorithm evaluates the performance of each particle on both the UI and coal consumption objectives, guiding the particle swarm towards the Pareto front. Finally, an optimal scheme is selected from the Pareto solution set based on the requirement of prioritizing temperature stability or prioritizing reducing coal consumption, resulting in the optimal pulverized coal flow rate Q for the four pulverized coal injection pipes. m1 Q m2 Q m3 Q m4 ;

[0029] S5: Control command issuance and execution

[0030] The instructions corresponding to the optimal pulverized coal flow rate calculated by the optimization algorithm are sent to the four-channel adjustable pulverized coal injection pipes respectively, and each channel adjusts the pulverized coal injection volume according to the instructions.

[0031] S6: Feedback and Adaptive Adjustment

[0032] The raw material decomposition rate is continuously monitored by an online analyzer or by periodic sampling. If the raw material decomposition rate continues to deviate from the ideal range of 90%-95%, the reference temperature T0 in the temperature field model is automatically fine-tuned and the process returns to step S3, or the model parameters are re-identified and the process returns to step S2, thereby achieving long-term adaptive optimization.

[0033] Preferably, step S4 includes the following steps:

[0034] S4.1: Optimization Objective and Variable Definition

[0035] We set two objectives: Objective 1 is to maximize the temperature uniformity index (UI), and the formula for calculating UI is as follows:

[0036] (2)

[0037] In the above formula, K represents the number of temperature monitoring points, and T... k The measured temperature at point k is represented by UI. The closer UI is to 1, the more uniform the temperature field. Objective 2 is the total coal powder consumption Q. m =Q m1 +Q m2 +Q m3 +Q m4 Minimize, where the pulverized coal flow rates of the four pulverized coal injection pipes are Q m1 Q m2 Q m3 Q m4 The range of values ​​for each variable is constrained by the maximum capacity of the pulverized coal injection pipe;

[0038] S4.2: PSO Algorithm Parameter Initialization

[0039] The algorithm parameters are set in the controller, where the population size is 30 particles, each particle represents a flow allocation scheme; the maximum number of iterations is 100, balancing real-time performance and optimization accuracy; the learning factor is c1=c2=1.49445, the inertia weight is 0.729, ensuring convergence; the weight coefficients are: UI weight w1=0.7, coal consumption weight w2=0.3.

[0040] S4.3: Multi-objective evaluation and Pareto frontier search

[0041] For each particle, calculate its integrated objective function value:

[0042] (3)

[0043] In the above formula:

[0044] F: The comprehensive objective function value, which is the evaluation index that needs to be maximized. The closer the value is to 1, the better the overall performance of the optimization scheme in terms of temperature uniformity and coal consumption control.

[0045] w1: Weighting coefficient of temperature uniformity index UI;

[0046] UI: Temperature Uniformity Index;

[0047] w2: Weighting coefficient for pulverized coal consumption;

[0048] Qm Total pulverized coal consumption, which is the sum of the flow rates of the four pulverized coal injection pipes: Q m =Q m1 +Q m2 +Q m3 +Q m4 ;

[0049] Q max Maximum total pulverized coal flow rate, used for standardizing coal consumption items to prevent Q m An excessively large value will distort the objective function; the value should be based on the design capacity of the decomposition furnace.

[0050] The PSO algorithm is used to evaluate the performance of particles in terms of UI and coal consumption, update the individual optimal and global optimal positions, and guide the particle swarm to move towards the Pareto front.

[0051] S4.4: Optimal Solution Selection Strategy

[0052] From the Pareto solution set, select a compromise based on actual needs: if prioritizing temperature stability, choose the solution with the highest UI; if prioritizing reducing coal consumption, choose the solution with the lowest coal consumption; output the final optimized pulverized coal flow rate setpoint [Q]. m1 Q m2 Q m3 Q m4 ];

[0053] Step 4.5: Real-time and Adaptive Processing

[0054] The optimization period is set to 60 seconds to ensure response speed; if the matching degree exceeds the threshold for multiple consecutive periods, the model parameter self-tuning is triggered.

[0055] Preferably, the self-tuning of the trigger model parameters in step S4.5 includes adjusting Q0.

[0056] Preferably, in step S1, the controller is an S7-1500 PLC.

[0057] Preferably, in step S1, the infrared thermal imager array includes at least 6 high-temperature thermal imagers, which are respectively arranged in the upper, middle and lower parts of the decomposition furnace to ensure that the viewing angle covers the entire cross-section of the decomposition furnace.

[0058] Preferably, in step S1, the thermocouple array consists of 12 K-type thermocouples, divided into 4 groups, with 3 measuring points in each group, arranged near the outlets of the 4 pulverized coal injection pipes, with an insertion depth of 1 / 3 of the furnace radius.

[0059] Preferably, in step S2, the filter window width of the moving average filter is 5, and the sampling interval Δt = 30s.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] This invention introduces the Ramanujan mode function into the field of cement industry process control. Compared with traditional PID control, fuzzy control, or model predictive control based on simplified thermal balance, the model proposed in this invention has an inherent advantage in describing the dynamic characteristics of complex nonlinear and spatiotemporally coupled temperature fields in the decomposition furnace, providing a completely new perspective on system modeling.

[0062] This invention employs a distributed temperature measurement scheme combining an infrared thermal imager array and a thermocouple array. This not only overcomes the limitation of single-point temperature measurement in reflecting the global temperature field distribution, but also improves the system's reliability and data integrity in high-temperature and high-dust environments through the combination of point and surface measurements. The combination of the S7-1500 PLC and the four-channel adjustable pulverized coal injection pipe constitutes a complete closed-loop system of perception-decision-execution.

[0063] This invention innovates control strategies and enhances intelligence by explicitly proposing a multi-objective collaborative optimization approach that considers temperature uniformity index (UI) and pulverized coal consumption, surpassing the limitations of traditional single-objective control (such as stabilizing only the outlet temperature). The introduction of particle swarm optimization (PSO) algorithms for online real-time optimization enables the system to automatically find the optimal operating conditions under given operating conditions, significantly improving the level of control intelligence.

[0064] This invention balances engineering practicality with adaptability: by truncating the infinite series into a finite number of terms (N=50) and designing a complete data preprocessing, optimization, and feedback adjustment process, the feasibility of advanced algorithms in industrial environments is ensured. The system possesses a certain degree of adaptability, capable of adjusting key parameters based on process results such as raw material decomposition rate, adapting to changes in coal quality and fluctuations in operating conditions. Attached Figure Description

[0065] Figure 1 This is an overall schematic diagram of the hardware structure and control process provided in the embodiments of the present invention.

[0066] Figure 2 The flowchart illustrates a multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function, provided in an embodiment of the present invention.

[0067] Figure 3A The temperature field optimization effect of the traditional PID control method provided in the embodiments of the present invention.

[0068] Figure 3B The temperature field optimization effect of the modulus function optimization method provided in the embodiments of the present invention.

[0069] Figure 4 A multi-dimensional performance comparison radar chart provided for embodiments of the present invention. Detailed Implementation

[0070] The technical concept of this invention is as follows:

[0071] A core mathematical model based on the Ramanujan modulus function is established to characterize the nonlinear mapping relationship between the temperature field of the precalciner and the pulverized coal flow rate. The core expression is:

[0072] (1)

[0073] in:

[0074] T opt The optimal temperature field distribution function (unit: °C);

[0075] T0 is the ideal reference temperature for the decomposition furnace (usually 870-890℃).

[0076] τ(n) is the Ramanujan τ function, used to describe the nonlinear characteristics of the temperature field;

[0077] Q m Real-time flow rate of pulverized coal (unit: kg / h);

[0078] Q0 is the baseline value for pulverized coal flow (determined according to the specifications of the decomposer).

[0079] (x,y,z) are the three-dimensional spatial coordinates inside the decomposition furnace;

[0080] t is a time variable.

[0081] To facilitate engineering applications, this invention truncates the above infinite series into the first N terms (actually N=50) and introduces the temperature uniformity index UI as the optimization objective, as shown in the following formula:

[0082] (2)

[0083] Where K is the number of temperature monitoring points, T k Let UI be the measured temperature at point k. The closer UI is to 1, the more uniform the temperature field.

[0084] The core of the nonlinear mapping model based on the Ramanujan modulus function lies in its profound description of the temperature field distribution T inside the decomposition furnace. opt (x,y,z,t) and key operating variables (mainly pulverized coal flow rate Q) m The intrinsic connection between them. The theoretical advantage of this model lies in its infinite series form, which can approximate complex nonlinear systems with high accuracy. The modular form of the Ramanujan τ function τ(n) makes it particularly suitable for characterizing thermal processes such as image decomposition furnaces, which exhibit periodicity, oscillation, and multi-scale coupling characteristics. Exponential decay term This cleverly reflects the attenuation characteristics and saturation effect of the change in pulverized coal flow rate on the temperature field, which is consistent with the physical law that the contribution of a unit increase in pulverized coal to the temperature rise gradually weakens after reaching a certain concentration during actual combustion.

[0085] In existing technologies, PID control relies on linearized models, making it difficult to handle the large time lag and nonlinear characteristics of the decomposition furnace; while fuzzy control does not rely on precise mathematical models, its control rules often depend on operator experience, making it difficult to uncover deep, complex nonlinear relationships; and mechanistic models based on thermal equilibrium (…) While possessing clearly defined physical meaning, the model is complex, with strong coupling between variables, making some coefficients difficult to determine, and requiring significant simplification in practical applications. The modular function model proposed in this invention combines the flexibility of data-driven models with a strong ability to fit complex relationships. Simultaneously, the modular function structure introduces certain mathematical constraints and physical intuition, avoiding the potential physical ininterpretability issues of pure black-box models. For ease of engineering application, this invention truncates the aforementioned infinite series to the first N terms (simulation and experimental verification show that N=50 achieves a satisfactory balance of accuracy), and introduces the temperature uniformity index (UI) as one of the core optimization objectives.

[0086] 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.

[0087] Example 1

[0088] like Figure 1 The overall system provided in this embodiment consists of hardware and software algorithms. The hardware includes an infrared thermal imager array, an S7-1500 PLC controller, a four-channel adjustable pulverized coal injection pipe, and a thermocouple array; the core software is based on a temperature field optimization algorithm based on the Ramanujan mode function.

[0089] In terms of hardware, an infrared thermal imager array is arranged on the wall of the decomposition furnace to collect three-dimensional temperature field data inside the furnace every 30 seconds; a thermocouple array is arranged near the four pulverized coal injection pipes to monitor the local temperature in real time; an S7-1500 PLC receives the temperature data and runs an optimization algorithm to calculate the optimal pulverized coal injection rate; the four-channel adjustable pulverized coal injection pipes adjust the pulverized coal flow rate of each channel according to the instructions to achieve precise control of the temperature field.

[0090] like Figure 2 This embodiment provides a multi-objective optimization method for the temperature field of a decomposition furnace based on a modular function. It is a dynamic closed-loop control system based on the above hardware, and its detailed operation flow is as follows:

[0091] Step 1: Multi-source temperature data fusion and acquisition

[0092] Global perception: An array of infrared thermal imagers deployed at the top, middle and bottom of the decomposition furnace synchronously collects three-dimensional temperature field data inside the furnace every 30 seconds, providing spatial distribution information of temperature.

[0093] Key point monitoring: Thermocouple arrays are arranged near the outlets of the four pulverized coal injection pipes to monitor the local temperature in real time at a higher frequency (e.g., once per second) to verify the thermal imager data and capture rapid changes near the pulverized coal injection point in a timely manner.

[0094] Step 2: Data Preprocessing and Feature Extraction

[0095] The S7-1500 PLC first performs median filtering on the received raw temperature data to remove impulse noise, and then uses moving average filtering to suppress random fluctuations.

[0096] The preprocessed temperature field data is analyzed to extract key features, such as the highest temperature, lowest temperature, average temperature, and temperature standard deviation, to obtain the actual temperature field data T. actual (x,y,z,t) provides input for subsequent optimization calculations.

[0097] Step 3: Calculation of temperature field matching degree based on modulus function

[0098] The actual temperature field data T collected and processed at the current moment actual Substituting (x,y,z,t) into the core mathematical model formula (1), we can calculate the current temperature field and the ideal temperature field T predicted by the model. opt The matching degree of (x,y,z,t) is usually evaluated using mean squared error (MSE) or a custom matching degree function.

[0099] Step 4: Solve for the optimal decision using Multi-Objective Particle Swarm Optimization (MOPSO).

[0100] This step is the core of the optimization decision-making process. Its purpose is to solve for the optimal allocation scheme of pulverized coal flow in the four pulverized coal injection pipes using an improved particle swarm optimization (PSO) algorithm. It is decomposed into the following 5 specific sub-steps:

[0101] Step 4.1: Optimize the definition of objectives and variables

[0102] Set two objectives: Objective 1 is to maximize the temperature uniformity index (UI), calculated using formula (2); Objective 2 is to maximize the total coal consumption (Q). m =Q m1 +Q m2 +Q m3 +Q m4 ) minimized.

[0103] Define the optimization variable as: the pulverized coal flow rate Q of the four pulverized coal injection pipes. m1 Q m2 Q m3 Q m4 The range of values ​​for each variable is constrained by the maximum capacity of the pulverized coal injection pipe (e.g., single channel ≤ 6 t / h).

[0104] Step 4.2: PSO Algorithm Parameter Initialization

[0105] In the S7-1500 PLC, set the algorithm parameters as follows: Population size: 30 particles, each particle represents a flow distribution scheme (e.g., particle position vector is [Q...). m1 Q m2 Q m3 Q m4 Maximum number of iterations: 100, balancing real-time performance and optimization accuracy. Learning factor: c1=c2=1.49445, inertia weight 0.729, ensuring convergence. Weight coefficients: UI weight w1=0.7, coal consumption weight w2=0.3 (emphasizing temperature stability).

[0106] Step 4.3: Multi-objective evaluation and Pareto frontier search

[0107] For each particle, calculate its integrated objective function value:

[0108] (3)

[0109] In the above formula:

[0110] F: The comprehensive objective function value, which is the evaluation index that needs to be maximized. The closer the value is to 1, the better the overall performance of the optimization scheme in terms of temperature uniformity and coal consumption control.

[0111] w1: The weighting coefficient of the temperature uniformity index (UI), such as "weighting coefficient w1=0.7". This value indicates that the system pays more attention to temperature stability (accounting for 70% weight), reflecting the tendency to prioritize ensuring the stability of the decomposition rate in the process requirements.

[0112] UI: Temperature uniformity index, defined in formula (2).

[0113] w2: The weighting coefficient for pulverized coal consumption, such as "coal consumption weight w2=0.3". This value indicates that 30% of the attention is paid to coal consumption, which complements w1 (w1+w2=1) and balances economic efficiency.

[0114] Q m Total pulverized coal consumption, sum of flow rates from the four pulverized coal injection pipes: Q m =Q m1 +Q m2 +Qm3 +Q m4 The optimization requires minimizing Q. m However, through the transformation of formula (3) (1 - Q) m / Q max Transform it into a maximization objective.

[0115] Q max Maximum total pulverized coal flow rate, used for standardizing coal consumption items to prevent Q m An excessively large value will distort the objective function. The value should be based on the design capacity of the precalciner (e.g., a 5000 t / d production line).

[0116] The PSO algorithm is used to evaluate the particle's performance in terms of UI and coal consumption, update the individual optimal and global optimal positions, and guide the particle swarm to move towards the Pareto front (non-dominated solution set).

[0117] Step 4.4: Optimal Solution Selection Strategy

[0118] From the Pareto solution set, select a compromise based on actual needs: if prioritizing temperature stability, choose the solution with the highest UI; if prioritizing reducing coal consumption, choose the solution with the lowest coal consumption. Output the final optimized pulverized coal flow rate setpoint [Q]. m1 Q m2 Q m3 Q m4 ].

[0119] Step 4.5: Real-time and Adaptive Processing

[0120] The optimization period is set to 60 seconds to ensure response speed. If the matching degree (e.g., RMSE) exceeds the threshold (e.g., 10℃) for multiple consecutive periods, model parameter self-tuning is triggered (e.g., adjusting Q0).

[0121] Step 5: Issuance and execution of control commands

[0122] This step is the execution phase of the decision, ensuring that optimization instructions are accurately implemented. For unclear issues, it is broken down into the following three sub-steps:

[0123] Step 5.1: Control command generation and verification

[0124] The S7-1500 PLC will use the optimal pulverized coal flow vector [Q] obtained in step 4. m1 Q m2 Q m3 Q m4 Convert to a 4-20mA standard control signal; System verification command rationality: Check whether the flow of each channel is within the safe range (such as no sudden change or exceeding the limit). If abnormal, trigger an alarm and maintain the command of the previous cycle.

[0125] Step 5.2: Instruction Issuance and Execution Mechanism Response

[0126] The signal is sent to the four-channel adjustable pulverized coal injection pipe through an analog output module (such as SM1232AQ4); each pulverized coal injection pipe channel responds independently: the high-precision weighing feeder (such as Coriolis scale) and the electric regulating valve adjust the opening according to the signal to achieve precise control of pulverized coal flow (accuracy ±0.5%).

[0127] Step 5.3: Execution Status Monitoring and Feedback

[0128] The system monitors the consistency between the actual flow rate of the pulverized coal injection pipe and the set value in real time, and verifies local temperature changes through a thermocouple array. If an execution deviation is detected (such as valve jamming), the system automatically switches to a backup control strategy (such as PID stability maintenance) and records the fault information.

[0129] Step 6: Feedback and Adaptive Adjustment

[0130] The system continuously monitors the raw material decomposition rate through online analyzers or timed sampling tests. If the raw material decomposition rate continues to deviate from the ideal range of 90%-95%, the system will automatically fine-tune the reference temperature T0 in the model or trigger the re-identification of model parameters to achieve long-term adaptive optimization.

[0131] Example 2

[0132] This embodiment takes a typical 5000-ton / day new dry process cement production line as the application scenario, and uses the multi-objective optimization method of decomposer temperature field based on modulus function provided in Embodiment 1 to optimize the decomposer temperature field.

[0133] This embodiment involves targeted hardware modifications and system integration based on a standard decomposition furnace system. The core of this embodiment is to construct a closed-loop control system that integrates perception, decision-making, and execution.

[0134] (1) Temperature detection system configuration

[0135] Infrared thermal imager array: Six FLIRA series high-temperature thermal imagers (working wavelength: 8-14μm, temperature range: 0-1500℃, accuracy: ±1% of reading) were selected. The installation positions are shown in Table 1 below, aiming to achieve comprehensive monitoring of the three-dimensional temperature field of the decomposition furnace.

[0136] Table 1 Hardware Installation Instructions

[0137] Installation location quantity Function Description Protective measures Upper part of the decomposition furnace 2 units Monitoring flue gas temperature and material distribution The furnace wall was perforated, fitted with high-temperature resistant quartz glass lenses, and equipped with a compressed air cleaning device. Middle part of the decomposition furnace 2 units Monitor the combustion and decomposition status in the main reaction zone Same as above Lower part of decomposition furnace 2 units Monitoring the ignition point of pulverized coal and the mixing of tertiary air Same as above

[0138] Thermocouple array: As a supplement and calibration to the infrared thermal imager, a set of K-type armored thermocouples (withstanding up to 1300℃) is placed near each of the four pulverized coal injection pipe outlets. Each set has 3 measuring points, distributed circumferentially at 120 degrees, with an insertion depth of 1 / 3 of the furnace radius to ensure measurement representativeness. The thermocouple signals are converted into a 4-20mA standard signal for transmission via a temperature transmitter (such as the WSY-1200 model).

[0139] (2) Core controller configuration

[0140] S7-1500 PLC system: Selects CPU1518-4PN / DP as the main controller (4MB working memory), equipped with the following modules:

[0141] Analog input module: SM1231AI8x16bit, used to receive signals from thermocouple transmitters.

[0142] Analog output module: SM1232AQ4x16bit, used to output control signals to the pulverized coal injection pipe regulating valve.

[0143] Communication module: CM1542-1, used for high-speed data exchange with infrared thermal imager array and host computer via PROFINET network.

[0144] Programming and Environment: Use TIAPortal V16 or later as the programming and configuration software. Its built-in APL (Advanced Process Library) function blocks can accelerate the development of basic functions such as PID control.

[0145] (3) Reform of the implementing agency

[0146] Four-channel adjustable pulverized coal injection pipe: A custom-designed pulverized coal injection pipe, each channel equipped with a high-precision weighing feeder (such as a German BMH Coriolis scale, accuracy ±0.5%) and an electric regulating valve (adjustment accuracy ±0.5%). The maximum coal feeding capacity of a single channel is 6t / h, and the total coal feeding capacity meets the requirements of a 5000t / d production line. The 4-20mA control signal output by the PLC directly drives the opening of the regulating valve, achieving precise control of the pulverized coal flow rate.

[0147] The system's integrated architecture is arranged as shown below, ensuring smooth data and control flow:

[0148] [Infrared Thermal Imager Array] + [Thermocouple Array] -- (PROFINET) -- -> [S7-1500 PLC] -- (4-20mA) -- -> [Four-Channel Adjustable Pulverized Coal Injection Pipe]

[0149] The implementation process of the algorithm provided in this embodiment on the S7-1500 PLC is as follows:

[0150] (1) System parameter initialization After the system is first put into operation or overhauled, set the following key initial parameters on the HMI (Human Machine Interface):

[0151] Modular function parameters: number of truncation terms N=50, reference temperature T0=880℃, reference pulverized coal flow rate Q0=4.5t / h.

[0152] Optimized algorithm parameters: Particle Swarm Optimization (PSO) algorithm population size = 30, maximum number of iterations = 100, inertia weight ω = 0.729, learning factor c1 = c2 = 1.49445.

[0153] Control weighting coefficients: temperature uniformity index weight w1=0.7, coal consumption weight w2=0.3, maximum total pulverized coal flow rate Q_max=24t / h.

[0154] (2) Data preprocessing and feature extraction Due to the harsh environment of the decomposition furnace, the raw temperature data needs to be filtered to improve the signal-to-noise ratio.

[0155] Median filtering: A sliding window with a window width of 5 is used to effectively remove impulse noise.

[0156] The moving average filtering formula is:

[0157] (4)

[0158] In the above formula, T filterest: The filtered temperature estimate represents the temperature value at time point t after the moving average process. It is used to replace noise points in the original data and improve data stability.

[0159] N: Half width of the sliding window, indicating that the total width of the filtering window is 2N+1=11 data points, which balances the smoothing effect and real-time performance (too large a window is prone to lag, and too small a window is insufficient for noise suppression).

[0160] i: Summation index, used to traverse all data points within the window. The upper and lower limits of the summation are from −N to N, ensuring symmetrical processing centered on the current point t.

[0161] Traw: Raw temperature measurement, representing unprocessed raw temperature data, sourced from infrared thermal imager arrays (three-dimensional temperature field) and thermocouple arrays (local point temperature), and may contain impulse noise or random fluctuations.

[0162] t: The current time point, representing the reference time point for the filtering calculation. The formula takes t as the center and averages the data within the time window before and after it.

[0163] Δt: Sampling interval, "Sampling interval Δt=30s". This means that temperature data is collected every 30 seconds, consistent with the synchronous acquisition frequency of the infrared thermal imager (see step 1).

[0164] Data fusion: The two-dimensional temperature field data obtained by the infrared thermal imager and the precise point temperature measurement data of the thermocouple array are fused using the Kalman filter algorithm to obtain a more reliable three-dimensional temperature field distribution.

[0165] (3) Modular function calculation and real-time matching

[0166] Pre-calculation of the τ function: The first 50 values ​​of the Ramanujan τ function are pre-calculated on the host computer and stored in the PLC's DB (data block) in the form of a look-up table, which greatly reduces the real-time calculation load.

[0167] Real-time matching degree calculation: Every 30 seconds, the PLC will calculate the pre-processed actual temperature field T. actual Compared with the ideal temperature field T predicted based on the modulus function opt The matching degree is calculated, and the root mean square error (RMSE) is used as the evaluation index. When the RMSE continuously exceeds the set threshold (e.g., 10℃), the model self-tuning procedure is triggered.

[0168] (4) Multi-objective optimization decision

[0169] Optimization model: The core is to maximize the comprehensive objective function, i.e., Formula 3.

[0170] Algorithm Execution: An improved Particle Swarm Optimization (PSO) algorithm is used to solve the above multi-objective problem. The algorithm output is the optimal pulverized coal flow rate setpoint [Q] for the four pulverized coal injection pipes. m1 Q m2 Q m3 Q m4 This achieves the Pareto optimal solution with uniform temperature field and minimum coal consumption.

[0171] System operation process and adaptive adjustment: The automated operation of this system follows a rigorous process and has adaptive capabilities. The steps are as follows:

[0172] 1. System Startup and Self-Test: After power-on, the system executes an initialization self-test program to check the status of all sensors, actuators, and network communication. Automatic mode can only be entered after the HMI interface displays "Ready".

[0173] 2. Data Acquisition and Monitoring: The infrared thermal imager array and thermocouple array begin synchronous data acquisition. The three-dimensional temperature field cloud map, key point temperature trend lines, and key system parameters can be monitored in real time on the HMI.

[0174] 3. Optimized Calculation and Control Output: The PLC automatically runs the optimization algorithm at a set cycle (e.g., 60 seconds) and sends the calculation results to the four-channel pulverized coal injection pipe. The operator can set the output limit rate to avoid sudden changes in flow rate from impacting the system.

[0175] 4. Closed-loop feedback and adaptive adjustment:

[0176] Short-term feedback: The system monitors the raw material decomposition rate in real time (through an online analyzer or manual sampling and testing every 2 hours).

[0177] If the decomposition rate continues to deviate from the ideal range of 90%-95%, the system will fine-tune the set value of the reference temperature T0 (e.g., ±5℃) until the decomposition rate returns to normal.

[0178] Long-term self-tuning: The system automatically performs model parameter self-tuning once every 24 hours. This process uses historical operating data from the past 24 hours to make minor optimizations to key parameters in the model function (such as Q0) to adapt to changes in coal quality and operating conditions.

[0179] A brief overview of subsequent calibration, maintenance, and expected results:

[0180] (1) Regular calibration and maintenance system To ensure the long-term stable operation of the system, the following maintenance system needs to be established:

[0181] Daily: Inspect the operating status of all equipment in the system and check whether the compressed air cleaning device is working properly.

[0182] Weekly: Shut down the infrared thermal imager to clean the lenses and prevent dust accumulation from affecting temperature measurement accuracy.

[0183] Monthly: Perform on-site calibration of thermocouples, compare the data of key measuring points with those of the infrared thermal imager, and replace or send for inspection in a timely manner if the deviation is too large.

[0184] Quarterly: Take advantage of production line overhauls to perform a comprehensive model parameter tuning and back up complete system parameters.

[0185] (2) Expected Implementation Effects Based on the practice of a similar optimized control system in a cement plant, the following effects can be expected after applying this invention:

[0186] Control precision: The temperature fluctuation range of the decomposition furnace has been reduced from ±50℃ in the traditional method to within ±15℃.

[0187] Quality indicators: The stability of raw material decomposition rate is significantly improved, and the pass rate of free calcium oxide (f-CaO) can be increased from 80% to over 99%.

[0188] Economic benefits: It is expected to save 2%-5% of coal, 2%-4% of electricity, and increase production by 1%-3%, with an investment payback period of usually less than 10 months.

[0189] Environmental protection and safety: Coal powder combustion is more complete, CO content in exhaust gas is reduced, the workload of central control personnel is reduced, and the safety of system operation is improved.

[0190] This implementation plan combines Ramanujan's modular function with S7-1500 PLC and multi-objective particle swarm optimization to construct a closed-loop control system with precise perception, intelligent decision-making, and reliable execution.

[0191] Figure 3A and Figure 3B All results are based on CFD simulations, demonstrating typical temperature field characteristics under both traditional PID control and the optimization method provided in Example 1. Detailed analysis follows:

[0192] 1. Traditional PID control methods (such as...) Figure 3A The disadvantages of )

[0193] Uneven temperature distribution: There are obvious local high-temperature zones (temperatures often above 1250K) and significant low-temperature zones (temperatures below 1100K) within the furnace, and the overall temperature field presents a "patchy" appearance. For example, high-temperature points are easily formed due to coal powder accumulation opposite the tertiary air duct or near the furnace wall, while low-temperature zones are formed near the raw material inlet due to endothermic reactions.

[0194] Huge temperature difference: The temperature difference between the high temperature zone and the low temperature zone often exceeds 150°C, which leads to thermal stress concentration and affects the life of the furnace body.

[0195] Disordered flow field: Poor airflow organization easily leads to recirculation zones and flow stagnation points, further exacerbating the non-uniformity of temperature and component distribution. Some pulverized coal may experience incomplete combustion due to short residence time or insufficient mixing.

[0196] Poor overall performance: This ultimately leads to large fluctuations in the outlet temperature of the decomposition furnace (±50℃), and an unstable raw material decomposition rate, usually between 85% and 87%, making it difficult to consistently meet the process requirements.

[0197] Based on the modulus function optimization method of Example 1 (e.g.) Figure 3B Advantages of )

[0198] Uniform temperature distribution: Through precise mapping of the Ramanujan mode function and dynamic optimization using the particle swarm optimization algorithm, the temperature field distribution inside the furnace is significantly improved. The mainstream field temperature is stabilized in the ideal range of 1150-1200K, and the high-temperature region is greatly reduced.

[0199] The temperature difference is significantly reduced: the maximum temperature difference is effectively controlled within 30℃, and the temperature gradient is gentle, creating an extremely stable thermal environment for the decomposition of raw materials.

[0200] Stable and reasonable flow field: The optimized pulverized coal injection strategy works better with the tertiary air to form a stable and orderly flow field, reduce undesirable backflow, and ensure full mixing and reaction of pulverized coal, raw materials and airflow.

[0201] Excellent overall performance: The temperature fluctuation range at the decomposer outlet has been reduced to ±15℃. The raw material decomposition rate has been significantly improved and stabilized at a high level of 90%-94%, while also helping to reduce coal consumption and pollutant generation.

[0202] like Figure 4 This radar chart demonstrates the comprehensive improvement achieved in implementation of the optimization method provided in Example 1 through four core process indicators:

[0203] 1. Temperature fluctuation range

[0204] Traditional method: The score is low, which reflects the large fluctuation of the decomposition furnace outlet temperature (e.g., ±50℃) and poor control accuracy.

[0205] Modular function optimization method: The score was significantly improved, indicating that the optimization control based on the modular function can stabilize the temperature fluctuation within an extremely narrow range (such as ±15℃), providing an extremely stable thermal environment for raw material decomposition.

[0206] 2. Stability of raw material decomposition rate

[0207] Traditional methods result in low scores, large fluctuations in raw material decomposition rates, and difficulty in maintaining them within the ideal range (90%-95%), directly affecting clinker quality.

[0208] Modular function optimization method: A high score indicates that the system can maintain a stable high raw material decomposition rate with minimal fluctuations through precise temperature field control, which significantly improves the consistency of product quality.

[0209] 3. Pulverized coal combustion rate

[0210] Traditional method: The score is average, indicating incomplete combustion of pulverized coal, leading to energy waste and increased pollutant emissions.

[0211] Modular function optimization method: High score. The optimized pulverized coal injection strategy ensures more complete combustion of pulverized coal in the furnace, improves combustion efficiency, and reduces heat loss and emissions caused by incomplete combustion.

[0212] 4. System heat consumption

[0213] Traditional method: moderate score, high heat consumption per unit product.

[0214] Modular function optimization method: High score, due to uniform temperature field and complete combustion, the total heat consumed by the system when producing the same quality of product is significantly reduced, thus achieving energy saving and consumption reduction.

[0215] Therefore, the modular function decomposition furnace temperature field optimization method is superior to the traditional control method in all key performance indicators, forming a fuller and more optimized polygon, reflecting the overall performance improvement of the system.

[0216] In terms of specific application effectiveness, the implementation of this embodiment has the following improvements:

[0217] 1. Improved temperature control accuracy: The temperature fluctuation range of the decomposition furnace has been reduced from ±50℃ in the traditional method to within ±15℃, improving the temperature control accuracy by 70%.

[0218] 2. Stable raw material decomposition rate: The raw material decomposition rate is stable in the ideal range of 90%-94%, which improves the quality of clinker and production stability.

[0219] 3. Reduced energy consumption: The pulverized coal is fully combusted, and coal consumption is expected to be reduced by 8%, which can save about 12,000 tons of standard coal per year for a 5,000t / d production line.

[0220] 4. Environmental benefits: The complete combustion of pulverized coal reduces CO and NOx emissions, meeting the requirements of green manufacturing.

[0221] 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 multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function, characterized in that: Includes the following steps: S1, Multi-source temperature data fusion acquisition An infrared thermal imager array is arranged in the upper, middle and lower parts of the decomposition furnace to synchronously collect three-dimensional temperature field data inside the furnace at a certain frequency; a thermocouple array is arranged at the four outlets of the four-channel adjustable pulverized coal injection pipe to monitor the local temperature in real time. S2: Data Preprocessing and Feature Extraction The controller first performs median filtering on the received raw temperature data to remove impulse noise, and then uses moving average filtering to suppress random fluctuations. The preprocessed temperature field data is analyzed to extract key features, including the highest temperature, lowest temperature, average temperature, and temperature standard deviation, to obtain the actual temperature field data T. actual (x,y,z,t); S3: Temperature field matching degree calculation based on modulus function A temperature field model based on the modulus function is constructed, and the temperature field model is based on the following formula: （1） Where N=50, T opt Q is the optimal temperature field distribution function, in °C; τ(n) is the Ramanujan τ function; T0 is the ideal reference temperature of the decomposition furnace, ranging from 870-890 °C; Q m y is the real-time flow rate of pulverized coal, Q0 is the reference value of pulverized coal flow rate; (x,y,z,t) are the three-dimensional spatial and temporal parameters inside the decomposition furnace. The ideal temperature field T is calculated. opt (x,y,z,t), the actual temperature field data T actual Substituting (x,y,z,t) into Equation 1, we can calculate the current temperature field and the ideal temperature field T predicted by the model. opt The matching degree of (x,y,z,t) is evaluated using mean squared error or a custom matching degree function. S4: Solving Optimal Decisions in Multi-Objective Particle Swarm Optimization Two optimization objectives are set: maximizing the temperature uniformity index (UI) and minimizing the total pulverized coal consumption. An improved particle swarm optimization (PSO) algorithm is used to solve these objectives, where each particle represents a possible pulverized coal flow allocation scheme. The PSO algorithm evaluates the performance of each particle on both the UI and coal consumption objectives, guiding the particle swarm towards the Pareto front. Finally, an optimal scheme is selected from the Pareto solution set based on the requirement of prioritizing temperature stability or prioritizing reducing coal consumption, resulting in the optimal pulverized coal flow rate Q for the four pulverized coal injection pipes. m1 Q m2 Q m3 Q m4 ; S5: Control command issuance and execution The instructions corresponding to the optimal pulverized coal flow rate calculated by the optimization algorithm are sent to the four-channel adjustable pulverized coal injection pipes respectively, and each channel adjusts the pulverized coal injection volume according to the instructions. S6: Feedback and Adaptive Adjustment The raw material decomposition rate is continuously monitored by an online analyzer or by periodic sampling. If the raw material decomposition rate continues to deviate from the ideal range of 90%-95%, the reference temperature T0 in the temperature field model is automatically fine-tuned and the process returns to step S3, or the model parameters are re-identified and the process returns to step S2, thereby achieving long-term adaptive optimization.

2. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 1, characterized in that: Step S4 includes the following steps: S4.1: Optimization Objective and Variable Definition We set two objectives: Objective 1 is to maximize the temperature uniformity index (UI), and the formula for calculating UI is as follows: （2） In the above formula, K represents the number of temperature monitoring points, and T... k The measured temperature at point k is represented by UI. The closer UI is to 1, the more uniform the temperature field. Objective 2 is the total coal powder consumption Q. m =Q m1 +Q m2 +Q m3 +Q m4 Minimize, where the pulverized coal flow rates of the four pulverized coal injection pipes are Q m1 Q m2 Q m3 Q m4 The range of values ​​for each variable is constrained by the maximum capacity of the pulverized coal injection pipe; S4.2: PSO Algorithm Parameter Initialization The algorithm parameters are set in the controller, where the population size is 30 particles, each particle represents a flow allocation scheme; the maximum number of iterations is 100, balancing real-time performance and optimization accuracy; the learning factor is c1=c2=1.49445, the inertia weight is 0.729, ensuring convergence; the weight coefficients are: UI weight w1=0.7, coal consumption weight w2=0.

3. S4.3: Multi-objective evaluation and Pareto frontier search For each particle, calculate its integrated objective function value: （3） In the above formula: F: The comprehensive objective function value, which is the evaluation index that needs to be maximized. The closer the value is to 1, the better the overall performance of the optimization scheme in terms of temperature uniformity and coal consumption control. w1: Weighting coefficient of temperature uniformity index UI; UI: Temperature Uniformity Index; w2: Weighting coefficient for pulverized coal consumption; Q m Total pulverized coal consumption, which is the sum of the flow rates of the four pulverized coal injection pipes: Q m =Q m1 +Q m2 +Q m3 +Q m4 ; Q max Maximum total pulverized coal flow rate, used for standardizing coal consumption items to prevent Q m An excessively large value will distort the objective function; the value should be based on the design capacity of the decomposition furnace. The PSO algorithm is used to evaluate the performance of particles in terms of UI and coal consumption, update the individual optimal and global optimal positions, and guide the particle swarm to move towards the Pareto front. S4.4: Optimal Solution Selection Strategy From the Pareto solution set, select a compromise based on actual needs: if prioritizing temperature stability, choose the solution with the highest UI; if prioritizing reducing coal consumption, choose the solution with the lowest coal consumption; output the final optimized pulverized coal flow rate setpoint [Q]. m1 Q m2 Q m3 Q m4 ]; Step 4.5: Real-time and Adaptive Processing The optimization period is set to 60 seconds to ensure response speed; if the matching degree exceeds the threshold for multiple consecutive periods, the model parameter self-tuning is triggered.

3. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 2, characterized in that: The self-tuning of the trigger model parameters in step S4.5 includes adjusting Q0.

4. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 1, characterized in that: In step S1, the controller is an S7-1500 PLC.

5. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 1, characterized in that: In step S1, the infrared thermal imager array includes at least 6 high-temperature thermal imagers, which are respectively arranged in the upper, middle and lower parts of the decomposition furnace to ensure that the viewing angle covers the entire cross-section of the decomposition furnace.

6. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 1, characterized in that: In step S1, the thermocouple array consists of 12 K-type thermocouples, divided into 4 groups, with 3 measuring points in each group, which are arranged near the outlets of the 4 pulverized coal injection pipes, with an insertion depth of 1 / 3 of the furnace radius.

7. The multi-objective optimization method for the temperature field of a decomposition furnace based on a modulus function according to claim 1, characterized in that: In step S2, the filter window width of the moving average filter is 5, and the sampling interval Δt = 30s.

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