Fuzzy control-based smelting waste gas recycling optimization system

Abstract

The invention discloses a smelting waste gas recycling optimization system based on fuzzy control, and relates to the technical field of automatic control. The problems of low control precision and response lag caused by the fact that an existing static membership function cannot adapt to multi-scale working condition changes in real time are solved. Comprising a sensing acquisition module, a membership reconstruction module, a feature decoupling module, a coupling compensation module, a rule optimization module and an execution control module. Standardized data are acquired through sensing acquisition and filtering, an adaptive membership function is constructed by adopting incremental fuzzy clustering, and closed-loop self-correction of a multi-modal control instruction is realized by combining wavelet packet decoupling, feed-forward compensation and double-depth Q network reinforcement learning online optimization; the waste gas desulfurization efficiency, energy consumption optimization and treatment system stability of waste gas treatment can be effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of automation control technology, and more particularly to a smelting waste gas recycling optimization system based on fuzzy control. BACKGROUND

[0002] The smelting waste gas recycling optimization system based on fuzzy control realizes intelligent optimization of the waste gas treatment process by real-time monitoring of waste gas temperature, dust concentration and harmful gas components, and dynamically adjusting key parameters such as recycling rate and adsorbent dosage in combination with a fuzzy rule base. The core technology lies in converting the complex nonlinear smelting process into quantitative control instructions based on the fuzzy rule base, balancing processing efficiency and energy consumption through a multi-module collaborative decision-making mechanism, adapting to dynamic working conditions such as raw material fluctuations and furnace load changes, and ultimately improving the removal rate of sulfur oxides and the efficiency of waste heat recovery, promoting the green and low-carbon transformation of the smelting process.

[0003] Among the existing smelting waste gas recycling optimization system technology solutions based on fuzzy control, the CN107630122A patent is a typical representative. This patent uses a mass spectrometer to monitor CO, CO2 and other components in waste gas in real time, establishes a decarburization mathematical model in combination with a neural network fuzzy control method, and dynamically adjusts oxygen blowing amount and vacuum chamber pressure parameters to achieve efficient decarburization treatment of smelting waste gas. The core of the fuzzy control technology lies in converting smelting process parameters that are difficult to accurately model into linguistic variables through fuzzification, and then making inferences and decisions based on a pre-set fuzzy rule base to finally output control instructions. The CN216604603U patent uses physical filtration and chemical adsorption to cooperatively treat waste gas, and the CN119896951A patent realizes waste gas classification and recovery based on multi-level control logic. These technologies combined with fuzzy control technology constitute the current technical system for smelting waste gas recycling. They process waste gas from different angles and to some extent meet the needs of the smelting industry for waste gas recycling.

[0004] In practical applications, the core of fuzzy control lies in the fuzzy mapping of membership functions to input variables (such as exhaust gas temperature, SO2 concentration, and dust flow rate). Existing systems mostly use membership functions of fixed shapes (such as triangles and trapezoids), and their parameters (such as center points and widths) are preset based on historical data or expert experience, which cannot dynamically adapt to sudden changes in the composition, flow rate, and thermal parameters of smelting exhaust gas. For example, the CN107630122A patent fixes the parameters of its membership functions through offline training of historical data. However, the flow rate and composition of actual smelting exhaust gas are affected by factors such as fluctuations in raw material impurities and changes in production rhythm, and exhibit multi-scale dynamic changes. Static membership degree calculation cannot accurately represent the characteristics of instantaneous working conditions, leading to control instructions deviating from the optimal solution. In addition, the smelting exhaust gas system has strong nonlinearity (such as the exponential relationship between sulfide oxidation reaction rate and temperature) and time-varying nature (such as changes in dust concentration with raw material batches), and static membership functions cannot adjust the coverage of input variable fuzzy sets in real time. For example, the filtering control logic of the CN216604603U patent uses a unified fuzzy strategy for exhaust gas characteristics at different time scales (such as instantaneous impact load and long-term trend drift), which leads to high-frequency fluctuations being smoothed out and low-frequency drift response lagging behind. Static membership functions further amplify multi-scale feature fusion errors, exacerbating system oscillation and precision loss. SUMMARY

[0005] To overcome the deficiencies of the prior art, the present application discloses a smelting exhaust gas recycling optimization system based on fuzzy control, aiming to solve the problems raised in the background art.

[0006] To achieve the above technical effects, the present application adopts the following technical solutions: A smelting exhaust gas recycling optimization system based on fuzzy control, comprising: a sensing and collecting module for collecting smelting exhaust gas temperature, sulfide concentration, dust flow rate, and environmental humidity parameters, using anti-aliasing filtering and sliding mean filtering to suppress high-frequency noise and eliminate transient interference, generating standardized time series data streams; A membership reconstruction module for extracting the mean, variance, and kurtosis features of the collected parameters based on a sliding window statistical analysis method, dynamically dividing the working condition intervals through an incremental fuzzy clustering algorithm; and using a historical data weight distribution mechanism to separate the steady-state and transient-state features, constructing an adaptive membership function model of input variables, dynamically adjusting the membership function center point offset and coverage range according to real-time working condition changes, outputting dynamic fuzzy parameters to the feature decoupling module, and transmitting the working condition label to the rule optimization module; A feature decoupling module is used to separate the dynamic fuzzy parameters using a wavelet packet transform method to obtain a high-frequency transient component and a low-frequency trend component; and to perform fuzzy reasoning on the high-frequency transient component through a short-time impulse response fuzzy reasoning mechanism to generate a transient compensation instruction; to perform fuzzy decision-making on the low-frequency trend component through a steady-state trend fuzzy decision-making model to generate a steady-state reference control quantity; and to integrate multi-scale control instructions through a dynamic weight fusion algorithm to generate a multimodal instruction set including a circulation rate reference value and an adsorbent dosage main control parameter, and output the set to a coupling compensation module; A coupling compensation module is used to correct the control instruction amplitude in real time based on the multi-variable coupling strength using a gain-scheduled feedforward compensation mechanism, and transmit the corrected instruction to the execution control module; The rule optimization module is used to construct a multi-objective reward function based on desulfurization efficiency, dust escape, and energy consumption data from operating condition labels and execution feedback. It uses a dual-deep Q-network reinforcement learning strategy to iteratively optimize the fuzzy rule trigger thresholds and weight coefficients, mapping the optimized parameters to the membership reconstruction module to drive the coordinated update of the rule base and membership function parameters. The execution control module is used to drive the circulation fan, adsorbent metering pump and heat exchanger valve to perform dynamic regulation, and collect actuator response data in real time and feed it back to the rule optimization module.

[0007] As a further technical solution of the present invention, the working condition interval division method of the incremental fuzzy clustering algorithm is: S1. Based on the cluster center of the previous moment and the current window characteristics, the improved membership calculation formula is used to calculate the membership. The calculation formula is: (1) In formula (1), Indicates the Data points for The degree of membership of the cluster; is the fuzzy index, which is used to control the fuzziness of membership; is the statistical feature vector at the current moment; and Respectively Hedi The center vector of each cluster; is the total number of clusters; is the Euclidean distance norm; S2, based on time decay factor Correct the historical membership weight, the formula is: (2) In formula (2), is the updated membership degree; is the historical membership value; is the currently calculated membership; time decay factor The expression is ,in is the attenuation coefficient, is the data time interval; S3. Dynamically update the cluster center based on the data membership and statistical characteristics in the window. The update formula is: (3) In formula (3), After the update Cluster center; Before the update Cluster center; For the window The feature vector of each data point; is the sliding window length; The historical center weight coefficient is used to balance the impact of new and old data; if the center is updated With the original center If the Euclidean distance exceeds the preset cluster drift threshold, the cluster splitting mechanism is triggered and a temporary cluster is added. , and reset The degree of membership is the entropy value of the data distribution within the window; S4. Calculate the mean membership of the current window data to each cluster center ; The expression is: ,choose The cluster number corresponding to the maximum value is used as the working condition label and output to the rule optimization module to drive the dynamic adjustment of the threshold.

[0008] Based on the above technical solutions, the positive beneficial effects of the present invention are: 1. By combining sliding window statistics with incremental fuzzy clustering and historical weighting to separate steady-state and transient characteristics, this solution dynamically adjusts the center point and width of the membership function when operating conditions suddenly change (such as a sudden increase in raw material impurities or a sudden change in load), achieving simultaneous capture of high-frequency transients and low-frequency trends. Consequently, when exhaust gas composition and flow rate fluctuate dramatically, control instructions can quickly track the actual operating conditions, avoiding the smoothing masking of sudden shocks and the delayed response to long-term drifts associated with traditional static methods. This significantly improves the system's transient compensation capability and steady-state regulation accuracy.

[0009] 2. This solution introduces wavelet packet transform to decouple dynamic fuzzy parameters in the frequency domain. High-frequency transient components and low-frequency trend components are subjected to short-term impact fuzzy inference and steady-state trend decision-making, respectively. Subsequently, gain-scheduled feedforward compensation is used to adjust the multivariable coupling strength in real time. This approach can quickly offset short-term perturbations in furnace temperature or sulfide concentration while maintaining stable long-term desulfurization and dust removal benchmarks. It significantly suppresses cross-coupling errors in the piping system and adsorbent dosing, preventing system oscillation and a decrease in control accuracy.

[0010] 3. Utilizing dual-deep Q-network reinforcement learning, with desulfurization efficiency, dust escape, and energy consumption as multi-objective reward functions, the system dynamically adjusts the trigger thresholds and weight coefficients of fuzzy rules, and maps the optimization results back to the membership reconstruction module. This enables the system to continuously "self-learn" and "self-correct" despite long-term changes in production rhythms and raw material properties, ensuring that the rule base and membership function configurations are constantly aligned with the latest operating conditions, avoiding the performance degradation and high maintenance costs associated with traditional offline curing.

[0011] 4. Through a tightly coupled closed-loop system of sensor acquisition, fuzzy decoupling, rule optimization, and execution feedback, this solution enables efficient information flow and closed-loop self-correction throughout the entire process. Consequently, whether improving recycling rates, precisely matching adsorbent dosage, or comprehensively optimizing desulfurization efficiency and energy consumption, this approach achieves higher levels of energy conservation, emission reduction, and environmental benefits while maintaining production stability. This effectively overcomes the bottleneck of existing technologies, which struggle to balance response speed and control accuracy under dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which: Figure 1 This is an architecture diagram of a smelting waste gas recycling optimization system based on fuzzy control according to the present invention; Figure 2 This is a step diagram of the working condition interval division method of the incremental fuzzy clustering algorithm of the present invention; Figure 3 It is a working principle framework diagram of the wavelet packet transform method of the present invention; Figure 4 This is a diagram showing the working principle steps of the steady-state trend fuzzy decision-making model of the present invention; Numbers in the figure: 101, sensor acquisition module, 102, membership reconstruction module, 103, feature decoupling module, 104, coupling compensation module, 105, rule optimization module, 106, execution control module. DETAILED DESCRIPTION

[0013] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions of this application will be clearly and completely described below in conjunction with the embodiments. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0014] To facilitate understanding of this embodiment, firstly, a smelting waste gas recycling optimization system based on fuzzy control disclosed in the embodiment of this application is introduced in detail, see Figure 1 The schematic diagram of a framework of a smelting waste gas recycling optimization system based on fuzzy control is shown, and the system includes: The sensor acquisition module 101 is used to collect parameters such as smelting waste gas temperature, sulfide concentration, dust flow rate, and ambient humidity. It uses anti-aliasing filtering and sliding mean filtering to suppress high-frequency noise and eliminate transient interference on the raw data to generate a standardized time series data stream. Sensor acquisition module 101 is used in scenarios such as smelting furnace exhaust outlets and purification equipment front-ends. It addresses the contamination of sensor raw data by high-frequency electromagnetic noise (e.g., inverter and motor radiation) and transient interference pulses (e.g., valve startup and shutdown, equipment vibration coupling) for four industrial parameters: smelting exhaust gas temperature, sulfide concentration, dust flow rate, and ambient humidity. In this application, "anti-aliasing filtering" refers to the use of a finite impulse response (FIR) filter to low-pass process the signal before sampling to prevent high-frequency noise from aliasing into the low-frequency band due to the sampling theorem and causing data distortion. "Sliding mean filtering" refers to the arithmetic average of a fixed-length time window or sample number window to eliminate the disruption of short-duration pulse interference to data trends. The parameter configuration and trigger logic of these two filtering technologies are dynamically adapted to the smelting process (e.g., blast furnace ironmaking, converter steelmaking) and sensor type (e.g., thermocouple temperature measurement, UV spectrometer sulfide concentration measurement). The specific configuration can be determined based on actual conditions and is not limited to this.

[0015] In terms of parameter collection, the smelting waste gas temperature T is obtained by using a K-type thermocouple (range 0∼400∘C0∼400∘C, accuracy ±1.5℃) or an infrared thermal imager (response time ≤50ms), covering the temperature gradient from the furnace gas outlet to the purification tower section; the sulfide concentration CS is measured by ultraviolet differential absorption spectroscopy (UV-DOAS) technology. Characteristic absorption peak (280-320 nm band) is inverted, and low concentration (<500 ppm) to medium concentration (500-2000 ppm) working conditions are adapted; Dust flow rate With the help of Pitot tube differential pressure principle, combined with flow rate-differential pressure calibration curve (such as , k is the calibration coefficient) conversion, the response frequency matches the turbulent flow characteristics of the exhaust gas (such as 50 Hz sampling to capture transient flow rate fluctuation); The environmental humidity H is collected by a capacitive humidity sensor (range 0~100%RH, accuracy ±2%RH), which reflects the influence of water vapor in the air around the purification system on the performance of the adsorbent. The four types of parameters are collected at the same time through IEEE 1588 precision time synchronization protocol, ensuring that the synchronization deviation of temperature, concentration, flow rate and humidity is ≤1ms at the same timestamp, providing a time reference consistent data source for multi-physical quantity coupling analysis.

[0016] Anti-aliasing filter link, based on Shannon sampling theorem to determine the cutoff frequency fc (such as sampling frequency fs=200Hz, fc=100Hz), using a 16-order FIR low-pass filter to truncate the original signal x(t) in frequency domain, and its transfer function is , where h[n] is the filter coefficient after Hanning window weighting, n is the filter tap index (value 0~15), corresponding to the coefficient position of different delay units of the filter; is a delay operator, which represents the delay of the signal by n sampling periods, ensuring that the signal distortion in the passband is <0.1% and the stopband attenuation is >40dB. When the power spectral density P(f) of the high-frequency noise of the sensor output signal is >0.1V2 / Hz (based on historical noise statistical distribution calibration), the anti-aliasing filter link is triggered to attenuate the interference such as electromagnetic radiation (such as 300Hz harmonic of frequency converter), turbulent high-frequency fluctuation (such as vortex noise >100Hz in flow rate signal), etc., and output the intermediate data stream without high-frequency noise .

[0017] Sliding mean filter link, for transient interference of intermediate data stream (such as concentration peak caused by electromagnetic valve start-stop, temperature jump coupled by equipment vibration), using time window Lt (such as 50ms, covering the typical interference duration) or sample number window Ln (such as 10 sampling points) to perform arithmetic mean, the formula is , where L is the window length, is the th sampling point in the window; is the current timestamp; is the sampling point index in the window, all sampling points from to t are traversed. − When the value is greater than 5% of the full scale (adjusted according to the dynamic range of the sensor, for example, when the full scale of the temperature sensor is 400°C, the mutation threshold is 20°C), the sliding mean filter is triggered to eliminate the distortion of the data trend caused by short-term pulses and output a preprocessed data stream without transient interference.

[0018] In order to adapt to the dynamic fluctuations of smelting waste gas (for example, the standard deviation of dust concentration increases by 3 times during the raw material switching period), an adaptive adjustment algorithm of the sliding mean window length is introduced: L(t) = L0+ k σ(t) , where L0 is the baseline window length (e.g., 10 sampling points), k is the adjustment coefficient (e.g., 2, optimized through offline simulation), and σ(t) is the standard deviation of the data within the current window. When exhaust gas turbulence intensifies (σ(t) increases), L(t) automatically increases to enhance filter suppression capabilities; when data stabilizes (σ(t) decreases), L(t) automatically decreases to preserve transient characteristics, achieving an adaptive logic of "stronger fluctuations, stronger smoothing; weaker fluctuations, faster response." In this formula, L0 ensures basic smoothing capabilities under normal operating conditions, k controls the window expansion rate with fluctuations, and σ(t) quantifies the intensity of data fluctuations. These three factors work together to deeply match the filtering effect with the dynamics of the operating conditions. The specific window length and adjustment coefficient values ​​can be determined based on actual process requirements and are not limited.

[0019] The standardized time series data stream output by the sensor acquisition module 101 is transformed by linear transformation (such as , The four types of parameters (the upper and lower limits of the physical range of the parameters) are mapped to the interval [0,1], providing unified dimension input for the membership reconstruction module 102 to extract features such as "mean, variance, and kurtosis." Anti-aliasing filtering eliminates high-frequency noise (such as temperature jumps caused by electromagnetic interference), preventing the membership function from misjudging the operating condition range due to noise. Sliding mean filtering eliminates transient interference (such as concentration spikes caused by valve switching), ensuring the accuracy of the incremental fuzzy clustering algorithm in dividing the operating conditions and reducing the probability of misjudgment when triggering fuzzy rules at the source of the data. Simultaneously, the time-synchronized acquisition of multiple sensors enables the wavelet packet transform of the feature decoupling module 103 to accurately separate high-frequency transients (such as temperature surges caused by slag falling) from low-frequency trends (such as dust drift caused by raw material batch switching) based on the synchronization of four-dimensional parameters. This provides reliable time-frequency domain input for short-term impulse response fuzzy reasoning and steady-state trend fuzzy decision-making, supporting the precise synthesis and coordinated output of multi-scale control commands.

[0020] The membership reconstruction module 102 is used to extract the mean, variance, and kurtosis characteristics of the collected parameters based on the sliding window statistical analysis method, and dynamically divide the operating condition intervals using an incremental fuzzy clustering algorithm. It also uses a historical data weight allocation mechanism to separate steady-state characteristics from transient characteristics, construct an adaptive membership function model for the input variables, dynamically adjust the membership function center point offset and coverage range according to real-time operating condition changes, output dynamic fuzzy parameters to the feature decoupling module 103, and transmit the operating condition label to the rule optimization module 105. In this application, "incremental fuzzy clustering" refers to a dynamic clustering algorithm that does not require offline training and only relies on real-time data streams to iteratively update the cluster center, which is different from the "offline batch training" mode of traditional fuzzy C-means (FCM). "Historical data weight allocation" refers to assigning differentiated weights to steady-state characteristics (long-term trend data) and transient characteristics (short-term impact data) (for example, a weight of 0.6 for steady-state data and a weight of 0.4 for transient data, which can be adjusted according to the intensity of process fluctuations and is not limited to this), thereby achieving decoupling and coordinated utilization of the two types of characteristics.

[0021] Specifically, the module first uses the sliding window statistical analysis method to extract three types of features from the standardized time series data stream (temperature, sulfide concentration, dust flow rate, and ambient humidity) output by the sensor acquisition module 101: mean μ (characterizing the average level of the parameter within the window, such as the temperature mean reflecting the thermodynamic state within the time period), variance σ (characterizing the intensity of parameter fluctuations, such as an increase in the variance of dust flow rate corresponding to intensified turbulence), and kurtosis K (characterizing the "peak / fat tail" characteristics of the parameter distribution, such as a sudden change in the kurtosis of sulfide concentration corresponding to an instantaneous emission pulse), to form a window feature vector The window length L can be configured as a time window (such as L = 500ms, covering the typical transient impact duration) or a sample number window (such as L = 20 sampling points). It can be determined based on the volatility of the exhaust gas (such as the raw material switching cycle and the slag falling frequency), and there is no limit on this.

[0022] like Figure 2 As shown in the figure, the module uses the improved fuzzy C-means (FCM) to implement incremental clustering. The cluster centers and membership degrees are updated iteratively through four steps to adapt to the time-varying characteristics of the exhaust gas operating conditions: Step S1: Real-time calculation of membership (trigger condition: arrival of new data window) based on the cluster center at the previous moment (j=1,2,...,k, k is the number of clusters, which is 3 to 8 according to the complexity of the working condition and can be determined according to the actual situation) and the current window feature vector F, and the improved membership calculation formula is used: ; Indicates the Data points for The degree of membership of the cluster, which quantifies the "closeness" of the data to the cluster center, takes values ​​[0,1]; is the fuzzy index (controls the fuzziness of the membership distribution, m=2∼5, the larger m is, the smoother the membership distribution is, avoiding the hard classification mutation of "either this or that"); is the center vector of the jj-th class (composed of mean, variance, and kurtosis, representing the typical characteristics of this working condition); is the Euclidean distance norm, quantifying the spatial distance between the data feature and the cluster center. A smaller distance indicates a higher membership. This step achieves soft classification of operating conditions based on multi-parameter coupling characteristics through a nonlinear "distance-membership" mapping (e.g., a data set with a membership of 0.7 for the "high-load transient" class and 0.3 for the "low-load steady-state" class indicates that it has characteristics of both operating conditions).

[0023] Step S2: Historical membership time decay correction (trigger condition: time interval To avoid "historical operating conditions excessively affecting current decisions" (such as low-load steady-state data from 3 hours ago interfering with current high-load transient judgments), a time decay factor is introduced. Corrected historical membership, the formula is: ; To update the membership, historical and current information are integrated; is the time attenuation factor, and its expression is (λ is the attenuation coefficient, ranging from 0.1 to 0.5; Δt is the time interval between the current data and the historical data), implementing the time series attenuation logic of "newer data has a higher weight, and older data has a lower weight"; is the historical membership (calculated result of the previous period); The current membership is calculated (output from step S1). This step ensures the module's rapid response to unexpected conditions such as "raw material switching, production load adjustment," by using time-dependent weight decay (e.g., after a kiln refueling, the weight of old steady-state data decreases rapidly, and new transient data dominates the cluster).

[0024] Step S3: Dynamic update of cluster centers (trigger condition: the sliding window data is full L) based on the new membership of the data in the window and statistical characteristics , combined with historical cluster centers , iteratively update the cluster centers: ; is the updated center vector of the jth class, reflecting the fusion characteristics of the current window and historical working conditions; is the historical center weight coefficient (take 0.3∼0.7 to balance the "sensitivity" of new data clustering and the "stability" of old centers. For example, α=0.5 means that new and old data each contribute 50% weight); the numerator is the weighted sum of the data features in the window ( is the fuzzy weight of membership, which strengthens the influence of high membership data) and the weighted sum of the historical center; the denominator is the normalization factor of the weighted sum to ensure the dimensional consistency of the center vector.

[0025] If the updated center With the original center If the Euclidean distance of the cluster exceeds the cluster drift threshold δ (such as δ = 0.2 × characteristic range, indicating a significant change in the working condition), the cluster splitting mechanism is triggered: a temporary cluster is added. , reset its membership to the entropy value of the data distribution in the window, and realize the “divide and classify” of working condition categories as they change (for example, the new transient working condition caused by slag falling is promptly identified as a new category).

[0026] Step S4: Output of working condition labels (trigger condition: completion of window feature extraction and cluster update) Calculate the mean membership of the current window data to each cluster center choose The cluster number corresponding to the maximum value is used as the working condition label (such as "Class 1 - low load steady state", "Class 2 - high load transient", "Class 3 - raw material switching transition period"), and is output to the rule optimization module 105 to drive the dynamic adjustment of the fuzzy rule trigger threshold (for example, under high load transient conditions, the trigger threshold of the "spray compensation" rule is lowered to achieve rapid response).

[0027] In practical applications, taking "sulfide concentration pulse caused by slag falling (high-frequency transient condition)" as an example, In step S1, m=3 (higher fuzzy index) makes the membership distribution smoother, avoids cluster jump caused by single data point mutation, and ensures smooth transition of membership between "transient pulse" and "steady-state baseline"; in step S2, λ=0.3 (medium attenuation coefficient) makes the weight of historical data 10 seconds ago decay to about 5%, highlighting the dominance of current pulse data and avoiding the old steady-state data "covering" the new transient characteristics; in step S3, α=0.4 (biased towards new data) makes the cluster center shift quickly toward the pulse characteristics, and the "kurtosis" component of the new center vector increases significantly, accurately capturing the "peak" characteristics of transient emissions; in step S4, the membership mean of the transient class is =0.8 (much higher than other categories), the “high load transient” label is output, and the triggering rule optimization module 105 lowers the trigger threshold of the “adsorbent emergency addition” rule to achieve rapid suppression of the pollution pulse.

[0028] The adaptive membership function dynamically updates the cluster center and membership degree, so that the "center point" of the membership function drifts with the working condition (e.g. after the raw material is switched, the concentration membership function center point moves from 200 ppm to 300 ppm), and the "coverage range" adjusts with the fluctuation intensity (e.g. when the turbulence intensifies, the flow rate membership function width expands from 5 m / s to 8 m / s), ensuring that the fuzzy mapping of the feature decoupling module 103 always fits the real-time working condition; the output working condition label provides "working condition identity" for the rule optimization module 105, so that the double-depth Q network reinforcement learning strategy can iteratively optimize the fuzzy rules (e.g. in high-load transient working conditions, prioritize optimizing the trigger threshold and weight of the "short-time impact response rule"), realizing the full-link adaptive of "working condition-rule-control instruction".

[0029] The adaptive membership function model is deployed in the whole process monitoring scene of smelting waste gas from the furnace discharge end to the front end of the purification device (e.g. converter flue gas pipeline, desulfurization tower inlet chamber), aiming at the multi-scale dynamic characteristics of two core parameters of smelting waste gas temperature and sulfide concentration (temperature "slag falling rapid rise / environmental heat dissipation slow descent", sulfide concentration "raw material impurity pulse / adsorbent attenuation drift"), breaking through the limitations of traditional fuzzy control "fixed shape (triangle / trapezoidal), static parameters (offline calibration center point and width)", through two types of adaptive function structures of double exponential type (temperature) and asymmetric Gaussian type (sulfide concentration), combined with historical-current feature weighted fusion and statistical quantity driven width adjustment mechanism, realizing the "center point drifts with the working condition, coverage range adapts to the fluctuation" of the membership function, providing time-varying rule support for the "fuzzy mapping" of the feature decoupling module 103, while ensuring the accurate matching of the working condition label and control instruction of the rule optimization module 105.

[0030] It should be clear that the "double exponential membership function" refers to an asymmetric membership function spliced by left and right exponential functions, which is different from the traditional symmetric triangular / trapezoidal function, and adapts to the asymmetric dynamics of temperature "rapid rise, slow descent" (e.g. when the slag falls, the temperature rises by 20°C in 10 seconds, and then naturally cools down for 30 minutes); "asymmetric Gaussian membership function" refers to a Gaussian function with different left and right half-widths driven by different statistical quantities, which adapts to the asymmetric distribution of sulfide concentration "emission pulse (steep right side), adsorption attenuation (gentle left side)" (e.g. raw material impurities cause SO2 concentration to jump by 50 ppm instantaneously, and under the action of adsorbent, it slowly decreases to baseline in 30 minutes); "History data weight distribution" refers to assigning different weights to steady-state features (e.g. 30-minute sliding window concentration mean, reflecting long-term adsorbent attenuation trend) and transient features (e.g. 5-second window concentration spike, reflecting raw material impurity pulse) (e.g. steady-state weight takes 0.6, transient weight takes 0.4, which can be adjusted according to process fluctuation intensity, and is not limited in this regard).

[0031] Specifically, the module constructs a double exponential membership function for the temperature parameter, and the core realizes time-varying adaptation by "center point weighted fusion of anchor trend and transient, coverage variance driven adaptive fluctuation intensity": when the temperature mean value fluctuation amplitude exceeds the preset threshold (such as ±5℃, calibrated according to process parameters such as furnace thermal inertia and production load), the center point drift mechanism is started. In actual operation, the temperature center point is obtained by weighted calculation of the historical 30-minute sliding window mean value (reflecting long-term stable trends such as environmental heat dissipation and equipment thermal inertia) and the current 10-second sliding window mean value (capturing transient impacts such as slag falling and valve opening and closing). By adjusting the historical mean weight coefficient a (value range 0.3~0.7, a=0.6 in the stable production period to strengthen the anchoring effect of historical trend on the center point; a=0.4 in the raw material switching and furnace condition fluctuation period to highlight the response sensitivity of the current window mean value to transient conditions), the balance between "long-term trend stability" and "current transient sensitivity" is achieved. For example, in the slag falling scenario, the current 10-second window temperature mean value rises to 250℃ (the historical 30-minute mean value is 200℃), and if a=0.4, the center point quickly drifts to 0.4x200+0.6x250=230℃, avoiding the fixed center point that cannot timely capture the transient condition due to the lag, resulting in the subsequent fuzzy control instruction being inaccurate.

[0032] When the temperature variance exceeds 1.5 times the historical variance mean value (calibrated according to process disturbance characteristics such as equipment vibration level and turbulence intensity), the coverage range expansion mechanism is started. The left width of the double exponential membership function (corresponding to the cooling process, exponential decay section) and the right width (corresponding to the heating process, exponential growth section) are dynamically adjusted according to the temperature variance - the larger the temperature variance (such as fan impeller wear causing waste gas turbulence to intensify, temperature variance from 10℃² to 30℃²), the stronger the expansion range of left and right width. In actual operation, the variance sensitivity coefficient β (value range 0.5~2, β=2 when the process disturbance is severe to enhance the width expansion response to fluctuations; β=0.5 when the process is stable to moderately suppress excessive expansion) drives the left width (baseline value set to 20℃, calibrated according to the equipment thermal response time) and the right width (baseline value set to 15℃, calibrated according to the slag impact heating rate) to expand synchronously. For example, when the temperature variance doubles, the left width expands from 20℃ to 40℃ and the right width expands from 15℃ to 30℃, making the membership function cover a wider temperature interval, avoiding "fluctuation data being misjudged as abnormal values due to exceeding the fixed membership function range", resulting in frequent oscillation of control instructions such as spray cooling and fan speed regulation.

[0033] The module uses an asymmetric Gaussian membership function for the sulfide concentration parameter. When the first-order derivative of the concentration rate of change exceeds a preset threshold (e.g., 5 ppm / s, calibrated based on process parameters such as the adsorbent's transient adsorption capacity and pipeline mixing time), the right-side width expansion mechanism is activated. The right-side width of the asymmetric Gaussian function (corresponding to the steepest rising edge of the emission pulse) dynamically adjusts with the concentration rate of change. The greater the rate of change (e.g., when a feedstock batch is switched and high sulfur impurities are mixed, the SO2 concentration jumps from 200 ppm to 250 ppm in 3 seconds, a rate of change of 16.7 ppm / s), the greater the right-side width expansion. In practice, the right-side width (set to a baseline of 5 ppm and calibrated based on the adsorbent's initial response rate to transient pulses) is driven by the rate-of-change sensitivity coefficient γ (ranging from 0.3 to 1; for high pulse intensity, γ is set to 1 to maximize the expansion and quickly capture extreme pulses; for low pulse intensity, γ is set to 0.3 for a more moderate response and avoid oversensitivity to small fluctuations) to dynamically expand. For example, when the concentration change rate reaches twice the threshold (i.e. 10 ppm / s), if γ is taken as 0.5, the width on the right side will expand from 5 ppm to 10 ppm, so that the membership of 240 ppm concentration (only 10 ppm beyond the center) can still reach 0.85, ensuring that transient response rules such as "emergency addition of adsorbent" are triggered in time to avoid the risk of exceeding the standard due to the continued spread of high sulfur pulses.

[0034] When the historical concentration distribution entropy exceeds a preset threshold (e.g., 1.5, calibrated based on process parameters such as adsorbent lifecycle and regeneration frequency), the left-side width expansion mechanism is activated. The left-side width of the asymmetric Gaussian function (corresponding to the gently falling edge of adsorption decay) dynamically adjusts with the historical concentration distribution entropy. The greater the distribution entropy (e.g., as adsorbent capacity decays after 8 hours of continuous operation, the "disorder" of the concentration data increases from 0.8 to 1.6, reflecting a decrease in the adsorbent's ability to retain pollutants), the greater the left-side width expansion. In practice, the dynamic expansion of the left-side width (set to a baseline of 20 ppm and calibrated based on the concentration decay rate during the adsorbent's high-efficiency period) is driven by the distribution entropy sensitivity coefficient δ (ranging from 0.2 to 0.8, with δ set to 0.8 for severe adsorbent decay, enhancing the response and providing a timely regeneration warning; and δ set to 0.2 for stable adsorbent performance, weakening the response and preventing false regeneration triggering) is used. For example, when the historical concentration distribution entropy increases from 0.8 (the adsorbent is in a brand new state, and the data distribution is orderly) to 1.6 (the adsorbent needs to be regenerated, and the data distribution is disordered), if δ is taken as 0.5, the left width expands from 20ppm to 31ppm, so that the membership of the 220ppm concentration (lower than the center 10ppm) can still be maintained at 0.7, ensuring that steady-state trend rules such as "adsorbent regeneration warning" are accurately triggered, avoiding excessive attenuation of the adsorbent and a cliff-like drop in purification efficiency.

[0035] Taking "SO2 concentration pulses caused by high sulfur impurities in raw materials (transient operating conditions)" as an example, the concentration center point is weighted by combining the historical mean (200ppm during the adsorbent's high-efficiency period) and the current window mean (250ppm during the pulse period) using a historical mean weight coefficient α=0.4 to obtain 230ppm. This quickly anchors the pulse center and ensures that the membership function accurately focuses on the transient "cognitive focus"; The right width is triggered by a concentration change rate of 10 ppm / s (γ = 0.5, threshold 5 ppm / s), expanding from 5 ppm to 10 ppm. This increases the membership degree of the 240 ppm concentration (only 10 ppm beyond the center) to 0.85, directly driving the "emergency adsorbent addition" rule to activate, achieving rapid suppression of high sulfur pulses. The left-side width is maintained at 20 ppm, starting from the distribution entropy of 0.8 when the adsorbent is not decaying and not reaching the threshold. This keeps the membership at a concentration of 220 ppm (center 10 ppm) at only 0.6, preventing "normal fluctuations from falsely triggering regeneration commands" and ensuring the control strategy strikes a balance between economy and stability. A dual exponential adaptation to temperature "steep rise and slow fall" and an asymmetric Gaussian adaptation to sulfide concentration "steep reduction and slow decay" ensure that the fuzzy mapping is highly consistent with the physical nature of the industrial process. For example, when the temperature rises suddenly due to slag dropping, the right-side exponential segment responds quickly, preventing a delay in the spray cooling command. When the concentration slowly decreases due to adsorbent decay, the left-side wide-band segment responds with a delayed response, preventing the adsorbent regeneration command from being falsely triggered by small fluctuations. The center point drifts dynamically with the "historical-current mean weighting", and the coverage range is adaptively expanded according to the "variance (temperature), rate of change (concentration pulse), and distribution entropy (concentration decay)", so that the feature decoupling module 103 can accurately separate "high-frequency transient shocks (such as temperature surges, concentration pulses)" and "low-frequency steady-state drifts (such as environmental heat dissipation, adsorbent decay)", providing the input basis of "time-varying granularity" for short-term shock response fuzzy reasoning and steady-state trend fuzzy decision-making - high-sensitivity fuzzy parameters are output in transient shock scenarios, and high-robustness fuzzy parameters are output in steady-state drift scenarios.

[0036] The feature decoupling module 103 is used to separate the dynamic fuzzy parameters by using the wavelet packet transform method to obtain high-frequency transient components and low-frequency trend components; and to perform fuzzy reasoning on the high-frequency transient components through the short-time impulse response fuzzy reasoning mechanism to generate transient compensation instructions; to perform fuzzy decision-making on the low-frequency trend components through the steady-state trend fuzzy decision model to generate steady-state reference control quantities; to integrate multi-scale control instructions through the dynamic weight fusion algorithm to generate a multi-modal instruction set including the circulation rate reference value and the adsorbent dosage main control parameters, and output it to the coupling compensation module 104; It should be noted that the wavelet packet transform method of this scheme is different from the Unlike traditional wavelet transform which only focuses on low-frequency decomposition, wavelet packets can perform fine decomposition of high-frequency sub-bands, adapting to the complex dynamic characteristics of smelting waste gas, namely "high-frequency transient impact (such as a sudden rise in slag falling temperature) + low-frequency trend drift (such as slow change in dust concentration due to raw material switching)". Short-term impact response fuzzy reasoning is a fast reasoning mechanism for millisecond-level transient disturbances (such as concentration pulses caused by pipeline vibration), which is different from the long-term control logic of steady-state trend decision-making. The dynamic weight fusion algorithm dynamically adjusts the priority and coupling relationship between transient compensation instructions and steady-state reference control quantities, and outputs multi-modal execution instructions (such as circulation rate and adsorbent dosage).

[0037] See also Figure 3 The wavelet packet transform achieves precise separation of high-frequency transients and low-frequency trends through four steps: adaptive basis function selection, self-optimization of the decomposition level, subband energy entropy screening, and dual-channel reconstruction enhancement. The adaptive basis function selection module matches the transient "spike characteristics." The wavelet basis is selected based on the signal's kurtosis (a statistical measure of the degree of "spike and fat tail"). When the kurtosis of the dynamic fuzzification parameter exceeds a preset threshold (e.g., 3, calibrated using historical transient data statistics and adjustable based on actual operating conditions), the db4 basis is selected (due to its tight support and excellent high-frequency resolution, enabling it to capture temporal details of millisecond-level temperature surges, such as slag drop). If the threshold is not exceeded, the sym5 basis is selected (which balances time-frequency localization and adapts to slowly changing trends, such as adsorbent decay). For example, when the temperature signal kurtosis jumps from 2 to 4.5 (exceeding the threshold of 3) during slag impact, the db4 basis is selected, enabling fine separation of the transient high-frequency components between 20 and 100 Hz. When the sulfide concentration kurtosis during the feedstock stabilization period is 1.8 (not exceeding the threshold), the sym5 basis is selected to balance trend preservation with computational efficiency.

[0038] The number of decomposition layers is automatically optimized, and the approximate entropy and sample entropy of the signal within the sliding window are weighted (each weight is 0.5, and can be adjusted based on the signal's chaos level, with no specific limit) to obtain a complexity index. When the complexity exceeds a threshold (e.g., 2, calibrated through offline simulation of the complexity distribution under different operating conditions), a three-layer decomposition is triggered (decomposing the signal into 8 subbands to finely separate turbulent high-frequency noise and thermal inertia trends); otherwise, a two-layer decomposition is adopted (decomposing into 4 subbands to balance accuracy and efficiency). For example, if fan impeller wear causes increased exhaust turbulence, the approximate entropy of the temperature signal increases from 1.2 to 2.5, and the sample entropy increases from 1.1 to 2.3, resulting in a weighted complexity of 2.4 (exceeding the threshold), triggering a three-layer decomposition. During stable production, if the complexity is 1.5 (not exceeding the threshold), a two-layer decomposition is adopted to avoid computational overload caused by excessive decomposition.

[0039] Subband energy entropy screening removes "noise subband interference" from the decomposed subband nodes and calculates energy entropy (which quantifies the disorder of the subband energy distribution; lower entropy indicates more concentrated energy and a more effective signal). If the node's energy entropy falls below a preset noise threshold (e.g., 0.5, calibrated using historical noise subband statistics), the node is removed (e.g., a 100Hz noise subband caused by electromagnetic interference, with an energy entropy of 0.3, is removed); otherwise, it is retained (e.g., a 20-50Hz transient subband caused by slag impact, with an energy entropy of 1.2, is retained). This step ensures that the subsequently reconstructed components contain only "valid operating condition characteristics," preventing noise from contaminating the accuracy of transient and trend separation.

[0040] Improved dual-channel reconstruction: By improving the dual-channel reconstruction algorithm, high-frequency node coefficients are reconstructed into transient impact components (such as the sudden temperature rise caused by slag falling), and low-frequency node coefficients are reconstructed into steady-state trend components (such as the slow concentration drop caused by adsorbent attenuation): a tightly supported rectangular window (window length 50ms, calibrated according to the duration of the transient) is used to intercept short-term peaks in transient components; for high-frequency detail node coefficients, if the energy entropy is lower than the noise baseline (such as 0.4, the statistical value of the energy entropy of the noise subband), it is set to zero for noise reduction (such as the high-frequency noise node coefficient of electromagnetic interference is set to zero); the steady-state component is filtered by sliding average (window length 300ms, calibrated according to the steady-state time scale) to extract long-term drift; for low-frequency approximation node coefficients, sliding window energy normalization (window length 1000ms, calibrated according to the production batch cycle) is used to eliminate baseline drift (such as the temperature baseline offset caused by ambient temperature); Transient feature extraction captures the "three-dimensional fingerprint" of the shock by taking a sliding window (100 ms long, 50 ms step, calibrated by transient duration) of the transient waveform (e.g., 80 ms process of temperature from 200°C to 220°C) at the current time, and using an extreme point detection algorithm (difference method to find peak value, rising / falling edge) to extract the shock amplitude (220-200=20°C), rising edge slope (20°C / 30 ms≈0.67°C / ms), and duration (time from peak to falling, e.g., 50 ms), forming a feature vector ([20, 0.67, 50]\), providing quantitative basis for subsequent reasoning.

[0041] The module matches the feature vector based on a dynamic fuzzy rule base (updated by the working condition label affiliated to the membership reconstruction module 102, such as focusing on SO2 concentration pulse rules under "high sulfur transient" working conditions). When the shock amplitude exceeds 2 times the standard deviation of the historical mean value (e.g., historical temperature shock mean value 10°C, standard deviation 3°C, threshold value 16°C, current amplitude 20°C exceeds threshold value), emergency compensation is triggered: the width of the Gaussian membership function is narrowed to 50% of the original (e.g., original width 20°C→10°C), making the membership degree more sensitive to the shock (20°C amplitude membership degree from 0.7→0.9). For example, the slag shock triggers emergency compensation, strengthening the response priority of strong shocks, ensuring that the spray command is quickly started.

[0042] Next, the module calculates the spray increment using the gradient weighted fuzzy reasoning method: the product of the rising edge slope and the duration (e.g., 0.67×50=33.5) adjusts the compensation weight (the larger the product, the higher the weight), and the shock amplitude membership degree (e.g., 0.9 after narrowing) is fused to generate the compensation amount. For example, weight factor 0.8, membership degree 0.9, spray increment = baseline amount (e.g., 5 m³ / h) × 0.8 × 0.9 = 3.6 m³ / h. At the same time, the compensation command is superimposed with the steady-state baseline (e.g., cycle rate) through timestamp alignment (accuracy ≤1 ms), ensuring that the time bases of multi-scale commands are consistent, providing collaborative input for dynamic weight fusion.

[0043] In the smelting waste gas recycling optimization system, in order to quickly respond to working condition mutations and maintain long-term stability, the system is divided into "transient compensation" and "steady-state baseline" dual-path control. The steady-state trend fuzzy decision model is responsible for extracting long-term fluctuation rules from low-frequency trend components and generating steady-state baseline control amounts; the dynamic weight fusion algorithm dynamically fuses high-frequency transient instructions and low-frequency steady-state baselines according to the system running state, and finally outputs the main control parameters (e.g., cycle rate baseline value and adsorbent dosage).

[0044] Please refer to Figure 4The core of the steady-state trend fuzzy decision model lies in the use of multi-window statistics and fuzzy cognitive map (FCM) reasoning. Through the four steps of "trend feature vector → membership function reconstruction → fuzzy reasoning → defuzzification", a benchmark control quantity reflecting the long-term trend of the process is generated.

[0045] First, feature extraction uses a sliding window adaptive statistical analysis method. Define the window length L (e.g., 5 minutes to 30 minutes, which can be determined based on the actual system inertia and is not limited to this), and calculate the mean value within each window for the exhaust gas parameter sequence x(t) with a sampling frequency of f. and variance , forming a trend feature vector At the same time, exponentially weighted moving average (EWMA) smoothing is performed, with a smoothing factor α∈(0,1), typically ranging from 0.1–0.3. This can be tuned based on experience or online identification methods and is not limited. Smoothing aims to reduce the interference of sudden noise on long-term trends.

[0046] Subsequently, the low-frequency components are dynamically mapped based on the multi-dimensional membership function reconstruction mechanism. , calculated in each sliding window as ,in The low-frequency subband variance from the wavelet packet decomposition, is the total variance. The distribution of and standard deviation σ_E. According to the "Fuzzy Cognitive Map Rule Mapping": like >μ_E+k·σ_E (in the high energy range, k is generally 1–2 and can be adjusted), then the center c of the Gaussian membership function is shifted to the right by δ_c (e.g., δ_c = 0.1 × function width); like <μ_E−k·σ_E (low energy state interval), then shift the center c to the left by the same magnitude; Otherwise, the original center remains unchanged. The width σ_m can also be dynamically scaled according to the energy fluctuation amplitude: Δσ_m∝Var( ).

[0047] The specific implementation of the above offset operation can be achieved by online optimization or incremental update, such as , where β is the learning rate, β∈(0,1), which can be determined according to the system response speed and is not limited.

[0048] After the membership function is adjusted, the fuzzy cognitive graph inference engine is entered. FCM nodes correspond to trend features (mean nodes and variance nodes) and control objectives (circulation rate R and adsorbent dosage A), and edge weights represent the strength of causality. The rule base defines several general rules, such as "If the mean is high and the variance is stable, the circulation rate should be slightly increased while the adsorbent dosage remains unchanged"; "If the mean decreases and the variance significantly decreases, the adsorbent dosage can be appropriately reduced to reduce costs" and so on.

[0049] The rule weights can be initialized based on expert experience and subsequently optimized through online learning. For rule activation, the continuous window variance is lower than the preset threshold σ_th: when the continuous M windows (e.g. M=3) When <σ_th, the "long-term stability association rule" is triggered and activated first; the weights of other short-term disturbance related rules W_i are decayed according to the exponential decay factor γ^t (γ∈(0,1), t is the number of windows since the rule was last activated).

[0050] At the same time, a reinforcement learning ε-greedy strategy is introduced for rule weight adjustment: with a probability ε (which can be initially set to 0.2), new or low-weight rules are explored to find the rule most relevant to temperature baseline drift and adsorption efficiency gradient; the current optimal rule is used with a probability of 1−ε. ε increases nonlinearly with the number of windows.

[0051] Finally, defuzzification is performed using the entropy weight method and the center of gravity method: first, the membership of each activated rule μ_i and its corresponding output (R_i, A_i) are calculated; the entropy weight method is used to obtain the weight of each rule ω_i=(1−Entropy(μ_i)) / Σ(1−Entropy(μ_j)), and then the center of gravity method is used to calculate the output benchmark: After timestamp alignment, this reference control quantity and transient compensation instruction are sent to the dynamic weight fusion algorithm together.

[0052] The dynamic weight fusion algorithm is mainly divided into the following three stages: 1) Construction of multimodal weight vector: Within each time domain sliding window (length L′, which can be different from the steady-state model window), extract the following: high-frequency transient compensation instruction sequence u_h(t), calculate its peak intensity P=max|u_h|; steady-state reference control quantity sequence u_l(t), calculate the trend slope S=Δu_l / Δt; exhaust gas parameter covariance matrix Σ_x. Then, the vector V=[P,|S|,diag(Σ_x)] is normalized and used as the input for weight fusion. Apply the entropy weight method to V, calculate the dynamic entropy value E_j of each component and the corresponding weight α_j=(1−E_j) / Σ(1−E_k), and obtain the initial weight vector W. 0=[w_h 0 ,w_l 0 ], where w_h 0 with w_l 0 Corresponding to the synthesis weights of high and low frequency channels respectively.

[0053] 2) Entropy increase rule triggering and Lyapunov stability adjustment: If the high-frequency energy ratio η_h = Var_high / Var_total exceeds the historical mean μ_η + 2σ_η (i.e., encountering a large shock) in the current window, the entropy increase rule is triggered: the transient weight is increased according to the adaptive coefficient λ(η_h): λ(η_h) can be defined as a saturating function, such as λ=min(η_h / (μ_η+2σ_η),1). The specific value can be determined based on the system's response requirements and is not specified. Subsequently, to ensure that the fusion weights do not cause oscillations in the context of stability, a gradient correction is constructed based on the Lyapunov function V_L(y). Let y=[w_h,w_l]. The Lyapunov function can be V_L=½(y−y*)^TQ(y−y*), where y* is the equilibrium point and Q is a positive definite matrix (such as the identity matrix). Thus, the gradient direction ∇V_L=Q(y−y*). When the system detects that V_L exceeds the threshold V_th (i.e., trending towards instability), the system moves along the negative gradient direction: ynew=y−ηg ∇VL,y, where η_g is the gradient step size, which can be determined based on linear control theory and is not specified. This step ensures that the weights return to the stable region.

[0054] 3) Smoothing filtering, limiting, and execution output: fusion weight Smoothed by exponential decay filtering to produce the final weight : , is the filtering factor, usually 0.2–0.5. − |>Δ_th (preset threshold), the inertia compensation mechanism is activated, +sign( }− )·Δ_th to suppress the jump. Finally, according to The transient command u_h and the steady-state reference u_l are weighted and fused, and after saturation limiting (e.g., [u_min, u_max]), the result is output to the execution control module 106. Simultaneously, the system calculates stability evaluation indicators E_stab (e.g., amplitude variance, deviation integral, etc.) and feeds them back to the rule optimization module 105 for online updating of the fuzzy rule base and weight adjustment strategy.

[0055] In actual engineering implementation, various parameters (such as window length L, learning rate β, EWMA factor α, Lyapunov threshold V_th, filter factor Calibration and online adaptive optimization of various control modes (e.g., controller performance, and expert experience) can be performed based on on-site operating conditions, controller performance, and expert experience, with no strict restrictions. This solution can both cope with sudden shocks in smelting waste gas and maintain long-term stable operation, demonstrating its robustness and adaptability as a multimodal fusion control strategy.

[0056] The coupling compensation module 104 is configured to modify the control instruction amplitude in real time based on the multi-variable coupling strength using a gain-scheduled feedforward compensation mechanism, and transmit the modified instruction to the execution control module 106; It should be noted that the coupling strength is the degree of linear statistical correlation between parameters such as temperature, SO2 concentration, and dust flow rate in the exhaust system, which is different from the isolated control logic of single-parameter "self-feedback" (for example, SO2 concentration and dust flow rate increase at the same step due to slag impact, and the coupling strength between the two is high); the gain-scheduled feedforward compensation dynamically adjusts the feedforward control gain according to the coupling strength, which is different from the traditional "fixed gain feedforward" that cannot adapt to the time-varying coupling relationship (such as increasing the feedforward gain in a strong coupling scenario and maintaining the baseline gain in a weak coupling scenario); - The covariance matrix analysis method is a mathematical tool for quantifying the long-term statistical correlation characteristics of multiple parameters, which is different from the limitation of single-parameter "variance analysis" that can only characterize its own fluctuations (for example, the covariance matrix can simultaneously present the pairwise correlation between temperature and SO2, and SO2 and dust flow rate).

[0057] The multivariate coupling strength real-time calculation module (covariance matrix driven) is based on the covariance matrix analysis method to calculate the coupling strength of exhaust gas temperature, SO2 concentration and dust flow rate in real time. , construct the coupling coefficient matrix During operation, every time the dynamic weight fusion module outputs a new instruction (for example, a multimodal instruction set is generated every 200ms), the coupling strength calculation is triggered: 1) Data acquisition and preprocessing: Collect exhaust gas parameters within the current sliding window (the window length is 30 sampling points, calibrated based on parameter statistical stability, and can be adjusted according to actual conditions) and denoise the data (e.g., using median filtering to eliminate transient jumps caused by electromagnetic interference); 2) Covariance calculation: using the formula Quantization parameters and The coupling strength of . is the expected value of a random variable, used to quantify the long-term average characteristics of a parameter (e.g., calculating the correlation trend between SO2 concentration and dust flow rate within 30 minutes); and For any two parameters to be analyzed in the exhaust system (such as Take SO2 concentration, Take dust flow rate); 、 For parameters and The mean of the values ​​is used to eliminate the interference of dimensional differences on the calculation of coupling strength (e.g. the mean temperature is 200°C, the mean SO2 concentration is 150 ppm, and the fluctuation correlation is focused after subtracting the mean values).

[0058] 3) Matrix construction and scene adaptation: the coupling strength of all parameter pairs (such as temperature-SO2, SO2-dust flow rate, temperature-dust flow rate) integrated into the coupling coefficient matrix For example, in the slag impact scenario, SO2 concentration and dust flow rate increase simultaneously due to the particle entrainment effect, and the coupling strength between the two ( =0.9) (strong coupling); temperature and SO2 are related due to thermochemical reactions, and the coupling strength ( =0.6) (medium coupling).

[0059] (II) The module uses fuzzy cognitive graph to Mapping to the gain scheduling parameter space, using piecewise linear interpolation function to generate feedforward gain coefficients The operation logic is as follows: 1) Coupling interval determination: Based on process experiments and simulations, the strong coupling determination threshold is set to 0.8 (when ( >0.8), it is determined as a “strong coupling condition”, such as the simultaneous increase of multiple parameters caused by slag impact; when When the value is 0.8, it is judged as “weak / medium coupling condition”, such as the slow change trend of the adsorbent decay period); 2) Gain coefficient calculation: If 0.8< ≤1.0 (strong coupling range), using the formula Dynamically improve the feedforward gain. Among them, =0.5 is the base gain coefficient (default gain under weak coupling conditions), is the gain adjustment slope (controls the rate of increase of gain with coupling strength. The larger the slope, the more significant the gain improvement when coupling is strong. It can be adjusted according to the response capability of the actuator); if ≤0.8 (weak / medium coupling range), using the formula Maintain the reference gain to avoid overcompensation that may cause system oscillation.

[0060] 3) Scenario-based gain adaptation: Taking the slag impact scenario as an example, the coupling strength between SO2 concentration and dust flow rate =0.9, exceeding the threshold value 0.8), and substituting into formula (6) to obtain =0.5+2.0(0.9-0.8)=0.7, the feedforward gain is increased from the baseline 0.5 to 0.7, which enhances the compensation strength for strong coupling conditions; during the stable operation period of the adsorbent, the coupling strength of SO2 concentration and temperature is =0.6 (≤0.8), then =0.5, maintain the reference gain to ensure control stability.

[0061] (III) Gain weight allocation (parametric compensation driven by physical characteristics) module is based on the physical coupling mechanism of exhaust gas parameters, and adjusts the feedforward gain Perform weight distribution to generate targeted compensation gains for temperature-concentration and flow rate-concentration: 1) Temperature-concentration coupling gain : in is the temperature compensation factor (temperature increase will accelerate the SO2 catalytic reaction rate, but may reduce the activity of the adsorbent. It is necessary to increase the gain to enhance the temperature compensation for SO2 removal. The compensation factor The value range is 1.0~1.5, which can be calibrated according to the adsorbent temperature sensitivity experiment. For example, slag impact causes a sudden temperature rise (coupling strength =0.9, =0.7, then =0.7x1.2=0.84, the SO2 removal compensation of the spray system increases synchronously with the increase of temperature.

[0062] 2) Flow rate-concentration coupling gain : in =0.9 is the flow rate suppression factor (increasing the dust flow rate improves the mass transfer efficiency, but it is easy to cause the adsorbent to escape, and it is necessary to suppress excessive addition by reducing the gain. The suppression factor The value range is 0.8~1.0, and can be calibrated according to the adsorbent escape velocity experiment. For example, the turbulence in the pipeline causes a sudden increase in the dust flow rate (coupling strength =0.9, =0.7, then =0.63, the compensatory increase in adsorbent dosage is moderately reduced due to flow rate suppression, which prevents the adsorbent from being carried away by high-speed airflow after excessive dosage.

[0063] (IV) The feedforward superposition and limiting filtering (coordinated output of execution instructions) module superimposes the gain-corrected feedforward instruction with the feedback control quantity output by the dynamic weight fusion module (such as the feedback adjustment quantity of the cycle rate reference value) through the feedforward superposition mechanism, and outputs it to the actuator after limiting filtering: 1) Command superposition: Temperature-concentration compensation gain , flow rate-concentration compensation gain The corresponding feedforward instructions (such as spray increment, adsorbent dosage correction value) and the feedback control quantity (such as the circulation rate reference value based on the steady-state trend) are aligned by timestamp and then linearly superimposed (for example, if the feedforward instruction is a spray increment of 10% and the feedback control quantity is 20%, the output after superposition is 30%). 2) Limiting and filtering: The superimposed commands are amplitude-limited (e.g., spray volume commands are limited to 0%-100%, and adsorbent dosage is limited to 5kg / h-50kg / h, with limits calibrated based on the actuator's rated capacity) and high-frequency filtered (e.g., using a 100ms sliding average window to eliminate command oscillation). For example, if a transient high-gain command caused by slag impact reaches 110% after superposition, it will be output at 100% after limiting, preventing the actuator from operating over its range. High-frequency oscillating commands are filtered and output smoothly, ensuring the operational stability of equipment such as spray control valves and dosing pumps.

[0064] Formula (5) quantifies the long-term correlation characteristics of multiple parameters through the statistical logic of "expectation-mean correction", providing the core input of "coupling strength" for gain scheduling - the high coupling strength of SO2 and dust flow rate during slag impact drives the feedforward gain to increase, ensuring the compensation strength of control instructions in strong coupling scenarios; Formulas (6) and (7) achieve working condition adaptation of gain through "piecewise linear interpolation", increasing gain to strengthen compensation when coupling is strong, and maintaining baseline gain to ensure stability when coupling is weak, solving the problem of "insufficient compensation in strong coupling and excessive compensation in weak coupling" in traditional fixed gain feedforward. The gain weight distribution formula is based on the physical mechanism of "temperature promotes reaction and flow rate inhibits adsorption", and realizes directional compensation of coupling characteristics through compensation factors - SO2 removal compensation is enhanced when the temperature rises suddenly, and adsorbent addition is suppressed when the flow rate rises suddenly, so that the control instructions fit the multi-physical field coupling law of the exhaust gas system; the feedforward superposition and limiting filtering link, through the full process processing of "time base alignment-linear superposition-amplitude constraint-high-frequency filtering", ensures that the execution instructions not only respond to the dynamic changes of multi-parameter coupling, but also meet the physical constraints of the actuator (such as range, vibration threshold).

[0065] The rule optimization module 105 is used to construct a multi-objective reward function based on the desulfurization efficiency, dust escape, and energy consumption data of the working condition labels and execution feedback. It uses a dual deep Q network reinforcement learning strategy to iteratively optimize the fuzzy rule trigger threshold and weight coefficient, and maps the optimized parameters to the membership reconstruction module 102 to drive the coordinated update of the rule base and membership function parameters. In a possible implementation process, the rule optimization module 105 performs the following operations: 1) The system first obtains a variety of working condition labels in real time from on-site sensors and process information management systems, such as furnace temperature, furnace pressure, reducing gas composition, and number of cycles. These labels can be converted into one-dimensional numerical vectors through unique hot encoding or embedded vectors. The length of the vector is determined by the type of labels contained. The specific length can be set according to the on-site working conditions and there is no limit on this. At the same time, the system also records the difference between the actual desulfurization efficiency and the set target efficiency, the accumulated dust escape in the current cycle, and the fluctuation of energy consumption per unit time. In order to unify the scale, these feedback data are mapped to between zero and one or between negative one and one, and can be processed using minimum-maximum normalization or standard deviation normalization, and there is no limit on this.

[0066] 2) The operating condition label vector and the feedback data vector are combined to form a high-dimensional original state vector. Directly inputting this high-dimensional data into the deep network increases computational overhead and is prone to overfitting. Therefore, principal component analysis (PCA) is used to reduce the dimensionality of the original state. PCA calculates the covariance structure of historical data to extract a small number of "core features" that explain at least 90% of the cumulative variance. These core feature vectors retain the majority of critical information while significantly reducing the network input dimensionality, facilitating subsequent deep learning network training and online deployment. The proportion of principal components retained and the number of selected features can be flexibly set based on the amount of field data and system response requirements, and there is no set limit.

[0067] 3) Based on the extracted core features, the module constructs a pair of mutually referential deep Q networks: an online network and a target network. The online network is used to instantly evaluate the value of various "adjustment plans," while the target network uses a lower update frequency to stabilize the training process.

[0068] Candidate adjustment options include fine-tuning the trigger threshold of each fuzzy rule, increasing or decreasing the fuzzy rule weights, and making small adjustments to the center position and width of the membership function. For example, the trigger condition for temperature error determination could be adjusted within plus or minus half a degree, or the width of the membership function could be increased or decreased within 5 percent of the current width. The specific adjustment options can be determined based on the sensitivity and response speed of the on-site system and are not limited.

[0069] At each decision, the system randomly selects an adjustment option for "exploration" with a certain probability, and prioritizes the option with the highest current value for "exploitation" with the remaining probability. This balanced strategy between exploration and exploitation ensures the opportunity to discover superior options while accelerating overall convergence. The exploration probability changes with the number of iterations, and can be adjusted using either exponential decay or nonlinear increments, with no specific restrictions.

[0070] Each time an adjustment plan is tried, the system calculates multi-objective immediate rewards based on real-time feedback and stores this sample (including core features, the selected plan, immediate rewards, and core features for the next cycle) in the experience replay pool. The replay pool uses a preferential sampling mechanism, replaying samples with large errors or that contribute significantly to policy improvement more frequently to improve training efficiency and stability.

[0071] The online network parameters are continuously updated through the mini-batch gradient descent method, while the target network is periodically "soft updated" - that is, the latest parameters of the online network are synchronized to the target network in a smaller proportion, thereby ensuring the smoothness of the target estimation and avoiding training instability caused by frequent updates.

[0072] 4) The immediate reward function integrates three sub-goals: improving desulfurization efficiency, suppressing dust emissions, and reducing energy costs. The system first constructs a decision matrix based on the three dimensions of improved desulfurization efficiency, dust suppression ratio, and unit energy cost. It then uses the entropy weighting method to automatically calculate the importance weights for each dimension. These weights can be combined with expert experience or entirely data-driven, with no restrictions. The TOPSIS method is then used to generate a comprehensive evaluation score for each adjustment solution by comparing its distance to the best and worst ideal solutions. Based on this, the target network uses a probability distribution-based strategy (such as a probability distribution derived from Q-values ​​or the Boltzmann strategy) to select the most promising solutions from the "Pareto optimal solution set" as candidate outputs for the module in this round.

[0073] 5) The final selected solution, namely a set of updated fuzzy rule trigger thresholds and membership function parameters, is passed to the "Membership Reconstruction Module 102." This module re-adjusts the membership functions of each input variable under different fuzzy subsets based on these new parameters, enabling subsequent fuzzy reasoning to generate more optimal control variables based on the latest field conditions and historical experience. Simultaneously, the Rule Optimization Module 105 synchronizes the evaluation indicators and rule modification records from this round of optimization to the system monitoring and log analysis sub-platform, providing intuitive basis for experts to conduct subsequent strategy tuning and system maintenance.

[0074] The execution control module 106 is responsible for driving the circulation fan, adsorbent metering pump, and heat exchanger valves for dynamic control and real-time feedback of actuator response data to the rule optimization module 105. Specifically, the execution control module 106 first maps the three primary control variables derived from the fusion command: the "circulation rate baseline value," the "adsorbent dosage," and the "heat exchanger inlet and outlet water temperature difference." Upon receiving a new circulation rate baseline value, the controller calculates the fan speed adjustment, i.e., the change from the current fan speed to the target speed. To ensure a smooth transition between pipe network pressure and flow, the module typically incorporates a "ramp rate generator." This generator breaks down large instantaneous commands into several small, equal-amplitude steps based on preset maximum acceleration and deceleration ramps (e.g., fan speed changes of no more than 100 revolutions per minute). This ramp rate can be implemented using a linear or exponential function, such as an exponential inertia function: after a set response time τ, the fan speed can reach 63% of the command value, meeting industrial control requirements for low overshoot and low oscillation. The response time τ depends on the rotational inertia of the fan and its motor and the driver characteristics. It can be empirically calibrated or identified online based on the equipment nameplate and test results, and is not limited to this.

[0075] For the adsorbent metering pump, the execution control module 106 needs to convert the "dosage reference" into the pulse width or frequency signal of the pump. Generally, pulse modulation (PWM) or frequency modulation (FM) is used. For example, when the target dosage increases from the current 50 kg per hour to 60 kg per hour, the system will calculate the required percentage change in pump speed and smoothly transition from the original 45% to 54% through the PWM duty cycle. During the transition process, in order to avoid cavitation of the pump body or sudden changes in the pressure of the chemical feed pipeline, the module usually limits the duty cycle change rate to no more than 5% / second each time, and monitors the actual return pressure and flow feedback of the pump online. When the return pressure is detected to deviate from the normal range (for example, exceeding 0.2 MPa), the PWM ramp is immediately paused and an alarm is issued. At the same time, the abnormal data is fed back to the rule optimization module 105 for subsequent fault diagnosis and strategy adjustment.

[0076] For heat exchanger valve regulation, the execution control module 106 outputs a standard 4–20mA or 0–10V analog signal based on the heat exchanger's inlet and outlet temperature differential or energy-saving indicators, driving the control valve to the corresponding opening. The module internally sets the valve's minimum open and maximum closed positions (e.g., an opening range of 5%–95%) and maps the integrated temperature difference target value to the corresponding opening percentage. To improve temperature control accuracy, the execution control module 106 can also incorporate a first-order inertia compensation model. When the target temperature difference experiences a large jump, the module first calculates an intermediate target opening with hysteresis. It then applies deadband compensation (e.g., opening changes below 2% do not trigger valve movement) and full-scale nonlinear mapping (taking into account the valve's opening and closing characteristics). This ensures that the valve does not frequently actuate due to small fluctuations, nor does it top out due to large commands, causing fluid pulsation.

[0077] After the action is issued, the execution control module 106 collects the response data of each actuator in real time via a high-speed data bus (such as EtherCAT, Profinet, or ModbusTCP). For example, it reads the current speed, output current, and casing vibration value from the fan inverter; the actual pump speed, motor load, and return pressure from the metering pump driver; and the current opening, driver current, and valve stem displacement sensor feedback from the valve positioner. The acquisition frequency can be set according to control requirements, generally between 50Hz and 200Hz, to capture fast dynamics while limiting communication bandwidth usage. The specific frequency depends on the performance of the field network and controller and is not limited.

[0078] The execution control module 106 performs closed-loop performance evaluation on various feedback data, including quantitative calculations of command response time, steady-state error, overshoot, and small-signal jitter. For example, the command response time of a fan is defined as the time required from the issuance of a speed command to the actual speed reaching 95% of the set value; the steady-state error is defined as the long-term average deviation between the command value and the actual value; and the overshoot is the peak ratio of the actual speed exceeding the target speed after the first-order inertial response. Similar indicators can be calculated for valves and pumps. The execution control module 106 encapsulates these performance data into feedback vectors and transmits them to the rule optimization module 105 together with the current control command to form a state-action-feedback sample to drive the online update of the reinforcement learning strategy.

[0079] During the execution and feedback process, several abnormality monitoring logics are also running inside the module to guarantee safety and reliability. For example, when the fan output current continuously exceeds 110% of the rated value for more than 5 seconds, or the vibration value exceeds the set threshold (such as 3 mm / s), it is considered as a possible mechanical failure or pipe blockage, and the control module 106 will immediately issue an "emergency load shedding" instruction to reduce the fan speed to 70% of the rated value, and generate an alarm information to push to the upper maintenance system and operator interface; At the same time, the event is sent as a negative feedback to the rule optimization module 105 for adjusting the fuzzy rule trigger threshold to avoid similar faults caused by repeated control strategies. Such abnormality monitoring thresholds and response strategies can be set according to equipment specifications and safety regulations, and are not limited.

[0080] The execution control module 106 often combines transfer functions and state space models to achieve accurate modeling of the dynamic characteristics of actuators. For example, the fan and pipe network can be regarded as a second-order inertial system, and the transfer function form is the ratio of the output speed to the input frequency signal with two time constants; The metering pump can be described by a first-order inertia plus pure lag model, and the lag time corresponds to the length of the chemical agent delivery pipeline and the fluid flow rate; The regulating valve can be described by a compensation model containing dead zone and saturation nonlinearity. In actual software implementation, the module will load the corresponding transfer function model parameters for each execution channel, and online calculate the residual error between the model predicted output and the actual feedback, which is used for dynamic compensation and predictive control to improve the system's ability to suppress secondary disturbances such as pipeline nonlinearity and back pressure fluctuations.

[0081] The behavior of the entire execution control module 106 is closely coupled with other modules of the system: when the rule optimization module 105 proposes new fuzzy rule trigger thresholds or membership function parameters, the execution control algorithm will recalculate the fuzzy reasoning conclusions corresponding to each input according to the updated membership function curve, thereby adjusting the final expected execution value; At the same time, when the steady-state trend decision model and the dynamic weight fusion algorithm generate new multi-modal instructions, the execution control module 106 will implement different control strategies for the three types of actuators respectively - the fan executes ramp speed regulation, the metering pump executes duty cycle or frequency modulation, and the valve executes opening mapping - to ensure the best balance between transient compensation and steady-state control. By feeding back the actual response data of the actuators to the rule optimization module 105 in real time, the system can continuously iterate in a closed loop, gradually improving desulfurization efficiency, reducing dust emissions, and optimizing energy consumption levels.

[0082] While specific embodiments of the application have been described above, it will be appreciated that those skilled in the art within the scope of the application can make modifications, substitutions and changes in the methods and systems described above without departing from the spirit and essential characteristics of the application. For example, acts recited in the foregoing method steps in combination, in the same or an equivalent method, for carrying out the same functions to achieve the same results while maintaining the essential characteristic of that which is recited are within the scope of this application. Accordingly, the scope of the application is to be construed in accordance with the appended claims rather than read expansively with reference to the description.

Claims

1. A smelting waste gas recycling optimization system based on fuzzy control; characterized by: include: The sensor acquisition module is used to collect parameters such as smelting waste gas temperature, sulfide concentration, dust flow rate, and ambient humidity. It uses anti-aliasing filtering and sliding mean filtering to suppress high-frequency noise and eliminate transient interference in the raw data, generating a standardized time series data stream. The membership reconstruction module is used to extract the mean, variance and kurtosis characteristics of the collected parameters based on the sliding window statistical analysis method, and dynamically divide the working condition intervals through the incremental fuzzy clustering algorithm; A historical data weight distribution mechanism is used to separate steady-state features from transient features, and an adaptive membership function model of the input variables is constructed. The membership function center point offset and coverage range are dynamically adjusted according to real-time operating condition changes. Dynamic fuzzy parameters are output to the feature decoupling module, and the operating condition labels are transmitted to the rule optimization module. A feature decoupling module is used to separate the dynamic fuzzy parameters using a wavelet packet transform method to obtain a high-frequency transient component and a low-frequency trend component; and to perform fuzzy reasoning on the high-frequency transient component through a short-time impulse response fuzzy reasoning mechanism to generate a transient compensation instruction; and to perform fuzzy decision-making on the low-frequency trend component through a steady-state trend fuzzy decision-making model to generate a steady-state reference control variable; The multi-scale control instructions are integrated through the dynamic weight fusion algorithm to generate a multi-modal instruction set containing the circulation rate reference value and the adsorbent dosage main control parameters, and output it to the coupling compensation module; A coupling compensation module is used to correct the control instruction amplitude in real time based on the multi-variable coupling strength using a gain-scheduled feedforward compensation mechanism, and transmit the corrected instruction to the execution control module; The rule optimization module is used to construct a multi-objective reward function based on desulfurization efficiency, dust escape, and energy consumption data from operating condition labels and execution feedback. It uses a dual-deep Q-network reinforcement learning strategy to iteratively optimize the fuzzy rule trigger thresholds and weight coefficients, mapping the optimized parameters to the membership reconstruction module to drive the coordinated update of the rule base and membership function parameters. The execution control module is used to drive the circulation fan, adsorbent metering pump and heat exchanger valve to perform dynamic regulation, and collect actuator response data in real time and feed it back to the rule optimization module.

2. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The working condition interval division method of the incremental fuzzy clustering algorithm is: S1. Based on the cluster center of the previous moment and the current window characteristics, the improved membership calculation formula is used to calculate the membership. The calculation formula is: （1） In formula (1), Indicates the Data points for The degree of membership of the cluster; is the fuzzy index, which is used to control the fuzziness of membership; is the statistical feature vector at the current moment; and Respectively Hedi The center vector of each cluster; is the total number of clusters; is the Euclidean distance norm; S2, based on time decay factor Correct the historical membership weight, the formula is: （2） In formula (2), is the updated membership degree; is the historical membership value; is the currently calculated membership; time decay factor The expression is ,in is the attenuation coefficient, is the data time interval; S3. Dynamically update the cluster center based on the data membership and statistical characteristics in the window. The update formula is: （3） In formula (3), After the update Cluster center; Before the update Cluster center; For the window The feature vector of each data point; is the sliding window length; is the historical center weight coefficient, which is used to balance the influence of new and old data; if the center With the original center If the Euclidean distance exceeds the preset cluster drift threshold, the cluster splitting mechanism is triggered and a temporary cluster is added. , and reset The degree of membership is the entropy value of the data distribution within the window; S4. Calculate the mean membership of the current window data to each cluster center ; The expression is: ,choose The cluster number corresponding to the maximum value is used as the working condition label and output to the rule optimization module to drive the dynamic adjustment of the threshold.

3. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The adaptive membership function model constructs a double exponential membership function for the temperature parameter, the center point is calculated by the weighted sliding average of the historical mean and the current window mean, and the coverage range dynamically expands or shrinks according to the variance value; the adaptive membership function model adopts an asymmetric Gaussian membership function model for the sulfide concentration parameter, the right width is associated with the first-order derivative of the concentration change rate, and the left width is associated with the historical concentration distribution entropy value.

4. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The working principle of the wavelet packet transform method is: The optimal basis function is selected from the wavelet basis function library based on the kurtosis maximization method. The kurtosis maximization method selects the db4 basis when the signal kurtosis value is higher than the preset threshold, otherwise the sym5 basis is selected to balance the time-frequency positioning ability; The approximate entropy of the signal in the sliding window is weighted with the sample entropy to obtain a complexity index, and when the complexity index exceeds a preset threshold, a three-layer decomposition mode is triggered, otherwise a two-layer decomposition mode is adopted to match the non-stationary characteristics of the signal; The decomposed sub-band nodes are screened by energy entropy threshold. If the node energy entropy is lower than the preset noise threshold, it is eliminated and the effective frequency band node coefficient is retained. The high-frequency node coefficients and low-frequency node coefficients are reconstructed into transient impact components and steady-state trend components respectively through an improved dual-channel reconstruction algorithm. The transient impact component uses a compactly supported rectangular window function to intercept the short-term peak value, and the steady-state trend component uses a sliding average filter to extract the long-term drift trend. The improved dual-channel reconstruction algorithm uses a dynamic threshold compression noise reduction method to set the node energy entropy of the high-frequency detail node coefficient to zero when it is lower than the noise baseline. The baseline drift of the low-frequency approximation node coefficient is eliminated by sliding window energy normalization; and the reconstruction weight coefficient is dynamically allocated based on the frequency band mutual information entropy, where the high-frequency channel weight , low-frequency channel weight ,in 、 are the high frequency sub-band energy and the low frequency sub-band energy respectively.

5. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The short-term impulse response fuzzy inference mechanism intercepts the transient waveform data 100ms before the current moment through a sliding window mechanism, and uses an extreme point detection algorithm to extract the impulse amplitude, rising edge slope, and duration to form an instantaneous feature vector. The feature vector is then matched in real time based on a dynamic fuzzy rule base. If the impulse amplitude exceeds twice the standard deviation of the historical mean, an emergency compensation method is used to narrow the width of the Gaussian membership function to 50% of the original value. The gradient weighted fuzzy inference method is then used to calculate the spray increment instruction. The compensation weight factor is adjusted according to the product of the rising edge slope and the duration, and the instantaneous spray compensation amount is generated by integrating the impulse amplitude membership. At the same time, the compensation instruction is superimposed on the steady-state reference control quantity through the timestamp alignment mechanism and output to the dynamic weight fusion algorithm.

6. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The working principle of the steady-state trend fuzzy decision model is: The sliding window adaptive statistical analysis method is used to extract the mean and variance of the time series as the trend feature vector, and the historical data is smoothed by the exponentially weighted moving average algorithm; Based on a multidimensional membership function reconstruction mechanism, the center point and width of the Gaussian membership function are dynamically adjusted according to the low-frequency component energy proportion. The adjustment method is to calculate the low-frequency component energy proportion through a sliding window and map the energy proportion interval based on the fuzzy cognitive map rules. If the energy proportion is in the high-energy state, the center point of the membership function is shifted to the right. If it is in the low energy state interval, it shifts to the left to match the downward trend of the baseline; A fuzzy cognitive graph inference engine is used to construct a steady-state rule base. Trend feature vectors are mapped to fuzzy linguistic values ​​of control targets including circulation rate and adsorbent dosage. If the variance of three consecutive windows is below a preset threshold, the long-term stability association rule is preferentially activated through a fuzzy rule weight decay mechanism. This fuzzy rule weight decay mechanism exponentially decays the weights of historical fuzzy rules based on a time decay factor, prioritizing the activation of short-term perturbation association rules. At the same time, an ε-greedy strategy in reinforcement learning is used to dynamically increase the weight of rules strongly associated with temperature baseline drift and gradual changes in adsorption efficiency, allowing the rule base to focus on maintaining process stability. The attenuation coefficient of the ε-greedy strategy increases nonlinearly with the number of windows; The entropy weight of the association rule activation degree is calculated by the entropy weight method, and the steady-state reference control quantity is generated by combining the center of gravity method for defuzzification. The timestamp alignment mechanism is used to superimpose the compensation instructions and then output to the dynamic weight fusion algorithm.

7. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The working principle of the dynamic weight fusion algorithm is: A multimodal weight vector is constructed based on the peak intensity of the transient compensation command within the time domain sliding window, the trend slope of the steady-state reference control variable, and the exhaust gas parameter covariance matrix. The dynamic entropy value of the instantaneous energy proportion of the high-frequency transient component and the variance of the low-frequency trend component are calculated using the entropy weight method. If the high-frequency energy ratio exceeds 2 standard deviations of the historical mean, the entropy increase rule is triggered and the transient weight is increased according to the adaptive coefficient λ. , and calculate the gradient direction of the weight combination based on the Lyapunov stability function , the formula expression is: （4） In formula (4), is the Lyapunov function; is the weight of the high-frequency transient component; is the weight of the low-frequency steady-state component; is the correlation coefficient between weights, ranging from [−1,1], which is used to adjust the coupling relationship between high-frequency and low-frequency weights: When ρ > 0, the high-frequency and low-frequency weights are positively correlated, suppressing the conflict between weights; when ρ < 0, the weights are adjusted complementary; When detected , that is, when the system tends to be unstable, the weight distribution is corrected along the negative gradient projection; and the weight time series is smoothed and filtered through the exponential decay factor. If the weight change rate of adjacent cycles exceeds the preset threshold, the jump is suppressed through the inertia compensation mechanism; The corrected instructions are transmitted to the execution control module after saturation limiting processing, and the stability evaluation index is simultaneously fed back to the rule optimization module to drive the online update of the fuzzy rule base.

8. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The working principle of the gain-scheduled feedforward compensation mechanism is: First, the exhaust gas temperature, Coupling strength between concentration and dust velocity , construct the coupling coefficient matrix ; The coupling strength index The calculation formula is: （5） In formula (5), It represents the expected value of a random variable and is used to quantify the long-term average characteristics of the variable; and For exhaust system Random variables of concentration and dust velocity; 、 For variables and Then, through the fuzzy cognitive map, Mapped to the gain scheduling parameter space, the feedforward gain coefficients are mapped using a piecewise linear interpolation function , the formula is: If 0.8< ≤1.0, then (6) like ≤0.8, then (7) In formulas (6) and (7), =0.8, indicating the strong coupling judgment threshold; =0.5, indicating the reference gain coefficient; , represents the gain adjustment slope, which is used to control the growth rate of gain with coupling strength; based on the feedforward gain coefficient, the gain weight is distributed, and the temperature concentration coupling gain for: ;in , represents the temperature compensation factor; velocity concentration coupling gain for: ;in =0.9, which represents the flow rate suppression factor; finally, the gain-corrected feedforward instruction is superimposed on the feedback control quantity through the feedforward superposition mechanism, and is output to the actuator after limiting filtering.

9. The smelting waste gas recycling optimization system based on fuzzy control according to claim 1 is characterized by: The dual-deep Q-network reinforcement learning strategy achieves dynamic iterative optimization of the fuzzy rule base through an online network and a target network. The online network constructs a multidimensional state feature space based on the desulfurization efficiency deviation, dust accumulation escape, and energy consumption fluctuation coefficient of the real-time working condition label encoding vector and the execution feedback. The core feature vector is extracted through principal component analysis and dimensionality reduction, and then input into a fully connected layer to generate a set of candidate actions. The target network calculates the action value function based on the temporal difference error and uses the Boltzmann strategy to screen the Pareto optimal solution set. The experience replay pool of the dual-deep Q-network reinforcement learning strategy uses a priority sampling mechanism to extract historical state transition data. The online network parameters are updated using a mini-batch gradient descent method, and the target network parameters are synchronized using a periodic soft update strategy. Finally, the multi-objective reward function is decoupled into three sub-objectives: desulfurization efficiency gain, dust suppression rate, and energy consumption cost through an entropy weight method-TOPSIS hybrid evaluation model. After constructing a weighted decision matrix, the weights of the dynamic association rules in the fuzzy cognitive graph are combined with the sub-objective contribution, and the optimized rule trigger thresholds and membership function parameters are output to the membership reconstruction module.

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