A method for controlling the skimming of a molten aluminium furnace

Abstract

This invention belongs to the field of automatic control technology for non-ferrous metal smelting processes, and particularly relates to a slag removal control method for aluminum melting furnaces. The method involves acquiring multi-point temperature timing signals at different depths within the furnace wall, oxygen partial pressure signals from the furnace flue gas, and force signals at the end of the slag removal robotic arm; determining the slag layer thickness distribution on the surface of the molten aluminum in the furnace; calculating the integral exponent of the oxide film energy release rate and the evidence distance conflict degree; generating a slag removal trigger signal when the integral exponent is greater than or equal to the critical energy release rate and the conflict degree is lower than a preset conflict threshold; determining the slag removal path that minimizes the resistance work functional; calculating the optimal vibration frequency and amplitude in real time and controlling the vibration of the slag removal plate to promote the desorption of molten aluminum from the slag layer pores; and simultaneously determining whether the slag removal termination condition is met based on the real-time updated slag layer thickness distribution and force signals. This method overcomes the shortcomings of traditional direct-view optical sensors, which are susceptible to interference from smoke, strong light, and high temperatures, providing a reliable sensing basis for slag removal decision-making and path planning.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology for non-ferrous metal smelting processes, and particularly relates to a slag removal control method for aluminum melting furnaces. Background Technology

[0002] In the smelting of aluminum and aluminum alloys, the oxide slag continuously generated on the surface of the molten aluminum must be removed in a timely manner, otherwise it will seriously affect the purity of the melt and the performance of the product. Existing slag removal control methods mainly rely on manual experience, fixed timing, or direct-view optical sensors for slag layer thickness detection and decision-making. Direct-view sensors such as lasers and infrared sensors are easily interfered with by high-temperature flue gas, dust, and strong light radiation in the furnace, resulting in poor robustness of slag layer thickness measurement. The timing of slag removal is based solely on instantaneous slag layer thickness or timed judgment, lacking consideration of the mechanical nature of oxide film fracture, often leading to delayed slag removal and oxide entrainment in the melt. The slag removal path uses a fixed trajectory, failing to consider the non-Newtonian shear thinning rheological characteristics of the slag-aluminum mixture and the influence of path curvature on resistance, resulting in high energy consumption and easy to cause violent fluctuations in the liquid level. The aluminum loss during slag removal lacks active separation methods based on capillary adhesion and seepage mechanisms, relying solely on experience to adjust the tilt angle, resulting in low metal recovery. The model parameters rely on offline calibration and cannot be adaptively adjusted according to changes in alloy grade, furnace temperature, and furnace age, leading to a decline in control quality over long-term operation.

[0003] Therefore, there is a need for an intelligent slag removal control method that can achieve online inversion of the entire slag layer thickness through robust indirect sensing, accurately determine the timing of slag removal based on the oxide film energy release mechanism, plan the optimal path by integrating a non-Newtonian rheological model, actively suppress aluminum loss by utilizing vibration seepage, and has the ability to adapt parameters across operating conditions. Summary of the Invention

[0004] This invention addresses the technical problems existing in the slag removal control method of aluminum melting furnaces by proposing a reasonable, simple, and theoretically sound slag removal control method for aluminum melting furnaces.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] S1. Acquire multi-point temperature timing signals at different depths inside the aluminum melting furnace wall, oxygen partial pressure signals of the furnace flue gas, and force signals at the end of the slag removal robotic arm.

[0007] S2. Use the multi-point temperature timing signal as input to estimate the slag layer thickness distribution on the surface of the molten aluminum in the furnace;

[0008] S3. Based on the slag layer thickness distribution and the furnace flue gas oxygen partial pressure signal, calculate the integral index of oxide film energy release rate and calculate the evidence distance conflict degree of multiple information sources regarding the proposition of slag removal timing. When the integral index is greater than or equal to the critical energy release rate and the conflict degree is lower than the preset conflict threshold, generate a slag removal trigger signal and proceed to step S4 for slag removal path planning. When the integral index is less than the critical energy release rate and the conflict degree is higher than the preset conflict threshold, return to step S2 to continue collecting temperature data and oxygen partial pressure data for the next sampling cycle, recursively update the slag layer thickness distribution, and recalculate the integral index of oxide film energy release rate and evidence distance conflict degree, and enter the next round of judgment cycle.

[0009] S4. In response to the slag removal trigger signal, construct a resistance work functional including a non-Newtonian shear stress term and a path curvature penalty term. With the constraint of removing all slag layers with a thickness exceeding a set value, solve the slag removal path that minimizes the resistance work functional using the variational adjoint method.

[0010] S5. During the movement along the slag removal path, the optimal vibration frequency and optimal amplitude are calculated in real time according to the porous media vibration seepage separation model, and the slag removal plate is controlled to vibrate at the optimal vibration frequency and optimal amplitude to promote the desorption of aluminum liquid from the slag layer pores. At the same time, the integral index of the oxide film energy release rate, the evidence distance conflict degree, and the force signal at the end of the slag removal robot arm calculated in real time in step S3 are continuously monitored. When the integral index of the oxide film energy release rate is lower than the preset safety threshold, the evidence distance conflict degree is lower than the preset conflict threshold, and the force signal meets the no-load condition, it is determined that the slag removal termination condition is met, and the slag removal is ended in advance.

[0011] Preferably, the calculation formula for estimating the slag layer thickness distribution on the surface of the molten aluminum in the furnace in step S2 is as follows:

[0012] , , ,in, For the first Estimated slag layer thickness at each sampling time. This represents the measured temperature vector of multiple thermocouples within the furnace wall. Let be the slag layer thickness distribution vector to be solved. This is the temperature self-evolution matrix. For the first A vector composed of the temperature values ​​at all thermocouple measuring points inside the furnace wall at each sampling time. This is the slag layer thickness-temperature sensitivity matrix. For steady-state bias vector, To observe the noise covariance matrix, Let be the prior bias vector. The prior prediction error covariance matrix, For regularization parameters, For total variational regularization, The spatial gradient of slag layer thickness. This is an estimate of the slag layer thickness from the previous moment. The oxidation rate coefficient is... The sampling period is It is a nonlinear oxidation enhancement factor determined by oxygen partial pressure and melt temperature. For the efficiency of slag removal. This is the indicator vector for the slag cover grid in the previous time period. For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number Thickness of slag layer at the grid line.

[0013] Preferably, the formula for calculating the integral index of the oxide film energy release rate in S3 is as follows: , , , ,in, For the first The integral exponent of oxide film energy release rate at each sampling time For the first The integral exponent of oxide film energy release rate at each sampling time The rate of increase in slag surface density, For the internal stress of the slag film, The effective elastic modulus of the slag film, The sampling period is The pre-exponential factor for the oxidation reaction rate. The activation energy for the oxidation reaction. This is the universal gas constant. For the first The absolute temperature of the molten aluminum at any given time. For the first The oxygen partial pressure of the flue gas in the furnace at all times. The oxygen partial pressure index represents the oxidation reaction. Due to the difference in the coefficients of thermal expansion between oxide slag and molten aluminum, The temperature difference between the surface and the bottom of the slag film. For the first Total variation of slag layer thickness distribution at any given moment. The surface tension of molten aluminum, The average curvature of the liquid surface fluctuation. The porosity of the slag layer, The porosity-affected index, For reference temperature, The thermal softening characteristic temperature is used as the formula for calculating the degree of conflict of the evidence distance:

[0014] ,

[0015] , ,

[0016] in, For the first The degree of conflict between the evidence at each sampling time The total number of information sources. For the first The information source in the first The basic probability assignment vector at each sampling time. Jensen-Shannon divergence measures the difference in probability distribution between information sources and fusion centers. For the first Dynamic credibility weights for each information source As a weighted fusion center, The information entropy of the fusion result, This is the integral index of the current oxide film energy release rate. The critical energy release rate. For the first The recent prediction accuracy score of each information source. To prevent the coefficient from being zero.

[0017] Preferably, the formula for calculating the optimal slag removal path in S4 is:

[0018] ,

[0019] ,

[0020] in, The optimal path for removing slag. For the slag removal path curve, Let be the total arc length of the path. For information Riemannian metric tensor fields, The unit tangent vector of the path at the th... Components of coordinate direction, The unit tangent vector of the path at the th... Components of coordinate direction, For vertical coordinate index, For horizontal coordinate index, The longitudinal coordinate of the furnace is... The horizontal coordinate of the furnace is... The consistency coefficient of the slag-aluminum mixture. To estimate the mean field of slag layer thickness, For power-law rheological exponent. For uncertainty avoidance coefficient, To estimate the mean field of slag layer thickness, The symbol for Kronecker. This is the curvature tendency coefficient.

[0021] Preferably, the formula for calculating the optimal vibration frequency in S5 is:

[0022] ,

[0023] in, To achieve the optimal vibration frequency, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. The current sampling time The thickness of the local slag layer at the slag removal location, The dynamic viscosity of molten aluminum. Given the slag layer permeability, the formula for calculating the optimal amplitude is:

[0024] ,

[0025] in, For the optimal vibration amplitude, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. To achieve the optimal vibration frequency, The current sampling time The thickness of the local slag layer at the slag removal location. The dynamic viscosity of molten aluminum. This represents the permeability of the slag layer.

[0026] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0027] 1. By acquiring multi-point temperature time-series signals at different depths within the furnace wall, and using these signals as input to estimate the slag layer thickness distribution on the surface of the molten aluminum in the furnace, the defects of traditional direct-view optical sensors, which are susceptible to interference from smoke, strong light, and high temperatures, are overcome. This enables non-contact, highly robust online inversion of the entire slag layer thickness, providing a reliable sensing basis for slag removal decisions and path planning.

[0028] 2. A joint slag removal decision mechanism based on the integral index of oxide film energy release rate and the degree of conflict of evidence distance predicts the best slag removal time from the essence of oxide film fracture mechanics. By quantifying the consistency of multi-source information, the risk of false triggering by a single criterion is eliminated, which significantly improves the accuracy of slag removal timing and the reliability of decision-making.

[0029] 3. In the slag removal path planning, a resistance work functional containing non-Newtonian shear stress terms and path curvature penalty terms is constructed, and the slag removal path that minimizes this functional is solved by the variational adjoint method. This enables the path to automatically adapt to the non-Newtonian rheological properties of the slag-aluminum mixture and the spatial distribution of slag layer thickness, thereby reducing slag removal resistance and energy consumption and minimizing liquid surface fluctuations. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of a slag removal control method for an aluminum melting furnace. Detailed Implementation

[0032] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0033] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0034] Examples, such as Figure 1As shown, multi-point temperature time-series signals at different depths within the aluminum melting furnace wall, oxygen partial pressure signals from the furnace flue gas, and force signals from the end of the slag-removing robotic arm are acquired. These multi-point temperature time-series signals are used as input to solve for the slag layer thickness distribution on the surface of the molten aluminum in the furnace. This step involves acquiring temperature time-series signals using multi-point thermocouples embedded at different depths within the furnace wall. Using these multi-point thermocouple temperature time-series signals as input to solve for the overall slag layer thickness distribution aims to avoid severe interference from high-temperature flue gas, flame radiation, and dust within the aluminum melting furnace on the direct-view optical sensor, indirectly sensing the slag layer thickness through contact temperature measurement. This scheme provides stable signals, is unaffected by strong light and dust, exhibits high robustness, and can achieve millisecond-level real-time updates of the overall slag layer thickness using a surrogate model for acceleration and online recursion. It also includes estimations of the variance of each grid to provide objective confidence for subsequent decisions. This solves the problems of inaccurate measurement, incomplete spatial coverage, and insufficient response speed of traditional slag layer thickness detection methods under harsh furnace conditions, providing a reliable and high spatiotemporal resolution sensing foundation for intelligent slag removal control. The formula for calculating the slag layer thickness distribution on the surface of the molten aluminum in the furnace is:

[0035] , , ,

[0036] in, For the first Estimated slag layer thickness at each sampling time. This represents the measured temperature vector of multiple thermocouples within the furnace wall. Let be the slag layer thickness distribution vector to be solved. This is the temperature self-evolution matrix. For the first A vector composed of the temperature values ​​at all thermocouple measuring points inside the furnace wall at each sampling time. This is the slag layer thickness-temperature sensitivity matrix. For steady-state bias vector, To observe the noise covariance matrix, Let be the prior bias vector. The prior prediction error covariance matrix, For regularization parameters, For total variational regularization, The spatial gradient of slag layer thickness. This is an estimate of the slag layer thickness from the previous moment. The oxidation rate coefficient is... The sampling period is It is a nonlinear oxidation enhancement factor determined by oxygen partial pressure and melt temperature. For the efficiency of slag removal. This is the indicator vector for the slag cover grid in the previous time period. For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number The slag thickness at each grid point is calculated. The slag thickness calculation formula uses the measured temperature vectors of multiple thermocouples on the furnace wall as the observation input, physically bypassing the interference of smoke and strong light on the direct-view optical sensor. A physical mapping from the slag thickness at each grid point to the temperature at each measurement point is established by multiplying the slag thickness-temperature sensitivity matrix by the slag thickness distribution vector to be solved. A steady-state bias vector is used to separate the baseline contribution of non-slag thickness factors such as aluminum melt isothermal control to the wall temperature, avoiding interference from melt temperature adjustment on the inversion. The inverse of the observation noise covariance matrix is ​​used to perform Mahalanobis distance weighting on each thermocouple channel; channels with high signal-to-noise ratios automatically receive high weights, while faulty channels are automatically weighted lower. A priori bias vector is used to measure the difference between the current estimate and the slag thickness estimate from the previous moment, after considering the oxidation rate coefficient, sampling period, oxygen partial pressure, and temperature. The difference between the nonlinear oxidation enhancement factor determined by the degree of oxidation and the physical prior prediction obtained by recursively deriving the slag removal efficiency scalar and the slag coverage grid indicator vector of the previous time period forces the slag layer thickness evolution to follow the physical causality of oxidation growth and slag removal. The inverse of the prior prediction error covariance matrix is ​​used to realize the differential constraint of each grid. The direction determined by the physical model is forced to maintain the shape, while the constraint of uncertain directions is relaxed and driven by data. The sum of the absolute values ​​of the slag layer thickness difference between adjacent grids constitutes the total variational regularization, which applies only linear penalty to the large step of the slag block boundary while penalizing noise fluctuations, thus maintaining the edge sharpness and providing a clear slag area outline for slag removal path planning. The regularization parameter balances the weights of data fidelity, physical prior, and spatial smoothness. Each element undertakes physical forward mapping, temporal causal constraint, and spatial structure fidelity, respectively. After online recursion by a fast numerical solver, the full-field slag layer thickness distribution estimate is output at each sampling time, which solves the problems of unreliable measurement, incomplete spatial coverage, response lag, and edge blurring of traditional slag layer thickness detection methods under harsh furnace conditions.

[0037] Based on the slag layer thickness distribution and the furnace flue gas oxygen partial pressure signal, the integral index of oxide film energy release rate is calculated, and the evidence distance conflict degree of multiple information sources regarding the slag removal timing proposition is calculated. When the integral index is greater than or equal to the critical energy release rate and the conflict degree is lower than a preset conflict threshold, a slag removal trigger signal is generated, and the process proceeds to step S4 for slag removal path planning. When the integral index is less than the critical energy release rate and the conflict degree is higher than the preset conflict threshold, the process returns to step S2 to continue collecting temperature data and oxygen partial pressure data for the next sampling cycle, recursively updating the slag layer thickness distribution, and recalculating the integral index of oxide film energy release rate and the evidence distance conflict degree, thus entering the next round of judgment loop. The formula for calculating the integral index of oxide film energy release rate is: , , ,

[0038] ,

[0039] in, For the first The integral exponent of oxide film energy release rate at each sampling time For the first The integral exponent of oxide film energy release rate at each sampling time The rate of increase in slag surface density, For the internal stress of the slag film, The effective elastic modulus of the slag film, The sampling period is The pre-exponential factor for the oxidation reaction rate. The activation energy for the oxidation reaction. This is the universal gas constant. For the first The absolute temperature of the molten aluminum at any given time. For the first The oxygen partial pressure of the flue gas in the furnace at all times. The oxygen partial pressure index represents the oxidation reaction. Due to the difference in the coefficients of thermal expansion between oxide slag and molten aluminum, The temperature difference between the surface and the bottom of the slag film. For the first Total variation of slag layer thickness distribution at any given moment. The surface tension of molten aluminum, The average curvature of the liquid surface fluctuation. The porosity of the slag layer, The porosity-affected index, For reference temperature, The thermal softening characteristic temperature is used as the formula for calculating the degree of conflict of the evidence distance:

[0040] ,

[0041] , ,

[0042] in, For the first The degree of conflict between the evidence at each sampling time The total number of information sources. For the first The information source in the first The basic probability assignment vector at each sampling time. Jensen-Shannon divergence measures the difference in probability distribution between information sources and fusion centers. For the first Dynamic credibility weights for each information source As a weighted fusion center, The information entropy of the fusion result, This is the integral index of the current oxide film energy release rate. The critical energy release rate. For the first The recent prediction accuracy score of each information source. To prevent the elimination of zero constants, the slag thickness distribution and the oxygen partial pressure signal of the furnace flue gas are jointly input into the integral exponential recursive calculation model of the oxide film energy release rate. This model quantifies the continuous accumulation process of elastic energy within the slag film from three physical levels: oxidation reaction kinetics, thermoelasticity, and porosity. The slag surface density growth rate is selected to quantify the rate at which new slag is generated by the oxidation reaction, serving as the fundamental source for the continuous thickening of the oxide film and the storage of elastic energy, thus coupling the chemical oxidation process with the mechanical state. An oxidation kinetic expression determined by the pre-exponential factor of the oxidation reaction rate, the activation energy of the oxidation reaction, the universal gas constant, the absolute temperature of the aluminum melt, and the oxygen partial pressure is used to convert real-time oxygen partial pressure and temperature into a dynamic oxidation rate, allowing the exponent to track changes in furnace conditions rather than relying on fixed empirical constants. The slag film internal stress is selected to reflect the mechanical stress accumulated in the oxide film due to thermal expansion mismatch and liquid surface fluctuation bending. The greater the stress, the more elastic energy is stored per unit of newly added slag. Thickness monitoring is combined with stress monitoring to determine whether the film is close to rupture. The difference in thermal expansion coefficient between oxide slag and aluminum liquid and the temperature difference between the slag film surface and bottom are selected as the main thermodynamic sources of internal stress. The stress level difference under different alloys and temperature zones is reflected by explicit modeling. The total variation of slag layer thickness distribution is selected to characterize the degree of slag layer thickness non-uniformity and serve as the spatial concentration factor of bending internal stress. The greater the slag layer thickness gradient, the more concentrated the local stress. The effective elastic modulus of the slag film is selected to determine the elastic energy that the slag film can store under a given stress. This modulus is significantly affected by porosity and temperature; modulus variation is incorporated to avoid inaccurate energy estimation. Slag layer porosity and the porosity influence index are selected to reflect the physical characteristics of the oxidized slag as a porous and loose structure, where the elastic modulus decreases sharply with porosity. The true effective modulus is obtained through porosity correction. The thermal softening characteristic temperature is selected to reflect the significant decrease in slag film stiffness at high temperatures; the temperature softening effect is incorporated to avoid premature triggering due to overestimation of accumulated elastic energy. A recursive integral structure is used to discretize the continuous accumulation process into an online computable form where only the incremental term needs to be calculated for each sampling period without storing the complete historical curve, meeting the real-time operation requirements of the embedded controller. This energy accumulation model is constructed from three physical levels: oxidation chemical kinetics, thermoelasticity, and pore mechanics, giving physical interpretability to the timing of slag removal. All input quantities are updated in real time by online sensing and inversion, and the index evolves dynamically with the furnace conditions, adapting to actual production conditions of varying temperature, oxygen partial pressure, and slag distribution. The energy release rate criterion based on fracture mechanics detects fracture risks earlier than a simple thickness threshold, avoiding quality accidents caused by oxides being drawn into the melt. It solves the problems of lag and blindness caused by traditional methods that rely solely on instantaneous slag layer thickness or fixed time intervals, as well as the problems that empirical thresholds cannot adapt to changes in operating conditions and that a single thickness index cannot reflect the internal mechanical state of the slag film.

[0043] Simultaneously, multiple independent information sources are introduced, including an energy release rate criterion based on slag layer thickness inversion and an empirical model of slag layer thickness based on historical data. This transforms the judgments of each information source regarding the timing of slag removal into a unified basic probability allocation vector. The Jensen-Shannon divergence is used to measure the difference in probability distribution between each information source and the fusion center. This divergence is symmetrical and smooth, compatible with information entropy mathematics, and stably reflects the true degree of disagreement among information sources. Dynamic credibility weights are used, giving high weights to information sources with good historical performance and high current certainty, while automatically reducing the weight of faulty or hesitant information sources to prevent disagreements from being contaminated by faulty sources. A recent prediction accuracy score is used, using a sliding window to trace the consistency rate between each information source's historical judgments and actual needs, achieving online learning and dynamic ranking of information source reliability. A weighted fusion center is selected, representing the comprehensive opinion of multiple sources, serving as a benchmark for measuring the degree of deviation of each source. The weights adaptively shift the fusion center towards reliable sources. The information entropy of the fusion result is used to quantify the decision ambiguity of the comprehensive opinion. When all sources agree but all give high uncertainty, the entropy value remains high, avoiding rash actions in this state. An exponential decay term of the ratio of the integral exponent of the energy release rate to the critical energy release rate is selected. When physical conditions approach the critical point, the entropy penalty weight is appropriately reduced to reflect the principle that physical safety takes precedence over statistical consistency. Slag removal is only triggered normally when physical conditions are met and information sources are highly consistent, significantly reducing the probability of false triggering and missed triggering. Finally, the integral exponent of the oxide film energy release rate and the evidence distance conflict degree are combined to form a dual triggering condition. A slag removal trigger signal is generated normally only when the integral exponent is greater than or equal to the critical energy release rate and the conflict degree is lower than a preset threshold. This ensures the accuracy, robustness, and safety of slag removal timing judgment from both the physical and mechanical aspects and the reliability of information fusion. It achieves full-condition coverage and risk-level management of slag removal timing decisions, providing a precise and reliable start time for subsequent slag removal path planning and execution operations.

[0044] In response to the slag removal trigger signal, a resistance work functional is constructed, including a non-Newtonian shear stress term and a path curvature penalty term. With the constraint of removing all slag layers exceeding a set value, the slag removal path that minimizes the resistance work functional is solved using a variational adjoint method. The formula for calculating the optimal slag removal path is:

[0045] ,

[0046] ,

[0047] in, The optimal path for removing slag. For the slag removal path curve, Let be the total arc length of the path. For information Riemannian metric tensor fields, The unit tangent vector of the path at the th... Components of coordinate direction, The unit tangent vector of the path at the th... Components of coordinate direction, For vertical coordinate index, For horizontal coordinate index, The longitudinal coordinate of the furnace is... The horizontal coordinate of the furnace is... The consistency coefficient of the slag-aluminum mixture. To estimate the mean field of slag layer thickness, For power-law rheological exponent. For uncertainty avoidance coefficient, To estimate the mean field of slag layer thickness, The symbol for Kronecker. The curvature tendency coefficient is used. By responding to the slag removal trigger signal, a resistance work functional is constructed, including non-Newtonian shear stress and path curvature penalty terms. With the constraint of removing all slag layers exceeding a set value, the optimal slag removal path is transformed into a geodesic problem on an information Riemannian manifold. An information Riemannian metric tensor field is used to define the movement cost density at each point on the furnace liquid surface. This tensor field consists of a non-Newtonian resistance density term composed of the slag-aluminum mixture consistency coefficient, the slag layer thickness estimation mean field, and the power-law rheological exponent; an uncertainty equivalent resistance increment term composed of the uncertainty avoidance coefficient and the slag layer thickness estimation variance; and a curvature tendency correction term composed of the curvature tendency coefficient and the second spatial derivative of the slag layer thickness. Using the slag-aluminum mixture consistency coefficient and the slag layer thickness estimation mean field, the local slag layer thickness and material rheological properties are directly mapped to the non-Newtonian shear resistance density when the slag removal plate moves at that point. The thicker and denser the slag, the greater the cost, allowing the path to automatically avoid high-resistance areas. A power-law rheological exponent is selected to characterize the shear-thinning properties of the slag-aluminum mixture, reflecting the nonlinear law that the resistance at unit velocity gradually decreases with increasing slag layer thickness. An uncertainty avoidance coefficient and the slag layer thickness estimation variance are used to convert the estimated variance of each grid in the inversion output into an equivalent resistance increment. In high-variance regions, the eigenvalue of the metric tensor increases, and geodesics automatically detour, avoiding critical slag removal operations in sensor blind zones or model mismatch areas. A curvature tendency coefficient and the second spatial derivative of the slag layer thickness are used to construct a curvature tendency correction term, increasing the metric for steep slag layer thickness changes. The path prioritizes extending in directions with gentler slag layer thickness changes, reducing mechanical impact and surface disturbance when the slag removal plate climbs steep slag pile edges. Kronecker notation is used to make the resistance and uncertainty terms isotropic, ensuring that the basic cost of moving the slag removal plate is the same in any direction, simplifying the tensor structure and guaranteeing numerical stability. Instead of traditional grid search or discrete optimization, geodesic equations are used to express the slag removal path as a system of second-order ordinary differential equations under a metric tensor field. A continuous and smooth path is directly generated through numerical integration, achieving the global optimum without iterative optimization. The components of the path's unit tangent vector in the longitudinal and lateral coordinate directions are used to project the instantaneous movement direction of the slag removal plate onto the metric tensor, making the local cost vary with direction—lower cost along low-resistance directions and higher cost along high-resistance directions. The path starting point is chosen as one endpoint along the principal direction of the slag layer thickness gradient in the thick slag region, and the ending point is chosen as the relatively farthest point, ensuring that a single geodesic line traverses the entire thick slag region as much as possible. When the sweep width of a single geodesic line is insufficient to cover the entire thick slag region, it is translated vertically to generate a cluster of parallel geodesics to meet the constraint that the coverage rate is not lower than the target value.This path planning method encodes non-Newtonian rheological resistance, inversion uncertainty, and spatial curvature of slag layer thickness into a Riemannian metric. The slag removal path is directly generated by integrating the geodesic equation, automatically adapting to the spatial distribution of slag layer consistency, bypassing high-resistance areas and navigating low-resistance areas, thus reducing slag removal energy consumption. High-uncertainty regions are automatically avoided, exhibiting robustness to sensor noise and model mismatch. The path prioritizes directions with gentle slag layer thickness changes, reducing mechanical impact and liquid surface fluctuations. Continuous curves are directly optimized, resulting in a naturally smooth path that avoids the jaggedness and redundant curvature introduced by discretization. The geodesic equation can be solved quickly through numerical integration with constant computational load, meeting the requirements of online real-time planning. This method solves the problems of incomplete or repeated slag removal caused by the inability of traditional fixed trajectories to adapt to uneven slag layer distribution, the risk of the slag removal plate performing critical operations in sensor blind zones due to the lack of consideration for inversion uncertainty in traditional path planning, and the problems of uneven path, large mechanical impact, and high energy consumption caused by traditional discretization path generation methods.

[0048] During the movement along the slag removal path, the optimal vibration frequency and amplitude are calculated in real time based on the porous media vibration seepage separation model, and the slag removal plate is controlled to vibrate at this frequency and amplitude to promote the desorption of molten aluminum from the slag layer pores. Simultaneously, the integral index of the oxide film energy release rate, the evidence distance conflict degree, and the force signal at the end of the slag removal robotic arm, calculated in real time in step S3, are continuously monitored. When the integral index of the oxide film energy release rate is lower than a preset safety threshold, the evidence distance conflict degree is lower than a preset conflict threshold, and the force signal meets the no-load condition, the slag removal termination condition is determined to be met, and the slag removal is terminated early. The formula for calculating the optimal vibration frequency is:

[0049] ,

[0050] in, To achieve the optimal vibration frequency, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. The current sampling time The thickness of the local slag layer at the slag removal location. The dynamic viscosity of molten aluminum. Given the slag layer permeability, the formula for calculating the optimal amplitude is:

[0051] ,

[0052] in, For the optimal vibration amplitude, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. To achieve the optimal vibration frequency, The current sampling time The thickness of the local slag layer at the slag removal location. The dynamic viscosity of molten aluminum. The slag layer permeability is used. The surface tension of the molten aluminum is selected as the fundamental force driving capillary ascent and hindering desorption of the molten aluminum from the slag pores. The greater the surface tension, the more stable the tortuous liquid surface formed by the molten aluminum in the slag pores, and the higher the energy required for desorption. It constitutes a core parameter of capillary restoring force in frequency and amplitude calculations. The contact angle between the molten aluminum and the oxide slag is selected to characterize the degree of wetting of the molten aluminum on the slag skeleton. When the contact angle is greater than 90 degrees, the molten aluminum tends to be unwetted, which is conducive to desorption; when it is less than 90 degrees, the molten aluminum is partially wetted, making desorption difficult. This angle is incorporated into the cosine function to directly correct the effective component of capillary pressure. The density of the molten aluminum is selected to determine the magnitude of the vibrational inertial force. Under resonance conditions, it, together with the square of the frequency and the amplitude, constitutes the inertial term. The higher the density, the greater the inertial force generated at the same frequency and amplitude, which is more conducive to overcoming capillary adhesion. The equivalent pore radius of the slag layer is selected to define the characteristic size of the capillary channels inside the slag layer. The smaller the pore size, the greater the capillary pressure and the higher the resonant frequency. The pore size dynamically changes with the slag layer thickness, and its correlation with the local slag layer thickness allows the frequency and amplitude to automatically adapt to the microstructure of the slag layer. The local slag layer thickness at the current slag removal location is selected, which directly affects the pore radius and permeability. Simultaneously, the thicker the slag, the longer the seepage path of the molten aluminum in the pores and the greater the viscous damping. The frequency and amplitude must be adjusted in real time according to the slag layer thickness. The dynamic viscosity of the molten aluminum is selected to characterize the viscous resistance encountered by the molten aluminum when flowing in the pores. The higher the viscosity, the stronger the damping. In the frequency formula, it acts as a damping term to reduce the resonant frequency; in the amplitude formula, it acts as a denominator term to increase the required amplitude to overcome viscous losses. The slag layer permeability is selected to comprehensively reflect the smoothness of the molten aluminum seepage due to the slag layer porosity and pore size. The lower the permeability, the greater the viscous damping, which, together with viscosity, determines the strength of the damping term. In frequency calculation, the square root of the difference between the capillary restoring force term and the viscous damping term is taken as the resonant frequency, matching the applied vibration with the natural frequency of the molten aluminum within the pores. This maximizes energy injection efficiency, causing the molten aluminum to undergo forced oscillations with maximum amplitude within the pores, achieving maximum desorption with minimal energy consumption. In amplitude calculation, capillary pressure is used as the driving force, and the sum of the vibrational inertial force and the viscous damping force is used as the impedance. The resulting amplitude is precisely the critical value that allows the molten aluminum meniscus to reach maximum elastic deformation at the orifice, ensuring sufficient desorption without tearing the slag layer skeleton. This vibration separation method couples frequency and amplitude through the same seepage dynamics model, achieving physical self-consistency without requiring separation optimization. The vibration parameters automatically adjust as the slag removal plate passes through regions with different slag layer thicknesses: the frequency increases and the amplitude decreases in thick slag regions, while the frequency decreases and the amplitude increases in thin slag regions. The closed-loop analytical solution is directly calculated without online iterative optimization, meeting the requirements for millisecond-level real-time control. It solves the problems of high aluminum loss caused by traditional slag removal relying solely on experience to adjust the tilt angle and lacking active separation methods based on the pore seepage mechanism; it also solves the problems of insufficient desorption or energy waste caused by fixed vibration parameters being unable to adapt to spatial changes in slag layer thickness; and it solves the problems of slag layer skeleton breakage and secondary entrainment of molten aluminum caused by excessive vibration intensity.

[0053] In determining the termination condition for slag removal, the slag layer thickness distribution updated in real-time in step S2 is used to calculate the residual area ratio. The ratio of the grid area where the residual layer thickness exceeds the allowable threshold to the total area of ​​the furnace liquid surface is used as the real-time residual evaluation index. When this index is lower than the target residual area ratio, it indicates that the slag removal has met the cleanliness requirements. The force sensor signal at the end of the slag removal robotic arm is used to calculate the average normal force and the standard deviation of the force signal within the sliding window. When the average normal force is lower than the no-load threshold and the standard deviation is lower than the stability threshold, the slag removal plate is determined to be in a no-load state. The simultaneous satisfaction of the real-time residual evaluation condition and the force sensor no-load condition is used as the slag removal termination criterion. The maximum number of repeated scrapings and the maximum furnace door opening time are set as safety constraints. If any safety constraint is triggered, the process is forcibly terminated. This closed-loop termination determination, through the fusion of thermal inversion and force sensor dual-modal information, ensures that the slag removal process stops immediately after reaching the cleanliness target. This solves the problems of excessive scraping leading to increased aluminum liquid loss and temperature drop in traditional timed or fixed-path slag removal, as well as the problem of oxide residue affecting melt quality due to insufficient slag removal.

[0054] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A slag skimming control method for an aluminum melting furnace, characterized in that, Including the following steps: S1. Acquire multi-point temperature timing signals at different depths inside the aluminum melting furnace wall, oxygen partial pressure signals of flue gas in the furnace chamber, and force signals at the end of the slag removal robotic arm. S2. Use the multi-point temperature timing signal as input to estimate the slag layer thickness distribution on the surface of the molten aluminum in the furnace; S3. Based on the slag layer thickness distribution and the furnace flue gas oxygen partial pressure signal, calculate the integral index of oxide film energy release rate and calculate the evidence distance conflict degree of multiple information sources regarding the proposition of slag removal timing. When the integral index is greater than or equal to the critical energy release rate and the conflict degree is lower than the preset conflict threshold, generate a slag removal trigger signal and proceed to step S4 for slag removal path planning. When the integral index is less than the critical energy release rate and the conflict degree is higher than the preset conflict threshold, return to step S2 to continue collecting temperature data and oxygen partial pressure data for the next sampling cycle, recursively update the slag layer thickness distribution, and recalculate the integral index of oxide film energy release rate and evidence distance conflict degree, and enter the next round of judgment cycle. S4. In response to the slag removal trigger signal, construct a resistance work functional including a non-Newtonian shear stress term and a path curvature penalty term. With the constraint of removing all slag layers with a thickness exceeding a set value, solve the slag removal path that minimizes the resistance work functional using the variational adjoint method. S5. During the movement along the slag removal path, the optimal vibration frequency and optimal amplitude are calculated in real time according to the porous media vibration seepage separation model, and the slag removal plate is controlled to vibrate at the optimal vibration frequency and optimal amplitude to promote the desorption of aluminum liquid from the slag layer pores. At the same time, the integral index of the oxide film energy release rate, the evidence distance conflict degree, and the force signal at the end of the slag removal robot arm calculated in real time in step S3 are continuously monitored. When the integral index of the oxide film energy release rate is lower than the preset safety threshold, the evidence distance conflict degree is lower than the preset conflict threshold, and the force signal meets the no-load condition, it is determined that the slag removal termination condition is met, and the slag removal is ended in advance.

2. The slag removal control method for an aluminum melting furnace according to claim 1, characterized in that, The formula for estimating the slag layer thickness distribution on the surface of the molten aluminum in the furnace in S2 is as follows: ， ， ， in, For the first Estimated slag layer thickness at each sampling time. This represents the measured temperature vector of multiple thermocouples within the furnace wall. Let be the slag layer thickness distribution vector to be solved. This is the temperature self-evolution matrix. For the first A vector composed of the temperature values ​​at all thermocouple measuring points inside the furnace wall at each sampling time. This is the slag layer thickness-temperature sensitivity matrix. For steady-state bias vector, To observe the noise covariance matrix, Let be the prior bias vector. The prior prediction error covariance matrix, For regularization parameters, For total variational regularization, The spatial gradient of slag layer thickness. This is an estimate of the slag layer thickness from the previous moment. The oxidation rate coefficient is... The sampling period is It is a nonlinear oxidation enhancement factor determined by oxygen partial pressure and melt temperature. For the efficiency of slag removal. This is the indicator vector for the slag cover grid in the previous time period. For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number The thickness of the slag layer at the grid line, For the furnace liquid level line, number Thickness of slag layer at the grid line.

3. The slag removal control method for an aluminum melting furnace according to claim 1, characterized in that, The formula for calculating the integral exponent of the oxide film energy release rate in S3 is as follows: ， ， ， ， in, For the first The integral exponent of the oxide film energy release rate at each sampling time For the first The integral exponent of the oxide film energy release rate at each sampling time The rate of increase in slag surface density, For the internal stress of the slag film, The effective elastic modulus of the slag film, The sampling period is The pre-exponential factor for the oxidation reaction rate. The activation energy for the oxidation reaction. This is the universal gas constant. For the first The absolute temperature of the molten aluminum at any given time. For the first The oxygen partial pressure of the flue gas in the furnace at all times. The oxygen partial pressure index represents the oxidation reaction. Due to the difference in the coefficients of thermal expansion between oxide slag and molten aluminum, The temperature difference between the surface and the bottom of the slag film. For the first Total variation of slag layer thickness distribution at any given moment. The surface tension of molten aluminum, The average curvature of the liquid surface fluctuation. The porosity of the slag layer, The porosity-affected index, For reference temperature, The thermal softening characteristic temperature is used as the formula for calculating the degree of conflict of the evidence distance: ， ， ， in, For the first The degree of conflict between the evidence at each sampling time The total number of information sources. For the first The information source in the first The basic probability assignment vector at each sampling time. Jensen-Shannon divergence measures the difference in probability distribution between information sources and fusion centers. For the first Dynamic credibility weights for each information source As a weighted fusion center, The information entropy of the fusion result, This is the integral index of the current oxide film energy release rate. The critical energy release rate. For the first The recent prediction accuracy score of each information source. To prevent the coefficient from being zero.

4. The slag removal control method for an aluminum melting furnace according to claim 1, characterized in that, The formula for calculating the optimal slag removal path in S4 is as follows: ， ， in, The optimal path for removing slag. For the slag removal path curve, Let be the total arc length of the path. For information Riemannian metric tensor fields, The unit tangent vector of the path at the th... Components of coordinate direction, The unit tangent vector of the path at the th... Components of coordinate direction, For vertical coordinate index, For horizontal coordinate index, The longitudinal coordinate of the furnace is... The horizontal coordinate of the furnace is... The consistency coefficient of the slag-aluminum mixture. To estimate the mean field of slag layer thickness, For power-law rheological exponent. For uncertainty avoidance coefficient, To estimate the mean field of slag layer thickness, The symbol for Kronecker. This is the curvature tendency coefficient.

5. The slag removal control method for an aluminum melting furnace according to claim 1, characterized in that, The formula for calculating the optimal vibration frequency in S5 is as follows: ， in, To achieve the optimal vibration frequency, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. The current sampling time The thickness of the local slag layer at the slag removal location, The dynamic viscosity of molten aluminum. Given the slag layer permeability, the formula for calculating the optimal amplitude is: ， in, For the optimal vibration amplitude, The surface tension of molten aluminum, The contact angle between molten aluminum and oxide slag. The density of molten aluminum, The equivalent pore radius of the slag layer. To achieve the optimal vibration frequency, The current sampling time The thickness of the local slag layer at the slag removal location, The dynamic viscosity of molten aluminum. This represents the permeability of the slag layer.

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