A Closed-Loop Optimization Control Method for Gold Concentrate Grinding Particle Size

Abstract

This application provides a closed-loop optimization control method for gold concentrate grinding particle size, relating to the field of industrial control technology, including the following steps: collecting multi-dimensional time-series operation data of the grinding system, constructing a dynamic state space matrix based on a sliding time window, and performing time alignment and time lag correction on the dynamic state space matrix; inputting the corrected dynamic state space matrix into a particle size distribution prediction model, and outputting a particle size probability density function to characterize the multi-peak non-stationary characteristics; based on the particle size probability density function, using a tail-sensitive mechanism to calculate the fine-grained mudding risk index and the coarse-grained under-grinding risk index to enhance the response capability to changes in the tail of the particle size distribution; combining the risk index and mineralogical characteristic parameters to generate an adaptive target particle size probability density function, realizing the directional amplification and quantitative evaluation of the extreme abnormal intervals at both ends of the distribution curve, avoiding the defect of traditional mean values ​​masking local risks, and improving the accuracy and timeliness of risk warning.

Description

Technical Field

[0001] This application relates to the field of industrial control technology, and more specifically, to a closed-loop optimization control method for the particle size of gold concentrate grinding. Background Technology

[0002] Gold concentrate grinding is a core step in the pre-processing technology of gold smelting. Its operation efficiency and product quality directly determine the recovery rate and overall energy consumption of subsequent cyanide leaching operations. As mineral processing engineering develops towards refinement and intelligence, the detection and control technology of the grinding process has gradually evolved from early single-instrument monitoring to automated regulation based on distributed control systems. The industry generally adopts loop regulation strategies based on conventional PID control or simple feedforward control, which regulate the grinding and classification loop by monitoring macroscopic parameters such as mill current, feed rate and classifier overflow concentration.

[0003] However, existing control strategies often rely on feedback adjustments based on average particle size or the throughput of a single screening size, failing to fully utilize the overall morphological characteristics of the particle size distribution curve. In actual production, grinding products often exhibit multi-peak and time-varying particle size characteristics. Simply pursuing the achievement of average particle size standards can easily mask the micro-sludge formation caused by over-grinding or the coarse particle run-off caused by under-grinding. This limitation of representing a single characteristic value prevents the system from accurately intervening in abnormal morphologies at the tail end of the distribution curve.

[0004] Therefore, there is an urgent need for a closed-loop optimization control method for the grinding particle size of gold concentrate. Summary of the Invention

[0005] To address the aforementioned technical problems, this application is proposed. The first aspect of this application provides a closed-loop optimization control method for the grinding particle size of gold concentrate, comprising the following specific steps: collecting multi-dimensional time-series operating data of the grinding system, constructing a dynamic state space matrix based on a sliding time window, and performing time alignment and time lag correction processing on the dynamic state space matrix;

[0006] The corrected dynamic state space matrix is ​​input into the granularity distribution prediction model, and the output is the granularity probability density function used to characterize the multi-peak non-stationary characteristics.

[0007] Based on the particle size probability density function, a tail-sensitive mechanism is used to calculate the fine-grain mudding risk index and the coarse-grain undergrinding risk index to enhance the response capability to changes in the tail of particle size distribution.

[0008] By combining the risk index and mineralogical characteristic parameters, an adaptive target granularity probability density function is generated;

[0009] Based on the risk index and the adaptive target granularity probability density function, the optimal combination of control variables is solved through bi-objective optimization, and then converted into execution instructions by the decoupled controller and sent to the grinding actuator to achieve closed-loop control.

[0010] Preferably, the multidimensional time-series runtime data includes:

[0011] Multidimensional time-series operation data of the grinding system are collected by industrial field sensors and online detection instruments to obtain raw multidimensional data including mill feed rate, water replenishment rate, mill power, classifier overflow concentration and mill sound pressure.

[0012] Based on the preset sliding time window length and sliding step size, the original multidimensional data is cleaned and aligned to form a multidimensional state space matrix.

[0013] The cross-correlation function method is used to perform time lag correction on the data of each dimension in the multidimensional state space matrix to obtain the corrected dynamic state space matrix.

[0014] Preferably, the granularity probability density function includes:

[0015] By using the sliding time window differential accumulation technique, the granular distribution prediction vector at consecutive time points is differentially analyzed element by element. The difference values ​​with the same sign are accumulated by time weighting, and the difference values ​​with different signs are reduced by the attenuation factor in the direction, thus constructing the granular evolution trend quantity. The granular evolution trend quantity retains both the migration direction of the distribution pattern and the cumulative migration amplitude.

[0016] The granular evolution trend is processed using a two-parameter adaptive exponential smoothing technique. The smoothing coefficient is configured such that when the trend directions of adjacent time steps are consistent, the smoothing coefficient is set to a value close to 0.9 to enhance the memory effect; when the trend directions of adjacent time steps are reversed, the smoothing coefficient is automatically reduced to below 0.3 to suppress transient disturbances. This yields the granular evolution hidden state quantity, which maintains cumulative gain only for continuous unidirectional distribution migration and maintains rapid forgetting for reverse noise.

[0017] Using the probability distribution morphological migration extrapolation model, with the granular evolution hidden state variables as the driving condition, the morphological adjustment of the granular distribution prediction vector at the current moment is performed: the migration direction angle and migration intensity scalar are extracted from the hidden state variables, the horizontal displacement of the distribution peak is calculated using the direction angle, the distribution variance scaling factor is calculated using the intensity scalar, and the corresponding peak translation transformation and variance scaling transformation are applied to the probability density curve represented by the granular distribution prediction vector, respectively, to generate the extrapolation distribution under the condition of consistent trend, and the kernel density estimation is reconstructed on the extrapolation distribution to generate the granular probability density function.

[0018] Preferably, the calculation of the fine-grained mudification risk index and the coarse-grained undergrinding risk index includes:

[0019] Based on the preset critical particle size for fine particles and critical particle size for coarse particles in the ore grinding process, the particle size probability density function is divided into three parts: fine particle interval, qualified interval and coarse particle interval. The probability density value sequence corresponding to each particle size position in the fine particle interval and the probability density value sequence corresponding to each particle size position in the coarse particle interval are extracted.

[0020] By using the hidden state driving force decoupling technique, the particle size evolution hidden state vector is projected and decomposed according to the fine-grained direction basis vector and the coarse-grained direction basis vector to obtain the first evolution direction identifier and the first evolution intensity value acting on the fine-grained interval, and the second evolution direction identifier and the second evolution intensity value acting on the coarse-grained interval.

[0021] Using a two-factor nonlinear risk response function, the probability density value sequences of the fine-grained interval and the coarse-grained interval are mapped and transformed point by point to generate fine-grained trend-sensitive risk density distribution and coarse-grained trend-sensitive risk density distribution.

[0022] The two-factor nonlinear risk response function is configured such that, for any input probability density value, when the corresponding evolution direction indicator indicates that the probability density is in an increasing trend and the evolution intensity value exceeds a preset sensitivity threshold, a nonlinear amplification mapping is applied to the input density value, and the amplification factor increases monotonically with the increase of the evolution intensity value.

[0023] When the evolution direction indicator indicates that the probability density is in a downward trend, a nonlinear decay mapping is applied to the input density value, and the degree of decay increases monotonically with the increase of the evolution intensity value, so that the same original probability density value produces significantly differentiated risk density values ​​under different evolution driving forces.

[0024] The fine-grained trend-sensitive risk density distribution is numerically integrated and accumulated within the fine-grained interval using a partitioned adaptive integrator. During the integration process, the integration step size is automatically adjusted according to the gradient of the change of adjacent density points to obtain the fine-grained mudding risk index. The same adaptive integration process is performed on the coarse-grained trend-sensitive risk density distribution within the coarse-grained interval to obtain the coarse-grained under-grinding risk index.

[0025] The fine-particle mudding risk index and the coarse-particle undergrinding risk index are output to the monitoring system for coordinated adjustment of the mill's feed rate and grinding media replenishment strategy.

[0026] Preferably, the generation of the adaptive target granularity probability density function includes:

[0027] The current grinding stage identifier is obtained by matching and judging the obtained raw ore mineralogical characteristic parameters through the process mechanism rule base;

[0028] Using the current grinding stage identifier, the peak position of the preset baseline particle size probability density function is offset and adjusted to generate an adaptive target particle size probability density function.

[0029] Preferably, the optimal combination of control variables includes:

[0030] The deviation between the complete granularity probability density function and the adaptive target granularity probability density function is calculated using the integral squared error calculation method to obtain the full distribution morphological tracking error;

[0031] An optimization model is adopted with the constraint of minimizing the tracking error of the full distribution pattern and the dual objectives of minimizing pure ore power consumption and maximizing gold recovery rate. An improved differential evolution algorithm based on knowledge graph hot-start population is used to optimize the risk index and obtain the optimal combination of control variables.

[0032] Preferably, the closed-loop control includes:

[0033] The optimal combination of control variables is decoupled by combining internal model control with proportional-integral-derivative control method to obtain decoupled control variables;

[0034] The decoupled control variables are dynamically fine-tuned using a fuzzy control method to obtain a safe execution instruction.

[0035] The safety execution command is sent to the grinding actuator, and the multi-dimensional time-series operation data of the grinding system is collected again to form a closed-loop control.

[0036] Preferably, the closed-loop optimization control includes:

[0037] The online particle size analyzer collects real-time particle size distribution data of the grinding system and supplements the real-time particle size distribution data into the multi-dimensional time-series operation data.

[0038] The feed frequency converter, the water supply regulating valve, and the classifier speed regulator are used to receive the safety execution command to perform closed-loop optimization control of the grinding particle size of gold concentrate.

[0039] Preferably, the adaptive target granularity probability density function includes:

[0040] A historical operation case library is constructed. Each case in the case library records the original ore mineralogical characteristic parameters, fine-grained mudification risk index, coarse-grained under-grinding risk index, and the optimal target particle size probability density function after manual optimization and verification.

[0041] Using a similarity retrieval technique based on weighted Euclidean distance, several similar cases with the smallest combined distance to the current original ore mineralogical characteristic parameters and the current two risk indices are matched in the case library.

[0042] The optimal target granularity probability density function of the several similar cases is weighted and fused using a local weighted regression fusion method. The weights are determined by the case similarity and risk matching degree. The adaptive target granularity probability density function is generated after fusion.

[0043] A second aspect of the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, characterized in that: when the processor executes the computer program, it implements the steps of the above-described closed-loop optimization control method for gold concentrate grinding particle size.

[0044] Compared with existing technologies, the closed-loop optimization control method for gold concentrate grinding particle size provided in this application inputs the corrected matrix into the particle size distribution prediction model and outputs the particle size probability density function, realizing a full probability characterization of the particle size distribution morphology of the grinding product. This breaks through the limitations of traditional single-indicator prediction, accurately captures the multi-peak non-stationary characteristics, and provides high-fidelity data support for refined risk assessment. Based on the probability density function, a tail-sensitive mechanism is used to calculate the risk index of fine-grained mudding and coarse-grained under-grinding, realizing the directional amplification and quantitative assessment of the extreme abnormal intervals at both ends of the distribution curve. This avoids the defect of traditional mean values ​​masking local risks and improves the accuracy and timeliness of risk warning. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on the drawings without creative effort. In the drawings:

[0046] Figure 1 This is a flowchart of a closed-loop optimization control method for gold concentrate grinding particle size according to an embodiment of this application. Detailed Implementation

[0047] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0048] As mentioned in the background section, existing control strategies are mostly based on feedback adjustment of average particle size or the throughput of a single screening size, ignoring the overall morphological characteristics of particle size distribution. In actual production, grinding products often exhibit multi-peak non-stationary distribution characteristics. Simply pursuing the achievement of average particle size can easily mask the micro-sludge formation caused by "over-grinding" or the coarse particle run-off caused by "under-grinding." The "average value trap" makes it impossible to accurately intervene in the tail anomalies of the distribution curve.

[0049] Therefore, a closed-loop optimization control method for gold concentrate grinding particle size is urgently needed.

[0050] Figure 1 The flowchart below shows a closed-loop optimization control method for gold concentrate grinding particle size according to an embodiment of this application, including the following specific steps:

[0051] S1: Collect multi-dimensional time-series operation data of the grinding system, construct a dynamic state space matrix based on a sliding time window, and perform time alignment and time lag correction on the dynamic state space matrix.

[0052] In step S1, multi-dimensional time-series operation data of the grinding system are collected through industrial field sensors and online detection instruments to obtain raw multi-dimensional data including mill feed rate, water replenishment rate, mill power, classifier overflow concentration and mill sound pressure.

[0053] Based on the preset sliding time window length and sliding step size, the original multidimensional data is cleaned and aligned to form a multidimensional state space matrix.

[0054] The cross-correlation function method is used to perform time lag correction on the data of each dimension in the multidimensional state space matrix to obtain the corrected dynamic state space matrix.

[0055] Furthermore, considering that the effects of various operating variables on particle size distribution in the grinding system do not occur synchronously, but are transmitted step by step through multiple paths such as slurry transportation, particle crushing, and staged reflux, different variables have different response delays to the particle size formation process; if multidimensional operating data at the same sampling time is directly used as model input, it will lead to a phase mismatch between the time of variable action and particle size response, thus forming a spurious correlation in a statistical sense.

[0056] Furthermore, considering that the particle size distribution itself is a continuous probability distribution, directly using a single particle size as a response reference can easily lead to the loss of information about the overall changes in the particle size distribution. Therefore, before calculating the lag relationship of variables, a particle size distribution feature extraction function is first used. The particle size probability density function is converted into a characteristic quantity that can represent the distribution change, such as peak particle size, probability mass of the fine-grained interval, probability mass of the coarse-grained interval, or distribution mean. The correlation between each operating variable and the distribution characteristic quantity at different time offsets is compared to identify the lag position where the variable has an actual impact on the particle size distribution. The continuously sampled data is organized into a dynamic state space sequence using a sliding time window, and the cross-correlation function between each operating variable and the particle size characteristic is calculated with the particle size distribution response obtained from online particle size detection as a reference.

[0057] ;

[0058] in, For the first Dimensional running variables and granular distribution response over time offset The cross-correlation value under the following conditions For candidate time lag, Calculate the expected or mean value within the time window. For the first Dimensional runtime variables in The sampled value at time 10:00. In order to be in Time-of-flight particle size The granularity probability density function at that location, For particle size variable, This is a particle size distribution feature extraction function, used to convert the complete particle size probability density function into feature quantities such as peak particle size, mean particle size, probability mass of fine-grained intervals, or probability mass of coarse-grained intervals.

[0059] Furthermore, the data is time-rearranged according to the response lag of each variable, so that each operating variable is aligned according to the time sequence in which it actually affects the granularity distribution, thereby constructing a dynamic state-space data structure with process causal significance.

[0060] S2: Input the corrected dynamic state space matrix into the granularity distribution prediction model and output the granularity probability density function to characterize the multi-peak non-stationary characteristics.

[0061] In step S2, the granular distribution prediction vector at consecutive time points is subtracted element by element using the sliding time window differential accumulation technique. The difference values ​​with the same sign are accumulated by time weighting, and the difference values ​​with different signs are reduced by the attenuation factor to construct the granular evolution trend quantity. The granular evolution trend quantity retains both the migration direction of the distribution pattern and the cumulative migration amplitude.

[0062] The granular evolution trend quantity is processed using a two-parameter adaptive exponential smoothing technique. The smoothing coefficient is configured such that when the trend quantity is in the same direction at adjacent time points, the smoothing coefficient is taken to a value close to 0.9 to enhance the memory effect; when the trend quantity is in the opposite direction at adjacent time points, the smoothing coefficient is automatically reduced to below 0.3 to suppress transient disturbances. This yields the granular evolution hidden state quantity, which maintains cumulative gain only for continuous unidirectional distribution migration and maintains rapid forgetting for reverse noise.

[0063] Using a probability distribution morphological migration extrapolation model, with granular evolution hidden state variables as the driving condition, the morphological adjustment of the granular distribution prediction vector at the current moment is performed: the migration direction angle and migration intensity scalar are extracted from the hidden state variables, the horizontal displacement of the distribution peak is calculated using the direction angle, and the distribution variance scaling factor is calculated using the intensity scalar. The corresponding peak translation transformation and variance scaling transformation are applied to the probability density curve represented by the granular distribution prediction vector, respectively, to generate the extrapolated distribution under the condition of consistent trend. The extrapolated distribution is reconstructed by kernel density estimation to generate the granular probability density function.

[0064] Furthermore, considering the grinding particle size distribution During the time evolution process, it manifests as the migration and reconstruction of probability density in the particle size space, rather than the change of a single particle size index. If only discrete difference or single-point prediction methods are used, it is difficult to characterize the structural evolution process of the overall distribution in the particle size space.

[0065] Furthermore, considering that the change in particle size distribution between adjacent time points can be understood as a redistribution of probability mass in the particle size space, rather than an increase or decrease in a single particle size value, the difference in probability density between the current and previous time points at each particle size position is used as a local probability migration flux. This flux is used to determine the inflow or outflow of probability mass within the particle size range. When the difference is positive, it indicates an increase in the probability density at the particle size position; when the difference is negative, it indicates a decrease in the probability density at the particle size position. This provides a basis for subsequent migration trend extraction. The difference in particle size distribution between adjacent time points is defined as the local probability migration flux.

[0066] ;

[0067] in, Particle size In Local probabilistic migration flux at time t; for Time-of-flight particle size The probability density value at that location; The particle size at the previous moment The probability density value at that location. To increase the probability density of particle size positions, This reduces the probability density of particle size location.

[0068] Furthermore, considering that probability changes at a single moment may originate from detection fluctuations or short-term disturbances and cannot be directly used as the true distribution migration trend, the local probability migration flux at multiple historical moments is accumulated using time memory: a time decay weight is used as a memory term to give recent changes a higher impact; a sign function is used as a direction-preserving term to distinguish between migration towards the fine-grained side and migration towards the coarse-grained side; and the nonlinear power of the probability change amplitude is used as a trend enhancement term to amplify persistent changes and weaken random small fluctuations. By coupling the memory term, direction term, and enhancement term, a persistent distribution migration trend is extracted, and a nonlinear migration potential function with time memory and direction consistency constraints is constructed.

[0069] ;

[0070] in, Particle size In The nonlinear migration potential function at time t. The number of historical time steps accumulated to participate in the trend. For historical time step indexing, For the first The time decay weights corresponding to each historical time step typically satisfy the following: And it decreases as k increases. This is a sign function used to preserve the direction of probability migration. It is a nonlinear enhancement factor. It is used to amplify continuous changes. It is used to reduce the impact of amplitude differences on trend judgment.

[0071] Furthermore, considering that the migration potential function can only represent the cumulative strength of the trend at each particle size location, and not directly the migration direction and rate of the probability density in the particle size space, we examine the rate of change of the migration potential function along the particle size direction: when the migration potential increases along the fine-grained direction, it indicates that the probability density has a tendency to accumulate towards the fine-grained side; when the migration potential increases along the coarse-grained direction, it indicates that the probability density has a tendency to accumulate towards the coarse-grained side. Therefore, the gradient of the migration potential function in the particle size space is taken as the probability density migration velocity field, and the gradient of the migration potential function in the particle size space is defined as the probability density migration velocity field.

[0072] ;

[0073] in, Particle size In The probability density migration velocity field at time t. Let the gradient of the migration potential function along the grain size direction be given by... When positive or negative, it is used to characterize the tendency of the probability density to migrate along the preset particle size direction. The specific positive and negative directions can be determined according to the definition of particle size coordinates. The velocity field is used to characterize the migration direction and migration rate of the particle size distribution in the particle size space, so that the particle size evolution is transformed from a discrete change description into a migration dynamic process in continuous space.

[0074] Furthermore, considering that the velocity field reflects the migration trend at each particle size location, but the probability density at different particle size locations is different, and their contribution to the overall distribution evolution is also different, the velocity field is used as the migration driving force, and the current probability density is used as the weight. This allows the migration trend in regions with higher probability density to contribute more to the overall hidden state, while the local fluctuations in regions with lower probability density contribute less. By accumulating the product of the two in the particle size space, an overall hidden state variable that can simultaneously characterize the migration direction, migration intensity, and distribution weight is formed. The velocity field is coupled with the current particle size distribution to construct the particle size evolution hidden state variable:

[0075] ;

[0076] in, for The hidden state variable representing the particle size evolution at time step, with the integration range being the preset particle size detection range. , For the minimum detection particle size, For the maximum detectable particle size, For probability density migration velocity field, Let be the probability density function of the current particle size. The integral is a weighted accumulation of the migration velocities at different particle size positions with the current probability density as the weight. The hidden state variables simultaneously contain information on the probability density migration direction, migration intensity, and spatial distribution structure, which are used to characterize the overall evolution trend of particle size distribution.

[0077] Furthermore, structural evolution constraints are imposed on the current granularity distribution based on the hidden state variables, causing the peak position of the granularity distribution to shift and the distribution width to adjust along the migration direction during subsequent prediction processes, thereby generating granularity distribution projection results that conform to the actual evolution trend.

[0078] S3: Based on the particle size probability density function, a tail-sensitive mechanism is used to calculate the fine-particle mudification risk index and the coarse-particle undergrinding risk index to enhance the response capability to changes in the tail of particle size distribution.

[0079] In step S3, based on the preset critical particle size for fine particles and critical particle size for coarse particles in the ore grinding process, the particle size probability density function is divided into three parts: fine particle interval, qualified interval, and coarse particle interval. The probability density value sequence corresponding to each particle size position in the fine particle interval and the probability density value sequence corresponding to each particle size position in the coarse particle interval are extracted.

[0080] By using the hidden state driving force decoupling technique, the particle size evolution hidden state vector is projected and decomposed according to the fine-grained direction basis vector and the coarse-grained direction basis vector to obtain the first evolution direction identifier and the first evolution intensity value acting on the fine-grained interval, and the second evolution direction identifier and the second evolution intensity value acting on the coarse-grained interval.

[0081] Using a two-factor nonlinear risk response function, point-by-point mapping transformations are performed on the probability density value sequences of the fine-grained and coarse-grained intervals, respectively, to generate fine-grained trend-sensitive risk density distributions and coarse-grained trend-sensitive risk density distributions.

[0082] The two-factor nonlinear risk response function is configured such that, for any input probability density value, when the corresponding evolution direction indicator indicates that the probability density is in an increasing trend and the evolution intensity value exceeds a preset sensitivity threshold, a nonlinear amplification mapping is applied to the input density value, and the amplification factor increases monotonically with the increase of the evolution intensity value.

[0083] When the evolution direction indicator indicates that the probability density is in a downward trend, a nonlinear decay mapping is applied to the input density value, and the degree of decay increases monotonically with the increase of the evolution intensity value, so that the same original probability density value produces significantly differentiated risk density values ​​under different evolution driving forces.

[0084] By using a partitioned adaptive integrator, the fine-grained trend-sensitive risk density distribution within the fine-grained interval is numerically integrated and accumulated. During the integration process, the integration step size is automatically adjusted according to the gradient of the change of adjacent density points to obtain the fine-grained mudding risk index. The same adaptive integration process is performed on the coarse-grained trend-sensitive risk density distribution within the coarse-grained interval to obtain the coarse-grained under-grinding risk index.

[0085] The fine-particle mudification risk index and the coarse-particle undergrinding risk index are output to the monitoring system for coordinated adjustment of the mill's feed rate and grinding media replenishment strategy.

[0086] Furthermore, considering that the risks of fine-grained mud formation and coarse-grained undergrinding originate from the abnormal accumulation of probabilities at the tail ends of the particle size distribution, but the tail risk depends not only on the current probability magnitude, but also on whether the probability continues to migrate to the tail region, a probability inflow mechanism needs to be introduced for modeling.

[0087] Furthermore, considering that the risks of fine-grained mud formation and coarse-grained undergrinding primarily depend on the probability scale of particles already falling into their corresponding tail intervals, we first calculate the probability mass within the fine-grained and coarse-grained intervals. The fine-grained tail probability mass characterizes the cumulative probability of particles smaller than the fine-grained critical diameter in the particle size distribution, while the coarse-grained tail probability mass characterizes the residual probability of particles larger than the coarse-grained critical diameter. As a risk scale term, it describes the basic size of the tail anomaly at the current moment. We define the probability masses for the fine-grained tail and the coarse-grained tail separately:

[0088] ;

[0089] ;

[0090] in, for Time-varying fine-grained tail probability mass. for Time-based coarse-grained tail probability mass, The critical particle size for fine particles, The critical particle size for coarse particles, This is the lower limit for particle size detection. This represents the upper limit of particle size detection. for Time-of-flight particle size The probability density function at that location.

[0091] Furthermore, considering that the tail probabilistic mass can only represent the current anomalous scale and cannot determine whether the tail risk is continuing to worsen or is mitigating, the particle size spatial velocity field is used to determine whether the probabilistic mass is crossing the critical particle size boundary into the risk region. The velocity field is used as the direction and rate of probabilistic migration, and the probability density near the critical particle size is used as the migratable probability scale term. The coupling of the two is used to characterize the net inflow or net outflow trend of probabilistic mass to the tail region. Based on the particle size spatial velocity field, the migration flux of probability to the tail region is defined as follows:

[0092] ;

[0093] ;

[0094] in, This represents the probabilistic migration flux near the fine-grained critical boundary. This represents the probabilistic migration flux near the coarse-grained critical boundary. The critical particle size neighborhood width, This is a fine-grained orientation discriminant function used to determine whether the probability transition is moving towards the fine-grained risk region. This is a coarse-grained direction discrimination function used to determine whether the probability transition is moving towards the coarse-grained risk region. For the particle size spatial velocity field, The probability density value of the particle size location is introduced by... Neighborhood and direction discriminant functions can avoid the ineffectiveness of single-point integration and enable flux to characterize the trend of probabilistic quality crossing the critical boundary into or out of the risk zone. Flux is used to characterize the net inflow or outflow trend of granular distribution towards the tail region.

[0095] Furthermore, considering that risk assessment should reflect both the current scale and development trend of tail anomalies, tail probabilistic quality is used as the basis for risk scale, and tail probabilistic migration flux is coupled as a risk trend correction term. A bounded nonlinear mapping of flux is performed using a hyperbolic tangent function, so that tail inflow trends can amplify risk, and tail backflow trends can suppress risk, while avoiding infinite amplification of the risk index due to flux anomalies. The risk sensitivity coefficient is used to adjust the responsiveness of fine-grained mudification risk and coarse-grained undergrinding risk to trend changes. By coupling tail probabilistic quality with tail probabilistic migration flux, a dynamic risk response function is constructed.

[0096] ;

[0097] ;

[0098] in, This is the risk index for fine-grained mud formation. The risk index for coarse-grained under-grinding. This represents the sensitivity coefficient for fine-grained risk trends. This is the sensitivity coefficient for coarse-grained risk trends. The hyperbolic tangent function is used to map migration flux to a finite interval. , Each is considered as a risk size item. , These are respectively used as risk trend terms. Through nonlinear mapping, the risk is amplified when the tail probability continues to flow in, and the risk is suppressed when the tail probability flows back, so that risk assessment can distinguish between the worsening trend and the mitigation trend of tail anomalies.

[0099] Furthermore, an adaptive integration method is adopted to perform integral calculations on the tail region, which improves the calculation resolution in regions with drastic changes in probability density and reduces calculation redundancy in regions with gentle changes, thereby obtaining a fine-grained mudification risk index and a coarse-grained undergrinding risk index that simultaneously characterize the tail size and development trend.

[0100] S4: Combine the risk index and mineralogical characteristic parameters to generate an adaptive target granularity probability density function.

[0101] In step S4, the obtained raw ore mineralogical characteristic parameters are matched and judged by the process mechanism rule base to obtain the current grinding stage identifier.

[0102] By using the current grinding stage identifier, the peak position of the preset baseline particle size probability density function is offset and adjusted to generate an adaptive target particle size probability density function.

[0103] Furthermore, considering the differences in mineral composition, grain size, and grindability among different raw ores, the optimal grain size distribution target should be dynamically adjusted according to changes in ore properties. Given that a fixed target grain size distribution cannot adapt to changes in ore properties, a baseline grain size distribution is used as the basic form of the target distribution. Peak position adjustment parameters and distribution width adjustment parameters are set. The peak position adjustment parameter controls the shift of the target distribution towards the finer or coarser grain side, while the distribution width adjustment parameter controls the concentration or allowable fluctuation range of the target distribution. When the mineral grain size is finer or the liberation requirement is higher, the target peak value shifts towards the finer grain direction; when the risk of fine-grained mud formation increases, the target peak value is shifted back towards the relatively coarser grain direction or the distribution width is moderately increased; when the risk of coarse-grained under-grinding increases, the target distribution is adjusted towards enhanced grinding. Thus, mineralogical priors and online risk feedback jointly participate in the generation of the target distribution. Mineralogical characteristic parameters are used as constraints, and the current grinding stage is determined through process rule matching. The target distribution is then parameterized and adjusted based on the baseline grain size distribution function.

[0104] ;

[0105] in, For adaptive target granularity probability density function, The baseline granularity probability density function, Adjust parameters for the target distribution peak position. Adjust the parameters for the target distribution width. For particle size variable, It is jointly modified by mineral dispersal particle size, liberation requirements, and the risks of fine-grained mud formation or coarse-grained undergrinding. Used to adjust the concentration and allowable fluctuation range of the target distribution.

[0106] Furthermore, the risk index is used as a dynamic correction factor to adaptively adjust the target distribution parameters, so that the target particle size distribution can meet the mineral liberation requirements while suppressing the risk of mud formation and avoiding under-grinding.

[0107] S5: Based on the risk index and the adaptive target granularity probability density function, the optimal combination of control variables is solved through bi-objective optimization, and then converted into execution instructions by the decoupled controller and sent to the grinding actuator to achieve closed-loop control.

[0108] In step S5, the integral squared error calculation method is used to calculate the deviation between the complete granularity probability density function and the adaptive target granularity probability density function to obtain the full distribution morphological tracking error.

[0109] An optimization model with the constraint of minimizing the tracking error of the full distribution pattern and the dual objectives of minimizing the pure ore power consumption and maximizing the gold recovery rate is adopted. An improved differential evolution algorithm based on the knowledge graph hot-start population is used to optimize the risk index and obtain the optimal combination of control variables.

[0110] By combining internal model control with proportional-integral-derivative (PID) control, the optimal combination of control variables is decoupled to obtain decoupled control variables.

[0111] Fuzzy control is used to dynamically fine-tune the parameters of the decoupled control variables to obtain safe execution instructions. The safe execution instructions are then sent to the grinding actuator, and multi-dimensional time-series operation data of the grinding system are re-acquired to form closed-loop control.

[0112] The online particle size analyzer collects real-time particle size distribution data of the grinding system and supplements the real-time particle size distribution data into the multi-dimensional time-series operation data.

[0113] The feed frequency converter, water supply regulating valve and classifier speed regulator are used to receive safety execution commands to perform closed-loop optimization control of the grinding particle size of gold concentrate.

[0114] Furthermore, considering that a single particle size index cannot fully reflect the particle size distribution control deviation, the current particle size probability density function and the target particle size probability density function are compared point-by-point across the entire particle size range. The difference at each particle size position is used as the local deviation, and squaring is used to avoid the cancellation of positive and negative deviations and to amplify areas with large deviations such as peak shift, distribution width changes, and tail anomalies. Then, the local deviations across the entire particle size range are accumulated to obtain the overall distribution morphology tracking error, and a distribution error function based on the entire particle size range is constructed.

[0115] ;

[0116] Where E(t) is the total distribution morphological tracking error at time t. Let be the probability density function for the current granularity. This is the adaptive target granularity probability density function.

[0117] Furthermore, considering that grinding control not only needs to make the particle size distribution close to the target distribution, but also needs to take into account the pure ore power consumption, gold recovery rate, and the risks of fine-grained mud formation and coarse-grained under-grinding, different control objectives are transformed into a unified comprehensive optimization objective. Distribution error is used as the particle size quality term, energy consumption as the economic cost term, recovery rate as the revenue term, and the risks of fine-grained mud formation and coarse-grained under-grinding as safety penalty terms. Since the optimization objective is to minimize the comprehensive objective function, the recovery rate is introduced as a negative term, causing the algorithm to tend to select control variable combinations with higher recovery rates. The weighting coefficients are used to adjust the priority of different objectives in the optimization process. The particle size distribution error, energy consumption index, recovery rate index, and risk index are jointly used to construct a multi-objective optimization function.

[0118] ;

[0119] in, To comprehensively optimize the objective function; This represents the tracking error for the fully distributed morphology. Energy consumption index or pure ore electricity consumption per unit of ore processing volume; As an indicator of gold recovery rate; The fine-grained mudification risk index; The risk index for coarse-grained under-grinding; , , , These are the weighting coefficients for the energy consumption term, recovery rate term, fine-grained risk term, and coarse-grained risk term, respectively. Since the optimization objective is to minimize... ,therefore Introduced in the form of a pre-negative sign, it is used to make the optimization process tend to improve the gold recovery rate.

[0120] Furthermore, in the optimization process, historical working condition information is introduced to guide the initial solution, and intelligent optimization algorithms are combined to collaboratively optimize control variables such as feed rate, water replenishment, and classification parameters, so as to obtain a control strategy that takes into account the stability of particle size distribution, energy consumption reduction, and recovery rate improvement.

[0121] Furthermore, the optimized control variables are decoupled and transformed into independent adjustment commands for each execution unit, and dynamically corrected in conjunction with field constraints to form safety control commands. At the same time, online granularity detection data is used to continuously update the model input, so that granularity prediction, risk assessment and control optimization form a closed-loop adaptive adjustment process.

[0122] Example 2

[0123] Figure 1 The flowchart below shows a closed-loop optimization control method for gold concentrate grinding particle size according to an embodiment of this application, including: an adaptive target particle size probability density function comprising:

[0124] A historical operation case library was constructed. Each case in the library records the mineralogical characteristics of the raw ore, the fine-grained mudification risk index, the coarse-grained under-grinding risk index, and the optimal target particle size probability density function after manual optimization and verification.

[0125] By using a similarity retrieval technique based on weighted Euclidean distance, several similar cases with the smallest combined distance to the current original ore mineralogical characteristics and the two current risk indices are matched in the case library.

[0126] The optimal target granularity probability density function of several similar cases is weighted and fused using a local weighted regression fusion method. The weights are determined by the case similarity and risk matching degree. After fusion, an adaptive target granularity probability density function is generated.

[0127] Furthermore, considering the nonlinear coupling relationship between different raw ore mineralogical characteristic parameters and operational risk states, and that the optimal target particle size probability density function in historical cases is often obtained under specific ore properties and specific risk levels, if target distribution matching is performed solely based on mineralogical characteristics or a single risk index, the matching results may easily deviate from the actual optimal control requirements. Therefore, the raw ore mineralogical characteristic parameters, fine-grained mudification risk index, and coarse-grained under-grinding risk index are used as joint matching conditions. This allows the case retrieval process to simultaneously consider the similarity of ore properties and operational status, thereby improving the accuracy of target particle size distribution matching.

[0128] Furthermore, the weighted Euclidean distance does not apply equal weights to each feature quantity. Instead, it assigns differentiated weights to different feature dimensions based on the degree of dominance of mineralogical feature parameters on grain size distribution and the moderating effect of risk indices on grain size control deviation. Among these, mineral embedding grain size and grindability parameters are given higher weights as dominant structural terms, while fine-grained mudification risk index and coarse-grained undergrinding risk index are given adaptive weights as dynamic correction terms. This allows the similarity measure to simultaneously reflect "structural similarity" and "state similarity," thereby avoiding target distribution deviation caused by relying solely on single-dimensional matching.

[0129] Furthermore, considering that a single most similar case may be due to chance or local optima, several similar cases are selected to form a local neighborhood sample set during the case retrieval stage. Within the neighborhood, the probability density function of the target granularity is fused and calculated. The weight of each case is not only determined by the similarity distance, but also by the risk matching degree as an adjustment factor. This makes cases that are more consistent with the current risk state have a higher contribution in the fusion process, so that the generated target distribution can respond to the current mudding trend or under-grinding trend in a targeted manner.

[0130] Furthermore, the local weighted regression fusion method essentially treats multiple historical optimal target granularity probability density functions as discrete samples in the feature space. It constructs weighting coefficients through similarity weights and risk weights, and performs point-by-point weighted superposition of the sample functions. It linearly combines the target distributions of different cases in the granularity space, where the weights satisfy the normalization constraint so that the fused target probability density function still satisfies the basic properties of the probability distribution, thereby ensuring that the integral over the entire granularity range is 1.

[0131] Furthermore, the adaptive target particle size probability density function generated through the fusion mechanism is no longer a fixed form or a result inherited from a single case, but a dynamic distribution function that comprehensively reflects the current ore properties, real-time risk status, and historical optimization experience. The target distribution can automatically reduce the probability density ratio of the fine-grained interval when the risk of fine-grained mud formation increases, and increase the probability density concentration of the effective grinding interval when the risk of coarse-grained under-grinding increases, thereby achieving proactive suppression of tail risks while ensuring the mineral liberation requirements.

[0132] Furthermore, since the adaptive target granularity probability density function is generated under the coupling conditions of historical cases and the current state, it can serve as a reference benchmark for subsequent control optimization, transforming granular control from "fixed target tracking" to "dynamic target matching", thereby improving the system's adaptability and control stability under fluctuating ore properties.

[0133] Those skilled in the art will readily conceive of embodiments of the invention upon consideration of the specification and practice of the methods disclosed herein. The invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein.

[0134] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A closed-loop optimization control method for the particle size of gold concentrate grinding, characterized in that, The specific steps include the following: Collect multi-dimensional time-series operation data of the grinding system, construct a dynamic state space matrix based on a sliding time window, and perform time alignment and time lag correction on the dynamic state space matrix; The corrected dynamic state space matrix is ​​input into the granularity distribution prediction model, and the output is the granularity probability density function used to characterize the multi-peak non-stationary characteristics. Based on the particle size probability density function, a tail-sensitive mechanism is used to calculate the fine-grain mudding risk index and the coarse-grain undergrinding risk index to enhance the response capability to changes in the tail of particle size distribution. By combining the risk index and mineralogical characteristic parameters, an adaptive target granularity probability density function is generated; Based on the risk index and the adaptive target granularity probability density function, the optimal combination of control variables is solved through bi-objective optimization, and then converted into execution instructions by the decoupled controller and sent to the grinding actuator to achieve closed-loop control.

2. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The multidimensional time-series runtime data includes: Multidimensional time-series operation data of the grinding system are collected by industrial field sensors and online detection instruments to obtain raw multidimensional data including mill feed rate, water replenishment rate, mill power, classifier overflow concentration and mill sound pressure. Based on the preset sliding time window length and sliding step size, the original multidimensional data is cleaned and aligned to form a multidimensional state space matrix. The cross-correlation function method is used to perform time lag correction on the data of each dimension in the multidimensional state space matrix to obtain the corrected dynamic state space matrix.

3. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The granularity probability density function includes: By using the sliding time window differential accumulation technique, the granular distribution prediction vector at consecutive time points is differentially analyzed element by element. The difference values ​​with the same sign are accumulated by time weighting, and the difference values ​​with different signs are reduced by the attenuation factor in the direction, thus constructing the granular evolution trend quantity. The granular evolution trend quantity retains both the migration direction of the distribution pattern and the cumulative migration amplitude. The granular evolution trend is processed using a two-parameter adaptive exponential smoothing technique. The smoothing coefficient is configured such that when the trend directions of adjacent time steps are consistent, the smoothing coefficient is set to a value close to 0.9 to enhance the memory effect; when the trend directions of adjacent time steps are reversed, the smoothing coefficient is automatically reduced to below 0.3 to suppress transient disturbances. This yields the granular evolution hidden state quantity, which maintains cumulative gain only for continuous unidirectional distribution migration and maintains rapid forgetting for reverse noise. Using the probability distribution morphological migration extrapolation model, with the granular evolution hidden state variables as the driving condition, the morphological adjustment of the granular distribution prediction vector at the current moment is performed: the migration direction angle and migration intensity scalar are extracted from the hidden state variables, the horizontal displacement of the distribution peak is calculated using the direction angle, the distribution variance scaling factor is calculated using the intensity scalar, and the corresponding peak translation transformation and variance scaling transformation are applied to the probability density curve represented by the granular distribution prediction vector, respectively, to generate the extrapolation distribution under the condition of consistent trend, and the kernel density estimation is reconstructed on the extrapolation distribution to generate the granular probability density function.

4. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The calculation of the fine-grained mudification risk index and the coarse-grained undergrinding risk index includes: Based on the preset critical particle size for fine particles and critical particle size for coarse particles in the ore grinding process, the particle size probability density function is divided into three parts: fine particle interval, qualified interval and coarse particle interval. The probability density value sequence corresponding to each particle size position in the fine particle interval and the probability density value sequence corresponding to each particle size position in the coarse particle interval are extracted. By using the hidden state driving force decoupling technique, the particle size evolution hidden state vector is projected and decomposed according to the fine-grained direction basis vector and the coarse-grained direction basis vector to obtain the first evolution direction identifier and the first evolution intensity value acting on the fine-grained interval, and the second evolution direction identifier and the second evolution intensity value acting on the coarse-grained interval. Using a two-factor nonlinear risk response function, the probability density value sequences of the fine-grained interval and the coarse-grained interval are mapped and transformed point by point to generate fine-grained trend-sensitive risk density distribution and coarse-grained trend-sensitive risk density distribution. The two-factor nonlinear risk response function is configured such that, for any input probability density value, when the corresponding evolution direction indicator indicates that the probability density is in an increasing trend and the evolution intensity value exceeds a preset sensitivity threshold, a nonlinear amplification mapping is applied to the input density value, and the amplification factor increases monotonically with the increase of the evolution intensity value. When the evolution direction indicator indicates that the probability density is in a downward trend, a nonlinear decay mapping is applied to the input density value, and the degree of decay increases monotonically with the increase of the evolution intensity value, so that the same original probability density value produces significantly differentiated risk density values ​​under different evolution driving forces. The fine-grained trend-sensitive risk density distribution is numerically integrated and accumulated within the fine-grained interval using a partitioned adaptive integrator. During the integration process, the integration step size is automatically adjusted according to the gradient of the change of adjacent density points to obtain the fine-grained mudding risk index. The same adaptive integration process is performed on the coarse-grained trend-sensitive risk density distribution within the coarse-grained interval to obtain the coarse-grained under-grinding risk index. The fine-particle mudding risk index and the coarse-particle undergrinding risk index are output to the monitoring system for coordinated adjustment of the mill's feed rate and grinding media replenishment strategy.

5. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The method for generating the adaptive target granularity probability density function includes: The current grinding stage identifier is obtained by matching and judging the obtained raw ore mineralogical characteristic parameters through the process mechanism rule base; Using the current grinding stage identifier, the peak position of the preset baseline particle size probability density function is offset and adjusted to generate an adaptive target particle size probability density function.

6. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The optimal combination of control variables includes: The deviation between the complete granularity probability density function and the adaptive target granularity probability density function is calculated using the integral squared error calculation method to obtain the full distribution morphological tracking error; An optimization model is adopted with the constraint of minimizing the tracking error of the full distribution pattern and the dual objectives of minimizing pure ore power consumption and maximizing gold recovery rate. An improved differential evolution algorithm based on knowledge graph hot-start population is used to optimize the risk index and obtain the optimal combination of control variables.

7. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The closed-loop control includes: The optimal combination of control variables is decoupled by combining internal model control with proportional-integral-derivative control method to obtain decoupled control variables; The decoupled control variables are dynamically fine-tuned using a fuzzy control method to obtain a safe execution command. The safe execution command is then sent to the grinding actuator, and multi-dimensional time-series operating data of the grinding system are re-acquired to form a closed-loop control.

8. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The closed-loop optimization control includes: The online particle size analyzer collects real-time particle size distribution data of the grinding system and supplements the real-time particle size distribution data into the multi-dimensional time-series operation data. The feed frequency converter, the water supply regulating valve, and the classifier speed regulator are used to receive the safety execution command to perform closed-loop optimization control of the grinding particle size of gold concentrate.

9. The closed-loop optimization control method for gold concentrate grinding particle size according to claim 1, characterized in that, The adaptive target granularity probability density function includes: A historical operation case library is constructed. Each case in the case library records the original ore mineralogical characteristic parameters, fine-grained mudification risk index, coarse-grained under-grinding risk index, and the optimal target particle size probability density function after manual optimization and verification. Using a similarity retrieval technique based on weighted Euclidean distance, several similar cases with the smallest combined distance to the current original ore mineralogical characteristic parameters and the current two risk indices are matched in the case library. The optimal target granularity probability density function of the several similar cases is weighted and fused using a local weighted regression fusion method. The weights are determined by the case similarity and risk matching degree. The adaptive target granularity probability density function is generated after fusion.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the closed-loop optimization control method for gold concentrate grinding particle size as described in any one of claims 1-8.

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