Efficiency Prediction and Energy Consumption Optimization System and Method for Magnetic Separation Process of Low-Grade Iron Ore

Abstract

This invention belongs to the field of mineral processing process control and optimization technology. It discloses a system and method for efficiency prediction and energy consumption optimization in the magnetic separation process of low-grade iron ore. By acquiring data on the velocity distribution of the slurry flow field and the particle size distribution of the ore particles within the magnetic separator tank, the spatial location and intensity distribution of the eddy current zone are accurately identified. Three-dimensional distribution data of magnetic induction intensity are collected to identify magnetic field distortion regions. Based on the spatial overlap of these two data, a short-circuit risk coefficient is calculated, and a model for deviation in the ore particle trajectory is constructed. By real-time monitoring of the fluctuation characteristics of tailings grade and concentrate yield, abnormal separation patterns are identified. Based on the correlation between abnormal patterns and efficiency loss rates, process parameters such as magnetic field intensity distribution and slurry flow rate are dynamically adjusted. This invention achieves accurate prediction of ore particle behavior under the coupling effect of magnetic field and flow field, establishes a data-driven parameter adaptive optimization mechanism, significantly improves the concentrate grade and recovery rate of low-grade iron ore, and simultaneously reduces energy consumption.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ore dressing process control and optimization, and more particularly, relates to a low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system and method. BACKGROUND

[0002] Low-grade iron ore brings great challenges to ore dressing due to its complex mineral composition, fine dissemination size of useful minerals and high content of gangue minerals. As a high-efficiency and environmentally friendly iron ore separation method, magnetic separation plays an important role in the treatment of low-grade iron ore due to its selective separation ability for weakly magnetic minerals.

[0003] In actual production process, due to irregular geometry of the tank body, design defects of the feed inlet and uneven magnetic field gradient, etc., vortex regions with complex spatial distribution and different intensity are frequently formed in the process of slurry flow. These vortex regions are not normal flow field structures, which significantly interfere with the normal motion trajectory of the ore particles, causing some ore particles to be forced to stay in the vortex for a long time. When the vortex region overlaps with the magnetic field distortion region in space, a so-called "short circuit region" is formed, and the superposition of the two abnormal fields makes the ore particles subjected to a complex and unpredictable force system. In this case, high-grade iron ore particles that should enter the concentrate may be mistakenly directed to the tailings stream, while low-magnetic gangue minerals may be captured into the concentrate, resulting in a significant decrease in separation accuracy. The existing technology lacks accurate characterization means for the interaction between the vortex region and the magnetic field distortion region, and cannot identify the short circuit risk area in real time and carry out targeted intervention. At the same time, the traditional parameter adjustment method is mostly based on experience, which is difficult to realize precise regulation and control according to the differentiated retention behavior of different particle size ore particles, making it a technical bottleneck to maintain high recovery rate while optimizing energy consumption.

[0004] In view of this, the present application provides a low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system and method to solve the above problems. SUMMARY

[0005] In order to overcome the above-mentioned defects of the prior art and achieve the above-mentioned purposes, the present application provides the following technical solutions: a low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method, comprising:

[0006] Obtaining velocity distribution data and particle size composition data of the slurry flow field in the tank body of the magnetic separator;

[0007] Identifying the spatial position and vortex intensity distribution of the vortex region in the tank body according to the velocity distribution data, and calculating the retention probability of different particle size ore particles in the vortex region based on the particle size composition data;

[0008] The magnetic induction intensity three-dimensional distribution data of the magnetic field system of the magnetic separator is collected, and the magnetic field distortion region is identified according to the gradient change of the magnetic induction intensity between adjacent measuring points;

[0009] Based on the spatial overlap degree of the magnetic field distortion region and the eddy current region, the short-circuit risk coefficient of the ore particles in the overlapping region is calculated; and according to the short-circuit risk coefficient and the residence probability, a particle motion trajectory deviation model is constructed;

[0010] Based on the particle motion trajectory deviation model, the magnetic separation efficiency loss rate under different working conditions is predicted;

[0011] By monitoring the fluctuation characteristics of the tailing grade and the concentrate yield of the magnetic separator in real time, an abnormal separation mode of the ore particles in the tank is identified;

[0012] According to the correlation between the abnormal separation mode and the magnetic separation efficiency loss rate, the process parameters including the magnetic field intensity distribution and the pulp flow rate are dynamically adjusted;

[0013] Based on the adjusted process parameters, the magnetic separation equipment is controlled, and efficient separation and energy consumption optimization of low-grade iron ore are realized.

[0014] Preferably, the spatial position and the eddy current intensity distribution of the eddy current region in the tank are identified according to the velocity distribution data, including:

[0015] The velocity distribution data is divided into three-dimensional grids, and the velocity vector of each grid node is calculated;

[0016] The vorticity of the velocity vector between adjacent grid nodes is calculated to obtain the local vorticity distribution;

[0017] The spatial continuity of the local vorticity distribution is analyzed, and the region with a vorticity value greater than a preset vorticity threshold and spatial continuity is marked as a candidate eddy current region;

[0018] The spatial integral value of the vorticity in the candidate eddy current region is calculated as an eddy current intensity index;

[0019] According to the spatial distribution gradient of the eddy current intensity index, the core region and the boundary region of the eddy current region are determined.

[0020] Preferably, the residence probability of different particle size fractions of ore particles in the eddy current region is calculated based on the particle size composition data, including:

[0021] The particle size composition data is divided into multiple particle size intervals according to particle size, and the mass fraction of each particle size interval is counted;

[0022] According to Stokes' law, the settling velocity of different particle size fractions of ore particles in the pulp is calculated, and the relative motion velocity of the ore particles is determined in combination with the upward flow rate of the pulp;

[0023] Based on the relative motion velocity and the characteristic size of the eddy current region, the theoretical time for the ore particles to pass through the eddy current region is calculated.

[0024] Obtaining the turbulent intensity distribution in the vortex zone, and calculating the random walk step length of the ore particles according to the turbulent diffusion coefficient;

[0025] Taking the ratio of the theoretical time and the random walk step length as the residence time factor, and converting it into the residence probability through the exponential decay function.

[0026] Preferably, based on the spatial overlap degree of the magnetic field distortion region and the vortex zone, the short-circuit risk coefficient of the ore particles in the overlapping region is calculated; and according to the short-circuit risk coefficient and the residence probability, a trajectory deviation model of the ore particles is constructed, including:

[0027] Mapping the magnetic field distortion region and the vortex zone in three-dimensional space to obtain the spatial intersection region of the two;

[0028] Calculating the proportion of the volume of the spatial intersection region in the total volume of the vortex zone as the spatial overlap degree; and obtaining the product of the magnetic field gradient change rate and the vortex velocity in the spatial intersection region as the force disturbance degree of the ore particles;

[0029] According to the weighted sum of the spatial overlap degree and the force disturbance degree of the ore particles, the short-circuit risk coefficient of the ore particles in the overlapping region is calculated; and based on the short-circuit risk coefficient, the trajectory deviation probability distribution of the ore particles at different positions in the tank is calculated;

[0030] According to the residence probability and the magnetic susceptibility of the ore particles, a residence time distribution function of the ore particles in the vortex zone is established; and the trajectory deviation probability distribution and the residence time distribution function are convoluted to obtain the cumulative deviation degree of the ore particles;

[0031] Based on the cumulative deviation degree and the initial position of the ore particles, a trajectory deviation model of the ore particles is constructed, and the model includes the probability distribution of the final separation position of the ore particles.

[0032] Preferably, based on the trajectory deviation model of the ore particles, the magnetic separation efficiency loss rate under different working conditions is predicted, including:

[0033] According to the trajectory deviation model of the ore particles, the separation trajectories of different particle size iron ore particles are simulated;

[0034] The proportion of the iron ore particles deviating from the normal separation trajectory is counted as the trajectory deviation rate;

[0035] The difference between the grade of the iron ore particles entering the tailings and the theoretical recovery grade is obtained to calculate the grade loss coefficient;

[0036] The product of the trajectory deviation rate and the grade loss coefficient is combined with the pulp flow to calculate the magnetic separation efficiency loss rate.

[0037] Preferably, by real-time monitoring the fluctuation characteristics of the tailings grade and the concentrate yield of the magnetic separator, an abnormal separation mode of the ore particles in the tank is identified, including:

[0038] Wavelet decomposition is performed on the time series data of the tailings grade, and fluctuation components in different frequency bands are extracted;

[0039] The coefficient of variation of the concentrate yield is calculated, and cross-correlation analysis is performed with the fluctuation components to obtain a cross-correlation coefficient;

[0040] When the cross-correlation coefficient exceeds a preset correlation threshold, the process parameter features corresponding to the time period are extracted;

[0041] According to the correspondence between the process parameter features and the fluctuation mode, the dominant factor causing the separation anomaly is identified, and the separation anomaly mode is determined.

[0042] Preferably, according to the relevance of the separation anomaly mode and the loss rate of the magnetic separation efficiency, the process parameters are dynamically adjusted, including:

[0043] A mapping relationship matrix is established between the separation anomaly mode and the loss rate of the magnetic separation efficiency;

[0044] Based on the mapping relationship matrix, the adjustment amount of the magnetic field strength required to eliminate the separation anomaly is calculated;

[0045] According to the distribution of the vortex zone in the tank body, a partition control strategy of the slurry flow rate is determined;

[0046] The magnetic field strength adjustment amount and the partition control strategy are combined to generate a set of collaborative optimization control parameters.

[0047] Preferably, the spatial integral value of the vorticity in the candidate vortex zone is calculated as a vortex intensity index, including:

[0048] The volume elements of the candidate vortex zone are discretized to obtain the vorticity value of each volume element;

[0049] According to the distance from the volume element to the vortex center, a distance weight coefficient is assigned;

[0050] The product of the vorticity value and the distance weight coefficient is calculated to obtain the weighted vorticity;

[0051] The weighted vorticity of all volume elements is summed and divided by the total volume of the candidate vortex zone to obtain the vortex intensity index.

[0052] Preferably, the trajectory deviation probability distribution is convolved with the residence time distribution function to obtain the cumulative deviation degree of the ore particle, including:

[0053] The trajectory deviation probability distribution is discretized into a deviation probability sequence within a time step;

[0054] The residence time distribution function is subjected to Laplace transform to obtain a frequency domain expression;

[0055] The deviation probability sequence and the frequency domain expression are subjected to product operation;

[0056] inverse Laplace transform is performed on the result of the product operation to obtain a time-domain cumulative deviation function;

[0057] the cumulative deviation function is integrated in the total length of the magnetic separation process to obtain the cumulative deviation of the ore particles.

[0058] The low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system is used to implement a low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method, which comprises the following steps:

[0059] A data acquisition module is configured to acquire velocity distribution data and ore particle size composition data of a pulp flow field in a tank of a magnetic separator.

[0060] A vortex analysis module is configured to identify the spatial position and vortex intensity distribution of a vortex zone in the tank according to the velocity distribution data, and calculate the residence probability of different particle size fractions of ore particles in the vortex zone based on the ore particle size composition data.

[0061] A magnetic field analysis module is configured to acquire three-dimensional distribution data of magnetic induction intensity of a magnetic field system of the magnetic separator, and identify a magnetic field distortion region according to the gradient change of the magnetic induction intensity between adjacent measuring points.

[0062] A trajectory model construction module is configured to calculate a short-circuit risk coefficient of the ore particles in the overlapping region based on the spatial overlap degree of the magnetic field distortion region and the vortex zone, and construct an ore particle motion trajectory deviation model according to the short-circuit risk coefficient and the residence probability.

[0063] An efficiency prediction module is configured to predict the magnetic separation efficiency loss rate under different working conditions based on the ore particle motion trajectory deviation model.

[0064] An abnormality monitoring module is configured to identify an abnormal separation mode of the ore particles in the tank by monitoring the fluctuation characteristics of the tailings grade and the concentrate yield of the magnetic separator in real time.

[0065] A parameter optimization and control execution module is configured to dynamically adjust the process parameters according to the correlation between the abnormal separation mode and the magnetic separation efficiency loss rate, and control the magnetic separation equipment based on the adjusted process parameters.

[0066] The various modules are connected through wired and / or wireless means to realize data transmission between the modules.

[0067] The low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system and method have the following technical effects and advantages:

[0068] The present application realizes accurate characterization of the formation of the vortex zone and the behavior of the ore particle retention, effectively predicts and controls the risk of the ore particle motion trajectory deviation in the separation process. By establishing a model of the ore particle behavior under the coupling action of the magnetic field and the flow field, the adaptability to complex working conditions is improved, that is, even if the ore properties fluctuate and the process parameters change, stable separation effect can be maintained. The present application improves the concentrate grade and recovery rate, and significantly reduces energy consumption. In industrial applications, the present application forms a closed-loop optimization system through real-time monitoring and intelligent control, reduces human intervention, improves production continuity, and reduces equipment wear and maintenance cost. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 A low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method of the present application is shown in the figure.

[0070] Figure 2 A low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system of the present application is shown in the figure. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0072] The present application provides a low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system and method. The execution subject of the system includes but is not limited to the following: a magnetic separation device, a mineral processing control system, a mineral separation monitoring gateway, an ore dressing edge computing unit, etc., which can be regarded as a general computing node of the present application, and the mineral processing control system includes but is not limited to at least one of the following: a mineral separation PLC controller, a distributed ore dressing monitoring system, and a programmable ore dressing controller.

[0073] Please refer to Figure 1 In the embodiments of the present application, the detailed implementation steps of the low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method include:

[0074] The velocity distribution data of the pulp flow field in the tank body of the magnetic separator and the particle size composition data of the ore particles are obtained. The velocity distribution data includes the flow velocity vector information of the pulp at different positions in the tank body of the magnetic separator, which is obtained through a flow field monitoring device such as a Doppler flowmeter or a computational fluid dynamics simulation. The particle size composition data includes the mass fraction distribution of different particle sizes of the ore particles in the pulp, which is collected by a laser particle size analyzer or an image analysis system. These data provide a basis for subsequent analysis of the flow characteristics of the pulp and the behavior of the ore particles, ensuring the pertinence and accuracy of the optimization method.

[0075] The spatial position and vortex intensity distribution of the vortex region in the tank are identified according to the velocity distribution data. The vortex region is a key factor affecting the efficiency of magnetic separation, and its formation can cause the mineral particles to deviate from the ideal trajectory in the magnetic separation process. The identification process performs three-dimensional grid division on the velocity distribution data, calculates the velocity vector curl to obtain the local vorticity distribution, determines the candidate vortex region through spatial continuity analysis, and calculates the vortex intensity index. This step accurately locates the abnormal region of the flow field inside the magnetic separator, providing a spatial reference for the subsequent analysis of the motion behavior of mineral particles.

[0076] The residence probability of different particle size groups in the vortex region is calculated based on the particle size composition data. The residence probability reflects the possibility of different particle size groups staying in the vortex region, directly affecting the separation effect. The calculation process divides the mineral particles into multiple particle size intervals according to the particle size, calculates the settling velocity according to Stokes' law, and finally determines the residence time and probability relationship of the mineral particles in the vortex region considering the turbulent diffusion effect. This data provides important parameters for subsequent construction of the mineral particle motion model, ensuring that the model considers the differentiated behavior of different particle size groups.

[0077] The three-dimensional distribution data of the magnetic induction intensity of the magnetic field system of the magnetic separator is collected, and the magnetic field distortion region is identified according to the gradient change of the magnetic induction intensity between adjacent measurement points. The magnetic field distortion region is a position where the magnetic field is uneven or abnormal, which can interfere with the normal magnetization and motion trajectory of the mineral particles. The collection process uses a Hall effect magnetic induction intensity probe to establish a three-dimensional measurement grid inside the tank of the magnetic separator, obtains the magnetic induction intensity vector data of each point, and identifies the region with abnormal magnetic field gradient by calculating the magnetic field gradient tensor and its eigenvalues. This step provides key data for understanding the influence of the magnetic field on the motion of mineral particles and is the basis for optimizing the efficiency of magnetic separation.

[0078] Based on the spatial overlap degree of the magnetic field distortion region and the vortex region, the short-circuit risk coefficient of the mineral particles in the overlapping region is calculated; and according to the short-circuit risk coefficient and the residence probability, a mineral particle motion trajectory deviation model is constructed. The short-circuit risk coefficient quantifies the possibility of the mineral particles deviating from the ideal trajectory in the magnetic separation process, which is a key parameter for predicting the efficiency of magnetic separation. The calculation process maps the magnetic field distortion region and the vortex region in three-dimensional space, obtains the spatial intersection region, analyzes the force disorder degree of the mineral particles in the overlapping region, and establishes a probability distribution model of the trajectory deviation of the mineral particles combined with the residence probability. This model accurately describes the actual motion behavior of the mineral particles in the magnetic separation process, providing a theoretical basis for efficiency prediction.

[0079] Based on the trajectory deviation model of ore particles, the efficiency loss rate of magnetic separation under different working conditions is predicted. The efficiency loss rate of magnetic separation directly reflects the difference between the actual magnetic separation effect and the theoretical optimal effect, and is the core index for evaluating the performance of the magnetic separation process. The prediction process simulates the separation trajectory of different particle size iron ore particles, counts the proportion of particles deviating from the normal trajectory, and quantifies the efficiency loss under different working conditions by combining the grade loss coefficient. This step converts the theoretical model into a quantifiable efficiency index, providing an objective function for process parameter optimization.

[0080] By monitoring the fluctuation characteristics of the tailings grade and concentrate yield of the magnetic separator in real time, the abnormal separation mode of the ore particles in the tank is identified. The abnormal separation mode is an abnormal separation state that does not belong to the normal state in the magnetic separation process, which may be caused by factors such as flow field anomaly, magnetic field fluctuation or change of ore properties. The monitoring process performs wavelet decomposition on the time series of tailings grade, extracts fluctuation components of different frequency bands, and analyzes the variation coefficient of concentrate yield to identify the dominant factors causing abnormal separation. This step realizes real-time monitoring and abnormal diagnosis of the magnetic separation process, providing decision basis for dynamic adjustment.

[0081] According to the correlation between the abnormal separation mode and the efficiency loss rate of magnetic separation, the process parameters including the magnetic field intensity distribution and the slurry flow rate are dynamically adjusted. Process parameter adjustment is a direct means to optimize the efficiency of magnetic separation. By establishing the mapping relationship between the abnormal separation mode and the efficiency loss rate, the amount of parameter adjustment required to eliminate the abnormality is calculated to achieve precise control. The adjustment process considers the synergistic effect of magnetic field intensity and slurry flow rate, adopts a zoning control strategy, and differentiates adjustment according to the characteristics of different regions to ensure the comprehensiveness and accuracy of the optimization effect.

[0082] Based on the adjusted process parameters, the magnetic separation equipment is controlled to realize efficient separation of low-grade iron ore and energy consumption optimization. This is the final execution step of the entire method, which converts the optimized control parameters into actual equipment operation. The magnetic separation equipment adjusts the magnetic field intensity distribution and slurry flow rate according to the received control instructions, so that low-grade iron ore can be efficiently separated under optimized conditions, improving the recovery rate of iron concentrate and reducing energy consumption, achieving the dual goals of economy and environmental protection.

[0083] In the embodiment of the present application, the detailed implementation steps for identifying the spatial position of the vortex zone in the tank and the vortex intensity distribution according to the velocity distribution data include:

[0084] The velocity distribution data is divided into a three-dimensional grid, and the velocity vector of each grid node is calculated. Three-dimensional grid division is a discretization process of the flow field space, providing a standardized spatial reference for subsequent calculations. The division process uses adaptive grid technology to increase grid density in areas with rapid flow changes and reduce grid number in areas with slow changes, ensuring a balance between calculation accuracy and efficiency. The number of grid nodes is usually 10,000-50,000, depending on the size of the magnetic separator tank and the complexity of the flow field. Each grid node records three-dimensional velocity vector information , , ), which fully describes the flow state at that point.

[0085] The vorticity distribution is calculated by calculating the curl of the velocity vector between adjacent grid nodes. The curl is a physical quantity that characterizes the rotational motion of the fluid and directly reflects the formation and intensity of the vortex. The calculation uses the central difference method, and for each internal grid node, the curl vector of the point is calculated according to the velocity vectors of its adjacent nodes:

[0086] ;

[0087] where is the curl vector of the velocity field , with a unit of s -1 , representing the rotation characteristics of the fluid element at that point; is the component of the velocity vector in the direction, is the component of the velocity vector in the direction, is the component of the velocity vector in the direction;

[0088] The modulus of the curl vector is the vorticity value at that point, which directly quantifies the intensity of the local fluid rotation. The vorticity distribution map can intuitively show the spatial distribution characteristics of the vortex in the tank, providing basic data for subsequent vortex region identification.

[0089] Spatial continuity analysis is performed on the local vorticity distribution, and regions with vorticity values greater than the preset vorticity threshold and spatial continuity are marked as candidate vortex regions. Spatial continuity analysis aims to identify coherent vortex structures from discrete vorticity data. The analysis process first sets a preset vorticity threshold, usually taking the mean value plus twice the standard deviation, to filter out grid points with significant vorticity. Then, using the region growing algorithm, starting from the point with the maximum vorticity, gradually expanding to adjacent high vorticity points until the vorticity value is below the threshold or the spatial continuity condition is met. The spatial continuity condition considers the Euclidean distance and vorticity difference between adjacent points, ensuring that the identified vortex region structure is complete and has clear physical meaning.

[0090] The spatial integral value of the vorticity in the candidate vortex area is calculated as a vortex intensity index. The vortex intensity index is a comprehensive quantitative value for evaluating the degree of vortex influence, considering the spatial range and intensity distribution of the vortex. The calculation process discretizes the candidate vortex area into volume elements, obtains the vorticity value of each volume element, assigns a weight coefficient according to the distance from the volume element to the vortex center, calculates the sum of weighted vorticity and divides by the total volume of the vortex area to obtain the final intensity index. This index directly reflects the potential influence of the vortex on the movement of the ore particles, providing an important reference for subsequent analysis.

[0091] According to the spatial distribution gradient of the vortex intensity index, the core area and the boundary area of the vortex area are determined. The division of the core area and the boundary area of the vortex helps to accurately analyze the differential influence of the vortex on the ore particles at different positions. The determination process calculates the spatial gradient distribution of the vortex intensity index, identifies the area with significant gradient change as the boundary area, and the area with gentle gradient change and high intensity index as the core area. The core area usually accounts for 20%-40% of the total volume of the vortex area, which is the most significant part of the vortex influence, and the boundary area is the transition zone between the vortex and the normal flow field, which has a moderate influence on the movement of the ore particles. This fine division provides a spatial partition basis for subsequent calculation of the residence probability of the ore particles.

[0092] In the embodiments of the present application, the detailed implementation steps for calculating the residence probability of different particle size fractions of the ore particles in the vortex area based on the particle size composition data include:

[0093] The particle size composition data is divided into multiple particle size intervals according to particle size, and the mass fraction of each particle size interval is calculated. Particle size division is the basis for analyzing the behavior differences of different size ore particles, and equal ratio or equal difference division methods are usually used. For low-grade iron ore, typical particle size division includes <0.038mm, 0.038-0.074mm, 0.074-0.15mm, 0.15-0.3mm, 0.3-0.6mm and >0.6mm six intervals, covering the key particle size range in the magnetic separation process. The mass fraction of each interval is calculated by particle size analysis data, which reflects the proportion of the particle size ore in the total and provides a weight basis for subsequent calculation.

[0094] The settling velocity of different particle size fractions of the ore particles in the slurry is calculated according to Stokes' law, and the relative motion velocity of the ore particles is determined in combination with the upward flow velocity of the slurry. The settling velocity is a basic parameter for evaluating the motion characteristics of the ore particles in the flow field, which directly affects the separation behavior of the ore particles. The calculation formula is:

[0095] ;

[0096] wherein, is the settling velocity, representing the sinking rate of the ore particles in the slurry; is the density of the ore particles, ρp is the density of the ore particles, g is the acceleration due to gravity, dp is the diameter of the ore particles, μp is the dynamic viscosity of the ore particles. For each size interval, the median value of the interval is taken as the representative particle diameter for the calculation. The relative velocity is the vector difference between the settling velocity and the local upward flow velocity of the pulp, comprehensively considering the combined effects of gravity and flow field on the motion of ore particles.

[0097] Based on the relative velocity and the characteristic size of the vortex zone, the theoretical time for an ore particle to cross the vortex zone is calculated. The theoretical time reflects the time required for an ore particle to cross the vortex zone under ideal conditions, and is the benchmark value for assessing the risk of retention. The calculation method is to divide the characteristic size of the vortex zone by the modulus of the relative velocity, where the characteristic size is usually the projection length of the vortex zone in the main flow direction. For different vortex zones, the characteristic size may be different according to their spatial position and morphological characteristics, usually ranging from 5 to 30 cm. The theoretical time provides a time scale reference for the analysis of ore particle retention, and is the basis for subsequent calculation of retention probability.

[0098] The turbulent intensity distribution within the vortex zone is obtained, and the random walk step length of the ore particles is calculated based on the turbulent diffusion coefficient. The turbulent intensity describes the degree of turbulence of the flow field, directly affecting the random motion behavior of the ore particles. The turbulent intensity is calculated by the ratio of the velocity fluctuation component to the average velocity, and the turbulent diffusion coefficient is determined based on the turbulent intensity and the characteristic size of the vortex zone. The random walk step length represents the degree of deviation of the ore particles from the average trajectory under turbulent conditions, and the calculation formula is:

[0099] ;

[0100] where, is the random walk step length, is the turbulent diffusion coefficient, is the characteristic time scale (usually the turbulent energy dissipation time). The larger the random walk step length, the more unpredictable the motion of the ore particles in the vortex zone, and the higher the risk of retention.

[0101] The ratio of the theoretical time to the random walk step length is taken as the retention time factor, which is converted to the retention probability through an exponential decay function. The retention time factor comprehensively considers the deterministic motion and random motion characteristics of the ore particles, and is a comprehensive index for quantifying the risk of retention. The calculation formula of the retention probability is:

[0102] ;

[0103] where, is the retention probability, is the retention time factor (the ratio of the theoretical time to the random walk step length), This is a correction coefficient (typically ranging from 1.5 to 2.5, adjusted according to the type of magnetic separator and operating conditions). This conversion model, based on physical intuition and experimental verification, accurately reflects the retention behavior of mineral particles under eddy current conditions. The retention probability ranges from [0,1], with a larger value indicating a higher probability of the mineral particles remaining in the eddy current zone and a greater potential impact on magnetic separation efficiency.

[0104] In this embodiment of the invention, the method for identifying magnetic field distortion regions includes:

[0105] A three-dimensional measurement grid is established within the magnetic separator tank to obtain the magnetic flux density vector at each grid node. The three-dimensional measurement grid is a discretized representation of the magnetic field space, providing a standardized spatial reference framework for magnetic field analysis. The grid is typically established using either equal spacing or densification in key areas, setting multiple measurement points within the magnetic separator tank to form a three-dimensional spatial grid. The number of measurement points is typically 1,000-5,000, depending on the size of the magnetic separator and the required accuracy. The magnetic flux density vector at each grid node is measured using a Hall effect magnetic flux density probe. , , ), which fully describes the magnetic field state at that point.

[0106] The difference in magnetic field strength vectors between adjacent nodes is calculated and divided by the node spacing to obtain the magnetic field gradient tensor. The magnetic field gradient tensor describes the rate of change of the magnetic field in space and is a key indicator for identifying magnetic field distortion. The calculation employs the central difference method. For each internal grid node, the magnetic field gradient in each direction is calculated based on the magnetic field strength vectors of its adjacent nodes, forming a 3×3 magnetic field gradient tensor. :

[0107] ;

[0108] in, For the magnetic induction intensity vector in directional components, For the magnetic induction intensity vector in directional components, For the magnetic induction intensity vector in Component of direction;

[0109] This tensor comprehensively describes the variation characteristics of the magnetic field near this point, providing a mathematical basis for subsequent analysis of magnetic field inhomogeneity.

[0110] Eigenvalue decomposition is performed on the magnetic field gradient tensor to extract the largest eigenvalue as the magnetic field gradient intensity at that location. Eigenvalue decomposition is a mathematical method for extracting the main characteristics of a tensor, revealing the main patterns and intensity of magnetic field variations. The decomposition process involves solving the characteristic equation. ,in, I is a 3x3 matrix with diagonal elements of 1 and other elements of 0, is a scalar representing the eigenvalue to be solved; three eigenvalues of the magnetic field gradient tensor are obtained , wherein the maximum eigenvalue represents the gradient intensity in the direction where the magnetic field of the point changes most sharply, and is a direct indicator for evaluating the degree of magnetic field distortion. This method is superior to the simple gradient modulus calculation and can more accurately reflect the directional change characteristics of the magnetic field.

[0111] The spatial distribution of the magnetic field gradient intensity is counted, and the mean and standard deviation are calculated. Statistical analysis aims to establish a reference benchmark for the magnetic field gradient intensity, and to provide statistical basis for identifying abnormal values. The calculation process counts the magnetic field gradient intensity of all measurement points to obtain the mean and standard deviation , which reflect the overall distribution characteristics of the magnetic field gradient inside the magnetic separator. The mean represents the level of magnetic field change rate under normal working conditions, and the standard deviation reflects the fluctuation range of the magnetic field gradient, which together provide a scientific basis for setting the distortion judgment threshold.

[0112] Regions with magnetic field gradient intensity exceeding the mean plus twice the standard deviation are marked as candidate distortion regions. This step is based on statistical principles to identify spatial locations with significantly abnormal magnetic field gradients. The judgment criterion is:

[0113] If , the point is marked as a candidate distortion point;

[0114] This threshold setting is based on the normal distribution characteristics, and theoretically only about 2.3% of the points will be marked, ensuring the targeting of the screening. The candidate distortion points form a discrete distribution in three-dimensional space, providing raw data for subsequent connectivity analysis.

[0115] The connectivity analysis is performed on the candidate distortion region to determine the magnetic field distortion region with spatial continuity and volume greater than the preset threshold. Connectivity analysis aims to identify continuous distortion regions with physical meaning from discrete candidate distortion points. The analysis process uses a three-dimensional region growing algorithm to group spatially adjacent candidate distortion points into the same region, and then calculates the volume of each connected region. The preset volume threshold is usually 0.5%-2% of the total volume of the slot, which is determined based on the characteristics of the magnetic separator and empirical values. Only the connected regions with a volume exceeding the threshold are finally determined as the magnetic field distortion region, which avoids the noise points or small fluctuations being mistakenly identified as distortion regions, improving the reliability and practicality of the identification.

[0116] In the embodiment of the application, based on the spatial overlap degree of the magnetic field distortion region and the eddy current region, the short-circuit risk coefficient of the ore particles in the overlapping region is calculated; according to the short-circuit risk coefficient and the residence probability, the detailed implementation steps of the ore particle motion trajectory deviation model include:

[0117] The magnetic field distortion region and the vortex region are mapped in three-dimensional space to obtain the spatial intersection region. The spatial intersection region is the region where the magnetic field distortion and the vortex flow exist simultaneously, and it is the position with the highest risk of abnormal movement of ore particles. The mapping process first converts the two regions to a unified spatial coordinate system, discretizes the continuous regions into three-dimensional grid cells using voxelization technology, and then determines the set of grid cells that belong to both regions through Boolean operation to form an accurate representation of the spatial intersection. This step provides a clear spatial range definition for subsequent risk calculation.

[0118] The volume ratio of the spatial intersection region to the total volume of the vortex region is calculated as the spatial overlap degree, and the product of the magnetic field gradient change rate and the vortex velocity in the spatial intersection region is obtained as the ore particle force disorder degree. The spatial overlap degree is a direct indicator for assessing the mutual influence of the two abnormal regions, while the ore particle force disorder degree quantifies the strength of irregular force acting on the ore particles in the overlapping region. The formula for calculating the spatial overlap degree is:

[0119] ;

[0120] wherein, is the spatial overlap degree, is the volume of the intersection region, is the total volume of the vortex region. The calculation method of the ore particle force disorder degree is the point-by-point multiplication of the magnetic field gradient change rate and the local vortex velocity in the intersection region, and then taking the spatial average value as the comprehensive index. These two parameters together describe the potential disturbance degree of the overlapping region to the movement of ore particles.

[0121] According to the weighted sum of the spatial overlap degree and the ore particle force disorder degree, the short circuit risk coefficient of the ore particles in the overlapping region is calculated. The short circuit risk coefficient is a comprehensive index for evaluating the possibility of ore particles deviating from the normal separation trajectory, and directly affects the efficiency of ore separation. The calculation formula is:

[0122] ;

[0123] wherein, is the short circuit risk coefficient, is the spatial overlap degree, is the ore particle force disorder degree, and are weight coefficients (usually , , which can be adjusted according to the characteristics of the ore). This weighted model balances the influence of spatial and mechanical factors, providing a more comprehensive risk assessment. The short circuit risk coefficient is usually normalized to the interval [0, 1], and the larger the value, the higher the risk of ore particle short circuit.

[0124] Based on the short-circuit risk coefficient, the trajectory deviation probability distribution of the ore particles at different positions in the tank is calculated. The trajectory deviation probability distribution describes the possibility of the ore particles deviating from the ideal trajectory at each point in space, and is the basis for building a complete motion model. The calculation uses a risk diffusion model to determine the deviation probability at any position in the tank, with the overlapping area as the center and considering the distance attenuation effect. The model is based on the following observation: the influence of the ore particles on the overlapping area will weaken with the increase of distance, but the decay rate in different directions may be different, especially in the direction of the magnetic field line. This distribution provides a spatial probability field for subsequent trajectory simulation, enabling the model to consider the position-related risk differences.

[0125] According to the residence probability and the magnetic susceptibility of the ore particles, the residence time distribution function of the ore particles in the eddy current zone is established. The residence time distribution function describes the probability distribution of the residence time of ore particles with different magnetic susceptibilities in the eddy current zone, and reflects the time dynamic characteristics of the ore particles in the separation process. The establishment process first calculates the ratio of magnetic force to gravity according to the magnetic susceptibility of the ore particles and the strength of the applied magnetic field, estimates the average residence time of the ore particles combined with the residence probability, and then fits the complete time distribution function through Gamma distribution or Log-normal distribution. This function considers the influence of individual differences and random factors of the ore particles, and provides more rich time information than a single average value.

[0126] The trajectory deviation probability distribution and the residence time distribution function are convolved to obtain the cumulative deviation degree of the ore particles. The cumulative deviation degree considers the double influence of the deviation probability and the residence time of the ore particles, and comprehensively reflects the cumulative deviation effect of the ore particles in the separation process. The convolution operation combines the residence characteristics in the time dimension and the deviation characteristics in the space dimension, forming a comprehensive evaluation of time and space. The operation method first discretizes the trajectory deviation probability distribution into a sequence of deviation probabilities within a time step, and then performs frequency domain multiplication operation with the residence time distribution function, and finally obtains the cumulative deviation degree function in the time domain through inverse transformation. This method considers the interaction between the residence time and the deviation degree of the ore particles, and provides more accurate deviation prediction.

[0127] Based on the cumulative deviation and the initial position of the ore particle, a trajectory deviation model of the ore particle is constructed, and the model includes a probability distribution of the final separation position of the ore particle. The trajectory deviation model of the ore particle is a mathematical description of the actual motion behavior of the ore particle in the magnetic separation process, and is directly related to the accuracy of the separation efficiency prediction. The construction process is based on the initial position and the cumulative deviation, a large number of possible trajectories of the ore particle are generated by the Monte Carlo simulation method, and the distribution rule of the final position of the ore particle is counted. The final model includes two parts of information: a set of typical motion trajectories of the ore particle, and a probability distribution diagram of the final separation position. This model comprehensively considers multiple factors such as the influence of the vortex, the magnetic field distortion, the characteristics of the ore particle and the residence time, and can accurately predict the motion behavior of the ore particle in the actual separation process, and provides theoretical support for efficiency prediction and parameter optimization.

[0128] In the embodiment of the application, based on the trajectory deviation model of the ore particle, the detailed implementation steps for predicting the magnetic separation efficiency loss rate under different working conditions include:

[0129] According to the trajectory deviation model of the ore particle, the separation trajectories of iron ore particles of different particle sizes are simulated. The separation trajectory simulation is a key step for applying the theoretical model to actual prediction, and is directly related to the accuracy of the efficiency prediction. In the simulation process, the trajectory calculation of the iron ore particles of different particle sizes (usually divided into 5-7 particle size intervals) is carried out under the given working condition based on the trajectory deviation model of the ore particle. For each particle size, the initial position sample (usually 1,000-10,000) conforming to the actual distribution is randomly generated, and then the motion trajectory and the final position of each sample are predicted according to the model to form a complete trajectory set. The simulation considers the interaction between the ore particles, the influence of the boundary conditions and the random disturbance factors, and ensures the authenticity and reliability of the results.

[0130] The proportion of the iron ore particles deviating from the normal separation trajectory is counted as the trajectory deviation rate. The trajectory deviation rate directly reflects the degree of abnormal motion of the iron ore particles in the actual separation process, and is the main source of efficiency loss. The statistical process first defines the judgment standard of the normal separation trajectory (usually based on the trajectory simulation results under ideal conditions), then calculates the deviation of the actual trajectory from the normal trajectory, sets a reasonable deviation threshold, and judges the particles deviating from the threshold as the deviating particles. The trajectory deviation rate calculation formula is:

[0131] ;

[0132] Wherein, is the trajectory deviation rate, is the number of deviating particles, is the total number of simulated particles. This index directly quantifies the trajectory abnormality degree of the separation process, and provides basic data for efficiency loss evaluation.

[0133] The difference between the grade of iron ore particles entering the tailings and the theoretical recovery grade is obtained, and the grade loss coefficient is calculated. The grade loss coefficient reflects the degree of valuable component loss due to trajectory deviation, and is another important dimension of efficiency loss. The calculation process is based on simulation results, and the number and grade of iron ore particles entering the tailings stream are counted and compared with the values under the theoretical optimal separation conditions to obtain the grade difference. The grade loss coefficient calculation formula is:

[0134] ;

[0135] wherein, is the grade loss coefficient, is the iron grade entering the tailings under actual conditions, is the iron grade entering the tailings under theoretical conditions. This coefficient directly quantifies the grade loss of the separation effect, and is an important indicator for evaluating economic impact.

[0136] The product of the trajectory deviation rate and the grade loss coefficient is combined with the pulp flow to calculate the magnetic separation efficiency loss rate. The magnetic separation efficiency loss rate is a comprehensive indicator for evaluating the performance of the magnetic separation process, considering the three key factors of trajectory deviation, grade loss and processing capacity. The calculation formula is:

[0137] ;

[0138] wherein, is the magnetic separation efficiency loss rate, is the trajectory deviation rate, is the grade loss coefficient, is the actual pulp flow, is the standard design flow. This calculation model considers the nonlinear effect of flow variation on efficiency, and when the flow deviates from the design value, the efficiency loss will be further aggravated. The magnetic separation efficiency loss rate usually ranges from [0, 1], and the larger the value, the lower the actual magnetic separation efficiency, and the larger the optimization space. This index provides a direct objective function for subsequent process parameter optimization, guiding the optimization direction and intensity.

[0139] In the embodiments of the present application, by real-time monitoring of the fluctuation characteristics of the tailings grade and concentrate yield of the magnetic separator, the detailed implementation steps for identifying the abnormal pattern of particle separation in the tank body include:

[0140] Wavelet decomposition is applied to the time series data of tailings grade to extract fluctuation components in different frequency bands. Wavelet decomposition is an efficient signal analysis method that can decompose time series into fluctuation components of different frequency scales, revealing the underlying periodicity and abnormal patterns. The decomposition process selects a wavelet basis function (usually Daubechies or Symlet wavelet) that suits the characteristics of the beneficiation process, and decomposes the tailings grade time series into 3-5 layers to obtain fluctuation components in different frequency bands (such as high frequency, medium frequency, and low frequency). High frequency components usually reflect random disturbances and measurement noise, medium frequency components may be related to equipment fluctuations and flow field changes, and low frequency components may represent changes in ore properties or large-scale process fluctuations. This multi-scale analysis provides frequency domain features for abnormal pattern recognition.

[0141] The coefficient of variation of concentrate yield is calculated, and cross-correlation analysis is performed with the fluctuation components to obtain the cross-correlation coefficient. The coefficient of variation is a dimensionless index for evaluating the relative strength of data fluctuations, and cross-correlation analysis reveals the correlation between different parameters and time lag characteristics. Cross-correlation analysis calculates the correlation function of concentrate yield and fluctuation components of tailings grade in each frequency band, identifies significant time lags and correlation strengths, and reveals the internal relationship between process parameter fluctuations, providing important clues for identifying the causes of separation abnormalities.

[0142] When the cross-correlation coefficient exceeds the preset correlation threshold, the process parameter features in the corresponding period are extracted. Process parameter features are feature vectors that reflect the process conditions under abnormal separation conditions, and are key data for identifying abnormal patterns. The extraction process first sets a preset correlation threshold (usually 0.6-0.8) to filter out time periods with significant cross-correlation, and then extracts a complete set of process parameters from these time periods, including magnetic field strength, pulp concentration, feed size, flow rate distribution, and other key indicators. Extraction uses sliding time window technology to ensure that the complete process change process before and after the abnormality is captured. These parameter features provide a multi-dimensional feature space for abnormal pattern classification.

[0143] According to the correspondence between process parameter features and fluctuation patterns, the dominant factors leading to separation abnormalities are identified, and the separation abnormality patterns are determined. Separation abnormality patterns are a systematic classification of different types of magnetic separation abnormal states, directly guiding the direction and strategy of subsequent optimization and adjustment. The identification process uses pattern recognition and clustering analysis methods to find natural classification in the process parameter feature space, and combines expert knowledge to explain and name each category. Typical separation abnormality patterns include magnetic field strength fluctuation type, high pulp concentration type, vortex disturbance type, and magnetic field distortion type, each with its characteristic process parameter combination and fluctuation characteristics. The abnormal pattern recognition results are expressed in the form of decision trees or rule sets, providing clear diagnostic basis for subsequent parameter adjustment.

[0144] In the embodiments of the present application, according to the correlation between the sorting abnormal mode and the magnetic separation efficiency loss rate, the detailed implementation steps of dynamically adjusting the process parameters include:

[0145] A mapping relationship matrix of the sorting abnormal mode and the magnetic separation efficiency loss rate is established. The mapping relationship matrix quantifies the contribution of different abnormal modes to the efficiency loss, which is the theoretical basis for parameter optimization. The establishment process is based on historical data statistics and physical model derivation, and a corresponding relationship table between the abnormal mode category and the efficiency loss rate is constructed. The matrix is usually represented in the form of a heat map, with rows representing different abnormal modes and columns representing different dimensions of efficiency loss (such as total loss rate, trajectory deviation contribution, grade loss contribution, etc.), and the matrix element value reflects the contribution intensity. This matrix reveals the differential influence of various abnormalities on efficiency, guiding the rational allocation of optimization resources.

[0146] Based on the mapping relationship matrix, the magnetic field strength adjustment amount required to eliminate the sorting abnormality is calculated. The magnetic field strength is a core parameter that affects the magnetic separation effect, and its adjustment is directly related to the improvement of the separation efficiency. The calculation process first extracts the efficiency loss contribution corresponding to the current abnormal mode from the mapping relationship matrix, and then determines the theoretical optimal adjustment amount based on the sensitivity relationship between the magnetic field strength and the efficiency loss. The calculation takes into account the nonlinear effect and the constraint condition, ensuring that the adjustment amount can effectively improve the efficiency and will not cause other problems. For different regions of the magnetic field strength, differential adjustment may be needed to form a spatially distributed adjustment scheme.

[0147] According to the distribution of the eddy current zone in the tank, a partitioned control strategy for the flow rate of the ore slurry is determined. The flow rate of the ore slurry is another key parameter that affects the movement trajectory of the ore particles, and its partitioned control can solve local abnormal problems. The determination process is based on the spatial distribution and intensity characteristics of the eddy current zone, and the tank is divided into multiple control regions (usually 3-5), and differential flow rate adjustment targets are set for each region. The control strategy takes into account the hydrodynamic coupling relationship between regions to ensure that local adjustment will not cause new global problems. The partitioned control is usually represented by fuzzy control rules, which automatically determine the flow rate adjustment direction and amplitude for each region based on the eddy current intensity and position.

[0148] The magnetic field strength adjustment amount and the partitioned control strategy are integrated to generate a synergistic optimization control parameter group. The synergistic optimization control parameter group is a comprehensive scheme for coordinated adjustment of multiple parameters, taking into account the mutual influence between parameters and the overall response of the system. The generation process uses a multi-objective optimization algorithm to minimize the magnetic separation efficiency loss rate as the main objective, while considering energy consumption and equipment constraint conditions to solve the optimal parameter combination. The optimization results include the spatial distribution parameters of the magnetic field strength and the set values of the flow rate of the ore slurry in each region, forming a complete set of control instructions. Synergistic optimization ensures the coordination and consistency of parameter adjustment, avoiding the negative effects that may be caused by single-parameter optimization, and is a key technical means to achieve efficient and energy-saving magnetic separation.

[0149] In this embodiment of the invention, the detailed implementation steps for calculating the spatial integral value of vorticity within the candidate vortex region as an index of vortex intensity include:

[0150] The candidate vortex region is discretized using volume elements to obtain the vorticity value of each volume element. Volume element discretization is a numerical representation method for continuous vortex regions, providing a foundation for accurate calculation of vortex characteristics. The discretization process divides the candidate vortex region into a large number of small volume elements (usually cubes or tetrahedrons), with a volume element size typically 5-10 mm, ensuring that the fine structure of the vortex is captured. For each volume element, the vorticity value at its center point is extracted or interpolated from the vorticity distribution data to form a discrete vorticity field representation. This representation method preserves the spatial structural characteristics of the vortex region and facilitates subsequent numerical integration calculations.

[0151] Distance weighting coefficients are assigned based on the distance from each volume element to the vortex center. These coefficients reflect the differences in contribution of different locations within the vortex region to the overall vortex intensity, taking into account the spatial attenuation characteristics of the vortex. The vortex center is typically taken as the point of maximum vorticity or the vortex-weighted centroid. The Euclidean distance from each volume element to the center is calculated and then converted into weighting coefficients using a weighting function. The weighting function typically employs an exponential decay form.

[0152] ;

[0153] in, Distance The weighting coefficient at the location, The characteristic attenuation distance is typically half the equivalent radius of the eddy region. This weighting method emphasizes the contribution of the eddy core region and weakens the influence of the edge region, which is consistent with the physical characteristics of eddies.

[0154] The weighted vorticity is obtained by multiplying the vorticity value by the distance weighting coefficient. The weighted vorticity comprehensively considers both vorticity magnitude and spatial location, serving as the fundamental data for vortex intensity calculation. The calculation process involves multiplying the vorticity value of each volume element by its corresponding distance weighting coefficient to obtain the weighted contribution of that element. This weighting method considers both the dominant role of high vorticity regions and the cumulative effect of edge regions, providing a more reasonable basis for vortex intensity assessment.

[0155] The weighted vorticity of all volume elements is summed and divided by the total volume of the candidate vortex region to obtain the vortex intensity index. The vortex intensity index is a standardized and quantitative expression of the overall vortex intensity, facilitating lateral comparisons between different vortex regions. The calculation formula is:

[0156] ;

[0157] in, This is an index of eddy current intensity. For the first Distance weighting coefficients for each volume element For the first The vorticity value of a volume element This represents the total volume of the eddy region. This index comprehensively reflects the intensity and spatial distribution characteristics of the eddy, and its unit is s (s). -1 The typical range is 0.1-10s. -1 A higher value indicates a more significant potential impact of eddies on particle motion. Eddy current intensity provides a quantitative basis for subsequent analysis of the impact of eddies on magnetic separation efficiency and is an important parameter for constructing particle motion models.

[0158] In this embodiment of the invention, the detailed implementation steps for convolving the trajectory deviation probability distribution with the residence time distribution function to obtain the cumulative deviation of mineral particles include:

[0159] The trajectory deviation probability distribution is discretized into a sequence of deviation probabilities within a time step. Discretization transforms a continuous probability distribution into a discrete data structure suitable for numerical computation and is a preparatory step for convolution operations. The process first determines an appropriate time step. (Typically 0.01-0.1s, depending on the characteristics of the sorting process), then the entire sorting time range. Divided into time step ( For each time step i, the instantaneous deviation probability pi of the mineral particle at that moment is calculated, forming a complete probability sequence. Discretization takes into account the temporal evolution characteristics of the mineral particle position during magnetic separation, converting the spatial probability distribution into a time series representation, and providing standardized input for subsequent convolution.

[0160] A Laplace transform is applied to the dwell time distribution function to obtain its frequency domain expression. The Laplace transform is a mathematical tool for converting time-domain functions into frequency-domain representations, facilitating complex time convolution calculations. The transformation process applies the Laplace transform formula to the dwell time distribution function f(t):

[0161] ;

[0162] in, This is the transformed frequency domain expression. It is a complex variable; It is the original time-domain function, specifically referring to the residence time distribution function, which describes the probability density of the residence time of mineral particles in the eddy region; It is a time variable. In practical calculations, numerical Laplace transform methods, such as the Talbot algorithm or the Weeks method, are typically used to convert the distribution function of discrete sample points into a frequency domain representation. Frequency domain representation has computational advantages, especially for convolution operations on complex distribution functions, which can significantly improve computational efficiency and numerical stability.

[0163] The deviation probability sequence is multiplied with the frequency domain expression. The frequency domain multiplication is an efficient method to realize time domain convolution, based on the convolution theorem: time domain convolution is equivalent to frequency domain multiplication. The operation process first takes Laplace transform on the deviation probability sequence, obtaining its frequency domain expression Then the point-to-point multiplication of and is calculated This step converts the convolution relationship of two time functions into simple algebraic operation, greatly simplifying the calculation complexity, especially for long sequences or complex distribution functions.

[0164] The inverse Laplace transform is performed on the multiplication result to obtain the time domain cumulative deviation function. The inverse Laplace transform converts the frequency domain result back to the time domain to obtain the final cumulative deviation function. The transform adopts numerical inverse Laplace methods such as Stehfest algorithm or Fourier series method to convert the frequency domain expression back to the time domain function . The obtained is the cumulative deviation function considering the residence time distribution, which describes the deviation degree of the ore particles accumulated over time. This function directly reflects the dynamic evolution law of the deviation of the ore particles from the normal trajectory in the separation process, providing in-depth insight into the time dimension for evaluating the separation effect.

[0165] The cumulative deviation function is integrated over the total time length of the magnetic separation process to obtain the cumulative deviation degree of the ore particles. The integral operation converts the time function into a single comprehensive index, facilitating subsequent model construction and efficiency prediction. The calculation formula is:

[0166] ;

[0167] Wherein, is the cumulative deviation degree of the ore particles, is the cumulative deviation function, and the integral interval is [0, T], and T is the total time length of the magnetic separation process. In actual calculation, numerical integral methods such as trapezoidal rule or Simpson rule are adopted to perform weighted summation on the function values at discrete time points. The cumulative deviation degree is a dimensionless index, usually ranging from 0 to 1, and the larger the value, the more serious the cumulative deviation of the ore particles in the entire separation process, and the worse the separation effect. This index provides a core parameter for constructing a complete deviation model of the ore particle motion trajectory, which is directly related to the subsequent efficiency prediction and parameter optimization.

[0168] The above describes the low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method in the embodiments of the present application, and the following describes the low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system in the embodiments of the present application. Please refer to Figure 2The embodiment of the low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system in the application comprises:

[0169] A data acquisition module is configured to acquire velocity distribution data and particle size composition data of a pulp flow field in a tank of a magnetic separator.

[0170] A vortex analysis module is configured to identify the spatial position and vortex intensity distribution of a vortex zone in the tank according to the velocity distribution data, and calculate the residence probability of different particle sizes in the vortex zone based on the particle size composition data.

[0171] A magnetic field analysis module is configured to acquire three-dimensional distribution data of magnetic induction intensity of a magnetic field system of the magnetic separator, and identify a magnetic field distortion region according to the gradient change of the magnetic induction intensity between adjacent measuring points.

[0172] A trajectory model construction module is configured to calculate a short-circuit risk coefficient of the particles in the overlapping region based on the spatial overlap degree of the magnetic field distortion region and the vortex zone, and construct a particle motion trajectory deviation model according to the short-circuit risk coefficient and the residence probability.

[0173] An efficiency prediction module is configured to predict the magnetic separation efficiency loss rate under different working conditions based on the particle motion trajectory deviation model.

[0174] An abnormality monitoring module is configured to identify a particle separation abnormality mode in the tank by monitoring the fluctuation characteristics of the tailings grade and the concentrate yield of the magnetic separator in real time.

[0175] A parameter optimization and control execution module is configured to dynamically adjust process parameters according to the correlation between the separation abnormality mode and the magnetic separation efficiency loss rate, and control the magnetic separation equipment based on the adjusted process parameters.

[0176] The modules are connected through wired and / or wireless means to realize data transmission between the modules.

[0177] The application identifies the vortex zone and the magnetic field distortion region by acquiring the pulp flow field and particle size data in the tank of the magnetic separator, calculates the residence probability and short-circuit risk coefficient of the particles, constructs an accurate particle motion trajectory deviation model, combines the fluctuation characteristics of the tailings grade and the concentrate yield monitored in real time, realizes the high-efficiency prediction of the magnetic separation process and the dynamic optimization of the process parameters, has high adaptability, can adjust the magnetic separation parameters in real time according to different ore characteristics and working conditions, significantly improves the iron ore recovery rate, and reduces the energy consumption cost.

[0178] The above merely describes preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, the technical solutions recorded in the foregoing embodiments can be modified or some technical features thereof can be replaced equivalently by those skilled in the art, without departing from the spirit and principle of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall fall within the scope of the present application.

[0179] It should be noted that the formulas in the specification are dimensionless values, and the formulas are obtained by software simulation of a large amount of data to obtain a formula closest to the real situation. The preset parameters and threshold values in the formula are set by those skilled in the art according to the actual situation.

[0180] Although the embodiments of the present application have been shown and described, those skilled in the art can understand that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the claims and their equivalents.

Claims

1. A method for predicting the efficiency and optimizing the energy consumption of a low-grade iron ore magnetic separation process, characterized in that, The method comprises the following steps: acquiring velocity distribution data and particle size composition data of a pulp flow field in a tank of a magnetic separator; identifying spatial positions and vortex intensity distributions of vortex regions in the tank according to the velocity distribution data, and calculating a residence probability of different particle sizes of particles in the vortex regions based on the particle size composition data; acquiring three-dimensional distribution data of magnetic induction intensity of a magnetic field system of the magnetic separator, and identifying a magnetic field distortion region according to gradient changes of the magnetic induction intensity between adjacent measuring points; calculating a short-circuit risk coefficient of particles in an overlapping region based on a spatial overlap degree of the magnetic field distortion region and the vortex region, including: performing three-dimensional spatial mapping on the magnetic field distortion region and the vortex region to obtain a spatial intersection region of the two regions; calculating a proportion of a volume of the spatial intersection region to a total volume of the vortex region as the spatial overlap degree; and obtaining a product of a magnetic field gradient change rate in the spatial intersection region and a vortex velocity as a force disturbance degree of the particles; calculating the short-circuit risk coefficient of the particles in the overlapping region according to a weighted sum of the spatial overlap degree and the force disturbance degree of the particles; and constructing a particle motion trajectory deviation model according to the short-circuit risk coefficient and the residence probability; predicting a magnetic separation efficiency loss rate under different working conditions based on the particle motion trajectory deviation model; identifying a particle separation abnormal mode in the tank by monitoring fluctuation characteristics of tailings grade and concentrate yield of the magnetic separator in real time; dynamically adjusting process parameters according to a correlation between the separation abnormal mode and the magnetic separation efficiency loss rate; and controlling the magnetic separation equipment based on the adjusted process parameters.

2. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 1, characterized in that, The method of identifying spatial positions and vortex intensity distributions of vortex regions in the tank according to the velocity distribution data comprises the following steps: performing three-dimensional grid division on the velocity distribution data to calculate a velocity vector of each grid node; calculating a vorticity of the velocity vector between adjacent grid nodes to obtain a local vorticity distribution; performing spatial continuity analysis on the local vorticity distribution to mark a region with a vorticity value greater than a preset vorticity threshold and spatial continuity as a candidate vortex region; calculating a spatial integral value of the vorticity in the candidate vortex region as a vortex intensity index; determining a core region and a boundary region of the vortex region according to a spatial distribution gradient of the vortex intensity index.

3. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 1, characterized in that, The method of calculating a residence probability of different particle sizes of particles in the vortex regions based on the particle size composition data comprises the following steps: dividing the particle size composition data into a plurality of particle size intervals according to particle sizes, and counting mass fractions of each particle size interval; calculating a settling velocity of different particle sizes of particles in the pulp according to Stokes' law, and determining a relative motion velocity of the particles in combination with an upward flow velocity of the pulp; calculating a theoretical time of the particles passing through the vortex region based on the relative motion velocity and a characteristic size of the vortex region; acquiring a turbulent intensity distribution in the vortex region, and calculating a random walk step length of the particles according to a turbulent diffusion coefficient; taking a ratio of the theoretical time to the random walk step length as a residence time factor, and converting the residence time factor into the residence probability through an exponential decay function.

4. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 1, characterized in that, The method of constructing a particle motion trajectory deviation model according to the short-circuit risk coefficient and the residence probability comprises the following steps: calculating a trajectory deviation probability distribution of the particles at different positions in the tank based on the short-circuit risk coefficient; According to the residence probability and the magnetic susceptibility of the ore particles, a residence time distribution function of the ore particles in the eddy current zone is established; the trajectory deviation probability distribution is convoluted with the residence time distribution function to obtain a cumulative deviation degree of the ore particles; Based on the cumulative deviation degree and the initial position of the ore particles, a trajectory deviation model of the ore particles is constructed, and the model includes a probability distribution of a final separation position of the ore particles.

5. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 1, characterized in that, Based on the trajectory deviation model of the ore particles, a loss rate of the magnetic separation efficiency under different working conditions is predicted, including: According to the trajectory deviation model of the ore particles, a separation trajectory of the iron ore particles of different particle sizes is simulated; An occupancy ratio of the iron ore particles deviating from the normal separation trajectory is counted as a trajectory deviation rate; A difference between a grade of the iron ore particles entering tailings and a theoretical recovery grade is obtained to calculate a grade loss coefficient; A product of the trajectory deviation rate and the grade loss coefficient is combined with a pulp flow to calculate the loss rate of the magnetic separation efficiency.

6. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation process according to claim 1, characterized in that, The abnormal separation mode of the ore particles in the tank is identified by monitoring the fluctuation characteristics of the tailings grade and the concentrate yield of the magnetic separator in real time, including: Wavelet decomposition is performed on time series data of the tailings grade to extract fluctuation components of different frequency bands; A variation coefficient of the concentrate yield is calculated, and cross-correlation analysis is performed on the fluctuation components to obtain a cross-correlation coefficient; When the cross-correlation coefficient exceeds a preset correlation threshold, process parameter characteristics of a corresponding time period are extracted; According to a corresponding relationship between the process parameter characteristics and the fluctuation mode, a dominant factor causing the separation abnormality is identified to determine the separation abnormality mode.

7. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 1, characterized in that, According to the correlation between the separation abnormality mode and the loss rate of the magnetic separation efficiency, process parameters are dynamically adjusted, including: A mapping relationship matrix of the separation abnormality mode and the loss rate of the magnetic separation efficiency is established; Based on the mapping relationship matrix, an adjustment amount of the magnetic field strength required to eliminate the separation abnormality is calculated; According to the distribution of the eddy current zone in the tank, a partition control strategy of the pulp flow rate is determined; The magnetic field strength adjustment amount and the partition control strategy are comprehensively considered to generate a group of collaborative optimization control parameters.

8. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 2, characterized in that, The spatial integral value of the vorticity in the candidate eddy current zone is calculated as a vorticity intensity index, including: The candidate eddy current zone is discretized into volume elements to obtain the vorticity value of each volume element; According to the distance from the volume element to the center of the eddy current, a distance weight coefficient is assigned; The product of the vorticity value and the distance weight coefficient is calculated to obtain a weighted vorticity; The weighted vorticity of all volume elements is summed and divided by the total volume of the candidate eddy current zone to obtain the vorticity intensity index.

9. The process efficiency prediction and energy optimization method for low-grade iron ore magnetic separation according to claim 4, characterized in that, The trajectory deviation probability distribution is convoluted with the residence time distribution function to obtain the cumulative deviation degree of the ore particles, including: The trajectory deviation probability distribution is discretized into a deviation probability sequence within a time step; The residence time distribution function is subjected to Laplace transformation to obtain a frequency domain expression; The deviation probability sequence is multiplied with the frequency domain expression; Inverse Laplace transformation is performed on the result of the multiplication operation to obtain a cumulative deviation degree function in the time domain; The cumulative deviation degree function is integrated within the total time length of the magnetic separation process to obtain the cumulative deviation degree of the ore particles.

10. A low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization system for implementing the low-grade iron ore magnetic separation process efficiency prediction and energy consumption optimization method of any one of claims 1 to 9, characterized in that, including: The data acquisition module is configured to acquire velocity distribution data and particle size composition data of a flow field of a slurry in a tank of a magnetic separator. The vortex analysis module is configured to identify spatial positions and vortex intensity distributions of vortex zones in the tank according to the velocity distribution data, and to calculate residence probabilities of different particle sizes in the vortex zones based on the particle size composition data. The magnetic field analysis module is configured to acquire three-dimensional distribution data of magnetic induction intensity of a magnetic field system of the magnetic separator, and to identify magnetic field distortion regions according to gradient changes of the magnetic induction intensity between adjacent measuring points. The trajectory model construction module is configured to calculate a short-circuit risk coefficient of a particle in an overlapping region based on spatial overlapping degrees of the magnetic field distortion regions and the vortex zones. A particle motion trajectory deviation model is constructed according to the short-circuit risk coefficient and the residence probability. The efficiency prediction module is configured to predict a magnetic separation efficiency loss rate under different working conditions based on the particle motion trajectory deviation model. The abnormality monitoring module is configured to identify a particle separation abnormality mode in the tank by monitoring fluctuation characteristics of tailings grade and concentrate yield of the magnetic separator in real time. The parameter optimization and control execution module is configured to dynamically adjust process parameters according to a correlation between the separation abnormality mode and the magnetic separation efficiency loss rate, and to control the magnetic separation equipment based on the adjusted process parameters. The various modules are connected through wired and / or wireless means to realize data transmission between the modules.

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