A method for gradually optimizing the variable cross-section parameters of a spiral chute

Abstract

The present invention provides a method for gradually optimizing the variable cross-section parameters of a spiral chute, specifically relating to the technical field of spiral chute optimization design. By constructing an Eulerian Muti-fluid VOF model of the spiral chute, combining the Kriging interpolation method with an optimization algorithm, selecting the overall downward inclination angle as the optimization parameter and the separation efficiency as the optimization objective, the first optimal overall downward inclination angle is optimized; the local downward inclination angle and the progressive number of turns are used as the optimization parameters, and the separation efficiency is used as the optimization objective to optimize the second optimal local downward inclination angle and the optimal progressive number of turns, and the starting optimized cross-section shape is determined; a flow field monitoring cross-section is set to determine the starting optimized cross-section position; the starting optimized cross-section position, the first optimal overall downward inclination angle, the second optimal local downward inclination angle and the optimal progressive number of turns are used to optimize the local downward inclination angle to complete the gradual optimization of the variable cross-section parameters of the spiral chute. The present invention can improve the separation efficiency of the spiral chute and achieve efficient separation of minerals.

Description

Technical Field

[0001] The present invention relates to the technical field of spiral chute optimization design, and specifically to a method for gradually optimizing the variable cross-section parameters of a spiral chute. Background Art

[0002] A spiral chute is a device that realizes mineral separation by relying on the physical properties of minerals themselves as well as gravity, centrifugal force, etc. It has many advantages such as large processing capacity, low energy consumption, no pollution, high separation efficiency, and wide separation range, and is widely used in the field of mineral processing. However, currently, spiral chutes generally have problems such as low concentrate yield, large loss of fine-grained minerals, and low separation accuracy, which greatly limit their large-scale application.

[0003] The structural characteristics of a spiral chute have an important impact on the mineral separation effect. Among them, the cross-sectional shape of the spiral chute is the key to determining the separation results of minerals with different particle sizes. Currently, the cross-sectional shape curve generally adopts the form of a cubic parabola, and the downward slope angle is an important parameter that determines the change trend of the cubic parabola. A larger downward slope angle is beneficial for minerals with a larger specific gravity to gather inward, and reducing the downward slope angle can increase the tendency of minerals with a smaller specific gravity to move outward. The traditional downward slope angle of a spiral chute usually remains consistent as a whole, making it difficult to simultaneously consider the separation efficiency of both heavier and lighter minerals during separation. Currently, in the optimization design of spiral chutes, there are few optimization methods for the cross-sectional shape, such as changing the curve function expression, using a curve segmentation optimization strategy, etc. However, the universality of these methods is low, and the separation effect is not very ideal. Moreover, there is little research on variable cross-section optimization methods at present. Therefore, developing a method for gradually optimizing the variable cross-section parameters of a spiral chute, gradually optimizing the downward slope angle and the overall downward slope angle of the spiral chute, and reasonably determining the position of the variable cross-section has important theoretical research value and engineering practical application significance for improving the separation efficiency of the spiral chute and realizing efficient mineral separation.

[0004] Currently, optimization algorithms based on deep learning have begun to be applied to the optimization design of spiral chutes, and can perform optimization calculations under the condition of a small sample size. However, some optimization algorithms have problems such as slow convergence speed and high computational complexity when facing non-linear or systems with complex interaction effects, and the applications in this regard are not yet mature. At the same time, when verifying the results of the optimization algorithm, the method of numerical simulation calculation is usually adopted. Although the results obtained in this way are highly accurate, the cost is high and the calculation requires a large amount of resources, and it does not have good universality. The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure, and therefore it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The object of the present invention is to provide a method for gradually optimizing the variable cross-section parameters of a spiral chute to solve the problems raised in the above-mentioned background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for gradually optimizing the variable cross-section parameters of a spiral chute, the specific steps include:

[0008] Step 1: Use the Eulerian Muti-fluid VOF model to perform numerical calculations of the multiphase flow in the spiral chute, and optimize the Eulerian Muti-fluid VOF model through model tests;

[0009] Step 2: Take the overall downward inclination angle as the first optimization parameter, select the separation efficiency of the heavier mineral among the two minerals as the first optimization target, design an optimization target threshold according to the design efficiency, select R different overall downward inclination angles as the initial samples, and construct an initial sample scheme;

[0010] Step 3: Substitute the overall downward inclination angle in the initial sample scheme into the Eulerian Muti-fluid VOF model to obtain the mass flow rate data under different initial sample schemes, calculate the first optimization target value according to the mass flow rate data, and generate an initial data set based on the overall downward inclination angle and the separation efficiency of the heavier mineral among the two minerals;

[0011] Step 4: Set constraint conditions, analyze the initial data set based on the Kriging interpolation method, establish an approximate functional relationship between the first optimization parameter and the first optimization target, and determine the change range of the overall downward inclination angle according to the approximate functional relationship between the first optimization parameter and the first optimization target and in combination with the optimization target threshold;

[0012] Step 5: Use the overall downward inclination angle change range to constrain the feasible solution space, and use the particle swarm optimization algorithm to search in the feasible solution space to obtain the first optimal overall downward inclination angle;

[0013] Step 6: Set M monitoring cross-sections of the spiral chute flow field, use the Eulerian Muti-fluid VOF model to simulate the separation data, generate an optimized interface judgment coefficient according to the separation data, and determine the starting optimization cross-section position through the optimized interface judgment coefficient;

[0014] Step 7: Select the local downward inclination angle and the progressive number of turns as the second optimization parameters, select the separation efficiency of the lighter mineral among the two minerals as the second optimization target, repeat steps 2 to 5, obtain the second optimal local downward inclination angle and the optimal progressive number of turns, and optimize the local downward inclination angle based on the starting optimization cross-section position, the first optimal overall downward inclination angle, the second optimal local downward inclination angle, and the optimal progressive number of turns.

[0015] Furthermore, in step 1, the numerical calculation uses the simulation result of the gas-liquid two-phase flow in the spiral chute as the initial flow field. After the calculation stabilizes, the gas-liquid-solid three-phase flow simulation is carried out. In the numerical calculation, the multiphase flow model is selected as the Eulerian Muti-fluid VOF model; the turbulence model is selected as the RNG k-ε turbulence model; the inlet boundary condition is a velocity inlet, and the outlet boundary is a pressure outlet; the lower wall surface and the side wall surface are non-slip wall surfaces, and the upper surface is a free liquid surface. At the same time, the inlet velocity of the mineral phase is the same as that of water. The stability of the calculation is determined by the residual of each calculation of the model. If R < 10 -3 , it is determined that the calculation is stable, where R is the residual of each calculation of the model.

[0016] Furthermore, the optimization target threshold is η y ∈[0.8η D , η D , where η y is the optimization target threshold, and η D is the design efficiency;

[0017] Furthermore, the mass flow rate data includes the mass flow rates of the two minerals in the concentrate zone at the outlet of the spiral chute, the total mass flow rate of the two minerals at the outlet of the spiral chute, and the mass flow rates of the two minerals in the tailings zone at the outlet of the spiral chute;

[0018] The specific formula for calculating the separation efficiency is:

[0019]

[0020] where η1 is the separation efficiency of the mineral with a heavier specific gravity among the two minerals, and η2 is the separation efficiency of the mineral with a lighter specific gravity among the two minerals; Q a is the total mass flow rate of the mineral with a heavier specific gravity among the two minerals at the outlet of the spiral chute, Q b is the total mass flow rate of the mineral with a lighter specific gravity among the two minerals at the outlet of the spiral chute, Q a1 is the mass flow rate of the mineral with a heavier specific gravity among the two minerals in the concentrate zone at the outlet of the spiral chute, Q b1 is the mass flow rate of the mineral with a lighter specific gravity among the two minerals in the concentrate zone at the outlet of the spiral chute, Q a2 is the mass flow rate of the mineral with a heavier specific gravity among the two minerals in the tailings zone at the outlet of the spiral chute, Q b2 is the mass flow rate of the mineral with a lighter specific gravity among the two minerals in the tailings zone at the outlet of the spiral chute;

[0021] The initial data set is expressed as: where x n is the overall downward inclination angle of the nth group of samples, and z(x n ) is the overall downward inclination angle of xn Sorting efficiency of the sample

[0022] Furthermore, the constraint conditions include an unbiasedness constraint condition and an optimality constraint condition. Among them, the unbiasedness constraint condition is that the expected value of the predicted value is equal to the expected value of the true value, and the optimality constraint condition is that the prediction variance is minimized;

[0023] Based on the Kriging interpolation method, the specific logic for establishing the approximate functional relationship between the first optimization parameter and the first optimization objective is as follows: randomly select K samples from the initial dataset to form a random dataset, construct a mathematical expression for predicting the sorting efficiency, construct a covariance function, calculate the prediction variance through the covariance function, minimize the prediction variance under the unbiasedness constraint condition, construct a weight calculation function, construct a complete Kriging equation system according to the weight calculation function, solve the Kriging equation system to obtain the sorting efficiency weight, calculate the predicted sorting efficiency according to the sorting efficiency weight and the mathematical expression of the predicted sorting efficiency, calculate the corresponding predicted sorting efficiency for each value within the overall downslope angle value range, and draw the overall downslope angle - predicted sorting efficiency image, and obtain the overall downslope angle corresponding to 0.8η D and η D The corresponding overall downslope angle, and the change range of the overall downslope angle is: γ1 ≤ γ l ≤ γ2, where γ l is the overall downslope angle, γ1 is the smaller overall downslope angle among the overall downslope angles corresponding to 0.8η D and η D The corresponding overall downslope angle, and γ2 is the larger overall downslope angle among the overall downslope angles corresponding to 0.8η D and η D The corresponding overall downslope angle; η D is the design efficiency;

[0024] For heavy minerals, as the overall downslope angle increases, it is easier for them to concentrate towards the inner side of the chute, which will lead to an enhanced enrichment effect of heavy minerals in the concentrate zone and improve the sorting efficiency; for light minerals, as the overall downslope angle decreases, the light minerals are more likely to move with the water flow and increase their outward movement, which may enhance the separation effect; improve the overall sorting efficiency;

[0025] The predicted sorting efficiency is expressed as:

[0026]

[0027] z * (x0) is the predicted sorting efficiency when the overall downslope angle is x0, x0 is the overall downslope angle for which the sorting efficiency needs to be predicted, x k is the overall downslope angle of the kth sample, λ k is the sorting efficiency weight, and Let \(K\) be the number of samples in the random data set, \(k\) be the index of the samples in the random data set, and \(k\in[1, K]\);

[0028] The covariance function is expressed as:

[0029]

[0030] \(C(x\) i , \(x\) j ) is the covariance function, \(x\) i is the overall downward slope angle of the \(i\)-th sample in the random data set, \(x\) j is the overall downward slope angle of the \(j\)-th sample in the random data set, \(i\) and \(j\) are the indices of the samples in the random data set, and \(C_0\), \(C\), and \(a\) are model parameters obtained by fitting through a variation experiment function;

[0031] The specific logic for obtaining \(C_0\), \(C\), and \(a\) is as follows: First, construct a variation experiment function, input the samples in the initial data set into the variation experiment function to obtain a large number of fitting data, form a fitting data set, select an exponential covariance fitting mathematical model, and fit the fitting data set to the exponential covariance fitting mathematical model to obtain the model parameters;

[0032] The variation experiment function is expressed as:

[0033]

[0034] where \(\gamma(h)\) is the value of the variation experiment function, \(h\) is the reference interval distance, \(N_{\gamma(h)}\) is the number of point pairs with interval distance \(h\) in the initial sample set, \(x\) t is the overall downward slope angle of the \(t\)-th sample in the initial sample set, \(x\) r is the overall downward slope angle of the \(r\)-th sample in the initial sample set, and \(t\) and \(r\) are the indices of the samples in the initial sample set;

[0035] The exponential covariance fitting mathematical model is expressed as:

[0036] \(\gamma(h)=C_0 + C(1 - e\) -3h / a )

[0037] The specific formula for calculating the prediction variance is:

[0038]

[0039] where \(\sigma\) 2 is the prediction variance;

[0040] Under the unbiasedness constraint condition, to minimize the prediction variance, the constructed weight calculation function is expressed as:

[0041]

[0042] Among them, L is the weight calculation function, and μ is the Lagrange multiplier;

[0043] Based on the weight calculation function, a complete Kriging equation set is constructed, expressed as:

[0044]

[0045] Furthermore, M spiral chute flow field monitoring sections are set, and the setting method is as follows: Using the RNG k-ε turbulence model in the EulerianMuti-fluid VOF model in Step 1, a longitudinal section is set every α along the flow direction inside the spiral chute, and the section range is the range of the concentrate zone, where 5° ≤ α ≤ 30°;

[0046] The sorting data includes the mass flow rate of each spiral chute flow field monitoring section, the mass flow rate of the concentrate zone at the spiral chute outlet, the average inlet velocity of each spiral chute flow field monitoring section, the average outlet velocity of each spiral chute flow field monitoring section, the inlet turbulent kinetic energy of each spiral chute flow field monitoring section, and the outlet turbulent kinetic energy of each spiral chute flow field monitoring section;

[0047] Using the Eulerian Muti-fluid VOF model, simulate the sorting data of each spiral chute flow field monitoring section starting from the spiral chute inlet direction; analyze the sorting data to obtain the optimized interface judgment coefficient, preset the optimized interface judgment threshold. When the optimized interface judgment coefficient is less than or equal to the optimized interface judgment threshold, record the position at this time as the optimized section position. If there are multiple positions meeting the above requirements, set the first optimized section position as the starting optimized section position of the spiral chute;

[0048] The specific formula for calculating the optimized interface judgment coefficient is:

[0049]

[0050] Among them, YH is the optimized interface judgment coefficient, Q c is the mass flow rate of the c-th spiral chute flow field monitoring section, Q o is the mass flow rate of the concentrate zone at the spiral chute outlet, V c is the average inlet velocity of the c-th spiral chute flow field monitoring section, Vv c is the average outlet velocity of the c-th spiral chute flow field monitoring section, Ka c is the inlet turbulent kinetic energy of the c-th spiral chute flow field monitoring section, Kb c is the outlet turbulent kinetic energy of the c-th spiral chute flow field monitoring section, and c is the index of the spiral chute flow field monitoring section.

[0051] Furthermore, the specific formula for optimizing the local downward slope angle is:

[0052]

[0053] n ot = N e -N s

[0054] Among them, γ is the optimized local down angle, is the first optimal overall down angle, is the second optimal local down angle; The progressive circles inside the spiral chute are sequentially numbered along the flow direction. w is the index of the progressive circle, and w ∈ (1, W), where W is the total number of progressive circles inside the spiral chute. N s is the index of the progressive circle at the starting optimized section position, N e is the index of the progressive circle at the optimized end section position, n ot is the number of optimal optimized progressive circles.

[0055] Compared with the prior art, the beneficial effects of the present invention are:

[0056] The present invention provides a method for gradually optimizing the variable cross-section parameters of a spiral chute. By constructing a numerical simulation calculation model for multiphase flow in the spiral chute, the down angles of different regions of the spiral chute are gradually optimized, while taking into account the separation efficiencies of both heavier and lighter minerals, providing a new idea and method for the optimized design of the spiral chute structure. In addition, the present invention combines the advantages of the Kriging interpolation model and the optimization algorithm. By constructing an approximate response surface of the objective function with a small number of initial samples, it replaces the time-consuming numerical simulation and simulation calculations, and then uses the algorithm for iterative optimization, saving more than 90% of the computing resources. At the same time, the Kriging model also provides the prediction variance, and the optimization algorithm can design the fitness function accordingly to automatically balance "exploiting the known optimal region" and "exploring potential new regions". It saves the optimization time and the cost of numerical calculation verification, while improving the separation efficiency of the spiral chute, achieving the efficient separation of minerals, and having important theoretical research value and engineering practical application significance for improving the performance of the spiral chute, laying a foundation for the development of intelligent and automated spiral chutes. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a schematic diagram of the overall method flow of the present invention;

[0058] Figure 2 is a schematic diagram of the flow monitoring section of the spiral chute of the present invention;

[0059] Figure 3 is a schematic diagram of the overall down angle, local down angle and number of asymptotic circles of the spiral chute of the present invention;

[0060] Description of reference numerals: 1, lower wall, 2, side wall, 3, flow field monitoring section, N s , the number of progressive circles from the first spiral chute flow field monitoring section to the initial optimized section position, N e , the number of progressive turns from the first spiral chute flow field monitoring section to the optimization end position. DETAILED DESCRIPTION

[0061] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0062] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0063] Example:

[0064] See also Figure 1 , the present invention provides a technical solution:

[0065] A method for gradually optimizing the variable cross-section parameters of a spiral chute, the specific steps comprising:

[0066] Step 1: Use the Eulerian Muti-fluid VOF model to perform numerical calculations of multiphase flow in spiral chute, and optimize the Eulerian Muti-fluid VOF model through model tests;

[0067] In step 1, the numerical calculation uses the simulation results of the spiral chute gas-liquid two-phase flow as the initial flow field, and the gas-liquid-solid three-phase flow simulation is performed after the calculation is stable. The multiphase flow model selected in the numerical calculation is the Eulerian Muti-fluid VOF model; the turbulence model is the RNG k-ε turbulence model; the inlet boundary condition uses the velocity inlet, and the outlet boundary uses the pressure outlet; the lower wall and side wall are no-slip walls, and the upper surface is the free liquid surface. At the same time, the inlet velocity of the mineral phase is the same as that of water. The stability of the calculation is determined by the residual of each calculation of the model. If R<10 -3, it is determined that the calculation is stable, where R is the residual of each calculation of the model.

[0068] And optimize the Eulerian Muti-fluid VOF model through model tests to make it reflect the multiphase flow field in the spiral chute with high accuracy;

[0069] Step 2: Take the overall downward slope angle as the first optimization parameter, select the separation efficiency of the heavier mineral among the two minerals as the first optimization objective, design the optimization objective threshold according to the design efficiency, select R different overall downward slope angles as the initial samples, and construct the initial sample scheme;

[0070] The optimization objective threshold is η y ∈[0.8η D , η D , where η y is the optimization objective threshold, and η D is the design efficiency; the design efficiency is set with reference to industry standards.

[0071] Step 3: Substitute the overall downward slope angle in the initial sample scheme into the Eulerian Muti-fluid VOF model, obtain the mass flow data under different initial sample schemes, calculate the first optimization objective value according to the mass flow data, and generate the initial data set based on the overall downward slope angle and the separation efficiency of the heavier mineral among the two minerals;

[0072] The mass flow data includes the mass flow of the two minerals in the concentrate zone at the outlet of the spiral chute, the total mass flow of the two minerals at the outlet of the spiral chute, and the mass flow of the two minerals in the tailings zone at the outlet of the spiral chute;

[0073] The specific formula for calculating the separation efficiency is:

[0074]

[0075] Among them, η1 is the separation efficiency of the heavier mineral among the two minerals, η2 is the separation efficiency of the lighter mineral among the two minerals; Q a is the total mass flow of the heavier mineral among the two minerals at the outlet of the spiral chute, Q b is the total mass flow of the lighter mineral among the two minerals at the outlet of the spiral chute, Q a1 is the mass flow of the heavier mineral among the two minerals in the concentrate zone at the outlet of the spiral chute, Q b1 is the mass flow of the lighter mineral among the two minerals in the concentrate zone at the outlet of the spiral chute, Q a2 is the mass flow of the heavier mineral among the two minerals in the tailings zone at the outlet of the spiral chute, Q b2is the mass flow rate of the mineral with a relatively lighter specific gravity among the two minerals in the tailings belt at the outlet of the spiral chute;

[0076] The initial dataset is expressed as: where x n is the overall downward inclination angle of the nth group of samples, and z(x n ) is the separation efficiency of the samples with an overall downward inclination angle of x n .

[0077] Step 4: Set the constraint conditions, analyze the initial dataset based on the Kriging interpolation method, establish an approximate functional relationship between the first optimization parameter and the first optimization objective, and determine the variation range of the overall downward inclination angle according to the approximate functional relationship between the first optimization parameter and the first optimization objective and in combination with the optimization objective threshold;

[0078] The constraint conditions include the unbiasedness constraint condition and the optimality constraint condition. Among them, the unbiasedness constraint condition is that the expected value of the predicted value is equal to the expected value of the true value, and the optimality constraint condition is that the prediction variance is minimized;

[0079] Based on the Kriging interpolation method, the specific logic for establishing the approximate functional relationship between the first optimization parameter and the first optimization objective is as follows: Randomly select K samples from the initial dataset to form a random dataset, construct a mathematical expression for predicting the separation efficiency, construct a covariance function, calculate the prediction variance through the covariance function, minimize the prediction variance under the unbiasedness constraint condition, construct a weight calculation function, construct a complete Kriging equation set according to the weight calculation function, solve the Kriging equation set to obtain the separation efficiency weights, calculate the predicted separation efficiency according to the separation efficiency weights and the mathematical expression for predicting the separation efficiency, calculate the corresponding predicted separation efficiency for each value within the range of the overall downward inclination angle, and draw an overall downward inclination angle - predicted separation efficiency image, and obtain the overall downward inclination angles corresponding to 0.8η D and η D . The variation range of the overall downward inclination angle is: γ1 ≤ γ l ≤ γ2, where γ l is the overall downward inclination angle, γ1 is the smaller overall downward inclination angle among the overall downward inclination angles corresponding to 0.8η D and η D , and γ2 is the larger overall downward inclination angle among the overall downward inclination angles corresponding to 0.8η D and η D ;

[0080] For heavy minerals, as the overall downward inclination angle increases, they are more likely to concentrate towards the inner side of the chute, which will enhance the enrichment effect of heavy minerals in the concentrate zone and improve the separation efficiency; for light minerals, as the overall downward inclination angle decreases, the light minerals are more likely to move with the water flow and increase their movement towards the outer edge, which may enhance the separation effect and improve the overall separation efficiency.

[0081] The predicted separation efficiency is expressed as:

[0082]

[0083] z * (x0) is the predicted separation efficiency when the overall downward inclination angle is x0, x0 is the overall downward inclination angle for which the separation efficiency needs to be predicted, x k is the overall downward inclination angle of the k-th sample, λ k is the separation efficiency weight, and K is the number of samples in the random data set, k is the index of the samples in the random data set, and k ∈ [1, K];

[0084] The covariance function is expressed as:

[0085]

[0086] C(x i , x j ) is the covariance function, x i is the overall downward inclination angle of the i-th sample in the random data set, x j is the overall downward inclination angle of the j-th sample in the random data set, i and j are the indices of the samples in the random data set, and C0, C, and a are model parameters obtained through fitting with the variation experiment function;

[0087] The specific logic for obtaining C0, C, and a is as follows: First, construct the variation experiment function, input the samples in the initial data set into the variation experiment function to obtain a large number of fitting data, form a fitting data set, select the exponential covariance fitting mathematical model, and fit the fitting data set to the exponential covariance fitting mathematical model to obtain the model parameters;

[0088] The variation experiment function is expressed as:

[0089]

[0090] where γ(h) is the value of the variation experiment function, h is the reference interval distance, Nγ(h) is the number of point pairs with interval distance h in the initial sample set, x t is the overall downward inclination angle of the t-th sample in the initial sample set, x r is the overall downward inclination angle of the r-th sample in the initial sample set, and t and r are the indices of the samples in the initial sample set;

[0091] The exponential covariance fitting mathematical model is expressed as:

[0092] γ(h) = C0 + C(1 - e -3h / a )

[0093] The specific formula for calculating the predicted variance is:

[0094]

[0095] where σ 2 is the predicted variance;

[0096] Under the unbiasedness constraint condition, minimizing the predicted variance, the constructed weight calculation function is expressed as:

[0097]

[0098] where L is the weight calculation function and μ is the Lagrange multiplier;

[0099] According to the weight calculation function, the complete Kriging equation set is constructed, expressed as:

[0100]

[0101] Step 5: Using the overall down-tilt angle change range to constrain the feasible solution space, adopt the particle swarm optimization algorithm to search in the feasible solution space to obtain the first optimal overall down-tilt angle;

[0102] In the initial dataset, each group of optimization parameters that satisfy the overall down-tilt angle change range is used as an individual to form a particle swarm; initialize the particle swarm, and each particle has an initial position and velocity; calculate the fitness value of each particle on the objective function, that is, its performance under multiple objectives, and update the individual best position and individual best fitness of the particle; sort the particles according to the dominance relationship, and screen out the non-dominated solutions. Determine the individual optimal solution and global optimal solution of each particle, and update the velocity of each particle. Update the position of each particle according to the updated velocity; repeat the execution of evaluating the fitness value, selecting non-dominated solutions, and updating the velocity and position until the maximum number of iterations is reached or the fitness no longer improves significantly. Select and output the group with a large sorting efficiency in the non-dominated sorted solution set as the final solution, and the overall down-tilt angle of this group of final solutions is the first optimal overall down-tilt angle, where the fitness is the overall down-tilt angle and the sorting efficiency.

[0103] Step 6: Set M monitoring cross-sections of the spiral chute flow field, use the Eulerian Muti-fluid VOF model to simulate the sorting data, generate an optimized interface judgment coefficient according to the sorting data, and determine the starting optimized cross-section position through the optimized interface judgment coefficient;

[0104] Set M monitoring cross-sections for the spiral chute flow field. The setting method is as follows: Use the RNG k-ε turbulence model in the Eulerian Muti-fluid VOF model in Step 1 to set a longitudinal cross-section every α along the flow direction inside the spiral chute. The cross-section range is the range of the concentrate zone, where 5° ≤ α ≤ 30°;

[0105] The sorting data includes the mass flow rate of each spiral chute flow field monitoring cross-section, the mass flow rate of the concentrate zone at the spiral chute outlet, the average inlet velocity of each spiral chute flow field monitoring cross-section, the average outlet velocity of each spiral chute flow field monitoring cross-section, the inlet turbulent kinetic energy of each spiral chute flow field monitoring cross-section, and the outlet turbulent kinetic energy of each spiral chute flow field monitoring cross-section;

[0106] Use the Eulerian Muti-fluid VOF model to simulate the sorting data of each spiral chute flow field monitoring cross-section starting from the spiral chute inlet direction; analyze the sorting data to obtain an optimized interface judgment coefficient, preset an optimized interface judgment threshold. When the optimized interface judgment coefficient is less than or equal to the optimized interface judgment threshold, record the position at this time as the optimized cross-section position. If there are multiple positions meeting the above requirements, set the first optimized cross-section position as the starting optimized cross-section position of the spiral chute;

[0107] The specific formula for calculating the optimized interface judgment coefficient is:

[0108]

[0109] where, YH is the optimized interface judgment coefficient, Q c is the mass flow rate of the c-th spiral chute flow field monitoring cross-section, Q o is the mass flow rate of the concentrate zone at the spiral chute outlet, V c is the average inlet velocity of the c-th spiral chute flow field monitoring cross-section, Vv c is the average outlet velocity of the c-th spiral chute flow field monitoring cross-section, Ka c is the inlet turbulent kinetic energy of the c-th spiral chute flow field monitoring cross-section, Kb c is the outlet turbulent kinetic energy of the c-th spiral chute flow field monitoring cross-section, and c is the index of the spiral chute flow field monitoring cross-section.

[0110] is the overall mass flow rate deviation, which reflects the relative deviation between the mineral flow rate at the inlet cross-section of each spiral chute flow field monitoring cross-section and the mineral flow rate of the final outlet concentrate zone. The larger its value, the more unstable the mineral flow, indicating that there may be particle loss or deposition in the middle, and the sorting efficiency is relatively low; is the flow velocity deviation, which reflects the average deviation of the flow velocity changes at the inlet and outlet of each monitoring section of the spiral chute flow field. The larger its value, the more uneven the flow velocity, which will lead to unstable movement trajectories of minerals in the chute and reduce the separation accuracy. is the turbulent kinetic energy deviation, which reflects the difference in turbulent intensity between the inlet and outlet along the flow direction of each monitoring section of the spiral chute flow field. The larger its value, the stronger the turbulent fluctuations, and mineral particles may undergo turbulent disturbances, which will reduce the separation effect. The optimized interface judgment coefficient reflects the separation stability of the monitoring section of the spiral chute flow field. The smaller its value, the higher the separation stability of the monitoring section of the spiral chute flow field; the generation of this coefficient can provide an important basis for determining the optimized position.

[0111] Step 7: Select the local downward slope angle and the progressive number of turns as the second optimization parameters, select the separation efficiency of the lighter specific gravity mineral among the two minerals as the second optimization objective, repeat Steps 2 to 5, obtain the second optimal local downward slope angle and the optimal progressive number of turns, and optimize the local downward slope angle based on the starting optimization section position, the first optimal overall downward slope angle, the second optimal local downward slope angle, and the optimal progressive number of turns.

[0112] Repeating Steps 2 to 5 includes selecting the local downward slope angle and the progressive number of turns as the second optimization parameters, selecting the separation efficiency of the lighter specific gravity mineral among the two minerals as the second optimization objective, setting the design efficiency as the optimization objective threshold, selecting Q different local downward slope angles and progressive numbers of turns as the initial samples, and constructing the initial sample scheme; substituting the local downward slope angle and the progressive number of turns in the initial sample scheme into the Eulerian Muti-fluid VOF model to obtain the mass flow rate data under different initial sample schemes, calculating the second optimization objective value based on the mass flow rate data, generating the initial data set based on the local downward slope angle, the progressive number of turns, and the separation efficiency of the lighter specific gravity mineral among the two minerals, setting the constraint conditions, analyzing the initial data set based on the Kriging interpolation method to establish an approximate functional relationship between the second optimization parameters and the second optimization objective, and determining the change ranges of the local downward slope angle and the progressive number of turns according to the approximate functional relationship between the second optimization parameters and the second optimization objective and in combination with the optimization objective threshold; using the local downward slope angle and the progressive number of turns to constrain the feasible solution space, and using the particle swarm optimization algorithm to search in the feasible solution space to obtain the second optimal local downward slope angle and the optimal progressive number of turns.

[0113] The specific formula for optimizing the local downward slope angle is:

[0114]

[0115] n ot =N e -N s

[0116] Among them, y is the optimized local downward bevel angle, is the first optimal overall downward bevel angle, is the second optimal local downward bevel angle; The progressive circles inside the spiral chute are numbered in sequence along the flow direction. w is the index of the progressive circle, and w ∈ (1, W), where W is the total number of progressive circles inside the spiral chute, N s is the index of the progressive circle at the starting optimized section position, N e is the index of the progressive circle at the ending optimized section position, n ot is the optimal number of optimized progressive circles.

[0117] The above formulas are all dimensionless and take their numerical values for calculation. The formulas are obtained by collecting a large amount of data for software simulation to get a formula closest to the actual situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0118] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by the combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0119] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units. They can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0120] The above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art within the technical scope disclosed in this application should not easily think of changes or substitutions, and all should be covered by the protection scope of this application.

Claims

1. A method for gradually optimizing the variable cross-section parameters of a spiral chute, characterized in that: The specific steps include: Step 1: Use the Eulerian Muti-fluid VOF model to perform numerical calculations of multiphase flow in spiral chute, and optimize the Eulerian Muti-fluid VOF model through model tests; Step 2: Take the overall downward bevel angle as the first optimization parameter, select the sorting efficiency of the heavier mineral of the two minerals as the first optimization target, design the optimization target threshold according to the design efficiency, select N different overall downward bevel angles as the initial samples, and construct the initial sample plan; Step 3: Substitute the overall down-angle in the initial sample scheme into the Eulerian Muti-fluid VOF model, obtain the mass flow data under the initial different sample schemes, calculate the first optimization target value according to the mass flow data, and generate an initial data set based on the overall down-angle and the separation efficiency of the heavier mineral among the two minerals; Step 4: Set constraints, analyze the initial data set based on the Kriging interpolation method, establish an approximate functional relationship between the first optimization parameter and the first optimization target, and establish the overall down-slope angle variation range based on the approximate functional relationship between the first optimization parameter and the first optimization target and in combination with the optimization target threshold; Step 5: Constrain the feasible solution space with the overall down-slope angle variation range, and use the particle swarm optimization algorithm to search in the feasible solution space to obtain the first optimal overall down-slope angle; Step 6: Set M spiral chute flow field monitoring sections, use the Eulerian Muti-fluid VOF model to simulate the sorting data, generate the optimization interface judgment coefficient according to the sorting data, and determine the starting optimization section position by optimizing the interface judgment coefficient; Step 7: Select the local downward bevel angle and the number of progressive turns as the second optimization parameters, select the sorting efficiency of the lighter mineral among the two minerals as the second optimization target, repeat steps 2 to 5 to obtain the second optimal local downward bevel angle and the optimal optimized number of progressive turns, and optimize the local downward bevel angle based on the starting optimized section position, the first optimal overall downward bevel angle, the second optimal local downward bevel angle and the optimal optimized number of progressive turns.

2. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 1, characterized in that: In step 1, the numerical calculation uses the simulation results of the spiral chute gas-liquid two-phase flow as the initial flow field, and the gas-liquid-solid three-phase flow simulation is performed after the calculation is stable. The multiphase flow model selected in the numerical calculation is the Eulerian Muti-fluid VOF model; the turbulence model is the RNG k-ε turbulence model; the inlet boundary condition uses the velocity inlet, and the outlet boundary uses the pressure outlet; the lower wall and side wall are no-slip walls, and the upper surface is the free liquid surface. At the same time, the inlet velocity of the mineral phase is the same as that of water. The stability of the calculation is determined by the residual of each calculation of the model. If R<10 -3 , the calculation is considered stable, where R is the residual of each calculation of the model.

3. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 1, characterized in that: The optimization target threshold is η y ∈[0.8η D ,η D ], where η y Optimize the target threshold, η D For design efficiency.

4. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 1, characterized in that: The mass flow data include the mass flow of the two minerals in the concentrate zone at the spiral chute outlet, the total mass flow of the two minerals at the spiral chute outlet, and the mass flow of the two minerals in the tailings zone at the spiral chute outlet; The specific formula for calculating the sorting efficiency is: Among them, η1 is the separation efficiency of the heavier mineral of the two minerals, and η2 is the separation efficiency of the lighter mineral of the two minerals; Q a At the outlet of the spiral chute, the total mass flow rate of the heavier mineral of the two minerals, Q b At the outlet of the spiral chute, the total mass flow rate of the lighter mineral of the two minerals, Q a1 Q is the mass flow rate of the heavier mineral in the concentrate zone at the outlet of the spiral chute. b1 Q is the mass flow rate of the lighter mineral in the concentrate zone at the outlet of the spiral chute. a2 Q is the mass flow rate of the heavier mineral in the tailings zone at the outlet of the spiral chute, b2 It is the mass flow rate of the lighter mineral among the two minerals in the tailings zone at the outlet of the spiral chute; The initial data set is represented as: Among them, x n is the overall downward slope of the nth group of samples, z(x n ) is the overall lower slope angle x n The sorting efficiency of the sample.

5. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 4, characterized in that: The constraints include unbiasedness constraints and optimality constraints, wherein the unbiasedness constraints are that the expected predicted value is equal to the expected true value, and the optimality constraints are that the predicted variance is minimized; Based on the Kriging interpolation method, the specific logic for establishing the approximate functional relationship between the first optimization parameter and the first optimization objective is as follows: randomly select K samples from the initial data set to form a random data set, construct a mathematical expression for predicting sorting efficiency, construct a covariance function, calculate the predicted variance through the covariance function, minimize the predicted variance under the unbiased constraint, construct a weight calculation function, construct a complete Kriging equation group based on the weight calculation function, solve the Kriging equation group to obtain the sorting efficiency weight, calculate the predicted sorting efficiency based on the sorting efficiency weight and the mathematical expression of the predicted sorting efficiency, calculate the corresponding predicted sorting efficiency for each value within the range of the overall lower oblique angle, and draw the overall lower oblique angle-predicted sorting efficiency image to obtain 0.8η in the image. D and η D The corresponding overall downward bevel angle, the range of the overall downward bevel angle is: γ1≤γ l ≤γ2, where γ l is the overall downward slope angle, γ1 is 0.8η D and η D The smaller overall downslope angle among the corresponding overall downslope angles, γ2 is 0.8η D and η D The larger overall downslope angle among the corresponding overall downslope angles; η D For design efficiency; The predicted sorting efficiency is expressed as: z * (x0) is the predicted sorting efficiency when the overall down-angle is x0, x0 is the overall down-angle for which the sorting efficiency needs to be predicted, x k is the overall lower slope angle of the kth sample, λ k is the sorting efficiency weight, and K is the number of samples in the random data set, k is the index of the sample in the random data set, and k∈[1,K]; The covariance function is expressed as: C(x i x j ) is the covariance function, x i is the overall lower slope of the ith sample of the random data set, x j is the overall lower slope of the jth sample of the random data set, i and j are the indexes of the samples of the random data set, C0, C and a are model parameters, which are obtained by fitting the variation experiment function; The specific logic for obtaining C0, C and a is as follows: first construct a mutation experiment function, input the samples in the initial data set into the mutation experiment function, obtain a large amount of fitting data, form a fitting data set, select an exponential covariance fitting mathematical model, fit the exponential covariance fitting mathematical model with the fitting data set, and obtain model parameters; The mutation experiment function is expressed as: Among them, γ(h) is the value of the mutation experiment function, h is the reference interval distance, Nγ(h) is the number of point pairs with interval distance h in the initial sample set, and x t is the overall downward slope of the tth sample in the initial sample set, x r is the overall downward slope angle of the rth sample in the initial sample set, Δh is the allowable error, t and r are the indexes of the samples in the initial sample set; The exponential covariance fitting mathematical model is expressed as: γ(h)=C0+C(1-e -3h / a ) The specific formula used to calculate the forecast variance is: Among them, σ 2 is the prediction variance; Minimize the prediction variance under the unbiased constraint, and the constructed weight calculation function is expressed as: Among them, L is the weight calculation function, μ is the Lagrange multiplier; The complete Kriging equations are constructed based on the weight calculation function, which is expressed as:

6. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 1, characterized in that: M spiral chute flow field monitoring sections are set, and the setting method is: using the RNG k-ε turbulence model in the Eulerian Muti-fluid VOF model in step 1, a longitudinal section is set every α along the flow direction inside the spiral chute, and the section range is the range of the concentrate belt, 5°≤α≤30°; The sorting data includes the mass flow rate of each spiral chute flow field monitoring section and the mass flow rate of the concentrate belt at the spiral chute outlet, the average inlet velocity of each spiral chute flow field monitoring section, the average outlet velocity of each spiral chute flow field monitoring section, the inlet turbulent kinetic energy of each spiral chute flow field monitoring section and the outlet turbulent kinetic energy of each spiral chute flow field monitoring section; Using the Eulerian Muti-fluid VOF model, the sorting data of each spiral chute flow field monitoring section is simulated starting from the spiral chute inlet direction; the sorting data is analyzed to obtain the optimization interface judgment coefficient, and the optimization interface judgment threshold is preset. When the optimization interface judgment coefficient is less than or equal to the optimization interface judgment threshold, the position at this time is recorded as the optimization section position. If there are multiple positions that meet the above requirements, the first optimization section position is set as the starting optimization section position of the spiral chute; The specific formula for calculating the optimization interface judgment coefficient is: Among them, YH is the optimization interface judgment coefficient, Q c is the mass flow rate of the cth spiral chute flow field monitoring section, Q o is the mass flow rate of the concentrate belt at the spiral chute outlet, V c is the average inlet velocity of the cth spiral chute flow field monitoring section, Vv c is the average outlet velocity of the cth spiral chute flow field monitoring section, Ka c is the inlet turbulent kinetic energy of the cth spiral chute flow field monitoring section, Kb c is the outlet turbulent kinetic energy of the cth spiral chute flow field monitoring section, and c is the index of the spiral chute flow field monitoring section.

7. A method for gradually optimizing the variable cross-section parameters of a spiral chute according to claim 6, characterized in that: The specific formula for optimizing the local lower bevel angle is: n ot =N e -N s Where γ is the optimized local down-slope angle, is the first optimal overall downslope angle, is the second optimal local downward slope angle; the progressive circles inside the spiral chute are numbered in sequence along the flow direction, w is the index of the progressive circle, and w∈(1, W), W is the total number of progressive circles inside the spiral chute, N s is the index of the progressive circle at the starting optimization section position, N e is the index of the progressive circle at the end section position of the optimization, n ot Optimize the number of progressive turns for best performance.

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