CN109276945A - A self-healing control method for abnormal feeding conditions in dense dewatering process - Google Patents
A self-healing control method for abnormal feeding conditions in dense dewatering process Download PDFInfo
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Abstract
本发明提出一种浓密脱水过程入料异常工况的自愈控制方法，流程包括：对第一层优化模型进行描述，包括：将压力最大值最小化及将浓度最小值最大化；对第二层优化模型进行描述，在安全极限内，使生产能耗成本达到最低；对第三层优化模型进行描述，放宽经济指标，以满足现场操作人员的习惯；本发明针对某金矿厂选矿车间入料异常工况进行了自愈控制方法的研究，可实现当现场浓密脱水工序出现异常工况时，仍可以继续对后续生产过程进行操作指导，求解出更精准、合理的放矿时间，以协助操作员进行控制，保证浓密脱水过程安全、稳定运行，提高综合经济效益，同时减少压滤机的故障率。
The invention proposes a self-healing control method for abnormal feeding conditions in a dense dehydration process. The process includes: describing the first layer optimization model, including: minimizing the maximum pressure and maximizing the minimum concentration; The optimization model of the third layer is described, and the production energy consumption cost is minimized within the safety limit; the optimization model of the third layer is described, and the economic indicators are relaxed to meet the habits of the field operators; The research on the self-healing control method is carried out for the abnormal working conditions of the material, which can realize that when the abnormal working conditions occur in the on-site dense dewatering process, the operation guidance for the subsequent production process can still be continued, and a more accurate and reasonable ore drawing time can be solved to assist. The operator controls to ensure the safe and stable operation of the dense dewatering process, improve the comprehensive economic benefits, and reduce the failure rate of the filter press.
Description
Technical Field
The invention belongs to the field of concentration and metallurgy, and particularly relates to a self-healing control method for abnormal feeding working conditions in a concentration dehydration process.
Background
Mineral processing, which is a process for recovering high-grade minerals from poor, fine and miscellaneous ores, is a typical flow industrial process, and has the disadvantages of complex production mechanism, numerous process links, and mutual influence and mutual coupling of various processes. The thickening and dewatering process is an important process, and plays a role in improving the concentration of ore pulp, separating solid from liquid and adjusting the influence of production disturbance of an upstream process on a downstream process. The thickening and dewatering process mainly comprises two main devices, namely a thickener and a filter press. The thickener is a device for improving the concentration of ore pulp based on the gravity settling effect, and is a key device in the process, and the filter press is a device for performing solid-liquid separation based on pressure and further improving the concentration of the ore pulp. The invention uses a peripheral transmission thickener and a plate-and-frame filter press with the diameter of 30m, the process flow of the thickening dehydration process is shown in figure 14, and the specific introduction is as follows:
the feeding of the thickener is concentrate selected in the flotation process, the concentrate is scraped from the upper surface of the flotation column and flows into a concentrate pump pool, and then the concentrate is pumped into the thickener by a slurry pump. The central part of the thickener is provided with a feed well, the floated concentrate is sent into the central feed well for buffering and mixing, then flows into the thickener for sedimentation under the action of gravity, a walking motor is driven by a hydraulic system, a rake frame is driven to rotate around the center along a track on the outer wall of the thickener, and a scraper under the rake frame stirs a mud layer to promote the concentration of ore pulp and the movement towards an underflow outlet at the central position; the upper layer of the thickener is provided with an overflow groove, and clear water at the upper layer flows out of the overflow groove and returns to an upstream process to recycle the clear water. When the concentration of the bottom reaches a certain value, a underflow pump of the thickener is opened, the thickened ore pulp is pumped into the stirring tank through a pipeline, when the ore amount in the stirring tank reaches a certain amount, the ore pulp is pumped into a filter press by an ore pumping pump of the filter press for filter pressing, and a filter cake after filter pressing is sent to the next procedure.
Through the research of people on the optimization control of the thickening and dehydrating process in recent years, the optimization control problem of the process is solved to a certain extent, and the process performance of the process is improved. However, due to the complexity of the site, abnormal working conditions often occur in the thickening dehydration process, such as abnormal feeding caused by the unstable working state of the concentrate pump and the flotation column, and pipeline blockage and underflow abnormality caused by the unstable operation of underflow equipment of the thickener. At the moment, if the treatment is improper, equipment can be in failure, and serious production accidents such as rake pressing and the like are caused.
The invention takes a mineral processing workshop of a certain gold mine factory as a background, and researches two typical abnormal feeding working conditions:
1. the exhaust pipe of the flotation column is blocked, and the flotation column needs to be emptied of all ore pulp immediately, so that the feed flow and the concentration of the thickener are obviously increased, and if the operation and adjustment are not carried out in time, the risk of rake pressing is caused;
2. as the liquid level of the ore pulp in the flotation column is reduced, the feed flow and the concentration are both reduced to a lower level. At the moment, the ore pulp with low concentration enters the filter pressing machine, so that the failure rate of the ore pulp is increased, and the production efficiency is reduced.
At present, no research aiming at a self-healing control method under an abnormal working condition in a thickening and dewatering process is found. Plant operators mainly rely on respective experience to adjust, often have the problems of high energy consumption, low safety and the like, seriously restrict the industrial process of the thickening and dehydrating process, and further influence the comprehensive economic benefit.
Disclosure of Invention
Based on the problems, the application provides a self-healing control method for feed abnormal working conditions in a thickening dehydration process, which carries out layered description on optimization problems under the abnormal working conditions in the thickening dehydration process, and comprises the following specific steps:
step 1: describing the first layer optimization model, and under the abnormal working condition, the self-healing method in the dehydration process of the thickener comprises the following steps:
step 1.1: minimizing the maximum pressure value, and determining whether the current cabinet number meets the requirement of safety limit: the goal of the first layer optimization model is to optimize ore drawing timeThe maximum value of the pressure sensor l during operation of the process is reduced as far as possible if this value exceeds the upper limit value p of the pressure sensor lUIf the number of the rest cabinets N cannot meet the requirement of safety production, 1 cabinet needs to be added to avoid rake pressing of the thickener; otherwise, the remaining cabinet number N does not need to be adjusted, as shown in formula (1);
wherein N represents the number of the cabinets which need to be subjected to filter pressing in the current class,representing the maximum value taken by the pressure sensor i during operation of the process,the opening time of the underflow pump representing the number of the residual filter cabinets in the current shift;
the s.t. in the formula (1) is described later as a constraint condition for minimizing the maximum value of the pressure of the first layer optimization model:
for the closing time model constraint of the jth cabinet underflow pump, the value of the closing time model constraint is equal to the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And underflow concentration predicted value at the moment kRelatively, g (-) is the closing time of the jth cabinet underflow pump and the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And underflow concentration predicted value at the moment kThe correlation function of (a);
for ore drawing time constraints:
representing the opening time of the No. 1 cabinet underflow pumpShould not be less than the occurrence time k of abnormal conditionsa；
Representing that the opening time of the underflow pump of the jth cabinet is more than or equal to the closing time of the underflow pump of the previous cabinet
Representing the turn-off time of the last tank underflow pumpShould not exceed the end time k of the current shiftfRemoving shift time epsilonk；
Representing the predicted value of the underflow concentration in the thickening and dewatering processIt is required to be greater than the lower limit concentration value cLSo as to reduce the failure rate of the plate-and-frame filter press.
Step 1.2: maximizing the concentration minimum: the goal of the first layer optimization model is to optimize ore drawing timeIncreasing the minimum value of the underflow concentration during the operation of the process as much as possible, if this value is below the lower limit value c of the underflow concentrationL1 cabinet needs to be reduced to reduce the failure rate of the filter press; otherwise, the remaining number N of cabinets does not need to be adjusted, as shown in formula (2):
wherein N represents the number of the cabinets needing filter pressing in the current class, cufRepresenting the minimum value that the underflow concentration takes during the operation of the process,representing the number of cabinets needing filter pressing in the shift;
the s.t. in the formula (2) is described later as a constraint condition for maximizing the minimum value of the concentration of the first layer of optimization problem:
closing the time model constraint for the jth cabinet underflow pump, the meaning of the restriction of ore drawing time is the same as that of the formula (1);
pl(k)≤pUrepresenting the measured pressure value p of the pressure sensor l in the process of thickening and dewatering at the moment klNeeds to be less than the upper limit value p of the pressureUSo as to avoid the generation of rake pressing of the thickener;
step 2: describing the second layer optimization model, and enabling the production energy consumption cost to be the lowest within a safety limit according to the number of cabinets determined by the first layer optimization model:
wherein, formula (3) includes: economic indexes of energy consumption of the underflow pump and the ore pump;
the j < th > cabinet underflow pump energy consumption economic index is as follows:
wherein E isufThe unit energy consumption of the underflow pump is P (k), and the stepped electricity price at the moment k is P (k);
the j cabinet mining pump energy consumption economic indexes are as follows:
wherein E isfpFor the unit energy consumption of the ore pump, P (k) is the stepped electricity price at time k, deltajFor the operation time of the jth cabinet underflow pump,the required pump run time to complete the jth bin.
In the formula (3), N*Representing the number of remaining bins resolved by the first-level optimization;
the constraints of the second-layer optimization problem are described after s.t. in formula (3):
closing the time model constraint for the jth cabinet underflow pump, the meaning of the restriction of ore drawing time is the same as that of the formula (1);
pl(k)≤pUrepresenting the measured pressure value p of the pressure sensor l in the process of thickening and dewatering at the moment klNeeds to be less than the upper limit value p of the pressureUSo as to avoid the generation of rake pressing of the thickener;
representing the predicted value of the underflow concentration in the thickening and dewatering process at the moment kIt is necessary to be greater than the lower limit of concentration cLSo as to reduce the failure rate of the plate-and-frame filter press;
and step 3: describing a third-layer optimization model, and relaxing economic indexes to meet the habit of field operators, wherein the third-layer optimization model is divided into a case (1) and a case (2):
(1) the number N of the remaining cabinets obtained by the first layer optimization*And reference number of remaining cabinetsAnd (3) equally, further adjusting the ore drawing time according to the operation habit of field operators, wherein the formula is as follows:
in the formula (6), the first and second groups,the starting time of the underflow pump under the normal working condition is shown;
the constraints of the third layer of optimization problem are described after s.t. in formula (6): the description is the same as formula (3);
in, E*Optimum Total energy cost, ε, for the second layer optimizationETo relax economic index parameters;
(2) the number N of the remaining cabinets obtained by the first layer optimization*And reference number of remaining cabinetsUnequal, according to the operation habit of field operators, under the condition of increasing or decreasing 1 cabinet of ore, considering the adjustment rule of ore drawing time, namely replacing the optimization target with:
wherein, the constraint conditions of the third layer of optimization model condition (2) are the same as the formula (6);
wherein, in step 2, the operating time delta of the underflow pump is calculatedjAnd calculating the pump run timeComprises the following steps of 2.1-2.5:
step 2.1: establishing a pressure prediction model of the pressure sensors:
when the underflow pump is turned off, a pressure rise model is established:
wherein p isl(k) The pressure value, p, of the pressure sensor l at time kl(k-1) the value at the time on the pressure sensor l, i.e. the value at the time k-1, β1lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x1l(k-1) is the input variable of the pressure sensor l corresponding to the previous time, i.e. the time k-1, and is expressed as follows:
x1l(k-1)＝[pl(k-1),qf(k-1),cf(k-1)]T(9)
wherein q isf(k-1) is the feed rate at the time of k-1, cfAnd (k-1) is the feed concentration at the moment of k-1.
When the underflow pump is turned on, a pressure drop model is established:
wherein p isl(k) Value of the pressure sensor l at time k, pl(k-1) is the value of the pressure sensor l at the time k-1, β2lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x2l(k-1) is the input variable of the pressure sensor l at the time k-1, and is expressed as follows:
wherein q isf(k-1) the feed rate at the time of k-1, cf(k-1) the feed concentration at the moment of k-1, quf(k-1) is the underflow flow at the moment k-1,the underflow concentration is predicted for time k-1.
Step 2.2: establishing an underflow concentration prediction model:
wherein,for the prediction of the underflow concentration at time k, pl(k) Representing the pressure sensor/measurement, f (-) is a nonlinear function to be identified.
To predict the underflow concentrationFirstly, storing observation samples into a matrix, and setting an input matrix P ═ P1,p2,…,pn]TN is the number of samples, the corresponding output vector cuf，pi＝[p1i,p2i…pli]TRepresents the ith sample input, where i ═ 1,2liRepresenting the measured value of the pressure sensor l, since some inevitable abnormal data can influence the prediction performance, the KPRM algorithm is adopted to establish P and cufThe KPRM algorithm can extend the PRM algorithm to the nonlinear kernel form thereof, and can avoid displaying nonlinear mapping as in the KPLS algorithm. If a Gaussian kernel function is introduced, the overall kernel matrix can be calculated by:
wherein σ2As the variance of the input matrix P, e>0 is the kernel width parameter to be adjusted, and | | · | |, is a 2 norm.
The KPRM algorithm may also use the leveraging weights and residual weights to reduce the weight of outliers in the PRM algorithm. Leverage weight of ith sampleCalculated from the following formula:
wherein T is a latent variable matrix derived from the NIPALS step sequence in the KPLS algorithm, and TiFor the ith row of the matrix T, h (-) is a weight function, θ is a coordination constant, med is a median, and | l | · | | is a 2-norm.
Similarly, residual weightsCan be calculated from the following formula:
wherein r isiAnd outputting a residual error of the observed value and the output predicted value for the ith sample.
Then, the weight w of the ith sample as a whole is obtainediIs composed ofW represents WiIs a diagonal matrix of diagonal elements.
Finally, the KPRM algorithm is summarized in the following specific steps:
step 2.2.1: firstly, input matrix P and output vector c are combinedufTaking mean and unit variance, and taking n dimension as initial WAn identity diagonal matrix.
Step 2.2.2: obtaining a weighted kernel matrix K WKW and a corresponding weighted output vector cuf＝Wcuf。
Step 2.2.3: analyzing the weighted kernel matrix K and the weighted output vector c by using the KPLS algorithmufObtaining a latent variable T, and then calculating a residual error ri。
Step 2.2.4: the weight matrix W is updated by equation (14) and equation (15).
Step 2.2.5: loop back to step 2.2.2 until the regression coefficient vectorAnd (6) converging.Can be calculated from the following formula:
step 2.2.6: when a new input vector p appears, calculating elements in the new kernel vector by formula (13);
step 2.2.7: obtain a new kernel vector k ═ k (k)1,κ2,…,κn)TAnd further on the underflow concentrationAnd (6) performing prediction.Can be calculated from the following formula:
step 2.3: according to the pressure sensor prediction model and the underflow concentration prediction model, establishing a closing time model of the jth cabinet underflow pump, namely constraint conditions of formula (1), formula (2), formula (3), formula (6) and formula (7):
wherein,for the closing time of the jth cabinet underflow pump,for the opening time of the jth cabinet underflow pump, quf(k) The underflow flow rate at the moment k is shown,and the underflow concentration at the moment k is predicted value.
During the period from the opening of the underflow pump to the closing of the underflow pump, enough ore quantity is needed to complete one dehydration process, and when the opening time of the underflow pump is determinedAnd the amount M of dry ore required for completing one dehydration processfp，
Calculating the closing time of each cabinet underflow pumpThe method comprises the following specific steps:
step 2.3.1: determining the amount M of dry ore required for completing one-time dehydration procedurefpInitializing cumulative dry ore quantity M ═ 0 and underflow pump shut-off time
Step 2.3.2: calculated using the following formulaInstantaneous underflow density
WhereinIs composed ofUnderflow concentration, p, corresponding to the momentsAs dry ore density, plIs the liquid density.
Step 2.3.3: the cumulative dry ore quantity M is calculated. Calculated by the following formula:
wherein,is composed ofUnderflow flow rate corresponding to the moment;
step 2.3.4: closing time of underflow pump
Step 2.3.5: if the accumulated dry ore amount reaches the dry ore amount M required for completing one cabinetfpI.e. the closing time of the underflow pumpOtherwise, returning to the step 2.3.2,the underflow concentration at the next moment is calculated.
Step 2.4: calculating the running time delta of the underflow pumpj：
Step 2.5: calculating the operation time of the ore pump
The relationship between the concentration of the stirring tank and the operation time of the ore pump is as follows:
wherein,in order to start the pump for the time of the ore pump,α for stirred tank pulp average concentration1And α2The linear fitting parameters are calculated by a least square method;
wherein, in formula (1), formula (2), formula (3) and formula (6)And solving by adopting a PSO algorithm.
The beneficial technical effects are as follows:
the invention carries out research on the self-healing control method aiming at the abnormal feeding working condition of the ore dressing workshop of a certain gold ore factory, can realize that when the abnormal working condition occurs in the on-site concentration dehydration process, the operation guidance can still be continuously carried out on the subsequent production process, and the more accurate and reasonable ore drawing time can be solved, so as to assist the operator to control, ensure the safe and stable operation of the concentration dehydration process, improve the comprehensive economic benefit and reduce the fault rate of the filter press.
Drawings
FIG. 1 is a diagram of a three-layer optimization model architecture according to an embodiment of the present invention;
FIG. 2 is a data driven model architecture diagram of a thickener according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating an operation cycle of a thickening and dehydrating process according to an embodiment of the present invention;
FIG. 4 is a trend graph of abnormal operating conditions 1 according to an embodiment of the present invention;
FIG. 5 is a trend graph of abnormal operating conditions 2 for the embodiment of the present invention;
FIG. 6 is a comparison graph of underflow concentration prediction performance of a KPRM model and a KPLS model according to an embodiment of the present invention;
FIG. 7 is an ARX model prediction performance of internal thickener pressure according to an embodiment of the present invention;
FIG. 8 is an optimal solution for anomaly 1 first layer optimization and corresponding underflow concentration and pressure curves;
FIG. 9 is the optimal solution resulting from the second layer optimization for anomaly 1 and the corresponding underflow concentration and pressure curves;
FIG. 10 is an optimal solution for anomaly 1 third layer optimization and corresponding underflow concentration and pressure curves;
FIG. 11 is an optimal solution for anomaly 2 first layer optimization and corresponding underflow concentration and pressure curves;
FIG. 12 is the optimal solution resulting from the second layer optimization for anomaly 2 and the corresponding underflow concentration and pressure curves;
FIG. 13 is an optimal solution for the anomaly 2 third layer optimization and corresponding underflow concentration and pressure curves;
FIG. 14 is a process flow diagram of a thickening and dewatering process according to an embodiment of the present invention.
Detailed Description
The invention is further explained by combining the attached drawings and the specific embodiment, and the invention is practically applied to the concentration dehydration process of the ore dressing workshop of the concentrating plant by combining the specific embodiment to verify the effectiveness of the proposed self-healing control method. The following description will be made of examples of self-healing control performance under two feeding abnormal working conditions:
abnormity 1, an exhaust pipe of the flotation column is blocked, the flotation column needs to be immediately emptied of all ore pulp, so that the feed flow and the concentration of the thickener are obviously increased, and if operation and adjustment are not performed in time, the risk of rake pressing is generated, and the self-healing control process of abnormity 1 is described by using embodiment 1;
abnormity 2. due to the reduction of the ore pulp liquid level in the flotation column, the feed flow and the concentration are both reduced to a lower level. At the moment, the ore pulp with low concentration enters the filter pressing machine to increase the fault rate and reduce the production efficiency, and the self-healing control process of the abnormity 2 is described by using the embodiment 2;
example 1:
as shown in fig. 14, in the present embodiment, three pressure sensors are used to measure the pressures of slurries to be tested at different heights in the thickener, a pressure sensor 1 is located on a slurry-water interface of the slurries to be tested, a pressure sensor 3 is located at an ore outlet, and a pressure sensor 2 is located between the pressure sensor 1 and the pressure sensor 3;
the feeding of the thickener is concentrate selected in the flotation process, the concentrate is scraped from the upper surface of the flotation column and flows into a concentrate pump pool, and then the concentrate is pumped into the thickener by a slurry pump. The central part of the thickener is provided with a feed well, the floated concentrate is sent into the central feed well for buffering and mixing, then flows into the thickener for sedimentation under the action of gravity, a walking motor is driven by a hydraulic system, a rake frame is driven to rotate around the center along a track on the outer wall of the thickener, and a scraper under the rake frame stirs a mud layer to promote the concentration of ore pulp and the movement towards an underflow outlet at the central position; the upper layer of the thickener is provided with an overflow groove, and clear water at the upper layer flows out of the overflow groove and returns to an upstream process to recycle the clear water. When the concentration of the bottom reaches a certain value, a underflow pump of the thickener is opened, the thickened ore pulp is pumped into the stirring tank through a pipeline, when the ore amount in the stirring tank reaches a certain amount, the ore pulp is pumped into a filter press by an ore pumping pump of the filter press for filter pressing, and a filter cake after filter pressing is sent to the next procedure.
The invention provides a three-layer optimization model, as shown in fig. 1, the specific steps are as follows:
step 1: describing a first-layer optimization model:
step 1.1: minimizing the maximum pressure value, and determining whether the current cabinet number meets the requirement of safety limit;
wherein N represents the number of the cabinets which need to be subjected to filter pressing in the current class,representing the maximum value that the pressure sensor l takes during the process run, i.e. the pressure sensor 3 is used to optimize the problem, so the goal of the first layer optimization model is to optimize the ore drawing timeThe maximum value of the pressure sensor 3 during operation of the process is reduced as much as possible if this is the caseThe value exceeds the upper limit value p of the pressure sensor 3UWhen the pressure is equal to 0.055MPa, the number N of the rest cabinets cannot meet the requirement of safety production, and 1 cabinet needs to be added to avoid rake pressing of the thickener; otherwise, the rest cabinet number N does not need to be adjusted;
in the formula (1), the first and second groups,the opening time of the underflow pump representing the number of the residual filter cabinets in the shift,represents the maximum value taken by the pressure sensor 3 during process operation;
the s.t. in the formula (1) is described later as a constraint condition for minimizing the maximum value of the pressure of the first-layer optimization problem:
for the closing time model constraint of the jth cabinet underflow pump, the value of the closing time model constraint is equal to the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And underflow concentration predicted value at the moment kRelatively, g (-) is the closing time of the jth cabinet underflow pump and the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And underflow concentration predicted value at the moment kThe correlation function of (a);
for ore drawingAnd (3) time constraint:
representing the opening time of the No. 1 cabinet underflow pumpShould not be less than the occurrence time k of abnormal conditionsa；
Representing that the opening time of the underflow pump of the jth cabinet is more than or equal to the closing time of the underflow pump of the previous cabinet
Representing the turn-off time of the last tank underflow pumpShould not exceed the end time k of the current shiftfRemoving shift time epsilonk；
Representing the predicted value of the underflow concentration in the thickening and dewatering processIt is required to be greater than the lower limit concentration value cL55 percent to reduce the failure rate of the plate-and-frame filter press.
Step 1.2: maximizing the concentration minimum:
wherein N represents the number of the cabinets needing filter pressing in the current class, cufRepresenting the minimum value that the underflow concentration takes during the operation of the process, and therefore the goal of the first layer optimization model is to optimize the ore-drawing time by optimizing the ore-drawing timeIncreasing the minimum value of the underflow concentration during the operation of the process as much as possible, if this value is below the lower limit value c of the underflow concentrationLIf the filter press failure rate is 55%, 1 cabinet needs to be reduced; otherwise, the remaining number N of cabinets does not need to be adjusted.
In the formula (2), the first and second groups,representing the number of cabinets requiring filter pressing remaining on duty, cufRepresenting the minimum value of the underflow concentration obtained in the thickening and dewatering process;
the s.t. in the formula (1) is described later as a constraint condition for maximizing the minimum value of the concentration of the first layer of optimization problem:
closing the time model constraint for the jth cabinet underflow pump, for ore drawing time constraint, the description is the same as formula (1);
pl(k)≤pU(l ═ 3) represents that the measured pressure value of the pressure sensor 3 needs to be smaller than the upper pressure limit value p in the thickening and dewatering process at the moment kU0.055MPa to avoid pressing rake of the thickener;
step 2: describing the second layer optimization model, and enabling the production energy consumption cost to be the lowest within a safety limit according to the number of cabinets determined by the first layer optimization model:
wherein, formula (3) includes: economic indexes of energy consumption of the underflow pump and the ore pump;
the j < th > cabinet underflow pump energy consumption economic index is as follows:
wherein E isufFor the unit energy consumption of the underflow pump, p (k) is the stepped electricity price at time k, as follows:
the j cabinet mining pump energy consumption economic indexes are as follows:
wherein E isfpFor the unit energy consumption of the ore pump, P (k) is the stepped electricity price at time k, deltajFor the operation time of the jth cabinet underflow pump,the required pump run time to complete the jth bin.
In the formula (3), N*Representing the number of remaining bins resolved by the first-level optimization;
the constraints of the second-layer optimization problem are described after s.t. in formula (3):
closing the time model constraint for the jth cabinet underflow pump, for ore drawing time constraint, the description is the same as formula (1);
pl(k)≤pU(l ═ 3) represents that the measured pressure value of the pressure sensor 3 needs to be smaller than the upper pressure limit value p in the thickening and dewatering process at the moment kU0.055Mpa to avoid pressing rake of the thickener;
representing the predicted value of the underflow concentration in the thickening and dewatering process at the moment kIt is necessary to be greater than the lower limit of concentration cL55 percent to reduce the failure rate of the plate-and-frame filter press;
in the optimization process, the operation state of the underflow pump for one cycle is shown in fig. 3, and the formula (3) is described as follows: the optimization aims at deciding the opening time of the underflow pumpThereby minimizing production energy costs. Due to the pump-on time of each cabinetNot the same, underflow flow q during operationuf(k) With underflow concentrationThe difference is also such that the operating time delta of the underflow pump obtained in step 2jAnd the time of operation of the pumpDifferent from each other, combined with the step electricity price of different time, the obtained total energy consumption economic indexes are different, namely the formulaThe starting time of the first cabinet underflow pump is after the abnormal working condition occurs, namely the formulaThe time of opening the underflow pump is after the last underflow pump is closed, namely the formulaThe last pump-off time is before the end of the current shift, and the shift is left with time, namely the formulaDuring the optimization, the value of the pressure sensor 3 must not exceed an upper limit and the underflow concentration value must not fall below a lower concentration limit, i.e. the formula pl(k)≤pUAnd formula
And step 3: describing the third-layer optimization problem, and relaxing economic indexes to meet the habit of field operators, wherein the optimization problems are divided into a case (1) and a case (2):
(1) first-layer optimized cabinet number N*And reference number of remaining cabinetsAnd (3) equally, further adjusting the ore drawing time according to the operation habit of field operators, wherein the formula is as follows:
in the formula (6), the first and second groups,the starting time of the underflow pump under the normal working condition is shown;
the constraints of the third layer of optimization problem are described after s.t. in formula (6): the description is the same as formula (3);
in, E*Optimum Total energy cost, ε, for the second layer optimizationETo relax economic index parameters;
(2) first-layer optimized cabinet number N*And reference number of remaining cabinetsUnequal, according to the operation habit of field operators, under the condition of increasing or decreasing 1 cabinet of ore, considering the adjustment rule of ore drawing time, namely replacing the optimization target with:
wherein in step 2 the underflow pump run time, i.e. delta, is calculatedjAnd calculating the pump run timeComprises the following steps of 2.1-2.5:
the model structure of step 2.1 and step 2.2 is shown in fig. 2, and the underflow concentration prediction model is constructed by solving the underflow concentration in real time through pressure and predicting the underflow concentration to the pressure.
Step 2.1: establishing a pressure prediction model of the pressure sensors:
when the underflow pump is turned off, a pressure rise model is established:
wherein p isl(k) The pressure value, p, of the pressure sensor l at time kl(k-1) the value at the time on the pressure sensor l, i.e. the value at the time k-1, β1lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x1l(k-1) is the input variable of the pressure sensor l corresponding to the previous time, i.e. the time k-1, and is expressed as follows:
x1l(k-1)＝[pl(k-1),qf(k-1),cf(k-1)]T(9)
wherein q isf(k-1) is the feed rate at the time of k-1, cfAnd (k-1) is the feed concentration at the moment of k-1.
When the underflow pump is turned on, a pressure drop model is established:
wherein p isl(k) Value of the pressure sensor l at time k, pl(k-1) is the value of the pressure sensor l at the time k-1, β2lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x2l(k-1) is the input variable of the pressure sensor l at the time k-1, and is expressed as follows:
wherein q isf(k-1) the feed rate at the time of k-1, cf(k-1) the feed concentration at the moment of k-1, quf(k-1) is the underflow flow at the moment k-1,the underflow concentration is predicted for time k-1.
According to historical data, when an underflow pump is closed, only feeding is carried out on a thickener, no ore pulp is discharged, and the pressure rises; when the underflow pump is started, the discharge amount of the thickener is larger than the feeding amount, the pressure is reduced, and at the moment, the feeding flow and concentration, the underflow flow and concentration and the current pressure value data are counted for establishing a pressure reduction model. We identified the model regression coefficients by PLS algorithm and then used the test data to perform a check of the model predictive performance.
Fig. 7 shows the results of the prediction experiment of the pressure rise model and the pressure drop model. Wherein, the dotted line is a pressure prediction curve, the solid line is an actual measurement curve, and the accuracy of the pressure prediction model is verified. Wherein the root mean square error and the average absolute error of the pressure rise model are respectively 2.02 multiplied by 10-4And 8.00X 10-4(ii) a The root mean square error and the average absolute error of the pressure drop model are respectively 2.27 multiplied by 10-4And 6.81X 10-4And the model prediction performance of the two states can meet the self-healing control requirement.
Step 2.2: establishing an underflow concentration prediction model:
wherein,for the prediction of the underflow concentration at time k, pl(k) And (l ═ 1,2,3) denotes the pressure sensor l measurement, and f (-) is the nonlinear function to be identified.
To predict the underflow concentrationFirstly, storing observation samples into a matrix, and setting an input matrix P ═ P1,p2,…,pn]TN isNumber of samples, corresponding output vector cuf，pli＝[p1i,p2i…pli]TRepresents the ith sample input, where i ═ 1,2li(l ═ 1,2,3) represents the measured value of the pressure sensor l, and since some inevitable anomalous data affect the predicted performance, we use the KPRM algorithm to establish P and cufThe KPRM algorithm can extend the PRM algorithm to the nonlinear kernel form thereof, and can avoid displaying nonlinear mapping as in the KPLS algorithm. If a Gaussian kernel function is introduced, the overall kernel matrix can be calculated by:
wherein σ2As the variance of the input matrix P, e>0 is the kernel width parameter to be adjusted, and | | · | |, is a 2 norm.
The KPRM algorithm may also use the leveraging weights and residual weights to reduce the weight of outliers in the PRM algorithm. Leverage weight of ith sampleCalculated from the following formula:
wherein T is a latent variable matrix derived from the NIPALS step sequence in the KPLS algorithm, and TiFor the ith row of the matrix T, h (-) is a weight function, θ is a coordination constant, med is a median, and | l | · | | is a 2-norm.
Similarly, residual weightsCan be calculated from the following formula:
wherein r isiAnd outputting a residual error of the observed value and the output predicted value for the ith sample.
Then, the weight w of the ith sample as a whole is obtainediIs composed ofW represents WiIs a diagonal matrix of diagonal elements.
Finally, the KPRM algorithm is summarized in the following specific steps:
step 2.2.1: firstly, input matrix P and output vector c are combinedufTaking the mean and unit variance, and taking an n-dimensional unit diagonal matrix as the initial W.
Step 2.2.2: obtaining a weighted kernel matrix K WKW and a corresponding weighted output vector cuf＝Wcuf。
Step 2.2.3: analyzing the weighted kernel matrix K and the weighted output vector c by using the KPLS algorithmufObtaining a latent variable T, and then calculating a residual error ri。
Step 2.2.4: the weight matrix W is updated by equation (14) and equation (15).
Step 2.2.5: loop back to step 2.2.2 until the regression coefficient vectorAnd (6) converging.Can be calculated from the following formula:
step 2.2.6: when a new input vector p appears, calculating elements in the new kernel vector by formula (13);
step 2.2.7: obtain a new kernel vector k ═ k (k)1,κ2,…,κn)TAnd further on the underflow concentrationAnd (6) performing prediction.Can be calculated from the following formula:
we select 50 underflow concentration samples and the pressure values in the corresponding historical database for modeling, and then select 23 new samples for model predictive performance verification. The underflow concentration prediction effect pairs of the two algorithms are shown in fig. 6, the abscissa is the measured concentration, the ordinate is the predicted concentration, the blue dots in the graph represent KPRM algorithm calibration points, and the green dots represent KPLS calibration points. The closer the index point is to the diagonal line, the better the model prediction performance is, and it can be seen that the KPRM model is superior to the traditional KPLS model in prediction performance. The Root Mean Square Error (RMSE) of the former was 0.74, and the latter was 1.32.
Step 2.3: according to the pressure sensor prediction model and the underflow concentration prediction model, establishing a closing time model of the jth cabinet underflow pump:
wherein,for the closing time of the jth cabinet underflow pump,for the opening time of the jth cabinet underflow pump, quf(k) Is time kThe flow rate of the underflow is controlled,and the underflow concentration at the moment k is predicted value.
During the period from the opening of the underflow pump to the closing of the underflow pump, enough ore pulp is needed to complete one dewatering process, and when the opening time of the underflow pump is determinedAnd the amount M of dry ore required for completing one dehydration processfp＝20，
Calculating the closing time of each cabinet underflow pumpThe specific steps are summarized as follows:
step 2.3.1: determining the amount M of dry ore required for completing one-time dehydration procedurefpInitializing cumulative dry ore quantity M ═ 0 and underflow pump shut-off time
Step 2.3.2: calculated using the following formulaInstantaneous underflow density
WhereinIs composed ofUnderflow corresponding to timeConcentration, psAs dry ore density, plIs the liquid density.
Step 2.3.3: the cumulative dry ore quantity M is calculated. Calculated by the following formula:
wherein,is composed ofThe corresponding underflow flow at the moment.
Step 2.3.4: closing time of underflow pump
Step 2.3.5: if the accumulated dry ore amount reaches the dry ore amount M required for completing one cabinetfpI.e. the closing time of the underflow pumpOtherwise, return to step 2.3.2.
Step 2.4: calculating the running time delta of the underflow pumpj：
Step 2.5: calculating the operation time of the ore pump
The relationship between the concentration of the stirring tank and the operation time of the ore pump is as follows:
wherein,in order to start the pump for the time of the ore pump,α for stirred tank pulp average concentration1And α2For linear fitting of the parameters, calculated by the least squares method, α in examples 1 and 21＝11.2633，α2＝1.6167。
Wherein, in formula (1), formula (2), formula (3) and formula (6)And calling a PSO algorithm in matlab to solve.
For exception 1, the rule for determining this exception is: concentrate flow rate higher than 40m3And h, the concentration of the ore pulp exceeds 55%, the duration exceeds 10 minutes, and the abnormal emptying of the concentration tank in the concentration link occurs, as shown in figure 4.
When the abnormal working condition occurs, the actual production of the filter press also needs 6 filter presses, if the underflow pump is immediately started and the dehydration process is carried out according to the prior knowledge and the operation experience of staff, the actual energy consumption reaches 153.14 yuan. The results of the proposed multi-layer optimization control are shown in table 1:
table 1: multi-layer optimization control result of Exception 1
Tier 1-3 represents the first-third layer optimization results, the upper table is the three-layer optimization control results, including the startup time, energy consumption and maximum pressure of the underflow pump.
The result of the first layer optimization is shown in fig. 8, which plots the pressure curve and underflow concentration curve of the 3 rd pressure sensor, with a maximum pressure of 0.048MPa, not exceeding the upper pressure limit pUThe number of cabinets does not need to be increased because the pressure is 0.055 MPa. The opening time of the underflow pump is [1,23,62,119,145,194 ]]Off time [22,45,85,142,172,223 ]]The average concentration of each cabinet is { 67.29%, 65.93%, 65.05%, 64.42%, 59.54% and 57.02% }, and the energy consumption cost is slightly increased to 156.38 yuan because the energy consumption index is not considered at this time.
We then solve the problem of dynamic optimization of the second tier energy consumption cost. As shown in FIG. 9, the maximum pressure was 0.0534MPa, and the upper limit of pressure p was not exceededU0.055 MPa; the concentration of the underflow is at least 62.46 percent and is not lower than the lower limit of the concentration of 55 percent. The opening time of the underflow pump is [50,104,188,206,226,247 ]]Closing time [67,122,206,226,247,270]The average concentration of each cabinet was { 73.65%, 72.13%, 72.72%, 69.5%, 67.12%, 64.44% }. Compared with the first layer, the energy consumption cost of the layer is only 116.80 yuan, which is reduced by 25%.
Finally, we solve the dynamic optimization problem of the third layer, properly relax the economic indicators, and apply epsilonESet to 0.1. To avoid carrying out the concentration dehydration process in the time of high electricity price (from 150 to 210), the opening time of the underflow pump is [50,90,120,199,225,247 ]]Closing time [67,109,140,219,246,269]The average concentration of each cabinet is { 73.65%, 71.47%, 69.03%, 69.73%, 67.58%, 65.26% }, as shown in fig. 10, although the energy consumption of 122.76 yuan is slightly increased, the operation time is closer to the reference value, and the operation habit of staff is easily satisfied.
Example 2:
for exception 2, the rule for determining this exception is: the flow rate of the concentrate is lower than 15m3At a concentration of less than 20% over a period of timeThe time exceeded 5 minutes and it was considered that an abnormal operation of the concentrate pump occurred, as shown in fig. 5. The amount of ore fed into the thickener fluctuates, and the risk of overflowing the tank exists in the concentrate pump pool.
When the abnormal working condition occurs, the reference is given, the filter press machine needs 4 filter presses in actual production, and due to the fact that potential safety hazards cannot occur, according to the operation experience of workers, no treatment is performed, and the fault rate of the filter press machine is increased. In this regard, the results of the proposed multi-layer optimization control are shown in table 2:
table 2: multi-layer optimization control results for Exception 2
Tier 1-3 are expressed as the first-third layer optimization control results, including the startup time of the underflow pump, energy consumption and maximum pressure.
The result of the first layer of optimization is shown in fig. 11, in which the pressure curve of the 3 rd pressure sensor and the underflow concentration curve are plotted, the opening time of the underflow pump is [1,25,87,138], the closing time is [25,57,118,171], the average concentration of each cabinet is { 62.56%, 53.34%, 54.79%, 52.75% }, since the flow rate and the concentration of the feed are both significantly reduced, the minimum value of the underflow concentration is 45.94%, which is 55% lower than the lower limit of the concentration, and the total energy consumption is 129.01 yuan, so that 1 cabinet needs to be reduced to 3 cabinets in order to reduce the failure rate of the filter press.
We then solve the problem of dynamic optimization of the second tier energy consumption cost. As shown in FIG. 12, the maximum pressure was 0.0495MPa, and the upper limit of pressure p was not exceededU0.055 MPa; the concentration of the underflow is 60.64 percent at the lowest and is not lower than the lower limit of the concentration of 55 percent. The opening time of the underflow pump is [86,106,135 ]]Closing time [106,128,159]The average concentration of each bin was { 68.68%, 66.38%, 63.51% }. The energy consumption cost of the layer is greatly reduced to 75.93 yuan.
Finally, we solve the dynamic optimization problem of the third layer and properly relax the economic meaningAfter replacing the optimized objective function, the target is addedESet to 0.1. The opening time of the underflow pump is [60,120,147 ]]Closing time [81,141,170]The average concentration of each tank was { 67.2%, 66.81%, 64.45% }, as shown in FIG. 13, the energy consumption became 77.93.
From the specific operation condition, the method of the invention well solves the control problem under the abnormal working condition of the feeding in the thickening dehydration process, and utilizes the pressure prediction model, the underflow concentration model and the three-layer optimization model, thereby not only ensuring the safe and stable operation of the thickener under the abnormal working condition of the feeding and reducing the energy consumption and production cost, but also leading the ore drawing operation during the self-healing control to be more in line with the habit of field operators. According to the experimental data of the specific example, the pressure prediction model and the underflow concentration model can be predicted accurately, and the requirements of actual industrial production can be met; the final self-healing control effect shows that the ore drawing time planned by the three-layer optimization model is reasonable and feasible, the safety and the energy consumption of the process are considered, and the adaptability of field operators to the method is also fully considered.
Claims (4)
1. A self-healing control method for feed abnormal working conditions in a thickening dehydration process is characterized in that optimization problems under the abnormal working conditions in the thickening dehydration process are described in a layered mode, and the method comprises the following specific steps:
step 1: describing the first layer optimization model, and under the abnormal working condition, the self-healing method in the dehydration process of the thickener comprises the following steps:
step 1.1: minimizing the maximum pressure value, and determining whether the current cabinet number meets the requirement of safety limit: the goal of the first layer optimization model is to optimize ore drawing timeReducing the maximum value of the pressure sensor l during the process operation if this value exceeds the upper limit value p of the pressure sensor lUIf the number of the remaining cabinets N cannot meet the requirement of safety production, 1 cabinet needs to be added; otherwise, the remaining cabinet number N does not need to be adjusted, as shown in formula (1);
wherein N represents the number of the cabinets which need to be subjected to filter pressing in the current class,representing the maximum value taken by the pressure sensor i during operation of the process,the opening time of the underflow pump representing the number of the residual filter cabinets in the current shift;
the s.t. in the formula (1) is described later as a constraint condition for minimizing the maximum value of the pressure of the first layer optimization model:
for the closing time model constraint of the jth cabinet underflow pump, the value of the closing time model constraint is equal to the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And underflow concentration predicted value at the moment kRelatively, g (-) is the closing time of the jth cabinet underflow pump and the opening time of the jth cabinet underflow pumpUnderflow flow q at time kuf(k) And k isPrediction value of concentration of etching bottom flowThe correlation function of (a);
for ore drawing time constraints:
representing the opening time of the No. 1 cabinet underflow pumpShould not be less than the occurrence time k of abnormal conditionsa；
Representing that the opening time of the underflow pump of the jth cabinet is more than or equal to the closing time of the underflow pump of the previous cabinet
Representing the turn-off time of the last tank underflow pumpShould not exceed the end time k of the current shiftfRemoving shift time epsilonk；
Representing the predicted value of the underflow concentration in the thickening and dewatering processIt is required to be greater than the lower limit of concentration；
Step 1.2: maximizing the concentration minimum: the goal of the first layer optimization model is to optimize ore drawing timeIncreasing the minimum value of the underflow concentration during the operation of the process as much as possible, if this value is below the lower limit value c of the underflow concentrationLThen 1 cabinet needs to be reduced; otherwise, the remaining number N of cabinets does not need to be adjusted, as shown in formula (2):
wherein N represents the number of the cabinets needing filter pressing in the current class, cufRepresenting the minimum value that the underflow concentration takes during the operation of the process,representing the number of cabinets needing filter pressing in the shift;
the s.t. in the formula (1) is described later as a constraint condition for maximizing the minimum value of the concentration of the first layer of optimization problem:
closing the time model constraint for the jth cabinet underflow pump, the meaning of the restriction of ore drawing time is the same as that of the formula (1);
pl(k)≤pUrepresenting the measured pressure value p of the pressure sensor l in the process of thickening and dewatering at the moment klNeeds to be less than the upper limit value p of the pressureU；
Step 2: describing the second layer optimization model, and enabling the production energy consumption cost to be the lowest within a safety limit according to the number of cabinets determined by the first layer optimization model:
wherein, formula (3) includes: economic indexes of energy consumption of the underflow pump and the ore pump;
the j < th > cabinet underflow pump energy consumption economic index is as follows:
wherein E isufThe unit energy consumption of the underflow pump is P (k), and the stepped electricity price at the moment k is P (k);
the j cabinet mining pump energy consumption economic indexes are as follows:
wherein E isfpFor the unit energy consumption of the ore pump, P (k) is the stepped electricity price at time k, deltajFor the operation time of the jth cabinet underflow pump,the operation time of the ore pump required for completing the jth cabinet;
in the formula (3), N*Representing the number of remaining bins resolved by the first-level optimization;
the constraints of the second-layer optimization problem are described after s.t. in formula (3):
closing the time model constraint for the jth cabinet underflow pump, for the ore drawing timeA bundle, the meaning of which is the same as formula (1);
pl(k)≤pUrepresenting the measured pressure value p of the pressure sensor l in the process of thickening and dewatering at the moment klNeeds to be less than the upper limit value p of the pressureU；
Representing the predicted value of the underflow concentration in the thickening and dewatering process at the moment kIt is necessary to be greater than the lower limit of concentration cL；
And step 3: describing a third-layer optimization model, and relaxing economic indexes to meet the habit of field operators, wherein the third-layer optimization model is divided into a case (1) and a case (2):
(1) the number N of the remaining cabinets obtained by the first layer optimization*And reference number of remaining cabinetsAnd (3) equally, further adjusting the ore drawing time according to the operation habit of field operators, wherein the formula is as follows:
in the formula (6), the first and second groups,the starting time of the underflow pump under the normal working condition is shown;
the s.t. in the formula (6) is described later as the constraint condition of the third layer optimization model: the description is the same as formula (3);
in, E*Optimum Total energy cost, ε, for the second layer optimizationETo relax economic index parameters;
(2) first layerOptimizing the obtained number of remaining cabinets N*And reference number of remaining cabinetsUnequal, according to the operation habit of field operators, under the condition of increasing or decreasing 1 cabinet of ore, considering the adjustment rule of ore drawing time, namely replacing the optimization target with:
the constraint conditions of the third-layer optimization model case (2) are the same as the formula (6).
2. A self-healing control method for abnormal feeding conditions in the thickening and dewatering process according to claim 1, wherein in the step 2, the running time δ of the underflow pump is calculatedjAnd calculating the pump run timeComprises the following steps of 2.1-2.5:
step 2.1: establishing a pressure prediction model of the pressure sensors:
when the underflow pump is turned off, a pressure rise model is established:
wherein p isl(k) The pressure value, p, of the pressure sensor l at time kl(k-1) the value at the time on the pressure sensor l, i.e. the value at the time k-1, β1lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x1l(k-1) is the input variable of the pressure sensor l corresponding to the previous time, i.e. the time k-1, and is expressed as follows:
x1l(k-1)＝[pl(k-1),qf(k-1),cf(k-1)]T(9)
wherein q isf(k-1) is the feed flow at the time of k-1,cf(k-1) is the feed concentration at the moment of k-1;
when the underflow pump is turned on, a pressure drop model is established:
wherein p isl(k) Value of the pressure sensor l at time k, pl(k-1) is the value of the pressure sensor l at the time k-1, β2lIs a vector of regression coefficients, quf(k) Underflow flow at time k, x2l(k-1) is the input variable of the pressure sensor l at the time k-1, and is expressed as follows:
wherein q isf(k-1) the feed rate at the time of k-1, cf(k-1) the feed concentration at the moment of k-1, quf(k-1) is the underflow flow at the moment k-1,predicting the underflow concentration for the time k-1;
step 2.2: establishing an underflow concentration prediction model:
wherein,for the prediction of the underflow concentration at time k, pl(k) Representing the measured value of the pressure sensor l, f (-) is a nonlinear function to be identified;
to predict the underflow concentrationFirstly, storing observation samples into a matrix, and setting an input matrix P ═ P1,p2,...,pn]TN is the number of samplesCorresponding output vector cuf，pi＝[p1i,p2i…pli]TRepresents the ith sample input, where i ═ 1,2liRepresenting the measured value of the pressure sensor l, using the KPRM algorithm to establish P and cufThe KPRM algorithm introduces a Gaussian kernel function, and an integral kernel matrix can be calculated by the following formula:
wherein σ2As the variance of the input matrix P, e>0 is the kernel width parameter to be adjusted, | | | · | |, is a 2 norm;
the KPRM algorithm uses the leverage and residual weights to reduce the weight of outliers in the PRM algorithm, the leverage weight of the ith sampleCalculated from the following formula:
wherein T is a latent variable matrix derived from the NIPALS step sequence in the KPLS algorithm, and TiFor the ith row of the matrix T, h (-) is a weight function, theta is a coordination constant, med is a median, and | l | · | | is a 2-norm;
residual weightsCan be calculated from the following formula:
wherein r isiOutputting a residual error of the observed value and the output predicted value for the ith sample;
determining the weight w of the ith sampleiIs composed ofW represents WiA diagonal matrix being diagonal elements;
step 2.3: according to the pressure sensor prediction model and the underflow concentration prediction model, establishing a closing time model of the jth cabinet underflow pump, namely constraint conditions of formula (1), formula (2), formula (3), formula (6) and formula (7):
wherein,for the closing time of the jth cabinet underflow pump,for the opening time of the jth cabinet underflow pump, quf(k) The underflow flow rate at the moment k is shown,the predicted value of the underflow concentration at the moment k is obtained;
wherein,solving by adopting a PSO algorithm;
step 2.4: calculating the running time delta of the underflow pumpj：
Step 2.5: calculating the operation time of the ore pump
The relationship between the concentration of the stirring tank and the operation time of the ore pump is as follows:
wherein,in order to start the pump for the time of the ore pump,α for stirred tank pulp average concentration1And α2The parameters are linear fitting parameters and are calculated by a least square method.
3. A self-healing control method for abnormal working conditions of feeding materials in the thickening and dewatering process according to claim 1, wherein the KPRM algorithm is summarized as follows:
step 2.2.1: firstly, input matrix P and output vector c are combinedufTaking a mean value and a unit variance, and taking an n-dimensional unit diagonal matrix for initial W;
step 2.2.2: obtaining a weighted kernel matrix K WKW and a corresponding weighted output vector cuf＝Wcuf；
Step 2.2.3: analyzing the weighted kernel matrix K and the weighted output vector c by using the KPLS algorithmufObtaining a latent variable T, and then calculating a residual error ri；
Step 2.2.4: upgrading the weight matrix W by formula (14) and formula (15);
step 2.2.5: loop back to step 2.2.2 until the regression coefficient vectorConverging;can be calculated from the following formula:
step 2.2.6: when a new input vector p appears, calculating elements in the new kernel vector by formula (13);
step 2.2.7: obtain a new kernel vector k ═ k (k)1,κ2,…,κn)TAnd further on the underflow concentrationThe prediction is carried out in such a way that,can be calculated from the following formula:
and predicting the underflow concentration.
4. A self-healing control method for abnormal feeding conditions in a thickening and dewatering process according to claim 1,
the closing time of each cabinet underflow pumpThe concrete solving steps are as follows:
step 2.3.1: determining the amount M of dry ore required for completing one-time dehydration procedurefpInitializing cumulative dry ore quantity M ═ 0 and underflow pump shut-off time
Step 2.3.2: calculated using the following formulaInstantaneous underflow density
Wherein,is composed ofUnderflow concentration, p, corresponding to the momentsAs dry ore density, plIs the liquid density;
step 2.3.3: calculating the accumulated dry ore amount M by the following formula:
wherein,is composed ofUnderflow flow rate corresponding to the moment;
step 2.3.4: closing time of underflow pump
Step 2.3.5: if the accumulated dry ore amount reaches the dry ore amount M required for completing one cabinetfpI.e. the closing time of the underflow pumpOtherwise, returning to the step 2.3.2, and calculating the underflow concentration at the next moment.
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| CN110276128A (en) * | 2019-06-21 | 2019-09-24 | 东北大学 | A kind of thickener underflow concentration prediction method based on DAJYPLS algorithm |
| CN112257248A (en) * | 2020-10-16 | 2021-01-22 | 山东黄金矿业(莱州)有限公司三山岛金矿 | Dense filter pressing process coordinated optimization control method based on layered optimization model |
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| CN112257248A (en) * | 2020-10-16 | 2021-01-22 | 山东黄金矿业(莱州)有限公司三山岛金矿 | Dense filter pressing process coordinated optimization control method based on layered optimization model |
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