CN110728329A - Concentrate grade prediction method based on feedback compensation mechanism optimization in zinc flotation process - Google Patents

Concentrate grade prediction method based on feedback compensation mechanism optimization in zinc flotation process Download PDF

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CN110728329A
CN110728329A CN201911008874.0A CN201911008874A CN110728329A CN 110728329 A CN110728329 A CN 110728329A CN 201911008874 A CN201911008874 A CN 201911008874A CN 110728329 A CN110728329 A CN 110728329A
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唐朝晖
唐励雍
高小亮
范影
刘亦玲
肖文辉
李涛
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Abstract

The invention provides a concentrate grade prediction method in a zinc flotation process based on feedback compensation mechanism optimization, which comprises the following steps: firstly, collecting image characteristic data and corresponding concentrate grade data in a zinc flotation process as sample data, and preprocessing the collected data; dividing the preprocessed sample data into five independent sub-sample spaces according to the grade of the concentrate, and respectively carrying out time difference; adopting KPCA to extract high-contribution-rate characteristics as key characteristics; training an LSSVM (least squares support vector machine) based on the key feature samples, and establishing a relation between image features and concentrate grade; optimizing two parameters of a penalty factor xi and a nuclear width sigma of the LSSVM by using an improved flora algorithm; establishing a model error feedback compensation mechanism, and starting the feedback compensation mechanism to compensate the model when the model error is not controlled; the invention can be directly realized by programming on a computer, has low cost, high precision and good timeliness and has important significance for guiding field production.

Description

Concentrate grade prediction method based on feedback compensation mechanism optimization in zinc flotation process
Technical Field
The invention belongs to the technical field of froth flotation, and particularly relates to a method for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization of model error estimation
Technical Field
The froth flotation is one of the most main mineral separation methods in lead and zinc smelting at present, and the flotation method is a method for separating minerals by utilizing different hydrophilicity caused by different physical and chemical properties of the surfaces of mineral particles, and has strong practical value. However, because the flotation process has a long flow, an internal mechanism is not clear, influence factors are numerous, and the flotation process relates to the reasons that variables are various and nonlinearity is serious, and many process indexes cannot be detected on line, the foam state is determined by 'looking at bubbles' through artificial naked eyes all the time, the obtained concentrate grade is predicted, and field operation is completed according to the foam state, so that the method has the advantages of strong subjectivity, dependence on experience knowledge, difficulty in realizing accurate and stable prediction of the concentrate grade, frequent fluctuation of the concentrate grade, serious loss of mineral raw materials, large medicament consumption and low resource recovery rate. Therefore, the research on the real-time online detection method of the concentrate grade in the flotation process has important significance for improving the utilization rate of nuclear mineral resources of the concentrate grade.
With the rapid development of computer technology and digital image processing technology, the application of the soft measurement technology based on machine vision to the flotation process brings a new breakthrough to the real-time monitoring of flotation indexes, and obtains more flotation indexes related to the grade. The characteristics of the flotation froth, such as color, size, shape, stability, flow velocity and texture, are closely related to the flotation working condition, concentrate grade and production index. The visual characteristics of the flotation froth surface are important indicators of production indexes, so the flotation froth surface characteristics are always important bases for the adjustment of the flotation production of a dressing plant. However, the zinc flotation process is a complex industrial process, the traditional method for directly predicting the concentrate grade through the characteristics of the flotation froth surface has the problems of difficult modeling, low precision and the like, and the strong coupling among various characteristics of the froth image greatly increases the calculation reproducibility and influences the precision and the failure of the prediction model. Therefore, the feature complexity is reduced, and the problems of low precision, poor timeliness and the like of the traditional prediction model can be solved by establishing a simple and effective prediction model.
Disclosure of Invention
Aiming at the defects that the concentrate grade is difficult to detect on line in the flotation process and the zinc flotation concentrate grade is predicted in the prior art, the invention provides a data-driven concentrate grade prediction method in the zinc flotation process based on an improved flora algorithm by utilizing various characteristics related to the zinc concentrate grade.
The technical scheme adopted comprises the following specific steps:
s1: and acquiring zinc fast and coarse image characteristic acquisition and corresponding fine mineral grade data by using a flotation process image acquisition and processing system.
S2: carrying out data preprocessing on the collected zinc flotation data and production data as follows:
(1) eliminating error data of which the measured data value exceeds the variation range;
(2) rejecting unmatched data and data with a vacancy value;
s3: due to the fact that information redundancy exists among the foam characteristics, accuracy of concentrate grade prediction is seriously influenced, and complexity of calculation is increased. Therefore, correlation analysis is performed on the characteristics by a Kernel Principal Component Analysis (KPCA), and the characteristics with high contribution rate are taken as key foam characteristics. The method mainly comprises the following steps:
(1) because the dimensions of different characteristic data are different, the raw data are firstly standardized:
Figure BDA0002242660830000011
data x to be normalized by the above equationvu' composition data matrix X, where XvuIn order to be able to normalize the data before it is normalized,
Figure BDA0002242660830000012
and SvThe sample mean and the sample standard deviation of the v index are respectively;
(2) calculating a covariance matrix:
Figure BDA0002242660830000013
where C is the covariance matrix, M is the number of samples,
Figure BDA0002242660830000014
is a high-dimensional mapping function;
(3) calculating eigenvalues and eigenvectors of the covariance matrix C
γVv＝Cγ (3)
γ is the eigenvalue, V is the eigenvector, and the corresponding eigenvector is shown in equation (4):
since the feature vector V is composed of a nonlinear mapping space, equation (3) is equivalent to the following form:
Figure BDA0002242660830000022
carry (2), (3) and (4) into (5), and let the kernel matrix
Figure BDA0002242660830000023
Get KaM＝MγvaMThe eigenvector of the kernel matrix is a1，a2，...，aMThe characteristic value is M gammavSorting the eigenvalues in descending order, extracting the first L eigenvalues (L < M) and corresponding eigenvectors a1，a2，...，aL；
(4) Calculating the characteristic contribution rate;
the contribution rate is determined by the size of the characteristic value, and the calculation formula is as follows:
wherein M is the number of principal component, CRnIs a principal component contribution rate, γvFor the value of the v-th characteristic,
Figure BDA0002242660830000025
is the total eigenvalue; when CR is reachednWhen the content is 85% or more, the main component is contained, and the corresponding characteristic is a key characteristic.
S4: the extracted key characteristics are combined into X, the corresponding concentrate grade data are combined into y, 5 different concentrate grade intervals are divided according to the concentrate grade y, and the 5 different concentrate grade intervals and the corresponding characteristic data are combined into 5 sub-sample spaces (X)1，y1)，(X2，y2)，(X3，y3)，(X4，y4)，(X5，y5)；
S5: respectively carrying out time difference on the 5 sub-sample spaces to form a difference sequence (delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) The method comprises the following specific steps:
and respectively carrying out time difference on the 5 sub-sample sequences to form a difference sequence, which specifically comprises the following steps:
Figure BDA0002242660830000026
to obtainRespectively forming a (delta X, delta y) time difference sequence space by the zinc fast coarse foam image characteristic data and the first-order time difference component of the corresponding fine mineral bit data.
Then, a regression model between the input-output difference components can be built:
Δy(t)＝f(ΔX(t)) (8)
after training and regression model, when inputting a new set of samples x (tnew), the time difference components of the input are:
ΔX(tnew)＝X(tnew)-X(tnew-1) (9)
thus, the first order difference component of its output can be predicted by a trained regression model:
y(tnew)＝Δy(tnew)+y(tnew-1) (10)
s6: 5 time difference sequence spaces (Delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) The data is used as training data to train the LSSVM together, and the relationship between the image characteristics and the concentrate grade is established, and the method comprises the following specific steps:
(1) for training data (Δ X, Δ y) ∈ RLTaking x R and L as the space dimension of the key characteristic sample, and selecting nonlinear mapping
Figure BDA0002242660830000028
Mapping the training samples to a high-dimensional linear space;
Figure BDA0002242660830000029
omega is the weight coefficient, omegaTOmega controls the generalization ability of the model, pbiasFor the offset, f (x) is the estimation function.
(2) Establishing a quadratic programming solving problem according to a structured risk minimum principle:
Figure BDA00022426608300000210
in the formula, J (omega, epsilon) is structure risk, xi is punishment coefficient, epsilonuTo allow for errors.
(3) Defining a lagrange function:
Figure BDA0002242660830000031
wherein alpha isuE is R as Lagrange multiplier;
(4) according to the KKT optimization conditions, the following conditions can be obtained:
wherein y is [ y ═ y1，y2，...，yN]T，IN＝[1，1，...，1]T，θv′u′＝K(Xv′，Xu)，K(Xv′，Xu′) Selecting a Gaussian radial kernel function, taking a as a vector parameter and xi as an adjustable parameter, and performing the optimization according to Mercer conditions
Figure BDA0002242660830000033
Wherein
Figure BDA0002242660830000034
(5) And obtaining the output of the least square support vector machine:
Figure BDA0002242660830000035
pbiasfor biasing, a Gaussian radial basis kernel function [ RFB ] is used]As a kernel function of the LSSVM, there are 2 parameters of penalty coefficient ξ and kernel function width σ that need to be determined. Research shows that the larger the penalty coefficient xi is, the larger the penalty on the empirical error is, and the smaller the regression error of the model is, but too large xi can lead to over-learning of the model, and too small xi can lead to under-learning. The kernel function width σ also affects the performance of the model. Therefore, the proper ξ and σ are the key to obtain a high-performance LSSVM model. And (3) optimizing 2 parameters of the LSSVM by using a flora algorithm (BFO) to obtain an optimized prediction model, and outputting a predicted grade value.
S7: the flora algorithm (BFO) is a bionic search algorithm provided by simulating the foraging process of escherichia coli, and the optimal solution is continuously and iteratively searched by judging the goodness of the fitness evaluation solution. The main operations are tendency, aggregation, replication and migration. The specific steps of the algorithm are shown in fig. 1.
(1) Firstly, initialization:
p: a dimension representing a search space;
s: represents the size of the bacterial population;
Nc: representing the number of times the bacteria performed a tropism;
Ns: representing the maximum number of steps in the trending operation that go forward in one direction;
Nre: representing the number of times the bacterium performs replicative behaviour;
Ned: representing the number of times the bacteria performs migratory behaviour;
Ped: representing a migration probability;
c (i): representing the step size of the forward walk.
Define P (j, k, l) { θ }i(J, k, l) | i ═ 1., S } represents the location of the individual in the population after the jth tropism maneuver, the kth replication maneuver, and the l migration maneuver, and J (J, k, l) represents the fitness function value of the bacterium i after the jth tropism maneuver, the kth replication maneuver, and the l migration maneuver.
(2) Tropism of operation
The flora algorithm simulates that escherichia coli has two basic movements in the whole foraging process: rotation and play. Rotation is to find a new direction of movement, while swimming is to keep the direction unchanged. Each step of tropism profile for bacterium i represents:
Figure BDA0002242660830000036
where Δ represents one unit vector in the random direction.
Since the step size is not easily determined. If the step length is too large, the bacteria can move to the target area quickly, so that the searching efficiency is improved, but the bacteria can easily leave the target area and cannot find the optimal solution or fall into local optimal solution. The step length is too small, so that the calculation efficiency is reduced while high-precision calculation results are obtained, and in addition, the algorithm is possibly trapped in a local minimum area to cause the algorithm to be premature or immature. Secondly, the bacteria with different energies adopt the same step length, so that the step length difference between the bacteria with different energies cannot be reflected, and the optimizing precision of the tendency behavior of the bacteria is reduced to a certain extent. Therefore, the step size of each bacterium plays a major role in the convergence rate and calculation accuracy.
The algorithm is improved by the concept of conferring sensitivity to bacteria to adjust the walk step size.
Defining an energy factor expression as:
Figure BDA0002242660830000041
wherein J (i, J, k, l) is the adaptive value of the current backward trend, and J (i, J-1, k, l) is the adaptive value of the previous backward trend.
The individual bacteria are far away from the global optimum point, and the walking step length should be large in order to increase the global searching capacity of the algorithm. However, as the iteration continues, many bacterial individuals get closer to the global optimum, at which point the walking step size should be decreased to increase the local search power per bacterial individual, thus defining the sensitivity:
C(i)＝C(i)·V (20)
the formula (19) and (20) can satisfy the self-adaptive adjustment of the step length along with the adaptation value of bacteria and the number of iterations.
(3) Collective operations
During the process of the flora seeking food, the bacterial individuals achieve aggregation behavior through interaction with each other. There are both attractive and repulsive forces between bacteria. The attractive force causes the bacteria to be gathered together, the repulsive force causes each cell to have a certain position, and simulating this behavior in the algorithm is called gathering operation. The mathematical expression for the aggregation behavior between bacteria is:
Figure BDA0002242660830000043
wherein d isattractantDepth of gravity, wattractantWidth of gravity, hrepellantHeight of repulsion, wrepellantIn order to be the width of the repulsive force,
Figure BDA0002242660830000044
the m-th component of bacterium i, θmIs the m-th component of other bacteria in the entire population. Due to Jcc(θ, P (j, k, l)) represents the influence value of the transmission signal between the population bacteria, so that after the aggregation operation is introduced in the tropism cycle, the calculation formula of the fitness value of the ith bacterium becomes:
J(i，j+1，k，l)＝J(i，j，k，l)+Jcc(θi(j+1，k，l)，P(j+1，k，l)) (22)
(4) replicative operations
The mode of excellence and disadvantage by simulating the process of biological evolution in the BFO algorithm is called replicative operation. For a given k, l and each i 1.
Figure BDA0002242660830000045
The above formula represents the health function of bacterium i.
Figure BDA0002242660830000046
Smaller means that the bacteria are healthier and more capable of foraging. Transferring the bacterial energy JhealthArranged in the order from big to small, before being eliminated
Figure BDA0002242660830000047
Individual bacteria, after replication of the bacteriaThe number of bacteria is one.
(5) Migratory manipulation
The local area where bacteria live may change. This may result in the bacterial population living in the local area migrating to a new area. Simulating this phenomenon in the BFO algorithm is called migratory operation. Simulating this process, after several generations of replication of the flora in the algorithm, the bacteria have a given probability PedAnd executing the migration operation, and randomly reallocating the migration operation to the optimization interval. The new individual randomly generated by the migration behavior can be closer to the global optimal solution, so that the local optimal solution can be better jumped by the trending operation, and the global optimal solution can be searched.
S8: in practice, the accuracy of the prediction model cannot be guaranteed according to different ore entering grades in the flotation process, and in order to solve the problem, the conventional method can retrain when the prediction accuracy does not meet the requirement, so that the conventional method meets the prediction accuracy requirement under the current ore entering condition, undoubtedly, the model error compensation mechanism can be set to solve the defects that the model is frequently trained, the calculated amount is large and the like.
And (3) determining whether a confidence interval of the confidence level 1-alpha of the mu of the model error distribution conforms to a set interval range (0, eta), and starting a model error compensation mechanism, wherein the method specifically comprises the following steps:
(1): firstly, D predicted model errors are selected, whether a confidence interval of a confidence level 1-alpha of mu of model error distribution accords with a set interval range (0, eta) or not is judged, and when the judgment condition is not met, an error compensation mechanism is started by a system to carry out fuzzy compensation on the errors; according to the empirical condition, the distribution of model errors accords with Gaussian distribution, s is the standard deviation of D model errors, and the confidence interval of mu with the confidence level of 1-alpha is
Figure BDA0002242660830000049
Taking alpha to be 0.05, namely ensuring that the confidence level of the average model error in the range of (0, eta) reaches 95 percent;
(2): the following compensation rules are set: when the confidence interval with the confidence level of 1-alpha is not satisfied
Figure BDA0002242660830000051
When the range of the set interval is met, the model error compensation value
Figure BDA0002242660830000052
S9: real-time data acquired by the froth image acquisition and processing system is input into the established prediction model, so that the online prediction of the concentrate grade in the flotation process is realized.
S4, dividing the concentrate grade y into 5 different concentrate grade intervals, wherein the concentrate grade value is in y 1E [51.5, 52.5 ]]Identity low, y2∈(52.5，53.5]Low mark, y3∈(53.5，54.5]In the symbol, y4∈(54.5，55.5]Mark is higher, y5∈(55.5，56.5]The flag is high.
In the initialization parameter S72 described in S7, S is 20, Nc＝20，Ns＝4，Nre＝4，Ned＝2，Ped＝0.1，p＝2。
In S73 described in S7, 4) said dattractant＝0.1，wattractant＝0.2，hrepellant＝0.1，wrepellant＝0.2。
D e (100,120) and eta e (0.8, 1) as described in (1) in S8.
The invention provides a concentrate grade prediction method based on data driving of a zinc flotation process and based on an improved flora algorithm, aiming at the problems that concentrate grade prediction modeling is difficult, off-line detection time lag is serious, the dimension of the characteristics of a foam image is multiple, the redundancy is strong, most characteristics are difficult to extract and the like, and the online prediction calculation of the concentrate grade is complex, the prediction precision is low and the like. Calculating the contribution rate of different features by a kernel principal component analysis method, sorting according to the contribution rate of the features, and selecting key features with the forward contribution rate; training a least square support vector machine with a Gaussian radial basis function based on the extracted key characteristics to obtain a prediction model to fit a nonlinear relation between the foam image characteristics and the concentrate grade; because two parameters of a penalty factor xi and a kernel width sigma in the prediction model need to be estimated, the precision of the prediction model is influenced by the parameters xi and sigma, while the traditional parameter estimation method is usually in local optimum, the invention provides an improved flora algorithm to search the reference of a prediction model, because the swimming step length of the bacteria in the iterative process is not easy to be directly determined, the step length difference between the bacteria with different energy levels cannot be reflected by the bacteria with different energy levels with the same step length, the optimization precision of the trend behavior of the bacteria is reduced to a certain extent, and the bacteria easily skip the optimal solution due to overlarge step length in the later iteration period, so that the sensitivity factor is introduced in the method, the step length can be adaptively adjusted according to the difference of self states and the superposition of iteration times in the iteration process of the bacteria, and the problem that the optimization algorithm is difficult to avoid is solved. The iteration termination condition of the improved flora algorithm cannot take the accuracy of the prediction model as the termination condition, and the parameters after the initial iteration are probably not the optimal parameters, so the accuracy of the prediction model is evaluated by using the root mean square error at last, the iteration is terminated when the accuracy is reached to obtain the optimal prediction model, and the improved flora algorithm is continuously used for the next cycle optimization when the accuracy is not reached. The method can be directly realized by programming on a computer, has low cost and high prediction precision, can show the variation trend of the level of the concentrate in the field zinc flotation process in real time, and has important significance for guiding industrial production.
Drawings
FIG. 1 is a flow chart of the present invention for optimizing LSSVM parameters using a modified population algorithm.
Detailed Description
The technical solutions adopted in the present invention are described and explained in more detail and clearly with reference to the accompanying drawings. The invention provides an online measuring method for zinc concentrate grade based on key characteristic selection, aiming at the complexity of a flotation process, unclear internal mechanism, multiple feature dimensions, strong coupling characteristics and low training difficulty and precision of a traditional prediction model. It should be apparent that the described embodiments are only some of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the relevant art without any inventive step based on the embodiments of the present invention, shall be within the scope of the present invention.
A prediction model is established by analyzing the relation between the foam image characteristics and the concentrate grade, 13 foam image characteristics (speed, stability, gray average, red component, green component, blue component, foam size, size variance, bearing rate, chroma, brightness, peak value and skewness) capable of showing the concentrate grade are selected as model input, and the concentrate grade is output. The flotation grade change states are reflected by the image characteristics to different degrees, but information redundancy exists among the characteristics, the accuracy of concentrate grade prediction is seriously influenced, and the complexity of calculation is increased. According to research, the ore concentrate grade can be well predicted only by selecting partial images which can fully express the working condition characteristics. Therefore, the method comprises the steps of firstly selecting key features in the multi-dimensional image features through kernel principal component analysis, forming a training sample with the concentrate grade index, then training a least square support vector machine by using the training sample to obtain a prediction model, and finally optimizing the parameters of the prediction model of the least square support vector machine by using an improved flora algorithm.
The invention discloses an online prediction method of concentrate grade in a zinc flotation process, which comprises the following steps:
s1: and acquiring zinc fast and coarse image characteristic acquisition and corresponding fine mineral grade data by using a flotation process image acquisition and processing system.
S2: carrying out data preprocessing on the collected zinc flotation data and production data as follows:
(1) eliminating error data of which the measured data value exceeds the variation range;
(2) rejecting unmatched data and data with a vacancy value;
s3: due to the fact that information redundancy exists among the characteristics, accuracy of the concentrate grade prediction is seriously influenced, and the complexity of calculation is increased. Therefore, the characteristics are subjected to correlation analysis through a principal component analysis method, and the characteristics with high contribution rate are taken as key foam characteristics. The method mainly comprises the following steps:
(1) because the dimensions of different characteristic data are different, the raw data are firstly standardized:
Figure BDA0002242660830000061
data x to be normalized by the above equationvu' composition data matrix X, where XvuIn order to be able to normalize the data before it is normalized,
Figure BDA0002242660830000062
and SvThe sample mean and the sample standard deviation of the v index are respectively;
(2) calculating a covariance matrix:
Figure BDA0002242660830000063
where C is the covariance matrix, M is the number of samples,
Figure BDA0002242660830000064
is a high-dimensional mapping function;
(3) calculating eigenvalues and eigenvectors of the covariance matrix C
γVv＝Cγ (3)
γ is the eigenvalue, V is the eigenvector, and the corresponding eigenvector is shown in equation (4):
Figure BDA0002242660830000065
since the feature vector V is composed of a nonlinear mapping space, equation (3) is equivalent to the following form:
Figure BDA0002242660830000066
carry (2), (3) and (4) into (5), and let the kernel matrix
Figure BDA0002242660830000067
Get KaM＝MγvaMThe eigenvector of the kernel matrix is a1，a2，...，aMThe characteristic value is M gammavSorting the eigenvalues in descending order, extracting the first L eigenvalues (L < M) and corresponding eigenvectors a1，a2，...，aL；
(4) Calculating the characteristic contribution rate;
the contribution rate is determined by the size of the characteristic value, and the calculation formula is as follows:
Figure BDA0002242660830000068
wherein M is the number of principal component, CRnIs a principal component contribution rate, γvFor the value of the v-th characteristic,
Figure BDA0002242660830000069
is the total eigenvalue; when CR is reachednWhen the content is 85% or more, the main component is contained, and the corresponding characteristic is a key characteristic.
S4: the extracted key characteristics form X, the corresponding concentrate grade data form y, and 5 ore concentrate grade data are divided according to the grade y of the ore concentrateDifferent concentrate grade intervals and corresponding characteristic data form 5 sub-sample spaces (X)1，y1)，(X2，y2)，(X3，y3)，(X4，y4)，(X5，y5) The value of the grade of the concentrate is y1∈[51.5，52.5]Identity low, y2∈(52.5，53.5]Low mark, y3∈(53.5，54.5]In the symbol, y4∈(54.5，55.5]Mark is higher, y5∈(55.5，56.5]The flag is high.
S5: respectively carrying out time difference on the 5 sub-sample spaces to form a difference sequence (delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) The method comprises the following specific steps:
and respectively carrying out time difference on the 5 sub-sample sequences to form a difference sequence, which specifically comprises the following steps:
to obtain
Figure BDA00022426608300000611
Respectively forming a (delta X, delta y) time difference sequence space by the zinc fast coarse foam image characteristic data and the first-order time difference component of the corresponding fine mineral bit data.
Then, a regression model between the input-output difference components can be built:
Δy(t)＝f(ΔX(t)) (8)
after training and regression models, when a new set of samples X (t) is inputnew) The input time difference component is:
ΔX(tnew)＝X(tnew)-X(tnew-1) (9)
thus, the first order difference component of its output can be predicted by a trained regression model:
y(tnew)＝Δy(tnew)+y(tnew-1) (10)
s6: 5 time difference sequence spaces (Delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) The data is used as training data to train the LSSVM together, and the relationship between the image characteristics and the concentrate grade is established, and the method comprises the following specific steps:
(1) for training data (Δ X, Δ y) ∈ RLTaking x R and L as the space dimension of the key characteristic sample, and selecting nonlinear mapping
Figure BDA0002242660830000071
Mapping the training samples to a high-dimensional linear space;
Figure BDA0002242660830000072
omega is the weight coefficient, omegaTOmega controls the generalization ability of the model, pbiasFor the offset, f (x) is the estimation function.
(2) Establishing a quadratic programming solving problem according to a structured risk minimum principle:
Figure BDA0002242660830000073
in the formula, J (omega, epsilon) is structure risk, xi is punishment coefficient, epsilonuTo allow for errors.
(3) Defining a lagrange function:
Figure BDA0002242660830000074
wherein alpha isuE is R as Lagrange multiplier;
(4) according to the KKT optimization conditions, the following conditions can be obtained:
Figure BDA0002242660830000075
wherein y is [ y ═ y1，y2，...，yN]T，IN＝[1，1，...，1]T，θv′u′＝K(Xv′，Xu)，K(Xv′，Xu′) Selecting a Gaussian radial kernel function, taking a as a vector parameter and xi as an adjustable parameter, and performing the optimization according to Mercer conditions
Figure BDA0002242660830000076
Wherein
Figure BDA0002242660830000077
(5) And obtaining the output of the least square support vector machine:
Figure BDA0002242660830000078
pbiasfor biasing, a Gaussian radial basis kernel function [ RFB ] is used]As a kernel function of the LSSVM, there are 2 parameters of penalty coefficient ξ and kernel function width σ that need to be determined. Research shows that the larger the penalty coefficient xi is, the larger the penalty on the empirical error is, and the smaller the regression error of the model is, but too large xi can lead to over-learning of the model, and too small xi can lead to under-learning. The kernel function width σ also affects the performance of the model. Therefore, the proper ξ and σ are the key to obtain a high-performance LSSVM model. And (3) optimizing 2 parameters of the LSSVM by using a flora algorithm (BFO) to obtain an optimized prediction model, and outputting a predicted grade value.
S7: and (3) optimizing 2 parameters of the LSSVM by using an improved flora algorithm to obtain an optimized prediction model, and outputting a predicted grade value.
The specific implementation steps are as follows:
s71: setting RMSE as the evaluation function:yuthe test value of the concentrate grade is obtained,
Figure BDA00022426608300000710
and n is the number of verification samples for predicting the concentrate grade estimated value output by the model.
S72: according to algorithm debugging experience, the initialization parameter S is 20, Nc＝20，Ns＝4，Nre＝4，Ned＝2，PedP is 0.1 and 2. S is bacterial size, NcTo trend times, NsNumber of plays, NreFor the number of breeding, NedTo number of migrations, PedP is a search dimension for the basic migration probability;
s73: tending to circulate:
1) the number of bacteria i ═ 1.., S;
2)Jlast＝J(i，j，k，l)，Jlastused for storing the best adaptive value in the bacterial iterative process;
3) trending behavior updates bacterial location θ:
Figure BDA0002242660830000081
j represents the number of trends, k represents the number of reproductions, l represents the number of migrations, thetai(j +1, k, l) represents the position after bacterial renewal;
wherein c (i) ═ c (i) · V, for step size updates;
definition of sensitivity:
defining an energy factor expression as:
Figure BDA0002242660830000083
c (i) is the bacteria movement step length;
Nj: representing the current times of the bacteria to perform tropism;
a denotes a unit vector in a random direction,
4) the ith bacterial fitness expression:
J(i，j+1，k，l)＝J(i，j，k，l)+Jcc(θi(j+1，k，l)，P(j+1，k，l)) (20)
Jcc(θithe (j +1, k, l), P (j +1, k, l)) aggregation behavior between bacteria can be calculated by the formula (9):
Figure BDA0002242660830000084
wherein d isattractantDepth of gravity, wattractantWidth of gravity, hrepellantHeight of repulsion, wrepellantIn order to be the width of the repulsive force,
Figure BDA0002242660830000085
is the m-dimensional component of bacterium i, θmD is set for the m-dimensional component of other bacteria in the whole floraattractant＝0.1，wattractant＝0.2，hrepellant＝0.1，wrepellant＝0.2；
P(j+1，k，l)＝{θi(j，k，l)，i＝1，2...，S} (22)
5) Swimming:
i) number of initial plays ms＝0，
ii) if ms≤Ns
Calculating J (i, J +1, k, l) ═ J (i, J, k, l) + Jcc(θi(j+1，k，l)，P(j+1，k，l))；
If J (i, J +1, k, l) > JlastExecution of JlastJ (i, J +1, k, l), otherwise JlastKeeping the same;
ms＝ms+1：
6) if i is less than S, i is i +1, returning to the step 2), and calculating the adaptation value of the next bacterium;
s74: and (3) replication circulation:
Figure BDA0002242660830000086
Figure BDA0002242660830000087
the health degree of the bacteria i is shown, and the total bacterial energy value J ishealthArranged in the order from small to large and before being eliminated
Figure BDA0002242660830000088
Individual bacteria, after replication of the bacteria
Figure BDA0002242660830000089
The number of bacteria is one, and the number of bacteria,
s75: if k is less than NreExecuting k ═ k +1, returning to S73;
s76: migration circulation:
after the flora is subjected to a plurality of generations of replication operations, each bacterium has a probability PedIs re-randomly distributed in the optimization space if l < NedExecuting l ═ l +1, returning to S73; if l > NedAnd ending the optimization and finding the optimal parameters ([ xi ], sigma).
S8: in practice, the accuracy of the prediction model cannot be guaranteed according to different ore entering grades in the flotation process, and in order to solve the problem, the conventional method can retrain when the prediction accuracy does not meet the requirement, so that the conventional method meets the prediction accuracy requirement under the current ore entering condition, undoubtedly, the model error compensation mechanism can be set to solve the defects that the model is frequently trained, the calculated amount is large and the like.
And (3) determining whether a confidence interval of the confidence level 1-alpha of the mu of the model error distribution conforms to a set interval range (0, eta), and starting a model error compensation mechanism, wherein the method specifically comprises the following steps:
s8: in practice, the accuracy of the prediction model cannot be guaranteed according to different ore entering grades in the flotation process, and in order to solve the problem, the conventional method can retrain when the prediction accuracy does not meet the requirement, so that the conventional method meets the prediction accuracy requirement under the current ore entering condition, undoubtedly, the model error compensation mechanism can be set to solve the defects that the model is frequently trained, the calculated amount is large and the like.
And (3) determining whether a confidence interval of the confidence level 1-alpha of the mu of the model error distribution conforms to a set interval range (0, eta), and starting a model error compensation mechanism, wherein the method specifically comprises the following steps:
(1): firstly, selecting D predicted model errors, determining whether a confidence interval of a mu confidence level 1-alpha of model error distribution accords with a set interval range (0, eta) by means of D epsilon (100,120), and determining whether eta epsilon (0.8, 1) meets the determination condition, wherein when the determination condition is not met, the system starts an error compensation mechanism to perform fuzzy compensation on the errors; according to the empirical condition, the distribution of model errors accords with Gaussian distribution, s is the standard deviation of D model errors, and the confidence interval of mu with the confidence level of 1-alpha isTaking alpha to be 0.05, namely ensuring that the confidence level of the average model error in the range of (0, eta) reaches 95 percent;
(2): the following compensation rules are set: when the confidence interval with the confidence level of 1-alpha is not satisfiedWhen the range of the set interval is met, the model error compensation value
Figure BDA0002242660830000093
S9: real-time data acquired by the froth image acquisition and processing system is input into the established prediction model, so that the online prediction of the concentrate grade in the flotation process is realized.

Claims (6)

1. A concentrate grade prediction method in a zinc flotation process based on feedback compensation mechanism optimization is characterized by comprising the following steps:
s1: collecting zinc fast coarse foam image characteristic data and corresponding concentrate grade data through a flotation process image collecting and processing system to form sample data;
s2: preprocessing the collected zinc fast coarse foam image characteristic data and corresponding concentrate grade data, and removing unreasonable data and missing data to obtain preprocessed sample data;
s3: performing correlation analysis on the characteristics by a kernel principal component analysis method, and taking the contribution ratio CRnFeatures > 85% as key foam features;
s4: combining the extracted key characteristics X and the corresponding concentrate grade data y into an (X, y) sample space, dividing 5 different concentrate grade intervals according to the concentrate grade y, and forming 5 sub-sample spaces (X) with the corresponding characteristic data1，y1)，(X2，y2)，(X3，y3)，(X4，y4)，(X5，y5)；
S5: respectively carrying out time division difference on the 5 sub-sample spaces to form a time difference sequence space (delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) And expressing the sequence number of the sub-sample space by K to form a time difference sequence space, which comprises the following steps:
Figure FDA0002242660820000011
to obtainRespectively forming a (delta X, delta y) time difference sequence space by using the zinc fast coarse foam image characteristic data and the first-order time difference component of the corresponding fine mineral bit data; where M represents the number of features, N represents the number of samples,
Figure FDA0002242660820000013
is the input column vector of dimension v of the K-th sub-sample space;
and then establishing a regression model between the input and output difference components:
Δy(t)＝f(ΔX(t)) (2)
when inputting a new set of samples X (t)new) The input time difference component is:
ΔX(tnew)＝X(tnew)-X(tnew-1) (3)
thus, y (t) is outputnew) Comprises the following steps:
y(tnew)＝Δy(tnew)+y(tnew-1) (4)
in the formula, X (t)new-1) is the previous sample input, y (t)new-1) is the previous output;
s6: 5 time difference sequence spaces (Delta X)1，Δy1)，(ΔX2，Δy2)，(ΔX3，Δy3)，(ΔX4，Δy4)，(ΔX5，Δy5) The data is used as training data to train the LSSVM together;
s7: optimizing two parameters of a penalty factor xi and a nuclear width sigma of the LSSVM by using an improved flora algorithm; obtaining an optimized prediction model and outputting a predicted grade value, wherein the specific steps are as follows:
s71: setting RMSE as the evaluation function:
Figure FDA0002242660820000014
yuthe test value of the concentrate grade is obtained,
Figure FDA0002242660820000015
the estimated value of the grade of the concentrate output by the prediction model is obtained, and n is the number of verification samples;
s72: initializing parameters S, Nc，Ns，Nre，Ned，PedP, S is bacterial size, NcTo trend times, NsNumber of plays, NreFor the number of breeding, NedTo number of migrations, PedP is a search dimension for the basic migration probability;
s73: tending to circulate:
1) the number of bacteria i ═ 1.., S;
2)Jlast＝J(i，j，k，l)，Jlastused for storing the best adaptive value in the bacterial iterative process;
3) trending behavior updates bacterial location θ:
Figure FDA0002242660820000016
j represents the number of trends, k represents the number of reproductions, l represents the number of migrations, thetai(j +1, k, l) denotes the position of the bacteria which tend to renew after they have taken place, [ theta ]i(j, k, l) represents a position before the trend occurs, and Δ represents one unit vector in a random direction;
wherein c (i) ═ c (i) · V, for step size updates;
the sensitivity V is defined as:
Figure FDA0002242660820000017
defining the energy factor β as:
Figure FDA0002242660820000021
c (i) is the bacteria movement step length; j (i, J-1, k, l) and J (i, J, k, l) are adaptive values before and after the trend occurs, respectively;
Nj: representing the current times of the bacteria to perform tropism;
4) the ith bacterial fitness expression:
J(i，j+1，k，l)＝J(i，j，k，l)+Jcc(θi(j+1，k，l)，P(j+1，k，l)) (8)
Jcc(θi(j +1, k, l), P (j +1, k, l)) represents the aggregation behavior between bacteria, calculated by the formula (9):
Figure FDA0002242660820000022
wherein d isattractantDepth of gravity, wattractantWidth of gravity, hrepellantHeight of repulsion, wrepellantIn order to be the width of the repulsive force,
Figure FDA0002242660820000023
is the m-dimensional component of bacterium i, θmThe m-dimension component of other bacteria in the whole flora;
P(j，k，l)＝{θi(j，k，l)，i＝1，2，…，S} (10)
5) swimming:
i) number of initial plays ms＝0，
ii) calculating J (i, J +1, k, l) ═ J (i, J, k, l) + Jcc(θi(j+1，k，l)，P(j+1，k，l))；
If J (i, J +1, k, l) > JlastExecution of JlastJ (i, J +1, k, l), otherwise JlastKeeping the same;
ms＝ms+1, if ms≤NsRepeating ii);
6) if i is less than S, i is i +1, returning to the step 2) to calculate the adaptation value of the next bacterium; if i is S, the next step is carried out;
s74: and (3) replication circulation:
Figure FDA0002242660820000025
the health degree of the bacteria i is shown, and the total bacterial energy value J ishealthArranged in the order from small to large and before being eliminated
Figure FDA0002242660820000026
Individual bacteria, after replication of the bacteria
Figure FDA0002242660820000027
The number of bacteria is one, and the number of bacteria,
s75: if k is less than NreExecuting k ═ k +1, returning to S73;
s76: migration circulation:
after the flora is subjected to a plurality of generations of replication operations, each bacterium has a probability PedIs re-randomly distributed in the optimization space if l < NedExecuting l ═ l +1, returning to S73; if l > NedIf yes, ending the optimization and finding the optimal parameters (xi, sigma);
s8: establishing a model error feedback compensation mechanism, determining whether a confidence interval of a confidence level 1-alpha of the mu of the model error distribution conforms to a set interval range (0, eta), starting the model error feedback compensation mechanism, wherein the mu is a model error distribution mean value,
Figure FDA00022426608200000211
is an unbiased estimate of μ, η is a critical value that μ cannot be exceeded by interval estimates at the 1- α confidence level;
s81: firstly, D predicted model errors are selected, whether a confidence interval of a mu confidence level 1-alpha of model error distribution meets a set interval range (0, eta) or not is judged, and when the judgment condition is not met, an error compensation mechanism is started by a system to carry out fuzzy compensation on the errors; according to the empirical condition, the distribution of model errors accords with Gaussian distribution, s is the standard deviation of D model errors, and the confidence interval of mu with the confidence level of 1-alpha is
Figure FDA0002242660820000029
Taking alpha to be 0.05, namely ensuring that the confidence level of the average model error in the range of (0, eta) reaches 95 percent;
s82: the following compensation rules are set: when the confidence interval with the confidence level of 1-alpha is not satisfied
Figure FDA00022426608200000210
When the range of the set interval is met, the model error compensation value
S9: real-time zinc fast coarse foam image characteristic data are collected by a foam image collecting and processing system and input into the established prediction model, the output of the concentrate grade is obtained through prediction, and the online prediction of the concentrate grade in the flotation process is realized.
2. The method of claim 1 for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization, wherein the method comprises the following steps: d e (100,120) in S81.
3. The method of claim 1 for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization, wherein the method comprises the following steps: eta e (0.8, 1) as described in S82.
4. The method of claim 1 for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization, wherein the method comprises the following steps: dividing the concentrate grade y into 5 different concentrate grade intervals, wherein the concentrate grade value is in y1∈[51.5，52.5]Identity low, y2∈(52.5，53.5]Low mark, y3∈(53.5，54.5]In the symbol, y4∈(54.5，55.5]Mark is higher, y5∈(55.5，56.5]The flag is high.
5. The method of claim 1 for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization, wherein the method comprises the following steps: in the initialization parameter of S72, S is 20, Nc＝20，Ns＝4，Nre＝4，Ned＝2，Ped＝0.1，p＝2。
6. The method of claim 1 for predicting concentrate grade in a zinc flotation process based on feedback compensation mechanism optimization, wherein the method comprises the following steps: in the S73, 4) the dattractant＝0.1，wattractant＝0.2，hrepellant＝0.1，wrepellant＝0.2。
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