CN108536979B - Underflow concentration prediction method based on thickener mechanism model - Google Patents

Underflow concentration prediction method based on thickener mechanism model Download PDF

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CN108536979B
CN108536979B CN201810347673.2A CN201810347673A CN108536979B CN 108536979 B CN108536979 B CN 108536979B CN 201810347673 A CN201810347673 A CN 201810347673A CN 108536979 B CN108536979 B CN 108536979B
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thickener
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mechanism model
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CN108536979A (en
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肖冬
江隆强
于志超
李康
刘新新
单丰
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Northeastern University China
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Abstract

The invention provides a underflow concentration prediction method based on a thickener mechanism model, which comprises the following steps: collecting field data of the thickener; converting the fluid pressure to a flow rate; and predicting the underflow concentration by using a parameter-identified hierarchical thickener mechanism model with parameters. The field data of the thickener comprises: top layer volume flow, feed flow, fluid pressure, and underflow volume density. After the fluid pressure is converted into the flow velocity, the abnormal value is processed by adopting a 3 sigma principle. The establishment of the thickener mechanism model with the layered parameters is as follows: collecting historical data of field data of the thickener; establishing a thickener mechanism model; converting the fluid pressure into flow rate and preprocessing data; and constructing a thickener mechanism model with hierarchical parameters. The method reduces the prediction error caused by a pure mechanism model and improves the prediction precision of the mechanism model.

Description

Underflow concentration prediction method based on thickener mechanism model
Technical Field
The invention belongs to the technical field of metallurgy, and particularly relates to a underflow concentration prediction method based on a thickener mechanism model.
Background
With the large-scale, centralized and continuous production of hydrometallurgy industry, high-efficiency and stable automatic production lines are urgently required. The automation level of the hydrometallurgical production process in China is low, and the automation technology greatly restricts the development of the hydrometallurgical industry in China. The underflow concentration of a certain concentrate thickener in Shandong is difficult to detect at present, and an operator draws ores by depending on production experience, so that the production of a downstream filter pressing process fluctuates sharply, and the moisture of a filter cake product is difficult to reach the standard. The tailing thickener is controlled by the experience of operators, so the randomness is high, if the optimization control can be well done, the pressure of a tailing pond can be reduced, and the production efficiency can be improved. Therefore, establishing a thickener mechanism model meeting the industrial field requirements is important for accurately predicting the concentration of the underflow.
The thickener has the advantages of small occupied area, low energy consumption, high efficiency and the like, is widely applied to the industries of wet metallurgy, coal, sewage treatment and the like at home and abroad, and is particularly commonly used in the concentrating mills in China. At present, the following problems mostly exist in the application process of a thickener in a concentrating mill in China: many key variables in the production process still cannot be detected on line; the production process of the thickener is still in a manual operation state, and most production personnel judge the production condition by virtue of own experience and feeling so as to operate; the working load of the thickener, the concentration of bottom flowing water, the turbidity of overflow water and other key links cannot be effectively controlled, so that the concentration and flow fluctuation of the thickener is large, the production index of the subsequent mineral separation process is seriously influenced, the medicament dosage of the subsequent flotation process is likely to be increased, the mineral separation cost is increased, and the improvement of the production efficiency of the thickener is seriously restricted. With the development of computers and automation technologies, it is urgently needed to introduce a computer control system into a full process to form full-process automatic control and resource sharing, so that the productivity is improved, and the enterprise competitiveness is improved.
In recent decades, the solid-liquid separation technology has been greatly developed, but the research on the mechanism model of the dense washing process is far from enough. The mechanism model of the dense washing process is helpful for describing and understanding the reaction mechanism of the sedimentation process, provides theoretical guidance for system design and equipment model selection, is helpful for researching the change of sludge yield, simulates the dynamic change of the sedimentation process, and can guide actual production. With the development of the solid-liquid separation technology, research on a mechanism model must be developed, so that the phenomenon and the law of solid-liquid separation are more deeply known. At present, no accurate dense washing process model capable of being applied to optimization control still exists, and model research of the dense washing process is still in an exploration stage.
Since 1905 j.v.n.dorr invented a continuously operating thickener, many scholars performed mathematical simulations of the thickening washing process. In many beneficiation processes, the production practice of thickeners seems to lead scientific research. The study of variables affecting settling performance was initiated in 1908 and was performed by Nichols. He studied the effect of solids and electrolyte concentration, degree of flocculation and temperature during the process. Then, the sedimentation theory was further studied by Ashley (1909), Forbes (1912), Mishler (1912 and 1918), Clark (1915), Coe Clevenger (1916), Free (1916) and the like.
From the dalberg thickener to the control device, only the design theory of the com Clevenger thickener, which is the only method based on the micro-equilibrium of solids and liquids in different settling zones in the thickener, does not have a true sedimentation theory at the time. The first one who really establishes the theory of sedimentation is the mathematician cauchy who published a famous paper "sedimentation theory" in 1952, which establishes the theory of dynamic sedimentation based on the diffusion of sedimentation waves in suspension. The continuous uniform sedimentation theory becomes the basic theory of thickener design, which assumes that the suspension is a continuous body, the concentration is uniform in any horizontal layer, and the shape, size and composition of the particles have no influence on the sedimentation process.
In recent years, some scholars have established a dynamic sedimentation theory based on the diffusion of sedimentation waves in a suspension, which "sedimentation theory" considers that a suspension is a continuum. And then more detailed consideration is added to the basic model, so that the sedimentation process can be further understood through simulation. Various scholars have expanded the "sedimentation theory" such as the introduction of "sedimentation theory" into continuous sedimentation processes, the limitation of sedimentation flux between layers, diffusion and compression, etc. The cauchy sedimentation theory can be described by the partial differential equation of equation (1),
Figure BDA0001632387040000021
wherein C is the pulp concentration in kg/m3And t is the settling time,
Figure BDA0001632387040000022
is the change of the pulp concentration C with time, and z is from the top of the thickenerHeight in m, CvhsIs the sedimentation flux, influenced only by gravity, vhsMore than or equal to 0 is the downward settling rate of the ore pulp, and the unit is m/s. Concentration C of ore slurry and sedimentation velocity v in equationsIs unknown, and solving this equation requires establishing the pulp concentration C and the settling rate vhsReconstructing a new mechanism model formula (2) according to the theory of B ü rger for the formula (1):
Figure BDA0001632387040000023
where F (C, z, t) is the flux function, γ (z) represents the area in which the height z lies, dcomIs the compression factor, ddisIs the coefficient of diffusion, and is,
Figure BDA0001632387040000024
the variation of the pulp concentration C with height, Qf(t) is the feed flow, Cf(t) is the feed concentration and A is the cross-sectional area of the thickener.
The establishment of the mechanism model starts from the ore pulp sedimentation principle in the dense washing process, fully considers the compression action and the diffusion action, and establishes the ore pulp concentration distribution mechanism model in the dense washing process according to the solid flux theory and the mass conservation theory. The authors have learned the steady-state and dynamic behavior of the heavy wash process by performing simulation on the established mechanism model. However, the method faces a difficult problem of difficult direct application, a real-time prediction result cannot be obtained on an industrial field, and meanwhile, because the mechanism model has a plurality of uncertain parameters, another problem exists in how to perform parameter identification on the mechanism model according to the actual process on the field.
Disclosure of Invention
The invention aims to provide an underflow concentration prediction method based on a thickener mechanism model, which comprises the following steps:
collecting field data of the thickener;
converting the fluid pressure to a flow rate;
and predicting the underflow concentration by using a parameter-identified hierarchical thickener mechanism model with parameters.
The field data of the thickener comprises: top layer volume flow, feed flow, fluid pressure, and underflow volume density.
Before the thickener mechanism model with the parameter identification hierarchical band parameters is utilized, abnormal values in the collected data are processed by adopting a 3 sigma principle.
The establishment of the thickener mechanism model with the layered parameters is as follows:
collecting historical data of field data of the thickener;
establishing a thickener mechanism model;
converting the fluid pressure into flow rate, and performing data preprocessing on historical data and the flow rate;
constructing a thickener mechanism model with layered parameters: the internal part of the thickener is subdivided into n layers, three critical layers are set between the layers, namely an overflow layer, a feed layer and a bottom flow layer, two more layers are respectively added corresponding to an overflow area and a bottom flow area, the top two layers simulate the overflow area, the bottom two layers simulate the bottom flow area, the top layer volume flow, the feed flow, the flow velocity and the bottom flow volume density are used as input variables, and the bottom flow concentration is used as an output variable, so that a hierarchical parameter-carrying thickener mechanism model is constructed.
The fluid pressure is converted into the flow rate, specifically, the fluid pressure is converted by using a Bernoulli equation of fluid mechanics, and pressure data measured by a field instrument is converted into the flow rate suitable for a mechanism model of the thickener.
The data preprocessing is to process abnormal values by adopting a 3 sigma principle.
The mechanism model of the thickener with the layered parameters comprises the following specific steps:
Figure BDA0001632387040000031
wherein A is the cross-sectional area of the thickener, H is the height of the clarification zone, B is the depth of the sedimentation zone, ([ delta ] z ═ B + H)/n is the height of each layer, Q iseIs the top layer volume flow, QfFor feed flow, QuThe volume density of the underflow is,
Figure BDA0001632387040000032
is the compression factor comprising pulp concentration and density, GiContaining the sedimentation velocity, gamma, as a function of the density of the fluid1,γ2,γ3,γ4,γ5Are parameters to be determined.
The parameter identification adopts a recursive least square method.
Has the advantages that:
the predictability of the mechanical model in the prior art is verified through field measured data, but a large deviation still exists between a predicted value and an actual value. According to the method, the parameters of the mechanism model of the thickener are identified by a least square method (RLS), and the predicted output of the mechanism model of the thickener after comparison and identification is close to the actual value, so that the prediction error caused by a pure mechanism model is reduced, and the prediction precision of the mechanism model is improved.
Drawings
FIG. 1 is a schematic view of the spatial distribution of the internal operation of a thickener in accordance with an embodiment of the present invention;
FIG. 2 is a layered structure diagram in accordance with an embodiment of the present invention;
FIG. 3 is a flowchart of a Recursive Least Squares (RLS) procedure in accordance with an embodiment of the present invention;
FIGS. 4(a) - (i) are dynamic changes over time of the internal concentration profile of the thickener in an embodiment of the present invention;
FIG. 5 is a plot of underflow concentration versus time in an embodiment of the present invention;
FIG. 6 is a model prediction error of a mechanism in an embodiment of the present invention;
FIG. 7 is a comparison of the error between the predicted output and the actual value of the mechanism model in an embodiment of the present invention;
FIG. 8 is a model of a parameter identification mechanism in accordance with an embodiment of the present invention;
FIG. 9 shows the result of the RSL parameter identification procedure in accordance with one embodiment of the present invention;
FIG. 10 is an underflow concentration prediction error in an embodiment of the present invention;
fig. 11(a) to (b) are comparisons between the output value of the unoptimized mechanism model and the output value of the optimized mechanism model and the actual value, respectively, in the embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
The method adopts the steps of establishing a layering mechanism model of the thickener in the thickening washing process, simplifying the complex mechanism model of the thickener, and identifying the model parameters by using a recursive least square method, namely RLS (recursive least square) for online real-time estimation. Based on the limitation of field equipment, the required variables cannot be acquired through a detection device, model input variables need to be converted into variables of a mechanism model by introducing a Bernoulli principle, and finally, model parameters are identified by adopting an RLS algorithm. The RLS algorithm is simple in principle, convenient to use, good in accuracy and good in estimation performance, and is a correct and effective parameter estimation method which is proved by simulation and has the characteristics of small calculated amount, high identification speed, high modeling efficiency and the like. The modeling precision requirement of the thickener mechanism model is high, the data volume is large, and the RLS is suitable for identifying the thickener mechanism model parameters and provides a good method.
The embodiment provides a underflow concentration prediction method based on a thickener mechanism model, which specifically comprises the following steps:
the first step is as follows: gather concentrator field data, include: top layer volume flow, feed flow, fluid pressure, underflow volume density;
the second step is that: converting the fluid pressure to a flow rate;
before a parameter-identified hierarchical parameter-carrying thickener mechanism model is utilized, abnormal values in the acquired data are processed by adopting a 3 sigma principle, wherein the abnormal values comprise top layer volume flow, feeding flow, flow velocity and underflow volume density.
The third step: and predicting the underflow concentration by using a parameter-identified hierarchical thickener mechanism model with parameters. And inputting the collected field data of the thickener into a thickener mechanism model with parameters in layers identified by the parameters to obtain a predicted value of the underflow density.
The establishment process of the thickener mechanism model with the layered parameters is as follows:
step1, collecting historical data of field data of the thickener, and adopting five groups of data according to a field detection instrument, wherein the five groups of data are top layer volume flow, feeding flow, fluid pressure, underflow volume density and underflow concentration.
Part of the data is shown in table 1 below:
TABLE 1 data acquisition Table
Figure BDA0001632387040000051
Figure BDA0001632387040000061
The data in table 1 are five groups, wherein four groups of data of top layer volume flow, feeding flow, fluid pressure and underflow volume density are collected from instruments and meters (flow meters, pressure meters and the like) of a concentrate thickener detection device in Shandong, while underflow concentration data cannot be directly collected and are manually sampled through a field concentration arc device.
And 2, establishing a thickener mechanism model and carrying out simulation analysis.
The thickening process is based on gravity settling, and it is obvious that the pulp consistency must be a quantity depending on the settling time and the space height, so the pulp consistency can be expressed as C (z, t), where the z-axis is downward in the positive direction and t represents time, as shown in figure 1. Rationalized assumptions were made: assuming that the sedimentation process is one-dimensional, the one-dimensional sedimentation model can capture the basic characteristics of the process well because the gravity sedimentation and the compression effect are one-dimensional in nature. The mass conservation relationship of the settling process can be described by the partial differential equation of equation (3):
Figure BDA0001632387040000062
wherein v issAnd the more than or equal to 0 is the downward settling rate of the ore pulp, z is the height from the top of the thickener, and t is time. The equation comprises two unknown ore pulp concentration C and sedimentation rate vsTherefore, solving this equation requires establishing the pulp concentration C and the settling rate vsConstitutive relation between them. The following assumptions were made for the mechanism model:
1. hindered settling velocity vs(C) Is a function which is dependent only on the local concentration in the vicinity of the particle, usually using the formula of Tak-cs and the formula proposed by Vesilind et al;
Figure BDA0001632387040000063
vhs(C)＝v0e-nc (5)
2. in the high concentration zone, the slurry may be compressed by its own weight. More specifically, when the pulp concentration is greater than a critical concentration CcDuring this process, the particles continuously agglomerate and form a solid body which can withstand a certain pressure (effective solid stress σ)e) The network of (2). Stress σ of solideAt a concentration greater than CcIs assumed to be an increasing function, less than CcTime is 0, function σeSatisfies the following formula (6)
Figure BDA0001632387040000064
A semi-empirical formula proposed by De Clercq et al is typically employed,
Figure BDA0001632387040000071
wherein α >0, β > 0;
3. in any horizontal layer of the suspension high-concentration area, the suspension concentration is uniform, and the settling rate of all solid particles is the same;
4. the composition of the solid particles has no influence on the sedimentation process;
5. the initial concentration is uniform throughout the settling zone of the thickener, with the concentration gradually increasing with increasing depth.
According to the theory of continuous medium mechanics derivation by Burger et al, assuming that the rate of downward settling is as shown below,
Figure BDA0001632387040000072
where ρ issIs the solid density, g is the acceleration of gravity, Δ ρ ═ ρs-ρfIs the difference in density between a solid and a liquid. CcIs a critical concentration above which the solid particles begin to collide with each other and the solid pressure begins to be transmitted, creating a compression phenomenon. As seen in the formula, when the concentration increases with depth more than CcThe settling rate decreases due to the compression effect. The compression effect is the same as the solution for non-linear diffusion. Substituting formula (8) for formula (3) to obtain a degenerate parabolic partial differential equation with formula (9) having only one unknown variable C
Figure BDA0001632387040000073
Wherein the compression factor is expressed as
Figure BDA0001632387040000074
There is a diffusion phenomenon between the high-consistency pulp and the low-consistency pulp, especially near the feed layer, the fluid diffusion phenomenon making the longitudinal consistency change smoother, by Fick's proposed analysis of the constitutive relation of the diffusion phenomenon, assuming that the corresponding flux is equal to
Figure BDA0001632387040000075
Wherein the diffusion coefficient ddispIs more than or equal to 0. Diffusion coefficient ddispIs a quantity related to the height z, and the ore pulp can not return after flowing out of the overflow port of the thickener, so the diffusion phenomenon does not need to be considered outside the height range of the thickener, and the concentration of the ore pulp can be controlled by the quantity related to the height zThe diffusion coefficient is required to satisfy the formula (11).
Figure BDA0001632387040000081
Diffusion coefficient ddispGenerally related to the flow rate and height of the liquid. Thus, select ddispThe following formula is shown in the specification,
Figure BDA0001632387040000082
wherein alpha is1And alpha2Are all positive parameters, α1Related to the cross-sectional area of the thickener; alpha is alpha2QfThe width of the region in which the diffusion phenomenon occurs is determined, and the region must not exceed the range of the formula (11), so that the parameter α must be limited2，
Figure BDA0001632387040000083
From the above analysis it can be seen that the compressibility and diffusivity are independent of each other and d can be set for different materials and different settling process requirementsdispEither [ identical to ] 0 or dcompIs equal to 0. In the present embodiment, both the compression phenomenon and the diffusion phenomenon are explicitly taken into consideration.
Given that the various unknowns have been determined, a more specific equation of conservation of mass can be derived that describes the process. At an arbitrary interval (z) per unit time1,z2) Mass increase equal to z1High inflow rate
Figure BDA0001632387040000084
Minus z2High outflow rate
Figure BDA0001632387040000085
The expression, plus the flow rate generated in the interval, is shown in equation (14).
Figure BDA0001632387040000086
Wherein Q isfIs the feed flow rate; a is the cross-sectional area of the thickener; cfIs the feed concentration; δ (z) is a δ function, δ (z) being 1 only at the feed layer and other heights δ (z) being 0; the flow rate phi is expressed as
Figure BDA0001632387040000087
Wherein
Figure BDA0001632387040000088
Figure BDA0001632387040000091
One key factor of the sedimentation model is the sedimentation velocity function vhsThe common sedimentation velocity models are mainly a Tak-cs model and a Vesilind model. Regarding various sedimentation states as a uniform sedimentation process, when the concentration of the ore pulp is very low, the sedimentation process depends on the properties of particles and the concentration of the ore pulp, and therefore, the velocity model of the low-concentration sedimentation process is obtained as follows:
vL＝k0drexp(-n0C) (18)
wherein d is the particle diameter, r, n0And k0Is the parameter to be determined and C is the concentration of the pulp. When the concentration of the ore pulp is higher, the settling velocity depends on the concentration of the ore pulp, and then a Vesilind model is selected as the interference settling and pressure settling velocity model, but the parameters of the models are different. The interference sedimentation and pressure sedimentation velocity models are respectively shown as a formula (19) and a formula (20).
vG＝k1exp(-n1C) (19)
vY＝k2exp(-n2C) (20)
Wherein n is1、n2、k1、k2Is the parameter to be determined and C is the pulp concentration.
Fig. 2 shows four regions into which the thickener is divided according to the embodiment of the present invention, namely, an overflow region, a clarification region, a sedimentation region, and a underflow region, the inside of the thickener is subdivided into n layers, and three critical layers are set between the layers, namely, an overflow layer, a feed layer, and an underflow layer. The height of each layer is then (B + H)/n. N. the height of the boundary line of each layer is z ═ i Δ z-H, i ═ 0, and the overflow layer z0And underflow layer znFalling on the boundary, overflow layer z0-H, underflow layer znB, setting the feed inlet z as 0 (z)m-1,zm]In the interval, the corresponding mth layer is a feed material layer. In the simulation scheme, two more layers are added at the top and the bottom of the equation corresponding to the overflow area and the underflow area respectively, the overflow area is simulated by the two layers at the top, the underflow area is simulated by the two layers at the bottom, and the overflow turbidity CeTaking the concentration of the 0 th layer and the underflow concentration CnIs the n +1 layer concentration. Thus, the calculation region is composed of n +4 intervals of length Δ z.
For each layer, equation (14) can be rewritten as a precise version of the mass conservation equation as follows:
Figure BDA0001632387040000092
can be simplified into
Figure BDA0001632387040000101
Figure BDA0001632387040000102
Figure BDA0001632387040000103
Wherein the content of the first and second substances,
Figure BDA0001632387040000104
is the compression factor.
Since each term of equation (21) does not exist in every layer, the layers establish a more detailed differential equation:
in the subsidence zone, the i-2., m-1 layers:
Figure BDA0001632387040000105
m, feed layer:
Figure BDA0001632387040000106
for the underflow layer:
Figure BDA0001632387040000107
wherein, CfIs the feed concentration; n is the number of layers of the laminate; z is the height of the thickener; z is a radical offIs the feed height; v. ofsIs the sedimentation velocity; c is the concentration of the ore pulp; giAs shown in equation (25).
Figure BDA0001632387040000108
The thickener mechanism model can be summarized as follows:
Figure BDA0001632387040000111
wherein A is the cross-sectional area of the thickener, Deltaz is the height of each layer, H is the height of the clarification zone, B is the depth of the sedimentation zone, n is the number of layered layers, and QeIs the top layer volume flow, QfFor feed flow, QuIs the volume density of the underflow,
Figure BDA0001632387040000112
including pulp concentration anddensity, GiInclusion of sedimentation velocity for fluid density function (distinguished by subscript because of the layering concept used) Gm,Gn,GiG expressions at the mth layer, the n layer, and the i layer, respectively; cfIs the feed concentration, Cm,Cn,Ci,Ci+1Respectively showing the ore pulp concentration of the mth layer, the n layer, the i layer and the i +1 layer,
Figure BDA0001632387040000113
Figure BDA0001632387040000114
the compression coefficients of the ith layer, the m +1 layer, the n layer and the n +1 layer are respectively; ddisp,i、ddisp,m、ddisp,m-1The diffusion coefficients of the i-th layer, the m-th layer and the m-1 layer are respectively.
For the next simulation analysis, the parameters of the mechanical model of the thickener are given, and are shown in table 2.
TABLE 2 thickener mechanism model parameters
Figure BDA0001632387040000115
Figure BDA0001632387040000121
The established mechanism model is subjected to analog simulation, and the accuracy of the mechanism model can be checked:
(1) dynamic simulation
In a thickener, the underflow concentration as well as the pulp concentration profile are mainly studied, and simulation studies will be performed in both aspects.
Fig. 4(a) to (i) are dynamic changes of the internal concentration distribution of the thickener with different times, which are respectively the change curves of the pulp concentration with the depth when the time t is 0.1h, 0.2h, 0.3h, 0.4h, 0.5h, 1h, 5h, 10h and 100 h. In order to verify the reliability of the established mechanism model of the thickener, the embodiment of the invention divides the thickener into 20 layers and simulates the initial concentration valueIs 0kg/m3The top layer volume flow rate is 250kg/m3The feed flow is 300m3H, liquid flow rate of 9.4m/s, and underflow bulk density of 180kg/m3. The horizontal axis is the internal depth of the thickener, the vertical axis is the pulp concentration, the simulated time periods are dynamic changes of the internal concentration of the thickener, wherein t is 0.1h, 0.2h, 0.3h, 0.4h, 0.5h, 1h, 5h, 10h and 100h, and the concentration distribution is basically unchanged after the simulation time reaches 10h, so that the settling process reaches a stable state.
FIG. 5 is a simulation of the results of a thickener underflow concentration simulation over time in accordance with an embodiment of the present invention. The abscissa is the time of the thickening process, and the ordinate represents the change condition of the underflow concentration, so that the underflow concentration can be visually seen to be continuously increased along with the change of the time, the change of the underflow concentration tends to be stable about 12 hours, and the actual condition of an industrial field is met.
(2) The mechanism model of the unoptimized system parameters predicts the output simulation result as follows:
fig. 6 is a diagram illustrating a comparison of prediction errors of the established mechanism model according to the embodiment of the present invention, in which the abscissa represents the number of selected test sample points, and the ordinate represents an error between an actual value and a predicted value, and it can be seen from a simulation result that a large error still exists between the predicted value and the actual value of the mechanism model that is not optimized, so that further correction is required to make the predicted value and the actual value of the mechanism model closer.
Fig. 7 is a comparison between a predicted output and an actual value of an established mechanism model according to the embodiment of the present invention, in which an abscissa represents the number of selected test sample points, an ordinate represents underflow concentration, and two curves are an actual measured value and a predicted value of the mechanism model in an industrial field, respectively.
Step3, converting the fluid pressure into flow rate, and performing data preprocessing on historical data and the flow rate;
applying the bernoulli principle to a mechanistic model: the bernoulli principle is one of the fundamental laws of fluid mechanics, and its essence is the conservation of mechanical energy of a fluid. Bernoulli's principle is often expressed as
Figure BDA0001632387040000131
This equation is called bernoulli's equation. Where p is the pressure at a point in the fluid, v is the flow velocity at the point, ρ is the fluid density, g is the gravitational acceleration, h is the height at the point, and C is a constant. The derivation process is as follows: the use of bernoulli's principle must meet the following assumptions before it can be applied; the solution is also an approximation if the following assumptions are not fully met.
(1) In a flow system, the properties of the fluid at any point do not change over time.
(2) Density is constant and is suitable for mach numbers (Ma) <0.3 when the fluid is a gas.
(3) The rubbing effect is negligible and the viscosity effect is neglected.
(4) The fluid elements flow along streamlines that do not intersect one another.
Energy of fluid due to stress:
Figure BDA0001632387040000132
energy lost by fluid due to gravitational work:
Figure BDA0001632387040000133
the kinetic energy obtained by the fluid can be rewritten as:
Figure BDA0001632387040000134
according to the law of conservation of energy, the energy obtained by the fluid due to stress and the energy lost by the fluid due to the work done by gravity are equal to the kinetic energy obtained by the fluid:
A1v1＝A2v2＝c (29)
after finishing, the following can be obtained:
Figure BDA0001632387040000135
the gravitational potential energy of the fluid at the same level can be offset, so the simplification continues to be:
Figure BDA0001632387040000141
note: p is the pressure of a certain point in the fluid, v is the flow velocity of the fluid at the point, ρ is the density of the fluid, g is the gravitational acceleration, h is the height of the point, A is the cross-sectional area, m is the mass of the fluid, Δ t is any time period, and C is a constant.
Based on the limitation of field conditions, the flow velocity of the fluid cannot be measured by an instrument, so that the Bernoulli equation of fluid mechanics is introduced for conversion, pressure data measured by a field instrument is converted into the flow velocity suitable for a mechanism model, and great convenience is brought to subsequent data processing. Meanwhile, the gravitational potential energy of the fluid on the same level is neglected, so that the conversion formula of the flow velocity and the pressure of the fluid is as follows:
Figure BDA0001632387040000142
the converted partial data are shown in table 3:
table 3 numerical conversion table
Figure BDA0001632387040000143
And (3) preprocessing data, namely processing abnormal values of top layer volume flow, feed flow, underflow volume density and flow velocity in the acquired historical data by adopting a 3 sigma principle:
in actual measurement data, data used for experiments are measured by a detection device installed on site, and the measurement data inevitably contain errors due to the influence of instrument precision, environmental factors and the like. Errors are classified into significant errors and random errors. If the unprocessed field data is directly used for a mechanism model, a correct predicted value cannot be obtained necessarily, and further field operation is misled, so that the normal operation of the production process is influenced. Therefore, after modeling the mechanism model, it is necessary to perform necessary error screening and data preprocessing on the measurement data for modeling. Often, individual measurement data are significantly outside the general range of measurement data, i.e., measurement values deviate too far from the average of the remaining measurement values, such data are often referred to as outliers. Outliers can typically be handled using the 3 sigma principle.
In general, for a sample set x1,x2,x3,x4If only random errors exist in the samples, counting the normal distribution rule of the random errors, and regarding the data with the deviation absolute value larger than 3 sigma as abnormal data to be removed. The specific implementation method comprises the following steps:
for the measured data [ x ]1,x2,...,xn]First, the average value is calculated according to equation (33), and then the estimated value of the standard deviation is calculated according to equation (34).
Figure BDA0001632387040000151
Figure BDA0001632387040000152
Suppose for an arbitrary data point xdIf it satisfies
Figure BDA0001632387040000153
Then according to the 3 σ principle, the data is treated as an outlier and x should be considered asdAnd (5) removing the measurement data. Then x is putdAfter elimination, the sigma value of the retained data is recalculated, abnormal value detection is carried out again, and iteration operation is repeated until all the data are removedAll abnormal values are eliminated.
Table 4 input data handling table
Figure BDA0001632387040000154
Figure BDA0001632387040000161
In the embodiment, data preprocessing is performed on top layer volume flow, feeding flow and underflow volume density and flow speed in collected historical data, partial data after data preprocessing are shown in table 4, and the processed field data are used for a mechanism model to obtain accurate predicted values, so that field operation can be guided, and normal operation of a production process is facilitated.
Step4, constructing a thickener mechanism model with layered parameters;
due to Qe、Qf、QuAnd v is an inseparable part of the mechanism model, and in order to improve the prediction precision of the mechanism model, a parameter identification model between input and output is adopted by combining data acquired on site to construct a thickener mechanism model with parameters. The RLS optimization thickener mechanism model is shown in FIG. 8:
FIG. 8 is a model of a parameter identification mechanism according to an embodiment of the present invention, wherein Qe、Qf、QuV is the original data of the input mechanism model, the original data is input into the mechanism model after data preprocessing, undetermined parameters of the mechanism model are identified through an RLS algorithm,
Figure BDA0001632387040000162
for the predicted output of the mechanism model,
Figure BDA0001632387040000163
and outputting the prediction after the mechanism model parameters are identified by the recursive least square method.
The following are constructed thickener mechanism models with parameters:
Figure BDA0001632387040000164
wherein A is the cross-sectional area of the thickener, H is the height of the clarification zone, B is the depth of the sedimentation zone, ([ delta ] z ═ B + H)/n is the height of each layer, Q iseIs the top layer volume flow, QfFor feed flow, QuThe volume density of the underflow is,
Figure BDA0001632387040000165
is the compression factor comprising pulp concentration and density, GiContaining the sedimentation velocity, gamma, as a function of the density of the fluid1,γ2,γ3,γ4,γ5Are parameters to be determined.
The fifth step: recursive Least Squares (RLS) parameter identification
The identification of the mechanism model parameters adopts a recursive least square method (RLS), which is an identification method capable of carrying out online real-time estimation on the model parameters. In order to reduce the amount of calculation, reduce the amount of memory occupied by data in a computer and to make it possible to identify the characteristics of a dynamic system in real time, when the least square method is used for parameter identification, it is converted into an economic and effective parameter recurrence identification, also called sequential estimation. The recursive least square parameter identification means that when the identified system is in operation, after new observation data is obtained every time, the result of the previous estimation is corrected by using the newly introduced observation data on the basis of the result of the previous estimation according to a recursive algorithm, so that a new parameter estimation value is recursively obtained. Thus, with the successive introduction of new observation data, parameter estimation is performed one after another until the parameter estimation value reaches a satisfactory degree of accuracy. The basic idea of the least squares recursion algorithm can be summarized as follows: new estimated value
Figure BDA0001632387040000171
Figure BDA0001632387040000172
The batch least squares method is rewritten to the recursive form, i.e., the computational method of recursive least squares parameter estimation, below.
Batch least squares estimation
Figure BDA0001632387040000173
Is composed of
Figure BDA0001632387040000174
Let the batch least squares estimate at time k be:
Figure BDA0001632387040000175
order to
Figure BDA0001632387040000176
The least squares estimate for time K can be expressed as
Figure BDA0001632387040000177
In the formula
Figure BDA0001632387040000178
Because the recursion equations for P (k) and K (k) are derived, the following matrix inversion theorem is introduced here: let A, (A + BC) and (I + CA)-1B) Are all nonsingular square matrix, then (A + BC)-1＝A-1-A-1B(I+CA-1B)- 1CA-1By applying matrix inversion lemma, complex matrix inversion is converted into scalar inversion, and the calculated amount is greatly reduced. The recursive least square parameter recursive estimation formula is finally obtained as follows:
Figure BDA0001632387040000179
Figure BDA00016323870400001710
Figure BDA00016323870400001711
recursive Least Squares (RLS) procedure flow chart (as shown in fig. 3):
FIG. 3 is a flowchart of a Recursive Least Squares (RLS) procedure in accordance with an embodiment of the present invention, wherein a first step is to perform an initialization operation to set an initial value; then, data preprocessing is carried out on input and output data, and if the unprocessed field data are directly used for a mechanism model, correct predicted values cannot be obtained; then calculating K (k) in the k step by a formula,
Figure BDA00016323870400001712
And P (k) a recurrence equation; and (5) after the k step is completed, turning to the (k + 1) step, continuing to circulate until the set step length stops calculating, and ending the process.
The Recursive Least Squares (RLS) procedure is as follows:
step 1: initialization: setting an initial value
Figure BDA0001632387040000181
And P (0), inputting initial data;
step 2: sampling the current output y (k), and the input u (k);
step 3: calculating K (k) by using the above formulas (38), (39), (40),
Figure BDA0001632387040000182
And P (k);
step 4: k → k +1, return to step2 and continue the loop.
Firstly, carrying out data preprocessing on 190 groups of data actually measured on site, then randomly taking out 50 groups of data from the processed data to carry out parameter identification training of a mechanism model, and carrying out error correction on the rest data after obtaining identification parameters of the mechanism modelThe error is between +/-1-5% according to experimental analysis, and the actual error requirement is met. FIG. 9 is a running chart of the RLS parameter identification procedure, in which the present invention is implemented by randomly selecting 40 sets of input/output data for verification, wherein the abscissa is the set step size and the ordinate is the identified parameter, and the parameter γ is seen from the above parameter estimation step-by-step variation trace image1,γ2,γ3,γ4,γ5The recursion estimation curve has unobvious change, the curve is relatively smooth, and the model parameter gamma1,γ2,γ3,γ4,γ5The recursive least squares estimation of (c) is substantially satisfactory within the error tolerance.
The identified mechanism model parameters are as follows:
TABLE 5 RLS parameter identification results
Parameter(s) γ1 γ2 γ3 γ4 γ5
The result of the recognition 0.2327 0.0293 0.2585 0.7427 0.5155
And bringing in the identified parameters to obtain a mechanism model identified by the RLS algorithm, wherein the mechanism model is as follows:
Figure BDA0001632387040000183
wherein A is the cross-sectional area of the thickener, H is the height of the clarification zone, B is the depth of the sedimentation zone, ([ delta ] z ═ B + H)/n is the height of each layer, Q iseIs the top layer volume flow, QfFor feed flow, QuThe volume density of the underflow is,
Figure BDA0001632387040000184
is the compression factor comprising pulp concentration and density, GiThe sedimentation velocity is included as a function of the fluid density.
Measured input variable Q on sitee,Qf,Qu,QvAnd (4) performing prediction output of a thickener mechanism model, wherein the following two tables are used for comparing a predicted value of the underflow concentration before and after identification with an actual value.
TABLE 6 comparison of underflow concentration prediction output of mechanism model with actual value
Figure BDA0001632387040000191
TABLE 7 comparison of underflow concentration prediction output of mechanism model after RLS parameter identification with actual value
Figure BDA0001632387040000192
And (4) analyzing results: randomly selecting 50 groups of data from 190 groups of data measured on site to perform recursive least square method (RLS) identification on the parameters of the thickener mechanism model, and outputting data Qe,Qf,QuV, y defines the parameter γ to be identified of the mechanism model1,γ2,γ3,γ4,γ5Then subject parameters are performedInitializing, setting a step length range of 1-10, and then calculating K (k),
Figure BDA0001632387040000193
And p (k) performing parameter estimation one after the other until the parameter estimation value reaches a satisfactory degree of accuracy. The post-identification model parameters are shown in Table 5, and the resulting γ1,γ2,γ3,γ4,γ5The parameter values achieve a satisfactory accuracy. As can be seen from table 6, the difference between the underflow concentration prediction of the thickener performed on the pure mechanism model and the actual value is large, the error reaches 67.5 to the maximum, the error rate reaches 10.1%, and it can be seen that the prediction output of the pure mechanism model does not achieve satisfactory effect, does not meet the measurement requirement of the actual field, and needs to be optimized and improved. In view of the fact that the prediction output under the pure mechanical model does not meet the industrial requirements, the mechanical model parameters are optimized, as can be seen from table 7, the recursive least square method is used for identifying the mechanical model parameters of the thickener to obtain good effect, the prediction output of the underflow concentration is approximate to the actual value, the maximum error is only about 5%, and the requirements of the field industry are met.
Fig. 10 shows the result of error prediction by randomly selecting 50 sets of input and output data according to the embodiment of the present invention, where the abscissa represents the selected test sample point, and the ordinate represents the error between the actual value and the predicted value, and the error between the predicted value and the actual value of the mechanism model identified by the RLS parameters is significantly reduced, so that the prediction accuracy of the mechanism model is significantly improved, and a good method is provided for prediction of data suitable for industrial fields.
Fig. 11(a) - (b) show that 50 sets of input and output data are randomly selected to perform underflow concentration prediction effect comparison in the embodiment of the present invention, the abscissa represents the selected test sample point, the ordinate represents the underflow concentration, the abscissa of the two curves represents the actual measured value and the predicted value of the mechanism model in the industrial field, respectively, and it can be known through comparison that the mechanism model output identified by the RLS parameter has a better prediction effect on the process trend than the non-optimized mechanism model parameter, the deviation between the predicted value and the actual value is significantly reduced, and the prediction accuracy can be applied to prediction of the underflow concentration data of the thickener in the industrial field.
Finally, through comparison and analysis of the pure mechanism model and the RLS-based identification mechanism model parameters, the RLS parameter identification method can be reasonably applied to the thickener mechanism model, the mechanism model is optimized to a certain degree, and through simulation results, the RLS identification thickener mechanism model parameters have a better prediction effect on the trend of the thickening process, and meanwhile, the prediction precision of the underflow concentration is improved, and the provided method is proved to be effective.

Claims (2)

1. The underflow concentration prediction method based on the thickener mechanism model is characterized by comprising the following steps of:
collecting field data of the thickener; the field data of the thickener comprises: top layer volume flow, feed flow, fluid pressure and underflow volume density;
converting the fluid pressure to a flow rate;
processing abnormal values in the acquired data by adopting a 3 sigma principle, and then predicting the underflow concentration by utilizing a parameter-identified hierarchical thickener mechanism model with parameters; the parameter identification adopts a recursive least square method;
the establishment of the thickener mechanism model with the layered parameters is as follows:
collecting historical data of field data of the thickener;
establishing a thickener mechanism model;
converting the fluid pressure into flow rate, and performing data preprocessing on historical data and the flow rate;
constructing a thickener mechanism model with layered parameters: the method comprises the following steps of subdividing the inside of a thickener into n layers, setting three critical layers among the layers, namely an overflow layer, a feed layer and a bottom flow layer, adding two more layers corresponding to an overflow area and a bottom flow area, simulating the overflow area at the top and the bottom flow area at the bottom, and constructing a thickener mechanism model with parameters in layers by taking the top layer volume flow, the feed flow, the flow speed and the bottom flow volume density as input variables and the bottom flow concentration as output variables;
the method comprises the following specific steps:
Figure FDA0003034797260000011
wherein, A is the cross-sectional area of the thickener, H is the height of the clarification zone, B is the depth of the sedimentation zone, Δ z ═ B + H)/n is the height of each layer, and n is the number of layered layers; qeIs the top layer volume flow, QfFor feed flow, QuUnderflow bulk density, gamma1,γ2,γ3,γ4,γ5Is a parameter to be determined; cm,Cn,Ci,Ci+1Respectively showing the ore pulp concentration of the mth layer, the n layer, the i layer and the i +1 layer, CfIs the feed concentration, ddisp,i、ddisp,m、ddisp,m-1The diffusion coefficients of the i-th layer, the m-th layer and the m-1 layer, GiIncluding settling velocity, G, as a function of fluid densitym,Gn,GiRespectively representing the G expressions at the m-th layer, the n-th layer and the i-th layer,
Figure FDA0003034797260000012
for compressibility to include pulp concentration and density,
Figure FDA0003034797260000013
respectively represents the compression coefficients of the ith layer, the m +1 layer, the n +1 layer and the n layer;
the fluid pressure is converted into the flow rate, specifically, the fluid pressure is converted by using a Bernoulli equation of fluid mechanics, and pressure data measured by a field instrument is converted into the flow rate suitable for a mechanism model of the thickener.
2. The method of claim 1, wherein the data preprocessing is to process outliers using 3 σ principle.
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