CN112734166A - Robust coordination and significant error detection method for copper industry data - Google Patents
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- 238000001514 detection method Methods 0.000 title claims abstract description 30
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 title claims abstract description 16
- 229910052802 copper Inorganic materials 0.000 title claims abstract description 16
- 239000010949 copper Substances 0.000 title claims abstract description 16
- 238000000034 method Methods 0.000 claims abstract description 68
- 239000000463 material Substances 0.000 claims abstract description 52
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 25
- 238000011084 recovery Methods 0.000 claims abstract description 25
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- 238000005457 optimization Methods 0.000 claims abstract description 17
- 238000004364 calculation method Methods 0.000 claims abstract description 10
- 238000006243 chemical reaction Methods 0.000 claims abstract description 10
- 238000003723 Smelting Methods 0.000 claims abstract description 6
- 230000008569 process Effects 0.000 claims description 22
- 239000002184 metal Substances 0.000 claims description 19
- 229910052751 metal Inorganic materials 0.000 claims description 19
- 230000008878 coupling Effects 0.000 claims description 8
- 238000010168 coupling process Methods 0.000 claims description 8
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- BQCADISMDOOEFD-UHFFFAOYSA-N Silver Chemical compound [Ag] BQCADISMDOOEFD-UHFFFAOYSA-N 0.000 abstract description 2
- NINIDFKCEFEMDL-UHFFFAOYSA-N Sulfur Chemical compound [S] NINIDFKCEFEMDL-UHFFFAOYSA-N 0.000 abstract description 2
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 abstract description 2
- 229910052737 gold Inorganic materials 0.000 abstract description 2
- 239000010931 gold Substances 0.000 abstract description 2
- 229910052709 silver Inorganic materials 0.000 abstract description 2
- 239000004332 silver Substances 0.000 abstract description 2
- 229910052717 sulfur Inorganic materials 0.000 abstract description 2
- 239000011593 sulfur Substances 0.000 abstract description 2
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Abstract
The invention provides a copper industry data robust coordination and significant error detection method, which relates to the technical field of information, and adopts real material inventory data, and firstly, the inventory data standard deviation of each data item is roughly calculated according to the inventory data; according to the recovery rate of copper, sulfur, gold and silver in a smelting plant of a copper production enterprise; in order to prevent interference of significant errors in the inventory data to other data items during data coordination, a robust data coordination model is established; in order to realize rapid data coordination and obvious error detection of the full material attribute of the inventory data of the materials of the smelting plant, the invention adopts a Lagrange multiplier conversion method to express a high-dimensional variable space by a low-dimensional constraint multiplier space. In addition, a differential evolution algorithm is adopted for optimization iteration solution. The method has the advantages that the obtained result is more accurate in obvious error detection, the data is more stable after coordination, the calculation efficiency meets the actual requirement, and the method can be popularized and applied in copper production enterprises and other production enterprises.
Description
Technical Field
The invention relates to the technical field of information, in particular to the technologies of robust calculation, meta-heuristic optimization and the like, and discloses a method for performing robust coordination and significant detection on colored copper production data by combining a robust calculation method and a meta-heuristic method.
Background
As an important component of the whole nonferrous copper production, the smelting plant directly influences the production control and profit accounting of the whole enterprise to play a decisive role in the recovery condition of valuable metals such as copper, sulfur, gold, silver and the like. The metal balance report of the month can be obtained by measuring the quality of each stock material at the end of the month and testing the grade of the valuable elements contained in the stock material, and the production condition of the month can be measured by calculating the recovery rate and the unknown loss rate of each valuable element. Under the normal production condition, the element recovery rate is within the artificial experience estimation interval, but due to the influence of error factors such as material metering, sampling, inspection and analysis, the data contains measurement errors and significant errors, so that the unknown loss of metal balance is large, and the element mass conservation deviation is large. Therefore, significant error detection and data coordination are required to be performed on the counted data, and the influence of the error on the metal balance is reduced.
With the wide development of research and application work, the data coordination of a dynamic system can be realized by a meta-heuristic method and a method represented by gradient optimization. In the methods, errors in the acquired data are assumed to be in accordance with Gaussian distribution, but the data of the industrial inventory has significant errors due to the influence of manual operation, sampling and the like. Therefore, directly performing data coordination on the data can spread significant error differences in the data to other data items to cause the result after coordination to deviate from a normal value, and in view of this, a distribution detection method is adopted to perform significant error detection on the data first.
In view of this, in addition to the significant error detection method based on the measurement error and the measurement residual, a robust objective function may be used to limit the contribution of data items with residuals larger than the tuning parameters in the objective function (hounting. power system multi-source coordination optimization scheduling research based on data-driven robust optimization [ D. However, because the dimensionality of the data coordination data item of the copper production enterprise is high, and the constraint condition of the data coordination model is a bilinear form of the product between variable attributes, which is difficult to decouple, the direct adoption of the meta-heuristic method for solving results in slow algorithm iteration and difficult convergence; in this case, since a plurality of significant error terms may exist at the same time, a cyclic detection method is required, which may result in an excessively long detection time. Although a plurality of significant errors can be detected simultaneously by using a robust data coordination model, the objective function is in a nonlinear form, which makes it difficult to solve the model. If the idea of variable conversion is adopted, the original high-dimensional variable is represented by a constraint multiplier with a lower dimension, and a robust data coordination technology is adopted to simultaneously determine a plurality of significant error items, the significant errors in the data can be expected to be determined while the solution is rapidly solved.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects in the prior art and provides a method for detecting robust coordination and significant errors of copper industry data.
The invention is realized by the following technical scheme: a copper industry data robust coordination and significant error detection method is characterized by comprising the following steps:
s1: data pre-processing
Reading current month inventory data including the quality of materials and corresponding valuable element grade values by a production field SAP database, calculating the mean value and standard deviation of measured values, and estimating the recovery rate and unknown loss rate of each metal element of a smelting plant according to the current month production condition;
s2: data robust collaborative modeling
Firstly, considering the stability of metal recovery rate and unknown loss rate of a factory;
s21: the metal amount recovery rate and the unknown loss rate of the metal element are respectively expressed by the following formulas (1) (2):
wherein x represents the mass of the material, omega represents the grade value of the material element, subscript in represents that the variable attribute is input or initial settlement, subscript end represents that the variable attribute is final settlement, subscript out represents that the variable attribute is output, subscript loss represents that the material attribute is known loss, alphaul (i)A nameless loss rate constraint target, α, representing element ire (i)Representing a recovery constraint objective for element i;
s22: the method is characterized in that a robust function as an objective function shown in formula (3) can be established for the data coordination and coordination of metal balance based on a designed robust function, and a data coordination model of a constraint set consisting of the recovery rate of each valuable element, the stability of unknown loss rate and the physical upper and lower limits of each variable is obtained by deduction of element conservation:
in order to eliminate the influence of different variable orders on the coordination result, the coordinated relative residual is represented by dividing the coordinated residual by the relative standard deviation;
ρWelschthe formula is shown as (4):
wherein
qx (j)＝σx (j)·xm (j)，swTo tune the parameter, σx (j)Is the relative standard deviation of the jth material,
wherein
Is the relative standard deviation, g, of the ith element corresponding to the jth materialul (i)And gre (i)Respectively are a nameless loss rate and a recovery rate constraint derivation formula,
xl (j)and xu (j)Corresponding to the coordination lower limit and coordination upper limit, w, of the material qualityl (i)(j)And wu (i)(j)The coordination lower limit and the coordination upper limit of the ith grade of the jth material are set;
s3: multiplier dimension reduction conversion of high-dimensional variables
The corresponding lagrangian function of the original model when only the equality constraint is considered is shown as (5):
wherein λul (i)、λre (i)Lagrange multipliers corresponding to the recovery rate constraint and the unknown loss rate constraint of the ith element;
s31: to solve for L
And
simultaneous solution can yield:
where Lambert W (0, x) is Lambert W Function, which represents a single valued Function, s, over the domain of definition at (0, + ∞)wIs the tuning constant of the Welsch function. The material attribute is lambda when the material is put into or deposited at the beginning of the period(i)＝-λul (i)-λre (i)λ when the material attribute is end of term(i)＝λul (i)+λre (i)(ii) a When the material property is output, lambda(i)＝λul (i)+λre (i)·kre (i)(ii) a When the material attribute is famous loss, lambda(i)＝λul (i)·kul (i)；
S32: and according to the historical data of the inventory, the results of multiple measurements and the physical limits of the production workshop, the upper and lower coordination limits of each coordination variable can be obtained. In order to further reduce the dimension number of the multiplier subspace, each variable is processed in a segmented mode in the coordination process. From equation (6), it can be seen that λ is the multiplier for each group(i)All can solve a set of uniquely determined variables
And
and only the quantity and element grade of the same material have a coupling relation;
under the condition of considering upper and lower limits of variables, each variable is estimated
Variables are only considered
Variation range under upper and lower limit:
according to λ(i)The estimated interval and the set interval of the variable can be classified into the following three states according to the positive and negative conditions:
the state is that: if the range completely exceeds the upper and lower limit constraint ranges of the variable, the solution without upper and lower limit constraints must fall outside the upper and lower limit ranges according to lambda(i)The symbol directly takes the variable as its upper limit wl (i)(j)(if λ)(i)< 0) or lower limit wl (i )(j)(if λ)(i)＞0)；
State two: if the range is completely contained in the variable upper and lower limit ranges, the upper and lower limits do not need to be concerned in the solving process, and the solution of the variable upper and lower limits does not fall into the upper and lower limit ranges;
state (c): if the range is intersected with the upper and lower limit ranges and no inclusion relation exists, marking is carried out, and the upper and lower limit limits of the variable still need to be concerned in the solving process.
After estimation, solving is carried out, variables in the first state are directly fixed to an upper limit or a lower limit, the variables in the second state and the third state are not subjected to upper and lower limit constraints, and if the variables in the group are in the upper and lower limit ranges after the solving, a solution is directly obtained without carrying out the next operation; if the variable exceeds the limit of the upper limit range and the lower limit range, the next search operation for the solution is executed, and the search range is according to the variable
The cases of (a) are divided into the following three cases:
1) variables of
Fixed to the upper limit, then variable
The decoupling relation can be solved directly according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
2) Variables of
Fixed to the lower limit, then variable
The decoupling relation can be solved directly according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
3) Variables of
Not touching the upper and lower limits, then the variable
There is still a coupling relationship between each
There are two situations of touching the upper limit and the lower limit and not touching the upper limit and the lower limit (the variable of the state I only has the situation of touching the upper limit and the lower limit, and the variable of the state II only has the situation of not touching the upper limit and the lower limit), wherein if the variable of the state III exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
S4: global optimization of long-term batching plan:
the basic idea of the DE algorithm is to simulate a stochastic model of biological evolution, with iterative iterations (mutation, crossover and selection) such that those individuals that are more environmentally compliant are preserved. The PSO algorithm characteristics are combined in the evolution process, the global optimal individual guidance information is added, the population density in the calculation is judged whether the calculation method converges or not by taking turns as a unit,the random search performance of the algorithm is increased, so that the algorithm can more easily jump out of the locally optimal solution. Initializing a population to [ P ]1,P2…Ppsize]Where each individual P contains a set of Lagrange multiplier variables and psize is the population size. The population density is defined as shown in formula (8), and the density threshold TI, the continuous convergence-free turn threshold TNC and the fitness function threshold TF of the population are defined. The fitness function of DE when performing a solution search is given by equation (9). The variation process of the algorithm is shown as a formula (10), the crossing process is shown as a formula (11), and the selection process is shown as a formula (12).
Wherein
For two different individuals, V, randomly selected in the population except for the variant individualiTo produce new individuals, GmaxIs the maximum number of iterations, G is the current number of iterations F0Is in the interval of [0,2 ]]The evolutionary factor of (1).
Where CR is the crossover probability, jrIs [ 1. ], psize]Random integer of (1), Uj,iFor the j gene of the i chromosome after crossing, Vj,iIs the j gene of the ith mutated chromosome.
The method comprises the following steps of solving a robust data coordination model by combining a DE method with a multiplier conversion technology:
s41: initializing global planning vector populations
Wherein each individual comprises a set of lagrangian multipliers, and d is the population size;
s42: performing individual variation operation by using the formula (10):
s43: the crossover operation is performed using equation (11):
s44: obtaining new population after propagation through the process
And calculating a corresponding fitness function (9);
s45: mixing the new and old populations, reserving the first d individuals with longer total duration of the batching scheme by a greedy optimization mode to form a new population, and marking the optimal individual as Gbest;
s46: calculating the population density by adopting a formula (8), if the density is less than the preset TF, reserving Gbest and reinitializing the rest population individuals;
if the algorithm does not reach the maximum iteration number, returning to the step S42; otherwise, returning the optimal individual and the corresponding data coordination value.
S5: and (3) significant error detection:
computing the relative residual e of data reconciliationiAnd determining the relation between the residual error and Welsch tuning parameter s if eiS is marked as significant error.
The invention has the beneficial effects that: the data robust coordination and significant error detection method combines a multiplier transformation method, robust optimization and a meta heuristic optimization method, overcomes the problem that the traditional method for directly coordinating data is influenced by significant error terms, and can solve the problem of difficulty in solving the problem of high-dimensional data coordination containing complex bilinear constraint. The provided robust data coordination method can realize data coordination and obvious error detection on data items at the same time, and reduces the problem of cycle detection caused by adopting distributed detection. . In addition, by the multiplier conversion method, the variable dimension of the meta-heuristic algorithm is greatly reduced, the search space of the algorithm is reduced, the efficiency of iterative optimization is increased, and the calculation efficiency of the method meets the actual application requirement.
Drawings
FIG. 1 is a schematic diagram of the material flow of a non-ferrous copper manufacturing enterprise;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a box plot of relative variation indicators for the method of the present invention and the comparative method;
FIG. 4 is a comparison graph of AVTI statistical parameters for the method of the present invention and the comparison method;
FIG. 5 is a comparison graph of OP statistical parameters for the inventive and comparative methods.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings and preferred embodiments.
As shown in the figure, the invention provides a copper industry data robust coordination and significant error detection method, which is characterized by comprising the following steps:
s1: data pre-processing
Reading current month inventory data including the quality of materials and corresponding valuable element grade values by a production field SAP database, calculating the mean value and standard deviation of measured values, and estimating the recovery rate and unknown loss rate of each metal element of a smelting plant according to the current month production condition;
s2: data robust collaborative modeling
Firstly, considering the stability of metal recovery rate and unknown loss rate of a factory;
s21: the metal amount recovery rate and the unknown loss rate of the metal element are respectively expressed by the following formulas (1) (2):
wherein x represents the mass of the material, omega represents the grade value of the material element, subscript in represents that the variable attribute is input or initial settlement, subscript end represents that the variable attribute is final settlement, subscript out represents that the variable attribute is output, subscript loss represents that the material attribute is known loss, alphaul (i)A nameless loss rate constraint target, α, representing element ire (i)Representing a recovery constraint objective for element i;
s22: the method is characterized in that a robust function as an objective function shown in formula (3) can be established for the data coordination and coordination of metal balance based on a designed robust function, and a data coordination model of a constraint set consisting of the recovery rate of each valuable element, the stability of unknown loss rate and the physical upper and lower limits of each variable is obtained by deduction of element conservation:
in order to eliminate the influence of different variable orders on the coordination result, the coordinated relative residual is represented by dividing the coordinated residual by the relative standard deviation;
ρWelschthe formula is shown as (4):
wherein
qx (j)＝σx (j)·xm (j)，swTo tune the parameter, σx (j)Is the relative standard deviation of the jth material,
wherein
Is the relative standard deviation, g, of the ith element corresponding to the jth materialul (i)And gre (i)Respectively are a nameless loss rate and a recovery rate constraint derivation formula,
xl (j)and xu (j)Corresponding to the coordination lower limit and coordination upper limit, w, of the material qualityl (i)(j)And wu (i)(j)The coordination lower limit and the coordination upper limit of the ith grade of the jth material are set;
s3: multiplier dimension reduction conversion of high-dimensional variables
The corresponding lagrangian function of the original model when only the equality constraint is considered is shown as (5):
wherein λul (i)、λre (i)Lagrange multipliers corresponding to the recovery rate constraint and the unknown loss rate constraint of the ith element;
s31: to solve for L
And
simultaneous solution can yield:
where Lambert W (0, x) is Lambert W Function, which represents a single valued Function, s, over the domain of definition at (0, + ∞)wIs the tuning constant of the Welsch function. The material attribute is lambda when the material is put into or deposited at the beginning of the period(i)＝-λul (i)-λre (i)λ when the material attribute is end of term(i)＝λul (i)+λre (i)(ii) a When the material property is output, lambda(i)＝λul (i)+λre (i)·kre (i)(ii) a When the material attribute is famous loss, lambda(i)＝λul (i)·kul (i)；
S32: and according to the historical data of the inventory, the results of multiple measurements and the physical limits of the production workshop, the upper and lower coordination limits of each coordination variable can be obtained. In order to further reduce the dimension number of the multiplier subspace, each variable is processed in a segmented mode in the coordination process. From equation (6), it can be seen that λ is the multiplier for each group(i)All can solve a set of uniquely determined variables
And
and only the quantity and element grade of the same material have a coupling relation;
in consideration of the changeUnder the condition of upper and lower limit of quantity, each is estimated
Variables are only considered
Variation range under upper and lower limit:
according to λ(i)The estimated interval and the set interval of the variable can be classified into the following three states according to the positive and negative conditions:
the state is that: if the range completely exceeds the upper and lower limit constraint ranges of the variable, the solution without upper and lower limit constraints must fall outside the upper and lower limit ranges according to lambda(i)The symbol directly takes the variable as its upper limit wl (i)(j)(if λ)(i)< 0) or lower limit wl (i )(j)(if λ)(i)＞0)；
State two: if the range is completely contained in the variable upper and lower limit ranges, the upper and lower limits do not need to be concerned in the solving process, and the solution of the variable upper and lower limits does not fall into the upper and lower limit ranges;
state (c): if the range is intersected with the upper and lower limit ranges and no inclusion relation exists, marking is carried out, and the upper and lower limit limits of the variable still need to be concerned in the solving process.
After estimation, solving is carried out, variables in the first state are directly fixed to an upper limit or a lower limit, the variables in the second state and the third state are not subjected to upper and lower limit constraints, and if the variables in the group are in the upper and lower limit ranges after the solving, a solution is directly obtained without carrying out the next operation; if the variable exceeds the limit of the upper limit range and the lower limit range, the next search operation for the solution is executed, and the search range is according to the variable
The cases of (a) are divided into the following three cases:
1) variables of
Fixed to the upper limit, then variable
The decoupling relation can be solved directly according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
2) Variables of
Fixed to the lower limit, then variable
The decoupling relation can be solved directly according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
3) Variables of
Not touching the upper and lower limits, then the variable
There is still a coupling relationship between each
There are two situations of touching the upper limit and the lower limit and not touching the upper limit and the lower limit (the variable of the state I only has the situation of touching the upper limit and the lower limit, and the variable of the state II only has the situation of not touching the upper limit and the lower limit), wherein if the variable of the state III exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit.
S4: global optimization of long-term batching plan:
the basic idea of the DE algorithm is to simulate a stochastic model of biological evolution, with iterative iterations (mutation, crossover and selection) such that those individuals that are more environmentally compliant are preserved. The characteristics of a PSO algorithm are combined in the evolution process, and global optimal individual guidance is addedAnd the judgment of the population density in the calculation is carried out by taking turns as a unit to consider whether the calculation method is converged, so that the random search performance of the algorithm is improved, and the algorithm is easier to jump out of a local optimal solution. Initializing a population to [ P ]1,P2…Ppsize]Where each individual P contains a set of Lagrange multiplier variables and psize is the population size. The population density is defined as shown in formula (8), and the density threshold TI, the continuous convergence-free turn threshold TNC and the fitness function threshold TF of the population are defined. The fitness function of DE when performing a solution search is given by equation (9). The variation process of the algorithm is shown as a formula (10), the crossing process is shown as a formula (11), and the selection process is shown as a formula (12).
Wherein
For two different individuals, V, randomly selected in the population except for the variant individualiTo produce new individuals, GmaxIs the maximum number of iterations, G is the current number of iterations F0Is in the interval of [0,2 ]]The evolutionary factor of (1).
Where CR is the crossover probability, jrIs [ 1. ], psize]Random integer of (1), Uj,iFor the j gene of the i chromosome after crossing, Vj,iIs the j gene of the ith mutated chromosome.
The method comprises the following steps of solving a robust data coordination model by combining a DE method with a multiplier conversion technology:
s41: initializing global planning vector populations
Wherein each individual comprises a set of lagrangian multipliers, and d is the population size;
s42: performing individual variation operation by using the formula (10):
s43: the crossover operation is performed using equation (11):
s44: obtaining new population after propagation through the process
And calculating a corresponding fitness function (9);
s45: mixing the new and old populations, reserving the first d individuals with longer total duration of the batching scheme by a greedy optimization mode to form a new population, and marking the optimal individual as Gbest;
s46: calculating the population density by adopting a formula (8), if the density is less than the preset TF, reserving Gbest and reinitializing the rest population individuals;
if the algorithm does not reach the maximum iteration number, returning to the step S42; otherwise, returning the optimal individual and the corresponding data coordination value.
S5: and (3) significant error detection:
computing the relative residual e of data reconciliationiAnd determining the relation between the residual error and Welsch tuning parameter s if eiS is marked as significant error.
The tuning parameter s of the robust model is set to 2.9846, and the upper and lower limits of the material storage bin are set as shown in table 1. In the aspect of data coordination, the method of the invention and a data coordination method using PSO as a solver are respectively adopted to perform a comparison experiment, and Iteration Times (IT), Fitness function values (FF), Constrained Residuals (CR) and relative variation indexes of data coordination results of the two methods are respectively counted, wherein the relative variation index formula is shown as (13). And CV values of the respective inventory data items are respectively a manual method, a data coordination method based on PSO and the method of the invention. Table 2 shows the results of the data coordination experiment from 1 to 6 months, and fig. 3 is a comparison graph of CV value box lines of the method of the present invention and the data coordination method based on PSO. In the aspect of significant error detection, the detection method and the detection method based on the residual error, the Logitics robust function and the Fair robust function are respectively adopted to carry out comparison experiments, and the detection accuracy (OP) and the Type 1 error Average Value (AVTI) of the methods are respectively counted. Fig. 4 and 5 are graphs comparing AVTI and OP parameters for the above methods. The comprehensive graph result shows that the method is superior to a data coordination method based on PSO in precision performance and operation efficiency, and instability of the inventory data can be greatly reduced, so that the coordinated data is closer to a true value.
TABLE 1 Upper and lower limits of Material storage Bin level
| Name of the position | Material(s) | Lower limit of stock | Upper limit of stock | Unit of | |
| | Matte | 0 | 7000 | t | |
| Concentrate | Concentrate ore | 0 | 1400 | m3 | |
| Proportioning bin | Solvent, concentrate | 0 | 4400 | t | |
| | Matte | 0 | 2000 | t | |
| Slag concentrate | Slag concentrate | 0 | 1400 | mw | |
| Mineral separation slow cooling storage yard | Reducing slag of top-blown |
0 | 40000 | t | |
| Mineral separation slow cooling storage yard | Beneficiation high |
0 | 5000 | t |
TABLE 21-6 monthly data coordination experiments
The invention has the beneficial effects that: the data robust coordination and significant error detection method combines a multiplier transformation method, robust optimization and a meta heuristic optimization method, overcomes the problem that the traditional method for directly coordinating data is influenced by significant error terms, and can solve the problem of difficulty in solving the problem of high-dimensional data coordination containing complex bilinear constraint. The provided robust data coordination method can realize data coordination and obvious error detection on data items at the same time, and reduces the problem of cycle detection caused by adopting distributed detection. . In addition, by the multiplier conversion method, the variable dimension of the meta-heuristic algorithm is greatly reduced, the search space of the algorithm is reduced, the efficiency of iterative optimization is increased, and the calculation efficiency of the method meets the actual application requirement.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (1)
1. A copper industry data robust coordination and significant error detection method is characterized by comprising the following steps:
s1: data pre-processing
Reading current month inventory data including the quality of materials and corresponding valuable element inventory values from a production field SAP database, calculating the mean value and standard deviation of the measured values, and estimating the recovery rate and the unknown loss rate of each metal element of a smelting plant according to the current month production condition;
s2: data robust collaborative modeling
Firstly, considering the stability of metal recovery rate and unknown loss rate of a factory;
s21: the metal amount recovery rate and the unknown loss rate of the metal element are respectively expressed by the following formulas (1) (2):
wherein x represents the mass of the material, omega represents the grade value of the material element, subscript in represents that the variable attribute is input or initial settlement, subscript end represents that the variable attribute is final settlement, subscript out represents that the variable attribute is output, subscript loss represents that the material attribute is known loss, alphaul (i)A nameless loss rate constraint target, α, representing element ire (i)Representing a recovery constraint objective for element i;
s22: the method is characterized in that a robust function which is shown as a formula (3) and takes the robust function as an objective function can be established for the data coordination and coordination of metal balance based on a designed robust function, and a data coordination model of a constraint set is obtained by deducing the recovery rate and the unknown loss rate of each valuable element and the physical upper and lower limits of each variable through element conservation:
in order to eliminate the influence of different variable orders on the coordination result, the coordinated relative residual is represented by dividing the coordinated residual by the relative standard deviation;
ρWelschthe formula is shown as (4):
wherein
qx (j)＝σx (j)·xm (j)，swTo tune the parameter, σx (j)Is the relative standard deviation of the jth material,
wherein
Is the relative standard deviation of the ith element corresponding to the jth material, gul (i)And gre (i)Respectively are a nameless loss rate and a recovery rate constraint derivation formula,
xl (j)and xu (j)Corresponding to the coordination lower limit and coordination upper limit, w, of the material qualityl (i)(j)And wu (i)(j)The coordination lower limit and the coordination upper limit of the ith grade of the jth material are set;
s3: multiplier dimension reduction conversion of high-dimensional variables
The corresponding lagrangian function of the original model when only the equality constraint is considered is shown in (5):
wherein λul (i)、λre (i)Lagrange multipliers corresponding to the recovery rate constraint and the unknown loss rate constraint of the ith element;
s31: to solve for L
And
simultaneous solution can yield:
where Lambert W (0, x) is Lambert W Function, which represents a single valued Function, s, over the domain of definition at (0, + ∞)wIs a tuning constant of Welsch function, the material property being λ at the time of input or initial settlement(i)＝-λul (i)-λre (i)λ when the material attribute is end of term(i)＝λul (i)+λre (i)(ii) a When the material property is yield, lambda(i)＝λul (i)+λre (i)·kre (i)(ii) a When the material attribute is famous loss, lambda(i)＝λul (i)·kul (i)；
S32: according to the historical data of inventory, the results of multiple measurements and the physical limit of a production workshop, the coordination upper and lower limits of each coordination variable can be obtained, in order to further reduce the dimension of multiplier space, each variable is processed in a segmentation way in the coordination process, and the lambda of each group of multipliers can be seen from the formula (6)(i)All can solve a set of uniquely determined variables
And
and only the quantity and element grade of the same material have a coupling relation;
under the condition of considering upper and lower limits of variables, each variable is estimated
Variables are only considered
The range of variation under the upper and lower limits:
according to λ(i)The estimated interval and the set interval of the variable can be classified into the following three states according to the positive and negative conditions:
the state is that: if the range completely exceeds the upper and lower limit constraint range of the variable, the solution without upper and lower limit constraint must fall outside the upper and lower limit range, then according to lambda(i)The symbol directly takes the variable as its upper limit wl (i)(j)(if λ)(i)< 0) or lower limit wl (i)(j)(if λ)(i)＞0)；
State two: if the range is completely contained in the variable upper and lower limit ranges, the upper and lower limits do not need to be concerned in the solving process, and the solution of the variable upper and lower limits does not fall into the upper and lower limit ranges;
state (c): if the range is intersected with the upper and lower limit ranges and no inclusion relation exists, marking is carried out, and the upper and lower limit limits of the variable still need to be concerned in the solving process;
after estimation, solving is carried out, variables in the first state are directly fixed to the upper limit or the lower limit, the variables in the second state and the third state are not subjected to upper and lower limit constraints, and if the variables in the group are in the upper and lower limit ranges after the solving, a solution is directly obtained without carrying out the next operation; if the variable exceeds the limit of the upper limit range and the lower limit range, the next search operation for the solution is executed, and the search range is according to the variable
The cases of (a) are classified into the following three cases:
1) variables of
Fixed to the upper limit, then variable
The coupling relation is removed, and the solution can be directly carried out according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit;
2) variables of
Fixed to the lower limit, then variable
The coupling relation is removed, and the solution can be directly carried out according to the estimated state, wherein if the variable of the state (c) exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit;
3) variables of
Not touching the upper and lower limits, then the variable
There is still a coupling relationship between each
The upper limit and the lower limit are touched and not touched under two conditions (the variable of the state I only has the condition of touching the upper limit and the lower limit, and the variable of the state II only has the condition of not touching the upper limit and the lower limit), wherein if the variable of the state III exceeds the upper limit or the lower limit, the variable is pulled back to the upper limit or the lower limit;
s4: global optimization of long-term batching plan:
the basic idea of the DE algorithm is to simulate a random model of biological evolution, to make the individuals more adaptive to the environment preserved by repeated iteration (variation, intersection and selection), to combine the PSO algorithm characteristics in the evolution process, to add global optimal individual guidance information, and to judge the population density in calculation to consider whether the algorithm converges or not in turn, to increase the random search performance of the algorithm to make the algorithm more easily jump out the local optimal solution, to initialize the population as [ P ]1,P2…Ppsize]Each individual P comprises a group of Lagrange multiplier variables, psize is the size of a population, the population density is defined as shown in a formula (8), the density threshold TI of the population, a continuous non-convergence round threshold TNC and a fitness function threshold TF, the fitness function of DE is shown in a formula (9) when solving and searching is carried out, the variation process of an algorithm is shown in a formula (10), the cross process is shown in a formula (11), and the selection process is shown in a formula (12):
F＝F0·2λ
wherein
For two different individuals, V, randomly selected in the population except for the variant individualiTo produce new individuals, GmaxIs the maximum number of iterations, G is the current number of iterations F0Is in the interval of [0,2 ]]The evolution factor of (1);
where CR is the crossover probability, jrIs [ 1. ], psize]Random integer of (1), Uj,iFor the j gene of the i chromosome after crossing, Vj,iThe j gene of the ith mutated chromosome;
the method comprises the following steps of solving a robust data coordination model by combining a DE method with a multiplier conversion technology:
s41: initializing global planning vector populations
Wherein each individual comprises a set of lagrangian multipliers, and d is the population size;
s42: performing individual variation operation by using the formula (10):
s43: the crossover operation is performed using equation (11):
s44: through the above-mentionedThe process obtains new population after reproduction
And calculating a corresponding fitness function (9);
s45: mixing the new and old populations, reserving the first d individuals with longer total duration of the batching scheme by a greedy optimization mode to form a new population, and marking the optimal individual as Gbest;
s46: calculating the population density by adopting a formula (8), if the density is less than the preset TF, reserving Gbest and reinitializing the rest population individuals;
s47: if the algorithm does not reach the maximum iteration number, returning to the step S42; otherwise, returning the optimal individual and the corresponding data coordination value;
s5: and (3) significant error detection:
computing the relative residual e of data reconciliationiAnd determining the relation between the residual error and Welsch tuning parameter s if eiS is marked as significant error.
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