CN117828905A - Rolling load distribution optimization design method based on shape integrated control - Google Patents
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Abstract
The invention provides a rolling load distribution optimization design method based on shape integrated control, which relates to the technical field of automatic control of steel rolling.
Description
Technical Field
The invention relates to the technical field of automatic control of steel rolling, in particular to a rolling load distribution optimization design method based on shape integrated control.
Background
With the rapid development of national economy, the national living standard is gradually improved, and the requirements for high-quality and high-performance plate and strip materials are increasingly increased. In the hot continuous rolling production process, the three-dimensional size and the internal performance are the most important quality indexes of the product. Therefore, products with excellent three-dimensional size and internal performance are obtained in the production process, and the method has very important significance for various iron and steel enterprises.
In the hot rolling production process, three-dimensional size control and performance control are generally divided into independent setting and control units. For example, for three-dimensional control, there are relatively independent thickness control systems, width control systems, and strip control systems, and control of product properties is provided by a finishing temperature and a coiling temperature control system. The three-dimensional size control and performance control systems are relatively independent, but are actually coupled with each other, and the change or fluctuation of the process parameters can affect the two and affect the final quality of the product. In order to realize high-quality control of products, the invention provides an optimization design method for rolling load distribution based on shape integrated control, and a process design capable of simultaneously ensuring the three-dimensional size and the product performance of the products is obtained through the design of load distribution, so that a good foundation is provided for shape integrated control in the production process.
The design of the rolling load distribution optimization usually adopts an empirical method, such as a rolling reduction distribution coefficient method and an energy consumption curve method. These methods require a large amount of field measurements and empirical data and update the curves as the production environment changes, which is inefficient and does not meet the needs of modern steel rolling production. With the development of computer technology, researchers have performed more efficient load distribution by finding the optimal solution of the objective function. For the design of a single objective function, the process parameters such as rolling force, finish rolling temperature, power or energy consumption and the like can be used as optimization objects to establish a prediction model, for example, a rolling mill load distribution method based on a chaotic particle swarm optimization algorithm in China patent CN110751414 optimizes and calculates load through chaotic particle swarm optimization, and equal load distribution is used as the single objective function to calculate. However, as the rolling process becomes finer, it is increasingly difficult for such a single objective function to meet the requirements of the rolling process, and multi-objective optimization methods are becoming more and more important. According to the hot rolling rough rolling load distribution method considering the convexity of the intermediate billet, a multi-objective optimization function based on weight is established according to three single objective functions, namely the convexity of the intermediate billet, power balance and electric power cost, and an optimization algorithm is utilized to calculate the optimal solution of the multi-objective optimization function. The Chinese patent CN107716560 discloses a strip hot continuous rolling load distribution method, which is characterized in that a mathematical model is established by taking power proportionality, minimum energy consumption and good shape as objective functions, and process optimization is designed by solving through a mixed particle swarm optimization algorithm.
The existing method applied to the rolling load distribution optimization has two defects, on one hand, in the design process of the load distribution optimization, the control of the three-dimensional size of the product is more considered, and the control of the product performance is not considered; in the actual rolling process, the austenite grain size can be recrystallized and the grain grows along with the rolling process, and the final austenite grain size determines the internal performance of the product, which is not considered in the current rolling load distribution optimization design; on the other hand, in the load distribution optimization design process, the multi-objective optimization algorithm used by the related research has the phenomena of low solving speed and low solving efficiency, and is easy to sink into local optimization. Therefore, in order to realize the integrated control of the rolling process, optimization must be performed on the design and solving modes of the objective function, and the rolling load distribution optimization must be rapidly performed by improving the convergence and the universality of the solving method.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a rolling load distribution optimization design method based on shape integrated control.
A rolling load distribution optimization design method based on shape integrated control specifically comprises the following steps.
Step 1: PDI data, rolling line basic parameters and rolling data in the production plan are determined.
The PDI data comprise steel types, slab sizes and finished product specifications; wherein the steel grade includes: name and chemical composition, slab dimensions include: slab length, width and thickness, finished product specifications include: width and thickness of the finished product.
The basic parameters of the rolling line comprise the number of rough rolling passes and finish rolling frames, the distance between the frames and the diameter of the roller.
Step 2: process constraints and equipment constraints of the rolling process are determined.
The process constraints include:
bite angle constraint:the method comprises the steps of carrying out a first treatment on the surface of the Wherein the biting condition is a biting angle +.>Representation, deltahFor depression amount->For friction angle>For friction coefficient>Is the radius of the roller;
reduction of each pass of rough rolling or each frame of finish rollingIs limited in a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a frame->Maximum rolling reduction of (2);
temperature condition constraints: finish rolling inlet temperature according to production process requirementsFinishing temperature of last stand +.>Within a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->The minimum finish rolling inlet temperature, the maximum finish rolling inlet temperature, +.>And->The final rolling temperature of the minimum final stand and the final rolling temperature of the maximum final stand are respectively;
the device constraints include:
rolling force limitation: for the frameRolling force->Less than the maximum allowable rolling force: />；
Wherein,is the maximum allowable rolling force;
motor power limit: for the frameCorresponding motor device, motor power->Should be less than the maximum allowable motor power: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is the maximum allowable motor power.
Step 3: a multi-objective function decision variable is determined.
The outlet thickness of each frame for rough rolling each pass and finish rolling each passAs a decision variable; wherein,for the total number of passes>The exit thickness for the n-th pass.
Step 4: and respectively establishing a rolling power objective function, a three-dimensional size objective function and an internal performance objective function.
Step 4.1: the rolling power objective function is established, and the rolling power summation of each pass of rough rolling and each stand of finish rolling is used for representing the rolling piece:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a rolling power objective function; />The total number of passes; />Is a functional relationship between decision variables and rolling power.
Step 4.2: establishing a three-dimensional size objective function using the rolled piece expressed by the sum of the relative convexity differences of each pass of rough rolling or each stand of finish rolling:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a three-dimensional size objective function; />The relative convexity of each frame is for rough rolling each pass or finish rolling; />Is the relative convexity of the target; />Is a functional relationship between decision variables and relative convexity differences.
Step 4.3: establishing an internal performance objective function expressed by deviations of the average grain size of the rolled piece from the target size:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is an internal performance objective function; />The average grain size after rolling is +.>；/>The unit is +.about.>；/>Is a functional relationship between decision variables and grain size.
Step 5: and solving a rolling power objective function, a three-dimensional size objective function and an internal performance objective function by using an NSGA-III-DE algorithm to obtain the value of the optimized objective function.
Step 5.1: initializing a population.
Step 5.1.1: determining decision variables: outlet thickness of each pass of rough rolling or each frame of finish rolling。
Step 5.1.2: setting upper and lower limits of decision variables based on outlet thickness of each pass to enable iteration times to be setObtaining the first generation of the powder with the size ofNPIs a parent population of (c).
Step 5.2: generating population sizes ofNPAnd combining the parent and offspring to obtain a size of 2NPIs a new population of (a).
Step 5.3: selecting a previous selection from a new population by a selection mechanism of reference pointsNPIndividual members of the new offspring。
Step 5.3.1: generating a reference point:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the number of reference points +.>For the purpose ofMark dimension->And->The number of boundary layer and inner layer divisions, respectively.
Step 5.3.2: adaptive normalization of populations.
Step 5.3.2.1: an ideal point is determined.
Step 5.3.2.1.1: selecting a minimum value of an objective function in a current populationAnd constructing ideal points.
Step 5.3.2.1.2: translating the population to make the ideal point as the origin:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->The objective function values before and after translation, respectively.
Step 5.3.2.2: calculating extreme points:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the extreme point after deformation, < >>Is the unit direction vector of the coordinate axis.
Step 5.3.2.3: and constructing a hyperplane consisting of the ideal point and each extreme point.
Step 5.3.3: individuals in the population are associated with reference points, respectively.
Step 5.3.4: and selecting the reserved individuals according to the association degree of the reference points.
Step 5.4: will beAs a new parent population +.>The operator replaces the mutation and crossover process of the NSGA-III algorithm to generate a new generation of offspring population and mixes the parent and offspring populations.
Step 5.4.1: variation operation, generation and base vectorVariant individuals corresponding to one by one->：The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For scaling factor +.>And->Is different from +.>Is a subject of (a).
Step 5.4.2: cross operation fromAnd->Cross-generating new individuals->：/>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For crossover probability->Is a random number.
Step 5.4.3: selecting, namely, base vectors in a populationIndividuals obtained by crossing->And comparing the quality to select the next generation population: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->Individual->And->A corresponding fitness function.
Step 5.5: repeating steps 5.3 to 5.4, and allowingUntil the number of iterations +>Reach maximum iteration number->。
Step 6: and selecting an optimal solution of the rolling power objective function, the three-dimensional size objective function and the internal performance objective function, and obtaining a corresponding load distribution result.
Step 6.1: performing satisfaction sequencing to obtain an optimal target functionNumerical value:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Satisfaction for the objective function; />Is->Mean value of the individual objective function solutions, +.>Is->Standard deviation of individual objective function solutions +.>Is->And the weight coefficient of each objective function solution.
Step 6.2: substituting the value of the decision variable corresponding to the selected optimal solution, namely the optimal objective function value, into the step 4 to obtain a rolling load distribution result comprising the thickness, rolling force, power, temperature, convexity and average grain size of each pass of rough rolling and each stand outlet of finish rolling.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in:
compared with the prior art, the invention has the following beneficial effects: the invention provides a rolling load distribution optimization design method based on shape integrated control, which is characterized in that operators are introduced to replace the variation and crossing process of an NSGA-III algorithm, the obtained NSGA-III-DE algorithm is combined with load distribution optimization of hot continuous rolling production, the shape integrated control is considered, a hot continuous rolling full-flow optimization model with minimum power, good shape and minimum final rolling grain size deviation as objective functions is established, and the outlet thickness of each rough rolling pass and each finish rolling frame is used as decision variables to optimize load distribution. The effectiveness of the NSGA-III-DE optimization algorithm is proved by comparing the optimization results obtained by different methods, and the method can provide assistance for the production of hot rolled plate strip products.
Drawings
Fig. 1 is a schematic diagram of a hot continuous rolling line according to an embodiment of the present invention.
Fig. 2 is a flowchart of the overall design method for optimizing rolling load distribution according to the embodiment of the invention.
FIG. 3 is a flow chart of an embodiment of the present invention employing NSGA-III-DE.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
A rolling load distribution optimization design method based on shape integrated control adopts a typical hot continuous rolling production line in the embodiment, the arrangement form is shown in fig. 1, the whole flow chart is shown in fig. 2, and the method specifically comprises the following steps.
Step 1: PDI data, rolling line basic parameters and rolling data in the production plan are determined.
The PDI data includes steel grade, slab size, and finished product specifications.
Wherein the steel grade includes: name and chemical composition, slab dimensions include: slab length, width and thickness, finished product specifications include: width and thickness of the finished product.
The basic parameters of the rolling line comprise the number of rough rolling passes and finish rolling frames, the distance between the frames and the diameter of the roller.
The PDI data in this example are shown in table 1 and the mill pass line base parameters are shown in table 2.
TABLE 1 PDI data sheet
| Sequence number | Content | Numerical value | Unit (B) |
| 1 | Name of steel grade | Q235B | - |
| 2 | Slab size | 9600×1500×250 | mm×mm×mm |
| 3 | Size of finished product | 1500×3.0 | mm×mm |
| 4 | Mn | 0.34 | % |
| 5 | C | 0.16 | % |
| 6 | Si | 0.10 | % |
| 7 | Al | 0.03 | % |
| 8 | Cr | 0.01 | % |
Table 2 basic parameter table of rolling line
| Sequence number | Content | Numerical value | Unit (B) |
| 1 | Number of rough rolling passes | 6 | - |
| 2 | Number of finishing stands | 6 | - |
| 3 | Roughing stand spacing | 5.5 | m |
| 4 | Finishing mill stand spacing | 5.5 | m |
| 5 | Diameter of roughing roll | 1197 | mm |
| 6 | Diameter of finish rolling roll | 761 | mm |
Step 2: process constraints and equipment constraints of the rolling process are determined.
The process constraints include:
bite angle constraint:the method comprises the steps of carrying out a first treatment on the surface of the Wherein the biting condition is a biting angle +.>Representation, deltahFor the reduction in mm, ++>For friction angle>For friction coefficient>The radius of the roller is in mm;
reduction of each pass of rough rolling or each frame of finish rollingIs limited in a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a frame->Maximum rolling reduction of (2);
temperature condition constraints: finish rolling inlet temperature according to production process requirementsFinishing temperature of last stand +.>Within a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->The minimum finish rolling inlet temperature and the maximum finish rolling inlet temperature are respectively expressed in DEG C, +.>And->The final rolling temperature of the minimum final stand and the final rolling temperature of the maximum final stand are respectively in the unit of DEG C;
the device constraints include:
rolling force limitation: the rolling force meets the requirements of hydraulic equipment and aims at the frameRolling force->Less than the maximum allowable rolling force：/>；
Wherein,the maximum allowable rolling force is given in kN;
motor power limit: the rolling power meets the load requirement of the motor and aims at the frameCorresponding motor device, motor power->Should be less than the maximum allowable motor power: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>The maximum allowable motor power is in kW.
The limiting conditions in this example are shown in table 3.
TABLE 3 Process equipment limitation table
| Sequence number | Content | Numerical value | Unit (B) |
| 1 | Coefficient of friction | 0.26 | - |
| 2 | Maximum rolling reduction | 55% | - |
| 3 | Maximum finish rolling inlet temperature | 1070 | °C |
| 4 | Minimum finish rolling inlet temperature | 970 | °C |
| 5 | Maximum finishing temperature | 910 | °C |
| 6 | Minimum finishing temperature | 850 | °C |
| 7 | Maximum allowable rolling force | 44000 | kN |
| 8 | Maximum allowable motor power | 8000 | kW |
Step 3: a multi-objective function decision variable is determined.
The outlet thickness of each frame for rough rolling each pass and finish rolling each passAs decision variables.
Wherein,for the total number of passes>The exit thickness in mm is the n-th pass.
Step 4: and respectively establishing a rolling power objective function, a three-dimensional size objective function and an internal performance objective function.
Step 4.1: the rolling power objective function is established, and the rolling power summation of each pass of rough rolling and each stand of finish rolling is used for representing the rolling piece:
。
wherein,is a rolling power objective function; />The total number of passes; />Is a functional relationship between decision variables and rolling power.
In this embodiment, n=12, and has the following formula:
，/>。
wherein,the rolling moment of each pass of rough rolling or each stand of finish rolling is N.m; />The unit is rad/min for rough rolling each pass or finish rolling each frame rotation speed.
Step 4.2: establishing a three-dimensional size objective function using the rolled piece expressed by the sum of the relative convexity differences of each pass of rough rolling or each stand of finish rolling:
。
wherein,is a three-dimensional size objective function; />The relative convexity of each frame is for rough rolling each pass or finish rolling; />Is the relative convexity of the target; />A functional relationship between the decision variable and the relative convexity difference; in this embodiment, the following formula is provided:
，/>，/>。
wherein,and->Convexity and outlet thickness of each frame of finish rolling, mm, < >>And->The final product was taken to be 0.04mm and 3.0mm for the target convexity and target thickness, respectively.
In this embodiment, the change of the thickness of the strip steel mainly occurs in the rough rolling stage, and the rolling reduction of each stand is required to be reasonably distributed in the finish rolling stage, so that the relative convexity value of the strip steel is more approximate to the relative convexity of the target product, and therefore, the three-dimensional size objective function only considers the finish rolling 6 stands.
Step 4.3: establishing an internal performance objective function expressed by deviations of the average grain size of the rolled piece from the target size:。
wherein,is an internal performance objective function; />The average grain size after rolling is +.>；/>The unit is +.about.>；/>Is a functional relationship between decision variables and grain size.
In this embodiment, the following formula is provided:
，。
wherein,is the grain size after static recrystallization, the unit is +.>；/>Is carbon equivalent; />Temperature in->；Is the time between passes, the unit is->。
When the Q235B steel is finish rolled, the average grain size is 20The corresponding internal performance index is optimal.
Thus in this embodimentTake 20%>。
Step 5: and solving a rolling power objective function, a three-dimensional size objective function and an internal performance objective function by using an NSGA-III-DE algorithm to obtain the value of the optimized objective function.
The NSGA-III-DE algorithm flow chart is shown in FIG. 3 and the algorithm parameters are set forth in Table 4.
Table 4 parameter setting Table of NSGA-III-DE algorithm
| NSGA-III parameters | Numerical value |
| Population size | 200 |
| Algebra of evolution | 1000 |
| Selection mode | Tournament Selection |
| Probability of variation | 0.5 |
| Crossover probability | 0.3 |
Step 5.1: initializing a population.
Step 5.1.1: determining decision variables: outlet thickness of each pass of rough rolling or each frame of finish rolling。
Step 5.1.2: setting upper and lower limits of decision variables based on outlet thickness of each pass to enable iteration times to be setObtaining the first generation of the powder with the size ofNPIs a parent population of (a); in the present embodimentNP=100。
Step 5.2: generating population sizes ofNPAnd combining the parent and offspring to obtain a size of 2NPIs a new population of (a).
Step 5.3: selecting a previous selection from a new population by a selection mechanism of reference pointsNPIndividual members of the new offspring。
Step 5.3.1: generating a reference point:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the number of reference points +.>For the target dimension +.>And->The number of boundary layer and inner layer divisions, respectively.
Step 5.3.2: adaptive normalization of populations.
Step 5.3.2.1: an ideal point is determined.
Step 5.3.2.1.1: selecting a minimum value of an objective function in a current populationAnd constructing ideal points.
Step 5.3.2.1.2: translating the population to make the ideal point as the origin:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->The objective function values before and after translation, respectively.
Step 5.3.2.2: calculating extreme points:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the extreme point after deformation, < >>Is the unit direction vector of the coordinate axis.
Step 5.3.2.3: and constructing a hyperplane consisting of the ideal point and each extreme point.
Step 5.3.3: individuals in the population are associated with reference points, respectively.
Step 5.3.4: and selecting the reserved individuals according to the association degree of the reference points.
Step 5.4: will beAs a new parent population +.>The operator replaces the mutation and crossover process of the NSGA-III algorithm to generate a new generation of offspring population and mixes the parent and offspring populations.
Step 5.4.1: variation operation, generation and base vectorVariant individuals corresponding to one by one->：The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For scaling factor +.>And->Is different from +.>Is a subject of (a).
Step 5.4.2: cross operation fromAnd->Cross-generating new individuals->：/>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For crossover probability->Is a random number.
Step 5.4.3: selecting, namely, base vectors in a populationIndividuals obtained by crossing->And comparing the quality to select the next generation population: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->Individual->And->A corresponding fitness function.
Step 5.5: repeating steps 5.3 to 5.4, and allowingUntil the number of iterations +>Reach maximum iteration number->. In this embodiment +.>。
Step 6: and selecting an optimal solution of the rolling power objective function, the three-dimensional size objective function and the internal performance objective function, and obtaining a corresponding load distribution result.
Step 6.1: performing satisfaction sequencing to obtain an optimal objective function value:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Satisfaction for the objective function; />Is->Mean value of the individual objective function solutions, +.>Is->Standard deviation of individual objective function solutions +.>Is->Weight coefficients of the objective function solutions; in this embodiment +.>。
Step 6.2: substituting the value of the decision variable corresponding to the selected optimal solution, namely the optimal objective function value, into the step 4 to obtain a rolling load distribution result comprising the thickness, rolling force, power, temperature, convexity and average grain size of each pass of rough rolling and each stand outlet of finish rolling.
According to the field data and the load distribution results of each rack obtained by the NSGA-III-DE optimization method used in the invention, and by combining with NSGA-III algorithm optimization results, comparison analysis is carried out, the rough rolling area is shown in table 5-1, and the finish rolling area is shown in table 5-2. And combining the data in the table to obtain each objective function value for comparison.
TABLE 5-1 load distribution results for each pass-roughing zone
TABLE 5-2 load distribution results for each frame-finish rolling zone
The sum of rolling power of NSGA-III-DE optimization results is as follows: 8404kW, the sum of the relative convexity differences is: 1.382, the deviation of the rolled grain size from the target size was 1.695 μm.
The sum of rolling power of NSGA-III optimization results is as follows: 8450kW, the sum of the relative convexity differences is: 1.580, the deviation of the rolled grain size from the target size was 2.187 μm.
The sum of rolling power of the field data is: 8717kW, the sum of the relative convexity differences is: 1.690 the deviation of the grain size after rolling from the target size was 2.439. Mu.m.
Therefore, the load distribution result obtained by optimizing the method is better than the field data in the aspects of rolling power objective function, three-dimensional size objective function and internal performance objective function, and the effectiveness of the method is proved.
And (3) carrying out load distribution optimization on each frame/pass through an NSGA-III-DE algorithm, and establishing a hot continuous rolling full-flow optimization model by taking the minimum power, good plate shape and minimum final rolling grain size deviation as three objective functions. Compared with the original rolling data, the total flow load distribution process of the hot continuous rolling mill reduces the sum of rolling power, the sum of relative convexity difference and the grain size deviation after rolling by 3.59%, 18.2% and 30.5%, which shows that the rolling power objective function, the three-dimensional size objective function and the internal performance objective function of the optimized result are all better than the original rolling result, and the purpose of shape integrated control can be achieved.
The foregoing description is only of the preferred embodiments of the present disclosure and description of the principles of the technology being employed. It will be appreciated by those skilled in the art that the scope of the invention in the embodiments of the present disclosure is not limited to the specific combination of the above technical features, but encompasses other technical features formed by any combination of the above technical features or their equivalents without departing from the spirit of the invention. Such as the above-described features, are mutually substituted with (but not limited to) the features having similar functions disclosed in the embodiments of the present disclosure.
Claims (3)
1. The rolling load distribution optimization design method based on the shape integrated control is characterized by comprising the following steps of:
step 1: determining PDI data, rolling line basic parameters and rolling data in a production plan;
the PDI data comprise steel types, slab sizes and finished product specifications; wherein the steel grade includes: name and chemical composition, slab dimensions include: slab length, width and thickness, finished product specifications include: width and thickness of the finished product;
the basic parameters of the rolling line comprise the number of rough rolling passes and finish rolling frames, the distance between the frames and the diameter of the roller;
step 2: determining process constraints and equipment constraints of the rolling process;
the process constraints include:
bite angle constraint:the method comprises the steps of carrying out a first treatment on the surface of the Wherein the biting condition is a biting angle +.>Representation, deltahFor depression amount->For friction angle>For friction coefficient>Is the radius of the roller;
reduction of each pass of rough rolling or each frame of finish rollingIs limited in a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a frame->Maximum rolling reduction of (2);
temperature condition constraints: finish rolling inlet temperature according to production process requirementsFinal rolling of final standTemperature->Within a certain range: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->The minimum finish rolling inlet temperature, the maximum finish rolling inlet temperature, +.>And->The final rolling temperature of the minimum final stand and the final rolling temperature of the maximum final stand are respectively;
the device constraints include:
rolling force limitation: for the frameRolling force->Less than the maximum allowable rolling force: />；
Wherein,is the maximum allowable rolling force;
motor power limit: for the frameCorresponding motor device, motor power->Should be less than the maximum allowable motor power:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Maximum allowable motor power;
step 3: determining multiple objective function decision variables;
in step 3, the outlet thickness of each frame for rough rolling each pass and finish rolling each passAs a decision variable; wherein (1)>For the total number of passes>The outlet thickness of the n-th pass;
step 4: respectively establishing a rolling power objective function, a three-dimensional size objective function and an internal performance objective function;
the step 4 comprises the following steps:
step 4.1: the rolling power objective function is established, and the rolling power summation of each pass of rough rolling and each stand of finish rolling is used for representing the rolling piece:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a rolling power objective function; />The total number of passes;the function relation between the decision variable and the rolling power is adopted;
step 4.2: establishing a three-dimensional size objective function using the rolled piece expressed by the sum of the relative convexity differences of each pass of rough rolling or each stand of finish rolling:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is a three-dimensional size objective function; />The relative convexity of each frame is for rough rolling each pass or finish rolling; />Is the relative convexity of the target; />A functional relationship between the decision variable and the relative convexity difference;
step 4.3: establishing an internal performance objective function expressed by deviations of the average grain size of the rolled piece from the target size:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is an internal performance objective function; />The average grain size after rolling is +.>；/>The unit is +.about.>；/>Is a functional relationship between decision variables and grain size;
step 5: solving a rolling power objective function, a three-dimensional size objective function and an internal performance objective function by using an NSGA-III-DE algorithm to obtain an optimized objective function value;
step 6: and selecting an optimal solution of the rolling power objective function, the three-dimensional size objective function and the internal performance objective function, and obtaining a corresponding load distribution result.
2. The optimization design method for rolling load distribution based on shape integrated control according to claim 1, wherein the step 5 comprises the following steps:
step 5.1: initializing a population;
step 5.1.1: determining decision variables: outlet thickness of each pass of rough rolling or each frame of finish rolling；
Step 5.1.2: setting upper and lower limits of decision variables based on outlet thickness of each pass to enable iteration times to be setObtaining the first generation of the powder with the size ofNPIs a parent population of (a);
step 5.2: generating population sizes ofNPAnd combining the parent and offspring to obtain a size of 2NPIs a new population of (a);
step 5.3: selecting a previous selection from a new population by a selection mechanism of reference pointsNPIndividual members of the new offspring；
Step 5.3.1: generating a reference point:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the number of reference points,for the target dimension +.>And->Dividing the boundary layer and the inner layer respectively;
step 5.3.2: self-adaptive standardization of population;
step 5.3.2.1: determining ideal points;
step 5.3.2.1.1: selecting a minimum value of an objective function in a current populationConstructing ideal points;
step 5.3.2.1.2: translating the population to make the ideal point as the origin:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Andrespectively the objective function values before and after translation;
step 5.3.2.2: calculating extreme points:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the extreme point after deformation, < >>A unit direction vector of the coordinate axis;
step 5.3.2.3: constructing a hyperplane consisting of ideal points and extreme points;
step 5.3.3: associating individuals in the population with reference points, respectively;
step 5.3.4: selecting a reserved individual according to the association degree of the reference points;
step 5.4: will beAs a new parent population +.>The operator replaces the mutation and crossover process of NSGA-III algorithm to generate a new generation of offspring population and mixes the parent and offspring population;
step 5.4.1: variation operation, generation and base vectorVariant individuals corresponding to one by one->：The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For scaling factor +.>And->Is different from +.>Is a subject of (2);
step 5.4.2: cross operation fromAnd->Cross-generating new individuals->：/>The method comprises the steps of carrying out a first treatment on the surface of the Wherein,for crossover probability->Is a random number;
step 5.4.3: selecting, namely, base vectors in a populationIndividuals obtained by crossing->And comparing the quality to select the next generation population: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->Individual->And->A corresponding fitness function;
step 5.5: repeating steps 5.3 to 5.4, and allowingUntil the number of iterations +>Up to the maximum number of iterations。
3. The optimization design method for rolling load distribution based on shape integrated control according to claim 1, wherein the step 6 comprises the following steps:
step 6.1: performing satisfaction sequencing to obtain an optimal objective function value:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Satisfaction for the objective function; />Is->Mean value of the individual objective function solutions, +.>Is->Standard deviation of individual objective function solutions +.>Is->Weight coefficients of the objective function solutions;
step 6.2: substituting the value of the decision variable corresponding to the selected optimal solution, namely the optimal objective function value, into the step 4 to obtain a rolling load distribution result comprising the thickness, rolling force, power, temperature, convexity and average grain size of each pass of rough rolling and each stand outlet of finish rolling.
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