CN107391809A - A kind of method of key parameter in equilibrium assignment industrial products - Google Patents
A kind of method of key parameter in equilibrium assignment industrial products Download PDFInfo
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- CN107391809A CN107391809A CN201710524184.5A CN201710524184A CN107391809A CN 107391809 A CN107391809 A CN 107391809A CN 201710524184 A CN201710524184 A CN 201710524184A CN 107391809 A CN107391809 A CN 107391809A
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Abstract
The present invention relates to product simulation design field, the method for key parameter in more particularly to a kind of equilibrium assignment industrial products.Including following preparation process：Including following preparation process：（1）Key parameter is represented with the form of form；（2）Form is converted into P matrixes；（3）The characteristic value of each species is represented with constant column matrix X；（4）P matrixes are multiplied with X matrix, are expressed as Metzler matrix；（5）Metzler matrix optimal solution is solved, the data volume of optimal solution is judged, performs step（6）Or step（7）；（6）Optimal solution set is solved, the standard deviation of the optimal solution set is solved according to optimal solution set, it is last solution to take the minimum optimal solution of optimal solution set internal standard difference；（7）Optimal case is selected with scatter diagram.The present invention is mainly used to solve by limited resource allocation into different objects, event, and obtains the practical problem of target.
Description
(I) technical field
The invention relates to the technical field of product simulation design, in particular to a method for balancing key parameters in industrial products.
(II) background of the invention
With the development trend of diversification of the industry in the future, a plurality of diversified industrial designs which are suitable for market demands will be generated, and how to enable the performances of machinery, load and the like to meet the requirements of multiple aspects is a common problem faced by people. An efficient scheduling assignment method is more desirable. Although there are many domestic and foreign documents on algorithm research relating to allocation problems, most of the domestic and foreign documents are not suitable for allocation problems actually encountered in industrial design, and few methods are not suitable for the allocation problems, but the algorithm is not targeted and the calculation efficiency is also influenced.
Disclosure of the invention
The invention provides a method for balancing and distributing key parameters in industrial products in order to make up for the defects of the prior art.
The invention is realized by the following technical scheme:
a method for evenly distributing key parameters in an industrial product, comprising: the preparation method comprises the following preparation steps:
(1) sequentially listing distribution parameters of products to be distributed, then determining key parameters needing to solve problems from the distribution parameters, and expressing the key parameters in a form of a table;
(2) converting the table in the step (1) into a matrix form, wherein the matrix is represented by P;
(3) expressing the characteristic value of each kind by a constant column matrix X; the characteristic value can be a characteristic parameter with a specific value such as volume, weight, value and the like;
(4) multiplying the P matrix by the X matrix, denoted as M matrix, where each element is denoted as Mn；
(5) Solving the optimal solution of the M matrix, judging the data volume of the optimal solution, executing the step (6) when the data volume is large, and executing the step (7) when the data volume is small;
(6) converting the problem into a multi-target mathematical model according to the M matrix and the problem to be solved, and expressing the limiting condition of the problem to be solved in a mathematical form, wherein the mathematical expression is a constraint condition of the multi-target problem; solving the optimal solution set, solving the standard deviation of the optimal solution set according to the optimal solution set, and taking the optimal solution with the minimum standard deviation in the optimal solution set as a final solution;
(7) expressing the limiting conditions of the problem to be solved in a mathematical form, listing W solution sets in the limiting conditions according to requirements, expressing the solution sets as P matrixes, and then assigning values under the limiting conditions, wherein each solution set needs to calculate the solution set according to the step four to obtain a group of m solutionsnValue of m, the set of mnThe values are represented by a scatter distribution diagram, and the optimal scheme can be directly selected.
Wherein, P matrix:。
wherein, the X matrix:。
wherein M is a matrix of。
The method can be applied to the solution of the following problems, but is not limited to the following problems: such as load distribution problems encountered in mechanical design, force distribution problems in architectural design, current distribution problems in circuit design, etc.
The invention has the beneficial effects that:
the present invention is primarily intended to solve the practical problem of distributing limited resources to different objects, events and achieving the desired goal. The method provides different path selections according to the size of the data volume, and can select a more concise and intuitive method under the condition of small data volume, so that the operation cost is saved.
(IV) description of the drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a solution set distribution diagram of the present invention.
(V) detailed description of the preferred embodiments
Example 1
For convenience of understanding, the application process of the method is demonstrated by taking the example that the weight differences of parts borne by three positions in the design of the massage chair are approximately balanced, and the specific method is as follows:
assuming that the product of the massage chair is designed with three parts, namely 5 g, 3 g and 2 g, and the number of the parts is 7, 4 and 3 respectively, the parts are expected to be placed at three positions of the massage chair, and how to place the parts can bear approximately equal weight differences.
(1) The distribution parameters of the products to be distributed are listed in sequence, then the key parameters of the problems to be solved are determined from the distribution parameters, and the key parameters are expressed in a form of a table.
The method comprises the following specific steps:
in the first position, a1 parts with 5 g are placed, b1Part of piece 3 g, c1Part 2 grams; is arranged at a second position to place a2Part of piece 5 g, b2Part of piece 3 g, c2Part 2 grams; placing a in a third position3Part of piece 5 g, b3Part of piece 3 g, c3Part 2 grams. The key parameters are tabulated as follows:
(2) converting the table into a matrix form, the matrix being denoted by P:
；
(3) the characteristic value of each category is represented by a constant column matrix X:
the characteristic value may be volume, weight, value, etc., where weight is taken as the characteristic value;
；
(4) multiplying the P matrix by the X matrix, denoted as M matrix, where each element is denoted as Mn：
Then the total weight matrix experienced by all positions is
；
Further may be expressed as:
5 a1+3 b1+2 c1=m1
5 a2+3 b2+2 c2=m2
5 a3+3 b3+2 c3=m3；
(5) and (5) if the data size is small, performing the step (7) as follows:
list a1+ a2+ a3=7，b1+ b2+ b3=4，c1+ c2+ c36 solutions under the condition of =3, and calculates m1，m2，m3A scatter plot is generated as shown in fig. 1.
F1：At this time m1=15，m2=15，m3=23
F2：At this time m1=18，m2=15，m3=20
F3：At this time m1=16，m2=17，m3=20
F4：At this time m1=16，m2=15，m3=22
F5：At this time m1=18，m2=17，m3=18
F6：At this time m1=20，m2=15，m3=18；
From the scatter plot, it is clear that F5 is the optimal solution.
For example, in order to verify the consistency of the results of the two paths, the second path is selected to solve the same case problem; step one to step four are completely the same, and step six is executed after step five is finished on the assumption that the data size is large;
step six, the multi-target mathematical model is as follows:
and (ii) in the step (min. S),
s.t. wherein, ua1+vb1+……=m1…
Further:
a1+a2+a3=7；
b1+b2+b3=4；
c1+c2+c3=3；
wherein,；
s.t, among others.
5a1+3b1+2c1=m1；
5a2+3b2+2c2=m2；
5a3+3b3+2c3=m3；
After solving, still selecting a solution set which is the same as the solution set in the first way;
F1：at this time m1=15，m2=15，m3=23，S=3.77；
F2：At this time m1=18，m2=15，m3=20，S=2.05；
F3：At this time m1=16，m2=17，m3=20，S=1.70；
F4：At this time m1=16，m2=15，m3=22，S=3.09；
F5：At this time m1=18，m2=17，m3=18，S=0.47；
F6：At this time m1=20，m2=15，m3=18，S=2.05；
From the results, it can be seen that a good solution can be selected from the non-inferior solutions according to the requirements, and in the solution set, the optimal solution is F5 which is easily found according to the S value.
It can be seen by the case that the results obtained by the two approaches are consistent. In some cases, it may happen that the S values of multiple solution sets are the same and minimum at the same time, and accordingly, such multi-objective problem has more than one optimal solution at the same time. The user of the method selects one or more protocols as desired. When the number of samples is large and a plurality of targets need to be considered simultaneously, the algorithm shows more superiority.
The present invention has been described above by way of example, but the present invention is not limited to the above-described specific embodiments, and any modification or variation made based on the present invention is within the scope of the present invention as claimed.
Claims (4)
1. A method for evenly distributing key parameters in an industrial product, comprising: the preparation method comprises the following preparation steps: (1) sequentially listing distribution parameters of products to be distributed, then determining key parameters needing to solve problems from the distribution parameters, and expressing the key parameters in a form of a table; (2) converting the table in the step (1) into a matrix form, wherein the matrix is represented by P; (3) expressing the characteristic value of each kind by a constant column matrix X; (4) multiplying the P matrix by the X matrix, denoted as M matrix, where each element is denoted as Mn(ii) a (5) Solution M matrix optimal solution, pairJudging the data quantity of the optimal solution, executing the step (6) when the data quantity is large, and executing the step (7) when the data quantity is small; (6) converting the problem into a multi-target mathematical model according to the M matrix and the problem to be solved, and expressing the limiting condition of the problem to be solved in a mathematical form, wherein the mathematical expression is a constraint condition of the multi-target problem; solving the optimal solution set, solving the standard deviation of the optimal solution set according to the optimal solution set, and taking the optimal solution with the minimum standard deviation in the optimal solution set as a final solution; (7) expressing the limiting conditions of the problem to be solved in a mathematical form, listing W solution sets in the limiting conditions according to requirements, expressing the solution sets as P matrixes, and then assigning values under the limiting conditions, wherein each solution set needs to calculate the solution set according to the step four to obtain a group of m solutionsnValue of m, the set of mnThe values are represented by a scatter distribution diagram, and the optimal scheme can be directly selected.
2. The method for balanced distribution of key parameters in industrial products according to claim 1, characterized in that: the P matrix is。
3. The method for balanced distribution of key parameters in industrial products according to claim 1, characterized in that: the X matrix is。
4. The method for balanced distribution of key parameters in industrial products according to claim 1, characterized in that: the M matrix is。
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| CN106774162A (en) * | 2016-12-06 | 2017-05-31 | 天津商业大学 | A kind of digital control processing parameter Multipurpose Optimal Method |
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| CN106774162A (en) * | 2016-12-06 | 2017-05-31 | 天津商业大学 | A kind of digital control processing parameter Multipurpose Optimal Method |
Non-Patent Citations (1)
| Title |
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| 尚树川等: "基于多目标算法的玩具产品风险监测研究", 《滨州学院学报》 * |
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