CN105808848A - Method for processing discrete standard optimization design variable - Google Patents

Abstract

The invention discloses a method for processing discrete standard optimization design variable for mechanical structure optimization design. The method comprises following steps of 1, assuming that there is a design variable x and an optimization variable y, wherein xi stands for the ith value of the design variable x, and xij stands for the jth value of the optimization variable y corresponding to the xi; 2, assuming that there is an interval [0,s]; equally dividing the interval [0,s] into s subintervals interval [0,1 ), [1,2 ), [2,3 ),..., [s-1,s], wherein each subinterval is equipped with a corresponding value of the optimization variable y; 3, generating a random number rand; determining the subinterval in which the random number falls, wherein if the rand falls in the subinterval [s-1,s], the xij value in the subinterval [s-1,s] is the value of the optimization variable y. According to the method, the verification processes in the prior art are reduced, the optimization efficiency is improved, and the relevance problem of the discrete standard design variable is solved.

Description

A Method for Dealing with Discrete Standardized Optimal Design Variables

technical field

The invention relates to the technical field of structural optimization design, in particular to a method for processing discrete standardized design variables, which is used in the optimal design of mechanical structures.

Background technique

In structural optimization design, the optimization problem of discrete variables is often encountered. If the design variables are not correlated, only the discrete values need to be input when defining the optimal design variables; if the design variables are correlated, the correlation between variables should also be considered sex. At present, structural analysis generally requires finite element analysis software, and the real constants of the elements need to be input when establishing a parametric model. For example, when the structural finite element software ANSYS uses the pipe element Pipe16 for mesh division, it needs to input two real constants of the pipe element, namely The outer diameter and wall thickness of the pipe unit; when optimizing the size of the structure, the outer diameter and wall thickness become design variables, and there is correlation between these two variables, the reason is that the steel pipe size is standardized, the same outer diameter Diameters may correspond to different wall thicknesses. If the correlation between outer diameter and wall thickness is not considered when defining the optimal design variables, and the discrete values of outer diameter and wall thickness are directly input, many erroneous solutions will be generated. For example, there are five options for the outer diameter of the main chord: 57mm, 65mm, 76mm, 85mm, and 95mm, and four options for the wall thickness: 4mm, 5mm, 5.5mm, and 6.5mm. After optimization, the optimal solution is 85mm for the outer diameter and 5mm for the wall thickness. , but the optimization result does not match the size of the existing steel pipe, there is no corresponding steel pipe, and the optimal solution is not within the value range of the design variable, so it is an incorrect solution. Obviously, with the increase in the number of outer diameters and wall thicknesses of steel pipes, the probability of optimizing the outer diameters and wall thicknesses by using this processing method and satisfying the corresponding relationship will be greatly reduced, resulting in low optimization efficiency, increased optimization iteration time, and even The optimal solution may not be obtained.

The current solution to this situation is to treat the design variable as a continuous variable, round the optimal solution after the optimization, or take the standardized value near the optimal solution as the optimization result, and then check whether the optimization result satisfies the constraint conditions ; but this approach needs to add an additional verification process. If there are many design variables and the rounded optimization result does not meet the constraint conditions, it needs to be re-optimized or re-rounded, resulting in lower optimization efficiency, and at the same time, the optimization cannot be guaranteed. The result is the optimal solution.

Contents of the invention

In order to overcome the defects in the prior art, the purpose of the present invention is to provide a method for dealing with discrete standardized design variables, which reduces the verification process in the prior art and improves optimization efficiency.

In order to achieve the above object, the present invention adopts the following technical solutions.

A method for processing discrete standardized optimization design variables, characterized in that it comprises the following steps:

Step 1, assuming that there is a design variable x and an optimization variable y, x _i represents the i-th value of the design variable x, x _ij represents the j-th value of the optimization variable y corresponding to the x _i , i and j are natural numbers respectively;

Step 2, set an interval [0, s], wherein, s is the number of values of the design variable x corresponding to the optimization variable y, and then divide the interval [0, s] into s subintervals [0, 1), [ 1, 2), [2, 3), ..., [s-1, s], and each sub-interval has an optimization variable y value corresponding to the sub-interval;

Step 3, generate a random number rand, determine the subinterval that the random number rand falls into, if the random number rand falls into the subinterval [s-1, s], then x _ij in the subinterval [s-1, s] The value is the value of the optimization variable y.

The random number rand is uniformly distributed on the interval [0, s].

Compared with the prior art, the beneficial effect of the present invention is that the method for dealing with discrete standardized design variables in the present invention is determined by random selection in each iterative optimization, without rounding the optimization result or taking the value near the optimal solution. The standardized value is the optimization result, and then the optimization result is tested. This method reduces the verification process, improves the optimization efficiency, and solves the correlation problem of discrete standardized design variables.

detailed description

The present invention will be described in further detail below in conjunction with specific examples, but the following examples are not intended to limit the protection scope of the present invention.

Table 1

Shown with reference to table 1, table 1 is the value list of the discrete design variable of the present embodiment, namely the outer diameter and wall thickness data of the main chord, and the outer diameter and wall thickness are standardized steel pipes, and the outer diameter is represented by x, The wall thickness is represented by y, x _i represents the value of the outer diameter x, and x _ij represents the value of the wall thickness y. The wall thickness corresponding to each outer diameter is not exactly the same, and there are single values and multiple values.

There is an interval [0, s], s is the number of values of the wall thickness y corresponding to the outer diameter x;

Divide the interval [0, s] into s subintervals [0, 1), [1, 2), [2, 3), ..., [s-1, s], where each subinterval has and only There is a value corresponding to the value x _ij of the wall thickness y;

Assume a random number rand, random number rand∈[0, s], select the value of wall thickness y from the subinterval [s-1, s] where the random number rand is located.

After the optimization method determines the value x _i of the outer diameter x of the main chord, if the value x _ij of the corresponding wall thickness y is a value (i.e. s=1), then the wall thickness y is the value; if the value x _ij of the wall thickness y corresponding to the value x _i of the outer diameter x has multiple values (that is, s > 1), the random positioning method can be used to determine the value of x _ij during each iterative optimization value.

The specific operation method is as follows:

(1) When i=1, the value x _i of the outer diameter x of the main chord is 57mm, and there is only one value x _ij of the corresponding wall thickness y, that is, s=1, then the wall thickness The value x _ij of y is 4mm.

(2) When i=2, the value x _i of the outer diameter x of the main chord is 65mm, and there is only one value x _ij of the corresponding wall thickness y, that is, s=1, then the wall thickness The value x _ij of y is 4mm.

(3) When i=3, the value x _i of the outer diameter x of the main chord is 76 mm, and there are three values x _ij of the corresponding wall thickness y, so the value x _ij of the wall thickness y can be The values are 4mm, 5.5mm, and 6.5mm, that is, s=3.

Now, if an interval [0,3] is set, then the sub-intervals are [0,1), [1,2) and [2,3];

Assume that a random number rand is generated, and the random number rand obeys the uniform distribution on the interval [0, s]. When the random number rand falls within the interval [0, 1), the value x _ij of the wall thickness y is 4mm; if When the random number rand falls within the interval [1, 2), the value x _ij of the wall thickness y is 5.5 mm; if the random number rand falls within the interval [2, 3], then the value x ij of the wall thickness y _ij is 6.5mm;

It may be advisable to set the random number rand=1.234, then the random number rand falls within the interval [1, 2), so this iteration x _ij takes 5.5mm for optimization.

(4) When i=4, the value x _i of the outer diameter x of the main chord is 85mm, and there is only one value x _ij of the corresponding wall thickness y, that is, s=1, then the wall thickness The value of x _ij is 4mm.

(5) When i=5, the value x _i of the outer diameter x of the main chord is 95mm, and there are two values x _ij of the corresponding wall thickness y, then the value x _ij of the wall thickness y is Possible values are 4mm and 5mm, that is, s=2.

At this time, if there is an interval [0, 2], then the sub-intervals are [0, 1), [1, 2];

Assume that a random number rand is generated, and the random number rand obeys the uniform distribution on the interval [0, s]. When the random number rand falls within the interval [0, 1), the value x _ij of the wall thickness y is 4mm; if When the random number rand falls within the interval [1, 2], the value x _ij of the wall thickness y is 5mm;

It may be advisable to set the random number rand=1.234, then the random number rand falls within the interval [1, 2], so this iteration x _ij takes 5 mm for optimization.

This processing method can ensure that the value x _ij of the wall thickness y will not exceed its value range, and ensure the corresponding relationship between the outer diameter of the steel pipe and the wall thickness.

Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and equivalent technologies thereof, the present invention also intends to include these modifications and variations.

Claims (2)

1. A method for processing discrete standardized optimization design variables, characterized in that, comprising the following steps: Step 1, assuming that there is a design variable x and an optimization variable y, x _i represents the i-th value of the design variable x, x _ij represents the j-th value of the optimization variable y corresponding to the x _i , i and j are natural numbers respectively; Step 2, set an interval [0, s], where s is the number of values of the design variable x corresponding to the optimization variable y, and then divide the interval [0, s] into s sub-intervals [0, 1), [ 1,2),[2,3),...,[s-1,s], and each sub-interval has an optimization variable y value corresponding to the sub-interval; Step 3, generate a random number rand, determine the subinterval that the random number rand falls into, if the random number rand falls into the subinterval [s-1, s], then x _ij in the subinterval [s-1, s] The value is the value of the optimization variable y. 2. The method for processing discrete standardized optimization design variables according to claim 1, wherein the random number rand is uniformly distributed on the interval [0, s].