A method for solving inverse design points in turbine blade fatigue life reliability design

Abstract

This invention provides a method for solving the inverse design point in the fatigue life reliability design of turbine blades, comprising: 1) standardizing the input variables of the turbine blade fatigue life reliability design under given design parameters; 2) determining a hyperspherical sampling domain centered at the origin and with the target reliability index as the radius within the standard normal space; 3) generating a candidate sample pool for solving the inverse design point within the determined hyperspherical sampling domain; 4) constructing a coarse Kriging model by extracting a small number of training sample points from the candidate sample pool; 5) selecting new training sample points from the candidate sample pool and updating the Kriging model according to the steepest extremum search learning function until the Kriging model converges; 6) using the converged Kriging model to solve the inverse design point in the fatigue life reliability design of turbine blades, thereby quickly evaluating whether the fatigue life reliability constraints of turbine blades are satisfied, which helps to efficiently optimize the reliability design of turbine blades and improve efficiency.

Description

Technical Field

[0001] This invention belongs to the field of reliability design technology, and in particular relates to a method for solving the inverse design point in the reliability design of turbine blade fatigue life. Background Technology

[0002] Solving for the inverse design point is a crucial step in functional measurement methods and sequence-like decoupling methods for reliability optimization design. Turbine blades have complex structures and are subjected to complex loads; gradient-based methods for solving the inverse design point are prone to local convergence, while simulation methods require a large sample size and are extremely time-consuming. Therefore, a high-precision and efficient method for solving the inverse design point of turbine blade structures is currently lacking. Summary of the Invention

[0003] The purpose of this invention is to provide a method for solving the inverse design point in the fatigue life reliability design of turbine blades, characterized by the following steps:

[0004] S1: Standardize the input variables for the reliability design of turbine blade fatigue life under given design parameters;

[0005] S2: Within the standard normal space, determine the hyperspherical sampling domain centered at the origin and with the target reliability index as the radius;

[0006] S3: Generate a pool of candidate samples for solving the inverse design point within the hyperspherical sampling domain;

[0007] S4: Extract training sample points from the candidate sample pool and establish an initial training sample set. Use the initial training sample set to construct a coarse Kriging model.

[0008] S5: Select new training sample points from the candidate sample pool according to the fastest extremum search learning function, add the new training sample points to the training sample set, and then update the Kriging model with the new training sample set. Repeat this step until the coarse Kriging model converges.

[0009] S6: Use the convergent Kriging model to solve for the inverse design point in the fatigue life reliability design of turbine blades.

[0010] Furthermore, in S1, the input variables are x = {x1, x2, ... x}. n}, where n is the dimension of the input variables; after standard normalization of the input variables, we obtain the standard normal input variables u={u1,u2,...u n The corresponding fatigue life effective function is expressed as: y = g(u).

[0011] Furthermore, in S2, the hyperspherical sampling domain is centered at the origin O, and the target reliability β T Let be the radius, expressed as:

[0012]

[0013] Furthermore, in S3, the candidate sample pool is represented as: S u ={u1,u2,...u N} T , where N is the size of the sample pool.

[0014] Furthermore, in S5, the SES learning function is used to select new training sample points, which can be expressed by the formula:

[0015]

[0016] in, For the training sample set T u The minimum value of the function. and Kriging model The predicted values ​​and the standard deviation of the predictions; Φ and Φ(·) are the probability density function and cumulative distribution function of the standard normal distribution, respectively.

[0017] Furthermore, the new training sample points are denoted as u. u , is represented as:

[0018] Furthermore, the Kriging model The convergence condition is the sample pool S. u The probability of all strictly non-misjudgmentable minimum values ​​is less than 2.28%, expressed as:

[0019]

[0020] Furthermore, in S6, the converged Kriging model is used. Solving for the inverse design point u in the reliability design of turbine blade fatigue life IMPP , is represented as:

[0021] Furthermore, based on the corresponding fatigue life effective function, the corresponding function value is obtained and compared. When the function value is greater than or equal to 0, it is determined that the turbine blade structure meets the reliability constraints, so there is no need to perform reliability optimization design on the turbine blade structure; when the function value is less than 0, it is determined that the turbine blade structure does not meet the reliability constraints, so reliability optimization design on the turbine blade structure is required.

[0022] Compared with the prior art, the beneficial effects of the present invention are mainly reflected in the following: The present invention discloses a method for solving the inverse design point in the fatigue life reliability design of turbine blades, thereby quickly evaluating whether the fatigue life reliability constraints of turbine blades are met, which helps to efficiently optimize the reliability design of turbine blades and improve the efficiency of existing reliability optimization design methods. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the method for solving the inverse design point in the reliability design of turbine blade fatigue life according to the present invention.

[0024] Figure 2 This is a schematic diagram of the turbine blade used in an embodiment of the present invention. Detailed Implementation

[0025] The following will describe in more detail, with reference to the schematic diagram, a method for solving the inverse design point in the fatigue life reliability design of turbine blades according to the present invention. The diagram illustrates a preferred embodiment of the present invention. It should be understood that those skilled in the art can modify the present invention described herein while still achieving the advantageous effects of the present invention. Therefore, the following description should be understood as being widely known to those skilled in the art and is not intended to limit the present invention.

[0026] like Figure 1 As shown, a method for solving the inverse design point in the fatigue life reliability design of turbine blades includes the following six steps:

[0027] Step 1: Under given design parameters, determine the input variables x = {x1, x2, ... x} for the fatigue life reliability design of turbine blades. n Perform standard normalization (where n is the dimension of the input variables) to obtain the standard normal input variables u = {u1, u2, ... u}. n The corresponding fatigue life failure function is denoted as y = g(u);

[0028] Step 2: Within the standard normal space, determine the target reliability index β centered at the origin O. T The hyperspherical sampling domain with radius , i.e.

[0029] Step 3: Within the hyperspherical sampling domain determined in step S2, generate a candidate sample pool S for solving the inverse design point. u ={u1,u2,...u N} T , where N represents the size of the sample pool;

[0030] Step 4: In the candidate sample pool S u A small number of training sample points are extracted from the data to establish an initial training sample set T.u Using T u Constructing a coarse Kriging model

[0031] Step 5: Select new training sample points from the candidate sample pool according to the steepest extremum searching (SES) learning function shown in the formula. Add the sample point to the training sample set T u In, that is, T u =T u ∪u u Then use T u Update Kriging model Until Obtain the convergent Kriging model The process of selecting new training sample points in the candidate sample pool according to the steepest extremum search learning function shown in the equation is expressed as follows:

[0032]

[0033] Step 6: Use a convergent Kriging model Solving for the inverse design point in the reliability design of turbine blade fatigue life

[0034] The following detailed explanation, through specific examples, illustrates the method for determining the inverse design point in the reliability design of turbine blade fatigue life:

[0035] Example

[0036] In step S1, for example Figure 2 The turbine blade structure shown has four input variables: film cooling orifice radius (x1), longitudinal movement distance of the film cooling orifice (x2), elastic modulus (x3), and maximum rotational speed (x4). The distribution and parameters of each input variable are shown in Table 1. For x... i (i = 1, 2, 3, 4) are then subjected to standard normalization to obtain standard normal input variables:

[0037]

[0038]

[0039] Table 1 Distribution form and distribution parameters of the input random variables for turbine blade structure

[0040] The following functions can be created:

[0041]

[0042] Where, N f (u1,u2,u3,u4) represents the fatigue life of the turbine blade, N f =1500 represents the fatigue life threshold.

[0043] In step two, the target reliability index β is set. T =3.

[0044] In step three, the sample pool size is set to N = 10. 5 .

[0045] In step four, an initial training sample set T is established using 12 initial training sample points. u and using T u Constructing a coarse Kriging model

[0046] In step S5, by adding 8 training sample points, the converged Kriging model is obtained. at this time

[0047] In step six, a convergent Kriging model is used. The inverse design point for solving the reliability design of turbine blade fatigue life is u. IMPP ={-2.6213,0.3032,-0.1015,1.4236}, the corresponding function value is g(u IMPP ) = -0.2847. Because g(u IMPP Since the value is less than 0, the reliability constraint is not met, so the reliability optimization design of the turbine blade structure needs to be carried out.

[0048] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method for solving the inverse design point in the fatigue life reliability design of turbine blades, characterized in that, Includes the following steps: S1: Standardize the input variables for the reliability design of turbine blade fatigue life under given design parameters; S2: Within the standard normal space, determine the hyperspherical sampling domain centered at the origin and with the target reliability index as the radius; S3: Generate a pool of candidate samples for solving the inverse design point within the hyperspherical sampling domain; S4: Extract training sample points from the candidate sample pool and establish an initial training sample set. Use the initial training sample set to construct a coarse Kriging model. S5: Select new training sample points from the candidate sample pool according to the fastest extremum search learning function, add the new training sample points to the training sample set, and then update the Kriging model with the new training sample set. Repeat this step until the coarse Kriging model converges. S6: Use the convergent Kriging model to solve for the inverse design point in the fatigue life reliability design of turbine blades; In step S5, the steepest extremum search learning function is used to select new training sample points, which can be expressed by the following formula: ； in, For training sample set The minimum value of the function. and Kriging model The predicted values ​​and the standard deviation of the predictions; and These are the probability density function and cumulative distribution function of the standard normal distribution, respectively; The standard normalized input variables are obtained by standardizing the input variables. .

2. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 1, characterized in that, In S1, the input variable is ,in, Let be the dimension of the input variables; the corresponding fatigue life effective function is expressed as: .

3. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 1, characterized in that, In S2, the hyperspherical sampling domain is defined by the origin of the coordinate system. Centered on the target reliability Let be the radius, expressed as: 。 4. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 1, characterized in that, In S3, the candidate sample pool is represented as follows: ,in, This represents the size of the sample pool.

5. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 1, characterized in that, The new training sample points are denoted as , is represented as: .

6. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 5, characterized in that, The Kriging model The convergence condition is the sample pool The probability of all strictly non-misjudgmentable minimum values ​​is less than 2.28%, expressed as: 。 7. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 1, characterized in that, In S6, the converged Kriging model is used. Solving for the inverse design point in the reliability design of turbine blade fatigue life , is represented as: .

8. The method for solving the inverse design point in the fatigue life reliability design of turbine blades according to claim 7, characterized in that, Based on the corresponding fatigue life effective function, the corresponding function value is obtained and compared. When the function value is greater than or equal to 0, it is determined that the turbine blade structure meets the reliability constraints, so there is no need to perform reliability optimization design on the turbine blade structure; when the function value is less than 0, it is determined that the turbine blade structure does not meet the reliability constraints, so reliability optimization design on the turbine blade structure is required.

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