Method and device for determining natural vibration frequency

Abstract

The invention provides a method and device for determining natural vibration frequency. The method comprises the steps that a regression prediction model is established, and the regression prediction model is configured to generate one-order or multi-order natural vibration frequency according to an Euler angle; obtaining a plurality of first Euler angles, and converting each Euler angle in the plurality of first Euler angles into an orientation angle; and generating a corresponding first-order or multi-order target natural vibration frequency according to a plurality of second Euler angles in the plurality of first Euler angles and the regression prediction model, the orientation angles corresponding to the plurality of second Euler angles being located in a preset orientation angle range.

Description

Technical Field

[0001] This disclosure relates to the field of reliability analysis technology, and more specifically, to a method and apparatus for determining natural vibration frequencies. Background Technology

[0002] In engineering applications, failures caused by object vibration frequently occur. For example, when the external excitation frequency is close to or equal to the object's natural vibration frequency, resonance is easily generated, leading to structural damage and reduced service life. In practical engineering applications, there may be a significant deviation between the object's natural vibration frequency and the natural vibration frequency determined through analysis during the engineering design phase. Therefore, it is necessary to improve the analysis of the object's vibration characteristics. Summary of the Invention

[0003] One of the purposes of this disclosure is to provide a method and apparatus for determining natural vibration frequencies.

[0004] According to a first aspect of this disclosure, a method for determining natural vibration frequencies is provided, comprising:

[0005] Establish a regression prediction model, wherein the regression prediction model is configured to generate first-order or multiple-order natural vibration frequencies based on Euler angles;

[0006] Obtain the first plurality of Euler angles, and convert each Euler angle in the first plurality of Euler angles into an orientation angle; and

[0007] The first or multiple natural vibration frequencies of the target are generated based on the second or multiple Euler angles in the first or multiple Euler angles and the regression prediction model, wherein the orientation angles corresponding to the second or multiple Euler angles are within a preset orientation angle range.

[0008] In some embodiments, establishing a regression prediction model includes:

[0009] Obtain a training set, wherein the feature portion of the training set includes a third or more Euler angles, and the label portion of the training set includes one-to-one first-order or multiple-order first natural frequencies corresponding to the third or more Euler angles; and

[0010] The regression prediction model is trained based on the training set.

[0011] In some embodiments, obtaining the training set includes:

[0012] A third set of Euler angles is obtained through random sampling, wherein the Euler angles include a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1, and the first Euler angle parameter α1 of the third set of Euler angles follows a first uniform distribution within a first domain, the second Euler angle parameter β1 follows a second uniform distribution within a second domain, and the third Euler angle parameter γ1 follows a third uniform distribution within a third domain; and

[0013] For each of the third plurality of Euler angles, the finite element method is used to calculate the prestressed mode under the preset working conditions to obtain the corresponding first or multiple first natural vibration frequencies.

[0014] In some embodiments, establishing a regression prediction model further includes:

[0015] Obtain a test set, wherein the test set includes a fourth plurality of Euler angles, and at least one of the fourth plurality of Euler angles is different from the third plurality of Euler angles;

[0016] The fourth plurality of Euler angles are input into the regression prediction model to generate corresponding first-order or multi-order predicted natural vibration frequencies.

[0017] The distribution range of first-order or multi-order natural vibration frequencies is determined based on the label portion of the training set, where:

[0018] If at least one of the predicted natural vibration frequencies falls outside the corresponding distribution range, then the Euler angles corresponding to that first-order or multiple-order predicted natural vibration frequency do not meet the preset accuracy condition.

[0019] When the predicted natural vibration frequencies of the first or multiple orders are within the corresponding distribution range, determine that the Euler angles corresponding to the first or multiple predicted natural vibration frequencies meet the preset accuracy conditions.

[0020] If there are Euler angles in the test set that do not meet the preset accuracy condition, update the training set according to the Euler angles in the test set that do not meet the preset accuracy condition, and return the operation of training the regression prediction model based on the training set.

[0021] In some embodiments, obtaining the first plurality of Euler angles includes: obtaining the first plurality of Euler angles from the fourth plurality of Euler angles in the test set when all of the fourth plurality of Euler angles in the test set meet the preset accuracy condition; generating the corresponding first or multiple order target natural vibration frequency based on the second plurality of Euler angles in the first plurality of Euler angles and the regression prediction model includes: using the first or multiple order predicted natural vibration frequency corresponding to the second plurality of Euler angles as the corresponding first or multiple order target natural vibration frequency.

[0022] In some embodiments, updating the training set based on Euler angle combination samples in the test set that do not meet the preset accuracy condition includes:

[0023] Euler angles in the test set that do not meet the preset accuracy conditions are added to the training set to update the feature part of the training set.

[0024] For Euler angles that do not meet the preset accuracy conditions, the finite element method is used to calculate the prestressed modes under the preset working conditions to obtain the corresponding first-order or multiple-order second natural vibration frequencies, and the obtained first-order or multiple-order second natural vibration frequencies are added to the training set to update the label part of the training set.

[0025] In some embodiments, converting each Euler angle in the first plurality of Euler angles into an orientation angle includes:

[0026] For each Euler angle:

[0027] Based on the transformation model, the Euler angles are converted to Tetbryan angles; and

[0028] The orientation angle is generated based on the Tate Brian angle.

[0029] In some embodiments, Euler angles include a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1, and Tetbryan angles include a first Tetbryan angle parameter α2, a second Tetbryan angle parameter β2, and a third Tetbryan angle parameter γ2, wherein the transformation model is established through the following operations:

[0030] Obtain the reference coordinate system;

[0031] The reference coordinate system is rotated into a first crystal coordinate system based on the first Euler angle parameter α1, the second Euler angle parameter β1, and the third Euler angle parameter γ1.

[0032] The reference coordinate system is rotated into a second crystal coordinate system based on the first Tetbryan angle parameter α2, the second Tetbryan angle parameter β2, and the third Tetbryan angle parameter γ2.

[0033] Based on the fact that the first rotation matrix R1 between the reference coordinate system and the first crystal coordinate system and the second rotation matrix R2 between the reference coordinate system and the second crystal coordinate system are equal, the first transformation relationship of α2 with respect to α1, β1 and γ1, the second transformation relationship of β2 with respect to α1, β1 and γ1 and the third transformation relationship of γ2 with respect to α1, β1 and γ1 are determined.

[0034] In some embodiments, the first rotation matrix R1 is:

[0035] And the second rotation matrix R2 is:

[0036] In this case,

[0037] The first conversion relationship is The second transformation relationship is β2 = arcsin(-R) 13 The third transformation relationship is: Among them, R ij Let i represent the element in the i-th row and j-th column of matrix R, where R = R1 = R2, i = 1, 2 or 3, and j = 1, 2 or 3.

[0038] In some embodiments, generating an orientation angle based on the Tetbryan angle includes:

[0039] The primary and secondary crystal orientation angles are determined based on the second crystal coordinate system corresponding to the Tetbryan angle.

[0040] The primary crystal orientation angle indicates the angle between the third coordinate axis of the second crystal coordinate system and the third coordinate axis of the reference coordinate system, while the secondary crystal orientation angle indicates the angle between the intersection line between the first plane containing the first and third coordinate axes of the second crystal coordinate system and the second plane containing the first and second coordinate axes of the reference coordinate system and the first axis of the reference coordinate system.

[0041] In some embodiments, the orientation angles within the preset orientation angle range satisfy the following: the primary crystal orientation angle is less than 15 degrees, and the secondary crystal orientation angle is 0 to 5 degrees, 5 to 10 degrees, 10 to 15 degrees, or 15 to 20 degrees.

[0042] In some embodiments, the method further includes:

[0043] The analysis parameters are determined based on the first-order or multi-order target natural vibration frequencies, wherein the analysis parameters include at least one of the minimum, maximum, mean, and standard deviation of each order of target natural vibration frequencies.

[0044] According to a second aspect of this disclosure, an apparatus for determining a natural vibration frequency is provided, comprising:

[0045] Processor; and

[0046] A memory storing instructions that, when executed by the processor, implement the method for determining the natural vibration frequency as described above.

[0047] According to a third aspect of this disclosure, a non-transitory computer-readable storage medium is provided, wherein instructions are stored on the non-transitory computer-readable storage medium, which, when executed by a processor, implement the operation of the method for determining an inherent vibration frequency as described above.

[0048] According to a fourth aspect of this disclosure, a computer program product is provided, including instructions that, when executed by a processor, implement the operation of the method for determining an inherent vibration frequency as described above.

[0049] Other features and advantages of this disclosure will become clearer from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0050] The accompanying drawings, which form part of this specification, illustrate embodiments of this disclosure and, together with the specification, serve to explain the principles of this disclosure.

[0051] This disclosure will become clearer with reference to the accompanying drawings and the following detailed description, wherein:

[0052] Figure 1 A flowchart illustrating a method for determining a natural vibration frequency according to an exemplary embodiment of the present disclosure is shown.

[0053] Figure 2 A schematic diagram of the process for establishing a regression prediction model according to an exemplary embodiment of the present disclosure is shown;

[0054] Figure 3 A schematic diagram of Euler angles according to a specific example of this disclosure is shown;

[0055] Figure 4 A schematic diagram of Tate Blaine's Corner, according to a specific example of this disclosure, is shown;

[0056] Figure 5 A schematic diagram of a process for establishing a conversion model according to an exemplary embodiment of the present disclosure is shown;

[0057] Figure 6 A projection diagram of crystal orientation determined by Laue method according to a specific example of this disclosure is shown;

[0058] Figure 7 A block diagram of an apparatus for determining an inherent vibration frequency according to an exemplary embodiment of the present disclosure is shown.

[0059] Note that in the embodiments described below, the same reference numerals are sometimes used across different figures to denote the same parts or parts having the same function, and repeated descriptions are omitted. In this specification, similar reference numerals and letters are used to denote similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0060] For ease of understanding, the positions, dimensions, and extents of the structures shown in the accompanying drawings and other materials may not represent actual positions, dimensions, and extents. Therefore, the disclosed invention is not limited to the positions, dimensions, and extents disclosed in the accompanying drawings and other materials. Furthermore, the drawings are not necessarily drawn to scale, and some features may be enlarged to show details of specific components. Detailed Implementation

[0061] Various exemplary embodiments of the present disclosure will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present disclosure.

[0062] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this disclosure or its application or use. Those skilled in the art will understand that they merely illustrate exemplary ways that can be used to implement this disclosure, and are not exhaustive.

[0063] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0064] In some engineering applications, resonance can often lead to structural damage and reduced service life of objects, thus placing higher demands on the reliability analysis of these objects. For example, in the field of aero-engines, turbine blades often experience unintended failures due to vibration. This is partly due to imperfections in the design of turbine blades during the design phase and insufficient experimental verification, and partly due to the large number of parameters affecting the natural vibration frequency of turbine blades, the large dispersion of the natural vibration frequency, and the complex variation of its patterns.

[0065] In practical engineering applications, the values ​​of parameters affecting the natural vibration frequency of an object are not necessarily equal to the design values ​​given during the engineering design phase. This can lead to a significant deviation between the actual natural vibration frequency and the natural vibration frequency determined during the engineering design phase. Taking turbine blades as an example, some vibration characteristic analysis methods can analyze multiple operating modes of the turbine blade, calculate the variation curves of each natural vibration frequency at different speeds, and obtain the resonance margin of the blade by combining it with Campbell's diagram. When the obtained resonance margin is greater than a preset threshold, the turbine blade can be considered to have no resonance risk. However, in practical engineering applications, the natural vibration frequency of a turbine blade is affected by multiple parameters, and the values ​​of these parameters are not necessarily exactly equal to the design values. Under the combined influence of multiple parameters, the deviation between the natural vibration frequency of the object and the natural vibration frequency analyzed during the engineering design phase can be large, causing blades that were previously considered to have no resonance risk to still resonate, or even break.

[0066] Parameters affecting the natural vibration frequency of an object include, for example, elastic modulus, orientation angle, structural dimensions, rotational speed, and aerodynamic excitation. Among these parameters, the orientation angle has a significant impact on the natural vibration frequency, especially for objects made of single-crystal materials. Furthermore, single-crystal materials are anisotropic; the elastic modulus, Poisson's ratio, and other parameters differ depending on the crystal orientation, thus affecting the object's natural vibration frequency. For single-crystal turbine blades, due to limitations in crystal orientation detection and control methods in practical engineering, the crystal coordinate system corresponding to the same orientation angle is not unique. This means that the same orientation angle may correspond to different crystal planes or orientations, resulting in different parameters (such as elastic modulus and Poisson's ratio). Consequently, the natural vibration frequency of the turbine blade at the same orientation angle may differ and fluctuate within a certain range; that is, the natural vibration frequency of the turbine blade at the same orientation angle exhibits dispersion. In engineering applications, it is often difficult to determine the dispersion of the natural vibration frequency of an object.

[0067] To address the aforementioned issues, this disclosure provides a method for determining natural vibration frequencies. By inputting the Euler angles corresponding to orientation angles within a preset orientation angle range into a regression prediction model, first-order or multi-order target natural vibration frequencies are obtained. This method considers the influence of orientation angles on natural vibration frequencies and obtains a more accurate variation law of the object's natural vibration frequencies, enabling the analysis of the dispersion of natural vibration frequencies caused by deviations in object orientation. This allows for a better analysis of the object's reliability.

[0068] like Figure 1 As shown, in an exemplary embodiment of this disclosure, a method for determining the natural vibration frequency may include:

[0069] Step S110: Establish a regression prediction model.

[0070] The regression prediction model can be configured to generate first-order or multiple-order natural vibration frequencies based on Euler angles. In some embodiments, the regression prediction model may include a neural network-based regression model, a Kriging model, and an SVR model.

[0071] like Figure 2 As shown, in an exemplary embodiment of this disclosure, establishing a regression prediction model may include:

[0072] Step S210: Obtain the training set;

[0073] Step S220: Train the regression prediction model based on the training set.

[0074] The training set may include a feature portion and a label portion. In some embodiments, the feature portion of the training set may include multiple Euler angles (hereinafter referred to as the multiple Euler angles in the feature portion of the training set). In a specific example, the Euler angles may include a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1. For example, Euler angles may include nutation angle, precession angle (i.e., rotation angle), and rotation angle.

[0075] Euler angles can indicate the orientation of one coordinate system relative to another. In some embodiments, a coordinate system can be rotated three times in sequence based on a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1 to form another coordinate system. In a specific example, such as Figure 3 As shown, coordinate system Oxyz is rotated sequentially around the z-axis, x-axis, and z-axis by the first Euler angle parameter α1, the second Euler angle parameter β1, and the third Euler angle parameter γ1 to form coordinate system OXYZ. Each rotation is performed around the corresponding coordinate axis of the previously obtained coordinate system. For example, after coordinate system Oxyz is rotated around the z-axis by the first Euler angle parameter α1 to obtain an intermediate coordinate system, the next rotation will be around the x-axis of the intermediate coordinate system (i.e.,...). Figure 3 The rotation is performed around the N-axis (in the coordinate system). Euler angles based on this rotation order (rotating sequentially around the z-axis, x-axis, z-axis) can be denoted as ZXZ Euler angles. Similarly, based on different rotation orders of the coordinate axes, Euler angles can also be ZYZ Euler angles, XYX Euler angles, XZX Euler angles, YXY Euler angles, and YZY Euler angles. In this document, ZXZ Euler angles will be used as an example to describe some embodiments of this disclosure. In other embodiments, Euler angles can also be Euler angles based on any of the above rotation orders.

[0076] In some embodiments, the third plurality of Euler angles can be obtained by random sampling. In some embodiments, the first Euler angle parameter α1 of the third plurality of Euler angles can follow a first uniform distribution within a first domain, the second Euler angle parameter β1 can follow a second uniform distribution within a second domain, and the third Euler angle parameter γ1 can follow a third uniform distribution within a third domain. In a specific example, the first Euler angle parameter α1 can follow a first uniform distribution with a domain of (0, 360) (i.e., the value of α1 is greater than 0 degrees and less than 360 degrees), denoted as α1~U(0, 360). The second Euler angle parameter β1 can follow a second uniform distribution with a domain of (0, 15) (i.e., the value of β1 is greater than 0 degrees and less than 15 degrees), denoted as β1~U(0, 15). The third Euler angle parameter γ1 can follow a third uniform distribution with a domain of (0, 90) (i.e., the value of γ1 is greater than 0 degrees and less than 90 degrees), denoted as γ1~U(0, 90). By collecting a third set of Euler angles, where each Euler angle parameter conforms to a corresponding uniform distribution, it is possible to simulate the prestressed modes of the object under multiple different Euler angle conditions, thereby obtaining the range of the object's first or multiple natural vibration frequencies. In a specific example, 300 sets of Euler angles, where each Euler angle parameter conforms to a corresponding uniform distribution, can be randomly sampled as a feature portion of the training set. In some embodiments, the object can be a turbine blade, wherein the turbine blade can be a single-crystal turbine blade.

[0077] In some embodiments, the label portion of the training set may include one or more first natural vibration frequencies corresponding one-to-one with a third plurality of Euler angles. In some embodiments, for each Euler angle among the third plurality of Euler angles, the prestressed modes under a preset operating condition can be calculated using the finite element method to obtain the first or more first natural vibration frequencies corresponding to the corresponding Euler angles. In a specific example, the preset operating condition may be the approach idle condition of a turbine blade of an aero-engine, or it may be a high-temperature takeoff condition. Calculating the prestressed modes under the preset operating condition using the finite element method may include calculating the prestressed modes of the object at each Euler angle in a finite element analysis-based environment (e.g., finite element analysis software), thereby obtaining the corresponding first or more first natural vibration frequencies.

[0078] By inputting Euler angles and the corresponding first-order or multiple-order first natural vibration frequencies as training data into the regression prediction model, the regression prediction model can better simulate the relationship between Euler angles and natural vibration frequencies, so that the regression prediction model can more accurately output the corresponding first-order or multiple-order natural vibration frequencies when a specified Euler angle is input.

[0079] In some embodiments, the regression prediction model can be trained multiple times based on the training set; for example, it can be trained 20,000 times. In some embodiments, the regression prediction model can be trained multiple times until its prediction accuracy meets a preset requirement, such as the statistical index RV of the regression prediction model. 2 The mean squared error (MSE) of the regression prediction model is greater than or equal to 0.9999, and / or the mean squared error (MSE) of the regression prediction model is less than 0.01.

[0080] return Figure 2 In an exemplary embodiment of this disclosure, establishing a regression prediction model may further include:

[0081] Step S230: Obtain the test set, wherein the test set includes a fourth or more Euler angles;

[0082] Step S240: Input the fourth or more Euler angles into the regression prediction model to generate the corresponding first-order or multi-order predicted natural vibration frequencies.

[0083] In some embodiments, at least one of the fourth plurality of Euler angles differs from the third plurality of Euler angles in the training set, to ensure that the Euler angles in the test set are not completely identical to those in the training set, so as to test the regression prediction model. Specifically, two Euler angles are considered identical if all their corresponding Euler angle parameters are the same, and different if any one of their corresponding Euler angle parameters is different. For example, in one Euler angle, the first Euler angle parameter α1 is 200 degrees, the second Euler angle parameter β1 is 10 degrees, and the third Euler angle parameter γ1 is 50 degrees; in another Euler angle, the first Euler angle parameter α1 is 180 degrees, the second Euler angle parameter β1 is 10 degrees, and the third Euler angle parameter γ1 is 50 degrees, then these two Euler angles are considered different.

[0084] In some embodiments, each of the fourth plurality of Euler angles is different from any one of the third plurality of Euler angles in the training set, in order to better test the prediction accuracy of the regression prediction model.

[0085] In some embodiments, the fourth plurality of Euler angles can be obtained through random sampling. In a specific example, a fourth plurality of Euler angles can be randomly sampled, where each Euler angle parameter conforms to a corresponding uniform distribution (e.g., the first Euler angle parameter α1 ~ U(0, 360), the second Euler angle parameter β1 ~ U(0, 15), and the third Euler angle parameter γ1 ~ U(0, 90)), to test the regression prediction model. In a specific example, the number of the fourth plurality of Euler angles can be no less than 4000 to better test the prediction accuracy of the regression prediction model.

[0086] In some embodiments, the prediction accuracy of the regression prediction model for the corresponding Euler angles can be determined based on the first-order or multi-order predicted natural vibration frequencies generated by the regression prediction model to determine whether the prediction accuracy meets the preset accuracy conditions. Furthermore, the training set can be updated based on Euler angles in the test set that do not meet the prediction accuracy conditions, so that the regression prediction model can learn the relationship between Euler angles with low prediction accuracy in the test set and the corresponding preset natural vibration frequencies, thereby improving the training effect and prediction accuracy of the regression prediction model.

[0087] return Figure 2 In an exemplary embodiment of this disclosure, establishing a regression prediction model may further include:

[0088] Step S250: Determine the distribution range of first-order or multi-order natural vibration frequencies based on the label portion of the training set.

[0089] In step S260, if there are Euler angles in the test set that do not meet the preset accuracy conditions, update the training set according to the Euler angles in the test set that do not meet the preset accuracy conditions, and return to step S220.

[0090] In some embodiments, if at least one of the first or more predicted natural vibration frequencies is outside the corresponding distribution range, it can be determined that the Euler angle corresponding to the first or more predicted natural vibration frequencies does not meet a preset accuracy condition. In a specific example, for the first six predicted natural vibration frequencies corresponding to an Euler angle, if a specific order of predicted natural vibration frequency is outside the corresponding distribution range (e.g., the third-order predicted natural vibration frequency is outside the distribution range of the third-order natural vibration frequency, or the fourth-order predicted natural vibration frequency is outside the distribution range of the fourth-order natural vibration frequency), it can be determined that the Euler angle does not meet the preset accuracy requirement. In a specific example, if one or more predicted natural vibration frequencies are outside the corresponding distribution range, i.e., all predicted natural vibration frequencies are outside the corresponding distribution range, it can be determined that the Euler angle corresponding to the first or more predicted natural vibration frequencies does not meet the preset accuracy condition.

[0091] In some embodiments, when the first-order or multiple-order predicted natural vibration frequencies are within the corresponding distribution range, that is, when each order of predicted natural vibration frequencies is within the corresponding distribution range, it can be determined that the Euler angles corresponding to the first-order or multiple-order predicted natural vibration frequencies meet the preset accuracy conditions.

[0092] Therefore, updating the training set based on Euler angles that do not meet the preset accuracy conditions, and training the regression prediction model based on the updated training set, can improve the training effect of the regression prediction model and enhance its prediction accuracy.

[0093] In some embodiments, updating the training set based on Euler angle combination samples in the test set that do not meet the preset accuracy conditions may include adding the Euler angles in the test set that do not meet the preset accuracy conditions to the training set to update the feature portion of the training set. In some embodiments, updating the training set based on Euler angle combination samples in the test set that do not meet the preset accuracy conditions may include, for the Euler angles in the test set that do not meet the preset accuracy conditions, using the finite element method to calculate the prestressed modes under preset working conditions to obtain the corresponding first-order or multiple-order second natural vibration frequencies, and adding the obtained first-order or multiple-order second natural vibration frequencies to the training set to update the label portion of the training set.

[0094] return Figure 1 In an exemplary embodiment of this disclosure, the method for determining the natural vibration frequency may include:

[0095] Step S120: Obtain the first plurality of Euler angles and convert each Euler angle in the first plurality of Euler angles into an orientation angle.

[0096] Step S130: Generate the corresponding first-order or multi-order target natural vibration frequency based on the second plurality of Euler angles in the first plurality of Euler angles and the regression prediction model, wherein the orientation angle corresponding to the second plurality of Euler angles is within the preset orientation angle range.

[0097] In some embodiments, obtaining the first plurality of Euler angles may include obtaining the first plurality of Euler angles from the fourth plurality of Euler angles in the test set, provided that all fourth plurality of Euler angles in the test set meet a preset accuracy condition, thereby obtaining Euler angles with higher prediction accuracy. In a specific example, the first plurality of Euler angles may be a portion of the fourth plurality of Euler angles in the test set. In a specific example, the fourth plurality of Euler angles in the test set may be used as the first plurality of Euler angles.

[0098] In some embodiments, when the fourth plurality of Euler angles are obtained from the test set based on the first plurality of Euler angles, and when the fourth plurality of Euler angles are input into the regression prediction model based on step S240 to generate the corresponding first or multiple order predicted natural vibration frequencies, generating the corresponding first or multiple order target natural vibration frequencies based on the second plurality of Euler angles in the first plurality of Euler angles and the regression prediction model may include: taking the first or multiple order predicted natural vibration frequencies corresponding to the second plurality of Euler angles as the corresponding first or multiple order target natural vibration frequencies.

[0099] In other embodiments, the first plurality of Euler angles may be obtained by random sampling, and generating the corresponding first-order or multi-order target natural vibration frequencies based on the second plurality of Euler angles in the first plurality of Euler angles and the regression prediction model may include inputting the second plurality of Euler angles into the regression prediction model to generate the corresponding first-order or multi-order target natural vibration frequencies.

[0100] In some embodiments, each Euler angle in a plurality of Euler angles can be converted into Tet Bryan angles based on a pre-established conversion model, and then an orientation angle can be generated based on the Tet Bryan angles. The conversion model is used to convert Euler angles into Tet Bryan angles. In this way, Euler angles that are typically used in finite element analysis environments and are undetectable and uncontrollable in engineering can be converted into orientation angles that are detectable and controllable in engineering. This allows the corresponding first-order or multi-order target natural vibration frequencies to be obtained based on the Euler angles corresponding to orientation angles within a preset orientation angle range (e.g., orientation angles that meet preset acceptance criteria in engineering projects) and a regression prediction model.

[0101] In one specific example, the Tetbryan angle may include a first Tetbryan angle parameter α2, a second Tetbryan angle parameter β2, and a third Tetbryan angle parameter γ2. The Tetbryan angle can indicate the orientation of one coordinate system relative to another. In some embodiments, one coordinate system may be rotated three times sequentially based on the first Tetbryan angle parameter α2, the second Tetbryan angle β2, and the third Tetbryan angle γ2 to form another coordinate system. In one specific example, such as... Figure 4 As shown, coordinate system Oxyz (which includes the origin O, x-axis, y-axis, and z-axis) is rotated sequentially around the x-axis, y-axis, and z-axis by the first Tetbryn angle parameter α2, the second Tetbryn angle parameter β2, and the third Tetbryn angle parameter γ2, to form coordinate system OXYZ (which includes the origin O, x-axis, y-axis, and z-axis). Each rotation is performed around the corresponding coordinate axis of the coordinate system obtained from the previous rotation. For example, after coordinate system Oxyz is rotated around the x-axis by the first Tetbryn angle parameter α2 to obtain intermediate coordinate system OxNZ', the next rotation will be around the y-axis of intermediate coordinate system OxNZ' (i.e., the first Tetbryn angle parameter α2). Figure 4 Rotate around the N-axis of the coordinate system obtained from the previous rotation, and then rotate around the z-axis of the coordinate system obtained from the previous rotation (i.e., the z-axis of the coordinate system obtained from the previous rotation). Figure 4 The rotation is based on the Z-axis. The Tetbryan angle based on this rotation order (rotating sequentially around the x-axis, y-axis, z-axis) can be denoted as the XYZ Tetbryan angle. Similarly, based on different rotation orders of the coordinate axes, the Tetbryan angle can also be YZX Tetbryan angle, ZXY Tetbryan angle, XZY Tetbryan angle, ZYX Tetbryan angle, and YXZ Tetbryan angle. In this document, some embodiments of the present disclosure will be described using the XYZ Tetbryan angle as an example. In some embodiments, the Tetbryan angle can also be based on any of the above rotation orders.

[0102] like Figure 5 As shown, in an exemplary embodiment of this disclosure, establishing a conversion model may include:

[0103] Step S510: Obtain the reference coordinate system;

[0104] Step S520: Rotate the reference coordinate system to the first crystal coordinate system based on the first Euler angle parameter α1, the second Euler angle parameter β1 and the third Euler angle parameter γ1.

[0105] Step S530: Rotate the reference coordinate system to the second crystal coordinate system based on the first Tetbryan angle parameter α2, the second Tetbryan angle parameter β2 and the third Tetbryan angle parameter γ2;

[0106] Step S540: Based on the equality of the first rotation matrix R1 between the reference coordinate system and the first crystal coordinate system and the second rotation matrix R2 between the reference coordinate system and the second crystal coordinate system, determine the first transformation relationship of α2 with respect to α1, β1 and γ1, the second transformation relationship of β2 with respect to α1, β1 and γ1 and the third transformation relationship of γ2 with respect to α1, β1 and γ1.

[0107] In some embodiments, the first crystal coordinate system and the second crystal coordinate system have the same orientation relative to the reference coordinate system. In some embodiments, the first crystal coordinate system and the second crystal coordinate system may indicate the same coordinate system, that is, based on the fact that the first crystal coordinate system and the second crystal coordinate system have the same orientation relative to the reference coordinate system, the origin of the first crystal coordinate system coincides with the origin of the second crystal coordinate system.

[0108] In a specific example, the rotation matrix between the coordinate system and the reference coordinate system obtained when the reference coordinate system is rotated by 'a' degrees around the X-axis is RX(a), where

[0109] Alternatively, the rotation matrix between the coordinate system and the reference coordinate system obtained when the reference coordinate system is rotated by b degrees around the Y-axis is RY(b), where

[0110] Alternatively, when the reference coordinate system is rotated c degrees around the Z-axis, the rotation matrix between the resulting coordinate system and the reference coordinate system is RZ(c), where...

[0111] Taking Z×Z Euler angles as an example, after rotating the reference coordinate system to the first crystal coordinate system based on the first Euler angle parameter α1, the second Euler angle parameter β1, and the third Euler angle parameter γ1, the first rotation matrix R1 between the first crystal coordinate system and the reference coordinate system satisfies:

[0112] R1 = RZ(α1)·RX(β1)·RZ(γ1), where "·" denotes matrix multiplication.

[0113] Taking the Tetbryan angle as XYZ Tetbryan angle as an example, after rotating the reference coordinate system to the second crystal coordinate system based on the first Tetbryan angle parameter α2, the second Tetbryan angle parameter β2, and the third Tetbryan angle parameter γ2, the second rotation matrix R2 between the second crystal coordinate system and the reference coordinate system satisfies:

[0114] R2 = RX(α2)·RY(β2)·RZ(γ2), where "·" denotes matrix multiplication.

[0115] In some embodiments, the first rotation matrix R1 is:

[0116] And the second rotation matrix R2 is:

[0117] In this case, the first transformation relation is The second transformation relationship is β2=arcsin(-R) 13 The third transformation relationship is: Among them, R ij Let represent the element in the i-th row and j-th column of matrix R, where R = R1 = R2, i = 1, 2, or 3, and j = 1, 2, or 3. Thus, Euler angles can be converted to Tet Bryan angles using the first, second, and third transformation relations.

[0118] In some embodiments, orientation angles can be generated based on the Tetbryan angle, wherein the orientation angles may include a primary crystal orientation angle θ and a secondary crystal orientation angle τ. In a specific example, the primary crystal orientation angle, secondary crystal orientation angle θ, and secondary crystal orientation angle τ can be determined based on the second crystal coordinate system corresponding to the Tetbryan angle, wherein the second crystal coordinate system corresponding to the Tetbryan angle is a second crystal coordinate system obtained by rotating the reference coordinate system based on the first Tetbryan angle parameter α2, the second Tetbryan angle parameter β2, and the third Tetbryan angle parameter γ2. The primary crystal orientation angle θ can indicate the angle between the third coordinate axis of the second crystal coordinate system and the third coordinate axis of the reference coordinate system, and the secondary crystal orientation angle τ can indicate the angle between the intersection line between the first plane containing the first and third coordinate axes of the second crystal coordinate system and the second plane containing the first and second coordinate axes of the reference coordinate system and the first coordinate axis of the reference coordinate system. Figure 4 Taking the specific example shown, the reference coordinate system is Oxyz and the second crystal coordinate system is OXYZ. The primary crystal orientation angle θ can indicate the angle between the Z-axis and the z-axis, and the secondary crystal orientation angle τ can indicate the angle between the intersection line between the first plane formed by the X-axis and the Z-axis and the second plane formed by the x-axis and the y-axis and the x-axis. Figure 6A projection diagram of crystal orientation determined by the Laue method according to a specific example of this disclosure is shown. Figure 6

[001] in the figure indicates the third coordinate axis of the crystal coordinate system (e.g., Figure 4 The Z-axis of the coordinate system OXYZ shown.

[0119] In a specific example, the mathematical expressions for the primary crystal orientation angle θ and the secondary crystal orientation angle τ can be expressed as:

[0120]

[0121]

[0122] In this way, Euler angles can be converted to Tet Bryan angles, and then orientation angles can be generated based on the Tet Bryan angles. This transforms Euler angles, which are undetectable and uncontrollable in engineering, into orientation angles that are detectable and controllable in engineering. This allows for the analysis of the first or more natural vibration frequencies corresponding to orientation angles within a preset orientation angle range (e.g., orientation angles that meet preset acceptance criteria in engineering). In a specific example, X-ray diffraction can be used to detect the orientation angles of an object in engineering applications.

[0123] In some embodiments, the preset orientation angle range may be determined based on preset qualification conditions that meet engineering acceptance standards. In a specific example, the orientation angles within the preset orientation angle range satisfy that the primary crystal orientation angle θ is less than 15 degrees and the secondary crystal orientation angle τ is around 10 degrees, wherein the secondary crystal orientation angle τ can be, for example, 0 to 5 degrees, 5 to 10 degrees, 10 to 15 degrees, or 15 to 20 degrees.

[0124] In some embodiments, based on the first or multiple target natural vibration frequencies generated in step S130 (generating corresponding first or multiple target natural vibration frequencies based on the second multiple Euler angles in the first multiple Euler angles and the regression prediction model, wherein the orientation angles corresponding to the second multiple Euler angles are within a preset orientation angle range), and the first or multiple target natural vibration frequencies corresponding to the orientation angles within the preset orientation angle range, the influence of the orientation angle on the natural vibration frequency can be obtained, and a more accurate variation law of the object's natural vibration frequency can be obtained, so as to analyze the dispersion of the natural vibration frequency caused by the deviation of the object's orientation.

[0125] In some embodiments, analytical parameters can be determined based on the first-order or multiple-order natural vibration frequencies of the target to more intuitively illustrate the variation patterns of the natural vibration frequencies. In some embodiments, the analytical parameters may include at least one of the minimum, maximum, mean, and standard deviation of each order of the target's natural vibration frequencies. This allows for focused attention on the natural vibration frequencies of corresponding orders that exhibit outliers in the analytical parameters, and enables adjustments to the object during the engineering design phase to reduce the likelihood of outliers in the analytical parameters. In a specific example, the minimum, maximum, mean, and standard deviation of the first six natural vibration frequencies of the object can be determined to ascertain the dispersion and variation patterns of the first six natural vibration frequencies.

[0126] In a specific example, the analytical parameters for the first six natural vibration frequencies of the object can be found in Table 1 below.

[0127] Table 1

[0128]

[0129] As can be seen from Table 1, the standard deviations of the third and sixth natural vibration frequencies of the object are relatively large, indicating that the third and sixth natural vibration frequencies of the object are highly dispersed. Therefore, the third and sixth natural vibration frequencies of the object should be given special attention so that appropriate adjustments can be made to the object during the engineering design phase.

[0130] In some embodiments, the natural frequencies of each order in the Campbell diagram of an object can be corrected based on the above analysis parameters. For example, a line representing a certain natural frequency can be corrected into a frequency dispersion band with a width. In this case, since the frequency dispersion caused by orientation deviation is taken into account, the calculated resonance margin will be more in line with reality, thereby enabling a more reasonable assessment of the resonance risk of the object.

[0131] According to another aspect of this disclosure, an apparatus for determining a natural vibration frequency is also provided. For example... Figure 7 As shown, an apparatus 700 for determining a natural vibration frequency according to a disclosed exemplary embodiment may include a processor 710 and a memory 720, wherein the memory 720 stores instructions that, when executed by the processor 710, can implement the operation of the method for determining the natural vibration frequency described above.

[0132] The processor 710 can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components, to implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of this disclosure. The general-purpose processor can be a microprocessor or any conventional processor, and can be an x86 architecture or an ARM architecture, etc.

[0133] Memory 720 may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may be random access memory (RAM) used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct memory bus random access memory (DRRAM). It should be noted that the memory described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0134] According to another aspect of this disclosure, a non-transitory computer-readable storage medium is also provided, on which instructions can be stored, which, when executed by a processor, can implement the operation of the method described above for determining the natural vibration frequency.

[0135] The non-transitory computer-readable storage medium in the embodiments of this disclosure may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. It should be noted that the non-transitory computer-readable storage medium described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0136] According to another aspect of this disclosure, a computer program product is also provided, which may include instructions that, when executed by a processor, can implement the operation of the method described above for determining the natural vibration frequency.

[0137] Instructions can be any set of instructions that will be executed directly by one or more processors, such as machine code, or any set of instructions that will be executed indirectly, such as a script. The terms “instruction,” “application,” “process,” “step,” and “program” used herein are interchangeable. Instructions can be stored in object code format for direct processing by one or more processors, or stored in any other computer language, including scripts or sets of independent source code modules that are interpreted on demand or compiled ahead of time. Instructions can include instructions that cause one or more processors to act as the various neural networks described herein. The function, methods, and routines of instructions are explained in more detail in other parts of this document.

[0138] This disclosure obtains first-order or multi-order target natural vibration frequencies by inputting the Euler angles corresponding to orientation angles within a preset orientation angle range into a regression prediction model. This considers the influence of orientation angles on natural vibration frequencies and obtains a more accurate variation law of the object's natural vibration frequencies, enabling the analysis of the dispersion of natural vibration frequencies caused by deviations in object orientation, thereby allowing for better analysis of the object's reliability. Furthermore, according to some embodiments of this disclosure, the dispersion of natural vibration frequencies of single-crystal turbine blades can be determined during the engineering design stage, facilitating the assessment of blade resonance failure risks, saving development costs, and accelerating the development of aero-engines. According to some embodiments of this disclosure, the fault location problem of blades that pass inspection still experience resonance failure can be solved, and important guidance is provided for improved blade design and orientation angle control.

[0139] The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “upper,” “lower,” “high,” “lower,” etc., used in the specification and claims, if present, are for descriptive purposes and not necessarily for describing unchanging relative positions. It should be understood that such terms are interchangeable where appropriate, enabling embodiments of this disclosure described herein to operate, for example, in orientations different from those shown or otherwise described herein. For example, when the device in the drawings is reversed, a feature previously described as “above” other features may now be described as “below” other features. The device may also be oriented in other ways (rotated 90 degrees or in other orientations), in which case the relative spatial relationships will be interpreted accordingly.

[0140] In the specification and claims, when an element is described as being "on top of," "attached to," "connected to," "coupled to," or "in contact with" another element, the element may be directly located on top of, directly attached to, directly connected to, directly coupled to, or directly in contact with the other element, or one or more intermediate elements may be present. Conversely, when an element is described as being "directly" located on top of, directly attached to, directly connected to, directly coupled to, or directly in contact with another element, no intermediate elements are present. In the specification and claims, when a feature is arranged "adjacent" to another feature, it may mean that a feature has a portion overlapping with the adjacent feature or a portion located above or below the adjacent feature.

[0141] As used herein, the term “exemplary” means “serving as an example, instance, or illustration” and not as a “model” to be precisely copied. Any implementation described herein by example is not necessarily to be construed as preferred or advantageous over other implementations. Moreover, this disclosure is not limited to any theory expressed or implied as given in the field of art, background art, summary of invention, or detailed description.

[0142] As used herein, the term "substantially" means any minor variation resulting from design or manufacturing defects, device or component tolerances, environmental influences, and / or other factors. The term "substantially" also allows for differences from the perfect or ideal situation due to parasitic effects, noise, and other practical considerations that may exist in the actual implementation.

[0143] Furthermore, terms such as “first,” “second,” etc., may be used in this document for reference purposes only and are not intended to be limiting. For example, unless the context clearly indicates otherwise, the words “first,” “second,” and other such numerical terms relating to structures or elements do not imply order or sequence.

[0144] It should also be understood that when the term “including / contains” is used herein, it indicates the presence of the indicated feature, whole, step, operation, unit and / or component, but does not preclude the presence or addition of one or more other features, wholes, steps, operations, units and / or components and / or combinations thereof.

[0145] In this disclosure, the term “provide” is used broadly to cover all ways of obtaining an object, and therefore “provide an object” includes, but is not limited to, “purchasing,” “preparing / manufacturing,” “arranging / setting up,” “installing / assembling,” and / or “ordering” an object.

[0146] As used herein, the term “and / or” includes any and all combinations of one or more of the listed items in association. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of this disclosure. As used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise.

[0147] Those skilled in the art will recognize that the boundaries between the above operations are merely illustrative. Multiple operations may be combined into a single operation, a single operation may be distributed among additional operations, and operations may be performed with at least partial overlap in time. Moreover, alternative embodiments may include multiple instances of a particular operation, and the order of operations may be changed in various other embodiments. However, other modifications, variations, and substitutions are equally possible. Aspects and elements of all the embodiments disclosed above may be combined in any way and / or in combination with aspects or elements of other embodiments to provide multiple additional embodiments. Therefore, this specification and the accompanying drawings should be considered illustrative rather than restrictive.

[0148] While specific embodiments of this disclosure have been described in detail by way of example, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this disclosure. The various embodiments disclosed herein can be combined in any way without departing from the spirit and scope of this disclosure. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of this disclosure. The scope of this disclosure is defined by the appended claims.

Claims

1. A method for determining natural vibration frequencies, characterized in that, The method includes: Establish a regression prediction model, wherein the regression prediction model is configured to generate first-order or multiple-order natural vibration frequencies based on Euler angles; Obtain the first plurality of Euler angles, and convert each Euler angle in the first plurality of Euler angles into an orientation angle; and The first or multiple natural vibration frequencies of the target are generated based on the second or multiple Euler angles in the first or multiple Euler angles and the regression prediction model, wherein the orientation angles corresponding to the second or multiple Euler angles are within a preset orientation angle range.

2. The method according to claim 1, characterized in that, Building a regression prediction model includes: Obtain a training set, wherein the feature portion of the training set includes a third or more Euler angles, and the label portion of the training set includes one-to-one first-order or multiple-order first natural frequencies corresponding to the third or more Euler angles; and The regression prediction model is trained based on the training set.

3. The method according to claim 2, characterized in that, Obtaining the training set includes: A third set of Euler angles is obtained through random sampling, wherein the Euler angles include a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1, and the first Euler angle parameter α1 of the third set of Euler angles follows a first uniform distribution within a first domain, the second Euler angle parameter β1 follows a second uniform distribution within a second domain, and the third Euler angle parameter γ1 follows a third uniform distribution within a third domain; and For each of the third plurality of Euler angles, the finite element method is used to calculate the prestressed mode under the preset working conditions to obtain the corresponding first or multiple first natural vibration frequencies.

4. The method according to claim 2, characterized in that, Building a regression prediction model also includes: Obtain a test set, wherein the test set includes a fourth plurality of Euler angles, and at least one of the fourth plurality of Euler angles is different from the third plurality of Euler angles; The fourth plurality of Euler angles are input into the regression prediction model to generate corresponding first-order or multi-order predicted natural vibration frequencies. The distribution range of first-order or multi-order natural vibration frequencies is determined based on the label portion of the training set, where: If at least one of the predicted natural vibration frequencies falls outside the corresponding distribution range, then the Euler angles corresponding to that first-order or multiple-order predicted natural vibration frequency do not meet the preset accuracy condition. When the predicted natural vibration frequencies of the first or multiple orders are within the corresponding distribution range, determine that the Euler angles corresponding to the first or multiple predicted natural vibration frequencies meet the preset accuracy conditions. If there are Euler angles in the test set that do not meet the preset accuracy condition, update the training set according to the Euler angles in the test set that do not meet the preset accuracy condition, and return the operation of training the regression prediction model based on the training set.

5. The method according to claim 4, characterized in that: Obtaining the first multiple Euler angles includes: If all the fourth or more Euler angles in the test set meet the preset accuracy condition, then the first or more Euler angles are obtained from the fourth or more Euler angles in the test set. The generation of corresponding first-order or multi-order target natural vibration frequencies based on the second or more Euler angles in the first plurality of Euler angles and the regression prediction model includes: The first or multiple predicted natural vibration frequencies corresponding to the second or multiple Euler angles are used as the corresponding first or multiple target natural vibration frequencies.

6. The method according to claim 4, characterized in that, The training set is updated based on Euler angle combinations in the test set that do not meet the preset accuracy conditions, including: Euler angles in the test set that do not meet the preset accuracy conditions are added to the training set to update the feature part of the training set. For Euler angles that do not meet the preset accuracy conditions, the finite element method is used to calculate the prestressed modes under the preset working conditions to obtain the corresponding first-order or multiple-order second natural vibration frequencies, and the obtained first-order or multiple-order second natural vibration frequencies are added to the training set to update the label part of the training set.

7. The method according to claim 1, characterized in that, Converting each Euler angle in the first plurality of Euler angles into an orientation angle includes: For each Euler angle: Based on the transformation model, the Euler angles are converted to Tetbryan angles; and The orientation angle is generated based on the Tate Brian angle.

8. The method according to claim 7, characterized in that, Euler angles include a first Euler angle parameter α1, a second Euler angle parameter β1, and a third Euler angle parameter γ1; Tetbryan angles include a first Tetbryan angle parameter α2, a second Tetbryan angle parameter β2, and a third Tetbryan angle parameter γ2. The transformation model is established through the following operations: Obtain the reference coordinate system; The reference coordinate system is rotated into a first crystal coordinate system based on the first Euler angle parameter α1, the second Euler angle parameter β1, and the third Euler angle parameter γ1. The reference coordinate system is rotated into a second crystal coordinate system based on the first Tetbryan angle parameter α2, the second Tetbryan angle parameter β2, and the third Tetbryan angle parameter γ2. Based on the fact that the first rotation matrix R1 between the reference coordinate system and the first crystal coordinate system and the second rotation matrix R2 between the reference coordinate system and the second crystal coordinate system are equal, the first transformation relationship of α2 with respect to α1, β1 and γ1, the second transformation relationship of β2 with respect to α1, β1 and γ1 and the third transformation relationship of γ2 with respect to α1, β1 and γ1 are determined.

9. The method according to claim 8, characterized in that, In the first rotation matrix R1: And the second rotation matrix R2 is: In this case, The first conversion relationship is The second transformation relationship is β2 = arcsin(-R) 13 The third transformation relationship is: Among them, R ij Let i represent the element in the i-th row and j-th column of matrix R, where R = R1 = R2, i = 1, 2 or 3, and j = 1, 2 or 3.

10. The method according to claim 7, characterized in that, The orientation angle generated based on the Tate Brian angle includes: The primary and secondary crystal orientation angles are determined based on the second crystal coordinate system corresponding to the Tetbryan angle. The primary crystal orientation angle indicates the angle between the third coordinate axis of the second crystal coordinate system and the third coordinate axis of the reference coordinate system, while the secondary crystal orientation angle indicates the angle between the intersection line between the first plane containing the first and third coordinate axes of the second crystal coordinate system and the second plane containing the first and second coordinate axes of the reference coordinate system and the first axis of the reference coordinate system.

11. The method according to claim 10, characterized in that, Orientation angles within the preset orientation angle range satisfy: The primary crystal orientation angle is less than 15 degrees; and The orientation angle of the secondary crystal is 0–5 degrees, 5–10 degrees, 10–15 degrees, or 15–20 degrees.

12. The method according to claim 8, characterized in that, The method further includes: The analysis parameters are determined based on the first-order or multi-order target natural vibration frequencies, wherein the analysis parameters include at least one of the minimum, maximum, mean, and standard deviation of each order of target natural vibration frequencies.

13. A device for determining a natural vibration frequency, characterized in that, The device includes: Processor; and A memory storing instructions that, when executed by the processor, implement the operation of the method according to any one of claims 1 to 12.

14. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores instructions that, when executed by a processor, implement the operation of the method according to any one of claims 1 to 12.

15. A computer program product, characterized in that, The computer program product includes instructions that, when executed by a processor, implement the operation of the method according to any one of claims 1 to 12.

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