Bayesian model polycondensation and main degree-of-freedom selection method based on load prior

Abstract

The invention discloses a Bayesian model polycondensation and main degree-of-freedom selection method based on load prior, which comprises the following steps of: S1, establishing a system load time domain signal sample based on load prior information; s2, establishing a covariance matrix of each degree-of-freedom response of the system; s3, constructing a main degree-of-freedom set related to the polycondensation system; s4, calculating a conversion matrix between the initial system and the polycondensation system and a system matrix after polycondensation; and S5, calculating the response of the polycondensation system, and reconstructing the global response of the system. According to the method, the problems of model polycondensation and main degree-of-freedom selection of structures with dense modals and non-proportional damping characteristics can be solved, higher calculation precision and wider applicability are achieved, and the method has wide application prospects in the fields of structural health monitoring, aerospace, automobile industry and civil engineering.

Description

Technical Field

[0001] The present invention belongs to the field of structural dynamic model condensation, and particularly relates to a Bayesian model condensation and master degree-of-freedom selection method based on load prior information. Background Art

[0002] In fields such as aerospace and civil engineering, structural dynamic analysis of finite element models with large scale and high degrees of freedom is usually involved. Directly calculating the time history response of such models requires extremely high computational costs, such as calculation time, storage resources, etc. Model condensation technology aims to equivalently transform the initial system into a smaller-scale condensed model to reduce computational complexity, improve computational efficiency, and at the same time maintain the accuracy of numerical results. The effect of model condensation depends on the master degree-of-freedom selection criterion and the quality of the condensation algorithm, and the latter determines the conversion format of the responses of the master and slave degrees of freedom.

[0003] The existing technologies have deficiencies: First, the prior information of complex loads is not fully considered, and the condensation format cannot be adaptively adjusted according to the load characteristics under actual service conditions, resulting in limited adaptability and accuracy, and the calculation accuracy for structures with dense modal characteristics is not high; Second, the derivation of existing methods is based on the Rayleigh proportional damping assumption, and their application to non-proportional damping structural systems is limited. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a Bayesian model condensation and master degree-of-freedom selection method based on load prior information.

[0005] The Bayesian model condensation and master degree-of-freedom selection method based on load prior information of the present invention includes the following steps:

[0006] S1. Based on the load prior information, establish a system load time-domain signal sample;

[0007] S2. Based on the load time-domain signal sample, establish the covariance matrix of the responses of each degree of freedom of the system;

[0008] S3. According to the covariance matrix of the responses of each degree of freedom of the system, construct the set of master degrees of freedom involved in the condensed system;

[0009] S4. According to the system response covariance matrix and the set of master degrees of freedom, calculate the transformation matrix between the initial system and the condensed system, and the condensed system matrix;

[0010] S5. According to the given test load signal, calculate the response of the condensed system and reconstruct the global response of the system.

[0011] The said S1 includes the following steps:

[0012] S11. Construct an excitation load vector formula;

[0013] S12. Generate a time-domain signal sample according to the power spectral density of the load source.

[0014] The said S2 includes the following steps:

[0015] S21. Calculate the system time-domain response sample corresponding to the load time-domain signal sample;

[0016] S22. Establish the response covariance matrix of each degree of freedom of the system from the system time-domain response sample.

[0017] The response covariance matrix of each degree of freedom of the system is

[0018]

[0019] where, x a,l represents the response of the a-th degree of freedom at the time point t = t l , represents the average value of the time-domain response of the a-th degree of freedom, x b,l represents the response of the b-th degree of freedom at the time point t = t l , represents the average value of the time-domain response of the b-th degree of freedom, and N1 is the total number of time nodes considered in the calculation

[0020] The said S3 includes the following steps:

[0021] S31. Input the total number of main degrees of freedom, select the degree of freedom corresponding to the position of the largest element on the diagonal of the system response covariance matrix as the first main degree of freedom, and the remaining degrees of freedom except the main degrees of freedom as the secondary degrees of freedom;

[0022] S32. Establish the posterior covariance matrix of the secondary degree of freedom response, and select the degree of freedom corresponding to the position of the largest element on the diagonal of the matrix as the second main degree of freedom, and the remaining degrees of freedom except the main degrees of freedom as the secondary degrees of freedom;

[0023] S33. Repeat the steps in S32 until all the main degrees of freedom are selected.

[0024] According to the first main degree of freedom, divide the total degrees of freedom x of the system into the first main degree of freedom set and the first secondary degree of freedom set The mean vector of the secondary degree of freedom response is,

[0025]

[0026] where, the superscript (1) represents the intermediate variable formed in the process of selecting the first main degree of freedom, is the expectation operator.

[0027] The posterior covariance matrix of the secondary degree of freedom response For

[0028]

[0029] wherein, is the block form of the covariance matrix rearranged according to the first set of primary degrees of freedom and the first set of secondary degrees of freedom.

[0030] S4 includes the following steps:

[0031] S41. Calculate the transformation matrix between the initial system degrees of freedom response variables and the condensed system degrees of freedom response variables according to the system response covariance matrix and the set of primary degrees of freedom;

[0032] S42. Establish the condensed system matrix according to the established transformation matrix and the initial system matrix.

[0033] The transformation relationship between the initial system degrees of freedom variables and the condensed system degrees of freedom variables can be expressed as x = Tx m , where the transformation matrix T is

[0034]

[0035] wherein, x m is the final set of primary degrees of freedom, and I m is the identity matrix of dimension m.

[0036] The condensed system matrix is

[0037]

[0038] wherein, are respectively the mass, damping, stiffness matrices and load vector of the condensed system, M, C and K are respectively the initial mass matrix, damping matrix and stiffness matrix, and x m (t) is the displacement vector corresponding to the final set of primary degrees of freedom, is the velocity vector, is the acceleration vector.

[0039] S5 includes the following steps:

[0040] S51. Establish the condensed system load according to the given test load signal;

[0041] S52. Calculate the condensed system response according to the condensed system load and reconstruct the full-field response;

[0042] S53. Substitute the system test load signal into the initial system, calculate the system response, and compare it with the reconstructed response obtained in step S52 to evaluate the condensation accuracy.

[0043] The beneficial effects of the present invention are that the method of the present invention can handle the problems of model condensation and selection of master degrees of freedom for structures with dense modes and non-proportional damping characteristics, has higher calculation accuracy and wider applicability, has broad application prospects in the fields of structural health monitoring, aerospace, automotive industry and civil engineering, and is of great significance to the dynamic analysis of complex structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic flow chart of the method for selecting master degrees of freedom and model condensation of the present invention.

[0045] Figure 2 It is a schematic diagram of the helicopter tail beam structure in the embodiment of the present invention.

[0046] Figure 3 It is a schematic diagram of the natural frequency and load power spectral density of the structure in the embodiment of the present invention.

[0047] Figure 4 It is a schematic diagram of the numerical results of the displacement response in the x direction of the nodes established by different methods in Embodiment 1 of the present invention: (a) time domain response, (b) frequency domain response.

[0048] Figure 5 It is a schematic diagram of the numerical results of the displacement response in the y direction of the nodes established by different methods in Embodiment 1 of the present invention: (a) time domain response, (b) frequency domain response.

[0049] Figure 6 It is a schematic diagram of the numerical results of the displacement response in the z direction of the nodes established by different methods in Embodiment 1 of the present invention: (a) time domain response, (b) frequency domain response.

[0050] Figure 7 It is a schematic diagram of the numerical results of the displacement response in the x direction of the nodes established by different methods in Embodiment 2 of the present invention: (a) time domain response, (b) frequency domain response.

[0051] Figure 8 It is a schematic diagram of the numerical results of the displacement response in the y direction of the nodes established by different methods in Embodiment 2 of the present invention: (a) time domain response, (b) frequency domain response.

[0052] Figure 9 It is a schematic diagram of the numerical results of the displacement response in the z direction of the nodes established by different methods in Embodiment 2 of the present invention: (a) time domain response, (b) frequency domain response. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0054] The method for Bayesian model condensation and selection of master degrees of freedom based on load prior in the present invention includes the following steps:

[0055] S1. Based on prior information such as load position and power spectral density, establish a system load time-domain signal sample;

[0056] S11. Construct an excitation load vector formula;

[0057] The structural dynamics equation with n degrees of freedom is expressed as

[0058]

[0059] where t is time, and are the mass matrix, damping matrix, and stiffness matrix respectively. is the excitation load vector, are the displacement, velocity, and acceleration vectors respectively.

[0060] The excitation load with n degrees of freedom consists of p known power spectral density (PSD) and random excitation load sources at the application positions, and the excitation load vector is expressed in matrix form;

[0061]

[0062] where, is the random excitation load source, is the spatial distribution matrix corresponding to the load source.

[0063] S12. Generate a load time-domain signal sample according to the power spectral density of the load source.

[0064] Discretize time with a step size h to obtain nodes t0, t1, t2,..., t N , and according to the power spectral density and spatial distribution of the load source, use the random phase method to generate q groups of load time-domain signal samples F1 * , F2 * ,..., F q * , each group of samples corresponds to the same time nodes t0, t1, t2,..., t N , randomly select one group of sample signals as the training load F for constructing the condensed system train , and the remaining samples as the test signals F for testing the condensation effect test .

[0065] S2. Based on the load training time-domain signal sample F train , establish the covariance matrix Σ of the responses of each degree of freedom of the system;

[0066] S21. Calculate the system time-domain response samples corresponding to the load time-domain signal samples;

[0067] Substitute the load training time-domain signal sample F train into the structural dynamics equation, and use the Newmark method to calculate the system time-domain response samples corresponding to the load time-domain signal samples

[0068] X = [x1, x2,..., x N (3)

[0069] where, x i = x(t j ), i = 1, 2,..., N represents the system responses at each time node.

[0070] S22. Establish the covariance matrix Σ of the responses of each degree of freedom of the system from the system time-domain response samples.

[0071]

[0072] where, x a,l represents the response of the a-th degree of freedom at the time point t = t l , represents the average value of the time-domain response of the a-th degree of freedom, x b,l represents the response of the b-th degree of freedom at the time point t = t l , represents the average value of the time-domain response of the b-th degree of freedom, and N1 is the total number of time nodes considered in the calculation.

[0073] S3. Construct the set of master degrees of freedom involved in the condensed system according to the covariance matrix of the responses of each degree of freedom of the system;

[0074] S31. Input the total number m of master degrees of freedom, and select the degree of freedom corresponding to the position of the largest element on the diagonal of the covariance matrix Σ as the first master degree of freedom;

[0075] S32. Establish the posterior covariance matrix, and select the degree of freedom corresponding to the position of the largest covariance as the second master degree of freedom;

[0076] According to the first master degree of freedom selected in S31, divide the total degrees of freedom x of the system into the first master degree of freedom set and the first slave degree of freedom set

[0077] Partition the covariance matrix according to the first master degree of freedom set and the first slave degree of freedom set

[0078]

[0079] The mean vector of the slave degree of freedom response is,

[0080]

[0081] Among them, the superscript (1) represents the intermediate variable formed in the process of selecting the first principal degree of freedom. is the expectation operator.

[0082] Establish the posterior covariance matrix of the degrees of freedom response

[0083]

[0084] Select the posterior covariance matrix Among them, the degree of freedom corresponding to the position of the largest element on the diagonal is the second principal degree of freedom.

[0085] S33. Repeat the steps in S32 until all m principal degrees of freedom are selected.

[0086] S4. According to the system response covariance matrix Σ and the final set of principal degrees of freedom x m , calculate the transformation matrix between the initial system degrees of freedom variables and the condensed system degrees of freedom variables, and the condensed system matrix;

[0087] S41. According to the system response covariance matrix Σ and the final set of principal degrees of freedom x m , calculate the transformation matrix between the initial system degrees of freedom response variables and the condensed system degrees of freedom response variables;

[0088] Based on the final set of principal degrees of freedom x m and the final set of secondary degrees of freedom x s , block the system degrees of freedom

[0089] Block the covariance matrix Σ

[0090] The posterior mean vector of the secondary degrees of freedom response is

[0091]

[0092] Therefore, the system degrees of freedom variables can be expressed as

[0093]

[0094] The conversion relationship between the initial system degrees of freedom variables and the condensed system degrees of freedom variables can be expressed as x = Tx m , where the transformation matrix T is

[0095]

[0096] Among them, I mis an identity matrix of dimension m.

[0097] S42. Based on the established transformation matrix and the mass, damping, stiffness matrices and load vector of the initial system, establish the condensed system matrix.

[0098]

[0099] Among them, are respectively the mass, damping, stiffness matrices and load vector of the condensed system, M, C and K are respectively the initial mass matrix, damping matrix and stiffness matrix, and x m (t) is the displacement vector corresponding to the final set of master degrees of freedom, is the velocity vector, is the acceleration vector.

[0100] The calculation formula is

[0101] Among them, the superscript T represents matrix transpose.

[0102] S5. According to the given test load signal, calculate the response of the condensed system and reconstruct the global response of the system.

[0103] S51. According to the test load signal sample F test generated in step S12, establish the load of the condensed system

[0104]

[0105] S52. Substitute the load of the condensed system into the condensed system equation (10), and use Newmark to calculate the response x m (t) of the condensed system. The response of the condensed system is the time-domain response of the master degrees of freedom. According to the system response, reconstruct the full-field response x(t) = Tx m (t);

[0106] S53. Substitute the system test load signal F test generated in step S12 into the initial system (Equation (1)), and use Newmark to calculate the system response x 0 (t), and compare it with the reconstructed response obtained in step S52 to evaluate the condensation accuracy.

[0107] Example 1

[0108] Consider Figure 2 the helicopter tail beam structure shown. The material parameters are Young's modulus E = 2×10 11 Pa, Poisson's ratio ν = 0.3, density ρ = 7850 kg / m 3, the entire structure consists of rectangular cross-section bars with a cross-sectional size of 0.01m×0.01m. Using Abaqus software, the structure is spatially discretized with three-dimensional space beam elements (B31, Timoshenko beam elements), and finally a finite element system containing 306 elements and 1410 degrees of freedom is obtained. The mass and stiffness matrices can be further derived.

[0109] In this example, the damping matrix adopts the Rayleigh proportional damping assumption. Considering the first 40 modes, the Rayleigh damping coefficients are calculated as follows

[0110]

[0111] where a and b are the Rayleigh damping coefficients, ξ = 0.06 is the damping ratio, ω1 = 6.93HZ, and ω 40 = 147.37HZ are the first and 40th natural frequencies respectively, and M, C, and K are the system mass, damping, and stiffness matrices. The natural frequencies of each mode of the structure are as shown in Figure 3 (a). It can be seen that the structure exhibits obvious dense mode characteristics.

[0112] The structure is fixed at the bottom surface and subjected to base acceleration excitation in the x- and y-directions. The power spectral density of the acceleration excitation is as shown in Figure 3 (b), and the specific expression form is as follows

[0113]

[0114] where P x (ω) is the power spectral density function, and ω represents the frequency. As can be seen from Figure 3 (a), the frequency range of the excitation PSD distribution is located within the frequency domain corresponding to the dense modes of the structure, so the dense modes will be excited.

[0115] According to the power spectral density of the acceleration, the time-domain signal training samples and test samples are generated using the random phase method. Both sample signals are sampled at a sampling rate of 300HZ for a duration of 10 seconds. According to the acceleration signal training samples, the reduced system is established using the method proposed in the present invention. The load vector is established from the acceleration time-domain signal test samples and substituted into the structural dynamic equations of the initial system and the reduced system. The Newmark method is used to calculate the time history response of the system.

[0116] The purpose of the model reduction technology is to establish numerical results that are as consistent as possible with the calculated response of the initial system. Therefore, the response of the initial system calculated using the Newmark method is used as a reference to evaluate the accuracy and effectiveness of the reduction method and the main degree of freedom selection criterion proposed in this patent. And it is compared with the calculation results of several publicly proposed methods.

[0117] Among them, the compared condensation methods include: SEREP method (Literature 1), Weng (Literature 2), IIRS method (Literature 3).

[0118] The methods for selecting the main degrees of freedom include: modal kinetic energy method (MKE, Literature 4), effective independence method (EI, Literature 5).

[0119] In this example, the number of main degrees of freedom is selected as m = 16. For the combined condensation schemes formed by different condensation methods and main degree of freedom selection criteria, a condensed system is established respectively, and the Newmark method is used to calculate the time history response. Further, the root mean square value of the error of the time history response is calculated, and the following index is used to measure the condensation accuracy

[0120]

[0121] where RE represents the error index, x i , x R,i respectively represent the displacement responses at the i-th degree of freedom calculated from the initial system and the condensed system, N is the total number of time nodes in the calculation process, n represents the total number of degrees of freedom of the initial system, and t j represents the j-th time node.

[0122] Using the above index, the statistical results of the accuracy indexes of the numerical results of different combined condensation schemes are shown in Table 1. Among them, the horizontal row represents the main degree of freedom selection criterion, the vertical column represents different condensation methods, and the table lists the RE values of the error indexes of different combinations. It can be seen that: using the combined condensation scheme formed by the condensation method and the main degree of freedom selection criterion of this patent, the error of the established numerical result is significantly smaller than that of other methods, and it has a significant advantage in calculation accuracy.

[0123] Table 1 Error indexes of the displacement time domain response of the numerical results established by the combined condensation schemes formed by different condensation methods and main degree of freedom selection criteria in Example 1

[0124]

[0125] To further investigate the accuracy of the condensation method proposed in this patent, the main degrees of freedom are selected using the proposed criterion, a condensed system is established using different condensation methods, and the Figure 2 red nodes in are selected as the display nodes, and the numerical results established by different condensation methods are compared with the calculation results of the initial system at Figure 4 , 5 and 6. Figure 4 , 5Figures 6 respectively show the time - history responses of the displacements in the x -, y -, and z - directions of the display node established by different polycondensation methods. Among them, the initial system curve represents the initial system response, Weng represents the response established by the method in Document 2, IIRS represents the response established by the method in Document 3, and BayeCov represents the response established by the method of the present invention. It can be seen that the results of the method proposed by the present invention are in good agreement with the reference results, and the calculation accuracy is better than other methods.

[0126] Further, the time - history response is subjected to Fourier transform to obtain the amplitude of the frequency - domain response at each frequency node, and the following error index is defined for accuracy analysis.

[0127]

[0128] Among them, RE f represents the frequency - domain response error index, A(ω i ) and A R (ω i ) are the amplitudes of the initial system and the reduced - order system responses at the frequency ω i respectively, and n f is the total number of frequency nodes.

[0129] The numerical results established by various reduction schemes are shown in Table 2. It can be seen that the frequency - domain response error of the proposed method is significantly smaller than that of other methods.

[0130] Table 2 Error indices of the displacement frequency - domain responses at the display node established by different reduction methods using the main - degree - of - freedom selection criterion proposed in this application in Example 1

[0131]

[0132] Example 2

[0133] The structural geometry, material parameters, loads, and boundary conditions in Example 2 are the same as those in Example 1. The difference is that a damper is applied in the x - direction of the display node in Figure 2 . Therefore, the system damping no longer conforms to the Rayleigh proportional - damping assumption, and the specific form of the system damping matrix C is

[0134] C = aM + bK+diag(V c ) (17)

[0135] Among them, is an n - dimensional vector, is the system number corresponding to the degree of freedom in the x - direction of the display node, the damping coefficient a = 4.99 s -1 HZ, b = 1.24×10 -4 s, and M and K are the system mass matrix and stiffness matrix respectively.

[0136] When 16 main degrees of freedom are selected, the time-domain error indicators of the numerical results established by different condensation combination schemes are shown in Table 3. Figure 7 and 8 As shown in Fig. 9, when the main degrees of freedom are selected according to the criterion proposed by the present invention and different condensation methods are applied, the comparison between the numerical results established and the calculation results of the initial system respectively shows the time-history response calculation results of the displacements of the nodes in the x-, y-, and z-directions. Since dampers are only added in the x-direction of the nodes for display, Figure 8 the calculation results of the displacements in the y-direction shown in Figure 5 are basically the same as those in Example 1. Further, the Fourier transform is performed on the time-domain response and the frequency-domain response error indicators are calculated. The specific results are shown in Table 4. It can be seen that the time-domain and frequency-domain responses of the numerical results of the method proposed in this application are in good agreement with the response of the initial system, and the errors are significantly smaller than those of other comparison methods, showing great advantages in calculation accuracy.

[0137] Table 3 Error indicators of the displacement time-domain response of the numerical results established by the combined condensation schemes formed by different condensation methods and the main degree-of-freedom selection criteria in Example 2

[0138]

[0139]

[0140] Table 4 Error indicators of the displacement frequency-domain response at the display nodes of the numerical results established by different condensation methods under the main degree-of-freedom selection criterion proposed in this application in Example 2

[0141]

[0142] In the present invention, the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0143] Although the above embodiments have been shown and described, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions, and variations made by those of ordinary skill in the art to the above embodiments are within the protection scope of the present invention.

[0144] References

[0145] [1] O'Callanhan J. System equivalent reduction and expansion process. Proceedings of the 7th International Modal analysis conference, Society of Experimental Mechanics, 1989, 7: 29 - 37.

[0146] [2] M.I. Friswell, S.D. Garvey, and J.E.T. Penny. The convergence of the iterated irsm method. Journal of Sound and Vibration, 1998, 211(1): 123 - 132.

[0147] [3] Shun Weng, Wei Tian, Hongping Zhu, Yong Xia, Fei Gao, Yaoting Zhang, and Jiajing Li. Dynamic condensation approach to calculation of structural responses and response sensitivities. Mechanical Systems and Signal Processing, 2017, 88: 302 - 317.

[0148] [4] M. Salama, T. Rose, and J. Garba. Optimal placement of excitations and sensors for verification of large dynamical systems. In 28th Structures, Structural Dynamics and Materials Conference, Monterey, CA, U.S.A., 1987. American Institute of Aeronautics and Astronautics.

[0149] [5] Michael Papadopoulos and Ephraim Garcia. Sensor placement methodologies for dynamic testing. AIAA Journal, 1998, 36: 256 - 263。

Claims

1. A Bayesian model condensation and master degree of freedom selection method based on load prior, characterized in that: The following steps are involved: S1. Based on the load prior information, establish the system load time domain signal sample; S2. Establish the covariance matrix of each degree of freedom response of the system; S3. The set of master degrees of freedom involved in constructing the polycondensation system; S4. Calculate the conversion matrix between the initial system and the condensed system, and the system matrix after condensation; S5. Calculate the condensation system response and reconstruct the global response of the system.

2. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 1 is characterized in that: The S1 comprises the following steps: S11. Construct the excitation load vector formula; S12. Generate a load time domain signal sample according to the power spectrum density of the load source.

3. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 1 is characterized in that: The S2 comprises the following steps: S21. Calculate the system time domain response sample corresponding to the load time domain signal sample; S22. Establish the response covariance matrix of each degree of freedom of the system based on the system time domain response samples.

4. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 3 is characterized in that: The covariance matrix of each degree of freedom response of the system is: Among them, x a,l It means that the ath degree of freedom is at time t=t l The response on represents the average value of the time domain response of the ath degree of freedom, x b,l represents the bth degree of freedom at time t=t l The response on represents the average value of the time domain response of the bth degree of freedom, and N1 is the total number of time nodes considered in the calculation.

5. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 4 is characterized in that: The S3 comprises the following steps: S31. Input the total number of master degrees of freedom, select the degree of freedom corresponding to the position of the largest element on the diagonal of the system response covariance matrix as the first master degree of freedom, and the remaining degrees of freedom except the master degree of freedom as slave degrees of freedom; S32. Establish a posterior covariance matrix of the slave degree of freedom response, and select the degree of freedom corresponding to the position of the largest element on the diagonal of the matrix as the second master degree of freedom, and the remaining degrees of freedom except the master degree of freedom as slave degrees of freedom; S33. Repeat the steps in S32 until all the master degrees of freedom are selected.

6. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 5 is characterized in that: According to the first master degree of freedom, the total degree of freedom x of the system is divided into the first master degree of freedom set With the first from the degrees of freedom set The posterior covariance matrix of the response from the degrees of freedom for The superscript (1) indicates the intermediate variable formed in the first principal degree of freedom selection process. The block form of the covariance matrix is ​​obtained by rearranging the covariance matrix according to the first master degree of freedom set and the first slave degree of freedom set.

7. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 6 is characterized in that: The S4 comprises the following steps: S41. Calculate the conversion matrix between the initial system degree of freedom response variable and the condensed system degree of freedom response variable according to the system response covariance matrix and the master degree of freedom set; S42. Establish a condensed system matrix based on the established conversion matrix and the initial system matrix.

8. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 7 is characterized in that: The conversion relationship between the initial system degree of freedom variables and the polycondensation system degree of freedom variables can be expressed as x=Tx m , where the transformation matrix T is Among them, x is the system degree of freedom variable, x m is the final set of master degrees of freedom, I m is the identity matrix of dimension m.

9. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 8 is characterized in that: The system matrix after polycondensation is: in, are the mass, damping, stiffness matrix and load vector of the system after polycondensation, x m is the final set of master degrees of freedom, x m (t) is the displacement vector corresponding to the final set of master degrees of freedom, is the velocity vector, is the acceleration vector.

10. The method for Bayesian model condensation and master degree of freedom selection based on load prior according to claim 1, characterized in that: The S5 comprises the following steps: S51. Establishing a polycondensation system load according to a given test load signal; S52. Calculate the response of the polycondensation system according to the polycondensation system load and reconstruct the full-field response; S53. Substitute the system test load signal into the initial system, calculate the system response, compare it with the reconstructed response obtained in step S52, and evaluate the condensation accuracy.

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