A mechanical system transmission path contribution amount analysis method based on a Bayesian algorithm

Abstract

The application discloses a mechanical system transmission path contribution analysis method based on a Bayesian algorithm, first, a working condition transmission path analysis model is established after a mechanical vibration system is determined; then, a complex matrix equation in the working condition transmission path analysis model is converted into a real number system, and a likelihood function of the working condition transmission path analysis model is defined; a prior distribution model of a transmission rate matrix under different frequency points is established, a posterior distribution of the transmission rate matrix is calculated by using an evidence maximization method, and the transmission rate matrix is obtained; finally, each transmission path contribution under a target working condition is calculated according to the transmission rate matrix, and the mechanical vibration system transmission path contribution analysis is completed. The method does not need to select a regularization parameter for the transmission rate matrix under each frequency point, avoids the influence of unreasonable selection of the regularization parameter on the solution accuracy of the transmission rate matrix, and greatly improves the solution efficiency of the transmission rate matrix.

Description

Technical Field

[0001] This invention belongs to the field of mechanical vibration reduction and noise reduction technology, specifically relating to a method for analyzing the contribution of transmission paths in mechanical systems based on Bayesian algorithms. Background Technology

[0002] Currently, vibration and noise issues are receiving increasing attention in both civilian and military fields, severely impacting product quality and customer experience. Taking tractor cab noise as an example, prolonged exposure to noisy environments can cause irreversible hearing damage to drivers, and even lead to physiological symptoms such as insomnia and anxiety. Furthermore, cab noise can impair a driver's judgment of environmental safety, and may even make it difficult for them to hear external sounds, resulting in numerous accidents each year. Therefore, conducting research on vibration and noise reduction methods and theories for mechanical structures is a significant challenge and an urgent need to address this problem, as well as a hot and difficult issue that has long been a focus of scholarly attention.

[0003] The fundamental approach to reducing vibration and noise levels in mechanical structures lies in addressing the vibration (sound) sources and transmission paths. This involves identifying, decomposing, and evaluating the main vibration (sound) sources and transmission paths to reveal the mechanisms of vibration and noise generation, guiding engineers to control vibration and noise in mechanical products during the design phase. In the 1980s, Verheij first proposed the Transfer Path Analysis (TPA) method and applied it to noise synthesis and the decomposition of its source contributions. Over the subsequent 40 years, the TPA method has seen significant development, giving rise to various TPA approaches. Among these, the most important are the traditional TPA method, the Extended Operational-X TPA (OPAX) method, and the Operational Transfer Path Analysis (OTPA) method.

[0004] Wu Jianghai et al. used the TPA method based on singular value decomposition to study the vibration transmission law of typical ship machinery in ship piping systems and floating raft foundations. This research provides a reference for the location optimization and frequency selection of low-frequency line spectrum active control actuators in ship machinery systems. Gao Yu et al. used the TPA method to identify the transmission path of tire cavity noise inside vehicles and determined the components requiring optimization along this path through CAE simulation. They then proposed an optimization scheme that effectively suppressed tire cavity noise inside vehicles. However, the traditional TPA method requires the removal of its active system, and the number of reference points must be at least twice the number of vibration (sound) sources. Therefore, the measurement of the transfer function requires a significant amount of time and manpower. To avoid the measurement burden of the traditional TPA method, Karl Janssens proposed the OPAX method, which uses parametric modeling of the load and the order information of the operating data to solve the load parameter identification model. Subsequently, Wang et al. proposed the OPAX method based on a moving multi-band model to reduce the impact of random noise on the accuracy of load parameter identification. Liu et al. used OPAX (Optical Multi-band Amplifier) ​​to analyze the source contribution of vehicle passing noise, providing a theoretical basis for guiding the reduction of vehicle passing noise. Although this method requires only a few indicator points, reducing the measurement burden of the transfer function to some extent, it still requires the removal of active sound sources to measure the transfer function, and the selection of the load parameterization model directly affects the load identification accuracy. To compensate for the measurement burden of the transfer function, the OTPA (Optical Transmission Path Approach) method was proposed. This method only requires the acquisition of working condition data to calculate the transmission path contribution, making OTPA experiments easy to implement and saving a lot of time and manpower costs. Zhang Lei et al. used the OTPA method based on the least squares method to analyze the noise contribution of underwater vehicles with single and double-layer cylindrical shell structures, effectively guiding the implementation of underwater vehicle noise prediction and the correct implementation of vibration reduction and noise reduction measures. Pang Xiaoke et al. used an OTPA method improved by singular value decomposition technology to analyze the source contribution rate of a certain excavator test vehicle from engine vibration to cab seat vibration, effectively solving the vibration problem of the excavator. Cheng Wei et al. proposed an OTPA inverse problem model based on the Tikhonov regularization method. The proposed method significantly reduces the errors in total contribution and path contribution, as well as path misjudgment. This research can provide a theoretical basis for vibration and noise monitoring and noise reduction. While the above-mentioned use of multiple regularization methods effectively suppresses ill-posed problems in the load identification process, when the function curve has multiple inflection points or the curve change is too smooth, the determined regularization parameters may not be optimal, leading to inaccurate sound source load identification and consequently affecting the results of vibration (sound) source identification and transmission path analysis.

[0005] Among the existing publicly available OTPA methods, Cheng Wei et al. from Xi'an Jiaotong University proposed an OTPA method based on damped singular value decomposition. This method uses damped singular value decomposition to process the transmission path matrix, eliminating the truncation error caused by truncating the singular values ​​of the coefficient matrix in traditional operating condition transmission path analysis, thus improving the accuracy of transmission path contribution calculation. Zhang Zhifei et al. from Chongqing University published an OTPA method based on regularized total least squares, using the Tikhonov regularized total least squares method to solve the operating condition transmission path analysis equations. This overcomes the problem of ignoring indicator point data errors in traditional operating condition transmission path analysis, improving the accuracy of operating condition transmission path contribution calculation. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a method for analyzing the contribution of mechanical system transmission paths based on Bayesian algorithm. This method establishes a "source-path-target point" transmission path analysis model based on the theory of working condition transmission path analysis, and uses Bayesian algorithm to solve the transmission rate function matrix, thereby improving the accuracy of solving the transmission rate function matrix.

[0007] Technical solution: This invention discloses a method for analyzing the contribution of transmission paths in mechanical systems based on Bayesian algorithms. The method includes the following steps:

[0008] (1) Determine the active end and the response end of the mechanical vibration system. The excitation force acts on the active end to cause vibration, and the vibration is transmitted to the response end through several transmission paths. At this time, the working condition transmission path analysis model is established as follows:

[0009] Y = XT + N (1)

[0010] In the formula, Y is the system output matrix, X is the system input matrix, T is the transmissivity matrix, and N is the noise vector;

[0011] (2) After transforming the complex matrix equation in the working condition transmission path analysis model into a real number system, define the likelihood function of the working condition transmission path analysis model;

[0012] (3) Establish a prior distribution model of the transmissivity matrix at different frequency points, use the evidence maximization method to calculate the posterior distribution of the transmissivity matrix, and then obtain the transmissivity matrix.

[0013] (4) Solve the contribution of each transmission path under the target working condition based on the transmission rate matrix to complete the analysis of the contribution of the transmission path of the mechanical system.

[0014] Preferably, the working condition transmission path analysis model established in step (1) is a complex matrix equation, and when converting the complex matrix equation in the working condition transmission path analysis model into a real number system in step (2),

[0015] In the formula, Y∈R 2n , X∈R 2m×2n , T∈R 2n , n∈R 2m Re(·) corresponds to the real part, Im(·) corresponds to the imaginary part, n is the number of active excitation sources, and m is the number of response points at the response end.

[0016] Preferably, the specific method for defining the likelihood function of the working condition transfer path analysis model in step (2) is as follows:

[0017] Define n as a Gaussian distribution with zero mean and variance σ. 2 Let the hyperparameter β = 1 / σ 2 To ensure the accuracy of the noise variance, the likelihood function expression for the load transfer path analysis model is obtained from the definition of the Gaussian distribution:

[0018] p(Y|XT,β)=N(XT,β -1 (2)

[0019] Preferably, the prior distribution model of the transmissivity matrix at different frequency points in step (3) is as follows:

[0020] p(T|α)=N(T|α -1 I) (3)

[0021] In the formula, α is the accuracy of the transmissivity variance at each frequency point, and I is the identity matrix.

[0022] Preferably, the posterior distribution of the transmission rate matrix T in step (3) is as follows:

[0023] p(T|Y)=N(μ T , ∑ T (4)

[0024] In the formula, μ r Let ∑ be the mean of the transitivity matrix T. T Let T be the variance of the transitivity matrix;

[0025] The mean and variance of the transitivity matrix T are calculated analytically, as follows:

[0026] μ T =β∑ T X T Y (5)

[0027] ∑ T =(αI+βX) T X) -1 (6)

[0028] In the formula, β and α are both hyperparameters used to obtain the maximum a posteriori estimate of the transmission rate T;

[0029] The evidence maximization method is used to estimate the hyperparameters β and α.

[0030] Preferably, the specific method for estimating hyperparameters β and α using the evidence maximization method is as follows:

[0031] According to Bayes' theorem, the posterior distributions of parameters β and α are as follows:

[0032] p(α,β|Y)Np(Y|α,β)p(α,β) (7)

[0033] In the formula, p(Y|α,β) is the marginal likelihood function of the response signal Y;

[0034] By calculating and taking the logarithm of the marginal likelihood function of the response signal Y, we obtain the evidence function containing α and β, as follows:

[0035]

[0036] In the formula, Γ=αI+βX T X;

[0037] Maximize α and β respectively to obtain estimates of β and α.

[0038] Preferably, the specific method for calculating β and α is as follows:

[0039] Let the eigenvalues ​​of Γ be α+λ i By taking the partial derivatives of the evidence function with respect to α and β respectively and setting them to zero, the update formulas for β and α are obtained as follows:

[0040]

[0041]

[0042] In the formula, λ i Let X be the i-th eigenvalue of matrix X;

[0043] First, given the initial values ​​of hyperparameters β and α, calculate the mean and variance of the transitivity matrix T. Then, update the hyperparameters according to the update formulas for β and α until the evidence function converges.

[0044] Preferably, in step (4), the contribution amount and contribution ratio of each transmission path are calculated based on the transmission rate matrix to complete the transmission path contribution analysis of the mechanical system. The contribution amount of each transmission path is the product of the excitation signal of the excitation source corresponding to the active end and the corresponding element of the transmission rate matrix, wherein the contribution of the i-th excitation source to the j-th response point is Y. j =Xi *H ij .

[0045] Furthermore, since the likelihood function expression of the working condition transmission path analysis model and the prior distribution model of the transmission rate matrix at different frequency points are both Gaussian distributions that satisfy the condition of conjugate distribution, it can be concluded that the posterior distribution of the transmission rate matrix T is also a Gaussian distribution, and the posterior distribution of the transmission rate is proportional to the product of the likelihood probability distribution and the prior probability distribution.

[0046] Furthermore, when the posterior distributions of parameters β and α are obtained according to Bayes' theorem as p(α, β|Y) ∝ p(Y|α, β) p(α, β), they can be obtained by integrating over the transitivity T:

[0047] p(Y|α,β)=∫p(Y|XT,β)p(T|α)dT (11)

[0048] Substituting the likelihood function expression of the load transfer path analysis model and the prior distribution of the transfer rate matrix T into the above equation, we obtain:

[0049]

[0050] Where, E(T)=βE D (T)+αE q (T); E D (T) represents the sum of squares error of the model. E q (T) represents the penalty item. but

[0051]

[0052] Based on the characteristics of the Gaussian distribution, completing the square of the transferability matrix yields:

[0053]

[0054] make

[0055] Γ=αI+βX T X (15)

[0056]

[0057] μ T =βΓX T Y (17)

[0058] Substituting formula (14) into formula (12), the integral term in formula (12) can be rearranged to obtain the following:

[0059]

[0060] Then, by substituting formula (17) into formula (19) and taking the logarithm of the marginal likelihood function, we can obtain formula (8), which is the evidence function containing the unknowns α and β.

[0061] Furthermore, let the eigenvalues ​​of Γ be α+λ. i Taking the partial derivative of the evidence function with respect to α and setting it to zero, we get:

[0062]

[0063] By rearranging the terms, we can obtain formula (9). Similarly, by taking the partial derivative of the evidence function with respect to β, we can obtain formula (10).

[0064] Furthermore, for the estimation process of hyperparameters β and α, firstly, an initial value for hyperparameters β and α is given, and the mean and variance of the posterior distribution are calculated according to formulas (5) and (6). Then, the hyperparameters are updated using formulas (9) and (10) respectively, until the evidence function converges.

[0065] Furthermore, the active end in a vibration system is a structure that receives excitation force and generates vibration, and the sound source is one type of active end.

[0066] Furthermore, the response end is a monitoring device for responding to vibration signals, including one or more of an accelerometer, strain gauge, and microphone, used to monitor different signals such as acceleration signals, sound / vibration signals, and stress signals as needed.

[0067] Beneficial effects: Compared with existing technologies, this method for analyzing the contribution of mechanical system transmission paths based on Bayesian algorithms starts from Bayesian theory and combines the idea of ​​statistical probability models to estimate the posterior distribution of the transmission rate matrix. It effectively avoids the problem of poor accuracy in solving the transmission rate matrix due to unreasonable selection of regularization parameters in traditional regularization methods, and improves the accuracy and efficiency of solving the transmission matrix. Attached Figure Description

[0068] Figure 1 This is a schematic diagram illustrating the basic principles of the path analysis method.

[0069] Figure 2 This is a flowchart of a method for analyzing the contribution of transmission paths in a mechanical system based on a Bayesian algorithm, as described in this invention.

[0070] Figure 3 This is a diagram showing the arrangement of sound sources for verification testing in a specific embodiment of the present invention.

[0071] Figure 4 This is a schematic diagram illustrating the results of solving the transitivity matrix using the Tikhonov method in a specific embodiment of the present invention.

[0072] Figure 5 This is a schematic diagram of the result of solving the transitivity matrix based on the Bayesian algorithm in a specific embodiment of the present invention.

[0073] Figure 6 This is a schematic diagram of the response signal solution obtained by the Tikhonov method in a specific embodiment of the present invention.

[0074] Figure 7 This is a schematic diagram of the response signal solution based on the Bayesian algorithm in a specific embodiment of the present invention. Detailed Implementation

[0075] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0076] In existing transmission path analysis methods, the vibration system is divided into an active end, transmission paths, and a response end. The excitation force acts on the active end, and the vibration is transmitted to the response end through several transmission paths, such as... Figure 1 As shown, when the system has multiple input values, the relationship between the system's input and output can be expressed as follows:

[0077]

[0078] In the formula, X j H is the j-th input in the system (j = 1, 2, ..., m). i，j The above equation represents the transfer function from the i-th input to the j-th output of the system, and can be simplified as follows:

[0079] Y = XH

[0080] In the formula, Y is the system output matrix, X is the system input matrix, and H is the transfer function matrix. However, existing transfer path analysis methods require measuring a large number of transfer functions, and the excitation source needs to be removed during measurement, resulting in low measurement efficiency and failing to meet the requirements for rapid diagnosis of structural vibration and noise.

[0081] To reduce the measurement burden and improve the efficiency of structural vibration noise source analysis, the load case transfer path analysis method has been proposed. This method avoids the measurement burden of the transfer function by establishing a transfer rate matrix T between response points, i.e.

[0082] Y=XT

[0083] Multiply both sides of the above expression by X on the left. T We can obtain:

[0084]

[0085] In the formula, G xx G is the auto-power spectral matrix of the input signal. xyIt is the cross-power spectrum matrix of the input and output signals. The condition for the transfer rate function matrix T to have a solution is the self-power spectrum matrix G of the input signal. xx Reversible, i.e., G xx Let X be a full-rank matrix. Therefore, matrix X must satisfy the condition that all columns are full-rank, meaning that the input signals in each column are uncorrelated. Since the row rank and column rank of a matrix are equal, the input signal matrix X must also satisfy the condition that the number of rows is greater than or equal to the number of columns, i.e., the number of operating conditions is not less than the number of input signals. Thus, the transfer rate matrix T can be expressed as...

[0086]

[0087] In the formula, r represents the number of operating conditions, m represents the number of excitation sources, and n represents the number of response points.

[0088] However, due to interference from test noise and the influence of system modal coupling, even small perturbations can lead to significant errors in the transitivity matrix solution. To address the ill-posedness of the transitivity matrix solution, common existing solutions include singular value decomposition and Tikhonov regularization.

[0089] The two methods described above can improve the accuracy of the transitivity matrix solution to some extent by appropriately selecting truncated singular values ​​and regularization parameters. However, for the singular value decomposition method, the accuracy of the transitivity matrix solution is extremely sensitive to the selection of truncated singular values; improper selection of truncated singular values ​​will seriously affect the accuracy of the transitivity matrix solution. For the Tikhonov regularization method, when the error terms in the signal have strong correlation, the selection of regularization parameters may be unreasonable, leading to large errors in the solution of the transitivity matrix.

[0090] To address the issues of large errors and low accuracy in solving the transferability matrix in existing technologies, this specific embodiment provides a method for analyzing the contribution of the transmission path in a mechanical system based on a Bayesian algorithm, as detailed below. Figure 2 As shown, the specific steps of this method are as follows:

[0091] Step 1: Divide the vibration system into an active end, a transmission path, and a response end. Set several operating conditions and let the active end operate under each condition. Since the response obtained in the actual test includes noise, the input and output relationship of the system, i.e., the operating condition transmission model, is as follows:

[0092] Y = X T + N (1)

[0093] In the formula, Y is the system output matrix, X is the system input matrix, T is the transitivity matrix, and N is the noise vector. Since formula (1) is a complex matrix equation, but Bayesian methods are often used to solve real number systems, the complex matrix equation in formula (1) is transformed into a real number system. In the formula, Y∈R 2n , x∈R 2m×2n , T∈R 2n , n∈R 2m Re(·) corresponds to the real part, Im(·) corresponds to the imaginary part, n is the number of active excitation sources, and m is the number of response points at the response end.

[0094] Step 2, given that n is a Gaussian distribution with zero mean and variance σ. 2 Let the hyperparameter β = 1 / σ 2 To ensure the accuracy of the noise variance, the likelihood function expression for the OTPA model is obtained from the definition of the Gaussian distribution as follows:

[0095] p(Y|XT,β)=N(XT,β -1 (2)

[0096] The prior model of the transitivity matrix T is a Gaussian distribution with zero mean, as follows:

[0097] p(T|α)=N(T|α -1 I) (3)

[0098] In the formula, α represents the accuracy of the transferability variance at each frequency point.

[0099] Step 3: Since both formulas (2) and (3) are Gaussian distributions, satisfying the condition for conjugate distributions, the posterior distribution of the transmission rate matrix T is also a Gaussian distribution. In this case, the posterior distribution of the transmission rate is proportional to the product of the likelihood probability distribution and the prior probability distribution. Completing the square on the exponent term yields the following form of the posterior distribution:

[0100] p(T|Y)=N(μ T , ∑ T (4)

[0101] The mean and variance can be obtained analytically, as follows:

[0102] μ T =β∑ T X T Y (5)

[0103] ∑ T =(αI+βX) T X) -1 (6)

[0104] By introducing hyperparameters β and α to control the likelihood function and the propagation a priori, the maximum a posteriori estimate of the propagation rate T is obtained.

[0105] Step 4: Since the hyperparameters β and α are unknown, the evidence maximization method is used to estimate the hyperparameters β and α. The specific method is as follows:

[0106] According to Bayes' theorem, the posterior distributions for parameters β and α are as follows:

[0107] p(α,β|Y)∝p(Y|α,β)p(α,β) (7)

[0108] In formula (7), p(Y|α,β) is the marginal likelihood function of the response signal Y, which can be obtained by integrating over the transmissibility T, i.e.

[0109] p(Y|α,β)=∫p(Y|XT,β)p(T|α)dT (8)

[0110] Substituting the likelihood function in formula (2) and the prior distribution in formula (3) into formula (8), we get:

[0111]

[0112] in,

[0113] E(T)=βE D (T)+αE q (T) (10)

[0114] Among them, E D (T) represents the sum of squares error of the model. E q (T) represents the penalty item. but

[0115]

[0116] Based on the characteristics of the Gaussian distribution, the transferability matrix can be completed to obtain...

[0117]

[0118] make

[0119] Γ=αI+βX T X (13)

[0120]

[0121] μ T =βΓX T Y (15)

[0122] Substituting formula (12) into formula (9), the integral term in formula (9) can be rearranged as follows:

[0123]

[0124] Then, substituting formula (15) into formula (9) and taking the logarithm of the marginal likelihood function, we can obtain...

[0125]

[0126] Formula (17) is the evidence function containing unknowns α and β. Therefore, by maximizing α and β respectively, we can obtain the estimates of α and β.

[0127] Let the eigenvalues ​​of Γ be α+λ i Take the partial derivative of the evidence function with respect to α and set it to zero, as follows:

[0128]

[0129] rearrangement yields

[0130]

[0131] In the formula,

[0132] Similarly, we can obtain

[0133]

[0134] For the estimation process of hyperparameters β and α, firstly, an initial value for hyperparameters β and α is given, and the mean and variance of the posterior distribution are calculated according to formulas (5) and (6). Then, the hyperparameters are updated using formulas (19) and (20) respectively until the evidence function converges.

[0135] Step 5: By calculating the product of the response signal and the transmissibility matrix under different operating conditions, the contribution and proportion of each transmission path under different operating conditions are obtained, thus completing the operating condition transmission path analysis. The contribution of the i-th excitation source to the j-th response point is Y. j =X i *H ij .

[0136] Step 6: Adjust the structure of the mechanical product based on the contribution amount and contribution ratio of each transmission path under different working conditions, and control the vibration and noise of the mechanical product.

[0137] In this embodiment, the effectiveness of the Bayesian algorithm-based mechanical system transmission path contribution analysis method is verified through simulation analysis. Assuming three sound sources in free field space, the sound sources are arranged as follows... Figure 3 As shown, three points S1, S2 and S3 are taken on a circle with a radius of 0.5m as three simulated sound sources. The human ear response point L is selected 0.5m above the center of the circle. The distance from the human ear response point to the three sound source points is the same. The specific coordinates of each point are shown in Table 1.

[0138] Table 1 Coordinates of the sound source and response points

[0139]

[0140] Given a fixed sound velocity in the spatial sound field, the time it takes for the emitted signals from the three sound sources to reach the target response point remains constant, facilitating the identification of correlations between signals. Given random signals from sound sources under six random operating conditions, 20 dB white noise is randomly added to the response point signals. The transmissibility matrix is ​​solved using both the Tikhonov method and the Bayesian method, and the results are compared with theoretical results. Figure 4 and Figure 5 As shown, the solid line represents the simulation results, and the dashed line represents the theoretical results. Compared to the Tikhonov method, the simulation results of the Bayesian method are in better agreement with the theoretical results. Given a set of random operating conditions, the response signal is solved based on the transmissibility matrix obtained above, and the results are as follows. Figure 6 and Figure 7 As shown in the figure, the solid line represents the simulation results, and the dashed line represents the theoretical results. It can be seen from the figure that the simulation curve obtained by the Bayesian method fits the theoretical curve better. Compared with the Tikhonov method, the OTPA analysis method based on the Bayesian method improves the accuracy of solving the target point response by 15%.

[0141] In summary, this Bayesian-based OTPA analysis method does not require the selection of regularization parameters for the transmissibility matrix at each frequency point, effectively avoiding the problem of unreasonable selection of regularization parameters affecting the accuracy of transmissibility matrix solution, thus improving the accuracy and efficiency of transmissibility matrix solution, and consequently enhancing the accuracy and efficiency of contribution analysis of mechanical systems.

Claims

1. A method for analyzing the contribution of transmission paths in mechanical systems based on Bayesian algorithms, characterized in that: The method includes the following steps: (1) Determine the active end and the response end of the mechanical vibration system. The excitation force acts on the active end to cause vibration, and the vibration is transmitted to the response end through several transmission paths. At this time, the working condition transmission path analysis model is established as follows: Y = XT + N In the formula, Y is the system output matrix, X is the system input matrix, T is the transmissivity matrix, and N is the noise vector; (2) After transforming the complex matrix equation in the working condition transmission path analysis model into a real number system, define the likelihood function of the working condition transmission path analysis model; (3) Establish a prior distribution model of the transmissivity matrix at different frequency points, use the evidence maximization method to calculate the posterior distribution of the transmissivity matrix, and then obtain the transmissivity matrix. (4) Solve the contribution of each transmission path under the target working condition based on the transmission rate matrix to complete the analysis of the contribution of the transmission path of the mechanical system.

2. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 1, characterized in that: The working condition transmission path analysis model established in step (1) is a complex matrix equation. When converting the complex matrix equation in the working condition transmission path analysis model into a real number system in step (2), In the formula, Y∈R 2n , X∈R 2m×2n , T∈R 2n , n∈R 2m Re(·) corresponds to the real part, Im(·) corresponds to the imaginary part, n is the number of active excitation sources, and m is the number of response points at the response end.

3. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 2, characterized in that: The specific method for defining the likelihood function of the working condition transfer path analysis model in step (2) is as follows: Define n as a Gaussian distribution with zero mean and variance σ. 2 Let the hyperparameter β = 1 / σ 2 To ensure the accuracy of the noise variance, the likelihood function expression for the load transfer path analysis model is derived from the definition of the Gaussian distribution as p(Y|XT,β)=N(XT,β). -1 ).

4. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 3, characterized in that: The prior distribution model of the transmissivity matrix at different frequency points in step (3) is as follows: p(T|α)=N(T|α -1 I) In the formula, α is the accuracy of the transmissivity variance at each frequency point, and I is the identity matrix.

5. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 4, characterized in that: The posterior distribution of the transitivity matrix T in step (3) is as follows: p(T|Y)=N(μ T ,∑ T ) In the formula, μ T Let Σ be the mean of the transitivity matrix T. T Let T be the variance of the transitivity matrix. The mean and variance of the transitivity matrix T are calculated analytically, as follows: m T =βΣ T X T Y ∑ T =(αI+βX T X) -1 In the formula, β and α are both hyperparameters used to obtain the maximum a posteriori estimate of the transmission rate T; The evidence maximization method is used to estimate the hyperparameters β and α.

6. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 5, characterized in that: The specific method for estimating hyperparameters β and α using the evidence maximization method is as follows: According to Bayes' theorem, the posterior distributions of parameters β and α are as follows: p(α,β|Y)∝p(Y|α,β)p(α,β) In the formula, p(Y|α,β) is the marginal likelihood function of the response signal Y; By calculating and taking the logarithm of the marginal likelihood function of the response signal Y, we obtain the evidence function containing α and β, as follows: wherein, Γ=αI+βX T X; Maximize α and β respectively to obtain estimates of β and α.

7. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 6, characterized in that: The specific method for calculating β and α is as follows: Let the eigenvalues ​​of Γ be α+λ i By taking the partial derivatives of the evidence function with respect to α and β respectively and setting them to zero, the update formulas for β and α are obtained as follows: In the formula, λ i Let X be the i-th eigenvalue of matrix X; First, given the initial values ​​of hyperparameters β and α, calculate the mean and variance of the transitivity matrix T. Then, update the hyperparameters according to the update formulas for β and α until the evidence function converges.

8. The method for analyzing the contribution of transmission paths in a mechanical system based on Bayesian algorithm according to claim 6, characterized in that: In step (4), the contribution amount and contribution ratio of each transmission path are calculated according to the transmission rate matrix to complete the transmission path contribution analysis of the mechanical system. The contribution amount of each transmission path is the product of the excitation signal of the excitation source corresponding to the active end and the corresponding element of the transmission rate matrix.

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