Structural load and parameter joint identification method based on Gibbs sampling

Abstract

The invention discloses a structure load and parameter joint identification method based on Gibbs sampling. The method comprises the following steps: S1, establishing a discrete state space model of a linear time-invariant dynamic system; s2, fitting an unknown external load by adopting an orthogonal polynomial, and representing the external load as a linear combination of an orthogonal polynomial basis function and a fitting coefficient; s3, defining an uncertainty parameter set, wherein the set comprises the fitting coefficient, the measurement noise, the unknown structure parameter and the fitting error; s4, constructing a multilayer Bayesian model based on the Bayesian theory, wherein the model comprises a likelihood function layer, a load prior model layer and hyper-parameters; s5, solving the multilayer Bayesian model by adopting a Gibbs sampling method, and obtaining posterior probability density distribution of each uncertainty parameter through iterative sampling; and S6, based on the posterior probability density distribution, obtaining an identification result of the external load and the unknown structure parameters. According to the method, the parameter uncertainty is considered, and the recognition precision and robustness of the dynamic load and parameters of the complex structure are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of load and parameter identification in structural dynamics, and particularly relates to a structural load and parameter joint identification method based on Gibbs sampling. BACKGROUND

[0002] Load identification, as a core inverse problem of structural dynamics, is widely used in structural design, fault diagnosis and other scenarios. Existing technologies are divided into frequency domain method and time domain method: the frequency domain method realizes load identification through Fourier transform, but the identification accuracy of transient loads such as impact is low; the time domain method directly solves the time domain load history, and has wider applicability, but the traditional method assumes that the structural parameters are completely known, and ignores the parameter uncertainty (such as material property error, geometric size deviation, etc.) which exists universally in engineering, resulting in distorted identification results.

[0003] The traditional regularization method (such as Tikhonov method) needs to manually set the regularization parameter, which is difficult to adapt to dynamic adjustment under complex working conditions, and has the risk of over-regularization or under-regularization. Therefore, there is an urgent need for a joint identification technology that can consider the structural parameter uncertainty and has adaptive regularization capability. SUMMARY

[0004] The purpose of the application is to solve the above problems, and a joint identification method is proposed, which regards the load and the parameter as random variables, and realizes dynamic regularization and efficient inference through the Bayesian framework and Gibbs sampling.

[0005] To solve the above technical problems, the application adopts the following scheme:

[0006] A structural load and parameter joint identification method based on Gibbs sampling includes the following steps:

[0007] Step S1: a discrete state space model of a linear time-invariant dynamic system is established, and the model includes a system matrix, an input matrix, an output influence matrix, an output transfer matrix, a state variable, an external load vector and a response vector.

[0008] Step S2: the unknown external load is fitted by using orthogonal polynomials, and the external load is expressed as a linear combination of orthogonal polynomial basis functions and fitting coefficients.

[0009] Step S3: an uncertainty parameter set is defined, which includes the fitting coefficients, the measurement noise, the unknown structural parameters and the fitting error, and each parameter is assumed to follow a predetermined probability distribution.

[0010] Step S4: constructing a multi-layer Bayesian model based on Bayesian theory, the model comprising a likelihood function layer, a load prior model layer, and a hyperparameter layer, wherein: the likelihood function layer is constructed based on a response observation value containing noise and a load identification equation; the load prior model layer comprises a prior distribution of the fitting coefficient and the fitting error; and the hyperparameter layer comprises a preset hyperparameter, the hyperparameter being a known parameter of a probability distribution.

[0011] Step S5: solving the multi-layer Bayesian model by using a Gibbs sampling method, and obtaining a posterior probability density distribution of each uncertain parameter through iterative sampling, wherein: a conditional probability distribution of the load, the fitting coefficient, the fitting error, and the measurement noise is directly sampled, the conditional probability distribution being a normal distribution or a gamma distribution; and the Metropolis-Hastings algorithm is used to sample the unknown structure parameter.

[0012] Step S6: obtaining an identification result of the external load and the unknown structure parameter based on the posterior probability density distribution.

[0013] The scheme described in the application is the result of further research based on the previous research results of the inventors. The previous research results are: Wang Ting, Wan Zimin, et al. Structure time-domain load identification based on Gibbs sampling [J], Vibration and Shock, Vol. 37 No. 2 2018: 85-90. The paper assumes that the structure parameters (such as stiffness and elastic modulus) are known, and the unknown quantities only contain the load and the measurement noise (random variables), and does not consider the influence of parameter uncertainty on the identification result. In the present application, the unknown structure parameters (such as elastic modulus and stiffness), the fitting coefficient (orthogonal polynomial fitting load), the fitting error, and the structure parameter are included in the set of uncertain parameters, a more complex multi-layer Bayesian model is constructed; and the continuous load is converted into a finite-dimensional coefficient identification by orthogonal polynomial fitting load, the problem complexity is reduced, the parameter correlation is decoupled by using the orthogonality, and the identification distortion problem caused by parameter error in engineering is solved. In addition, because the unknown structure parameters are included in the set of uncertain parameters in the present application, the Metropolis-Hastings algorithm is used to process the complex posterior distribution, forming a hybrid sampling strategy that combines Gibbs sampling (processing load, coefficient, and noise) and Metropolis-Hastings (processing structure parameters), which provides a feasible and efficient numerical solution scheme for complex Bayesian models.

[0014] Further optimization, in the step S1, the matrix form equation of the discrete state space model is:

[0015] Y = HF + W

[0016] wherein Y is a response vector, H is a load influence matrix, F is an external load vector, and W is a measurement noise vector and subject to a normal distribution with a mean of 0.

[0017] Further optimization, in the step S1, the expression of the load influence matrix H is:

[0018]

[0019] wherein H1=D, H t =R(A) nt-1 B, t≥2, A is the system matrix, B is the input matrix, R is the output influence matrix, and D is the output transfer matrix.

[0020] Further optimization, in the step S2, the orthogonal polynomial is the Legendre orthogonal polynomial, and the fitting expression of the external load is:

[0021] F=Φm+η

[0022] wherein Φ is the base function of the orthogonal polynomial, m is the fitting coefficient, and η is the fitting error and satisfies the gamma distribution. The unknown load is a continuous time function, and it is difficult to directly identify the values at infinite time points. Through orthogonal polynomial fitting, the load identification is converted into the identification of the fitting coefficient, which greatly reduces the dimension; at the same time, the orthogonality of the orthogonal polynomial can eliminate the correlation between the coefficients, provide support for the “parameter independence assumption” in the subsequent Bayesian model, and avoid the problem of unidentifiability caused by parameter coupling.

[0023] Further optimization, in the step S3, the set of uncertainty parameters wherein: m is the fitting coefficient, is the measurement noise variance, is the fitting error variance, and α is an unknown structure parameter;

[0024] The measurement noise W satisfies the gamma distribution with parameters (k w ,β w ), that is,

[0025] The fitting error η satisfies the gamma distribution with parameters (kη, βη); that is,

[0026] The fitting coefficient m satisfies the normal distribution with a mean of 0, that is, m ~ N(0, σ m 2 );

[0027] The unknown structure parameter α includes the elastic modulus and the stiffness, and satisfies the uniform distribution.

[0028] Further optimization, in the step S4,

[0029] Likelihood function:

[0030] Prior distribution:

[0031] Hyperparameter layer: hyperparameters {k w ,β w ,kη,βη} are known constants;

[0032] where p(·) denotes the probability density function, N(·) denotes the normal distribution probability density function, n t denotes the number of measured responses.

[0033] Further optimization, in the step S5, the iteration process of Gibbs sampling includes:

[0034] Step S5.1: initialization, extract initial values of fitting coefficients, measurement noise, unknown structure parameters and fitting errors from prior distribution, set starting point for iterative sampling;

[0035] Step S5.2: loop the following sampling steps until convergence:

[0036] a. based on the current parameter value, sample the posterior value of the external load;

[0037] b. based on the current external load and noise parameters, sample the posterior value of the fitting coefficient;

[0038] c. based on the current external load and fitting coefficient, sample the posterior value of the fitting error;

[0039] d. based on the current response and external load, sample the posterior value of the measurement noise;

[0040] e. use Metropolis-Hastings algorithm to sample the posterior value of the unknown structure parameters.

[0041] Further optimization, in the step S6, the identification result is the mean value of the posterior probability density distribution, and the marginal probability density distribution of the external load is obtained by integrating the posterior distribution of the fitting coefficient, noise and error parameters.

[0042] A system for implementing the above method, characterized by comprising:

[0043] Model construction module: for establishing a discrete state space model of the structure;

[0044] Load fitting module: for fitting unknown external load using orthogonal polynomials;

[0045] Probability modeling module: for defining uncertainty parameters and constructing a multi-layer Bayesian model;

[0046] Sampling calculation module: used for performing Gibbs sampling and Metropolis-Hastings algorithm to obtain a posterior distribution;

[0047] Result output module: used for outputting the identification result of the load and the structural parameter based on the posterior distribution.

[0048] Compared with the prior art, the beneficial effects of the present application are:

[0049] 1. Joint identification is more robust: the method breaks the assumption that the structural parameter is known, and simultaneously inverts the load and the parameter, overcoming the interference of parameter error on identification.

[0050] 2. Regularization is adaptive: the method is based on the Bayesian framework and Gibbs sampling, and naturally realizes regularization without manual parameter adjustment, and is suitable for complex dynamic scenarios.

[0051] 3. Uncertainty is quantifiable: the method outputs the probability characteristics of the posterior distribution, and provides a risk quantification basis for engineering decision-making. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 Fig. 1 is a schematic diagram of a planar truss structure (a) and a finite element model (b);

[0053] Figure 2 Fig. 3 is a comparison between the true value and the identified value of the load in Case 1 (sinusoidal load);

[0054] Figure 3 Fig. 4 is a comparison between the true value and the identified value of the load in Case 2 (double sinusoidal load);

[0055] Figure 4 Fig. 6 is a schematic diagram of sensor arrangement and excitation position of a simply supported plate;

[0056] Figure 5 Fig. 7 is a comparison between the load identification results of a simply supported plate;

[0057] Figure 6 Fig. 8 is a comparison between the adaptive regularization parameter and the GCV method parameter. DETAILED DESCRIPTION

[0058] The technical solutions of the present application will be described in detail below in combination with embodiments, but the protection scope of the present application is not limited to the embodiments.

[0059] A joint identification method of structural load and parameter based on Gibbs sampling, comprising the following steps:

[0060] S1: a discrete state space model of a linear time-invariant dynamic system is established, which includes a system matrix, an input matrix, an output influence matrix, an output transfer matrix, a state variable, an external load vector and a response vector.

[0061] For a linear time-invariant dynamic system, its discrete state space equation is expressed as:

[0062] x t+1 =Ax t +Bf t (1)

[0063] y t =Rx t +Df t (2)

[0064] Wherein: t ∈ [1, n t ] represents a discrete time; x t is a state space variable; f t is an external load vector; A, B, R and D are respectively a system matrix, an input matrix, an output influence matrix and an output transfer matrix; y t is a response vector.

[0065] Assuming that the initial state x1 is zero, and letting H1 = D, H t = R(A) nt-1 B, the matrix form is obtained by simultaneous equations:

[0066] Y = HF + W (3)

[0067] Wherein, Y is a response vector, H is a load influence matrix, F is an external load vector, W is a measurement noise vector and obeys a normal distribution with a mean of 0.

[0068]

[0069] S2: unknown external load is fitted by using orthogonal polynomials, and the external load is expressed as a linear combination of orthogonal polynomial basis functions and fitting coefficients. The orthogonal polynomial is Legendre orthogonal polynomial, and the fitting expression of the external load is:

[0070] F = Φm + η (5)

[0071] Wherein, Φ is a basis function of orthogonal polynomials, m is a fitting coefficient, and η is a fitting error and obeys a gamma distribution.

[0072] S3: an uncertainty parameter set is defined, wherein: m is a fitting coefficient, is a measurement noise variance, is a fitting error variance, and α is an unknown structure parameter.

[0073] The measurement noise W obeys a gamma distribution with parameters (k w ,β w ), that is

[0074] The fitting error η obeys a gamma distribution with parameters (kη,βη); that is

[0075] The fitting coefficient m obeys a normal distribution with mean 0, that is m ~ N(0,σ m 2 );

[0076] The unknown structure parameter α includes elastic modulus, stiffness, and obeys a uniform distribution.

[0077] Because then:

[0078]

[0079] where the prior distribution is

[0080]

[0081] is a normal distribution, and p(m) is assumed to be a uniform distribution.

[0082] As can be seen from formula (6), the uncertainty parameters θ of the load identification under the Bayesian framework include F, m, α, and each parameter is independent. In addition, the hyperparameters {k W ,β W ,k η ,β η} are assumed to be known. Since the hierarchical Bayesian model is very stable for the value of the hyperparameter, the hyperparameters in the above prior can take any value.

[0083] S4: A multi-layer Bayesian model is constructed based on the Bayesian theory, and the model includes a likelihood function layer, a load prior model layer, and a hyperparameter layer.

[0084] Likelihood function:

[0085] Prior distribution:

[0086] Hyperparameter layer: the hyperparameters {k w ,β w ,kη,βη} are known constants;

[0087] where p(·) represents a probability density function, N(·) represents a normal distribution probability density function, n tThe number of measured responses.

[0088] S5: Gibbs sampling method is used to solve the multi-layer Bayesian model, and the posterior probability density distribution of each uncertainty parameter is obtained by iterative sampling, wherein: the conditional probability distribution of the load, the fitting coefficient, the fitting error and the measurement noise is directly sampled, and the conditional probability distribution is a normal distribution or a gamma distribution; the Metropolis-Hastings algorithm is used to sample the unknown structure parameters.

[0089] In addition to the unknown structure parameters, the prior distribution and the likelihood function used in the application are standard distributions (normal distribution and gamma distribution), so the conditional probability density function of each parameter can be derived as a standard distribution form, and the specific derivation process is as follows:

[0090] 1), the conditional probability density function of the load:

[0091]

[0092] Taking the logarithm of the right side of formula (8), we have:

[0093]

[0094] Taking the first-order partial derivative of formula (9) with respect to the load F to find the extreme value, and the extreme point is:

[0095]

[0096] Taking the second-order partial derivative of formula (9) with respect to the load F to find the extreme value, and the extreme point is

[0097]

[0098] The above and That is, the mean and variance of the conditional posterior normal distribution (or the mean and variance of the normal distribution can be directly obtained by multiplying two normal distributions), denoted as:

[0099]

[0100] 2), the conditional probability density function of the fitting coefficient is a normal distribution, as shown below:

[0101]

[0102] Wherein,

[0103]

[0104] 3), the conditional probability density function of the orthogonal polynomial fitting error of the load:

[0105]

[0106] where

[0107] 4) The conditional probability density function of the measurement noise variance:

[0108]

[0109] where,

[0110] 5) The conditional probability density function of the unknown structural parameters is obtained using the Metropolis-Hastings algorithm

[0111] (1) A candidate point is first generated

[0112] α' ~ q(α | α (i) (19)

[0113] where q(α) is the probability density function chosen by the user.

[0114] (2) The acceptance probability is calculated

[0115]

[0116] (3) The acceptance or rejection decision is as follows, a: U(0, 1)

[0117]

[0118] There are many MCMC (Markov Chain Monte Carlo) algorithms in the prior art. Since all the conditional posterior probability distributions derived in the present application are standard distributions, such as normal distribution, gamma distribution, the application conditions of the Gibbs sampling method are met. Based on the Gibbs sampling, the load identification algorithm is summarized as follows:

[0119] 1. Initialization: m, α and

[0120] 2. Sampling

[0121]

[0122] 3. Sampling

[0123]

[0124] 4. Sampling

[0125]

[0126] 5. Sampling

[0127]

[0128] 6. Using Metropolis-Hastings algorithm to sample

[0129] 7. Go back to Step 2 and repeat the iteration of sampling until enough particles are sampled.

[0130] In the MCMC mechanism, there is a period of running time in the initial chain to ensure that the chain reaches a stationary state, which is called the burn-in period. As long as the chain runs for a long enough time, the burn-in period has little effect on the posterior inference. From the Bayesian point of view, the identified load is equivalent to the marginal probability density of the load, i.e., p(F|Y). The marginal probability density of the load is as follows:

[0131]

[0132] Combining equation (5), equation (23) can be written as follows:

[0133]

[0134] where,

[0135]

[0136] As can be seen from equations (23)-(25), the above expectation is approximately the average of the samples , where the sample point values are all obtained from equation (13) of the Gibbs sampling method, i.e., the normal distribution form of equation (23). The structural parameter a can be obtained by taking the mean value based on the load identification algorithm of the Gibbs sampling in Step 6.

[0137] S6: Based on the posterior probability density distribution, the identification results of the external load and unknown structural parameters are obtained. The identification result is the mean value of the posterior probability density distribution, and the marginal probability density distribution of the external load is obtained by integrating the posterior distribution of the fitting coefficient, noise and error parameters.

[0138] Comparison of Bayesian method and regularization method: equation (10) can be expanded as follows:

[0139]

[0140] It can be seen that formula (26) is somewhat related to the traditional regularization method. The essence of the standard Tikhonov method is to solve the load that satisfies the minimum mean square error,

[0141]

[0142] That is, the regularized solution form of the load is as follows:

[0143]

[0144] Comparing formula (26) with (28), it is found that the relationship between the two formulas, that is, the role of the prior coefficient is equivalent to the regularization parameter The difference is that the prior coefficient is self-adaptive with time history, while the regularization parameter λ is a constant value, which shows that the load identification method under the Bayesian framework has the intrinsic adaptive regularization property.

[0145] Verification example:

[0146] Two structural models are used to verify the feasibility of the method in this paper, which are plane truss structure model and four-side simply supported plate structure model.

[0147] Example 1: Plane truss:

[0148] In this embodiment, the object of the numerical simulation case is a plane truss, as shown in Figure 1 Fig. (a) is a plane truss structure diagram, and Fig. (b) is a finite element model of the truss. There are 31 bar elements in the structure, in which the length of the horizontal bar element is 2m, the length of the 45° inclined bar element is and the cross-sectional size of all bar elements is the same, and the cross-sectional area is 8.95×10 -5 m 2 . The remaining structural parameters are as follows: the elastic modulus is 2×10 7 Pa, the density is 7.85×10 3 kg / m3. The bar element is assumed to be a lumped mass model, which adopts two nodes at both ends, and each node contains two degrees of freedom of x / y (horizontal / vertical). The structural system damping adopts a viscous damping model C=δM+ζK, in which M represents the system mass matrix, K represents the stiffness matrix, and the damping coefficients are δ=0.1523 and ζ=4.6203×10 -4 , respectively. The dynamic external load is applied to node 9 (vertical direction), and the sine function excitation format is as follows:

[0149] f=40sin(2πt) (29)

[0150] In addition, nodes 1 and 17 are fixed constraints. Only acceleration measurement signals are used, in which the measurement degree numbers are [4, 6, 8, 12, 15, 16, 18] respectively, a total of 7, 5% background noise is integrated into the measurement signals, in which the stiffness of rod units 5, 10 and 14 is unknown, and the initial value is 759.5, 1342.5, 1163.5 N / m.

[0151] The method described in the present application is used below to verify the sine and double-sine load excitation functions respectively. Table 1 is the unit stiffness identification error value of Case 1-Case 2.

[0152] Case 1: 10 Legendre orthogonal polynomials are used to fit the external load, and the method described in the present application is used for joint identification of load / parameters, and the identified load is as shown in Figure 2 , it can be seen that the identification result of the load is relatively accurate, and the relative error rate is 2.75%. In addition, the unit stiffness identification value is also relatively accurate.

[0153] Case 2: The external load is the above-mentioned double-sine function curve, 10 Legendre orthogonal polynomials are used to fit the external load, and the method described in the present application is used for joint identification of load / parameters, and the result is as shown in Figure 3 , the identification accuracy is good, and the relative error rate is 3.04%. In addition, the accuracy of the unit stiffness identification value is high.

[0154] Table 1: Stiffness identification error value of truss

[0155] Relative error values (%) Case 1 Case 2 Unit 5 3.56 3.43 Unit 14 4.38 4.79 Unit 15 4.59 4.62

[0156] Example 2: Four-edge simply supported plate

[0157] The simply supported plate shown in Figure 4 is used as a verification object, and the geometric parameters of the plate are 1200x600x20mm (length, width, height), the Young's modulus, density and Poisson's ratio are 201 GPa, 7850 kg / m 3 , 0.3 respectively. The excitation load acts on the center (325mm, 225mm) of the thin plate, the direction is vertically upward, and the size is as follows

[0158] f=400sin(200πt)cos(400πt) (30)

[0159] Two acceleration signals are used as measurement signals for identification, the positions are as shown in Figure 4 , and the black box represents the acceleration sensor. The hyperparameters are set to (k W =10, β W =1), (k η =10, β η=1). The external load was fitted by 10 Legendre orthogonal polynomials, and the load and elastic modulus were identified by the method described in the application. The initial value of the elastic modulus was 180 GPa, the sampling time was 0.00003 s, the sampling particle number was 10000, and the identified load was as shown in Figure 5 It can be seen that the identified load value is stable and accurate, and the identified curve is very close to the true load. The average value of the identified elastic modulus after stabilization is 200.89 GPa. In addition, the regularization parameter of the method described in the application and the regularization parameter of the GCV criterion (assuming that the elastic modulus is known) are as shown in Figure 6 It can be seen that the regularization parameter of the method described in the application has an adaptive follow-up characteristic, while the regularization parameter of the GCV criterion is a constant value and is located between the adaptive regularization parameter intervals.

[0160] The application is based on the method of orthogonal polynomial curve fitting to fit the time domain history of unknown load, converts the identification of the load into the identification of the base function coefficients, and establishes the Gibbs method for the joint identification of the load and unknown structure parameters under the Bayesian framework. Compared with the traditional Tikhonov regularization method, the method has an intrinsic adaptive regularization performance. The numerical example verifies the effectiveness of the method by using the Legendre orthogonal polynomial fitting method.

[0161] The above is only an embodiment of the application in a certain specific river basin, but the protection scope of the application is not limited thereto. If a person skilled in the art is inspired thereby, without departing from the purpose of the application, similar methods and embodiments can be designed without creativity, which should belong to the protection scope of the application.

Claims

1. A method for structural load and parameter joint identification based on Gibbs sampling, characterized in that, The method comprises the following steps: Step S1: establishing a discrete state space model of a linear time-invariant dynamic system, the model comprising a system matrix, an input matrix, an output influence matrix, an output transfer matrix, a state variable, an external load vector and a response vector; Step S2: fitting the unknown external load by using orthogonal polynomials, and expressing the external load as a linear combination of orthogonal polynomial basis functions and fitting coefficients; Step S3: defining a set of uncertainty parameters, the set comprising the fitting coefficients, the measurement noise, the unknown structural parameters and the fitting error, and assuming that each parameter respectively obeys a preset probability distribution; Step S4: constructing a multi-layer Bayesian model based on the Bayesian theory, the model comprising a likelihood function layer, a load prior model layer and a hyperparameter layer, wherein: the likelihood function layer is constructed based on the response observation value containing noise and a load identification equation; the load prior model layer comprises the prior distribution of the fitting coefficients and the fitting error; the hyperparameter layer comprises preset hyperparameters, which are known parameters of the probability distribution; Step S5: solving the multi-layer Bayesian model by using the Gibbs sampling method, and obtaining the posterior probability density distribution of each uncertainty parameter through iterative sampling; wherein: the conditional probability distribution of the load, the fitting coefficients, the fitting error and the measurement noise is directly sampled, and the conditional probability distribution is a normal distribution or a gamma distribution; the Metropolis-Hastings algorithm is used to sample the unknown structural parameters; Step S6: obtaining the identification results of the external load and the unknown structural parameters based on the posterior probability density distribution.

2. The method of claim 1, wherein, In the step S1, the matrix form equation of the discrete state space model is: Y=HF+W Wherein, Y is the response vector, H is the load influence matrix, F is the external load vector, and W is the measurement noise vector and obeys a normal distribution with a mean value of 0.

3. The method of claim 2, wherein, In the step S1, the expression of the load influence matrix H is: where H1 = D, H t = R(A) nt-1 B, t≥2, t∈[2, n t ]; A is a system matrix, B is an input matrix, R is an output influence matrix, and D is an output transfer matrix.

4. The method of claim 3, wherein, In the step S2, the orthogonal polynomials are Legendre orthogonal polynomials, and the fitting expression of the external load is: F=Φm+η Wherein, Φ is the basis function of the orthogonal polynomials, m is the fitting coefficient, and η is the fitting error and obeys a gamma distribution.

5. The method of claim 4, wherein, The step S3 wherein: m is a fitting coefficient, is a measurement noise variance, is a fitting error variance, and a is an unknown structure parameter; The measurement noise W is subject to a gamma distribution with parameters (k w ,β w ), i.e. The fitting error η is subject to a gamma distribution with parameters (kη, βη); that is The fitting coefficient m obeys a normal distribution with a mean of 0, i.e., m ~ N(0, σ m 2 ) The unknown structural parameters α include the elastic modulus and the stiffness, and obey a uniform distribution.

6. The method of claim 5, wherein, In the step S4, Likelihood function: Prior distribution: Hyperparameter layer: hyperparameter {k w ,β w ,kη,βη} are known constants; where p(·) denotes a probability density function, N(·) denotes a normal distribution probability density function, n s denotes the number of measurements responses.

7. The method of claim 6, wherein, In the step S5, the iterative process of the Gibbs sampling comprises: Step S5.1: initialization, extracting initial values of the fitting coefficients, the measurement noise, the unknown structural parameters and the fitting error from the prior distribution, and setting a starting point for the iterative sampling; Step S5.2: cyclically executing the following sampling steps until convergence: a. based on the current parameter values, sampling to obtain the posterior value of the external load; b. based on the current external load and noise parameters, sampling to obtain the posterior value of the fitting coefficients; c. based on the current external load and fitting coefficients, sampling to obtain the posterior value of the fitting error; d. based on the current response and external load, sampling to obtain the posterior value of the measurement noise; e. using the Metropolis-Hastings algorithm to sample to obtain the posterior value of the unknown structural parameters.

8. The method of claim 7, wherein, In the step S6, the identification result is the mean value of the posterior probability density distribution, and the marginal probability density distribution of the external load is obtained by integrating the posterior distribution of the fitting coefficients, the noise and the error parameters.

9. A system for implementing the method of any one of claims 1 to 8, characterized in that, The method comprises the following steps: a model construction module for establishing a discrete state space model of the structure; a load fitting module for fitting the unknown external load by using orthogonal polynomials; a probability modeling module for defining uncertainty parameters and constructing a multi-layer Bayesian model; a sampling calculation module for performing Gibbs sampling and Metropolis-Hastings algorithm to obtain a posterior distribution; a result output module for outputting the identification result of the load and the structure parameters based on the posterior distribution.

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