On-line model updating hybrid test method based on dual adaptive UKF (Unscented Kalman Filter) algorithm

Abstract

The invention provides an online model updating hybrid test method based on a dual adaptive UKF algorithm, and the method comprises the steps: carrying out the initialization of a to-be-recognized constitutive model parameter, determining a parameter initial value seismic oscillation according to a genetic algorithm, inputting the seismic oscillation into a step-by-step integration algorithm, and obtaining the displacement response dk of an overall structure; obtaining the boundary displacement of the test substructure based on the displacement response dk and the constitutive model parameter estimation value of the previous step, carrying out real loading according to the boundary displacement, obtaining the real counterforce and real displacement of the test substructure, and carrying out parameter estimation based on a dual adaptive UKF algorithm; and obtaining a new constitutive model parameter value according to the new constitutive model parameter value and the displacement response dk of the overall structure, obtaining the counter-force Rk of the overall structure on each dynamic degree of freedom, realizing online identification and model updating of the constitutive model parameter, and performing loop iteration to the process of ending the test, thereby improving the precision and stability of parameter identification, and improving the test efficiency. The problem that the loading boundary of the test substructure is inaccurate is effectively solved.

Description

Technical Field

[0001] The present invention specifically relates to an online model updating hybrid test method based on a dual adaptive UKF algorithm, and belongs to the technical field of hybrid tests. Background Art

[0002] As a key technology in earthquake engineering, online model-updating hybrid testing methods have demonstrated excellent assessment capabilities and can effectively determine the nonlinear response characteristics of structures under earthquakes. The application of this technology not only improves the accuracy of structural seismic response predictions but also provides a more solid theoretical basis and practical guidance for the seismic design of engineering structures. However, existing model-updating techniques can be divided into two categories: non-model-based and model-based methods. Non-model-based methods do not require specific information about the structure, components, and materials. However, the ambiguity of model information and physical meaning often leads to heavy computational burdens, low efficiency, and overfitting, limiting their application in online model-updating hybrid testing methods. In contrast, model-based methods perform parameter identification based on a clear finite element numerical model. However, due to the uncertainty of the statistical characteristics of model noise, they often lead to reduced parameter identification stability and computational efficiency. Crucially, how to address the low identification accuracy and computational efficiency caused by model uncertainty is a key issue that urgently needs breakthroughs and innovations.

[0003] Furthermore, due to limitations in loading equipment and test site conditions, current technologies simplify the stress analysis of the test substructure, failing to fully or even approximate its multi-degree-of-freedom boundary conditions. This simplification inevitably alters the actual stress state of the specimen, leading to deviations in the measured reaction forces and displacements. This error accumulation is particularly pronounced when using measured forces for parameter identification to calculate the structural displacement response, potentially distorting the test results.

[0004] Therefore, there is an urgent need for a hybrid test method that can take into account both accurate identification of model parameters and precise loading of boundary conditions. Summary of the Invention

[0005] In order to solve the problems mentioned in the above background technology, the purpose of the present invention is to provide an online model updating hybrid test method based on the dual adaptive UKF algorithm, which initializes the constitutive model parameters to be identified and determines the initial values ​​of the parameters according to the genetic algorithm. The earthquake motion is input into the step-by-step integration algorithm and the displacement response of the whole structure is obtained. k , based on the displacement response d k and the estimated parameters of the constitutive model in the previous step Obtain boundary displacements of the test substructure According to the boundary displacement Perform real loading and obtain the real reaction force of the test substructure and true displacement Parameter estimation is performed based on the dual adaptive UKF algorithm to obtain new constitutive model parameter values According to the new constitutive model parameter values and the displacement response of the overall structure d k Obtain the reaction force R on each dynamic degree of freedom of the overall structure k , and realize the online identification of constitutive model parameters and model update, and iterate the process until the end of the test.

[0006] Preferably, the dual adaptive UKF algorithm comprises the following steps:

[0007] S1, the constitutive parameter vector to be identified in step k Generate (2n+1) Sigma points X for centrosymmetric sampling k,i , and generate the weight W corresponding to the Sigma point mean and covariance i m and W i c ;

[0008] S2, X k,i Substitute into the state equation to obtain the prior estimate And calculate the estimated mean under the k-th step prior state according to the weight and covariance

[0009]

[0010] In the above formula, Q k represents the process noise covariance matrix;

[0011] S3. Calculate the predicted mean of the k+1th step observation based on the observation equation g and the prior estimate of the Sigma point and its covariance

[0012]

[0013]

[0014] In the above formula, d k+1 represents the displacement input vector; w k+1 represents the system observation noise; R k+1 represents the observation noise covariance matrix;

[0015] S4. Through information sequence Determine the Sage-Husa adaptive noise estimation module and the adaptive variance module, and dynamically adjust the observed noise covariance matrix R through the Sage-Husa adaptive noise estimation module k+1 , the adaptive variance module is used to define the filter divergence criterion and the adaptive factor θ k ;

[0016]

[0017] In the above formula, y k+1 Represents the actual observed value of the system; represents the predicted value of the observed quantity;

[0018] S5. Recalculate the observation covariance according to the adaptive module

[0019]

[0020] S6. Calculate the cross-covariance matrix And the Kalman filter gain matrix K k+1 :

[0021]

[0022] S7. Update the mean value of state quantity and covariance P k+1 :

[0023]

[0024] Preferably, the Sage-Husa adaptive noise estimation module is used to dynamically adjust the observed noise covariance matrix R k+1 include:

[0025]

[0026] In the above formula, b represents the gradual disappearance memory factor.

[0027] Preferably, the adaptive variance module is used to define the filter divergence criterion and the adaptive factor θ k include:

[0028]

[0029] Preferably, the initial value of the parameter is determined according to the genetic algorithm The objective function is calculated by using a genetic algorithm and the constitutive model parameters to be identified are obtained. The objective function is the difference between the actual reaction force of the test and the simulated reaction force of the test substructure. The objective function is calculated as follows:

[0030]

[0031] In the above formula, F real,t represents the actual reaction force obtained by the test substructure test loading, F simulation,t represents the simulated reaction force obtained by numerical simulation based on the numerical model of the equivalent test substructure, λ represents the proportional coefficient, and x i Represents the constitutive model parameters to be identified.

[0032] Preferably, the method of determining the initial value of the parameter according to the genetic algorithm further comprises: determining the constitutive model parameter to be identified when the objective function is at the minimum value as the initial value of the parameter

[0033] Preferably, if the constitutive model parameters remain unchanged during identification, the process noise covariance matrix Q k The value of is 0.

[0034] Preferably, the displacement response d of the entire structure is obtained k It includes obtaining the structural response displacement through nonlinear static analysis of the overall structural refined finite element numerical model.

[0035] Preferably, the step-by-step integration algorithm is a central difference method.

[0036] Preferably, an error covariance matrix is ​​obtained, and the singular values ​​of the error covariance matrix are decomposed.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. The present invention is an innovative hybrid test method for online model updating based on the dual adaptive UKF algorithm. It uses finite element software to carry out refined modeling and integrates the Sage-Husa adaptive noise estimation module and the variance adaptive module to construct a parameter identification technology with dual adaptive characteristics. Among them, the Sage-Husa adaptive noise estimation module can estimate the observation noise matrix in real time, thereby effectively suppressing the interference of noise statistical uncertainty on the stability of parameter identification. In addition, the variance adaptive module uses an adaptive factor to determine whether the filter diverges, which greatly avoids the divergence of the filter and significantly improves the accuracy and stability of parameter identification.

[0039] Second, the present invention effectively solves the problem of inaccurate loading of the test substructure boundary conditions in existing online model update hybrid test methods, avoids the error accumulation of measured reaction forces during parameter identification, and thus the distortion of test results. By performing nonlinear static analysis on a refined finite element numerical model of the entire structure to obtain the structural displacement response, rather than relying on the existing method of calculating the structural boundary displacement through measured reaction forces, this method ensures the accuracy of the loading boundary of the test substructure.

[0040] 3. The present invention optimizes the initial values ​​of parameters through genetic algorithm and combines it with UKF algorithm for nonlinear processing to reduce the sensitivity to the initial parameters. It is applicable to the analysis of strong nonlinear structural response. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] For ease of explanation, the present invention is described in detail with reference to the following specific embodiments and accompanying drawings.

[0042] Figure 1 Schematic diagram of the hybrid experimental method for online model updating based on the dual adaptive UKF algorithm;

[0043] Figure 2 Schematic diagram of the dual adaptive UKF algorithm and finite element software parameter estimation method;

[0044] Figure 3 Schematic diagram of the process of the dual adaptive UKF algorithm;

[0045] Figure 4 Schematic diagram of the hybrid test method for online model updating based on the dual adaptive UKF algorithm for prefabricated shear wall structures;

[0046] Figure 5 Schematic diagram of the test substructure reinforcement in the prefabricated shear wall structure. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0048] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show structures and / or processing steps closely related to the solutions according to the present invention, while other details that are not closely related to the present invention are omitted.

[0049] Specific implementation method 1: Combination Figures 1 to 5 This embodiment only provides a preferred embodiment, wherein the online model updating hybrid test method based on the dual adaptive UKF algorithm is specifically to initialize the constitutive model parameters to be identified and determine the initial values ​​of the parameters according to the genetic algorithm. The earthquake motion is input into the step-by-step integration algorithm and the displacement response of the whole structure is obtained. k , based on the displacement response d k and the estimated parameters of the constitutive model in the previous step Obtain boundary displacements of the test substructure According to the boundary displacement Perform real loading and obtain the real reaction force of the test substructure and true displacement Parameter estimation is performed based on the dual adaptive UKF algorithm to obtain new constitutive model parameter values According to the new constitutive model parameter values and the displacement response of the overall structure d k Obtain the reaction force R on each dynamic degree of freedom of the overall structure k , and realize the online identification of constitutive model parameters and model update, and iterate the process until the end of the test.

[0050] Preferably, the present invention provides an innovative hybrid test method, which is based on the dual adaptive UKF algorithm for online model update. In this method, the nonlinear static analysis can be completed by executing the step-by-step integration algorithm and the dual adaptive UKF algorithm in the numerical calculation software, and the numerical calculation software and the finite element software can choose to exchange data through the TCP Socket protocol, combined with Figure 1 and Figure 2 This embodiment is described, wherein Figure 1 Schematic diagram of the hybrid experimental method for online model updating based on the dual adaptive UKF algorithm. Figure 2 Schematic diagram of a dual adaptive UKF algorithm and a finite element software parameter estimation method; this embodiment describes a hybrid test method for online model updating based on a dual adaptive UKF algorithm, comprising the following steps:

[0051] Step 1: Use finite element analysis software to establish a finite element numerical model, use the constitutive model parameters to be identified as state quantities, and determine the initial state vector mean based on the dual adaptive UKF algorithm. Initial state covariance matrix P0, initial process noise covariance matrix Q0, initial observation noise covariance matrix R0, wherein the initial state, i.e., the initial value of the state vector, can be determined by a genetic algorithm, and the parameters are initialized. The parameters may include, but are not limited to, the initial value x0 of the constitutive model parameter to be identified, the input working conditions d0, v0 and a0, and the integration step Δt, etc.;

[0052] Step 2: According to the research object and test loading requirements, Figure 1 As shown in the figure, the earthquake motion is input into the step-by-step integration algorithm to obtain the displacement response d of each dynamic degree of freedom of the overall structure. k , and the displacement response d k The dynamic degrees of freedom are transferred to the corresponding refined finite element numerical model of the overall structure.

[0053] Step 3: Based on the displacement response d in step 2 kand the estimated values ​​of the constitutive model parameters identified in the previous step, i.e., step k-1 Perform nonlinear static analysis of the refined finite element numerical model of the overall structure to obtain the displacement response in the direction of the dynamic freedom degree of the corresponding test substructure Then, the displacement Send to the electro-hydraulic servo loading system;

[0054] Step 4: The electro-hydraulic servo loading system receives the displacement command Complete the actual loading of the test substructure and collect the real force and true displacement Afterwards, and Passed to the constitutive model parameter estimation module;

[0055] Step 5: Parameter estimation is achieved based on the dual adaptive UKF algorithm. For example, in the k-1th step, the constitutive parameter vector to be identified is Generate (2n+1) Sigma points using UT transformation. These Sigma points and step 4 It is then transferred to the refined finite element numerical model of the test substructure to complete (2n+1) times nonlinear static analysis, thereby obtaining the restoring force of the test substructure in the corresponding dynamic degrees of freedom. use and step 4 To update the parameters, we can get the constitutive parameter vector to be identified in step k

[0056] Step 6: The new constitutive parameter values ​​identified in step 5 Send to the overall structure to refine the finite element numerical model and update it;

[0057] Step 7: According to and d k Complete the (2n+2)th nonlinear static analysis of the refined finite element numerical model of the overall structure and obtain the reaction force R on each dynamic degree of freedom of the overall structure k , where the number of nonlinear static analyses is determined according to the number of constitutive parameter vectors to be identified, which is 2n+2 times in total, and n represents the number of constitutive parameter vectors to be identified.

[0058] Step 8. Set the reaction force R k Feedback to the step-by-step integration algorithm to solve the displacement of the next integration step;

[0059] Step 9. Repeat steps 2 to 8 until the end.

[0060] Specific implementation method 2: This embodiment only provides a preferred implementation method. The dual adaptive UKF algorithm includes the following steps:

[0061] S1, the constitutive parameter vector to be identified in step k Generate (2n+1) Sigma points X for centrosymmetric sampling k,i , and generate the weight W corresponding to the Sigma point mean and covariance i m and W i c ;

[0062] S2, X k,i Substitute into the state equation to obtain the prior estimate And calculate the estimated mean under the k-th step prior state according to the weight and covariance

[0063]

[0064] In the above formula, Q k represents the process noise covariance matrix; represents the prior estimate, represents the estimated mean; represents covariance; W i m Represents the weight corresponding to the mean; W i c represents the covariance and the corresponding weight; X k,i Represents Sigma point;

[0065] S3. Calculate the predicted mean of the k+1th step observation based on the observation equation g and the prior estimate of the Sigma point and its covariance

[0066]

[0067] In the above formula, d k+1 Represents the displacement input vector, which here represents the true reaction force of this module w k+1 represents the system observation noise; R k+1 represents the observation noise covariance matrix;

[0068] In the present invention, the observation equation g is presented in a non-analytical form, i.e., a refined numerical model of the equivalent experimental substructure with dynamically adjustable constitutive model parameters is constructed based on finite element software. In each time step, (2n+1) nonlinear static analysis is performed to obtain the reaction force, which here represents the restoring force of the experimental substructure on the corresponding dynamic degree of freedom.

[0069] S4. Through information sequence Determine the Sage-Husa adaptive noise estimation module and the adaptive variance module, and dynamically adjust the observed noise covariance matrix R through the Sage-Husa adaptive noise estimation module k+1 , the adaptive variance module is used to define the filter divergence criterion and the adaptive factor θ k ;

[0070]

[0071] In the above formula, y k+1 Represents the actual observed value of the system, which here represents the real reaction force of this module Represents the predicted value of the observation quantity. This dual adaptive module can effectively improve the stability and recognition accuracy of the system.

[0072] S5. Recalculate the observation covariance according to the adaptive module

[0073]

[0074] S6. Calculate the cross-covariance matrix And the Kalman filter gain matrix K k+1 :

[0075]

[0076] S7. Update the mean value of state quantity and covariance P k+1 :

[0077]

[0078]

[0079] Preferably, for identifying time-invariant constitutive model parameters, the process noise covariance matrix Q k The value of can be 0.

[0080] Specific implementation method three: This embodiment only provides a preferred implementation method, which dynamically adjusts the observed noise covariance matrix R through the Sage-Husa adaptive noise estimation module. k+1 include:

[0081]

[0082] In the above formula, b represents the gradual disappearance memory factor.

[0083] Specific implementation method 4: This embodiment only provides a preferred implementation method, which defines the filter divergence criterion and the adaptive factor θ by the adaptive variance module. k include:

[0084]

[0085] Specific implementation method 5: This embodiment only provides a preferred implementation method. Figure 3 As shown in Figure 2, the specific method of using the dual adaptive UKF algorithm to identify the test substructure state online is:

[0086] (1) Prediction step

[0087] Assume that the state error covariance matrix at time k is P k , estimated mean value of state quantity The state covariance matrix P k Singular value decomposition, we get P k =USV T ;

[0088] Among them, U and V are P k The left and right singular vectors of S are diagonal matrices and the values ​​on the diagonal are P k The singular value of P k When it is a symmetric matrix, the left and right singular vectors are the same.

[0089] by Sampling 2n+1 Sigma sampling points X for central symmetry k,i ,

[0090]

[0091] Where i represents the matrix The number of columns; λ is the first scaling factor.

[0092] Generate Sigma sampling point mean and covariance P k The corresponding weight W i m and W i c ,

[0093]

[0094] X k,i Substitute into the state equation f to obtain the prior estimate Then calculate the mean of the k-th step prior state according to the weight and covariance

[0095]

[0096] Will Substitute into the observation equation g to obtain the observation vector of Sigma point Calculate the predicted mean of the k+1th step observation and its variance

[0097]

[0098] Where R k+1 represents the observation noise covariance matrix.

[0099] Furthermore, by using finite element software to construct a refined finite element numerical model of the equivalent test substructure, the observation equation g can be expressed in a non-analytical form, revealing the complex relationship between the restoring force of the test substructure and its constitutive model.

[0100] (2) Update step

[0101] First, define the information sequence

[0102]

[0103] Secondly, determine the Sage-Husa adaptive noise estimation module:

[0104]

[0105] Where b represents the gradual disappearance memory factor.

[0106] Again, define the filter divergence criterion and the adaptive factor θ k .

[0107]

[0108] Afterwards, according to the adaptive factor θ k , recalculate the observation covariance

[0109]

[0110] Then, the cross-covariance matrix is ​​calculated And the Kalman filter gain matrix K k+1 :

[0111]

[0112] Finally, update the state mean and covariance P k+1 :

[0113]

[0114] Adaptive factor θ kThe sum of squares of the differences between the actual observations and the predicted observations is used as the basis for judging the divergence of the filter, thereby correcting the observation covariance matrix and the cross-covariance matrix, effectively reducing the sensitivity of the initial parameter settings and greatly avoiding the divergence of the filter.

[0115] The Sage-Husa adaptive noise estimation module uses information sequences to estimate and correct the statistical characteristics of noise in real time, thereby reducing the impact of noise on recognition robustness.

[0116] Specific implementation method six: This embodiment only provides a preferred implementation method, which determines the initial value of the parameter according to the genetic algorithm. The objective function is calculated by a genetic algorithm and the constitutive model parameters to be identified are obtained. The Sheffield genetic algorithm may be used, but is not limited to the Sheffield genetic algorithm. The objective function is the difference between the actual reaction force of the test and the simulated reaction force of the test substructure. The objective function is minimized to find the optimal solution of the constitutive model parameters. The objective function is calculated as follows:

[0117]

[0118] In the above formula, F real,t represents the actual reaction force obtained by the test substructure test loading, F simulation,t represents the simulated reaction force obtained by numerical simulation based on the numerical model of the equivalent test substructure, λ represents the proportional coefficient, and x i Represents the constitutive model parameters to be identified.

[0119] Specific implementation method seven: This embodiment only provides a preferred implementation method. Determining the initial value of the parameter according to the genetic algorithm also includes: determining the constitutive model parameter to be identified when the objective function is the minimum value as the initial value of the parameter At this point, the actual reaction force is similar to the simulated reaction force. In the objective function, the difference between the actual and simulated force solutions is calculated and the sum of squares is taken. When this function reaches its minimum, the initial values ​​of the constitutive model parameters to be identified are determined. This approach effectively avoids the problem of poor identification accuracy caused by improper selection of the initial state mean.

[0120] Specific embodiment eight: This embodiment only provides a preferred embodiment to obtain the displacement response d of the overall structure. kIt includes obtaining the structural response displacement through nonlinear static analysis of the refined finite element numerical model of the overall structure; specifically, using finite element analysis software to establish a refined finite element numerical model of the overall structure and a refined finite element numerical model of an equivalent test substructure, dividing the part with stronger nonlinear characteristics in the overall structure into a test substructure, and using finite element analysis software to establish a numerical model of the test substructure, that is, a refined finite element numerical model of the equivalent test substructure; wherein the nonlinear static analysis content is the content calculated by the finite element software based on the refined finite element numerical model, which is the existing technology in this field and will not be elaborated in the present invention.

[0121] Specific implementation method 9: This embodiment only provides a preferred implementation method. The step-by-step integration algorithm in the present invention can be implemented by using, but is not limited to, the central difference method.

[0122] Specific implementation method 10. This embodiment only provides a preferred implementation method, obtaining the error covariance matrix, and performing error covariance matrix singular value decomposition in completing parameter estimation based on the dual adaptive UKF algorithm. Specifically, assuming that the state error covariance matrix at time k is P k , state quantity mean estimation The state covariance matrix P k Singular value decomposition, we get P k =USV T ; Among them, U and V are P k The left and right singular vectors of S are diagonal matrices and the values ​​on the diagonal are P k The singular value of P k When the matrix is ​​symmetric, the left and right singular vectors are the same. The use of singular value decomposition can effectively avoid recognition failures caused by differences in orders of magnitude, computer floating point errors, and calculation errors.

[0123] In the above-mentioned embodiment, a dual adaptive UKF algorithm is proposed to complete the constitutive model parameter identification, which effectively solves the problem of insufficient identification accuracy caused by noise statistical uncertainty; nonlinear static analysis is performed through a refined finite element numerical model of the overall structure to obtain the structural displacement response, rather than relying on the existing method of calculating the structural boundary displacement by measuring the reaction force, which effectively solves the problem of distortion of the test results caused by inaccurate loading of the boundary conditions of the test substructure.

[0124] Specific implementation method eleven, this embodiment provides a specific implementation method, which is applied to shear wall structures. This embodiment takes a two-layer prefabricated shear wall structure as an example to illustrate the basic principles and usage steps of the method of the present invention. In order to provide experimental data support for the design of prefabricated shear wall structures, it is necessary to conduct seismic tests on prefabricated shear wall structures. For this type of structure, the parameter identification method in the existing technology is easily affected by factors such as the selection of initial parameter values ​​and the uncertainty of noise statistical characteristics, and the identification error of the strong nonlinear stage is large. The dual adaptive UKF algorithm can improve the accuracy of online model parameter identification, effectively reduce the sensitivity of initial parameter settings, and adjust the observation noise covariance matrix in real time, thereby improving the parameter identification accuracy and robustness in the online model update test method.

[0125] This embodiment uses an innovative dual adaptive UKF algorithm to complete parameter identification to reduce the adverse effects of uncertainty in the observation model, thereby improving the accuracy and stability of parameter identification. Considering the shear deformation and bending deformation of the structure, a refined finite element numerical model based on layered shell elements is established and numerical simulation is completed. Figure 4 To the attached Figure 5 The present invention is described in detail. A hybrid test method based on online model update of dual adaptive UKF algorithm is described in detail. Figure 4 As shown, the prototype structure adopts a two-layer prefabricated shear wall structure, and the bottom layer structure is used as the test substructure. The steel bar diagram of the test substructure is shown in Figure 5 shown.

[0126] The method of this embodiment for performing an online model update hybrid experiment based on a dual adaptive UKF algorithm specifically includes the following steps:

[0127] Step 1: Use OpenSees finite element analysis software to establish the overall finite element numerical model of the prefabricated shear wall structure and the finite element numerical model of the equivalent test substructure. The bottom layer is the test substructure, and the top layer is the numerical substructure.

[0128] Determine the mass M and damping C of the overall structure, the step size Δt of the step-by-step integration algorithm, and the input working conditions (ground motion records);

[0129] Step 2: Use genetic algorithm (Sheffield algorithm) objective function:

[0130]

[0131] Where, F real,t is the actual reaction force obtained by the test substructure test loading, F simulation,t The reaction force of the physical substructure is obtained by numerical simulation based on the numerical model of the equivalent test substructure, λ is the proportional coefficient, x iare the constitutive model parameters to be identified. Determine the initial values ​​of the material constitutive model parameters and covariance P0, integration step Δt;

[0132] Step 3: Establish the dual adaptive UKF algorithm state equation:

[0133] x k+1 =x k

[0134] Step 4: Step-by-step integration algorithm, based on Matlab mathematical analysis software, establish the overall structure central difference method. The detailed calculation process is as follows:

[0135]

[0136] Step 5. The algorithm observation equation is: y k+1 =g(x k+1 ,d k+1 ), and define the initial process noise covariance matrix Q0 and the initial observation noise covariance matrix R0; d k+1 is the displacement input vector, where the experimental substructure is used

[0137] Step 6: Input the working condition, for example, the earthquake motion is El Centro, i.e. NS, 1940 wave;

[0138] Step 7: Change step 4d k and The displacement response of the test substructure is obtained by transferring the force to the finite element numerical model of the whole structure for nonlinear static analysis. The test substructure reaction force of the kth step is obtained by sending it to the MTS electro-hydraulic servo loading system through the HyTest Connector. and displacement

[0139] Step 8: and the k-1-step constitutive model parameters The numerical model of the equivalent test substructure is transferred to the nonlinear static analysis to obtain the observed reaction force of the test substructure. Re-transmit to the constitutive model parameter identification module;

[0140] Step 9: Based on the reaction observation of the substructure in the k-th step and the constitutive model parameters in the k-1 step The dual adaptive UKF algorithm is used to online identify the constitutive model parameters of the equal-generation test substructure to obtain the updated constitutive model parameters.

[0141] Specifically, the specific method of using the dual adaptive UKF algorithm to online identify the parameters of the equal generation test substructure model is as follows:

[0142] A1. Assume that the state error covariance matrix at time k is P k , state quantity mean estimation The covariance matrix P k Singular value decomposition, we get P k =USV T ;

[0143] A2. Find the symmetrical sampling 2n+1 Sigma sampling points X k,i :

[0144]

[0145] Where i represents the matrix The number of columns; λ is the first scaling factor.

[0146] A3. Determine the Sigma point weight. The mathematical expression for weight calculation is:

[0147]

[0148] A4, X k,i Substitute into the state equation f to obtain the prior estimate Then calculate the mean of the k-th step prior state according to the weight and covariance

[0149]

[0150] A5. Substitute into the observation equation g to obtain the observation vector Sigma point Calculate the predicted mean of the k+1th step observation and its variance

[0151]

[0152] Where R k+1 represents the observation noise covariance matrix.

[0153] A6. Define the information sequence:

[0154]

[0155] A7. Determine the Sage-Husa adaptive noise estimation module:

[0156]

[0157] A8. Define the filter divergence criterion and the adaptive forgetting factor ρ k choose:

[0158]

[0159] in,

[0160]

[0161] A9, according to the adaptive factor θ k , recalculate the k-th step observation variance

[0162]

[0163] A10. Calculate the cross-covariance matrix and Kalman gain matrix of the state and observation quantities:

[0164]

[0165] A11. Using the observed value y k+1 and K k+1 Update the prior estimates of mean and variance

[0166]

[0167] In the above formula, To complete the dual adaptive UKF algorithm identification value, it is used for the current step online model update.

[0168] The analysis method of the online model updating hybrid test based on the dual adaptive UKF algorithm is used to calculate the reaction force of the overall structure, and then the constitutive model parameters are updated based on this reaction force to calculate the response of the overall structure, thereby realizing the analysis of the overall structure.

[0169] Step 10: In step 4d k and step nine On this basis, the nonlinear static analysis of the refined finite element model of the overall structure is completed, and the reaction force R on each dynamic degree of freedom of the overall structure is calculated. k and fed back to the step-by-step integration algorithm;

[0170] Step 11. Repeat steps 6 to 10 until the test is completed.

[0171] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A hybrid experimental method for online model updating based on a dual adaptive UKF algorithm, characterized in that: The experimental method is to initialize the constitutive model parameters to be identified and determine the initial values ​​of the parameters according to the genetic algorithm The earthquake motion is input into the step-by-step integration algorithm and the displacement response of the whole structure is obtained. k , based on the displacement response d k and the estimated parameters of the constitutive model in the previous step Obtain boundary displacements of the test substructure According to the boundary displacement Perform real loading and obtain the real reaction force of the test substructure and true displacement Parameter estimation is performed based on the dual adaptive UKF algorithm to obtain new constitutive model parameter values According to the new constitutive model parameter values and the displacement response of the overall structure d k Obtain the reaction force R on each dynamic degree of freedom of the overall structure k , and realize the online identification of constitutive model parameters and model update, and iterate the process until the end of the test.

2. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 1 is characterized in that: The dual adaptive UKF algorithm includes the following steps: S1, the constitutive parameter vector to be identified in step k Generate (2n+1) Sigma points X for centrosymmetric sampling k,i , and generate the weight W corresponding to the Sigma point mean and covariance i m and W i c ; S2, X k,i Substitute into the state equation to obtain the prior estimate And calculate the estimated mean under the k-th step prior state according to the weight and covariance In the above formula, Q k represents the process noise covariance matrix; S3, according to the observation equation g and the prior estimate of Sigma point Calculate the predicted mean of the k+1th step observation and its covariance In the above formula, d k+1 represents the displacement input vector; w k+1 represents the system observation noise; R k+1 represents the observation noise covariance matrix; S4. Through information sequence Determine the Sage-Husa adaptive noise estimation module and the adaptive variance module, and dynamically adjust the observed noise covariance matrix R through the Sage-Husa adaptive noise estimation module k+1 , the adaptive variance module is used to define the filter divergence criterion and the adaptive factor θ k ; In the above formula, y k+1 Represents the actual observation value of the system; represents the predicted value of the observed quantity; S5. Recalculate the observation covariance according to the adaptive module S6. Calculate the cross-covariance matrix And the Kalman filter gain matrix K k+1 : S7. Update the mean value of state quantity and state covariance P k+1 :

3. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 2 is characterized in that: The Sage-Husa adaptive noise estimation module is used to dynamically adjust the observed noise covariance matrix R k+1 include: In the above formula, b represents the gradual disappearance memory factor.

4. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 3 is characterized in that: The adaptive variance module defines the filter divergence criterion and the adaptive factor θ k include:

5. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 4 is characterized in that: Determining the initial value of the parameter according to the genetic algorithm The objective function is calculated by using a genetic algorithm and the constitutive model parameters to be identified are obtained. The objective function is the difference between the actual reaction force of the test and the simulated reaction force of the test substructure. The objective function is calculated as follows: In the above formula, F real,t represents the actual reaction force obtained by the test substructure test loading, F simulation,t represents the simulated reaction force obtained by numerical simulation based on the numerical model of the equivalent test substructure, λ represents the proportional coefficient, and x i Represents the constitutive model parameters to be identified.

6. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 5 is characterized in that: The method of determining the initial value of the parameter according to the genetic algorithm further includes: determining the constitutive model parameter to be identified when the objective function is the minimum value as the initial value of the parameter 7. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 6 is characterized in that: If the constitutive model parameters remain unchanged during identification, the process noise covariance matrix Q k The value of is 0.

8. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 7 is characterized in that: The displacement response d of the whole structure is obtained k It includes obtaining the structural response displacement through nonlinear static analysis of the overall structural refined finite element numerical model.

9. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to any one of claims 1 to 8, characterized in that: The step-by-step integration algorithm is the central difference method.

10. The hybrid test method for online model updating based on the dual adaptive UKF algorithm according to claim 9 is characterized in that: Obtain the error covariance matrix and decompose the error covariance matrix singular values.

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