A hybrid test method based on double adaptive UKF algorithm online model updating

Abstract

The application provides an online model updating hybrid test method based on a double adaptive UKF algorithm, which comprises the following steps: initializing to-be-identified constitutive model parameters, inputting parameter initial value seismic vibration determined according to a genetic algorithm into a step-by-step integral algorithm, and obtaining displacement response d k of the overall structure k , obtaining boundary displacement of a test substructure based on displacement response d k and constitutive model parameter estimation value of the previous step, performing real loading according to the boundary displacement and obtaining real reaction force and real displacement of the test substructure, performing parameter estimation based on a double adaptive UKF algorithm, obtaining new constitutive model parameter value, obtaining reaction force R k on each dynamic degree of freedom of the overall structure based on the new constitutive model parameter value and the displacement response d k of the overall structure, and realizing online identification and model updating of the constitutive model parameters, which are iterated and circulate until the test is completed, thereby improving the precision and stability of parameter identification and effectively solving the problem of inaccurate loading boundary of the test substructure.

Description

Technical Field

[0001] This invention specifically relates to a hybrid experimental method for online model updating based on a dual adaptive UKF algorithm, belonging to the field of hybrid experimental technology. Background Technology

[0002] Online model-updated hybrid testing methods, as a key technology in earthquake engineering, have demonstrated excellent evaluation capabilities, effectively determining the nonlinear response characteristics of structures under seismic loading. This technology not only improves the accuracy of structural seismic response prediction 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 broadly categorized into model-free and model-based methods. Model-free methods do not require specific information about the structure, components, and materials, but the ambiguity of model information and physical meaning often leads to heavy computational burdens, low efficiency, and overfitting, limiting their application in online model-updated hybrid testing methods. In contrast, model-based methods perform parameter identification based on a defined finite element numerical model, but the uncertainty of model noise statistical characteristics often leads to decreased parameter identification stability and reduced computational efficiency. Crucially, addressing the problems of low identification accuracy and computational efficiency caused by model uncertainty is a key area requiring breakthroughs and innovations.

[0003] Furthermore, due to limitations in loading equipment and test site conditions, current techniques simplify the stress analysis of test substructures, failing to fully or approximately simulate their multi-degree-of-freedom boundary conditions. This simplification inevitably alters the actual stress state of the specimen, leading to deviations in measured reactions and displacements. This error accumulation is particularly pronounced when measured forces are used for parameter identification to calculate structural displacement responses, potentially resulting in distorted test results.

[0004] Therefore, there is an urgent need for a hybrid experimental method that can simultaneously achieve accurate identification of model parameters and precise loading of boundary conditions. Summary of the Invention

[0005] To address the problems mentioned in the background section, the present invention aims to provide a hybrid experimental method for online model updating based on a dual adaptive UKF algorithm. This method initializes the parameters of the constitutive model to be identified and determines the initial parameter values ​​according to a genetic algorithm. The seismic motion is input into a step-by-step integration algorithm to obtain the displacement response d of the overall structure. k Based on displacement response d k And the constitutive model parameter estimates from the previous step Obtain the boundary displacements of the test substructure According to boundary displacement Perform actual loading and obtain the actual reaction force of the experimental substructure. and actual displacement Parameter estimation is performed based on the dual adaptive UKF algorithm to obtain new constitutive model parameter values. Based on 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 It also enables online identification of constitutive model parameters and model updates, iterating in a loop until the end of the experiment.

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

[0007] S1, the constitutive parameter vector to be identified at step k. Generate (2n+1) Sigma points X for center-symmetric sampling k,i And generate the weights W corresponding to the mean and covariance of the Sigma points. i m and W i c ;

[0008] S2, X k,i Substituting into the state equation, we obtain the prior estimate. And calculate the estimated mean of the prior state at step k based on the weights. Covariance

[0009]

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

[0011] S3. Based on the observation equation g and the prior estimate of the Sigma point, calculate the predicted mean of the observations at step k+1. and its covariance

[0012]

[0013]

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

[0015] S4, via information sequence The Sage-Husa adaptive noise estimation module and adaptive variance module are determined, and the observation noise covariance matrix R is dynamically adjusted through the Sage-Husa adaptive noise estimation module. k+1 The filter divergence criterion and the adaptive factor θ are defined through an adaptive variance module. k ;

[0016]

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

[0018] S5. Based on the adaptive module, recalculate the observation covariance.

[0019]

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

[0021]

[0022] S7, Update the mean of state variables Covariance P k+1 :

[0023]

[0024] Preferably, the observation noise covariance matrix R is dynamically adjusted using the Sage-Husa adaptive noise estimation module. k+1 include:

[0025]

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

[0027] Preferably, the filter divergence criterion and the adaptive factor θ are defined using an adaptive variance module. k include:

[0028]

[0029] Preferably, the initial parameter values ​​are determined using a genetic algorithm. This includes using a genetic algorithm to calculate an objective function and obtain the parameters of the constitutive model to be identified, where the objective function is the difference between the actual reaction force in the experiment and the simulated reaction force of the experimental substructure. The objective function is calculated as follows:

[0030]

[0031] In the above formula, F real,t F represents the actual reaction force obtained from the experimental loading of the substructure. simulation,t The simulated reaction force is obtained through numerical simulation based on the numerical model of the substructure of the equivalent generation test, where λ represents the proportionality coefficient and x represents the simulated reaction force. i This represents the constitutive model parameters to be identified.

[0032] Preferably, the step of determining the initial parameter values ​​according to the genetic algorithm further includes: determining the constitutive model parameters to be identified when the objective function is minimized as the initial parameter values.

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

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

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

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

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] I. This invention presents an innovative online model update hybrid experiment method based on a dual adaptive UKF algorithm. It utilizes finite element software for refined modeling and integrates a Sage-Husa adaptive noise estimation module and a variance adaptive module to construct a parameter identification technology with dual adaptive characteristics. Specifically, the Sage-Husa adaptive noise estimation module can estimate the observed noise matrix in real time, effectively suppressing the interference of noise statistical uncertainty on the stability of parameter identification. Furthermore, the variance adaptive module uses an adaptive factor to determine whether the filter diverges, greatly avoiding filter divergence and significantly improving the accuracy and stability of parameter identification.

[0039] Second, this invention effectively solves the problem of inaccurate loading of boundary conditions of the test substructure in the existing online model update hybrid test method, avoids the accumulation of errors in measured reaction force during parameter identification, and thus avoids the distortion of test results. It obtains the structural displacement response by performing nonlinear static analysis through a refined finite element numerical model of the overall structure, instead of relying on the method of calculating the structural boundary displacement by measured reaction force in the existing technology. This method ensures the accuracy of the loading boundary of the test substructure.

[0040] Third, this invention optimizes the initial parameter values ​​through a genetic algorithm and combines it with the UKF algorithm for nonlinear processing, thereby reducing the sensitivity to the initial parameters and making it applicable to the response analysis of strongly nonlinear structures. Attached Figure Description

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

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

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

[0044] Figure 3 This is a flowchart illustrating the dual adaptive UKF algorithm.

[0045] Figure 4 A schematic diagram of a hybrid experimental method for online model updating based on a dual adaptive UKF algorithm in prefabricated shear wall structures;

[0046] Figure 5 This is a schematic diagram of the reinforcing steel bars in the experimental substructure of a prefabricated shear wall structure. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

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

[0049] Specific implementation method one: Combining Figures 1 to 5 This embodiment describes only a preferred implementation method, in which the online model update hybrid experiment method based on the dual adaptive UKF algorithm specifically initializes the parameters of the constitutive model to be identified and determines the initial values ​​of the parameters according to the genetic algorithm. The seismic motion is input into a step-by-step integration algorithm to obtain the displacement response d of the overall structure. k Based on displacement response d k And the constitutive model parameter estimates from the previous step Obtain the boundary displacements of the test substructure According to boundary displacement Perform actual loading and obtain the actual reaction force of the experimental substructure. and actual displacement Parameter estimation is performed based on the dual adaptive UKF algorithm to obtain new constitutive model parameter values. Based on 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 It also enables online identification of constitutive model parameters and model updates, iterating in a loop until the end of the experiment.

[0050] Preferably, this invention provides an innovative hybrid experimental method based on the dual adaptive UKF algorithm for online model updating. In this method, the successive integration algorithm and the dual adaptive UKF algorithm can be executed in numerical computation software, while nonlinear static analysis is performed using finite element software. The numerical computation software and the finite element software can optionally exchange data via the TCP Socket protocol. Figure 1 and Figure 2 This embodiment will be described, wherein Figure 1 This is a schematic diagram of a hybrid experimental method for online model updating based on a dual adaptive UKF algorithm. Figure 2 This diagram illustrates the combination of the dual adaptive UKF algorithm and the finite element software parameter estimation method. The embodiment describes a hybrid experimental method for online model updating based on the dual adaptive UKF algorithm, comprising the following steps:

[0051] Step 1: Establish a finite element numerical model using finite element analysis software, take the parameters of the constitutive model to be identified as state variables, and determine the mean of the initial state vector based on the dual adaptive UKF algorithm. The initial state covariance matrix P0, the initial process noise covariance matrix Q0, and the 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 can be initialized. The parameters may include, but are not limited to, the initial values ​​of the constitutive model parameters to be identified, x0, the input conditions d0, v0 and a0, and the integration step size Δt, etc.

[0052] Step 2: Based on the research subjects and experimental loading requirements, such as... Figure 1 As shown, by inputting the seismic motion into the stepwise integration algorithm, the displacement response d on each dynamic degree of freedom of the overall structure is obtained. k and the displacement response d k It is transferred to the dynamic degrees of freedom corresponding to the refined finite element numerical model of the overall structure.

[0053] Step 3: Displacement response d based on Step 2 kAnd the constitutive model parameter estimates identified in the previous step, i.e., the (k-1)th step. A refined finite element numerical model of the overall structure was used for nonlinear static analysis to obtain the displacement response in the dynamic degrees of freedom of the corresponding experimental substructure. Then, the displacement Send to the electro-hydraulic servo loading system;

[0054] Step 4: The electro-hydraulic servo loading system receives displacement commands. The experimental substructure underwent actual loading, and the actual forces were collected. and actual displacement After that, and Passed to the constitutive model parameter estimation module;

[0055] Step 5: Parameter estimation is performed based on the dual adaptive UKF algorithm. For example, in step k-1, the constitutive parameter vector to be identified... Generate (2n+1) Sigma points using the UT transformation. These Sigma points are related to those in step 4. The results were then passed to a refined finite element numerical model of the experimental substructure to complete (2n+1) nonlinear static analyses, thereby obtaining the restoring forces of the experimental substructure in the corresponding dynamic degrees of freedom. use and step 4 By updating the parameters, we can obtain the constitutive parameter vector to be identified at step k.

[0056] Step 6: The new constitutive parameter values ​​identified in Step 5 are... Send to and update the overall structural refined finite element numerical model;

[0057] Step 7, according to and d k The (2n+2)th nonlinear static analysis of the refined finite element numerical model of the overall structure was completed, and the reaction forces R on each dynamic degree of freedom of the overall structure were obtained. k The number of nonlinear static analyses is determined based on the number of constitutive parameter vectors to be identified, totaling 2n+2 times, where n represents the number of constitutive parameter vectors to be identified.

[0058] Step 8. Apply the reaction force R k Feedback is fed into the successive integration algorithm to solve for the displacement of the next integration step;

[0059] Step 9. Repeat steps 2 through 8 until finished.

[0060] Specific implementation method two, 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 at step k. Generate (2n+1) Sigma points X for center-symmetric sampling k,i And generate the weights W corresponding to the mean and covariance of the Sigma points. i m and W i c ;

[0062] S2, X k,i Substituting into the state equation, we obtain the prior estimate. And calculate the estimated mean of the prior state at step k based on the weights. Covariance

[0063]

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

[0065] S3. Based on the observation equation g and the prior estimate of the Sigma point, calculate the predicted mean of the observations at step k+1. and its covariance

[0066]

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

[0068] In this invention, the observation equation g is presented in a non-analytical form, that is, a refined numerical model of the equivalent experimental substructure with dynamically adjustable constitutive model parameters is constructed based on finite element software. At each time step, (2n+1) nonlinear static analyses are performed to obtain the reaction forces, which here represent the restoring forces of the experimental substructure in the corresponding dynamic degrees of freedom.

[0069] S4, via information sequence The Sage-Husa adaptive noise estimation module and adaptive variance module are determined, and the observation noise covariance matrix R is dynamically adjusted through the Sage-Husa adaptive noise estimation module. k+1 The filter divergence criterion and the adaptive factor θ are defined through an adaptive variance module. k ;

[0070]

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

[0072] S5. Based on the adaptive module, recalculate the observation covariance.

[0073]

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

[0075]

[0076] S7, Update the mean of state variables Covariance P k+1 :

[0077]

[0078]

[0079] Preferably, for constitutive model parameters that are invariant during identification, 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 uses the Sage-Husa adaptive noise estimation module to dynamically adjust the observation noise covariance matrix R. k+1 include:

[0081]

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

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

[0084]

[0085] Specific implementation method five: This embodiment only provides a preferred implementation method, such as... Figure 3 As shown, the specific method for online identification of the experimental substructure state using the dual adaptive UKF algorithm is as follows:

[0086] (1) Prediction step

[0087] Assume the state error covariance matrix at time k is P k mean of state quantity estimates The state covariance matrix P k Singular value decomposition yields P k =USV T ;

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

[0089] by To centrally symmetrically sample 2n+1 Sigma sampling points X k,i ,

[0090]

[0091] In the formula, i represents the matrix The column number; λ is the first proportionality coefficient.

[0092] Generate the mean of Sigma sampling points Covariance P k The corresponding weight W i m and W i c ,

[0093]

[0094] X k,i Substituting into the state equation f, we obtain the prior estimate. Then, the mean of the prior state at step k is calculated based on the weights. Covariance

[0095]

[0096] Will Substituting into the observation equation g, we obtain the observation vector of the Sigma point. Calculate the predicted mean of the observations at step k+1. and its variance

[0097]

[0098] In the formula, R k+1 This represents the observation noise covariance matrix.

[0099] Furthermore, by utilizing finite element software, a refined finite element numerical model of the equivalent experimental substructure was constructed, and the observation equation g was expressed in a non-analytical form, revealing the complex relationship between the restoring force of the experimental substructure and its constitutive model.

[0100] (2) Update step

[0101] First, define the information sequence.

[0102]

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

[0104]

[0105] In the formula, b represents the fading memory factor.

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

[0107]

[0108] Then, based on the adaptive factor θ k Recalculate the covariance of the observations

[0109]

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

[0111]

[0112] Finally, update the mean of the state variables. Covariance P k+1 :

[0113]

[0114] Adaptive factor θ kThe filter divergence is judged based on the sum of squared differences between the actual and predicted observations, thereby correcting the observation covariance matrix and cross-covariance matrix, effectively reducing the sensitivity of the initial parameter setting and greatly avoiding the divergence of the filter.

[0115] The Sage-Husa adaptive noise estimation module uses information sequences to estimate and correct noise statistical characteristics 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 parameter values ​​based on a genetic algorithm. This includes using a genetic algorithm to calculate the objective function and obtain the constitutive model parameters to be identified. This may include, but is not limited to, using the Sheffield genetic algorithm. The objective function is the difference between the actual experimental reaction force and the simulated reaction force of the experimental substructure. Minimizing the objective function yields the optimal solution for the constitutive model parameters. The objective function is calculated as follows:

[0117]

[0118] In the above formula, F real,t F represents the actual reaction force obtained from the experimental loading of the substructure. simulation,t The simulated reaction force is obtained through numerical simulation based on the numerical model of the substructure of the equivalent generation test, where λ represents the proportionality coefficient and x represents the simulated reaction force. i This represents the constitutive model parameters to be identified.

[0119] In specific implementation method seven, this embodiment only provides a preferred implementation method. Determining the initial parameter values ​​according to the genetic algorithm further includes: determining the constitutive model parameters to be identified when the objective function is at its minimum as the initial parameter values. 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 initial state means.

[0120] Specific implementation method eight: This embodiment only provides a preferred implementation method for obtaining the displacement response d of the overall structure. kThis includes obtaining structural response displacements through nonlinear static analysis using a refined finite element numerical model of the overall structure. Specifically, a refined finite element numerical model of the overall structure and a refined finite element numerical model of the equivalent test substructure are established using finite element analysis software. The parts of the overall structure with stronger nonlinear characteristics are divided into test substructures, and numerical models of these substructures, i.e., refined finite element numerical models of the equivalent test substructures, are established using finite element analysis software. The nonlinear static analysis content is calculated by the finite element software based on the refined finite element numerical model and is existing technology in this field; therefore, it will not be elaborated upon in this invention.

[0121] Specific implementation method nine. This embodiment only provides a preferred implementation method. In this invention, the step-by-step integration algorithm can be implemented by, but is not limited to, the central difference method.

[0122] Specific implementation method ten: This embodiment only provides a preferred implementation method, which obtains the error covariance matrix and performs singular value decomposition of the error covariance matrix during parameter estimation based on the dual adaptive UKF algorithm. Specifically, it is assumed that the state error covariance matrix at time k is P. k State variable mean estimation The state covariance matrix P k Singular value decomposition yields P k =USV T Where U and V are P k The left and right singular vectors, S is a diagonal matrix and the values ​​on the diagonal are P. k The singular values ​​of P k When the matrix is ​​symmetric, the singular vectors on the left and right are the same. Using singular value decomposition can effectively avoid problems such as differences in magnitude, computer floating-point operations, and computational errors that could lead to recognition failure.

[0123] In the above implementation, a dual adaptive UKF algorithm is proposed to complete the identification of constitutive model parameters, which effectively solves the problem of insufficient identification accuracy caused by the statistical uncertainty of noise. The structural displacement response is obtained by nonlinear static analysis through a refined finite element numerical model of the overall structure, instead of relying on the method of calculating the structural boundary displacement by measured reaction force in the existing technology. This effectively solves the problem of distorted 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 applied to shear wall structures. Taking a two-story prefabricated shear wall structure as an example, this embodiment illustrates the basic principles and usage steps of the method. To provide experimental data support for the design of prefabricated shear wall structures, seismic tests are required. For such structures, existing parameter identification methods are easily affected by factors such as the selection of initial parameter values ​​and the uncertainty of noise statistical characteristics, resulting in significant identification errors in the strongly nonlinear stage. 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 employs an innovative dual adaptive UKF algorithm for 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 and bending deformation of the structure, a refined finite element numerical model based on layered shell elements is established and numerical simulation is performed, combined with the attached... Figure 4 To be continued Figure 5 The present invention will be described in detail below. The architecture of a hybrid experimental method for online model updating based on a dual adaptive UKF algorithm is as follows: Figure 4 As shown, the prototype structure adopts a two-story prefabricated shear wall structure, with the bottom layer structure serving as the experimental substructure. A schematic diagram of the reinforcement in the experimental substructure is shown below. Figure 5 As shown.

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

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

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

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

[0130]

[0131] In the formula, F real,t F represents the actual reaction force obtained from the experimental loading of the substructure. simulation,t To obtain the reaction force of the physical substructure through numerical simulation based on the numerical model of the equivalent experimental substructure, λ is the scaling factor, and x iThese are the parameters of the constitutive model to be identified. Initial values ​​for the material constitutive model parameters are determined. Covariance P0, integration step size Δt;

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

[0133] x k+1 =x k

[0134] Step 4: Step-by-step integration algorithm. Based on Matlab mathematical analysis software, establish the central difference method for the overall structure. 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 The displacement input vector is used here, and the experimental substructure is employed.

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

[0138] Step 7: (The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full k and The data is passed to the overall structural finite element numerical model for nonlinear static analysis to obtain the displacement loading response of the experimental substructure. The reaction force of the test substructure at step k is obtained by sending the data to the MTS electro-hydraulic servo loading system via the HyTest Connector and performing the test loading. and displacement

[0139] Step 8: and constitutive model parameters at step k-1 The numerical model of the equivalent experimental substructure is passed to the nonlinear static analysis calculation to obtain the reaction force observation of the experimental substructure. The parameter is then passed back to the constitutive model parameter identification module.

[0140] Step 9: Based on the reaction force observations of the substructure in step k and the constitutive model parameters in step (k-1) The dual adaptive UKF algorithm is used to identify the constitutive model parameters of the equivalent generation experimental substructure online, and the updated constitutive model parameters are obtained.

[0141] Specifically, the method for online identification of parameters of the equivalent experimental substructure model using the dual adaptive UKF algorithm is as follows:

[0142] A1. Assume the state error covariance matrix at time k is P. k State variable mean estimation The covariance matrix P k Singular value decomposition yields P k =USV T ;

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

[0144]

[0145] In the formula, i represents the matrix The column number; λ is the first proportionality coefficient.

[0146] A3. Determine the weights of the Sigma points. The mathematical expression for weight calculation is as follows:

[0147]

[0148] A4, X k,i Substituting into the state equation f, we obtain the prior estimate. Then, the mean of the prior state at step k is calculated based on the weights. Covariance

[0149]

[0150] A5, will Substituting into the observation equation g, we obtain the observation vector Sigma point. Calculate the predicted mean of the observations at step k+1. and its variance

[0151]

[0152] In the formula, R k+1 This 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. Based on the adaptive factor θ k Recalculate the observation variance at step k.

[0162]

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

[0164]

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

[0166]

[0167] In the above formula, To complete the dual adaptive UKF algorithm identification values, which are used for the current step of online model update.

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

[0169] Step 10, in step four d k and step nine Based on this, a refined finite element model of the overall structure was completed for nonlinear static analysis, and the reaction forces R on each dynamic degree of freedom of the overall structure were calculated. k And feed it back to the successive integration algorithm;

[0170] Step 11: Repeat steps 6 through 10 until the experiment is completed.

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

Claims

1. A hybrid test method based on a double adaptive UKF algorithm online model updating, characterized in that, The test method is to initialize the constitutive model parameters to be identified and determine the initial values of the parameters according to the genetic algorithm , seismic input into the step-by-step integration algorithm and obtain the displacement response of the overall structure , based on the displacement response and the estimated value of the constitutive model parameters in the previous step obtain the boundary displacement of the test substructure , according to the boundary displacement real load and obtain the real reaction force of the test substructure and the real displacement , based on the double adaptive UKF algorithm to estimate the parameters and obtain the new constitutive model parameter value , according to the new constitutive model parameter value and the displacement response of the overall structure obtain the reaction force on each dynamic degree of freedom of the overall structure , and realize the online identification and model updating of the constitutive model parameters, and the process is iterated until the test is completed. The double adaptive UKF algorithm comprises the following steps: S1, the to-be-identified constitutive parameter vector of the kth step Generate (2n+1) Sigma points for the central symmetric sampling And generate the weight corresponding to the mean and covariance of the Sigma points And ; S2, the Substitute into the state equation to obtain the a priori estimate and the estimated mean at the kth step of the a priori state is calculated according to the weight and the covariance : ； ； ； In the above formula, represents the process noise covariance matrix; S3. Compute the predicted mean of the observations at step k+1 and the prior estimate of the Sigma point , compute the predicted mean of the observations at step k+1 and its covariance : ； ； ； In the above formula, represents a displacement input vector; represents a system observation noise; represents an observation noise covariance matrix; S4, passing the information sequence determining a Sage-Husa adaptive noise estimation module and an adaptive variance module, and dynamically adjusting the observation noise covariance matrix through the Sage-Husa adaptive noise estimation module defining a filter divergence criterion and an adaptive factor through the adaptive variance module ; ； In the above formula, represents the actual observation value of the system; represents the predicted value of the observation S5. Recompute the observation covariance according to the adaptive module : ； S6, compute cross-covariance matrix and Kalman filter gain matrix : ； ； S7, update the state quantity mean and the state quantity covariance : ； 。 2. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 1, characterized in that, the dynamically adjusting the observation noise covariance matrix by the Sage-Husa adaptive noise estimation module comprising: ； ； In the above formula, b represents a fading memory factor.

3. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 2, characterized in that, the filter divergence criterion and the adaptive factor are defined by an adaptive variance module comprising: ； 。 4. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 3, characterized in that, The parameter initial value is determined according to the genetic algorithm The method comprises calculating a target function by using a genetic algorithm and obtaining constitutive model parameters to be identified, wherein the target function is a difference between a test real force and a test substructure simulation force, and the target function is calculated as ； In the above formula, represents the real reaction force obtained by the test loading of the test substructure, represents the simulated reaction force obtained by numerical simulation based on the equivalent test substructure numerical model, represents the scale factor, represents the constitutive model parameters to be identified.

5. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 4, characterized in that, The 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 a minimum value as the initial value of the parameter .

6. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 5, characterized in that, If the constitutive model parameter identification is constant, the numerical value of the process noise covariance matrix is 0.

7. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 6, characterized in that, said acquiring displacement response of the overall structure comprising acquiring the displacement response of the structure by means of a refined finite element numerical model of the overall structure.

8. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to any one of claims 1 to 7, characterized in that, The step-by-step integration algorithm is a central difference method.

9. The hybrid test method based on the dual adaptive UKF algorithm online model updating according to claim 8, characterized in that, An error covariance matrix is obtained, and singular values of the error covariance matrix are decomposed.

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