A hybrid test method based on SVD-ACUKF online model updating

Abstract

The application discloses a kind of based on SVD-ACUKF online model updating hybrid test method, belongs to the technical field of hybrid test.To solve the problem of insufficient parameter identification accuracy, inaccurate test substructure loading boundary, insufficient model updating accuracy and test error in online model updating hybrid test method, the initial value of the parameter to be identified is first determined, the displacement response of the overall structure is obtained based on ground motion, and then the displacement response of the physical substructure is obtained and tested to be loaded, to obtain the counterforce and displacement of the physical substructure, based on the state of the physical substructure at step k-1, 2n+1 Sigma points are generated, and they are sent to the numerical model of the equivalent physical substructure together with the displacement, 2n+1 times of nonlinear static analysis are completed to obtain the restoring force, and then the constitutive model parameters are obtained by using the counterforce and displacement of the physical substructure and the state estimation value of the equivalent physical substructure at step k-1, and then the finite element refined numerical model of the overall structure is updated, and the above process is repeated until the test is completed.

Description

Technical Field

[0001] This invention belongs to the field of hybrid testing technology, specifically involving an online model update hybrid testing method and its analysis method, which belongs to the field of seismic testing of civil engineering structures. Background Technology

[0002] The online model-update hybrid experimental method can effectively study complex dynamic problems of complex structures. This method divides the research object (also known as the overall structure) into two parts: a physical substructure (also known as the specimen) and a numerical substructure. The physical substructure represents the part of the overall structure with complex or highly nonlinear dynamic performance, and loading tests are conducted in the laboratory. The numerical substructure represents the part of the overall structure with relatively simple dynamic performance, and simulations are performed on a computer using finite element method (FEM) software and mathematical analysis software. The physical and numerical substructures are coupled through boundary conditions, simultaneously satisfying both boundary force equilibrium and displacement equilibrium conditions. The physical substructure uses the measured displacements and forces obtained from loading to estimate the constitutive model parameters of the physical substructure online, and updates the refined numerical model parameters of the numerical substructure's FEM model. Thus, the structural response at each integration step is calculated based on the updated model parameters from the previous integration step. Therefore, the online model-update hybrid experimental method improves the calculation accuracy of the numerical substructure's FEM model through model updates.

[0003] Current model updates primarily rely on parameter identification methods. These methods are categorized into model-independent and model-based methods. Model-independent methods do not require specific information about the structure, components, and materials. However, due to the lack of clarity regarding model information and physical meaning, they suffer from high computational burden, low efficiency, and overfitting of identification results, making them unsuitable for experimental online model updates. Model-based methods identify model parameters based on a defined finite element model, which leads to insufficient accuracy and poor anti-interference capabilities. The issue of insufficient parameter identification accuracy in online model updates urgently requires new technologies to address.

[0004] Furthermore, current technologies, due to the limitations of loading devices and test sites, simplify the stress conditions of physical substructures, making it impossible to fully or approximately simulate the multi-degree-of-freedom boundary conditions of these substructures. This approach inevitably alters the actual stress conditions of the specimen, leading to discrepancies between the measured reaction force and the measured displacement. In particular, the need to use a numerical integration module to calculate the overall structure's displacement response, resulting in accumulated errors and distorted test results, further complicates the issue. New technologies are urgently needed to address the problem of inaccurate loading boundaries of physical substructures. Summary of the Invention:

[0005] This invention aims to address the problems of insufficient parameter identification accuracy and inaccurate physical substructure loading boundaries in online model update hybrid test methods, which lead to insufficient model update accuracy and test errors. Therefore, it provides an online model update hybrid test method based on SVD-ACUKF.

[0006] A hybrid experimental method for updating an online model based on SVD-ACUKF includes the following steps:

[0007] Step 1. Establish a refined finite element numerical model of the overall structure using finite element analysis software;

[0008] Physical substructures are divided into the overall structure, and a refined finite element numerical model of the physical substructure is established using finite element analysis software, namely, the equivalent physical substructure numerical model.

[0009] Step 2. Using the parameters of the constitutive model to be identified as the state vector, first determine the initial state. The initial state estimation error covariance matrix P0, the initial process noise covariance matrix Q0, and the initial observation noise covariance matrix R0; the initial state refers to the initial value of the state vector.

[0010] Step 3. Based on the research object and experimental loading requirements, input the seismic motion into the stepwise integration algorithm, perform the stepwise integration algorithm on the overall structure, and obtain the displacement response d of the overall structure in each dynamic degree of freedom direction. k ; the displacement response d k The degrees of freedom corresponding to the refined numerical model of the overall structure finite element element model are passed on.

[0011] Step 4. Based on the displacement response d k and the equivalent physical substructure state estimate obtained in step k-1. A refined finite element numerical model of the overall structure was used for nonlinear static analysis to obtain the displacement response in the corresponding physical substructure's dynamic degrees of freedom.

[0012] Step 5. Calculate the displacement response. The load is passed to the experimental loading system to complete the experimental loading of the boundary conditions of the physical substructure, and the reaction force of the physical substructure at step k is obtained. and displacement

[0013] Step 6. Apply the reaction force of the physical substructure in step k. and displacement Passed to the parameter recognition module;

[0014] Step 7. The parameter identification module performs equivalent physical substructure state estimation based on the SVD-ACUKF algorithm. The specific process includes a prediction step and an update step.

[0015] Prediction step: Let the state error covariance matrix at time k be P. k Perform singular value decomposition, in order to To centrally symmetrically sample 2n+1 Sigma sampling points T k,i The parameter θ is based on the sampling step size of each Sigma point. k,i The weights of the Sigma points are determined using a linear step-size weighting method.

[0016] Then T k,i Substituting the state equations into the prior estimates yields the prior estimates. Calculate the mean of the prior state at step k based on the weights. Covariance

[0017]

[0018]

[0019] In the formula, u k Indicates system input, W k,i Indicates the weight of the Sigma point;

[0020] Will Substituting into the observation equation, we obtain the observation vector Sigma point. Calculate the predicted mean of the observations at step k+1. and its variance

[0021]

[0022]

[0023] In the formula, For the observation equation, v k For system observation noise;

[0024] Update step: First, calculate the cross-covariance matrix and the Kalman gain matrix K. k+1 Using the system to observe the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance Update; recalculate the observation variance at step k+1.

[0025] Then, based on the adaptive forgetting factor ρ k Calculate the cross-covariance matrix P of the state variables and the observed variables. ty,k+1 and Kalman gain matrix K k+1 :

[0026]

[0027]

[0028] Using the observed value y k+1 and K k+1 The mean of the prior estimate and variance Update;

[0029] Step 8. Set the new constitutive model parameters Send the data to the refined finite element numerical model of the overall structure to update the constitutive model parameters in the refined finite element numerical model of the overall structure.

[0030] Step 9. Calculate the displacement response d using the successive integration method. k and Complete the 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 ;

[0031] Step 10. Apply the reaction force R k The displacement vectors on the dynamic degrees of freedom of the overall structure are obtained by solving the equations of motion of the overall structure in the next integration step using the stepwise integration algorithm.

[0032] Step 11. Repeat steps 3-10 until the experiment is over.

[0033] Furthermore, a genetic algorithm is used to determine the initial state. The specific process includes the following steps:

[0034] Minimize the objective function to find the optimal variables of the constitutive model;

[0035] The objective function is calculated as follows:

[0036]

[0037] In the formula, F experience,i F represents the actual reaction force obtained from the physical substructure test loading. simulation,i To obtain the reaction force of the physical substructure through numerical simulation based on the equivalent physical substructure numerical model, d experience,i d represents the actual displacement obtained from the physical substructure test loading. simulation,i The displacement of the physical substructure is obtained by numerical simulation based on the equivalent physical substructure numerical model, where t is the state to be identified, i.e. the constitutive model parameter to be identified.

[0038] When the objective function is minimized, the optimal solution for force and displacement is obtained, and then it is substituted into the finite element numerical model to determine the initial values ​​of the constitutive parameters to be identified.

[0039] Preferably, the step-by-step integration algorithm is implemented using the central difference method.

[0040] Furthermore, with To centrally symmetrically sample 2n+1 Sigma sampling points T k,i as follows:

[0041]

[0042] In the formula, (·) i This represents the i-th column of the matrix within the brackets.

[0043] Furthermore, the parameter θ of the sampling step size for each Sigma point... k,i as follows:

[0044]

[0045] In the formula,

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Among them, t U express The upper bound of the constraint, t L express The lower bound of the constraint, κ is a scaling parameter; The subscript j corresponds to The j-th element.

[0052] Furthermore, the Sigma point weights determined using the linear step-size weighting method are as follows:

[0053] W k,i =aθ k,0 +b=b,i=0

[0054] W k,i =aθ k,i +b, i = 1, 2, ..., 2n

[0055] In the formula,

[0056]

[0057]

[0058]

[0059] Furthermore, the cross-covariance matrix and the Kalman gain matrix K are calculated. k+1 The process is as follows:

[0060]

[0061]

[0062] Furthermore, by utilizing the system's observation of the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance The update process is as follows:

[0063]

[0064]

[0065] Furthermore, the adaptive forgetting factor ρ k as follows:

[0066]

[0067]

[0068]

[0069] Where, tr[·] is the trace of the matrix; y k+1 Represents the actual observed values ​​of the system; This represents the predicted value of the observation at step k.

[0070] Furthermore, the observation variance at step k+1 is recalculated in the update step. as follows:

[0071]

[0072] Beneficial effects:

[0073] (1) This invention solves the problem of insufficient parameter identification accuracy in existing online model update hybrid test methods.

[0074] Existing parameter identification methods are easily affected by factors such as the selection of initial parameter values ​​and noise, resulting in significant identification errors in the strongly nonlinear stage. This invention presents a hybrid experimental method for online model updates based on SVD-ACUKF, which can improve the accuracy of online model parameter identification. By utilizing singular value decomposition, it avoids the ill-conditioned nature of the error covariance matrix that could lead to incorrect identification. Constraints are placed on the initial parameter values, and the step size calculation is optimized to ensure that the Sigma point satisfies the boundary constraints and is as far away from the mean point as possible to avoid local nonlinear effects. Simultaneously, the symmetry of the Sigma point is maintained, and a forgetting factor is added as a criterion for judging filter divergence, effectively reducing the sensitivity of initial parameter settings and greatly avoiding filter divergence. Therefore, the accuracy and robustness of parameter identification in the online model update experimental method are improved.

[0075] (2) The present invention solves the problem of inaccurate physical substructure loading boundaries in the existing online model update hybrid test method.

[0076] Existing technologies, particularly those involving moderate physical substructure boundary conditions, are affected by loading equipment and site conditions, failing to fully simulate or approximate the true stress state of the physical substructure, leading to distorted experimental results. This invention presents a hybrid experimental method based on SVD-ACUKF online model updates. Instead of using measured reaction forces to calculate structural boundary displacements as in existing technologies, the structural displacement response is obtained from nonlinear static analysis of a refined finite element numerical model of the overall structure. This naturally solves the problem of inaccurate experimental results caused by inaccurate physical substructure loading boundaries. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the SVD-ACUKF-based model update method.

[0078] Figure 2 This diagram illustrates the SVD-ACUKF algorithm and the parameter estimation method of the finite element software OpenSees.

[0079] Figure 3 This is a flowchart illustrating the SVD-ACUKF algorithm.

[0080] Figure 4 This is a schematic diagram of the system architecture of the hybrid experimental method based on SVD-ACUKF online model update in the embodiment.

[0081] Figure 5 This is a schematic diagram of the physical substructure reinforcement in the embodiment. Detailed implementation method:

[0082] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will be further described below with reference to specific embodiments and accompanying drawings. However, the invention is not limited to these embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0083] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0084] Specific implementation method one: Combining Figures 1 to 2 This embodiment is described, wherein Figure 1 This is a schematic diagram of the SVD-ACUKF-based model update method. Figure 2 This diagram illustrates the SVD-ACUKF algorithm and the parameter estimation method of the finite element software OpenSees.

[0085] This embodiment presents a hybrid experimental method based on SVD-ACUKF online model update. It utilizes this method to calculate the overall structural reaction force, then updates the constitutive model parameters based on this reaction force, calculates the overall structural response, and thus achieves the analysis of the overall structure. The successive integration algorithm and SVD-ACUKF are performed in mathematical analysis software, while the nonlinear static analysis is performed in OpenSees finite element analysis software. The mathematical analysis software and the finite element software interact via TCP sockets. This embodiment uses Matlab and OpenSees; however, it should be understood that any software with the same or similar functions as Matlab and OpenSees can implement this invention. For example, other finite element analysis software can be used for OpenSees, and mathematical analysis software such as SCILAB can be used for MATLAB. The following is a detailed description. The hybrid experimental method based on SVD-ACUKF online model update described in this embodiment includes the following steps:

[0086] Step 1. Establish a refined finite element numerical model of the overall structure using OpenSees finite element analysis software;

[0087] The more complex dynamic performance part of the overall structure is divided into physical substructures. The OpenSees finite element analysis software is used to establish a refined finite element numerical model of the physical substructure, namely the equivalent physical substructure numerical model.

[0088] The more complex dynamic performance refers to the components of the structure that have a higher probability of entering strong nonlinearity, that is, the components of the structure that may exhibit nonlinear behavior, also known as the key parts of the structure.

[0089] It should be noted that the finite element numerical model is programmed using OpenSees software, and the structural dimensions, degrees of freedom, material constitutive model definitions, elements, nodes, HyTest Client update module, and data transfer are established accordingly.

[0090] Step 2. Using the parameters of the constitutive model to be identified as the state vector, establish the state equation f and the observation equation h based on the SVD-ACUKF algorithm. Determine the initial state of the SVD-ACUKF algorithm. The initial state estimation error covariance matrix P0, the initial process noise covariance matrix Q0, and the initial observation noise covariance matrix R0; the initial state refers to the initial value of the state vector.

[0091] The refined numerical model of the finite element method (FEM) is the main body, and the constitutive model is one of its components. Within the numerical model, material-based constitutive models need to be established, such as the constitutive model parameters for concrete and steel reinforcement. Among the constitutive model parameters for concrete and steel reinforcement, the steel reinforcement parameters include its yield strength f. y Initial elastic modulus E0, strain hardening rate b, etc.; concrete parameters include peak stress f. c Peak stress corresponds to strain ε0, and ultimate strain ε u The ultimate stress f corresponding to the ultimate strain u wait.

[0092] The form of the state equation f in the SVD-ACUKF algorithm is, in principle, consistent with that of UKF, i.e., t k+1 =f(t) k ,u k )+v k , where t k It is a state vector, u k For system input, v k This is to account for system observation noise. The state equations differ depending on the constitutive parameters being identified. For example, the state equations for updating the constitutive model parameters of Steel01 steel bars and Concrete01 concrete materials are: (The state equation is linear and the observation noise is defined as 0). For an unspecified research object, the specific material cannot be determined, therefore the form of the state equation is not specified. Similarly, the observation equation does not specify any particular form.

[0093] Furthermore, a genetic algorithm is used to determine the initial state. The process includes the following steps:

[0094] The objective function is set as the difference between the forces and parameters in the numerical simulation and those in the existing experimental data. Minimizing the objective function helps find the optimal variables for the constitutive model. The objective function is calculated as follows:

[0095]

[0096] In the formula, F experience,i The actual reaction force obtained from the physical substructure experiment is used as the training set, F. simulation,i To obtain the reaction force of the physical substructure through numerical simulation based on the equivalent physical substructure numerical model, d experience,i The actual displacements obtained from the physical substructure experiment are used as the training set, d simulation,i The displacement of the physical substructure is obtained by numerical simulation based on the equivalent physical substructure numerical model, where t is the state to be identified, i.e., the constitutive model parameter to be identified.

[0097] In the objective function, the ratio of the actual solution and the simulated solution for force and displacement is calculated and then subtracted by 1. The optimal solution for force and displacement is obtained when this function reaches its minimum value. This value is then substituted into the finite element numerical model to determine the initial values ​​of the constitutive parameters to be identified. This approach effectively avoids the problem of poor identification accuracy caused by improper selection of initial state mean values.

[0098] Step 3. Based on the research subjects and experimental loading requirements, such as... Figure 1 As shown, the seismic motion is input into the stepwise integration algorithm, and the stepwise integration algorithm is performed on the overall structure to obtain the displacement response d of the overall structure in each dynamic degree of freedom direction. k ; the displacement response d k The degrees of freedom are passed to the refined numerical model of the overall structure using finite element methods.

[0099] The successive integration algorithm is a component of online numerical simulation methods and is existing technology. The displacement obtained by the successive integration algorithm is input into the overall structural finite element numerical model. Data transmission is required between the successive integration algorithm and the overall structural finite element numerical model, which will be explained later.

[0100] Furthermore, the stepwise integration algorithm in this invention is implemented using the central difference method. The central difference method calculation formula is as follows:

[0101]

[0102]

[0103] In the formula, d, v, and a represent the displacement, velocity, and acceleration of the structure.

[0104] Step 4. Based on the displacement response d kand the equivalent physical substructure state estimate obtained in step k-1. A refined finite element numerical model of the overall structure was used for nonlinear static analysis to obtain the displacement response in the corresponding physical substructure's dynamic degrees of freedom.

[0105] The static analysis content is the content calculated by finite element software based on the model, which is existing technology in this field and will not be elaborated upon in this invention.

[0106] Step 5. Calculate the displacement response. The displacement command is transmitted to the experimental electro-hydraulic servo loading system, which then performs the boundary condition test loading on the physical substructure based on this displacement command, obtaining the reaction force of the physical substructure at the k-th step. and displacement

[0107] Furthermore, the displacement response in the dynamic degrees of freedom direction of the physical substructure That is, the displacement of the physical substructure boundary conditions. Send it to the electro-hydraulic servo loading system via HyTest Connector.

[0108] Step 6. Apply the reaction force of the physical substructure in step k. and displacement It is passed to the parameter recognition module.

[0109] Step 7. Online estimation of equivalent physical substructure states:

[0110] The parameter identification module uses the SVD-ACUKF algorithm to identify the state of the physical substructure, generating 2n+1 Sigma points based on the k-1 step physical substructure state. Will and Together, they are sent to the numerical model of the equivalent physical substructure to complete 2n+1 nonlinear static analyses to obtain the restoring force. And then send it back to the parameter recognition module, which uses... and the estimated state of the physical substructure at step k-1. Calculate the new constitutive model parameters

[0111] like Figure 3 As shown, the specific method for online identification of physical substructure states using the SVD-ACUKF algorithm is as follows:

[0112] (1) Prediction step

[0113] Assume the state error covariance matrix at time k is P k State variable mean estimation The state covariance matrix Pk Singular value decomposition yields P k =USV T ;

[0114] 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.

[0115] Singular value decomposition can effectively avoid recognition failures caused by differences in magnitude, computer floating-point operations, and computational errors.

[0116] by To centrally symmetrically sample 2n+1 Sigma sampling points T k,i ,

[0117]

[0118] In the formula, (\) i θ represents the i-th column of the matrix within the brackets; k,i The parameter representing the sampling step size for each Sigma point is calculated using the following formula:

[0119]

[0120] In the formula,

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] Among them, t U express The upper bound of the constraint, t L express The lower bound of the constraint, κ is a proportional parameter that can take any number, but it must be ensured that n+κ≠0. The subscript j corresponds to The j-th element.

[0127] The step size calculation not only adjusts the step size of the Sigma point to make the Sigma point as far away from the mean point as possible while satisfying the boundary constraints to avoid local nonlinear effects, but also ensures the symmetry of the Sigma point.

[0128] The Sigma point weights are determined using the linear step-size weighting method, and the mathematical expression for the weight calculation is as follows:

[0129] W k,i =aθ k,0 +b=b,i=0

[0130] W k,i =aθ k,i +b, i = 1, 2, ..., 2n

[0131] In the formula,

[0132]

[0133]

[0134]

[0135] T k,i Substituting 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

[0136]

[0137]

[0138]

[0139] In the formula, u k This represents the system input (using the previously mentioned physical substructure). and );W k,i This represents the weight of the Sigma point.

[0140] Will Substituting into the observation equation h, we obtain the observation vector Sigma point. Calculate the predicted mean of the observations at step k+1. and its variance

[0141]

[0142]

[0143]

[0144] In the formula, v k This is for system observation noise.

[0145] This section utilizes finite element software to establish numerical models of physical substructures, which are implicitly used as observation equations.

[0146] (2) Update step

[0147] Calculate the cross-covariance matrix and the Kalman gain matrix K. k+1 :

[0148]

[0149]

[0150] Using the system to observe the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance Update:

[0151]

[0152]

[0153] Define the information sequence:

[0154]

[0155] In the formula, y k+1 Represents the actual observed values ​​of the system; This represents the predicted value of the observation at step k.

[0156] Define the filter divergence criterion and the adaptive forgetting factor ρ k choose:

[0157]

[0158] Wherein, the trace of the tr[·] matrix;

[0159]

[0160] Recalculate the observation variance at step k+1

[0161]

[0162] Based on the adaptive forgetting factor ρ k Calculate the cross-covariance matrix P of the state variables and the observed variables. ty,k+1 and Kalman gain matrix K k+1 :

[0163]

[0164]

[0165] Using the observed value y k+1 and K k+1 The mean of the prior estimate and variance Update:

[0166]

[0167]

[0168] Adaptive factor ρ k The filter divergence is judged based on the sum of squared differences between the actual and predicted observations, thereby correcting the observation covariance matrix and the cross-covariance matrix between the state and the observation. This effectively reduces the sensitivity of the initial parameter setting and greatly avoids the divergence of the filter.

[0169] Step 8. Set the new constitutive model parameters Send the data to the refined finite element numerical model of the overall structure to update the constitutive model parameters in the refined finite element numerical model of the overall structure.

[0170] Step 9. Calculate the displacement response d using the successive integration method. k and Complete the 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 .

[0171] Step 10. Apply the reaction force R k Feedback is sent to the step-by-step integration module, which uses the step-by-step integration algorithm to solve the global structural motion equations corresponding to the next integration step, and obtain the displacement vectors on the dynamic degrees of freedom of the global structure.

[0172] Step 11. Repeat steps 3-10 until the experiment is over.

[0173] In this embodiment, the SVD-ACUKF algorithm is used to identify the parameters of the equivalent physical substructure constitutive model and update the parameters of the overall structural constitutive model, thus solving the problem of insufficient parameter identification accuracy. The structural displacement response is obtained by nonlinear static analysis of the refined finite element numerical model of the overall structure, instead of using measured reaction forces to calculate the structural boundary displacement as in existing technologies. This naturally solves the problem of inaccurate experimental results caused by inaccurate physical substructure loading boundaries. Meanwhile, existing technologies use the numerical substructure model with updated constitutive model parameters to calculate the numerical substructure reaction force, and combine it with the measured reaction force of the physical substructure to form the overall structural reaction force, which is used to calculate the next integral step displacement of the overall structure. Therefore, this invention is fundamentally different from existing technologies, and it is impossible for non-technical personnel to conceive of it or implement it. Even for those skilled in the art, it is not easy to conceive of and implement based on existing technologies.

[0174] Example

[0175] This invention enables the conduct of hybrid tests on shear wall structures based on SVD-ACUKF online model updates.

[0176] This embodiment uses a two-story prefabricated shear wall structure as an example to illustrate the basic principles and usage steps of the method of the present invention. To provide experimental data support for the design of prefabricated shear wall structures, seismic tests are required. For this type of structure, existing parameter identification methods are easily affected by factors such as the selection of initial parameter values ​​and noise, resulting in significant identification errors in the strongly nonlinear stage. The SVD-ACUKF algorithm can improve the accuracy of online model parameter identification, effectively reduce the sensitivity of initial parameter settings, and greatly avoid the divergence of filtering, thereby improving the accuracy and robustness of parameter identification in online model update test methods.

[0177] One of the challenges in the hybrid test of model updating for prefabricated shear wall structures is how to accurately and reliably identify and update constitutive model parameters. Considering the shear and bending deformations of the structure, a layered shell element-based modeling approach is adopted for numerical simulation. Furthermore, SVD-ACUKF is used as the parameter identification algorithm to reduce the sensitivity of initial parameter settings, thereby improving the accuracy and robustness of parameter identification.

[0178] The following is in conjunction with the appendix Figure 4 To be continued Figure 5 The present invention will be described in detail below. A system architecture for a hybrid experimental method based on SVD-ACUKF online model update 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 physical substructure. The reinforcement diagram of the physical substructure is shown below. Figure 5 As shown.

[0179] The method in this embodiment for conducting a hybrid experiment based on SVD-ACUKF online model update specifically includes the following steps:

[0180] Step 1: Use OpenSees finite element analysis software to establish the overall structural finite element numerical model and the equivalent physical substructure finite element numerical model of the prefabricated shear wall structure. The first layer is the physical substructure, and the second layer is the numerical substructure.

[0181] 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);

[0182] Step 2: Utilize the genetic algorithm (Sheffield algorithm) objective function:

[0183]

[0184] In the formula, F experience,i The reaction force obtained from the physical substructure experiment is used as the training set, F. simulation,i To obtain the reaction force of the physical substructure in numerical simulation, d experience,i The displacement obtained by loading the physical substructure in the experiment is used as the training set, d simulation,i To obtain the displacement of the physical substructure through numerical simulation, t represents the constitutive model parameter to be identified. Initial values ​​for the material constitutive model parameters are determined. Covariance P0, integration step size Δt;

[0185] Step 3: Establish the state equations for the SVD-ACUKF algorithm:

[0186]

[0187] In the formula, w k This refers to system process noise.

[0188] 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:

[0189]

[0190]

[0191] Step 5, the algorithm observation equation is: And define the initial process noise covariance matrix Q0 and the initial observation noise covariance matrix R0; k Input to the system (using physical substructure) and ), v k This is for system observation noise.

[0192] Step 6: Input the working condition (the ground motion is an El Centro (NS, 1940) wave);

[0193] Step 7: (The text appears to be incomplete and contains several typos. A more accurate translation would require the full context.) 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 physical substructure. The test load was sent to the MTS electro-hydraulic servo loading system via HyTest Connector to obtain the reaction force of the physical substructure at step k. and displacement

[0194] Step 8: and constitutive model parameters at step k-1 The numerical model of the equivalent physical substructure is passed to the nonlinear static analysis calculation to obtain the reaction force observation of the physical substructure. The parameter is then passed back to the constitutive model parameter identification module.

[0195] It should be noted that constitutive model parameters are a part of establishing a finite element model. The parameter identification module identifies the material constitutive model based on layered shell elements. Layered shell elements are existing elements in OpenSees and are considered existing technology. This embodiment uses this element for modeling. When using this element for modeling, it is necessary to define the material constitutive model parameters and update the constitutive model parameters under this element.

[0196] Step 9: Based on the reaction force observations of the physical substructure in step k and the constitutive model parameters in step (k-1) The SVD-ACUKF algorithm is used to identify the constitutive model parameters of equivalent physical substructures online, and the updated constitutive model parameters are obtained.

[0197] Step 10, in step four d k and step eight Based on this, a refined finite element model of the overall structure was completed for nonlinear static analysis, and the reaction force R on each dynamic degree of freedom of the overall structure was calculated. k And feed it back to the successive integration algorithm;

[0198] Step 11: Repeat steps 6 through 10 until the experiment is completed.

[0199] The specific method for online identification of physical substructure model parameters using the SVD-ACUKF algorithm in step nine is as follows:

[0200] (I) Assume that the state error covariance matrix at time k is P k State variable mean estimation The covariance matrix P kSingular value decomposition yields P k =USV T ;

[0201] (II) Find the 2n+1 Sigma sampling points T for symmetric sampling k,i and using θ k,i Sampling step size limitations:

[0202]

[0203] In the formula, θ k,i The mathematical parameter representing the sampling step size for each Sigma point is calculated using the following formula:

[0204]

[0205] In the formula,

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] (III) Determine the Sigma point weights using the linear step-size weighting method. The mathematical expression for weight calculation is as follows:

[0212] W k,i =aθ k,0 +b=b,i=0

[0213] W k,i =aθ k,i +b,i=1,2,…,2n

[0214] In the formula,

[0215]

[0216]

[0217]

[0218] (iv) T k,i Substituting the state equations into the prior estimates yields the prior estimates. Then, the mean of the prior state at step k is calculated based on the weights. and

[0219]

[0220]

[0221]

[0222] (V) Substituting the values ​​into the observation equation h, we can obtain the predicted mean of the observations at the k-th step. and its variance

[0223]

[0224]

[0225]

[0226] (vi) Calculate the cross-covariance matrix P ty,k+1 Kalman gain matrix:

[0227]

[0228]

[0229] (vii) Utilizing the system to observe the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance Update:

[0230]

[0231]

[0232] (VIII) Define the information sequence:

[0233]

[0234] (ix) Defining the filter divergence criterion and the adaptive forgetting factor ρ k choose:

[0235]

[0236] in,

[0237]

[0238] (x) Based on the adaptive forgetting factor ρ k Recalculate the observation variance at step k.

[0239]

[0240] (xi) Calculate the cross-covariance matrix and Kalman gain matrix of the state variables and observations:

[0241]

[0242]

[0243] (xii) Using the observed value y k+1 and K k+1 Update the mean and variance of the prior estimates.

[0244]

[0245]

[0246] In the formula, To complete the SVD-ACUKF identification values, which are used for the current step of online model update.

[0247] The analysis method based on the SVD-ACUKF online model update hybrid test 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.

[0248] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Anyone skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention should be defined by the claims. Furthermore, it should be noted that while the specification and accompanying drawings provide preferred embodiments, the invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are not intended as additional limitations on the content of the invention; their purpose is to provide a more thorough and comprehensive understanding of the disclosure. Moreover, the above-described technical features can be combined to form various embodiments not listed above, all of which are considered within the scope of the specification. Furthermore, those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the scope of protection of the appended claims. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A hybrid experimental method for online model updating based on SVD-ACUKF, characterized in that, Includes the following steps: Step 1. Establish a refined finite element numerical model of the overall structure using finite element analysis software; Physical substructures are divided into the overall structure, and a refined finite element numerical model of the physical substructure is established using finite element analysis software, namely, the equivalent physical substructure numerical model. Step 2. Using the parameters of the constitutive model to be identified as the state vector, first determine the initial state. The initial state estimation error covariance matrix P0, the initial process noise covariance matrix Q0, and the initial observation noise covariance matrix R0; the initial state refers to the initial value of the state vector. Step 3. Based on the research object and experimental loading requirements, input the seismic motion into the stepwise integration algorithm, perform the stepwise integration algorithm on the overall structure, and obtain the displacement response d of the overall structure in each dynamic degree of freedom direction. k ; the displacement response d k The degrees of freedom corresponding to the refined numerical model of the overall structure finite element element model are passed on. Step 4. Based on the displacement response d k and the equivalent physical substructure state estimate obtained in step k-1. A refined finite element numerical model of the overall structure was used for nonlinear static analysis to obtain the displacement response in the corresponding physical substructure's dynamic degrees of freedom. Step 5. Calculate the displacement response. The load is passed to the experimental loading system to complete the experimental loading of the boundary conditions of the physical substructure, and the reaction force of the physical substructure at step k is obtained. and displacement Step 6. Apply the reaction force of the physical substructure in step k. and displacement Passed to the parameter recognition module; Step 7. The parameter identification module performs equivalent physical substructure state estimation based on the SVD-ACUKF algorithm. The specific process includes a prediction step and an update step. Prediction step: P is the state error covariance matrix at step k. k Perform singular value decomposition, in order to To centrally symmetrically sample 2n+1 Sigma sampling points T k,i The parameter θ is based on the sampling step size of each Sigma point. k,i The weights of the Sigma points are determined using a linear step-size weighting method. Then T k,i Substituting the state equations into the prior estimates yields the prior estimates. Calculate the mean of the prior state at step k based on the weights. Covariance In the formula, W k,i Indicates the weight of the Sigma point; Will Substituting into the observation equation, we obtain the observation vector Sigma point. Calculate the predicted mean of the observations at step k+1. and its variance In the formula, The observation equation; Update step: First, calculate the cross-covariance matrix and the Kalman gain matrix K. k+1 Using the system to observe the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance Update; recalculate the observation variance at step k+1. Then, based on the adaptive forgetting factor ρ k Calculate the cross-covariance matrix P of the state variables and the observed variables. ty,k+1 and Kalman gain matrix K k+1 : Using the observed value y k+1 and K k+1 The mean of the prior estimate and variance Update; Step 8. Set the new constitutive model parameters Send the data to the refined finite element numerical model of the overall structure to update the constitutive model parameters in the refined finite element numerical model of the overall structure. Step 9. Calculate the displacement response d using the successive integration method. k and Complete the 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 ; Step 10. Apply the reaction force R k The displacement vectors on the dynamic degrees of freedom of the overall structure are obtained by solving the equations of motion of the overall structure in the next integration step using the stepwise integration algorithm. Step 11. Repeat steps 3-10 until the experiment is over.

2. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 1, characterized in that, Genetic algorithms are used to determine the initial state. The specific process includes the following steps: Minimize the objective function to find the optimal variables of the constitutive model; The objective function is calculated as follows: In the formula, F experience,t F represents the actual reaction force obtained from the physical substructure test loading. simulation,t To obtain the reaction force of the physical substructure through numerical simulation based on the equivalent physical substructure numerical model, d experience,t d represents the actual displacement obtained from the physical substructure test loading. simulation,t The displacement of the physical substructure is obtained by numerical simulation based on the equivalent physical substructure numerical model, where t is the state to be identified, i.e. the constitutive model parameter to be identified. The optimal solution for force and displacement is obtained when the objective function is minimized. This solution is then substituted into the finite element numerical model to determine the initial values ​​of the constitutive parameters to be identified.

3. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 2, characterized in that, The successive integration algorithm is implemented using the central difference method.

4. A hybrid experimental method for online model updating based on SVD-ACUKF according to any one of claims 1 to 3, characterized in that, by To centrally symmetrically sample 2n+1 Sigma sampling points T k,i as follows: In the formula, (·) i This represents the i-th column of the matrix within the brackets.

5. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 4, characterized in that, The parameter θ of the sampling step size for each Sigma point k,i as follows: In the formula, Among them, t U express The upper bound of the constraint, t L express The lower bound of the constraint, κ is a scaling parameter; The subscript j corresponds to The j-th element.

6. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 5, characterized in that, The weights of the Sigma points determined using the linear step-size weighting method are as follows: W k,i =aθ k,0 +b=b,i=0 W k,i =aθ k,i +b,i=1,2,…,2n In the formula, 7. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 6, characterized in that, Calculate the cross-covariance matrix and the Kalman gain matrix K. k+1 The process is as follows:

8. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 7, characterized in that, Using the system to observe the true value y k+1 and Kalman gain matrix K k+1 The mean of the prior estimate Covariance The update process is as follows:

9. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 8, characterized in that, The adaptive forgetting factor ρ k as follows: Where tr[·] represents the trace of the matrix; y k+1 Represents the actual observed values ​​of the system; This represents the predicted value of the observation at step k.

10. The hybrid experimental method for online model updating based on SVD-ACUKF according to claim 9, characterized in that, The observation variance recalculated in the (k+1)th step during the update step as follows:

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