A structure vulnerability evaluation method based on model updating hybrid test

Abstract

The application discloses a structure vulnerability evaluation method based on model updating hybrid test, and belongs to the technical field of anti-seismic performance evaluation. The purpose is to solve the problem of low precision and lack of applicability of the traditional vulnerability evaluation method of large complex civil engineering structures. The application combines online model updating technology, structure hybrid test technology and vulnerability calculation method to obtain the overall structure anti-seismic vulnerability curve. Firstly, 10-20 representative seismic records are selected, and the intensity parameters of the seismic records are ensured to be uniformly distributed; secondly, the selected seismic records are used for model updating hybrid test based on the SRCKF algorithm to obtain structure seismic response data; finally, the failure probability is calculated based on the structure damage index and the structure damage probability density function obtained by the test to obtain the structure vulnerability curve. The scheme provided by the application has the beneficial effect of improving the vulnerability evaluation precision of large complex civil engineering structures.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of seismic performance evaluation, and particularly relates to a structure vulnerability evaluation method based on model updating hybrid test. BACKGROUND

[0002] The performance-based seismic design method designs the structure seismic by setting appropriate seismic performance objectives, so that the damage degree and economic loss of the structure under different intensity earthquake actions meet the requirements of the owner. The performance-based seismic engineering full probability decision framework proposed by the Pacific Earthquake Engineering Research Center (PEER) divides the seismic performance evaluation of the structure into four parts, and the seismic vulnerability is an important part. The vulnerability evaluation can quantitatively describe the seismic performance of the structure from the probability angle, calculate the conditional probability of the structure exceeding a certain performance limit, and can statistically calculate the conditional probability under the required ground motion intensity and form the vulnerability curve and vulnerability matrix.

[0003] The traditional vulnerability evaluation method mainly includes three kinds: the first kind mainly adopts the empirical method, which is based on the experience of experts, and forms statistics by investigating the actual earthquake damage, so as to give a relatively simple vulnerability expression in a short time after the earthquake. The disadvantage is that the established vulnerability curve has great uncertainty, which is often the subjective judgment of experts and lacks experimental evidence; the second kind mainly adopts the theoretical method, which mainly obtains a large amount of required earthquake damage data by numerically simulating the state change of the structure under earthquake action, and draws the seismic vulnerability curve of the structure according to data regression analysis. The theoretical vulnerability analysis method can well overcome the defect of insufficient field earthquake damage data of the empirical method, but the precision of earthquake damage prediction depends on the precision of the established model, and once the model is inaccurate, the vulnerability curve and matrix will be damaged. The third kind is the hybrid method, which combines the empirical method of earthquake damage investigation and the theoretical calculation method of numerical simulation. When a certain structure lacks earthquake damage data, the hybrid method is very suitable, which combines a part of earthquake damage data and the established numerical model to complement each other, which can offset the subjectivity of the earthquake damage investigation method and make up for the defect of lack of actual earthquake damage data in the theoretical analysis. However, it needs to select the appropriate analytical method to supplement the missing data of the earthquake damage investigation method according to the actual situation, which will face the problems of time-consuming calculation and high calculation cost, and the definition of damage state also has subjectivity. The hybrid vulnerability evaluation method is less applied at present.

[0004] Obtaining the seismic response data of the building structure is the premise of establishing the vulnerability function, and the accuracy of the seismic response data will directly affect the construction precision of the seismic vulnerability function. For large and complex civil engineering structures, the traditional vulnerability evaluation method is limited by the limited earthquake damage data and the model precision of finite element analysis. SUMMARY

[0005] The problem to be solved by the present application is the precision of the vulnerability evaluation method, and a structure vulnerability evaluation method based on model updating hybrid test is proposed.

[0006] To achieve the above-mentioned purpose, the present application realizes by the following technical scheme:

[0007] A structure vulnerability evaluation method based on model updating hybrid test, comprising the following steps:

[0008] S1, collect seismic record data with uniform distribution of ground motion intensity parameters, for use;

[0009] S2, use step S1 to establish a finite element model of the overall structure using OpenSees, set the part of the overall structure that is easy to enter strong nonlinearity as a physical substructure, set the part that has similar mechanical behavior and structural response as the physical substructure as a numerical substructure to be updated, and set the remaining part as a numerical substructure that is not updated, for use;

[0010] S3, input the seismic record data obtained in step S1 into Matlab software, solve the structure motion equation, then obtain the displacement of the physical substructure and the displacement of the numerical substructure, input the obtained displacement of the physical substructure into the actuator to load and obtain the restoring force of the physical substructure;

[0011] S4, based on the displacement of the physical substructure and the restoring force of the physical substructure obtained in step S3, use the square root volume Kalman filtering algorithm as a parameter estimation method to identify the numerical model parameters of the physical substructure, and use the identified numerical model parameters of the physical substructure to update the numerical substructure model parameters obtained in step S2, and calculate the restoring force of the numerical substructure online according to the numerical substructure model, the updated numerical substructure model parameters and the displacement of the numerical substructure

[0012] S5, send the restoring force of the physical substructure and the restoring force of the numerical substructure to the motion equation to solve the displacement, velocity and acceleration at time k+1, repeat the above steps S3 to S5 until the end of the seismic record, and obtain the response data of the overall structure;

[0013] S6, use the seismic response data obtained in step S5 to calculate the seismic response parameters DM under different ground motion intensity parameters IM, then perform data regression analysis on the ground motion intensity parameters and the seismic response parameters, and obtain the seismic demand model;

[0014] S7, construct the structure damage probability density function according to the seismic demand model obtained in step S6, calculate the failure probability, and draw the vulnerability curve.

[0015] Further, the collected seismic record data in step S1 is 10-20, the source distance from the site is not more than 20 kilometers, the magnitude is greater than 6.0, and the PGA distribution is between 0.2-2.1g. The PGA is evenly divided into four regions, and the PGA distribution of the selected seismic record in each region is uniform.

[0016] Further, in step S2, a layer of support is set as a component-level physical substructure, one half of a layer of steel frame columns is a material-level physical substructure, layers two to six supports and the remaining steel materials are parts that have similar mechanical behavior and structural response to the physical substructure, and are set as numerical substructures to be updated, and the remaining parts are set as non-updated numerical substructures.

[0017] Further, in step S3, the structure motion equation is:

[0018]

[0019] wherein M is the mass matrix, a is the acceleration, C is the damping matrix, v is the velocity, R k is the restoring force of the kth step, is the ith seismic wave;

[0020] The displacement of the kth step physical substructure obtained by solving the structure motion equation is , the displacement of the kth step numerical substructure is , and the restoring force of the kth step physical substructure is .

[0021] Further, in step S4, the square root cubature Kalman filter algorithm is used as a parameter estimation method for the specific implementation method of numerical model parameter identification of the physical substructure, which includes the following steps:

[0022] S4.1, assuming that the initial value of the known state quantity is , the error covariance P k , the error covariance P k is subjected to Cholesky decomposition, and the formula is obtained.

[0023]

[0024] wherein S k is a lower triangular matrix of P k decomposition;

[0025] S4.2, calculate the cubature point set ζ j , the calculation formula is:

[0026]

[0027]

[0028] Where n is the dimension of the state, [e] j Let j be the initial volume point;

[0029] Then, based on S obtained in step S4.1 k Calculate volume point X j,k :

[0030]

[0031] S4.3, The volume point propagates through the state equation f, u k As the system input, the volume point after propagation is The calculation formula is:

[0032]

[0033] S4.4 Calculate the predicted state values ​​of the propagated volume points obtained in step S4.3. The calculation formula is:

[0034]

[0035] Where w is the weight, and its value is...

[0036] S4.5 Calculate the square root of the covariance matrix:

[0037]

[0038] in, Tria() represents the square root of the covariance matrix, and decomposes the matrix into QR values ​​by transposing the matrix.

[0039] matrix S Q Defined as:

[0040]

[0041] S Q =chol(Q)

[0042] In the formula, chol() represents performing Cholsky decomposition on the matrix;

[0043] S4.6, Based on step S4.5 Recalculate the volume point X j,k+1 The calculation formula is:

[0044]

[0045] S4.7, The recalculated volume point X obtained in step S4.6j,k+1 The measurement prediction value is calculated by propagating the observation equation and is given by:

[0046] Z j,k+1 = h(X j,k+1 , u k+1 )

[0047] where Z j,k+1 is the propagated volume point of the observation equation;

[0048]

[0049] where is the measurement prediction value;

[0050] S4.8, the square root of the residual covariance matrix S zz,k+1 is calculated from the measurement prediction value obtained in step S4.7 and is given by:

[0051] S zz,k+1 = Tria([γ k+1 S R ]),

[0052] where the matrix γ k+1 , S R is defined by:

[0053]

[0054] S R = chol(R)

[0055] The square root matrix P xz,k+1 of the cross covariance is then calculated and is given by:

[0056]

[0057] where the matrix X k+1 is defined by:

[0058]

[0059] S4.9, the Kalman gain K xz,k+1 is calculated from P k+1 obtained in step S4.8 and is given by:

[0060]

[0061] S4.10, the system posterior state estimate , the estimate of the square root of the error covariance S k+1 is calculated from the Kalman gain obtained in step S4.9 and is given by:

[0062]

[0063] S k+1 = Tria([X k+1 - K k+1 γ k+1 K k+1 S R ].

[0064] Further, the specific implementation method of step S6 includes the following steps:

[0065] S6.1, setting the ground motion intensity parameter IM including the peak acceleration PGA, the peak velocity PGV, the acceleration response spectrum value S a (T1, ξ) corresponding to the structural basic period of the damping ratio ξ, the seismic response parameter DM including the maximum base shear, the top displacement, the node rotation, the maximum ductility coefficient of the floor, the maximum inter-story drift angle θ max , the hysteretic energy consumption;

[0066] S6.2, based on the fact that the ground motion intensity parameter IM and the seismic response parameter DM obey normal distribution, the mathematical relationship is expressed as:

[0067] DM = α (IM) β

[0068] Wherein, α, β are regression parameters;

[0069] S6.3, according to step S6.1, the ground motion intensity parameter IM is selected as the ground peak acceleration PGA, and the seismic response parameter DM is the maximum inter-story drift angle θ max , then the formula is obtained as:

[0070] θ max = α (PGA) β ;

[0071] Taking the logarithm of both sides obtains the following formula:

[0072] ln θ max = ln α + β ln (PGA)

[0073] Linear regression is performed on the above formula to obtain the values of α and β, and the seismic demand model is obtained.

[0074] Further, the specific implementation method of step S7 includes the following steps:

[0075] S7.1, setting the failure probability formula of the response D of the structure under different seismic intensity exceeding the demand capacity parameter C of the structure as:

[0076] P f = P (θ c / θmax <1) = P(ln theta c -ln theta max <0)

[0077] Where P f is the failure probability, theta c is the structural demand capacity parameter;

[0078] S7.2, set Z = ln theta c -ln theta max And subject to normal distribution, the average value is represented as The standard deviation is The formula for deriving the failure probability is:

[0079]

[0080] Where Z is the representative value;

[0081] S7.3, convert N(mu z , sigma z ) to standard normal distribution N(0,1), and the failure probability is:

[0082]

[0083] S7.4, according to HAZUS99, when IM is PGA, The value is 0.5, and the vulnerability curve is drawn.

[0084] The beneficial effects of the present application are:

[0085] The structure vulnerability evaluation method based on model updating hybrid test provided by the present application obtains the seismic response data of the structure through the seismic test method, wherein the model updating hybrid test divides the dynamic system into a physical substructure, a numerical substructure to be updated and a numerical substructure not to be updated, and connects the three through a test loading system and a parameter estimation method, so that large-scale tests can be completed and the seismic response of the overall structure can be obtained, and the problem that all key parts in the structure cannot be subjected to real physical tests is solved. The structure response data obtained by using the model updating hybrid test are used for vulnerability evaluation, so that the vulnerability evaluation precision of large and complex civil engineering structures can be improved.

[0086] The structure vulnerability evaluation method based on model updating hybrid test provided by the present application combines online model updating technology, structure hybrid test technology and vulnerability calculation methods, adopts a model updating hybrid test method based on the SRCKF algorithm to obtain the seismic response data of a building structure, obtains the seismic vulnerability curve of the overall structure, and improves the vulnerability evaluation precision of large and complex civil engineering structures, so as to solve the problems of insufficient precision and lack of applicability in the vulnerability evaluation method of large and complex civil engineering structures. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 A flow chart of a structure vulnerability evaluation method based on model updating hybrid test according to the present application;

[0088] Figure 2 A principle diagram of a structure vulnerability evaluation method based on model updating hybrid test according to the present application;

[0089] Figure 3 A flow chart of square root cubature Kalman filter algorithm according to the present application;

[0090] Figure 4 A seismic demand model fitting curve of a structure vulnerability evaluation method based on model updating hybrid test according to the present application;

[0091] Figure 5 A vulnerability fitting curve of a structure vulnerability evaluation method based on model updating hybrid test according to the present application. DETAILED DESCRIPTION

[0092] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in combination with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application, that is, the specific embodiments described are only a part of the embodiments of the present application, but not all the specific embodiments. The components of the specific embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations, and the present application can also have other embodiments.

[0093] Therefore, the detailed description of the specific embodiments of the present application provided in the accompanying drawings below is not intended to limit the scope of the claimed present application, but only represents selected specific embodiments of the present application. Based on the specific embodiments of the present application, all other specific embodiments obtained by those skilled in the art without making creative efforts fall within the scope of the present application.

[0094] In order to further understand the inventive content, characteristics and effects of the present application, the following specific embodiments are exemplified, and the accompanying drawings are combined Figure 1 - the accompanying drawings Figure 5 The detailed description is as follows: Specific embodiment one

[0096] A structure vulnerability evaluation method based on model updating hybrid test, comprising the following steps:

[0097] S1, collecting seismic record data with uniform distribution of seismic intensity parameters, for later use;

[0098] Further, the seismic record data collected in step S1 is 10-20, the source distance from the site is not more than 20 kilometers, the magnitude is greater than 6.0, and the PGA distribution is between 0.2-2.1g. The PGA is evenly divided into four regions, and the PGA distribution of the selected seismic record in each region is uniform;

[0099] S2, using OpenSees to establish a finite element model of the whole structure in step S1, setting the part of the whole structure that is easy to enter strong nonlinearity as a physical substructure, setting the part that has similar mechanical behavior and structural response as the physical substructure as a numerical substructure to be updated, and setting the remaining part as a numerical substructure that is not updated;

[0100] Further, in step S2, one layer of support is set as a component-level physical substructure, one half of a steel frame column is set as a material-level physical substructure, layers two to six supports and the remaining steel materials are set as parts that have similar mechanical behavior and structural response to the physical substructure, and the remaining parts are set as numerical substructures to be updated;

[0101] S3, inputting the seismic record data obtained in step S1 into Matlab software, solving the structure motion equation, then obtaining the displacement of the physical substructure and the displacement of the numerical substructure, inputting the obtained displacement of the physical substructure into the actuator to load and obtain the restoring force of the physical substructure;

[0102] Further, in step S3, the structure motion equation is:

[0103]

[0104] Wherein, M is the mass matrix, a is the acceleration, C is the damping matrix, v is the velocity, R k is the restoring force of the kth step, is the ith seismic wave;

[0105] The displacement of the kth step physical substructure obtained by solving the structure motion equation is The displacement of the kth step numerical substructure is The restoring force of the kth step physical substructure is

[0106] S4, based on the displacement of the physical substructure and the restoring force of the physical substructure obtained in step S3, using the square root volume Kalman filter algorithm as the parameter estimation method to identify the numerical model parameters of the physical substructure, and using the identified physical substructure numerical model parameters to update the numerical substructure model parameters obtained in step S2, and calculating the restoring force of the numerical substructure online according to the numerical substructure model, the updated numerical substructure model parameters and the displacement of the numerical substructure

[0107] Further, the specific implementation method of using the square root cubature Kalman filter algorithm as the parameter estimation method for the numerical model parameter identification of the physical substructure in step S4 includes the following steps:

[0108] S4.1, assuming that the initial value of the known state quantity is , the error covariance P k is updated as k , and the formula for performing Cholesky decomposition is obtained.

[0109]

[0110] wherein S k is a lower triangular matrix of P k decomposition;

[0111] S4.2, the cubature point set ζ j is calculated, and the calculation formula is:

[0112]

[0113]

[0114] wherein n is the dimension of the state, [e] j is the jth initial cubature point;

[0115] Then, the cubature point X k is calculated according to S j,k obtained in step S4.1:

[0116]

[0117] S4.3, the cubature point is propagated through the state equation f, and u k is the system input, and the propagated cubature point is The calculation formula is:

[0118]

[0119] S4.4, the state quantity prediction value is calculated through the propagated cubature point obtained in step S4.3, and the calculation formula is:

[0120]

[0121] wherein w is the weight, and the value is

[0122] S4.5, the square root of the covariance matrix is calculated:

[0123]

[0124] in, Tria() represents the square root of the covariance matrix, and decomposes the matrix into QR values ​​by transposing the matrix.

[0125] matrix S Q Defined as:

[0126]

[0127] S Q =chol(Q)

[0128] In the formula, chol() represents performing Cholsky decomposition on the matrix;

[0129] S4.6, Based on step S4.5 Recalculate volume point X j,k+1 The calculation formula is:

[0130]

[0131] S4.7, The recalculated volume point X obtained in step S4.6 j,k+1 The propagation is performed through the observation equation, and the measured predicted value is calculated using the following formula:

[0132] Z j,k+1 =h(X) j,k+1 ,u k+1 )

[0133] Among them, Z j,k+1 The volume point after the propagation of the observation equation;

[0134]

[0135] in, To measure the predicted value;

[0136] S4.8. Based on the measurement prediction values ​​obtained in step S4.7, calculate the square root S of the residual covariance matrix. zz,k+1 The calculation formula is:

[0137] S zz,k+1 =Tria([γ k+1 S R ]),

[0138] Where, matrix γ k+1 S R Defined as:

[0139]

[0140] SR =chol(R)

[0141] Then calculate the square root matrix P of the cross-covariance. xz,k+1 The calculation formula is:

[0142]

[0143] Where, matrix X k+1 Defined as:

[0144]

[0145] S4.9, P obtained from step S4.8 xz,k+1 Calculate the Kalman gain K k+1 The calculation formula is:

[0146]

[0147] S4.10. Calculate the posterior state estimate of the system based on the Kalman gain obtained in step S4.9. The estimated value S of the square root of the error covariance k+1 The calculation formula is:

[0148]

[0149] S k+1 =Tria([X k+1 -K k+1 γ k+1 K k+1 S R ];

[0150] S5. Send the restoring forces of the physical substructure and the numerical substructure to the equation of motion to solve for the displacement, velocity and acceleration at time k+1. Repeat steps S3 to S5 until the earthquake record ends to obtain the earthquake response data.

[0151] S6. Using the seismic response data obtained in step S5, calculate the seismic response parameter DM under different ground motion intensity parameters IM, and then perform data regression analysis on the ground motion intensity parameters and seismic response parameters to obtain the seismic demand model.

[0152] Furthermore, the specific implementation method of step S6 includes the following steps:

[0153] S6.1 Set the seismic intensity parameters IM, including peak ground acceleration (PGA), peak ground velocity (PGV), and the acceleration response spectrum value S corresponding to the fundamental period of the structure with damping ratio ξ. a (T1, ξ), the seismic response parameters DM include maximum base shear force, vertex displacement, nodal rotation, maximum story ductility coefficient, and maximum inter-story drift angle θ.max hysteretic energy dissipation;

[0154] S6.2, based on the ground motion intensity parameter IM and the seismic response parameter DM obey normal distribution, the mathematical relationship is expressed as:

[0155] DM = a (IM) β

[0156] Wherein, a, β are regression parameters;

[0157] S6.3, according to step S6.1, the ground motion intensity parameter IM is selected as the peak ground acceleration PGA, and the seismic response parameter DM is the maximum interlayer displacement angle θ max , then the formula is:

[0158] θ max = a (PGA) β ;

[0159] Taking the logarithm of both sides, the following formula is obtained:

[0160] lnθ max = ln a + β ln (PGA)

[0161] Linear regression is performed on the above formula, and the values of a and β are obtained, and the seismic demand model is obtained;

[0162] S7, according to the seismic demand model obtained in step S6, the structure damage probability density function is constructed, the failure probability is calculated, and the vulnerability curve is drawn;

[0163] Further, the specific implementation method of step S7 includes the following steps:

[0164] S7.1, the formula of the failure probability of the response D of the structure under different seismic intensity exceeding the demand capacity parameter C of the structure is:

[0165] P f = P (θ c / θ max <1) = P (lnθ c -lnθ max <0)

[0166] Wherein, P f is the failure probability, and θ c is the demand capacity parameter of the structure;

[0167] S7.2, set Z = lnθ c -lnθ max And obey normal distribution, the mean value is expressed as μ z = μ θc -μ θmax The standard deviation is The formula for deriving the failure probability is:

[0168]

[0169] wherein Z is a representative value;

[0170] θ c and θ max are two independent variables and subject to normal distribution, so Z is also subject to normal distribution;

[0171] S7.3, convert N(mu z , sigma z ) to standard normal distribution N(0, 1), let then dZ = sigma z dt; Z = mu z + t sigma z , then The above formula is rewritten as:

[0172]

[0173] The failure probability is obtained as:

[0174]

[0175] S7.4, according to HAZUS99, when IM is PGA, the value is 0.5, and the fragility curve is drawn;

[0176] Further, when IM is S a , the value is 0.4.

[0177] The embodiment discloses a structure fragility evaluation method based on model updating hybrid test, taking a six-story steel frame structure with self-resetting friction energy dissipation support as an example, and describes the basic principle and use steps of the method.

[0178] In order to prepare the building structure before the earthquake disaster, it is necessary to reasonably estimate, predict and reduce the loss, and the seismic fragility curve is one of the important contents of evaluating the damage and loss of the earthquake event. As a kind of energy dissipation component, the self-resetting friction energy dissipation support has good energy dissipation effect and structural residual displacement control advantages. For a six-story steel frame structure with self-resetting friction energy dissipation support, the accuracy of the seismic response of the overall structure obtained by only using nonlinear time history analysis cannot be guaranteed. Therefore, the model updating hybrid test method in the seismic test method is used to obtain the seismic response of the structure, and a structure fragility evaluation method based on model updating hybrid test is proposed.

[0179] According to Figure 2 and Figure 4 andFigure 5 It can be seen that the seismic response data of the six-story steel frame structure with self-centering frictional energy dissipation braces is obtained based on the model updating hybrid test, the seismic demand model is obtained, and the seismic fragility curves of the six-story steel frame structure with self-centering frictional energy dissipation braces under slight damage, moderate damage, severe damage and collapse are finally drawn. When the PGA reaches 8 degree earthquake action, the structure is basically in a non-damage state, when the PGA reaches 8 degree fortification, there is a very small probability of slight damage, and when the PGA reaches 8 degree rare earthquake, the structure has a probability of 82.36% of slight damage. This is consistent with the working principle of the steel frame structure with self-centering frictional energy dissipation braces under different intensity earthquakes. Under the action of small earthquakes, the structure is basically in an elastic working state, and as the earthquake intensity reaches a rare earthquake, the structure begins to enter the elastic-plastic state to dissipate seismic energy, and the structure gradually produces damage accumulation. The collapse probability of the structure under 8 degree rare earthquake is 0, when the PGA reaches 0.8g, the structure has only a very small probability of collapse of 4.3%, and when the PGA reaches 2g, the collapse probability of the structure is 87.16%, which can fully meet the design requirement of “no collapse under rare earthquake”.

[0180] The fragility evaluation method based on model updating hybrid test described in the embodiment combines online model updating technology, structure hybrid test technology and fragility calculation method, adopts a model updating hybrid test method based on SRCKF algorithm to obtain the seismic response data of the six-story steel frame structure with self-centering frictional energy dissipation braces, and draws the fragility curve based on the data, thereby improving the fragility evaluation precision of large and complex civil engineering structures.

[0181] It should be noted that the terms “first” and “second” and the like are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the terms “include”, “contain” or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or device. Without more limitations, the element defined by the statement “including a…” does not exclude the presence of additional identical elements in the process, method, article or device including the element.

[0182] Although the present application has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the present application. In particular, various features and aspects of the present application can be used individually or in any combination depending on the specific application and implementation. Therefore, it is expressly intended that the specific embodiments of the present application both as set forth and including any equivalents thereof should not limit the present application or scope of the claims herein, but rather the overall scope of pertaining solely to the methods and the articles of manufacture specifically recited in the following claims.

Claims

1. A method for structural vulnerability assessment based on model-updated hybrid testing, characterized by, It comprises the following steps: S1, collecting seismic record data with uniform intensity parameter distribution, for standby; S2, using OpenSees to establish a finite element model of the overall structure in step S1, setting the part of the overall structure that is easy to enter strong nonlinearity as a physical substructure, setting the part that has similar mechanical behavior and structural response as the numerical substructure to be updated, and setting the remaining part as the numerical substructure not to be updated, for standby; In step S2, one layer of support is set as a component-level physical substructure, one half of a layer of steel frame column is set as a material-level physical substructure, layers two to six of support and the remaining steel material are set as the part that has similar mechanical behavior and structural response, and the remaining part is set as the numerical substructure not to be updated; S3, inputting the seismic record data obtained in step S1 into Matlab software, solving the structural motion equation, then obtaining the displacement of the physical substructure and the displacement of the numerical substructure, inputting the obtained displacement of the physical substructure into the actuator to load and obtain the restoring force of the physical substructure; S4, based on the displacement of the physical substructure and the restoring force of the physical substructure in step S3, using the square root volume Kalman filter algorithm as the parameter estimation method to identify the numerical model parameters of the physical substructure, and using the identified numerical model parameters of the physical substructure to update the model parameters of the numerical substructure to be updated in step S2, and online calculating the restoring force of the numerical substructure according to the numerical substructure model, the updated numerical substructure model parameters and the displacement of the numerical substructure; S5, sending the restoring force of the physical substructure and the restoring force of the numerical substructure to the motion equation to solve the displacement, velocity and acceleration at time k+1, repeating the above steps S3 to S5 until the end of the seismic record, and obtaining the response data of the overall structure; S6, using the seismic response data obtained in step S5 to calculate the seismic response parameters DM under different seismic intensity parameters IM, then performing data regression analysis on the seismic intensity parameters and the seismic response parameters to obtain a seismic demand model; S7, constructing a structural damage probability density function according to the seismic demand model obtained in step S6, calculating the failure probability, and drawing a fragility curve.

2. The method of claim 1, wherein, The seismic record data collected in step S1 is 10-20, the source distance from the site is not greater than 20 kilometers, the magnitude is greater than 6.0, and the PGA distribution is between 0.2-2.1g, the PGA is evenly divided into four regions, and the PGA of the selected seismic record in each region is evenly distributed.

3. The method of claim 2, wherein, The structural motion equation in step S3 is: ； where M is a mass matrix, a is an acceleration, C is a damping matrix, v is a velocity, R k is the restoring force at the kth step, is the ith seismic wave; The displacement of the kth step physical substructure obtained by solving the structural motion equation is , the displacement of the kth step numerical substructure is , and the restoring force of the kth step physical substructure is .

4. The method of claim 3, wherein, The specific implementation method of using the square root volume Kalman filter algorithm as the parameter estimation method to identify the numerical model parameters of the physical substructure in step S4 comprises the following steps: S4.1, assuming that the initial value of the known state quantity is , the error covariance , the error covariance is performed Cholesky decomposition, and the formula is ； wherein is a lower triangular matrix decomposed S4.2, calculating the volume point set The calculation formula is: ； ； where n is the dimension of the state, [e] j is the jth initial volume point; Then, according to the result of step S4.1 Computing volume points : ； S4.3, the volume points are propagated by the equation of state f, and the propagated volume points are , is the system input, and the calculation formula is: ， S4.

4. Calculate the state quantity prediction value of the propagated volume point obtained by step S4.3 The calculation formula is: ， wherein, is a weight having a value of ; S4.5, calculate the square root of the covariance matrix: ， wherein is a square root of the covariance matrix, denotes a QR decomposition of the transpose of the matrix; matrix , is defined as: ； ； wherein denotes the Cholesky decomposition of the matrix; S4.

6. The volume point is recalculated , recalculating the volume point , the calculation formula is: ， S4.

7. Re-computed volume points from step S4.6 The measurement prediction is calculated by propagating through the observation equation h and calculating the measurement prediction, given by: ； wherein, is the propagated volume point for the observation equation; ； wherein, is the measured prediction value; S4.

8. Calculate the square root of the residual covariance matrix from the measurement prediction values obtained in step S4.7 The calculation formula is: ， where the matrix is defined as: ， ； The square root matrix of the cross-covariance is then computed with the formula: ； where the matrix is defined as: ； S4.

9. The product obtained in step S4.8 Computing the Kalman gain with the formula ； S4.

10. Calculate the system posterior state estimate from the Kalman gain obtained in step S4.9 , the estimate of the error covariance square root , the calculation formula is: ， 。 5. The method for structural vulnerability assessment based on model updating hybrid test according to claim 4, characterized in that, The specific implementation method of step S6 comprises the following steps: S6.1, setting the ground motion intensity parameter IM including peak acceleration PGA, peak velocity PGV, damping ratio of the structure fundamental period corresponding to the acceleration response spectrum value S a (T1, ), the seismic response parameter DM including maximum base shear, vertex displacement, node rotation, maximum ductility coefficient of floor, maximum inter-story drift angle, hysteretic energy; S6.2, based on the fact that the seismic intensity parameter IM and the seismic response parameter DM obey normal distribution, the mathematical relationship is expressed as: Where, α and β are regression coefficients; S6.3、According to step S6.1, the ground motion intensity parameter IM is the peak ground acceleration PGA, and the seismic response parameter DM is the maximum inter-story drift angle The formula is obtained as follows: ； Taking the logarithm of both sides to obtain the following formula: ； Linear regression is performed on the above equation to obtain the value of and the seismic demand model.

6. The method for structural vulnerability assessment based on model updating hybrid test according to claim 5, characterized in that, The specific implementation method of step S7 comprises the following steps: S7.1, the formula of the failure probability of the response D of the setting structure under different seismic intensity exceeding the capacity parameter C of the setting structure is: ； where P f is the probability of failure, is the structural demand capacity parameter; S7.2, Setup and subject to a normal distribution, the mean is represented as with a standard deviation of The formula for deriving the probability of failure is: ； wherein, Z is a representative value; S7.3, to Transformed to standard normal distribution , the failure probability is: ； S7.

4. When IM is PGA, the fragility curve is drawn according to HAZUS99, The fragility curve is drawn with a value of 0.5.

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