A laminated rubber seismic isolation bearing damage identification method based on vibration power flow

Abstract

The application relates to a laminated rubber seismic isolation support damage identification method based on vibration power flow, characterized in that the laminated rubber seismic isolation support is taken as a finite period structure for damage identification, and the damage identification method comprises the following steps: obtaining the relationship between input power flow and shear modulus change before and after basic period unit damage based on the relationship between input power flow and natural frequency of the period structure; establishing a sensitivity identification equation group of input power flow change rate to unit damage; and solving the sensitivity identification equation group based on the relationship between input power flow and shear modulus change before and after basic period unit damage to realize damage identification of the laminated rubber seismic isolation support. The damage identification precision can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural testing, and in particular to a method for identifying damage to laminated rubber seismic isolation bearings based on vibration power flow. Background Technology

[0002] During an earthquake, laminated rubber seismic isolation bearings undergo significant horizontal deformation, making them the most vulnerable and sensitive structural components. Furthermore, the long-term coupled effects of adverse factors such as loads and environmental conditions lead to continuous performance degradation of the bearings, resulting in damage and failure, thus jeopardizing the overall safety of the isolated building. Therefore, health monitoring and damage identification studies of laminated rubber seismic isolation bearings are essential.

[0003] Damage detection methods for laminated rubber seismic isolation bearings in related technologies include: 1) direct replacement for severely damaged bearings; 2) repositioning bearings with residual deformation. However, this raises questions about whether internal damage exists after repositioning and how to detect such damage. Other related technologies mention disassembling all rubber seismic isolation bearings to be tested, then testing them one by one according to laboratory bearing mechanical performance test criteria and human experience before reinstalling. For large-scale construction projects, these methods are not only time-consuming and labor-intensive, affecting the normal operation of the structure, but also risk exacerbating overall structural damage or even causing collapse due to sudden aftershocks during disassembly and testing. Related technologies mention damage identification based on piezoresistive impedance information (CN109709150A), which requires measuring "piezoresistive impedance information." Because the variation in piezoresistive impedance information is small and difficult to collect, it introduces significant errors in damage identification; furthermore, it cannot consider the influence of the superstructure on the laminated rubber seismic isolation bearings, lacking practicality in engineering applications.

[0004] Therefore, accurately reflecting the damage dynamic characteristics of laminated rubber seismic isolation bearings and achieving rapid on-site identification of the bearing damage level is one of the key scientific problems that the academic and engineering communities urgently need to solve. Summary of the Invention

[0005] This invention provides a method for identifying damage to laminated rubber seismic isolation bearings based on vibration power flow, in order to solve problems in related technologies.

[0006] On the one hand, a method for damage identification of laminated rubber seismic isolation bearings based on vibration power flow is provided, characterized in that the laminated rubber seismic isolation bearings are treated as finite-period structures for damage identification, and the damage identification method includes the following steps:

[0007] The relationship between the input power flow and the natural frequency of the periodic structure is used to obtain the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element.

[0008] Establish a set of equations to identify the sensitivity of the input power flow rate to cell damage;

[0009] The sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element in order to achieve damage identification of the laminated rubber seismic isolation bearing.

[0010] In some embodiments, the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element is obtained based on the relationship between the input power flow and the natural frequency of the periodic structure, including the following steps:

[0011] The relationship between the change in shear modulus of the basic periodic element before and after damage and the natural frequency of the periodic structure was established.

[0012] The relationship between the input power flow and the natural frequency of the periodic structure is established based on the functional relationship between the input power flow, the boundary admittance of the periodic structure, and the excitation force.

[0013] Based on the relationship between the input power flow and the natural frequency of the periodic structure, and the relationship between the change in shear modulus of the basic periodic unit before and after damage and the natural frequency of the periodic structure, the relationship between the input power flow and the change in shear modulus of the basic periodic unit before and after damage is derived.

[0014] In some embodiments, the relationship between the change in shear modulus before and after damage to the basic periodic element and the natural frequency of the periodic structure is constructed, including the following steps:

[0015] The characteristic equation of the natural frequency of a periodic structure containing damaged elements is constructed based on the characteristic waveguide admittance method.

[0016] After simplifying the laminated rubber seismic isolation bearing into a periodic structure, the relationship between the shear modulus change and the element admittance of the basic periodic element of the laminated rubber seismic isolation bearing before and after damage is established.

[0017] Substituting the relationship between the shear modulus change and the element admittance into the characteristic equation of the natural frequency of the periodic structure, the relationship between the shear modulus change before and after damage to the basic periodic element and the natural frequency of the periodic structure is obtained.

[0018] In some embodiments, the characteristic equation for the natural frequency of a periodic structure containing damaged elements is constructed based on the characteristic waveguide admittance method, including the following steps:

[0019] Assume that the j-th basic periodic unit in a periodic structure composed of n identical basic periodic units is a damaged unit, and the boundaries of the periodic structure are C and D;

[0020] The two end nodes of the damaged unit are labeled A and B, respectively, and an excitation force F is applied at the boundary C of the periodic structure. C ;

[0021] The characteristic equation of the natural frequency of the periodic structure containing the damaged element is constructed based on the first formula.

[0022] The first formula is: 1 + Φ = 0, where Φ is the wave propagation constant, and

[0023]

[0024]

[0025]

[0026]

[0027] Where μ is the wave propagation constant and e is the natural constant.

[0028] To apply the excitation force F C The displacement caused by the forward propagating wave at boundary C,

[0029] To apply the excitation force F C The displacement caused by the reflected wave at boundary C

[0030] β is the wave propagating at point D on the boundary. and reflected waves The resulting displacement ratio, and

[0031] and These are the characteristic waveguide admittances corresponding to the forward propagation wave and the reflected wave, respectively, α D Let α be the admittance at the boundary D of the periodic structure. AA α BB α represents the direct admittances at nodes A and B at the two ends of the damaged element j, respectively. AB α BA This is the indirect admittance of the damaged unit j.

[0032] In some embodiments, after simplifying the laminated rubber seismic isolation bearing into a periodic structure, the relationship between the shear modulus change and the element admittance of the basic periodic element of the laminated rubber seismic isolation bearing before and after damage is established, including the following steps:

[0033] The laminated rubber seismic isolation bearing is simplified to the periodic structure described above, where boundary C is the lower boundary of the laminated rubber seismic isolation bearing and boundary D is the upper boundary of the laminated rubber seismic isolation bearing. Meanwhile,

[0034] Each fundamental periodic element in the laminated rubber seismic isolation bearing contains a mass m rA rubber layer with thickness d, rubber density ρ2, and cross-sectional area a, and two rubber layers, each with mass m. s / 2 steel plate;

[0035] The relationship between the direct and indirect unit admittances of the damaged unit j and the change in shear modulus is obtained according to the second formula.

[0036] The second formula is:

[0037]

[0038]

[0039]

[0040] Where, n * =ω(ρ2 / (G+ΔG)) 1 / 2 ,

[0041] G is the shear modulus of the laminated rubber seismic isolation bearing, ΔG is the change in shear modulus of damaged element j before and after damage, ω is the frequency, and α is the frequency. ll α rr Let α be the direct element admittance after damage occurs to damaged element j. lr α rl Let J be the indirect unit admittance after damage occurs to damaged unit j.

[0042] In some embodiments, the relationship between the input power flow and the natural frequency of the periodic structure is established based on the functional relationship between the input power flow and the boundary admittance and excitation force of the periodic structure, including the following steps:

[0043] The functional relationship between the input power flow and the boundary admittance of the periodic structure and the excitation force can be obtained from the third formula.

[0044] The third formula is:

[0045]

[0046] In the formula, Re denotes taking the real part, α D F is the admittance at the boundary D of the periodic structure. c For the generalized force of the base of the seismic isolation bearing, V * For the motivation F c The velocity response at the lower boundary C;

[0047] Substituting the second formula into the third formula yields the relationship between the input power flow and the natural frequency of the periodic structure.

[0048] The relationship between the input power flow and the natural frequency of the periodic structure is expressed as follows:

[0049]

[0050] Where N is the number of stories in the building structure, μ1 is the wave propagation constant of the upper periodic structure, and α lr1 For the indirect admittance of the upper periodic structure, F c This refers to the generalized force at the base of the seismic isolation bearing.

[0051] In some embodiments, a set of equations is established to identify the sensitivity of the input power flow rate of change to cell damage, including the following steps:

[0052] The relationship between the sensitivity coefficient of the basic periodic unit damage and the input power flow is obtained according to the fourth formula.

[0053] The fourth formula is:

[0054] Where ξ=ΔG / G,

[0055] S n,j p represents the sensitivity coefficient of damage element j to damage in a periodic structure with n basic periodic elements. u ξ is the input power flow in the undamaged state, p is the nth order input power flow, ξ is the degree of damage, G is the shear modulus of the periodic structure, ΔG is the change in shear modulus of damaged element j before and after damage, and Δξ is the change in degree of damage before and after damage occurs.

[0056] The input power flow changes caused by damage to a single basic periodic cell are linearly superimposed to obtain a set of equations for identifying the sensitivity of the input power flow change rate to cell damage.

[0057] The set of equations for identifying the sensitivity of the input power flow rate to cell damage is expressed as follows:

[0058]

[0059] in q represents the mode order of the periodic structure measurement, [S] represents the sensitivity coefficient matrix corresponding to the input power flow, and ξ represents the sensitivity coefficient matrix. n denoted as the damage level of the nth basic periodic unit, where n ranges from 1 to N.

[0060] In some embodiments, the sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element to achieve damage identification of the laminated rubber seismic isolation bearing, including the following steps:

[0061] The partial derivative of ω with respect to Δξ is obtained from the first formula. Then, the partial derivative of the input power flow p with respect to ω is obtained according to the third formula. make and Multiply to obtain make And p = p u Solve the fourth formula to obtain the sensitivity coefficient S. n,j The expression;

[0062] The actual measured input power flow p is compared with the sensitivity coefficient S. n,j Substituting the input power flow change rate into the sensitivity identification equations for unit damage, the damage degree equations {δξ} are obtained.

[0063] In some embodiments, the superstructure is considered as a single-degree-of-freedom structure consisting of a long column and multiple concentrated masses m spaced L apart on the long column.

[0064] The impedance of the single-degree-of-freedom structure is expressed as Z. D =-Mω 2 ,in,

[0065] M is the mass of the superstructure and M = Nm + Nρ1A1L, m is the concentrated mass of each floor in the superstructure, ρ1 is the material density of the long column, A1 is the cross-sectional area of ​​the long column, and ω is the angular frequency.

[0066] Introducing the impedance of the single-degree-of-freedom structure into the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure includes the following steps:

[0067] α D =1 / Z D Substituting the relationship between the change in shear modulus before and after damage of the basic periodic unit and the natural frequency of the periodic structure, the characteristic equation of the natural frequency of the laminated rubber seismic isolation bearing under the influence of the superstructure is obtained.

[0068] The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is:

[0069]

[0070] The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is substituted into the sensitivity identification equation set to achieve damage identification of the laminated rubber seismic isolation bearing with superstructure.

[0071] In some embodiments, the sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element to achieve damage identification of the laminated rubber seismic isolation bearing, including the following steps:

[0072] When solving the sensitivity identification equation system using the non-negative least squares curve fitting optimization algorithm, the optimset command is used to adjust the number of iterations during calculation, and the format long command in MATLAB programming is used to improve the calculation accuracy.

[0073] This embodiment establishes a set of equations to identify the sensitivity of the input power flow change rate to element damage, thereby achieving damage identification of laminated rubber seismic isolation bearings based on the measurement of input power flow changes. Considering that the input power flow, as a measurement parameter, changes significantly and is easy to identify, this approach can effectively improve the accuracy of parameter acquisition, thus further enhancing the accuracy of the identification results. Attached Figure Description

[0074] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 This is a schematic flowchart of a method for identifying damage to laminated rubber seismic isolation bearings based on vibration power flow, provided by an embodiment of the present invention.

[0076] Figure 2 This is a schematic diagram of a laminated rubber seismic isolation bearing structure provided in an embodiment of the present invention;

[0077] Figure 3 A simplified model diagram of a superstructure provided in an embodiment of the present invention;

[0078] Figure 4 A sensitivity coefficient diagram of the input power flow of the laminated rubber seismic isolation bearing to the basic periodic element for each order, provided in an embodiment of the present invention.

[0079] Figure 5 The damage identification results of the laminated rubber seismic isolation bearing under various working conditions provided in the embodiments of the present invention are based on the input power flow.

[0080] Figure 6 The sensitivity coefficients of each order of input power flow to the basic periodic element of the laminated rubber seismic isolation bearing when the superstructure is a single degree of freedom, provided in the embodiments of the present invention;

[0081] Figure 7 Damage identification results of laminated rubber seismic isolation bearings under various working conditions when the superstructure has a single degree of freedom, as provided in the embodiments of the present invention;

[0082] Figure 8 The frequency sensitivity coefficients of the laminated rubber seismic isolation bearings for multi-story buildings provided in this embodiment of the invention;

[0083] Figure 9 The damage identification results of the laminated rubber seismic isolation bearings under various working conditions when the superstructure is an 8-story building, as provided in the embodiments of the present invention. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] like Figure 1 As shown, this embodiment of the invention provides a method for damage identification of laminated rubber seismic isolation bearings based on vibration power flow. The method is characterized by treating the laminated rubber seismic isolation bearing as a finite-period structure for damage identification, and includes the following steps:

[0086] S100: Based on the relationship between the input power flow and the natural frequency of the periodic structure, the relationship between the input power flow and the change in shear modulus before and after damage of the basic periodic element is obtained.

[0087] S200: Establish a set of equations to identify the sensitivity of the input power flow rate to cell damage;

[0088] S300: Solve the sensitivity identification equation set based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic unit to achieve damage identification of the laminated rubber seismic isolation bearing.

[0089] This embodiment establishes a set of equations to identify the sensitivity of the input power flow change rate to element damage, thereby achieving damage identification of laminated rubber seismic isolation bearings based on the measurement of input power flow changes. Considering that the input power flow, as a measurement parameter, changes significantly and is easy to identify, this approach can effectively improve the accuracy of parameter acquisition, thus further enhancing the accuracy of the identification results.

[0090] Further, step S100 includes:

[0091] S110: Construct the relationship between the change in shear modulus of the basic periodic element before and after damage and the natural frequency of the periodic structure.

[0092] S120: Establish the relationship between the input power flow and the natural frequency of the periodic structure based on the functional relationship between the input power flow, the boundary admittance of the periodic structure, and the excitation force.

[0093] S130: Based on the relationship between the input power flow and the natural frequency of the periodic structure and the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure, derive the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic unit.

[0094] Further, step S110 includes:

[0095] S111: Constructing the characteristic equation of the natural frequency of a periodic structure containing damaged elements based on the characteristic waveguide admittance method;

[0096] S112: After simplifying the laminated rubber seismic isolation bearing into a periodic structure, establish the relationship between the shear modulus change and element admittance of the basic periodic element of the laminated rubber seismic isolation bearing before and after damage.

[0097] S113: Substitute the relationship between the shear modulus change and the element admittance into the characteristic equation of the natural frequency of the periodic structure to obtain the relationship between the shear modulus change before and after damage to the basic periodic element and the natural frequency of the periodic structure.

[0098] In some embodiments, step S111 includes:

[0099] S111-a: Assume that the j-th basic periodic unit in a periodic structure composed of n identical basic periodic units is a damaged unit, and the boundaries of the periodic structure are C and D;

[0100] S111-b: Mark the two end nodes of the damaged unit as A and B respectively, and apply an excitation force F at the boundary C of the periodic structure. C ;

[0101] S111-c: Construct the characteristic equation of the natural frequency of the periodic structure containing the damaged element according to the first formula;

[0102] The first formula is: 1 + Φ = 0, where Φ is the wave propagation constant, and

[0103]

[0104]

[0105]

[0106]

[0107] Where μ is the wave propagation constant and e is the natural constant.

[0108] To apply the excitation force F C The displacement caused by the forward propagating wave at boundary C,

[0109] To apply the excitation force F C The displacement caused by the reflected wave at boundary C

[0110] β is the wave propagating at point D on the boundary. and reflected waves The resulting displacement ratio, and

[0111] and These are the characteristic waveguide admittances corresponding to the forward propagation wave and the reflected wave, respectively, α D Let α be the admittance at the boundary D of the periodic structure. AA α BB For the direct admittance at segments A and B at both ends of the damaged unit j, α AB α BA The indirect admittance is for the damaged unit j (between points A and B).

[0112] Further, step S112 includes:

[0113] S112-a: Simplify the laminated rubber seismic isolation bearing into the periodic structure described above, such that boundary C is the lower boundary of the laminated rubber seismic isolation bearing and the boundary is also the upper boundary of the laminated rubber seismic isolation bearing. Meanwhile,

[0114] Each fundamental periodic element in the laminated rubber seismic isolation bearing contains a mass m r A rubber layer with thickness d, rubber density ρ2, and cross-sectional area a, and two rubber layers, each with mass m. s / 2 steel plate;

[0115] S112-b: Obtain the relationship between the direct and indirect unit admittances of the damaged unit j and the change in shear modulus according to the second formula;

[0116] The second formula is:

[0117]

[0118]

[0119]

[0120] Where, n * =ω(ρ2 / (G+ΔG)) 1 / 2 ,

[0121] G is the shear modulus of the laminated rubber seismic isolation bearing, ΔG is the change in shear modulus of damaged element j before and after damage, ω is the frequency, and α is the frequency.ll α rr Let α be the direct element admittance after damage occurs to damaged element j. lr α rl The indirect unit admittance after damage occurs to damaged unit j;

[0122] It is understandable that substituting the second formula into the first formula yields the relationship between the change in shear modulus before and after damage to the basic periodic element and the natural frequency of the periodic structure.

[0123] When ΔG = 0, the periodic structure is considered to be in a healthy state. The relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure can be expressed as:

[0124] When ΔG>0, the periodic structure is considered to be in a damaged state. The relationship between the change in shear modulus of the basic periodic unit before and after damage and the natural frequency of the periodic structure can be expressed as:

[0125] Further, step S120 includes:

[0126] S121: The functional relationship between the input power flow, the boundary admittance of the periodic structure, and the excitation force is obtained according to the third formula;

[0127] The third formula is:

[0128]

[0129] In the formula, Re denotes taking the real part, α D F is the admittance at the boundary D of the periodic structure. c For the generalized force of the base of the seismic isolation bearing, F c V is the excitation force applied at the boundary C of the periodic structure. * For the motivation F C The velocity response at the lower boundary C;

[0130] S122: Substitute the second formula into the third formula to obtain the relationship between the input power flow and the natural frequency of the periodic structure, and the relationship between the input power flow and the natural frequency of the periodic structure is expressed as:

[0131]

[0132] Where N is the number of stories in the building structure, μ1 is the wave propagation constant of the upper periodic structure, and α lr1 For the indirect admittance of the upper periodic structure, F c This refers to the generalized force at the base of the seismic isolation bearing.

[0133] Further, step S200 includes:

[0134] S210: The relationship between the sensitivity coefficient of the basic periodic unit damage and the input power flow is obtained according to the fourth formula;

[0135] The fourth formula is:

[0136] Where ξ=ΔG / G,

[0137] S n,j p represents the sensitivity coefficient of damage element j to damage in a periodic structure with n basic periodic elements. u ξ is the input power flow in the undamaged state, p is the nth order input power flow, ξ is the degree of damage, G is the shear modulus of the periodic structure, ΔG is the change in shear modulus of damaged element j before and after damage, and Δξ is the change in degree of damage before and after damage occurs.

[0138] S220: Linearly superimpose the input power flow changes caused by damage to a single basic periodic cell to obtain a set of equations for identifying the sensitivity of the input power flow change rate to cell damage;

[0139] The set of equations for identifying the sensitivity of the input power flow rate to cell damage is expressed as follows:

[0140]

[0141] in q represents the mode order of the periodic structure measurement, [S] represents the sensitivity coefficient matrix corresponding to the input power flow, and ξ represents the sensitivity coefficient matrix. n denoted as the damage level of the nth basic periodic unit, where n ranges from 1 to N.

[0142] Further, based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element, the sensitivity identification equation set is solved to achieve damage identification of the laminated rubber seismic isolation bearing. Step S300 includes:

[0143] S310: Obtain the partial derivative of ω with respect to Δξ according to the first formula. Then, the partial derivative of the input power flow p with respect to ω is obtained according to the third formula. make and Multiply to obtain make And p = p u Solve the fourth formula to obtain the sensitivity coefficient S. n,j The expression;

[0144] Specifically, based on the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure:

[0145]

[0146] in,

[0147]

[0148]

[0149]

[0150] and

[0151] This allows for further analysis of direct and indirect admittance (α) after injury. AA α BB α AB α BA Given the wave propagation constant μ, solve for the partial derivative of ω with respect to Δξ.

[0152] S320: Combine the actual measured input power flow p with the sensitivity coefficient S n,j Substituting the input power flow change rate into the sensitivity identification equations for unit damage, the damage degree equations {δξ} are obtained.

[0153] like Figure 3 As shown, in a preferred embodiment, the superstructure is considered as a single-degree-of-freedom structure consisting of a long column and a plurality of concentrated masses m spaced L apart on the long column.

[0154] The impedance of the single-degree-of-freedom structure is expressed as Z. D =-Mω 2 Where M is the mass of the superstructure and M=Nm+Nρ1A1L, m is the concentrated mass of each floor in the superstructure, ρ1 is the material density of the long column, A1 is the cross-sectional area of ​​the long column, and ω is the angular frequency.

[0155] Introducing the impedance of the single-degree-of-freedom structure into the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure includes the following steps:

[0156] α D =1 / Z D Substituting the relationship between the change in shear modulus before and after damage of the basic periodic unit and the natural frequency of the periodic structure, the characteristic equation of the natural frequency of the laminated rubber seismic isolation bearing under the influence of the superstructure is obtained.

[0157] The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is:

[0158]

[0159] The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is substituted into the sensitivity identification equation set to achieve damage identification of the laminated rubber seismic isolation bearing with superstructure.

[0160] In this embodiment, the damage identification model for laminated rubber bearings considers the influence of the superstructure on the bottom rubber bearing, making the calculation model more consistent with engineering reality. Simultaneously, considering the influence of the superstructure on the bottom rubber bearing, applying constraints to both ends of the model simultaneously can lead to the problem of "damage location symmetry." Therefore, a more refined derivation and calculation were performed at the formula level to address the damage location symmetry issue, ensuring accurate identification of damage locations when the superstructure is added to the later simulation model.

[0161] Preferably, the damage identification of the laminated rubber seismic isolation bearing is achieved by solving the sensitivity identification equation set based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element, including the following steps:

[0162] When solving the sensitivity identification equation system using the non-negative least squares curve fitting optimization algorithm, the optimset command is used to adjust the number of iterations during calculation, and the format long command in MATLAB programming is used to improve the calculation accuracy.

[0163] In the damage identification test of the laminated rubber seismic isolation bearing structure based on the method described in the embodiments of the present invention, it is assumed that the total number of periodic elements of the laminated rubber seismic isolation bearing structure is n = 10, and a set of geometric and physical parameters are given: shear modulus G = 1 × 10⁻⁶. 6 N / m 2 The density of rubber ρ2 = 1 × 10 3 kg / m 3 The diameter of the rubber layer is 800 mm, d = 1 cm, and the mass ratio of the steel plate to the rubber is φ = 5. The frequency order is selected as half the total number of periodic elements, and the first 5 frequencies of the laminated rubber seismic isolation bearing are calculated.

[0164] Table 1 shows the first five frequencies calculated when the laminated rubber seismic isolation bearing is undamaged. (The rest of the text appears to be a table or table and doesn't translate directly.) u Substituting the values ​​into the fourth formula, we can obtain the sensitivity coefficients of the input power flow to the overall stiffness of each periodic element under the excitation of the first 5 natural frequencies of a periodic laminated rubber seismic isolation bearing with a total of 10 elements.

[0165] Table 1. First 5 frequency values ​​of healthy laminated rubber seismic isolation bearings

[0166]

[0167] like Figure 4 As shown, the sensitivity coefficients of the input power flow under the same natural frequency excitation are different for different elements, and each natural frequency excitation has its own most sensitive element, corresponding to the tallest column element in each bar chart. Simultaneously, each natural frequency excitation also has its own least sensitive element, corresponding to the shortest column element in each bar chart.

[0168] In one embodiment, the damage identification problem of laminated rubber seismic isolation bearing structures based on input power flow is transformed into a non-negative least squares curve fitting problem, and the following formula is applied:

[0169] Damage identification results for the laminated rubber seismic isolation bearing structure can be obtained by performing non-negative least squares curve fitting. Three damage conditions can be assumed, including single damage and double damage conditions. The specific damage locations and damage degrees for each condition are shown in Table 2.

[0170] Table 2 Damage Conditions of Laminated Rubber Isolation Bearing Model

[0171]

[0172] In this embodiment, when using the sensitivity equation of the characteristic waveguide admittance method for damage identification, the required frequency order is half the number of periodic structural units. Using, for example... Figure 4 The first 5 orders of the sensitivity matrix calculated as shown are substituted into... By employing a non-negative least squares curve fitting numerical optimization algorithm, the damage identification results of laminated rubber seismic isolation bearings based on input power flow can be obtained for three damage conditions.

[0173] like Figure 5 As shown, the damage identification results for the three damage conditions demonstrate that the theoretically derived damage identification results are perfectly consistent with the actual damage, and there are no misidentified units. For the three preset damage conditions, whether it is single damage or multiple damage, the damage identification method based on input power flow proposed in this invention can accurately identify the damage location and damage degree of the laminated rubber bearing.

[0174] In one embodiment, the superstructure model is simplified to a single-degree-of-freedom concentrated mass block, which can be achieved through Z... D =-Mω 2 The impedance of the superstructure was calculated. The mass of the mass block was obtained using the formula M = Nm + Nρ1A1L, and the cross-sectional area of ​​the column was A1 = 2.581m². 2 The moment of inertia of the cross section is I = 0.3455m. 4 The elastic modulus E = 2.6 × 10⁻⁶ 10 N / m 2The material density ρ1 = 2.5 × 10 3 kg / m 3 The column height of each floor is L = 3m, and the concentrated mass of each floor is m = 4.2 × 10⁻⁶. 5 kg. A sensitivity analysis based on input power flow was performed on the laminated rubber seismic isolation bearing in the base isolation structure. The sensitivity coefficients of the input power flow to the overall stiffness of each element under the excitation of the first 5 natural frequencies of the periodic laminated rubber seismic isolation bearing with a total of 10 elements were calculated and plotted.

[0175] like Figure 6 As shown. Since the vibration power flow of a structure is affected by its natural frequency, when there are constraints on both boundaries, the element sensitivity coefficient is symmetrically distributed from the middle element to both sides. Therefore, the damage location symmetry problem often occurs during the damage identification process (that is, the problem of false damage appearing at symmetrical locations).

[0176] To eliminate the influence of structural longitudinal symmetry on damage identification results, the format long command was used in MATLAB programming to improve calculation accuracy (to 8 decimal places). At the same time, the optimset command was used to adjust the number of iterations during calculation when using the non-negative least squares curve fitting method.

[0177] For the base isolation structure model with a concentrated mass block as the superstructure, the damage of the laminated rubber isolation bearing model is considered in three damage conditions, including single damage, double damage and multi-damage conditions with symmetrical location. The specific damage location and damage degree of each condition are shown in Table 3.

[0178] Table 3 Damage conditions of the laminated rubber seismic isolation bearing model

[0179]

[0180] Will Figure 6 The first 5 orders of sensitivity matrix are substituted sequentially. In this study, a non-negative least squares curve fitting numerical optimization algorithm was used to obtain the damage identification results of the laminated rubber seismic isolation bearing under three damage conditions based on the input power flow.

[0181] like Figure 7 As shown, from Figure 8 The damage identification results for the three damage conditions show that the theoretically derived damage identification results have almost no error compared to the actual damage, and there are almost no misidentifications of damaged units under each condition. For the three preset damage conditions, when the superstructure is simplified to a single degree of freedom, whether it is single damage or multiple damage, the damage identification method based on input power flow proposed in this invention can accurately identify the support damage location and damage degree under each damage condition, while also effectively solving the problem of damage location symmetry.

[0182] In one embodiment, when the superstructure has multiple degrees of freedom, the parameters of the superstructure are assumed to be as follows: column cross-sectional area A1 = 2.581m². 2 The moment of inertia of the cross section is I = 0.3455m. 4 The elastic modulus E = 2.6 × 10⁻⁶ 10 N / m 2 The material density ρ1 = 2.5 × 10 3 kg / m 3 The column height of each floor is L = 3m, and the concentrated mass of each floor is m = 4.2 × 10⁻⁶. 5 kg. The superstructure has 8 and 32 stories, respectively, and is equipped with 36 and 144 laminated rubber seismic isolation bearings. The impedance of the superstructure can be calculated using the following formula:

[0183]

[0184] Where N is the number of stories in the building structure, μ1 is the wave propagation constant of the upper periodic structure, and α lr1 The indirect admittance of the superstructure is given. Sensitivity analysis is performed on the laminated rubber isolation bearings in the foundation isolation structure. The first five natural frequencies of the laminated rubber isolation bearing structure without damage are introduced to obtain a line graph of the sensitivity coefficient of the input power flow to the overall stiffness of each element under the excitation of the first five natural frequencies of the periodic laminated rubber isolation bearing with a total of 10 elements.

[0185] like Figure 6 , 8 As shown, the simplification method of the superstructure does not affect the characteristics of the periodic system of the laminated rubber seismic isolation bearing itself. The structural characteristics of the laminated rubber seismic isolation bearing are only affected by the constraint conditions at both ends and the magnitude of the impedance transmitted by the superstructure.

[0186] For the base isolation structure model of an 8-story building, the damage of the laminated rubber isolation bearing model is considered in three damage conditions, including single damage and multi-damage conditions. The specific damage location and damage degree of each condition are shown in Table 4.

[0187] Table 4 Damage Conditions of Laminated Rubber Isolation Bearing Model

[0188]

[0189] like Figure 8 The first 5 order sensitivity matrices are substituted sequentially. By employing a non-negative least squares curve fitting numerical optimization algorithm and a damage identification method based on vibration power flow, the damage identification results for three damage conditions of the base-stacked rubber seismic isolation bearing when the superstructure is an 8-story building can be obtained.

[0190] like Figure 9 The damage identification results for the three damage conditions shown are essentially identical to the actual damage, with no errors between the theoretically derived results and the actual damage, and there is no issue of misidentification of damaged elements. The damage identification method for laminated rubber seismic isolation bearings based on input power flow proposed in this invention can accurately identify the location and extent of damage in single-damage and multi-damage conditions of laminated rubber bearings.

[0191] In the description of this invention, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances.

[0192] It should be noted that in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0193] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A damage identification method for laminated rubber seismic isolation bearings based on vibration power flow, characterized in that, Damage identification is performed on the laminated rubber seismic isolation bearing as a finite-period structure. The damage identification method includes the following steps: The characteristic equation of the natural frequency of a periodic structure containing damaged elements is constructed based on the characteristic waveguide admittance method. After simplifying the laminated rubber seismic isolation bearing into a periodic structure, the relationship between the shear modulus change and the element admittance of the basic periodic element of the laminated rubber seismic isolation bearing before and after damage is established. Substituting the relationship between the shear modulus change and the element admittance into the characteristic equation of the natural frequency of the periodic structure, the relationship between the shear modulus change before and after damage to the basic periodic element and the natural frequency of the periodic structure can be obtained. The relationship between the input power flow and the natural frequency of the periodic structure is established based on the functional relationship between the input power flow, the boundary admittance of the periodic structure, and the excitation force. Based on the relationship between the input power flow and the natural frequency of the periodic structure and the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure, the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic unit is derived. Establish a set of equations to identify the sensitivity of the input power flow rate to cell damage; The sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic unit in order to achieve damage identification of the laminated rubber seismic isolation bearing. The characteristic equation for the natural frequency of a periodic structure containing damaged elements is constructed based on the characteristic waveguide admittance method, including the following steps: Assume that the j-th basic periodic unit in a periodic structure composed of n identical basic periodic units is a damaged unit, and the boundaries of the periodic structure are C and D; The two end nodes of the damaged unit are labeled A and B, respectively, and an excitation force is applied at the boundary C of the periodic structure. F C ; The characteristic equation of the natural frequency of the periodic structure containing the damaged element is constructed based on the first formula. The first formula is: ,and ， ， ， Where μ is the wave propagation constant and e is the natural constant. To apply the excitation force F C The displacement caused by the forward propagating wave at boundary C, To apply the excitation force F C The displacement caused by the reflected wave at boundary C Transmitting waves at boundary point D and reflected waves The resulting displacement ratio, and ， and These are the characteristic waveguide admittances corresponding to the forward propagation wave and the reflected wave, respectively. Let D be the admittance at the boundary of the periodic structure. , Let A and B be the direct admittances at nodes A and B at the two ends of the damaged element j, respectively. , For the indirect admittance of the damaged unit j; After simplifying the laminated rubber seismic isolation bearing into a periodic structure, the relationship between the shear modulus change and element admittance of the basic periodic element of the laminated rubber seismic isolation bearing before and after damage is established, including the following steps: The laminated rubber seismic isolation bearing is simplified to the periodic structure described above, where boundary C is the lower boundary of the laminated rubber seismic isolation bearing and boundary D is the upper boundary of the laminated rubber seismic isolation bearing. Meanwhile, Each fundamental periodic unit in the laminated rubber seismic isolation bearing contains a mass of Thickness is d, rubber density is And a rubber layer with a cross-sectional area of ​​a and two masses of each Steel plates; The relationship between the direct and indirect unit admittances of the damaged unit j and the change in shear modulus is obtained according to the second formula. The second formula is: ， in, , , , For the shear modulus of a periodic structure, The change in shear modulus of damaged element j before and after damage. For frequency, , The direct element admittance after damage occurs to damaged element j. , The indirect unit admittance after damage occurs to damaged unit j; The relationship between the input power flow and the natural frequency of the periodic structure is established based on the functional relationship between the input power flow, the boundary admittance of the periodic structure, and the excitation force, including the following steps: The functional relationship between the input power flow and the boundary admittance of the periodic structure and the excitation force can be obtained from the third formula. The third formula is: In the formula, Re denotes taking the real part. Let D be the admittance at the boundary of the periodic structure. F c For the generalized force of the seismic isolation bearing base, For motivation F c The velocity response at the lower boundary C; Substituting the second formula into the third formula yields the relationship between the input power flow and the natural frequency of the periodic structure. The relationship between the input power flow and the natural frequency of the periodic structure is expressed as follows: in, N The number of floors in the building structure. Let be the wave propagation constant of the upper periodic structure. This is the indirect admittance of the upper periodic structure. F c This refers to the generalized force at the base of the seismic isolation bearing.

2. The damage identification method for laminated rubber seismic isolation bearings based on vibration power flow as described in claim 1, characterized in that, Establish a set of equations to identify the sensitivity of the input power flow rate to cell damage, including the following steps: The relationship between the sensitivity coefficient of the basic periodic unit damage and the input power flow is obtained according to the fourth formula. The fourth formula is: ,in, , Let be the sensitivity coefficient of damaged element j to damage in a periodic structure with n basic periodic elements. The input power flow under the condition of no damage. For the nth order input power flow, As to the degree of damage, For the shear modulus of a periodic structure, The change in shear modulus of damaged element j before and after damage. This refers to the change in the degree of injury before and after the injury occurs; The input power flow changes caused by damage to a single basic periodic cell are linearly superimposed to obtain a set of equations for identifying the sensitivity of the input power flow change rate to cell damage. The set of equations for identifying the sensitivity of the input power flow rate to cell damage is expressed as follows: Where q is the order of the measurement modes of the periodic structure. denoted as the damage level of the nth basic periodic unit, where n ranges from 1 to N.

3. The damage identification method for laminated rubber seismic isolation bearings based on vibration power flow as described in claim 2, characterized in that, The sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element to achieve damage identification of the laminated rubber seismic isolation bearing, including the following steps: According to the first formula, we can obtain... right partial derivatives Then, the input power flow p is obtained according to the third formula. partial derivatives ,make and Multiply to obtain ,make And p= Solve the fourth formula to obtain the sensitivity coefficient. The expression; The actual measured input power flow p is compared with the sensitivity coefficient. Substituting the input power flow rate of change into the sensitivity identification equations for unit damage, the damage degree equations are obtained. .

4. The damage identification method for laminated rubber seismic isolation bearings based on vibration power flow as described in claim 2, characterized in that, The damage identification method includes the following steps: The superstructure is considered as a single-degree-of-freedom structure consisting of a long column and multiple concentrated masses m spaced L apart on the long column. The impedance of the single-degree-of-freedom structure is expressed as: ,in, The mass of the superstructure and , where m is the concentrated mass of each floor in the superstructure. The material density of the long column is given. Let be the cross-sectional area of ​​the long column. Angular frequency; Introducing the impedance of the single-degree-of-freedom structure into the relationship between the change in shear modulus before and after damage to the basic periodic unit and the natural frequency of the periodic structure includes the following steps: Will Substituting the relationship between the change in shear modulus before and after damage of the basic periodic unit and the natural frequency of the periodic structure, the characteristic equation of the natural frequency of the laminated rubber seismic isolation bearing under the influence of the superstructure is obtained. The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is: ； The natural frequency characteristic equation of the laminated rubber seismic isolation bearing affected by the superstructure is substituted into the sensitivity identification equation set to achieve damage identification of the laminated rubber seismic isolation bearing with superstructure.

5. The damage identification method for laminated rubber seismic isolation bearings based on vibration power flow as described in claim 4, characterized in that, The sensitivity identification equations are solved based on the relationship between the input power flow and the change in shear modulus before and after damage to the basic periodic element to achieve damage identification of the laminated rubber seismic isolation bearing, including the following steps: When solving the sensitivity identification equation system using the non-negative least squares curve fitting optimization algorithm, the optimset command is used to adjust the number of iterations during calculation, and the format long command in MATLAB programming is used to improve the calculation accuracy.

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