Bridge temperature response rule adaptive correction modeling method and device and storage medium

Abstract

The invention discloses a bridge temperature response law self-adaptive correction modeling method and device and a storage medium, and belongs to the technical field of bridge engineering transfer learning modeling, and the method comprises the following steps: selecting an alternative model method, and constructing a corresponding mathematical expression of a bridge vibration frequency about a damage variable and a temperature variable; establishing a source domain finite element model according to bridge data, and training the mathematical expression by using vibration frequency, damage variable and temperature variable data in the source domain finite element model to establish a source domain substitution digital model; acquiring actual measurement data of an actual bridge structure, wherein the actual measurement data comprises temperature data and vibration frequency data responded by the temperature data; and establishing a transfer learning update model, and updating a correlation expression related to the temperature in the source domain substitution digital model according to the transfer learning update model and the measured data to obtain a target domain digital substitution model. According to the method, accurate temperature response fitting and elimination can be realized, the bridge damage identification accuracy is improved, and the delay of the structure diagnosis opportunity is avoided.

Description

Technical Field

[0001] The invention relates to a bridge temperature response law adaptive correction modeling method, device and storage medium, and belongs to the technical field of bridge engineering transfer learning modeling. Background Art

[0002] The structural response data collected on bridges are often used to determine the health status of bridges and identify component damage. However, this type of measured response data usually contains structural response changes caused by temperature, which causes the data characteristics related to bridge component damage to be interfered with by the temperature data characteristics, greatly affecting the accuracy of data analysis, and ultimately making it impossible to determine component damage and structural health status. At the same time, there is a certain ambiguity in the correlation between temperature and structural response, which is difficult to express with a simple mathematical formula, and even the form of the mathematical formula cannot be clearly defined. Therefore, it is a prominent problem to remove the temperature-affected part from the measured response data to assist in structural damage identification. It is necessary to invent a modeling method for adaptively correcting the temperature influence law of bridges.

[0003] At present, the commonly used method for eliminating temperature influence laws in the field of bridge engineering is based on the assumption of temperature linear law in classical mechanics, that is, assuming that the influence law of temperature on a certain response of the bridge is linear, so as to identify the temperature influence part in the data by linearly fitting the mathematical expression between temperature and target response (such as structural frequency, main beam line shape, etc.), and eliminate it by model correction method. As mentioned above, when the correlation between temperature and target response is nonlinear, this method will cause errors in temperature response elimination and affect the accuracy of the remaining data analysis. In addition, the model correction method can only correct some parameter values ​​in the model, but cannot correct the temperature correlation law itself in the model, which will also affect the accuracy of data analysis. In summary, the structural temperature response law under the existing classical mechanics theory has a large error for large bridge structures due to the influence of complex structural forms. The correction of temperature response based on this law will greatly affect the accuracy of bridge damage identification based on measured data and delay the timing of structural diagnosis. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a bridge temperature response law adaptive correction modeling method, device and storage medium, which can achieve accurate temperature response fitting and elimination, improve the accuracy of bridge damage identification, and avoid delays in structural diagnosis.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] In a first aspect, the present invention provides a bridge temperature response law adaptive correction modeling method, comprising the following steps:

[0007] Construct a mathematical formula for the bridge vibration frequency with respect to damage variables and temperature variables;

[0008] A source domain finite element model is established based on bridge data, and the vibration frequency, damage variable and temperature variable data in the source domain finite element model are used to train mathematical formulas to establish a source domain alternative digital model of the source domain finite element model;

[0009] Obtaining measured data of an actual bridge structure under known damage variables, wherein the measured data includes temperature data and vibration frequency data corresponding to the temperature data;

[0010] A transfer learning update model is established, and the temperature-related expressions in the source domain replacement digital model are updated based on the transfer learning update model and measured data to obtain the target domain digital replacement model.

[0011] The mathematical formula adopts chaotic polynomial, specifically:

[0012] (1)

[0013] Where E is the damage variable, T is the temperature variable, and F is the bridge vibration frequency. represents the hyperparameters to be trained, Representative is the chaotic polynomial of the independent variable, is zero-mean Gaussian white noise, represents the error mixed in the data, Represents the variance of the error.

[0014] The finite element model established according to the bridge data includes:

[0015] Different combinations of E and T values ​​are assigned to the finite element model, namely { E ̂ , T ̂ } = E 1 , T 1 , E 1 , T 2 ,…, E 1 , T N , E 2 , T 1 , E 2 , T 2 ,…, E 2 , T N ,…, E M , T 1 ,…,[ E M , T N ] T , and obtain the bridge vibration frequency data set , where M represents the number of values ​​of the damage variable E, and N represents the number of values ​​of the temperature variable T.

[0016] The source domain alternative digital model is:

[0017] (2)

[0018] In the formula represent The solution.

[0019] The measured data are specifically: damage variable , is a known damage variable, and the temperature variable group , bridge vibration frequency data set , where p represents the number of measured data, represent the first, second and pth temperature variables respectively, Represent the 1st, 2nd and pth bridge vibration frequency data respectively.

[0020] The transfer learning update model is established, and the temperature-related expressions in the source domain replacement digital model are updated according to the transfer learning update model and the measured data to obtain the target domain digital replacement model, including:

[0021] The source domain alternative digital model is decomposed to obtain:

[0022] (3)

[0023] In the formula represent part of express Only the part related to variable E, express Only the part related to variable T, express The part related to both variables E and T in Eq. (3) is updated by using the transfer learning update method, that is,

[0024] (4)

[0025] In the formula is called the scale factor, As a supplementary item, represents the new hyperparameters to be trained, Adaptive PCE modeling method is used for order determination;

[0026] Since the coupled effects of temperature variable T and damage variable E on structural response are generally small or have no effect, equation (4) is approximated as:

[0027] (5)

[0028] Then the measured data , Substituting into formula (5), we can obtain the scale coefficient in formula (5): and hyperparameters Solution and , then the target domain digital substitution model is obtained:

[0029] (6)

[0030] The target domain digital substitution model is used for the identification of damage to bridge structures in operation by collecting temperature data and bridge frequency data. Substituting into equation (6), the actual damage parameter value of the bridge component can be obtained: ,

[0031] (7)

[0032] In the formula is the simplified expression of the right side of the equal sign in formula (6), that is .

[0033] The extreme value optimization problem of formula (7) is obtained by Regularization or Regularized solution.

[0034] In a second aspect, the present invention provides a bridge temperature response law adaptive correction modeling device, comprising a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 8.

[0035] In a third aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the bridge temperature response law adaptive correction modeling method is implemented.

[0036] Beneficial effects of the present invention: The present invention provides a bridge temperature response law adaptive correction modeling method, device and storage medium, which adopts transfer learning to transfer the physical law in the finite element simulation model to the digital replacement model in the target domain, and can directly correct the regular relationship between temperature and structural response, ensuring the accuracy of the basic physical law of the bridge response. On the basis of the digital replacement model of the basic physical law, the actual bridge response is used to update the temperature response law of the digital model. The actual bridge response data requires a small amount of data, the cost is low, and the consistency of the temperature-structure response law with the actual structure is guaranteed, and accurate temperature response fitting and elimination can be achieved, thereby improving the accuracy of bridge damage identification and avoiding delays in structural diagnosis.

[0037] Chaotic polynomials are used to construct mathematical formulas for bridge vibration frequency with respect to damage variables and temperature variables. Adaptive chaotic polynomials are used to achieve high-order nonlinear digital modeling and simulation, greatly improving the accuracy of temperature response fitting.

[0038] The obtained target domain digital substitution model can be further used in multiple application scenarios such as damage identification and structural response prediction, and has wide application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A metal beam bridge model used in the present invention;

[0040] Figure 2 It is a schematic diagram of the system block structure of the present invention;

[0041] Figure 3 for Figure 1 Damage diagram of the metal beam bridge model;

[0042] Figure 4 A comparison chart of the frequency results of the structure of the present invention after damage as the temperature changes;

[0043] Figure 5 This is a comparison diagram of the errors between the correction method of the present invention and the traditional correction method;

[0044] Figure 6 The present invention discloses a flow chart of a bridge temperature response law adaptive correction modeling method. DETAILED DESCRIPTION

[0045] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the protection scope of the present invention.

[0046] Example 1

[0047] like Figure 6 As shown, the present invention discloses a bridge temperature response law adaptive correction modeling method, which is based on the digital substitution modeling method to establish a substitution model of the source domain finite element model and update the digital substitution model under the target domain measured data, specifically including the following steps:

[0048] Step 1: Construct a mathematical formula for the bridge vibration frequency with respect to damage variables and temperature variables. The mathematical formula uses a chaotic polynomial, which is:

[0049] (1)

[0050] Where E is the damage variable, T is the temperature variable, and F is the bridge vibration frequency. represents the hyperparameters to be trained, Representative is the chaotic polynomial of the independent variable, is zero-mean Gaussian white noise, represents the error mixed in the data, Represents the variance of the error.

[0051] Step 2: Establish a source domain finite element model based on the bridge data, and use the vibration frequency, damage variable and temperature variable data in the source domain finite element model to train the mathematical formula to establish a source domain alternative digital model of the source domain finite element model.

[0052] (2)

[0053] In the formula represent The solution.

[0054] Step 3: Obtain the measured temperature-response data of the actual bridge structure under a known damage variable value. This is usually done when the bridge is built without any damage to the structure. The measured data is as follows: , is a known damage variable, and the temperature variable group , bridge vibration frequency data set , where p represents the number of measured data, represent the first, second and pth temperature variables respectively, Represent the 1st, 2nd and pth bridge vibration frequency data respectively.

[0055] Step 4: Establish a transfer learning update model, and update the temperature-related expressions in the source domain replacement digital model based on the transfer learning update model and measured data to obtain the target domain digital replacement model.

[0056] Decompose equation (1). Since PCE is a chaotic polynomial, decompose the source domain substitution digital model to obtain:

[0057] (3)

[0058] In the formula represent part of express Only the part related to variable E, express Only the part related to variable T, express The part related to both variables E and T in Eq. (3) is updated by using the transfer learning update method, that is,

[0059] (4)

[0060] In the formula is called the scale factor, As a supplementary item, represents the new hyperparameters to be trained, Adaptive PCE modeling method is used to determine the order. Through the above formula, the temperature-related expressions in the original model can be updated using measured data to achieve migration modeling of the target domain. Since the coupling effect of temperature variable T and damage variable E on structural response is generally small or no effect, equation (4) is approximated as:

[0061] (5)

[0062] Then the measured data , Substituting into formula (5), we can obtain the scale coefficient in formula (5): and hyperparameters Solution and , then the target domain digital substitution model is obtained:

[0063] (6)

[0064] The target domain digital substitution model obtained in this application is used for the identification of damage to bridge structures in operation by collecting temperature data and bridge frequency data. Substituting into equation (6), the actual damage parameter value of the bridge component can be obtained: , to achieve structural damage identification after eliminating the temperature corresponding law,

[0065] (7)

[0066] In the formula is the simplified expression of the right side of the equal sign in formula (6), that is The extreme value optimization problem of formula (7) is obtained by Regularization, Solved by regularization or other sparse solution methods.

[0067] In practical engineering applications, the data of bridge structures not only include the response of the structure itself, but also the impact of the environment on the bridge structure. Among the environmental effects, the impact of temperature is the largest and unavoidable. For complex bridges, the impact of temperature on the response of the bridge is affected by the boundary conditions and cannot be accurately expressed by classical physical laws, which greatly increases the difficulty of extracting effective information from the data. Compared with the traditional linear assumption or model correction method that only corrects the model parameter value, the temperature response law correction method described in the present invention can directly correct the regular relationship between temperature and structural response, and realize high-order nonlinear digital modeling simulation through the method of adaptive chaotic polynomials, which greatly improves the accuracy of temperature response fitting. At the same time, the idea based on transfer learning can retain the reliable physical laws in the finite element model, and the obtained digital model can be further used in multiple application scenarios such as damage identification and structural response prediction, and has a wide range of application value.

[0068] Example 2

[0069] This embodiment is based on the first embodiment and is described by taking the application in bridge engineering as an example:

[0070] Figure 1 This is a metal beam bridge model with two spans, fixed at both ends and hinged in the middle. An acceleration sensor is arranged on the upper side of the beam, and the frequencies of each order of the beam can be obtained through the beam vibration acceleration data; a heating plate is attached to the lower side of the beam, and the temperature T of the beam is controlled by a temperature controller. Figure 2 is the finite element model of the beam bridge, and Figure 1 Different from the actual model in the finite element model, one end of the finite element model is consolidated and the middle and the other end are hinged, which makes the structural response of the finite element model and the metal beam bridge model different under the influence of temperature. The beam body is divided into 20 units along the length direction, and the reduction of the cross-sectional area E of each unit is considered as damage. Figure 1 The metal beam bridge model is simulated by cutting the cross-sectional area of ​​the corresponding position unit to simulate the damage at the same position. The damage diagram is as follows Figure 3 .

[0071] First, according to the finite element model, different E and T values ​​are assigned to obtain a set of corresponding frequency values. This set of data is used to train formula (1) to obtain a PCE model, that is, a digital replacement model of the source domain. Then, in the undamaged metal beam bridge model ( ) applies different temperatures to obtain a set of frequency values ​​of the actual model at different temperatures. Substitute the data into formula (5) to train and obtain the target domain digital substitution model after transfer learning, that is, the digital substitution model after the temperature law is corrected.

[0072] In order to verify the accuracy of the above digital replacement model, damage is imposed on the beam of the actual model. After that, different temperatures are applied to obtain a set of actual model frequency values ​​after damage. The comparison of the first three frequency results of the digital substitution model, the modified digital substitution model and the physical model obtained by the traditional model modification method is shown in Figure 2. Figure 4 , Figure 5 .

[0073] Figure 4 This is a comparison chart of different model results after structural damage. The thick solid line represents the calculation result of the finite element simulation model, the dashed line represents the result calculated by the traditional model correction method, and the dotted line represents the calculation result of the corrected digital model of the present invention. The red circle represents the data obtained from the actual damage model. By comparison, it can be seen that the temperature-frequency relationship of the finite element simulation model is linear, which is inconsistent with the law shown in the actual data; the traditional model correction result is more accurate than the finite element model, but Figure 4 (b) shows that it cannot correct highly nonlinear laws. Figure 4 (c) shows that there is a possibility that the correction error will lead to a large deviation from the actual measured true value; the method of the present invention can effectively correct the temperature-frequency law and is most consistent with the actual measurement data.

[0074] Figure 5 It is the root mean square error between the model result of the present invention, the correction result of the traditional model and the actual measurement data. It can be seen from the figure that the modeling error of the model of the present invention is smaller and the result is more accurate.

[0075] Example 3

[0076] This embodiment discloses a bridge temperature response law adaptive correction modeling device, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method.

[0077] Example 4

[0078] This embodiment discloses a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the bridge temperature response law adaptive correction modeling method is implemented.

[0079] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0080] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0081] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0082] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A bridge temperature response law adaptive correction modeling method, characterized by: The following steps are involved: Select alternative modeling methods and construct corresponding mathematical formulas of bridge vibration frequency with respect to damage variables and temperature variables; A source domain finite element model is established based on bridge data, and the vibration frequency, damage variable and temperature variable data in the source domain finite element model are used to train mathematical formulas to establish a source domain alternative digital model of the source domain finite element model; Obtaining measured data of an actual bridge structure under known damage variables, wherein the measured data includes temperature data and vibration frequency data corresponding to the temperature data; A transfer learning update model is established, and the temperature-related expressions in the source domain replacement digital model are updated based on the transfer learning update model and measured data to obtain the target domain digital replacement model.

2. The bridge temperature response law adaptive correction modeling method according to claim 1 is characterized by: The substitution model method adopts the chaos polynomial method, and the mathematical formula adopts the chaos polynomial, which is specifically: （1）， Where E is the damage variable, T is the temperature variable, and F is the bridge vibration frequency. represents the hyperparameters to be trained, Representative is the chaotic polynomial of the independent variable, is zero-mean Gaussian white noise, represents the error mixed in the data, Represents the variance of the error.

3. The bridge temperature response law adaptive correction modeling method according to claim 2 is characterized by: The finite element model established according to the bridge data includes: Different combinations of E and T values ​​are assigned to the finite element model, namely , get the bridge vibration frequency data set , where M represents the number of values ​​of the damage variable E, and N represents the number of values ​​of the temperature variable T.

4. The bridge temperature response law adaptive correction modeling method according to claim 3 is characterized by: The source domain alternative digital model is: （2）， In the formula represent The solution.

5. The bridge temperature response law adaptive correction modeling method according to claim 4 is characterized by: The measured data are specifically: damage variable , is a known damage variable, and the temperature variable group , bridge vibration frequency data set , where p represents the number of measured data, represent the first, second and pth temperature variables respectively, Represent the 1st, 2nd and pth bridge vibration frequency data respectively.

6. The bridge temperature response law adaptive correction modeling method according to claim 5 is characterized by: The transfer learning update model is established, and the temperature-related expressions in the source domain replacement digital model are updated according to the transfer learning update model and the measured data to obtain the target domain digital replacement model, including: The source domain alternative digital model is decomposed to obtain: （3） In the formula represent part of express Only the part related to variable E, express Only the part related to variable T, express The part related to both variables E and T in Eq. (3) is updated by using the transfer learning update method, that is, （4）， In the formula is called the scale factor, As a supplementary item, represents the new hyperparameters to be trained, Adaptive PCE modeling method is used for order determination; Since the coupled effects of temperature variable T and damage variable E on structural response are generally small or have no effect, equation (4) is approximated as: （5）， Then the measured data , Substituting into formula (5), we can obtain the scale coefficient in formula (5): and hyperparameters Solution and , then the target domain digital substitution model is obtained: （6）。 7. The bridge temperature response law adaptive correction modeling method according to claim 6 is characterized by: The target domain digital substitution model is used for the identification of damage to bridge structures in operation by collecting temperature data and bridge frequency data. Substituting into equation (6), the actual damage parameter value of the bridge component can be obtained: , （7）， In the formula is the simplified expression of the right side of the equal sign in formula (6), that is 。 8. The bridge temperature response law adaptive correction modeling method according to claim 7 is characterized by: The extreme value optimization problem of formula (7) is obtained by Regularization or Regularized solution.

9. A bridge temperature response law adaptive correction modeling device, characterized by: It comprises a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the bridge temperature response law adaptive correction modeling method described in any one of claims 1-8 is implemented.

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