An unsupervised method for reconstructing the dynamic displacement response of bridges

Abstract

The present invention discloses a method for reconstructing the dynamic displacement response of a bridge without supervision. First, acceleration sensors and strain sensors are used to obtain the acceleration and strain responses of the bridge under unknown loads. Secondly, a PINN network is constructed, and physical logic is embedded into the neural network. The physical equations and the corresponding boundary conditions and initial conditions are used as penalty terms and put into the loss function to limit the space of feasible solutions. Subsequently, an approximate solution of the displacement at the target point is obtained through PINN. Finally, the reconstructed displacement is corrected by the AdaRNN network. The present invention is a meshless technology for bridge displacement reconstruction, which is particularly suitable for the case where there is no large amount of target point data. By transforming the problem of directly solving the bridge dynamics control equation into an optimization problem of a loss function and using the pre-training-fine-tuning method to correct the prediction results, the accuracy and reliability of displacement reconstruction are improved.

Description

Technical Field

[0001] The present invention relates to the field of bridge structure response reconstruction, and specifically to an unsupervised reconstruction method for bridge dynamic displacement response. Background Art

[0002] With the continuous development of the urbanization process, the scale of infrastructure construction in China has been continuously expanding, and various bridges and tunnels are emerging in an endless stream, including many long-span bridges. Although the design life of these bridges is generally long, due to the action of complex situations such as natural factors and human factors, various damage diseases may occur, leading to a decrease in the bearing capacity of the bridge and even causing serious safety accidents. Therefore, how to accurately evaluate the safety status of the bridge is very important. The dynamic displacement response of the beam under the action of load, as the direct deformation of the bridge, is an intuitive reflection of the bridge stiffness, and can be used to evaluate the safety status of the bridge structure, and help accurately identify and evaluate potential safety hazards to reduce accidents and unnecessary losses caused by bridge safety problems. The traditional bridge displacement response measurement methods directly obtain the displacement through sensors or satellite positioning technology, including optical displacement measurement methods, GPS measurement methods, and communicating pipe methods, etc. However, such methods have problems such as insufficient measurement accuracy, limited application range, and inconvenient data collection. Therefore, in recent years, displacement response reconstruction methods based on acceleration response or strain response have been widely studied. Such methods can generally be divided into two major types: physically driven and data driven.

[0003] The physically driven method uses known mechanism knowledge to construct a response reconstruction model, which has high accuracy. However, the actual bridge structure is usually relatively complex, and many factors need to be considered during modeling, including the connection between different components, environmental changes, and dynamic changes within the system, etc. The finite element model (mechanism model) inevitably deviates from the real bridge. The incomplete mechanism model will surely affect the accuracy of the reconstructed response. The data-driven response reconstruction method analyzes and regresses historical data without having a comprehensive understanding of the original system structure, and has an advantage in efficiency; however, the data-driven response reconstruction method still has the following problems: First, it highly depends on the sample data of the target point. In practical applications, if the number of target point samples is insufficient or lacking, the network model cannot fully learn and master the internal laws and characteristics, resulting in the response reconstructed by the model deviating from the actual situation. Second, the logical utilization of data is insufficient, and the required amount of data is huge. The network mainly relies on the characteristics and patterns of the data itself when processing data, rather than physical logic. Therefore, it cannot extract the spatio-temporal characteristics of the response. Under different loads and environments, in order to make the model have better reconstruction accuracy, it is necessary to obtain representative response data of the structure throughout its life cycle, which consumes a lot of time and cost. Summary of the Invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned existing technologies, and provides a method for reconstructing the unsupervised dynamic displacement response of a bridge, in order to accurately predict and reconstruct the displacement of the bridge structure under various external loads, thereby improving the accuracy and reliability of displacement reconstruction.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for reconstructing the unsupervised dynamic displacement response of a bridge according to the present invention is characterized by comprising the following steps:

[0007] Step 1: Arrange 1 acceleration sensor and 1 strain sensor at each of the m monitoring points of the bridge to record the acceleration and strain responses of the bridge, and randomly select one monitoring point as the target point, and the remaining monitoring points as non-target points;

[0008] Step 2: Use the finite element model to model the bridge to obtain the bridge finite element model, apply random loads to the bridge finite element model, and obtain the acceleration response matrix A = [a 1 , a 2 , … a i , …, a m T , the strain response matrix S = [s 1 , s 2 , …, s i , …, s n T and the frequency response function matrix H(ω) = [H 1 , H 2 , …, H i , …, H m T , the frequency response function matrix H′(ω) of the target point, where a i is the acceleration response at the i-th monitoring point, s i is the strain response at the i-th monitoring point, H i is the frequency response at the i-th monitoring point, H′(ω) is the frequency response at the target point, T represents transpose; ω represents the frequency domain;

[0009] Step 3: Construct a PINN network, which is composed of b gated recurrent unit layers, each gated recurrent unit layer has c hidden units, and process A to obtain the predicted displacement result for training the optimal PINN model;

[0010] Step 4: Input the acceleration responses at any two non-target points into the optimal PINN model for processing to obtain the reconstructed displacement result X 1 of the target point and the reconstructed displacement result X of any one non-target point​​​2 , thus constructing the sequence approximate displacement vector X = [X 1 , X 2 T ;

[0011] Step 5: Construct an AdaRNN network, which consists of c gated recurrent unit layers, and process S to obtain the reconstructed strain response sequence for training the optimal AdaRNN model;

[0012] Step 6: Input the acceleration data and strain data of the bridge into the optimal PINN model and the optimal AdaRNN model in sequence for prediction to obtain the reconstructed displacement of the bridge.

[0013] The feature of an unsupervised bridge dynamic displacement response reconstruction method described in the present invention also lies in that step 3 includes the following steps:

[0014] Step 3.1: Input the acceleration data matrix A into the PINN network, and after being processed by b gated recurrent unit layers, obtain the displacement feature vector X net ;

[0015] Step 3.2: After performing second-order difference processing on X net , obtain the acceleration feature vector Then, after combining with A, obtain the acceleration data set of the monitoring point and the target point

[0016] Step 3.3: Perform Fourier transform on to obtain the frequency-domain acceleration data set Thus, use Equation (1) to construct the relationship equation between the displacement response of the target point and the displacement response of the monitoring point in structural dynamics:

[0017]

[0018] In Equation (1), T aku (ω) is the transfer matrix, and T aku (ω) = H(ω)(H′(ω)) + ; + represents the pseudo-inverse of the matrix;

[0019] Step 3.4: Use Equation (2) to obtain the error f(ω) between the predicted acceleration of the target point and the true value:

[0020]

[0021] In Equation (2), f(ω) = [f 1 (ω), f 2 (ω), …, f j (ω), …, f​n (ω)], f j (ω) is the error between the predicted acceleration of the target point and the true value for the j-th prediction; n represents the total length of the error results;

[0022] Step 3.5: Obtain the predicted acceleration response transfer matrix T of the target point using Equation (3) net (ω):

[0023]

[0024] Step 3.6: Obtain the error T′(ω) between the predicted frequency response matrix of the target point and the true value using Equation (4):

[0025] T′(ω) = T net (ω) - T aku (ω) (4)

[0026] In Equation (4), T′(ω) = [T 1 ′(ω), T′ 2 (ω), …, T′ j (ω), …, T′ n (ω)], T′ j (ω) is the error between the predicted frequency response matrix of the target point and the true value for the j-th prediction;

[0027] Step 3.7: Obtain the error f′ between the predicted initial displacement and the true displacement of the target point using Equation (5):

[0028] f′ = X net0 - X 0 (5)

[0029] In Equation (5), X net0 is the predicted value obtained by inputting a matrix of all zeros into the PINN network, and X 0 is the displacement response result of the bridge finite element model under the initial conditions; f′ = [f 1 ′, f′ 2 , …, f′ j , …, f′ n , f′ j is the error between the predicted initial displacement and the true displacement of the target point for the j-th prediction;

[0030] Step 3.8: Construct the total loss function L using Equation (6):

[0031]

[0032] Equation (6), L 1 and L 2 represent the two losses of the relational equation, and L 3 represents the initial condition loss;

[0033] Step 3.9: Train the PINN network using the gradient descent method, and calculate the total loss function L to update the network parameters until the total loss function L converges, so as to obtain the optimal PINN model.

[0034] The said Step 5 includes the following steps:

[0035] Step 5.1: Define the number of candidate time periods as n, and initialize n = 1; the maximum number of candidate time periods is N;

[0036] Step 5.2: Divide S into n segments, and calculate the distribution distance of the segmented strain response data S using the distance function;

[0037] Step 5.3: After assigning n + 1 to n, return to Step 6.2 and execute sequentially until n > N, so as to obtain N distribution distances, and select the candidate time period corresponding to the maximum distribution distance as the best candidate time period. After segmenting S according to the best candidate time period, the segmented strain response sequence is obtained;

[0038] Step 5.4: Input the segmented strain response sequence into the AdaRNN network for processing to obtain the reconstructed strain response sequence;

[0039] Step 5.5: Based on the reconstructed strain response sequence and the segmented strain response sequence, construct the loss function L' of the AdaRNN network;

[0040] Step 5.6: Calculate the distribution distance of the reconstructed strain response sequence using the distance function and add it to the loss function of the AdaRNN network, so as to construct the new loss function L'' of the AdaRNN network;

[0041] Step 5.7: Pre-train the AdaRNN network, and calculate the new loss function L'' to update the network parameters until the new loss function L'' converges, so as to obtain the pre-trained AdaRNN network;

[0042] Step 5.8: Input the sequence approximate displacement vector X = [X 1 , X 2 T into the pre-trained AdaRNN network for backpropagation training, and calculate the loss function L' of the AdaRNN network to update the network parameters of the pre-trained AdaRNN network until L' converges, so as to obtain the optimal AdaRNN model.

[0043] ​An electronic device according to the present invention includes a memory and a processor, characterized in that the memory is used to store a program for supporting the processor to execute the reconstruction method, and the processor is configured to execute the program stored in the memory.

[0044] A computer-readable storage medium according to the present invention, on which a computer program is stored, is characterized in that the computer program executes the steps of the reconstruction method when run by a processor.

[0045] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0046] 1. Compared with traditional physical modeling, the present invention reduces the requirement for model accuracy. When the mechanism model is incomplete, it uses physical logic to establish the connection between known points and target points in the structure, and reconstructs the response of the target point through the data of the known points. Thus, it reduces the dependence on the finite element model and improves the generalization ability of the network model.

[0047] 2. Compared with data-driven machine learning, the present invention, on the basis of data-driven, supplements physical constraints, adds physical laws such as control equations to the loss function, reduces the dependence of the network on labeled data, and improves the generalization ability and application value of the model through the learning of the change characteristics of strain data, achieving the purpose of accurately reconstructing the displacement without the response data of the target point.

[0048] 3. The present invention avoids the problems of insufficient accuracy of the finite element model and lack of sample data of the target point. By embedding the physical model into the neural network, it uses physical logic to limit the space of feasible solutions, and effectively corrects the target solution by using the pre-training - fine-tuning method, effectively reconstructing the dynamic displacement of the structure, thereby improving the accuracy of the reconstructed displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the numerical simulation simply supported beam bridge model of the present invention under random loads;

[0050] Figure 2 It is a schematic diagram of the response reconstruction process of the method of the present invention;

[0051] Figure 3 It is a loss function diagram of the response reconstruction of the simply supported beam bridge with equal cross-section under random load excitation of the present invention;

[0052] Figure 4 It is a comparison diagram of the predicted value and the true value of the target point response reconstruction of the simply supported beam bridge with equal cross-section under random load excitation of the present invention;

[0053] Figure 5 It is a schematic diagram of the numerical simulation simply supported beam bridge model of the present invention under moving loads;

[0054] Figure 6 This is a comparison graph of the predicted value and the true value of the response reconstruction of the target point of a simply supported beam bridge with equal cross-section under moving load excitation of the present invention. Specific implementation mode

[0055] In this Example 1, a method for reconstructing the dynamic displacement response of a bridge without supervision is numerically simulated using Abaqus software. Parameters of the simply supported beam: beam length L = 2 m, height h = 0.2 m, width b = 0.1 m; elastic modulus E = 210 GPa, Poisson's ratio is 0.3, and density ρ = 7800 kg / m 3 . The time length is 8000, and the random load acts at one-eighth of the span of the bridge, and the magnitude range is between (10000 N and 20000 N). A finite element model is established to calculate the strain, acceleration, and displacement responses of the bridge under the random load. The simply supported beam bridge model used is as Figure 1 shown, and this method specifically includes the following steps:

[0056] Step 1: Arrange 1 acceleration sensor and 1 strain sensor at m = 2 monitoring points on the bridge to record the acceleration and strain responses of the bridge, and randomly select one monitoring point as the target point, and the remaining monitoring points as non-target points;

[0057] Step 2: Use the finite element model to model the bridge to obtain the bridge finite element model, apply a random load to the bridge finite element model, and obtain the acceleration response matrix A = [a 1 , a 2 T , strain response matrix S = [s 1 , s 2 T and frequency response function matrix H(ω) = [H 1 , H 2 T , frequency response function matrix H′(ω) of the target point, where a i is the acceleration response at the i-th monitoring point, s i is the strain response at the i-th monitoring point, H i is the frequency response at the i-th monitoring point, H′(ω) is the frequency response at the target point, T represents the transpose; ω represents the frequency domain.

[0058] Step 3: Construct a PINN network, which consists of b = 2 gated recurrent unit layers, and each gated recurrent unit layer has c = 64 hidden units;

[0059] Step 3.1: Input the acceleration data matrix A into the PINN network, and after being processed by b = 2 gated recurrent unit layers, obtain the displacement feature vector X net;

[0060] Step 3.2: After performing second-order difference processing on X net the acceleration feature vector is obtained Then is combined with A to obtain the acceleration data set of the monitoring point and the target point

[0061] Step 3.3: Perform Fourier transform on to obtain the frequency-domain acceleration data set Thus, the relationship equation between the displacement response of the target point and the displacement response of the monitoring point in structural dynamics is constructed using Equation (1):

[0062]

[0063] In Equation (1), T aku (ω) is the transfer matrix, and T aku (ω) = H(ω)(H′(ω)) + ; + represents the pseudo-inverse of the matrix;

[0064] Step 3.4: Use Equation (2) to obtain the error f(ω) between the predicted target point acceleration and the true value:

[0065]

[0066] Since the data input into the network is time series data and the result output by the network also has a certain length, the error result also has a corresponding length. Denote f(ω) = [f 1 (ω), f 2 (ω), …, f j (ω), …, f n (ω)], where f j (ω) is the error between the jth predicted target point acceleration and the true value, and n represents the total length of the error result.

[0067] Step 3.5: Use Equation (3) to obtain the predicted target point acceleration response transfer matrix T net (ω):

[0068]

[0069] Step 3.6: Use Equation (4) to obtain the error T′(ω) between the predicted target point frequency response matrix and the true value:

[0070] T′(ω) = T net (ω) - T aku (ω) (4)

[0071] where T′(ω) = [T 1′(ω), T′ 2 (ω), …, T′ j (ω), …, T′ n (ω)], T′ j (ω) is the error between the j-th predicted target point frequency response matrix and the true value.

[0072] Step 3.7: Use Equation (5) to obtain the error f′ between the predicted initial displacement and the true displacement of the target point:

[0073] f′ = X net0 -X 0 (5)

[0074] In Equation (5), X net0 is the all-zero matrix input into the PINN network to obtain the predicted value, and X 0 is the displacement response result of the bridge finite element model under the initial conditions; f′ = [f 1 ′, f′ 2 , …, f′ j , …, f′ n , and f′ j is the error between the predicted initial displacement and the true displacement of the j-th target point.

[0075] Step 3.8: Use Equation (6) to construct the total loss function L:

[0076]

[0077] Equation (6), L 1 and L 2 represent the 2 losses of the relational equation, and L 3 represents the initial condition loss.

[0078] Step 3.9: Use the gradient descent method to train the PINN network and calculate the total loss function L to update the network parameters until the total loss function L converges, thereby obtaining the optimal PINN model.

[0079] Step 4: Input the acceleration responses at any two non-target points into the optimal PINN model for processing to obtain the reconstructed displacement results X 1 of the target points and the reconstructed displacement results X 2 of any one non-target point, thereby constructing the sequence approximate displacement vector X = [X 1 , X 2 T .

[0080] Step 5: Construct an AdaRNN network, which consists of c = 2 gated recurrent unit layers;

[0081] ​Step 5.1: Define the number of candidate time periods as n and initialize n = 1; the maximum number of candidate time periods is N = 10;

[0082] Step 5.2: Divide S into n segments and calculate the distribution distance of the segmented strain response data S using the distance function;

[0083] Step 5.3: After assigning n + 1 to n, return to Step 6.2 and execute sequentially until n > 10, so as to obtain 10 distribution distances, and select the candidate time period corresponding to the maximum distribution distance as the best candidate time period. Then, after segmenting S according to the best candidate time period, the segmented strain response sequence is obtained;

[0084] Step 5.4: Input the segmented strain response sequence into the AdaRNN network for processing to obtain the reconstructed strain response sequence;

[0085] Step 5.5: Based on the reconstructed strain response sequence and the segmented strain response sequence, construct the loss function L′ of the AdaRNN network;

[0086] Step 5.6: Calculate the distribution distance of the reconstructed strain response sequence using the distance function and add it to the loss function of the AdaRNN network to construct the new loss function L″ of the AdaRNN network;

[0087] Step 5.7: Pre-train the AdaRNN network and calculate the new loss function L″ to update the network parameters until the new loss function L″ converges, so as to obtain the pre-trained AdaRNN network;

[0088] Step 5.8: Input the sequence approximate displacement vector X = [X 1 ,X 2 T into the pre-trained AdaRNN network for backpropagation training, and calculate the loss function L′ of the AdaRNN network to update the network parameters of the pre-trained AdaRNN network until L′ converges, so as to obtain the optimal AdaRNN model; The displacement reconstruction flow chart is as Figure 2 shown; First, construct the AdaRNN network and form an unsupervised response reconstruction network in combination with the PINN network. Secondly, perform temporal similarity quantization on the strain data and use the pre-training method to learn the change characteristics of the strain. Then, estimate the displacement response training values of the target points and non-target points through the PINN network and input them into the AdaRNN network for training, and correct the displacement response reconstructed by the PINN through the pre-training learning results.

[0089] ​Step 6: Input the acceleration data and strain data of the bridge into the optimal PINN model and the optimal AdaRNN model in sequence for prediction to obtain the reconstructed displacement of the bridge.

[0090] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0091] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is run by a processor, it executes the steps of the above method.

[0092] The prediction results of the network model under random loads under three different loss evaluation indexes are shown in Table 1, and the results of the loss function are shown in Figure 3 , and the comparison results between the true value and the reconstructed value of the network are shown in Figure 4 . It can be seen from Table 1 that the reconstruction results of this method under three different loss evaluation indexes are relatively accurate, and its RMSE value, MSE value, and L1 loss value are 0.00632, 4.0×10 -5 and 0.00516 respectively. It can be seen from Figure 3 that in the case of lacking the displacement data of the target point, this method can accurately reconstruct the displacement of the target point.

[0093] Table 1

[0094]

[0095] In this embodiment 2, a moving load is used for further verification. The bridge span length L = 25m, the elastic modulus is E = 3.5×10 10 N·m -2 , the moment of inertia I 0 = 1.3901m 4 , and the mass per unit length is ρ = 18358 kg / m. The two-node plane Euler beam element is used for simulation, and the schematic diagram of the moving load calculation model is shown in Figure 5 , the finite element model is established to calculate the dynamic response of the system, and the sampling frequency is set to 1000Hz. The reconstruction method and the response reconstruction process are the same as those in Embodiment 1. The prediction results of the network model under the moving load under three different loss evaluation indexes are shown in Table 2, and the comparison results between the true value and the reconstructed value of the response reconstruction of the target point are shown in Figure 6 .

[0096] Table 2

[0097]

[0098] As can be seen from Table 2, under the moving load, the RMSE value, MSE value, and L1 loss value are 0.00571, 3.26×10 -5 , and 0.00416 respectively. The reconstruction results are still relatively accurate. As can be seen from Figure 6 , under the action of the moving load, the reconstructed displacement is still relatively accurate.

Claims

1. A method for reconstructing the dynamic displacement response of an unsupervised bridge, characterized in that The following steps are involved: Step 1: Arrange one acceleration sensor and one strain sensor at each of the m monitoring points of the bridge to record the acceleration and strain responses of the bridge, and randomly select one monitoring point as the target point, and the remaining monitoring points as non-target points; Step 2: Model the bridge using the finite element model to obtain a bridge finite element model, apply a random load to the bridge finite element model, and obtain The acceleration response matrix of the sensors at the corresponding points , strain response matrix And the frequency response function matrix , the frequency response function matrix of the target point ,in, is the acceleration response at the ith monitoring point, is the strain response at the i-th monitoring point, is the frequency response at the i-th monitoring point, T represents the transposition; represents the frequency domain; Step 3: Construct a PINN network, which consists of b gated recurrent unit layers, each of which has c hidden units and Processing is performed to obtain predicted displacement results, which are used to train the optimal PINN model; Step 4: Input the acceleration responses at any two non-target points into the optimal PINN model for processing to obtain the reconstructed displacement result of the target point. and the reconstructed displacement result of any non-target point , thus constructing the sequence approximate displacement vector ; Step 5: Construct the AdaRNN network, which is composed of c gated recurrent unit layers and Processing is performed to obtain a reconstructed strain response sequence for training the optimal AdaRNN model; Step 6: Input the acceleration data and strain data of the bridge into the optimal PINN model and the optimal AdaRNN model in turn for prediction to obtain the reconstructed displacement of the bridge.

2. The unsupervised bridge dynamic displacement response reconstruction method according to claim 1 is characterized in that: The step 3 comprises the following steps: Step 3.1: Convert the acceleration data matrix Input into the PINN network and after being processed by b gated recurrent unit layers, the displacement feature vector is obtained ; Step 3.2: After secondary difference processing, the acceleration eigenvector is obtained , and then and After the combination, the acceleration data set of the monitoring point and the target point is obtained. ; Step 3.3: Perform Fourier transform to obtain frequency domain acceleration data set , and thus use formula (1) to construct the relationship equation between the displacement response of the target point and the displacement response of the monitoring point in structural dynamics: (1) In formula (1), is the transfer matrix, and ; + represents the pseudo-inverse of the matrix; Step 3.4: Use formula (2) to get the error between the predicted target point acceleration and the true value : (2) In formula (2), , is the error between the jth predicted acceleration of the target point and the true value; n represents the total length of the error result; Step 3.5: Use equation (3) to obtain the predicted target point acceleration response transfer matrix: : (3) Step 3.6: Use formula (4) to get the error between the predicted target point frequency response matrix and the true value : (4) In formula (4), , is the error between the j-th predicted target point frequency response matrix and the true value; Step 3.7: Use formula (5) to get the error between the predicted initial displacement of the target point and the actual displacement : (5) In formula (5), The all-zero matrix is ​​input into the PINN network to obtain the predicted value. is the displacement response result of the bridge finite element model under initial conditions; , is the error between the initial displacement and the actual displacement of the j-th predicted target point; Step 3.8: Use formula (6) to construct the total loss function L: (6) Formula (6): and Represents the 2 losses of the relationship equation, represents the initial condition loss; Step 3.9: Train the PINN network using the gradient descent method, and calculate the total loss function L to update the network parameters until the total loss function L converges, thereby obtaining the optimal PINN model.

3. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports a processor to execute the reconstruction method described in any one of claims 1 to 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the reconstruction method according to any one of claims 1 to 2 are executed.

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