CN115292780A - Large-span bridge buffeting response prediction method based on deep learning - Google Patents

Large-span bridge buffeting response prediction method based on deep learning Download PDF

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CN115292780A
CN115292780A CN202210826212.XA CN202210826212A CN115292780A CN 115292780 A CN115292780 A CN 115292780A CN 202210826212 A CN202210826212 A CN 202210826212A CN 115292780 A CN115292780 A CN 115292780A
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赖马树金
李惠
冯辉
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Abstract

The invention provides a method for predicting buffeting response of a large-span bridge based on deep learning. The method specifically comprises the following steps: step one, data set construction: calculating wind speed characteristics and bridge response characteristics to form a data set of the model; step two, model building and training: establishing a deep neural network model combined with a frequency domain response calculation formula by taking a GRU neural network as a basic network; step three, response prediction: and the model is used for prediction after training is finished, and for a given wind environment, corresponding response characteristics can be obtained by predicting by using the deep neural network model after the wind speed characteristics are determined. The method does not need finite element models and priori knowledge of wind tunnel test results, and extracts the structural behavior characteristics hidden in the massive monitoring data through a data mining technology. The method can carry out quick prediction once training is completed, and provides a solution for predicting buffeting response of the large-span bridge.

Description

Large-span bridge buffeting response prediction method based on deep learning
Technical Field
The invention belongs to the technical field of bridge wind engineering, and particularly relates to a method for predicting buffeting response of a long-span bridge based on deep learning.
Background
The bridge plays an important role in daily life as an important traffic system component. With the rapid development of bridge engineering, bridges are developing in a longer and lighter direction. With the large span and light weight of the bridge, the bridge is more easily affected by wind load. Buffeting, which is random vibration caused by pulsating wind speed, occurs frequently, and buffeting with a large amplitude affects the operation state of a large-span bridge. Therefore, how to predict the bridge buffeting becomes an important research problem.
The traditional buffeting prediction method depends on a finite element model and bridge pneumatic parameters obtained by a wind tunnel test. Taking a frequency domain method as an example, the natural vibration characteristic of a structure is generally required to be obtained, a force cross-spectrum matrix is established by combining a flutter derivative and an aerodynamic force model, and finally, a large-span frequency domain response is calculated through a frequency domain response calculation formula of a linear system under the action of a steady random load. The traditional method depends on the accuracy of a finite element model and a wind tunnel test result, but the problems that the finite element model usually comes in and goes out with an actual bridge structure, the wind tunnel test cannot consider the difference of Reynolds numbers and an uneven wind field exist, and the buffeting response predicted by the traditional method is inaccurate. The traditional buffeting prediction method also has the problem of complex calculation, and related parameters need to be adjusted by the wind environment. One possible solution is to use a data-driven predictive model. The monitoring data can provide information related to load borne by the structure and response due to the development of the structural health monitoring system and the development of the data mining technology, the advanced data mining technology can effectively extract structural behavior mode information contained in the monitoring data, and the data-driven buffeting prediction model becomes possible.
Disclosure of Invention
The invention aims to solve the technical problems in the prior art and provides a method for predicting buffeting response of a large-span bridge based on deep learning. The method of the invention can give the root mean square value of buffeting response and can also give the power spectrum of the response.
The invention is realized by the following technical scheme, and provides a method for predicting buffeting response of a large-span bridge based on deep learning, which specifically comprises the following steps:
step one, data set construction: calculating wind speed characteristics and bridge response characteristics to form a data set of the model;
step two, model building and training: establishing a deep neural network model combined with a frequency domain response calculation formula by taking a GRU neural network as a basic network, and outputting a response power spectrum result; training a deep neural network model by using the data set established in the first step, wherein the wind speed characteristic is used as input, and the response characteristic is used as output;
step three, response prediction: and the model is used for prediction after training is finished, and for a given wind environment, after the wind speed characteristic is determined, the corresponding response characteristic can be obtained by predicting by using the deep neural network model.
Further, the samples were divided with 10 minutes as the sample length.
Further, for the wind speed characteristic data, aiming at the section where the wind speed sensor is arranged, calculating the average wind speed, the wind direction angle, the wind attack angle and the pulsating wind frequency spectrum in each direction of the incoming flow of each section; for the response characteristic data, aiming at the position where the related sensor is arranged, calculating a response power spectrum of the position; and the spectrum and the power spectrum are cut off by combining the pulsating wind spectrum characteristic and the power spectrum characteristic, so that the influence of high-frequency vehicle-induced vibration is avoided, and a data set of the model is formed.
Further, the calculation formula of the wind speed characteristic and the bridge response characteristic is as follows:
Figure BDA0003746704150000021
Figure BDA0003746704150000022
Figure BDA0003746704150000023
u i ＝x i cos(θ i )+y i sin(θ i )-U i (4)
v i ＝-x i sin(θ i )+y i cos(θ i ) (5)
Figure BDA0003746704150000024
Figure BDA0003746704150000025
Figure BDA0003746704150000026
Figure BDA0003746704150000027
Figure BDA0003746704150000028
Figure BDA0003746704150000029
in the formula, x i 、y i 、z i The wind speeds of the i-th section along the bridge direction, the transverse bridge direction and the vertical incoming flow are respectively；
Figure BDA00037467041500000210
Average wind speeds along the bridge direction, the transverse bridge direction and the vertical direction are 10 minutes of the ith section respectively; u shape i 、θ i 、α i The average wind speed, the wind direction angle and the wind attack angle of the incoming flow of the ith cross section in 10 minutes are respectively; u. u i 、v i 、w i The downwind direction, the transverse wind direction and the vertical pulsating wind of the ith section are respectively; u. of i (ω)、v i (ω)、w i (omega) is the frequency spectrum corresponding to each pulsating wind; r is kk (τ) is the autocorrelation function of the kth position response, s k (ω)、σ k The power spectrum and the root mean square of the corresponding position response.
Further, the deep neural network model comprises two parts of sub networks, namely two threshold cycle units GRU, the generalized frequency response function matrix and the buffeting force vector are output respectively, and the two parts of sub networks are connected by using a frequency domain response calculation formula of a linear system, so that a response power spectrum result is output.
Further, the frequency domain response of the linear system is calculated as:
S(ω)＝(H(ω)F b (ω))(H(ω)F b (ω)) *T (12)
in the formula, H (omega) and F b (omega) is generalized frequency response function matrix and buffeting force vector output by the sub-network respectively; s (omega) is a response power spectrum matrix; * T is conjugate transposition; the formula (12) is a response power spectrum calculation method of the linear structure under the action of the stable random load.
And further, constructing a deep neural network model according to the Pythrch deep learning framework.
Further, the loss function of the deep neural network model is defined as:
Figure BDA0003746704150000031
in the formula, L and L re Respectively, a total loss function and a regularization penalty termThe form used is two-norm regularization; s kmn 、
Figure BDA0003746704150000032
Respectively obtaining a true value and a predicted value of the power spectral density of the kth position response at the nth frequency point of the mth sample; K. m and N are respectively the number of responses, the number of samples and the number of frequency points.
The invention provides electronic equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the step of the method for predicting the buffeting response of the large-span bridge based on deep learning when executing the computer program.
The invention provides a computer readable storage medium for storing computer instructions, which when executed by a processor implement the steps of the method for predicting buffeting response of a large-span bridge based on deep learning.
The invention has the beneficial effects that:
aiming at the problems of complex calculation and easy error introduction in the conventional buffeting response prediction method for the buffeting of the large-span bridge, the invention establishes a deep network which takes a threshold cycle unit neural network as a basic component, and realizes the buffeting response prediction of the large-span bridge under the action of real wind load. The method does not need finite element models and priori knowledge of wind tunnel test results, and extracts the structural behavior characteristics hidden in the massive monitoring data through a data mining technology. The method can perform quick prediction once training is completed, and provides a solution for predicting buffeting response of the large-span bridge.
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FIG. 1 is a flow chart of a method for predicting buffeting response of a large-span bridge based on deep learning;
FIG. 2 is a schematic diagram of a typical pulsating wind speed and the corresponding pulsating wind spectrum;
FIG. 3 is a diagram of a typical acceleration time course and a corresponding acceleration power spectrum;
FIG. 4 is a schematic diagram of a deep neural network model structure;
fig. 5 is a graph of typical prediction results.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The first embodiment is as follows:
the invention provides a method for predicting buffeting response of a large-span bridge based on deep learning, which specifically comprises the following steps:
step one, data set construction: calculating wind speed characteristics and bridge response characteristics to form a data set of the model; the samples were divided with 10 minutes as the sample length. For the wind speed characteristic data, aiming at the sections where the wind speed sensors are arranged, calculating the average wind speed, the wind direction angle, the wind attack angle and the fluctuating wind frequency spectrum of each section; for the response characteristic data, aiming at the position where the related sensor is arranged, calculating a response power spectrum of the position; and the spectrum and the power spectrum are cut off by combining the pulsating wind spectrum characteristic and the power spectrum characteristic, so that the influence of high-frequency vehicle-induced vibration is avoided, and a data set of the model is formed.
The calculation formula of the wind speed characteristic and the bridge response characteristic is as follows:
Figure BDA0003746704150000041
Figure BDA0003746704150000042
Figure BDA0003746704150000043
u i ＝x i cos(θ i )+y i sin(θ i )-U i (4)
v i ＝-x i sin(θ i )+y i cos(θ i ) (5)
Figure BDA0003746704150000044
Figure BDA0003746704150000045
Figure BDA0003746704150000046
Figure BDA0003746704150000047
Figure BDA0003746704150000048
Figure BDA0003746704150000049
in the formula, x i 、y i 、z i The wind speeds of the i-th section along the bridge direction, the transverse bridge direction and the vertical incoming flow are respectively;
Figure BDA0003746704150000051
average wind speeds along the bridge direction, the transverse bridge direction and the vertical direction are 10 minutes of the ith section respectively; u shape i 、θ i 、α i The average wind speed, the wind direction angle and the wind attack angle of the incoming flow of the ith cross section in 10 minutes are respectively; u. of i 、v i 、w i The downwind direction, the transverse wind direction and the vertical pulsating wind of the ith section are respectively; u. of i (ω)、v i (ω)、w i (omega) is each pulsating wind pairThe corresponding frequency spectrum; r kk (τ) is the autocorrelation function of the kth position response, s k (ω)、σ k The power spectrum and the root mean square of the corresponding position response.
Step two, model building and training: and constructing a deep neural network model according to the Pythrch deep learning framework. Establishing a deep neural network model combined with a frequency domain response calculation formula by taking a threshold cycling Unit (GRU) neural network as a basic network, and outputting a response power spectrum result; training a deep neural network model by using the data set established in the first step, wherein the wind speed characteristic is used as input, and the response characteristic is used as output;
in order to avoid the difficulty of model training caused by direct prediction and output by using a network, the deep neural network model comprises two parts of sub-networks, namely two threshold cycle units GRU, a generalized frequency response function matrix and a buffeting force vector are respectively output, and a frequency domain response calculation formula of a linear system is used for connecting the two parts of sub-networks, so that a response power spectrum result is output.
The frequency domain response calculation formula of the linear system is as follows:
S(ω)＝(H(ω)F b (ω))(H(ω)F b (ω)) *T (12)
in the formula, H (omega) and F b (omega) is generalized frequency response function matrix and buffeting force vector output by the sub-network respectively; s (omega) is a response power spectrum matrix; * T is conjugate transposition; and the formula (12) is a response power spectrum calculation method of the linear structure under the action of the stable random load.
Considering that the power spectrum amplitude difference corresponding to different samples is large, the problem of network training difficulty caused by the power spectrum amplitude difference is reduced by converting the power spectrum amplitude difference into a logarithm form during training, meanwhile, in order to improve the prediction precision of the large-amplitude power spectrum, weighting is carried out on each sample, and the loss function of a corresponding deep neural network model is defined as:
Figure BDA0003746704150000052
in the formula, L and L re Respectively a total loss function and a regularization punishment item, wherein the form of the punishment item is two-norm regularization; s kmn 、
Figure BDA0003746704150000053
Respectively representing the true value and the predicted value of the power spectral density of the kth position response at the nth frequency point of the mth sample; K. m and N are respectively the number of responses, the number of samples and the number of frequency points. And (4) training the deep neural network model according to the loss function designed by the formula (13). The purpose of adding 1 when taking logarithm of the power spectrum is to avoid the situation that the value of the power spectrum density is unstable when the value is close to 0, and the purpose of adding 1 at the weight position is to fully consider the frequency point of which the value of the power spectrum density is close to 0.
Step three, response prediction: and the model is used for prediction after training is finished, and for a given wind environment, corresponding response characteristics can be obtained by predicting by using the deep neural network model after the wind speed characteristics are determined.
Example two:
as shown in fig. 1, the invention provides a method for predicting buffeting response of a large-span bridge based on deep learning, which specifically comprises the following steps:
step one, calculating wind speed characteristics and bridge response characteristics: the explanation will be given by taking the main beam vibration acceleration response as the target response; calculating the characteristics of each sample by taking 10 minutes as the length of the sample, calculating the average wind speed, the wind direction angle and the wind attack angle of incoming flow of each section according to formulas (1) to (3), calculating corresponding pulsating wind in each direction according to formulas (4) to (6), and calculating the frequency spectrum of each pulsating wind according to formulas (7) to (9), wherein typical pulsating wind speed and the frequency spectrum of the pulsating wind are shown in FIG. 2; calculating corresponding power spectrums according to the formula (10) by the acceleration of each section, wherein a typical acceleration time-course graph and the power spectrums are shown in FIG. 3; and calculating according to the formula (11) to obtain a corresponding root mean square value.
Secondly, model building and training: constructing a deep learning model as shown in FIG. 4, wherein the sub-networks are composed of threshold cycle unit neural networks and connected according to a frequency domain calculation formula of the structure under the action of a steady random load, and U, theta, alpha and F (omega) in the graph are respectively an average wind speed vector, a wind direction angle vector, a wind attack angle vector and a pulsating wind spectrum vector which are composed of average wind speed of each section, a wind direction angle, a wind attack angle and pulsating frequency spectrum of each direction; the model is trained according to the loss function designed by equation (13).
Third, responding to the prediction: the model can be used for prediction after training is completed; calculating according to the wind speed characteristic calculation mode in the first step to obtain the wind speed characteristic of the existing wind environment, taking the wind speed characteristic as the input of the model, and obtaining the corresponding acceleration power spectrum calculation result after running the model; obtaining a corresponding prediction root mean square value according to a formula (11); typical prediction results are shown in fig. 5.
The method uses the Pythrch deep learning framework to build the model, can be used for predicting buffeting response of the large-span bridge, is a data driving model, does not need to acquire a finite element model and priori knowledge of a wind tunnel test result, and can rapidly complete prediction after the model is trained compared with a traditional buffeting prediction method.
The invention provides a method for predicting buffeting response of a large-span bridge based on deep learning, and relates to three steps of data set construction, model building and training and model prediction. In the data set construction step, calculating the wind speed characteristics and the response characteristics of each sample and forming a data set; in the model building and training step, building a model with a threshold cycle unit neural network as a basic network, and performing catenary on the model by using a data set; in the model prediction step, given the wind speed characteristics corresponding to the wind environment, the model can predict the corresponding response power spectrum and the root mean square value. Compared with the traditional buffeting prediction method which is complex in calculation and depends on a finite element model and a wind tunnel test result, the buffeting prediction method based on the wind tunnel model is a data-driven model, can perform fast prediction once being trained, and provides a solution for predicting buffeting response of a large-span bridge.
The invention provides electronic equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the step of the method for predicting the buffeting response of the large-span bridge based on deep learning when executing the computer program.
The invention provides a computer readable storage medium for storing computer instructions, wherein the computer instructions, when executed by a processor, implement the steps of the method for predicting buffeting response of a large-span bridge based on deep learning.
The memory in the embodiments of the present application may be either volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory. The non-volatile memory may be a Read Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an electrically Erasable EPROM (EEPROM), or a flash memory. Volatile memory can be Random Access Memory (RAM), which acts as external cache memory. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), synchronous Dynamic Random Access Memory (SDRAM), double data rate SDRAM, enhanced SDRAM, SLDRAM, synchronous Link DRAM (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memories of the methods described herein are intended to comprise, without being limited to, these and any other suitable types of memories.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the application to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored on a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, from one website, computer, server, or data center to another website, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a Digital Video Disk (DVD)), or a semiconductor medium (e.g., a Solid State Disk (SSD)), among others.
In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or by instructions in the form of software. The steps of a method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware processor, or may be implemented by a combination of hardware and software modules in a processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and completes the steps of the method in combination with hardware of the processor. To avoid repetition, it is not described in detail here.
It should be noted that the processor in the embodiments of the present application may be an integrated circuit chip having signal processing capability. In implementation, the steps of the above method embodiments may be performed by integrated logic circuits of hardware in a processor or by instructions in the form of software. The processor described above may be a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules may be located in ram, flash, rom, prom, or eprom, registers, etc. as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and combines hardware thereof to complete the steps of the method.
The method for predicting buffeting response of a large-span bridge based on deep learning provided by the invention is described in detail, specific examples are applied to explain the principle and the implementation mode of the invention, and the description of the examples is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (10)

1. The method for predicting buffeting response of the large-span bridge based on deep learning is characterized by specifically comprising the following steps of:
step one, data set construction: calculating wind speed characteristics and bridge response characteristics to form a data set of the model;
step two, model building and training: taking a GRU neural network as a basic network to establish a deep neural network model combined with a frequency domain response calculation formula and output a response power spectrum result; training a deep neural network model by using the data set established in the first step, wherein the wind speed characteristic is used as input, and the response characteristic is used as output;
step three, response prediction: and the model is used for prediction after training is finished, and for a given wind environment, corresponding response characteristics can be obtained by predicting by using the deep neural network model after the wind speed characteristics are determined.
2. The method of claim 1, wherein the samples are divided with 10 minutes as the sample length.
3. The method according to claim 2, characterized in that for the wind speed characteristic data, for the cross section where the wind speed sensor is arranged, the average wind speed, the wind direction angle, the wind attack angle and the fluctuating wind frequency spectrum in each direction of the incoming flow of each cross section are calculated; for the response characteristic data, aiming at the position where the related sensor is arranged, calculating a response power spectrum of the position; and the spectrum and the power spectrum are cut off by combining the pulsating wind spectrum characteristic and the power spectrum characteristic, so that the influence of high-frequency vehicle-induced vibration is avoided, and a data set of the model is formed.
4. The method of claim 3, wherein the wind speed characteristic and the bridge response characteristic are calculated as follows:
Figure FDA0003746704140000011
Figure FDA0003746704140000012
Figure FDA0003746704140000013
u i ＝x i cos(θ i )+y i sin(θ i )-U i (4)
v i ＝-x i sin(θ i )+y i cos(θ i ) (5)
Figure FDA0003746704140000014
Figure FDA0003746704140000015
Figure FDA0003746704140000016
Figure FDA0003746704140000017
Figure FDA0003746704140000018
Figure FDA0003746704140000019
in the formula, x i 、y i 、z i The wind speeds of the i-th section along the bridge direction, the transverse bridge direction and the vertical incoming flow are respectively;
Figure FDA0003746704140000021
average wind speeds along the bridge direction, the transverse bridge direction and the vertical direction are 10 minutes of the ith section respectively; u shape i 、θ i 、α i Respectively the 10-minute average wind speed, the wind direction angle and the wind attack angle of the incoming flow of the ith cross section; u. u i 、v i 、w i Respectively a downwind direction, a transverse wind direction and a vertical pulsating wind of the ith section; u. of i (ω)、v i (ω)、w i (omega) is the frequency spectrum corresponding to each pulsating wind; r is kk (τ) is the autocorrelation function of the kth position response, s k (ω)、σ k The power spectrum and the root mean square of the corresponding position response.
5. The method of claim 4, wherein the deep neural network model comprises two part sub-networks, namely two threshold cycle units GRU, which respectively output the generalized frequency response function matrix and the buffeting force vector, and the two part sub-networks are connected by using a frequency domain response calculation formula of a linear system, so as to output a response power spectrum result.
6. The method of claim 5, wherein the frequency domain response of the linear system is calculated as:
S(ω)＝(H(ω)F b (ω))(H(ω)F b (ω)) *T (12)
in the formula, H (omega) and F b (omega) is generalized frequency response function matrix and buffeting force vector output by the sub-network respectively; s (omega) is a response power spectrum matrix; * T is conjugate transposition; and the formula (12) is a response power spectrum calculation method of the linear structure under the action of the stable random load.
7. The method of claim 1, wherein the deep neural network model is constructed according to a Pytorch deep learning framework.
8. The method of claim 6, wherein the loss function of the deep neural network model is defined as:
Figure FDA0003746704140000022
in the formula, L and L re Respectively a total loss function and a regularization punishment item, wherein the form of the punishment item is two-norm regularization; s kmn 、
Figure FDA0003746704140000023
Respectively representing the true value and the predicted value of the power spectral density of the kth position response at the nth frequency point of the mth sample; K. m and N are respectively response number and sampleNumber and frequency bin number.
9. An electronic device comprising a memory and a processor, the memory storing a computer program, wherein the processor, when executing the computer program, performs the steps of the method according to any of claims 1-8.
10. A computer-readable storage medium storing computer instructions, which when executed by a processor implement the steps of the method of any one of claims 1 to 8.
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