Prediction Method for Wind-Induced Dynamic Response of Transmission Towers Based on Embedded Physics-Informed Learning

Abstract

The present invention discloses a method for predicting the wind-induced dynamic response of a transmission tower based on embedded physical information learning. First, vibration response data of the transmission tower under wind load is obtained through theoretical analysis, simulation, experiments and other means. Then, an internal mapping relationship between the wind load and the dynamic response of the transmission tower is established based on a deep residual recurrent neural network, and a forward model of the transmission tower structure under complex non-linear mapping is constructed. Then, the model is trained based on the training set data, a loss function for the inverse dynamic response and the true dynamic response is established, and the gradient descent method is used to learn and update the parameters of the deep learning model based on embedded physical information. Considering physical constraint information on the basis of data-driven can not only improve the generalization ability of the deep learning model, but also effectively shorten the training time and improve work efficiency. The present invention can solve the problems in the prior art such as low accuracy of dynamic response inversion, weak anti-interference ability, large amount of pure data-driven data and slow training.

Description

Technical Field

[0001] The present invention belongs to the field of electric power, and particularly relates to a method for predicting the wind-induced dynamic response of a transmission tower based on embedded physical information learning. Background Art

[0002] With the rapid development of modern industry and cities, people's demand for electric energy is increasing, and the dependence is also getting stronger. The development of electric power is related to the national economic lifeline. Once problems such as insufficient supply occur, it will seriously affect economic development and people's lives. High-voltage transmission lines are the carriers of electric energy transmission and the intermediate links for transmitting and distributing electric energy. The transmission tower-line system has the characteristics of light weight, high flexibility, large span and small damping, and is very sensitive to wind excitation. Local damage accidents of high-voltage transmission lines will lead to large-scale power outages. Once the transmission tower is damaged, it will cause the paralysis of the power supply system, directly affecting the production and living order, and even causing very serious secondary disasters, bringing irreparable losses of life and property to the country and the people. Therefore, studying the dynamic response reconstruction of transmission towers under wind loads is an important guarantee for the safety assessment and early warning of transmission tower structures and the safe operation of the power grid. Common structural dynamic response inversion techniques mainly include response reconstruction methods based on modal theory, response inversion based on transfer matrices, and response inversion methods based on Markov parameters. In traditional dynamic response inversion, it is easily affected by factors such as noise, initial value conditions, and sensor measurement point arrangements when forced to meet physical constraint conditions, and the inversion accuracy is not high.

[0003] In recent years, with the improvement of data acquisition capabilities and computer computing power, deep learning has achieved great success in fields such as data mining, machine translation, natural language processing, and image recognition, and the noise robustness and recognition accuracy have been continuously improved. As a kind of deep learning network, the Recurrent Neural Network (RNN) is widely used in processing time series data. In the data-driven process, RNN learns the time correlation of the system response through the hidden state vector, and then simulates the dynamic response changing with time. Introducing the deep learning method based on RNN into the reconstruction and prediction of the time series data of the dynamic response of transmission towers is expected to solve the prominent problems faced by traditional methods, such as poor noise resistance, excessive dependence on sensor arrangements, and high sensitivity to initial values. Since only the pure data-driven mode of input and output is considered in the training process, for complex transmission tower structures, the training is difficult, time-consuming, and the prediction accuracy is low. Summary of the Invention

[0004] The object of the present invention is to provide a method for predicting the wind-induced dynamic response of a transmission tower based on embedded physics-informed learning, so as to solve or improve the problems of low accuracy and low efficiency in predicting and identifying the vibration force response of a transmission tower in the prior art, and to meet the high requirements in terms of dynamic response identification accuracy, identification efficiency, online identification, noise robustness, and insensitivity to initial values, thereby improving the performance of predicting the dynamic response of a transmission tower.

[0005] The specific technical solution of the present invention: The present invention provides a method for predicting the wind-induced dynamic response of a transmission tower based on embedded physics-informed learning, including the following steps:

[0006] Step S1, establish a finite element model of the transmission tower according to the design drawings;

[0007] Step S2, modify the finite element model based on the measured data by the modal parameter method;

[0008] Step S3, obtain the wind load excitation data and dynamic response data of the transmission tower through simulation, theoretical analysis and experimental means, and construct a data set;

[0009] Step S4, construct a hybrid deep learning model based on physical constraint information and RNN data-driven;

[0010] Step S5, iteratively train the hybrid deep learning model based on the deep residual recurrent neural network;

[0011] Step S6, according to the measured wind load data, input it into the trained hybrid deep learning model to predict the wind-induced dynamic response of the transmission tower.

[0012] Preferably, consider the motion equation of the transmission tower structure

[0013]

[0014] In the formula, , and respectively represent the mass, damping and stiffness matrices of the system; , and respectively represent the displacement, velocity and acceleration vectors of the system, represents the external load vector, and acts on the corresponding degrees of freedom of the system through the mapping matrix .

[0015] Preferably, in step S2, the modal parameters of the structure are determined by the stochastic subspace identification method (SSI method) to further modify the finite element model. Introduce the state vector , then the motion equation of the transmission tower after modifying the finite element model is as follows:

[0016]

[0017] In the formula, is the state space vector, is the state vector of the structure, represents the external load vector, and are the system matrix and the control input matrix of the state space respectively,

[0018]

[0019] ,

[0020] In the formula, , and represent the mass, damping and stiffness matrices of the system respectively, represents the mapping matrix.

[0021] Preferably, in step S3, the wind speed and dynamic response are obtained through simulation, theoretical analysis and experimental means, and the measured data is obtained by installing power transmission tower dynamic response sensors and anemometers during on-site measurement.

[0022] Preferably, in step S3, the dynamic response refers to one or more of the displacement, velocity, acceleration and strain of the measurement points on the power transmission tower structure.

[0023] Preferably, in step S3, the data set is divided into a training set, a validation set and a test set according to the ratio of 6:2:2.

[0024] Preferably, in step S4, the minimization of the residual of the dynamic response is used as the objective function

[0025]

[0026] wherein, represents the residual at the (n + 1)-th moment, represents the state vector at the (n + 1)-th moment, represents the preset time step, represents the non-linear term operator.

[0027] Preferably, in step S5, the iterative calculation based on the deep residual recurrent neural network is as follows:

[0028]

[0029] wherein, represents the number of layers, represents the state vector at the (n + 1)-th moment in the k-th layer, represents the residual at the (n + 1)-th moment in the k-th layer, and represents the weight matrix, represents the bias parameter. To avoid a zero denominator, a small positive number is taken, the decay parameter calculation formula is as follows

[0030]

[0031] and represent the fractional factors respectively, and the recommended values are , .

[0032] Preferably, when the physical relationship between the state vector of the hidden layer in the recurrent neural network and the observed quantity is unknown, the approximation of the unknown physical relationship is realized in the data-driven layer, and the relationship between the hidden layer and the observed value is characterized in the data-driven layer through a multi-layer perceptron

[0033]

[0034]

[0035]

[0036] where m is the number of hidden layers, represents the output of the multi-layer perceptron on the m-th hidden layer at the (n + 1)-th moment, the RELU activation function is adopted, and represent the weight matrix and the bias vector on the m-th perceptron respectively, represents the state vector at the (n + 1)-th moment, and E represents the number of layers of the data-driven hidden layer.

[0037] The beneficial effects of the present invention are as follows: The present invention proposes a method for inverting the dynamic response of a transmission tower under wind vibration based on deep learning with embedded physical information. Based on the collected wind load information, the physical constraint information of the structure is introduced to form a dynamic response prediction method based on deep learning with embedded physical information, which can predict the dynamic response of the transmission tower. Compared with the traditional dynamic response reconstruction method and the pure data-driven method, this method can be regarded as a hybrid method based on the fusion of physical constraints and data-driven. It can not only describe the "black box" model of the input and output, but also be quickly trained under the condition of meeting physical constraints to achieve the rapid prediction of the dynamic response of the transmission tower under wind vibration. This method has the advantages of stronger noise robustness, not overly relying on sensor layout, and being insensitive to the initial value, etc., and can effectively improve the prediction accuracy of the dynamic response. Description of the Drawings

[0038] Figure 1 is the flowchart of the implementation of the present invention;

[0039] Figure 2 is the schematic diagram of the single-tower dynamic model of the transmission tower;

[0040] Figure 3 Wind speed time history diagram and wind power spectrum comparison diagram

[0041] Figure 4 is the network structure diagram based on the deep residual recurrent neural network (DR-RNN);

[0042] Figure 5 is the time history diagram of the transmission tower response inversion; (a) displacement response; (b) velocity response. Detailed implementation manners

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0044] It should be understood that when used in this specification and the appended claims, the terms "comprises" and "comprising" indicate the presence of the described features, wholes, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0045] It should also be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms.

[0046] It should be further understood that the term " / and / " used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0047] Embodiment

[0048] In order to solve or improve problems such as low accuracy of dynamic response inversion, weak anti-interference ability, large amount of pure data-driven data, and slow training, a wind-induced dynamic response prediction method for transmission towers based on embedded physical information learning as Figure 1 shown is proposed, including the following steps:

[0049] Step S1, establish a finite element model of the transmission tower according to the design drawings.

[0050] Step S2, modify the finite element model by the modal parameter method based on the measured data.

[0051] Consider the motion equation of the transmission tower structure

[0052]

[0053] where , and represent the mass, damping, and stiffness matrices of the system respectively; , and represent the displacement, velocity, and acceleration vectors of the system respectively, represents the external load vector, and acts on the corresponding degrees of freedom of the system through the mapping matrix .

[0054] Introduce the state vector , then the motion equation of the transmission tower after modifying the finite element model is as follows:

[0055]

[0056] where is the state space vector, is the state vector of the structure, represents the external load vector, and are the system matrix and control input matrix of the state space respectively,

[0057]

[0058] ,

[0059] where , and represent the mass, damping, and stiffness matrices of the system respectively, represents the mapping matrix.

[0060] Step S3, obtain wind speed and dynamic response information through means such as simulation, theoretical analysis, and experiments. During the actual measurement, install dynamic response sensors and anemometers on the transmission tower, set the sampling frequency, collect the excitation data and dynamic response data of the transmission tower under wind loads, and construct a data set.

[0061] Specifically, determine the time step and the number of sample points, and construct a data set from the measured wind speed data and the measured dynamic response data. The data set is divided into a training set, a validation set, and a test set in a ratio of 6:2:2. The dynamic response refers to one or more of the displacement, velocity, acceleration, and strain of the measurement points on the transmission tower structure.

[0062] Step S4, construct a hybrid deep learning model based on physical constraint information and RNN data-driven. Taking the minimization of the residual of the dynamic response as the objective function, update the corresponding hyperparameters through the training set data. The residual function is as follows:

[0063]

[0064] where, represents the residual at the (n + 1)-th moment, represents the state vector at the (n + 1)-th moment, represents the preset time step, represents the non-linear term operator.

[0065] Based on the residual function, the state vector at the next moment can be solved from the state vector and the structural physical information at the current moment.

[0066] Step S5, iteratively train the hybrid deep learning model based on the deep residual recurrent neural network. The traditional RNN network can also be used to process the prediction of the dynamic response. However, the method based on the pure data-driven mode does not consider the physical constraint conditions of the structural state system. In order to effectively utilize the physical information of the dynamic system, a forward model that establishes the input-output system mapping relationship is constructed based on the deep residual recurrent neural network (DR-RNN). The residual vector is minimized through iterative calculations of multiple stacked hidden layers. The output vector of the intermediate stacked layer in the DR-RNN is calculated according to the following iterative format. The iterative calculation process based on the deep residual recurrent neural network is as follows:

[0067]

[0068] where, represents the number of layers, represents the state vector at the (n + 1)-th moment in the k-th layer, represents the residual at the (n + 1)-th moment in the k-th layer, and represent the weight matrices, represents the bias parameter. To avoid a zero denominator, take a small positive number ( ), is the attenuation parameter calculation formula as follows

[0069]

[0070] and respectively represent fractional factors, and the recommended values are , .

[0071] The DR-RNN model is trained based on the data of the training set and the validation set, and the DR-RNN model is evaluated according to the results of the training and the test set. If necessary, the network structure of DR-RNN can be adjusted appropriately.

[0072] When the physical relationship between the state vector in the hidden layer of the DR-RNN cell and the observed quantity is unknown, an approximation of the unknown physical relationship can be achieved in the data-driven layer. The relationship between the hidden layer and the observed value can be characterized in the data-driven layer through a multi-layer perceptron

[0073]

[0074]

[0075]

[0076] where m is the number of hidden layers, represents the output of the multi-layer perceptron on the m-th hidden layer at the (n + 1)-th moment. The RELU activation function is adopted. and respectively represent the weight matrix and the bias vector on the m-th perceptron, and E represents the number of layers of the data-driven hidden layer.

[0077] Figure 2 The front view and side view of the dry-type transmission tower are given. The total height of the tower is 36 m, and there are three cross arms with heights of 19.64 m, 24.47 m, and 29.3 m respectively. This tower is taken as an example for analysis.

[0078] Figure 3 The time history curve of the wind speed is given, and the comparison diagram of the measured wind speed and the simulated wind speed power spectrum is given.

[0079] Figure 4 The network structure diagram of DR-RNN is given. Through comparative analysis, it is found that the DR-RNN training mode considering physical information requires 82% less training time than the pure data-driven RNN training mode. It can be found that the method based on DR-RNN can effectively improve the training efficiency and effectively solve the problem of slow training of traditional pure data-driven methods.

[0080] Step S6: Input the measured wind load data into the trained hybrid deep learning model to predict the wind-induced dynamic response of the transmission tower. The forward model for dynamic response prediction is established based on the deep residual recurrent neural network, which describes the inherent mapping relationship between wind load excitation and structural dynamic response.

[0081] The comparison diagrams of the time-history curve inversion of the displacement and velocity of the transmission tower at heights of 19.64 m, 24.47 m, and 29.3 m are respectively given, as Figure 5 shown. After calculation, the root mean square errors RMS of the displacement and velocity responses are 5.12; 6.84%, 7.19, 2.68%, 3.17%, 4.68%, and 5.12% respectively. At the same time, the performance of the model in aspects such as the prediction accuracy of dynamic response, noise robustness, and calculation efficiency is evaluated.

[0082] In summary, the present invention first obtains the vibration response data of the transmission tower under wind load through theoretical analysis, simulation, experiments, etc., and divides the vibration response data into a training set, a validation set, and a test set; then based on the deep residual recurrent neural network, an inherent mapping relationship between the wind load and the dynamic response of the transmission tower is established, and a forward model of the transmission tower structure under complex non-linear mapping is constructed; then the model is trained based on the training set data, a loss function between the inverted dynamic response and the true dynamic response is established, and the gradient descent method is used to learn and update the parameters of the deep learning model embedded with physical information. Considering physical constraint information on the basis of data-driven can not only improve the generalization ability of the deep learning model, but also effectively shorten the training time and improve work efficiency; finally, based on the trained model, the prediction of the wind-induced dynamic response of the transmission tower and the performance evaluation of the learning model are realized. The present invention can solve the problems in the prior art such as low accuracy of dynamic response inversion, weak anti-interference ability, large amount of pure data-driven data, and slow training.

[0083] Those of ordinary skill in the art can realize that the units of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the components of each example have been generally described according to their functions in the above description. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0084] In the embodiments provided in the present application, it should be understood that the division of units is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored, etc.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and the description of the present invention.

Claims

1. A method for predicting the wind-induced dynamic response of a transmission tower based on physics-informed learning, characterized in that, Including the following steps: Step S1: Establish a finite element model of the transmission tower according to the design drawings; Step S2: Modify the finite element model by the modal parameter method based on the measured data; Step S3: Obtain the wind load excitation data and dynamic response data of the transmission tower through simulation, theoretical analysis and experimental means, and construct a data set; Step S4, construct a hybrid deep learning model based on physical constraint information and RNN data-driven; wherein the physical constraint information includes the motion equation of the transmission tower, and the hybrid deep learning model realizes physical constraints by embedding the motion equation into the residual objective function, specifically: Among them, represents the residual at the (n + 1)-th moment, represents the state vector at the (n + 1)-th moment, represents a preset time step, represents a non-linear term operator; Step S5: Iteratively train the hybrid deep learning model based on the deep residual recurrent neural network; The iterative calculation process based on the deep residual recurrent neural network is as follows: Among them, represents the number of layers, represents the state vector at the k-th layer at the (n + 1)-th moment, represents the residual at the k-th layer at the (n + 1)-th moment, and represents the weight matrix, represents the bias parameter. To avoid division by zero, a small positive number is taken, and the attenuation parameter calculation formula is as follows and respectively represent fractional factors, and the recommended values are , ; Step S6: Input the measured wind load data into the trained hybrid deep learning model to predict the wind-induced dynamic response of the transmission tower.

2. The prediction method for the wind-induced dynamic response of a transmission tower based on the learning of embedded physical information according to claim 1, wherein In Step S2, the modal parameters of the structure are determined by the stochastic subspace method and then the finite element model is modified. The motion equation of the transmission tower is as follows: In the formula, is the state space vector, is the structural state vector, represents the external load vector, and are the system matrix and the control input matrix of the state space respectively, ， wherein, , and represent the mass, damping, and stiffness matrices of the system respectively, represents the mapping matrix.

3. The method for predicting the wind-induced dynamic response of a transmission tower based on the learning of embedded physical information according to claim 1, wherein In Step S3, the wind speed and dynamic response are obtained through simulation, theoretical analysis and experimental means. In the on-site measurement, the measured data is obtained by installing dynamic response sensors and anemometers on the transmission tower.

4. The method for predicting the wind-induced dynamic response of a transmission tower based on embedded physical information learning according to claim 1, wherein In Step S3, the dynamic response refers to one or more of the displacement, velocity, acceleration and strain of the measurement points on the transmission tower structure.

5. The prediction method for the wind-induced dynamic response of a transmission tower based on embedded physics-informed learning according to claim 1, wherein In Step S3, the data set is divided into a training set, a validation set and a test set according to the ratio of 6:2:

2.

6. The method for predicting the wind-induced dynamic response of a transmission tower based on embedded physical information learning according to claim 1, wherein , when the physical relationship between the state vector of the hidden layer in the recurrent neural network and the observed quantity is unknown, approximate the unknown physical relationship at the data-driven layer, and characterize the relationship between the hidden layer and the observed value at the data-driven layer through a multi-layer perceptron where m is the number of hidden layers, represents the output of the multi-layer perceptron on the m-th hidden layer at time n + 1, uses the RELU activation function, and represent the weight matrix and bias vector on the m-th perceptron respectively, represents the state vector at time n + 1, and E represents the number of layers of the data-driven hidden layer.

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