Real-time calculation method of displacement response of numerical substructures in real-time hybrid test of engineering structures, predictive control system and medium

Abstract

The present invention discloses a real-time calculation method, a predictive control system and a medium for displacement response of numerical substructures in real-time hybrid test of engineering structure dynamics, wherein the method comprises: using a deep operator network to learn the time evolution characteristics of nonlinear displacement response of numerical substructures in real-time hybrid test of engineering structure dynamics, obtaining a numerical substructure substitution model to realize real-time displacement response calculation of numerical substructures; obtaining time slices of external excitation of numerical substructures, as well as reaction time slices and displacement response time slices at the substructure division interface in real time, using the numerical substructure substitution model, and realizing step-by-step prediction of displacement response of numerical substructures through recursive operation. The problem of excessive time consumption when solving large and complex numerical models using traditional numerical integration methods is solved, the response solution time of numerical substructures is greatly shortened, and the strict requirements for real-time calculation of numerical substructures in real-time hybrid test of engineering structure dynamics are met.

Description

Technical Field

[0001] The present invention relates to the field of engineering structure dynamic test, and in particular to a real-time calculation method for displacement response of numerical substructure in real-time hybrid test of engineering structure dynamic, a prediction control system and a medium. Background Art

[0002] The real-time hybrid test splits the prototype structure into a numerical substructure and a test substructure. The numerical substructure usually uses numerical integration algorithms or finite element methods to solve its response. At the same time, the part with complex mechanical properties or strong nonlinearity is used as a test substructure for physical loading. The motion equations of the overall structure are solved in real time through boundary coordination between the two, which can realize the overall large-scale structural performance test. The use of real-time loading in the real-time hybrid test can effectively reproduce the rate-related effects in the displacement response of the specimen. It has high requirements on the response solution speed of the numerical model and the control accuracy of the loading equipment, and provides an effective test method for dynamic performance testing of large-scale models under limited laboratory conditions.

[0003] Real-time calculation of numerical substructures has always been a key issue in real-time hybrid tests. Traditional numerical model solving usually uses the finite element method to discretize the model in space, and uses the time domain integration algorithm to discretize the model in time domain. The second-order differential equation generated after discretization is the motion equation of the numerical substructure. The numerical integration algorithm should have good enough stability and accuracy to ensure the smooth and safe progress of the test. In addition, it should have good computational efficiency to meet the requirement that the solution time of the numerical substructure is less than the control time step, that is, the real-time requirement of the numerical substructure solution. In real-time hybrid tests with large-scale degrees of freedom and complex nonlinear numerical substructures, it is necessary to solve nonlinear numerical models with tens of thousands of computational degrees of freedom. In order to ensure the calculation accuracy, a small integration step must be used, and too small an integration step limits the real-time calculation scale of the numerical substructure. Therefore, it is necessary to propose a solution method that meets the real-time calculation requirements of complex numerical models. At the same time, the numerical model solution of previous real-time hybrid tests and the loading device are only signal transmissions, and the numerical model solution fails to provide more valuable information for loading control. The low solution efficiency of large and complex numerical models and the need to improve the loading control accuracy have greatly restricted the promotion, application and improvement of hybrid test methods in civil engineering, transportation engineering, aerospace engineering and energy engineering. Summary of the invention

[0004] The present invention provides a real-time calculation method for displacement response of numerical substructures in real-time hybrid tests of engineering structure dynamics, a predictive control system and a medium, so as to solve the problems that the calculation efficiency of numerical substructures with large-scale degrees of freedom and complex nonlinearity in real-time hybrid tests of engineering structure dynamics cannot meet the real-time requirements and the application effect of predictive control in hybrid tests is not good.

[0005] In a first aspect, a method for real-time calculation of displacement response of numerical substructures in a real-time hybrid test of an engineering structure dynamics is provided, comprising the following steps:

[0006] A deep operator network based on operator universal approximation theory is used to learn the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid dynamic test of the engineering structure, and a numerical substructure substitution model is obtained to realize the real-time displacement response calculation of the numerical substructure under the combined action of external excitation and the reaction force at the substructure division interface;

[0007] The time-history slices of the external excitation of the numerical substructure, as well as the time-history slices of the reaction force and the displacement response at the substructure division interface are obtained in real time. The numerical substructure is used to replace the model and the displacement response of the numerical substructure is gradually predicted through recursive calculation. Finally, the real-time displacement response calculation of the numerical substructure at the substructure division interface in the real-time hybrid dynamic test of the engineering structure is realized.

[0008] Furthermore, the deep operator network includes two sub-networks. The first sub-network is used to encode the external excitation time history slices at the current moment and a certain period of time in the past, the reaction force time history slices at the substructure division interface, and the displacement response time history slices; the second sub-network is used to encode the future time step vector that needs to be predicted; the output of the first sub-network is dot-multiplied with the output of the second sub-network to obtain the output of the deep operator network.

[0009] Furthermore, the numerical substructure substitution model is obtained by the following method:

[0010] S1: Establish a complete structural model: According to the requirements of the real-time hybrid test of engineering structure dynamics, a complete structural numerical model including a numerical substructure model and a numerical model of a test substructure is established, and a substructure partitioning interface is defined to distinguish between the numerical substructure and the test substructure;

[0011] S2: Perform finite element analysis: Obtain a set of external excitation time histories, perform finite element analysis on the complete structural numerical model described in S1, extract the reaction time histories and displacement response time histories at the substructure division interface, and combine the external excitation time histories, the reaction time histories and the displacement response time histories at the substructure division interface into a three-dimensional tensor ,in, is the total number of samples, is the number of time steps for each sample, The number of features included for each time step;

[0012] S3: Construct training data set: Use sliding window method to obtain the three-dimensional tensor in S2 Perform time slicing operations to obtain multiple time slices , and construct the future time step vector that needs to be predicted , to construct input and output pairs for network training and obtain training data sets;

[0013] S4: Build a deep operator network: Input to the first sub-network, the first sub-network outputs the implicit feature representation of historical incentive information and historical state information, denoted as ; The training data set Input to the second sub-network, the second sub-network outputs the implicit feature representation of the future time step vector that needs to be predicted, denoted as , the output of the first subnetwork The output of the second subnetwork After performing the dot multiplication, we get the output of the deep operator network, which is recorded as , , is the number of neurons in the output layer of the first sub-network and the second sub-network; Represent the output of the i-th neuron in the output layer of the first sub-network and the second sub-network respectively;

[0014] S5: Deep operator network training: Use the training data set to train the deep operator network, use the gradient descent method to minimize the loss function, and optimize and update the parameters in the first sub-network and the second sub-network through the back propagation algorithm;

[0015] S6: Application of deep operator networks: After training, the model is verified and tested to evaluate its generalization performance on unknown data sets, and the deep operator network with the best prediction accuracy and generalization performance is selected as the numerical substructure replacement model.

[0016] Furthermore, step S3 specifically includes:

[0017] S31: Define the sliding window size as , represents the number of time steps covered by the sliding window;

[0018] S32: Generate training samples using the sliding window method. time steps, the input of the first sub-network is based on the sliding window size The time slices obtained by division ,in, Is the first The feature vector corresponding to all samples in the time step;

[0019] The input of the second subnetwork is the future time step vector to be predicted, which is one or more time steps after the current sliding window; when predicting a future time step, the time step vector is , to predict the future time steps, the time step vector is ;

[0020] Output created The target displacement response of the future time step to be predicted is the displacement response data of one or more time steps after the current sliding window. When predicting the displacement response data of the next time step, the output , when predicting the future When the displacement response of a time step is , where the superscript disp represents the displacement response in the feature;

[0021] S33: Generate the After slicing the time history of time steps, the sliding window slides back one time step to generate the Time slices of time steps;

[0022] S34: Repeat step S33 until the time course ends, and finally generate a deep operator network training data set, which is input as a time course slice and the future time step vector to be predicted The output is the target displacement response for the future time step that needs to be predicted. , the training data set is represented as

[0023] ,

[0024] .

[0025] Furthermore, in S5, the loss function is obtained by the following method:

[0026] The predicted displacement response output by the deep operator network Target displacement response Calculate the root mean square error as the first loss function for network training , which is expressed as follows:

[0027]

[0028] The known hysteresis information of the experimental substructure is used as the second loss function , so that the deep operator network not only meets the data fitting accuracy, but also satisfies the physical constraints of known hysteresis characteristics, which is expressed as follows:

[0029]

[0030] is the known experimental substructure hysteresis information equation or constraint condition, which is related to the reaction force and displacement response at the substructure partition interface. is the derivative of the deep operator network output with respect to the input, which is calculated by the automatic differentiation mechanism of the neural network. Representing a time slice The reaction force at the interface of neutron structure division;

[0031] Finally, the loss function It is obtained by combining the first loss function and the second loss function, expressed as follows:

[0032]

[0033] A hyperparameter that balances the importance of the first loss function and the second loss function.

[0034] Furthermore, the numerical substructure is used to replace the model, and the displacement response of the numerical substructure is gradually predicted through recursive calculation, including:

[0035] S101: Determine initial conditions;

[0036] S102: From the initial moment To begin, call the trained numerical substructure replacement model with the input , after being input into the numerical substructure substitution model calculation, the predicted displacement response vector of the future time step to be predicted is obtained , the predicted displacement response vector The first element in acts on the test substructure; for Time slices of moments, including The external excitation time history slices at the moment and a certain period in the past, the reaction force time history slices at the substructure division interface, and the displacement response time history slices, for The vector of future time steps that need to be predicted at the moment;

[0037] S103: Use the sliding window method to move back one time step to obtain the next time step Input at time , for Time slices at a moment, moved out by sliding windows An old data element located at the left boundary is removed from the data, and a new data element located at the right boundary is introduced at the same time, resulting in ; In the new data element, for the external stimulus schedule, the schedule is defined in advance, The external excitation at time is known; for the reaction time history at the substructure division interface, The reaction force at the time is obtained by the test substructure feedback; for the displacement response time history at the substructure division interface, the last time step The predicted displacement response vector at time The first element in As the current time step The displacement response at time for The vector of future time steps that need to be predicted at the moment;

[0038] S104: Enter the next time step The operation at the moment calls the trained numerical substructure to replace the model, and the input is , and obtain the predicted displacement response vector of the future time step to be predicted , the predicted displacement response vector The first element in acts on the test substructure;

[0039] S105: Repeat steps S103 to S104 until the required end time is reached.

[0040] Furthermore, the first sub-network is one of a multi-layer feedforward neural network, a recurrent neural network, a convolutional neural network and a graph neural network, and the network form of the second sub-network is a multi-layer feedforward neural network.

[0041] In the second aspect, a numerical predictive control system for real-time hybrid test of engineering structure dynamics is provided, including a substitute model prediction module and a predictive control module;

[0042] The surrogate model prediction module is deployed with a numerical substructure surrogate model, which is used to predict the displacement response of the future time step as the target tracking signal within the prediction interval of the predictive control module according to the real-time acquired numerical substructure external excitation time history slice, the reaction time history slice at the substructure division interface and the displacement response time history slice at each control time step. The predictive control module solves the control signal within the control interval according to the defined constrained optimal problem, which is used for the time lag compensation control of the loading equipment in the real-time hybrid test of the engineering structure dynamics;

[0043] The numerical substructure replacement model adopts a deep operator network based on operator universal approximation theory to learn the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid test of engineering structure dynamics.

[0044] Furthermore, the constrained optimal problem is The control time step is to minimize the sum of the error between the target tracking signal and the predicted response of the controlled object within the prediction interval and the control command increment within the control interval, and the restrictions on the control command change range, the control command increment range and the predicted response range of the controlled object must be met. The specific definition is as follows:

[0045]

[0046] In the formula, is the size of the prediction interval, To control the interval size, The model of the controlled object is in the control command Output under action; diagonal matrix Used to weight the error between the target tracking signal and the predicted response of the controlled object, the diagonal matrix Used for weighted control command increment; Respectively represent the lower and upper limits of the control command; Respectively represent the lower and upper limits of the control command increment; They represent the lower and upper limits of the predicted response of the controlled object respectively; To predict the target tracking signal within the interval, it is calculated by the numerical substructure substitution model and is specifically defined as follows:

[0047]

[0048] Enter The numerical substructure replaces the model to execute the target tracking signal in the corresponding prediction interval under the current control time step, and solves the above constraint optimization problem to complete the control command of the current control time step. Generate and finally send to the controlled object for loading;

[0049] Repeat until the test loading is complete.

[0050] In a third aspect, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the real-time calculation method of the displacement response of a numerical substructure in a real-time hybrid test of engineering structure dynamics as described above is implemented.

[0051] The present invention proposes a real-time calculation method for displacement response of numerical substructures in a real-time hybrid test of an engineering structure, a predictive control system and a medium, which have the following beneficial effects:

[0052] (1) The present invention first solves the problem of excessive time consumption when using traditional numerical integration methods to solve large and complex numerical models in real-time hybrid dynamic tests of engineering structures. The present invention compresses and extracts the dynamic characteristics of large and complex numerical models through deep learning technology, and uses recursive calculations to gradually solve the displacement response in real-time hybrid dynamic tests of engineering structures, thereby greatly shortening the solution time of the displacement response of the numerical substructure and meeting the strict requirements for the real-time performance of the displacement response of the numerical substructure in real-time hybrid dynamic tests of engineering structures.

[0053] (2) The present invention also improves the control accuracy of the loading device in the real-time hybrid test of the engineering structure dynamics. Through the numerical substructure replacement model based on the deep operator network proposed in the present invention, the target tracking signal within the prediction interval is obtained, which broadens the perception domain of the predictive control method, thereby improving the control accuracy of the predictive control algorithm. The innovative fusion of the numerical substructure displacement response solution and the loading predictive control algorithm in the real-time hybrid test method is realized, which effectively improves the progress of the control signal applied to the loading device in the real-time hybrid test of the engineering structure dynamics, thereby improving the loading accuracy of the loading device and ensuring the accuracy of the experimental results. At the same time, it meets the real-time performance of the numerical response solution and the improvement of the loading control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0055] Figure 1 It is a schematic diagram of a real-time calculation method of numerical substructure of engineering structure dynamic real-time hybrid test based on recursive deep operator network and an improved predictive control system provided by an embodiment of the present invention;

[0056] Figure 2 is a schematic diagram of the structure of a deep operator network provided by an embodiment of the present invention;

[0057] Figure 3 It is a flow chart of establishing a numerical substructure substitution model using a recursive deep operator network provided by an embodiment of the present invention;

[0058] Figure 4 It is a schematic diagram of a recursive operation form of a substitution model based on a deep operator network provided in an embodiment of the present invention;

[0059] Figure 5 It is a schematic diagram of a studied framework structure provided by an embodiment of the present invention;

[0060] Figure 6 It is a comparison diagram of structural response prediction results of a deep operator network (the first sub-network adopts a fully connected network) provided in an embodiment of the present invention;

[0061] Figure 7 It is a comparison diagram of structural response prediction results of the deep operator network (the first sub-network adopts a one-dimensional convolutional network) provided in an embodiment of the present invention;

[0062] Figure 8It is a comparison diagram of structural response prediction results based on traditional long short-term memory network provided by an embodiment of the present invention;

[0063] Fig. 9 It is a schematic diagram of an improved predictive control system that combines a substitute model with a predictive control algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0064] To make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0065] The basic principle of the real-time hybrid test method is as follows: a complete structure is divided into two parts: a numerical substructure and a test substructure. The numerical substructure is calculated in real time in a computer. The test substructure generates a dynamic response under the loading of a loading device. The reaction force and external excitation load at the substructure division interface are input into the numerical substructure. The numerical substructure is solved to obtain the displacement response at the substructure division interface (the following embodiment is explained using the displacement response as an example) as the control command of the loading device in the next control time step. The present invention uses a deep operator network as a substitute model for a numerical substructure with large-scale degrees of freedom and complex nonlinearity, and uses a recursive operation form to realize the real-time solution of its dynamic response. Furthermore, based on the substitute model, the target tracking signal in the prediction interval in the predictive control method is calculated, which improves the prediction performance of the predictive control method in the hybrid test, and can further improve the control accuracy of the controlled object. The present invention is further described below in conjunction with specific embodiments.

[0066] The embodiment of the present invention provides a method for real-time calculation of displacement response of numerical substructure in real-time hybrid test of engineering structure dynamics, comprising the following steps:

[0067] Step 1: Use a deep operator network based on operator universal approximation theory to learn the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid test of engineering structure dynamics, and obtain a numerical substructure alternative model to realize the real-time displacement response calculation of the numerical substructure under the combined action of external excitation and reaction force at the substructure division interface;

[0068] Step 2: Obtain the external excitation time-history slices of the numerical substructure, as well as the reaction force time-history slices and displacement response time-history slices at the substructure division interface in real time. Use the numerical substructure replacement model to realize the step-by-step prediction of the displacement response of the numerical substructure through recursive calculation, and finally realize the real-time displacement response calculation of the numerical substructure at the substructure division interface in the real-time hybrid test of engineering structure dynamics.

[0069] The above-mentioned embodiment provides a real-time calculation method for the displacement response of a numerical substructure in a real-time hybrid test of engineering structure dynamics, which solves the problem of excessive time consumption when using traditional numerical integration methods to solve large and complex numerical models in real-time hybrid tests of engineering structure dynamics. By compressing and extracting the dynamic characteristics of large and complex numerical models using deep learning technology, a recursive operation form is used to gradually solve the displacement response in the real-time hybrid test of engineering structure dynamics, thereby greatly shortening the solution time of the displacement response of the numerical substructure and meeting the strict requirements for the real-time performance of obtaining the displacement response of the numerical substructure in the real-time hybrid test of engineering structure dynamics.

[0070] like Figure 1 As shown in the figure, a schematic diagram of the real-time calculation method of numerical substructure and the improved predictive control system for real-time hybrid test of engineering structure dynamics is given. In the real-time hybrid test of engineering structure dynamics, the main research object will establish a physical structure model according to the original size or a certain proportion of the size, that is, the test substructure, and some other structures that are convenient for modeling using numerical integration algorithms or finite element methods will be constructed as numerical substructures. The numerical substructure is simulated in the computer, and the test substructure is loaded in the laboratory, and the coupling of the numerical and physical structural parts is realized through loading equipment.

[0071] Take the real-time hybrid experiment for studying the state of a high-speed train / maglev train when passing over a bridge and optimizing the design of the high-speed train / maglev train structure as an example. In this example, the high-speed train / maglev train structure is the main research object, so a physical model of the high-speed train / maglev train with a reduced scale and containing some carriages will be constructed, called a test substructure, and a numerical model of the bridge and track will be built together, called a numerical substructure. The high-speed train / maglev train will be placed on a loading device (vibration table), and the physical model of the high-speed train / maglev train (test substructure) will be physically loaded by the loading device to simulate the mechanical response of the bridge and track (numerical substructure) to the physical model of the high-speed train / maglev train (test substructure). In this example, the external excitation time history slice of the numerical substructure is the track irregularity excitation signal time series. Of course, if the state of the high-speed train / maglev train when passing through the bridge under the earthquake scenario is tested, the external excitation time history slice should also include the seismic wave excitation signal time series; the reaction force time history slice at the substructure division interface is the time series of the force applied by the high-speed train / maglev train physical model to the track bridge at the contact point with the track bridge; the displacement response time history slice at the substructure division interface of the numerical substructure (the contact point between the high-speed train / maglev train and the track bridge) is the displacement response time series generated by the track bridge under the combined action of the track irregularity excitation signal time series (also including the seismic wave excitation signal time series in the earthquake simulation scenario) and the force applied by the high-speed train / maglev train to the track bridge.

[0072] Of course, the present invention is not limited to the test of the state of high-speed trains / maglev trains when passing through bridges, but is also applicable to other application scenarios, such as in the example of real-time hybrid test of earthquake resistance research on buildings, when the main research object is the load-bearing column, a physical model of the load-bearing column is established as a test substructure, and a numerical model is established for other non-load-bearing parts of the building as a numerical substructure, and a vibration table is used as a loading device to physically load the physical model of the load-bearing column. The external excitation time history slice of the numerical substructure in this example is the time series of the seismic wave excitation signal; the reaction force time history slice at the substructure division interface of the numerical substructure (where other non-load-bearing parts of the building contact with the load-bearing column) is the time series of the force of other non-load-bearing parts of the building on the load-bearing column; the displacement response time history slice at the substructure division interface of the numerical substructure is the displacement response time series of the load-bearing column under the combined action of the seismic wave excitation signal time series and the force of other non-load-bearing parts of the building on the load-bearing column.

[0073] like Figure 2As shown, in this embodiment, the deep operator network includes two subnetworks. The first subnetwork is used to encode historical excitation information and historical state information. The input of the first subnetwork is the external excitation time slices at the current moment and a certain period in the past, the reaction force time slices at the substructure division interface, and the displacement response time slices; the second subnetwork is used to encode the output coordinates. The input of the second subnetwork is the future time step vector that needs to be predicted; the output of the first subnetwork is multiplied by the output of the second subnetwork to obtain the output of the deep operator network. That is, the displacement response at the future time step that needs to be predicted, and the numerical substructure replacement model based on the deep operator network is obtained after network training.

[0074] like Figure 3 As shown in the figure, in order to build and train a deep operator network to obtain a numerical substructure replacement model, there are six steps, including:

[0075] S1: Establish a complete structural model: According to the requirements of real-time hybrid test of engineering structure dynamics, a complete structural numerical model including numerical substructure model and numerical model of experimental substructure is established, and a substructure partition interface is defined to distinguish between numerical substructure and experimental substructure.

[0076] S2: Perform finite element analysis: Obtain a set of external excitation time histories, perform finite element analysis on the complete structural numerical model described in S1, extract the reaction time histories and displacement response time histories at the substructure division interface, and combine the external excitation time histories, the reaction time histories and the displacement response time histories at the substructure division interface into a three-dimensional tensor ,in, is the total number of samples, is the number of time steps for each sample, The number of features to include for each time step.

[0077] S3: Construct training data set: Use sliding window method to obtain the three-dimensional tensor in S2 Perform time slicing operations to obtain multiple time slices , and construct the future time step vector that needs to be predicted , to construct input and output pairs for network training and obtain training data sets. Specifically include:

[0078] S31: Define the sliding window size as , represents the number of time steps covered by the sliding window;

[0079] S32: Generate training samples using the sliding window method. time steps, the input of the first sub-network is based on the sliding window size The time slices obtained by division ,in, Is the first The feature vector corresponding to all samples in the time step;

[0080] The input of the second subnetwork is the future time step vector to be predicted, which is one or more time steps after the current sliding window; when predicting a future time step, the time step vector is , to predict the future time steps, the time step vector is ;

[0081] Output created The target displacement response of the future time step to be predicted is the displacement response data of one or more time steps after the current sliding window. When predicting the displacement response data of the next time step, the output , when predicting the future When the displacement response of a time step is , where the superscript disp represents the displacement response in the feature;

[0082] S33: Generate the After slicing the time history of time steps, the sliding window slides back one time step to generate the Time slices of time steps;

[0083] S34: Repeat step S33 until the time course ends, and finally generate a deep operator network training data set, which is input as a time course slice and the future time step vector to be predicted The output is the target displacement response for the future time step that needs to be predicted. , the training data set is represented as

[0084] ,

[0085] .

[0086] S4: Build a deep operator network: Input to the first sub-network, the first sub-network outputs the implicit feature representation of historical incentive information and historical state information, denoted as ; The training data set Input to the second sub-network, the second sub-network outputs the implicit feature representation of the future time step vector that needs to be predicted, denoted as , the output of the first subnetwork The output of the second subnetwork After performing the dot multiplication, we get the output of the deep operator network, which is recorded as , , is the number of neurons in the output layer of the first sub-network and the second sub-network, Represent the output of the i-th neuron in the output layer of the first sub-network and the second sub-network respectively.

[0087] S5: Deep operator network training: Use the training data set to train the deep operator network, use the gradient descent method to minimize the loss function, and optimize and update the parameters in the first sub-network and the second sub-network through the back propagation algorithm.

[0088] S6: Application of deep operator networks: After training, the model is verified and tested to evaluate its generalization performance on unknown data sets, and the deep operator network with the best prediction accuracy and generalization performance is selected as the numerical substructure replacement model.

[0089] In this embodiment, in S5, the loss function is obtained by the following method:

[0090] The predicted displacement response output by the deep operator network Target displacement response Calculate the root mean square error as the first loss function for network training , which is expressed as follows:

[0091]

[0092] The known hysteresis information of the experimental substructure is used as the second loss function , so that the deep operator network not only meets the data fitting accuracy, but also satisfies the physical constraints of known hysteresis characteristics, which is expressed as follows:

[0093]

[0094] is the known experimental substructure hysteresis information equation or constraint condition, which is related to the reaction force and displacement response at the substructure partition interface. is the derivative of the deep operator network output with respect to the input, which is calculated by the automatic differentiation mechanism of the neural network. Representing a time slice The reaction force at the interface of neutron structure division;

[0095] Finally, the loss function It is obtained by combining the first loss function and the second loss function, expressed as follows:

[0096]

[0097] A hyperparameter that balances the importance of the first loss function and the second loss function.

[0098] It should be noted that the network form of the first sub-network can be selected from multi-layer feedforward neural networks, recurrent neural networks, convolutional neural networks and graph neural networks according to the characteristics of the input data, and the network form of the second sub-network can be selected from multi-layer feedforward neural networks. The number of layers and depth of the two sub-networks are selected according to the scale and nonlinear complexity of the numerical model to be learned.

[0099] Typical feature quantities of the deep operator network include: external excitation time history, reaction time history at the substructure division interface, and displacement response time history at the substructure division interface. In the case of multiple excitation points and multiple substructure division interfaces, the excitation time history, reaction force, and displacement response time history at all external excitation points and all substructure division interfaces must be included. In some other embodiments, the features may also include dynamic responses of other parts of the numerical substructure, including displacement, velocity, acceleration, and reaction force.

[0100] Figure 4 This is a schematic diagram of the recursive operation form of the numerical substructure replacement model based on the deep operator network. After the deep operator network training is completed and the mixed test numerical substructure replacement model is obtained, it is necessary to repeatedly call the numerical substructure replacement model in a recursive form to achieve a step-by-step forward solution in time steps, including:

[0101] S101: Determine initial conditions;

[0102] S102: From the initial moment To begin, call the trained numerical substructure replacement model with the input ,in , after being input into the numerical substructure substitution model calculation, the predicted displacement response vector of the future time step to be predicted is obtained , the predicted displacement response vector The first element in Acts on the test substructure; where for Time slices of moments, including The external excitation time history slices at the moment and a certain period in the past, the reaction force time history slices at the substructure division interface, and the displacement response time history slices, for The vector of future time steps that need to be predicted at the moment;

[0103] S103: Use the sliding window method to move back one time step to obtain the next time step Input at time , for Time slices at a moment, moved out by sliding windows An old data element located at the left boundary is removed from the data, and a new data element located at the right boundary is introduced at the same time, resulting in ; New data elements For the external stimulus schedule, the schedule is defined in advance. The external excitation at time is known; for the reaction time history at the substructure division interface, The reaction force at the time is obtained by the test substructure feedback; for the displacement response time history at the substructure division interface, the last time step The predicted displacement response vector at time The first element in As the current time step The displacement response at time

[0104] S104: Enter the next time step The operation at the moment calls the trained numerical substructure to replace the model, and the input is , and obtain the predicted displacement response vector of the future time step to be predicted , the predicted displacement response vector The first element in Acts on the test substructure;

[0105] S105: Repeat steps S103 to S104 until the required end time is reached.

[0106] Figure 5 This is an example of the real-time solution effect of the real-time calculation method of the hybrid test numerical substructure based on the deep operator network proposed in the present invention, wherein the complete structure is a three-layer bending-resistant steel frame structure with nonlinear beam-column nodes, and an energy-absorbing damper is installed at the second frame of each layer. In this example, the energy-absorbing damper of the first layer is used as the test substructure, and the remaining part of the three-layer steel frame structure is used as the numerical substructure. The real-time calculation method of the hybrid test numerical substructure based on the deep operator network proposed in the present invention is used to establish an alternative model for the numerical substructure, wherein the first subnetwork in the deep operator network uses a fully connected neural network and a one-dimensional convolutional neural network (to better handle the input format of three-dimensional tensors). At the same time, a traditional recurrent neural network, a long short-term memory network, is also used for performance comparison.

[0107] The training of the three networks uses a total of 39 earthquake inputs, of which 31 structural responses under earthquake motion are used as training sets, and the remaining 8 responses under earthquake motion are used as validation sets. The prediction accuracy of the three networks is adjusted to be consistent as much as possible to compare other index parameters of the network. Table 1 gives the performance indicators of each network. It can be seen that the trainable parameters of Network 1 and Network 2 using the deep operator network architecture are much smaller than the parameters of the network 3 long short-term memory network. Therefore, the use of the deep operator network structure can greatly reduce the time consumed by network training and network reasoning. It can be intuitively observed from Table 1 that the trainable parameters of Network 1 and Network 2 using the deep operator network architecture are reduced by more than 87% compared with the trainable parameters of the network 3 long short-term memory network, and the reasoning time of each time step is accelerated by more than 70%.

[0108]

[0109] Figure 6 , Figure 7 and Figure 8 The comparison diagrams of the numerical substructure displacement response prediction results and the actual results of the surrogate models established based on network 1, network 2 and network 3 respectively show that the predicted values ​​of network 1 and network 2 using the deep operator network architecture are consistent with the actual values, and can also accurately predict in the presence of residual displacement response, but the network 3 long short-term memory network cannot accurately predict the section with residual displacement response in the second half of the time history. The prediction accuracy of the three networks can be seen in Table 1. Network 1 and network 2 using the deep operator network architecture are superior to network 3 long short-term memory network in terms of peak error and root mean square error set correlation coefficient.

[0110] The embodiment of the present invention also provides a numerical prediction control system for real-time hybrid test of engineering structure dynamics, including a substitute model prediction module and a prediction control module;

[0111] The surrogate model prediction module is deployed with a numerical substructure surrogate model, which is used to predict the displacement response of the future time step as the target tracking signal within the prediction interval of the predictive control module according to the real-time acquired numerical substructure external excitation time history slice, the reaction time history slice at the substructure division interface and the displacement response time history slice at each control time step. The predictive control module solves the control signal within the control interval according to the defined constrained optimal problem, which is used for the time lag compensation control of the loading equipment in the real-time hybrid test of the engineering structure dynamics;

[0112] The numerical substructure replacement model adopts a deep operator network based on operator universal approximation theory to learn the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid test of engineering structure dynamics.

[0113] In this embodiment, the constrained optimal problem is The control time step is to minimize the sum of the error between the target tracking signal and the predicted response of the controlled object within the prediction interval and the control command increment within the control interval, and the restrictions on the control command change range, the control command increment range and the predicted response range of the controlled object must be met. The specific definition is as follows:

[0114]

[0115] In the formula, is the size of the prediction interval, To control the interval size, For the controlled object model in the control command Output under action; diagonal matrix Used to weight the error between the target tracking signal and the predicted response of the controlled object, , for The diagonal elements of For weighted control command increment, , for The diagonal elements of ; Respectively represent the lower and upper limits of the control command; Respectively represent the lower and upper limits of the control command increment; They represent the lower and upper limits of the predicted response of the controlled object respectively; To predict the target tracking signal within the interval, it is calculated by the numerical substructure substitution model and is specifically defined as follows:

[0116]

[0117] Enter The numerical substructure replaces the model to execute the target tracking signal in the corresponding prediction interval under the current control time step, and solves the above constraint optimization problem to complete the control command of the current control time step. Generate and finally send to the controlled object for loading;

[0118] Repeat until the test loading is complete.

[0119] The above-mentioned embodiment provides a numerical prediction control system for real-time hybrid test of engineering structure dynamics, which improves the control accuracy of the loading device in the real-time hybrid test of engineering structure dynamics. Through the numerical substructure replacement model based on the deep operator network proposed in the present invention, the target tracking signal in the prediction interval is obtained, the perception domain of the prediction control method is broadened, thereby improving the control accuracy of the prediction control algorithm, and innovatively realizing the fusion of the numerical substructure displacement response solution and the loading prediction control algorithm in the real-time hybrid test method, effectively improving the progress of the control signal applied to the loading device in the real-time hybrid test of engineering structure dynamics, thereby improving the loading accuracy of the loading device, ensuring the accuracy of the experimental results, and at the same time meeting the improvement of the real-time performance of the numerical response solution and the loading control accuracy.

[0120] Fig. 9 This is an example of a predictive control system proposed by the present invention that combines a numerical substructure replacement model with a predictive control algorithm. The key elements in the predictive control optimization process are the predictive model and the reference signal. However, in a hybrid test, the reference signal of the future time step is unknown, and each time step can only obtain the expected displacement of the current time step. Therefore, this limits the "prediction" ability of the predictive control. Therefore, the idea of ​​"predicting the reference signal in a future period based on the historical expected displacement" is adopted for improvement. At each control time step, after the numerical substructure replacement model is calculated, the prediction of the displacement response at the future time point is obtained as the target tracking signal in the prediction interval of the predictive control. The predictive control solves the control signal in the control interval according to the defined constrained optimal problem, which is used for the time-delay compensation control of the hybrid test loading equipment. The predictive control system improves the perception ability of the traditional predictive control for the target tracking signal of the future control time step, and overcomes the deficiency of the traditional predictive control in the hybrid test that lacks the target control command of the future period.

[0121] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for real-time calculation of displacement response of a numerical substructure in a real-time hybrid test of engineering structure dynamics described in the aforementioned embodiment is implemented.

[0122] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0123] It should be understood that the functional unit modules in various embodiments of the present invention may be concentrated in one processing unit, or each unit module may exist physically separately, or two or more unit modules may be integrated in one unit module, and may be implemented in the form of hardware or software.

[0124] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0125] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0126] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0127] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0128] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A real-time calculation method for displacement response of numerical substructures in real-time hybrid test of engineering structure dynamics, characterized in that: The steps include: A deep operator network based on operator universal approximation theory is used to learn the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid dynamic test of the engineering structure, and a numerical substructure substitution model is obtained to realize the real-time displacement response calculation of the numerical substructure. Obtain the time slices of external excitation of the numerical substructure, as well as the time slices of reaction force and displacement response at the substructure division interface in real time, and use the numerical substructure to replace the model and realize the step-by-step prediction of the displacement response of the numerical substructure through recursive operation; The deep operator network includes two subnetworks, the first subnetwork is used to encode the external excitation time history slices, the reaction force time history slices at the substructure division interface, and the displacement response time history slices at the current time and a certain period of time in the past input; The second sub-network is used to encode the future time step vector that needs to be predicted; the output of the first sub-network is dot-multiplied with the output of the second sub-network to obtain the output of the deep operator network; The numerical substructure substitution model is obtained by the following method: S1: Establish a complete structural model: According to the requirements of the real-time hybrid test of engineering structure dynamics, a complete structural numerical model including a numerical substructure model and a numerical model of a test substructure is established, and a substructure partitioning interface is defined to distinguish between the numerical substructure and the test substructure; S2: Perform finite element analysis: Obtain a set of external excitation time histories, perform finite element analysis on the complete structural numerical model described in S1, extract the reaction time histories and displacement response time histories at the substructure division interface, and combine the external excitation time histories, the reaction time histories and the displacement response time histories at the substructure division interface into a three-dimensional tensor ,in, is the total number of samples, is the number of time steps for each sample, The number of features included for each time step; S3: Construct training data set: Use sliding window method to obtain the three-dimensional tensor in S2 Perform time slicing operations to obtain multiple time slices , and construct the future time step vector that needs to be predicted , to construct input and output pairs for network training and obtain training data sets; S4: Build a deep operator network: Input to the first sub-network, the output of the first sub-network is recorded as ; The training data set Input to the second sub-network, the output of the second sub-network is recorded as , the output of the first subnetwork The output of the second subnetwork After performing the dot multiplication, we get the output of the deep operator network, which is recorded as ; S5: Deep operator network training: Use the training data set to train the deep operator network, use the gradient descent method to minimize the loss function, and optimize and update the parameters in the first sub-network and the second sub-network through the back propagation algorithm; S6: Application of deep operator networks: After training is completed, the model is verified and tested, and the deep operator network with the best prediction accuracy and generalization performance is selected as the numerical substructure replacement model.

2. The real-time calculation method for displacement response of numerical substructure in real-time hybrid test of engineering structure dynamics according to claim 1 is characterized in that: Step S3 specifically includes: S31: Define the sliding window size as , represents the number of time steps covered by the sliding window; S32: Generate training samples using the sliding window method. time steps, the input of the first sub-network is based on the sliding window size The time slices obtained by division ,in, Is the first The feature vector corresponding to all samples in the time step; The input of the second subnetwork is the future time step vector that needs to be predicted, which is one or more time steps after the current sliding window; Output created The target displacement response of the future time step to be predicted is the displacement response data of one or more time steps after the current sliding window. When predicting the displacement response data of the next time step, the output , when predicting the future When the displacement response of a time step is , where the superscript disp represents the displacement response in the feature; S33: Generate the After slicing the time history of time steps, the sliding window slides back one time step to generate the Time slices of time steps; S34: Repeat step S33 until the time course ends, and finally generate a deep operator network training data set, which is input as a time course slice and the future time step vector to be predicted The output is the target displacement response for the future time step that needs to be predicted. .

3. The real-time calculation method of displacement response of numerical substructure in real-time hybrid test of engineering structure dynamics according to claim 1 is characterized in that: In S5, the loss function is obtained by the following method: The predicted displacement response output by the deep operator network Target displacement response Calculate the root mean square error as the first loss function for network training , which is expressed as follows: ； The known hysteresis information of the experimental substructure is used as the second loss function , which is expressed as follows: ； is the known experimental substructure hysteresis information equation or constraint condition, Output the derivative of the input for the deep operator network, Representing a time slice The reaction force at the interface of neutron structure division; Finally, the loss function It is obtained by combining the first loss function and the second loss function, expressed as follows: ； A hyperparameter that balances the importance of the first loss function and the second loss function.

4. The real-time calculation method of displacement response of numerical substructure in real-time hybrid test of engineering structure dynamics according to claim 1 is characterized in that: The numerical substructure replacement model is used to realize the step-by-step prediction of the displacement response of the numerical substructure through recursive calculation, including: S101: Determine initial conditions; S102: From the initial moment To begin, call the trained numerical substructure replacement model with the input , after being input into the numerical substructure substitution model calculation, the predicted displacement response vector of the future time step to be predicted is obtained , the predicted displacement response vector The first element in acts on the test substructure; for Time slices of moments, including The external excitation time history slices at the moment and a certain period in the past, the reaction force time history slices at the substructure division interface, and the displacement response time history slices, for The vector of future time steps that need to be predicted at the moment; S103: Use the sliding window method to move back one time step to obtain the next time step Input at time , for Time slices at a moment, moved out by sliding windows An old data element located at the left boundary is removed from the data, and a new data element located at the right boundary is introduced at the same time, resulting in ; In the new data element, for the external stimulus time course, The external excitation at time is known; for the reaction time history at the substructure division interface, The reaction force at the time is obtained by the test substructure feedback; for the displacement response time history at the substructure division interface, the last time step The predicted displacement response vector at time The first element in is taken as the current time step The displacement response at time for The vector of future time steps that need to be predicted at the moment; S104: Enter the next time step The operation at the moment calls the trained numerical substructure to replace the model, and the input is , and obtain the predicted displacement response vector of the future time step to be predicted , the predicted displacement response vector The first element in acts on the test substructure; S105: Repeat steps S103 to S104 until the required end time is reached.

5. The real-time calculation method for displacement response of numerical substructure in real-time hybrid test of engineering structure dynamics according to claim 1 is characterized in that: The first sub-network is one of a multi-layer feedforward neural network, a recurrent neural network, a convolutional neural network and a graph neural network, and the network form of the second sub-network is a multi-layer feedforward neural network.

6. A numerical prediction control system for real-time hybrid test of engineering structure dynamics, characterized in that: It includes a substitute model prediction module and a prediction control module; The surrogate model prediction module is deployed with a numerical substructure surrogate model, which is used to predict the displacement response of the future time step as the target tracking signal within the prediction interval of the predictive control module according to the real-time acquired numerical substructure external excitation time history slice, the reaction time history slice at the substructure division interface and the displacement response time history slice at each control time step. The predictive control module solves the control signal within the control interval according to the defined constrained optimal problem, which is used for the time lag compensation control of the loading equipment in the real-time hybrid test of the engineering structure dynamics; The numerical substructure substitution model is obtained by learning the time evolution characteristics of the nonlinear displacement response of the numerical substructure in the real-time hybrid test of the engineering structure dynamics using a deep operator network based on the operator universal approximation theory; The deep operator network includes two subnetworks, the first subnetwork is used to encode the external excitation time history slices, the reaction force time history slices at the substructure division interface and the displacement response time history slices at the current time and a certain period of time in the past; the second subnetwork is used to encode the future time step vector that needs to be predicted; the output of the first subnetwork is dot-multiplied with the output of the second subnetwork to obtain the output of the deep operator network; The numerical substructure substitution model is obtained by the following method: S1: Establish a complete structural model: According to the requirements of the real-time hybrid test of engineering structure dynamics, a complete structural numerical model including a numerical substructure model and a numerical model of a test substructure is established, and a substructure partitioning interface is defined to distinguish between the numerical substructure and the test substructure; S2: Perform finite element analysis: Obtain a set of external excitation time histories, perform finite element analysis on the complete structural numerical model described in S1, extract the reaction time histories and displacement response time histories at the substructure division interface, and combine the external excitation time histories, the reaction time histories and the displacement response time histories at the substructure division interface into a three-dimensional tensor ,in, is the total number of samples, is the number of time steps for each sample, The number of features included for each time step; S3: Construct training data set: Use sliding window method to obtain the three-dimensional tensor in S2 Perform time slicing operations to obtain multiple time slices , and construct the future time step vector that needs to be predicted , to construct input and output pairs for network training and obtain training data sets; S4: Build a deep operator network: Input to the first sub-network, the output of the first sub-network is recorded as ; The training data set Input to the second sub-network, the output of the second sub-network is recorded as , the output of the first subnetwork The output of the second subnetwork After performing the dot multiplication, we get the output of the deep operator network, which is recorded as ; S5: Deep operator network training: Use the training data set to train the deep operator network, use the gradient descent method to minimize the loss function, and optimize and update the parameters in the first sub-network and the second sub-network through the back propagation algorithm; S6: Application of deep operator networks: After training is completed, the model is verified and tested, and the deep operator network with the best prediction accuracy and generalization performance is selected as the numerical substructure replacement model.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the real-time calculation method for displacement response of a numerical substructure in a real-time hybrid test of an engineering structure dynamics as claimed in any one of claims 1 to 5 is implemented.

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