Structural system identification method based on Bayesian updating and adaptive meta-learning sampling method

Abstract

The present invention proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling methods. The method first determines whether there is an adaptive meta-learning sampler adapted to the specific structural system identification task based on the task data. If not, an adaptive meta-learning sampler adapted to the task is trained. Finally, the trained sampler is used to execute the adaptive meta-learning sampling method based on Bayesian updating to achieve efficient sampling and complete the structural system identification task. The present invention proposes an adaptive meta-learning sampling method. Based on the detailed probability distribution identification results of Bayesian updating, the present invention uses the refined strategy learning ability of neural networks to improve sampling efficiency, and uses adaptive meta-learning design to save neural network training time, so that the method is applicable to more complex structural system identification problems, thereby better serving the field of structural health detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural system identification and structural health monitoring, and in particular relates to a structural system identification method based on Bayesian updating and adaptive meta-learning sampling methods. Background Art

[0002] In the past few decades, structural health monitoring systems have been widely deployed and a large amount of data has been accumulated. Based on this data, a variety of system identification techniques have emerged in order to understand the behavior and performance of civil infrastructure under real environmental conditions. Bayesian updating is a general, reasonable and robust tool that is widely used in structural system identification. It integrates prior knowledge and existing data according to Bayes' theorem to obtain the posterior distribution of parameter vectors, thereby achieving structural system identification. However, when calculating the posterior distribution, high-dimensional integrals that are difficult to calculate analytically are usually encountered. As a powerful computational tool, Markov Chain Monte Carlo (MCMC) sampling method is widely used in numerical simulation of posterior distribution.

[0003] Specifically, the MCMC method continuously generates parameter samples by simulating the state update process of a specific Markov chain. The stationary distribution of the Markov chain state is taken as the posterior distribution of the parameters. Therefore, under the assumption that each state has undergone ergodicity, the parameter samples generated after an initial warm-up phase simulation will obey the posterior distribution. Researchers have developed a series of classic general MCMC algorithms, including MH, TMCMC, HMC, and SGHMC. When it comes to specific Bayesian update problems, basic parameters such as step size can be adjusted and used directly, or the sampling efficiency can be further improved by manually debugging the sampling strategy. However, further multi-parameter refinement debugging is almost impossible to achieve by manpower, which limits the method's ability to deal with complex structural system identification problems.

[0004] In recent years, the application of neural networks has made it possible to expand the MCMC method and fine-tune multi-parameters. Some neural network-enhanced MCMC algorithms use neural networks to replace and debug specific components in the MCMC algorithm to obtain efficient sampling strategies for target problems and achieve rapid convergence and efficient exploration of the sampling process. However, as the ability to handle specific problems improves after training, the generalization ability of the sampling method tends to decrease. Therefore, its neural network often needs to be retrained when facing new tasks, and the time-consuming repeated training greatly weakens the competitiveness of the method.

[0005] Meta-learning technology refers to the effective acquisition of common knowledge contained in a set of similar tasks through targeted algorithm design, aiming to ensure the generalization ability of the algorithm to similar problems after training, so that it can effectively solve a series of similar tasks after learning only one or a few tasks. Based on the idea of ​​meta-learning, if a meta-learning sampling method can be designed, that is, the algorithm only needs to be trained once and can be directly used for a series of similar Bayesian update tasks, it can greatly reduce the training time while taking advantage of the refined strategy learning advantages of neural networks, becoming a more efficient sampling method than classical methods, suitable for structural system recognition based on Bayesian updates. Summary of the invention

[0006] The purpose of the present invention is to solve the problems in the prior art to meet the needs of actual situations, and proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling method. The method utilizes the refined strategy learning ability of neural networks to improve sampling efficiency, utilizes meta-learning design to save training time, and is ultimately applicable to more complex structural system identification problems. In response to the above needs, the present invention designs an adaptive meta-learning sampling method, and proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling method, which is applicable to structural system identification based on Bayesian updating.

[0007] The present invention is implemented by the following technical scheme. The present invention proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling method, and the method comprises the following steps:

[0008] Step 1: Arrange vibration sensors on the target structure to obtain the measurement data of the vibration index of each measuring point over a period of time;

[0009] Step 2: Find out whether there is a saved adaptive meta-learning sampler trained for the same structure. If yes, go to step 5, otherwise go to step 3.

[0010] Step 3: According to the parameter types of the target structure, a training structure of the same scale with similar parameters is modeled, and the vibration response measurement data of multiple measuring points of the similar structure simplified by the target structure is obtained by numerical simulation or scaled experimental method;

[0011] Step 4: Based on the measured data of the training structure and the Bayesian update method, run the adaptive meta-learning sampling method, start the training mode, obtain and save the trained adaptive meta-learning sampler;

[0012] Step 5: Based on the measurement data of the target structure and the Bayesian update method, run the adaptive meta-learning sampling method, use the trained adaptive meta-learning sampler, turn off the training mode, obtain samples that obey the joint posterior distribution of the structural parameters, and characterize the joint probability distribution of each parameter, thereby realizing structural system identification.

[0013] Furthermore, the vibration index includes acceleration, velocity, displacement and strain.

[0014] Furthermore, the adaptive meta-learning sampling process based on the Bayesian updating method in step 4 and step 5 is specifically as follows:

[0015] The adaptive meta-learning sampling process based on the Bayesian updating method in step 4 and step 5 is based on the Bayesian theorem, according to the structural parameter prior probability distribution p(θ) obtained from the known information and the measured data The likelihood function obtained The Markov chain is used to simulate the process of multiple parameter sample points that obey the posterior probability distribution of structural parameters, where is the structural model parameter, and its dimension D is the number of parameters. K Markov chains can be selected to be run in parallel according to the computational efficiency requirements and the performance limitations of the computing equipment.

[0016] Furthermore, the simulation process of the sampling method is specifically as follows:

[0017] Step 4.1. Define potential energy Where c* is an arbitrary constant for easy calculation;

[0018] Step 4.2: If there is a trained adaptive meta-learning sampler, use the neural network directly Otherwise, two artificial neural networks with positive outputs are selected. Used to construct the curl matrix sub-block in the adaptive meta-learning sampler in the subsequent steps and diffusion matrix sub-blocks The network parameterization architecture is constructed and its network parameters are randomly initialized, where the non-diagonal elements of the two sub-block matrices Q(z) and D(z) are zero, and the diagonal elements are calculated and determined according to the output of the neural network in subsequent steps;

[0019] Step 4.3: Each chain randomly generates an initial sample z0 = (θ0, p0) according to the prior distribution p(θ), where the model parameter θ is regarded as the position of a particle in the D-dimensional space in the subsequent simulation, and the auxiliary variable is regarded as the particle momentum and follows a standard normal distribution, thus augmenting the vector is called the state variable of the particle, let t = 0, t0 = 0;

[0020] Step 4.4: When t<N, repeat steps 4.5 to 4.11. Each repetition will be based on the current sample z. t =(θ t , p t ) simulates a new sample z t+1 =(θ t+1 , p t+1 ), the total number of simulation steps N is N=9000;

[0021] Step 4.5: Get the current sample information, including potential energy U(θ t ), position θ t , momentum p t and potential energy gradient The position component, momentum component, potential energy gradient component and corresponding parameter category of the particle in the i-th dimension are denoted as θ t，i 、p t，i , and Cate i , i=1,…,D;

[0022] Step 4.6: If the sampling process is in the adaptive adjustment stage, the potential energy U(θ t ) and each position component θ t，i , i = 1, ..., D, respectively update the first two moments μ of the potential energy U(θ) U and σ U Adaptive estimation of and standard deviation of each dimension of the posterior distribution of parameters i , i = 1, ..., adaptive estimation of D;

[0023] Step 4.7: Calculate the normalized potential energy and each normalized potential energy gradient component

[0024] Step 4.8: Enter the current sample information. p t，i , and Cate i , calling the neural network The learned meta-sampling strategy, under the control of this strategy The diffusion process is simulated by discrete dynamics to obtain a new sample z t+1 =(θ t+1 , p t+1 );

[0025] Step 4.9, let t = t + 1;

[0026] Step 4.10: If it is training mode, create z t A new copy of is used for subsequent computations to stop the gradient flow;

[0027] Step 4.11: If it is training mode and t can be T T Divide and calculate the loss function And back propagate to update the neural network parameters, let t0 = t, set T T =15, M=3, where For sample Approximate estimated sample probability density function;

[0028] Step 4.12: If it is training mode, save the adaptive meta-learning sampler, otherwise output all samples after the warm-up phase.

[0029] Furthermore, the adaptive adjustment stage in step 4.6 should be in the preheating stage of the sampling process, and the preheating stage is set to t<3000 and the adaptive adjustment stage is set to 500<t<2800.

[0030] Further, the potential energy U(θ t ) or any position component θ t，i Unified as y t,k , k=1,…,K, where k represents the kth Markov chain; adaptive estimators are established for the above 1 potential variable and D position components, i.e., D+1 variables, respectively, and the exponential decay rates β1, β2∈[0,1) of the estimation process are set; the call count variable t′ with an initial value of 0 is built-in; the initial values ​​of the estimated results of the first two moments are m0=0, in When the input is potential energy, When the input is a position component, it is acceptable Or a rough estimate based on training estimates, test structure differences, and test data size differences.

[0031] Furthermore, the adaptive estimation method in step 4.6 is specifically as follows:

[0032] Step 4.6.1, update the number of calls t′=t′+1;

[0033] Step 4.6.2. Calculate the mean input

[0034] Step 4.6.3: Update the first-order moment estimate

[0035] Step 4.6.4. Calculate the unbiased estimate of the first moment If it is training mode and the input is position component, the robust correction of the prior initial value is adopted Otherwise, use the deinitialization to completely correct

[0036] Step 4.6.5: If t′=1, let

[0037] Step 4.6.6. Calculate the variance attenuation term

[0038] Step 4.6.7. Calculate the variance input

[0039] Step 4.6.8: Update the second-order central moment estimate

[0040] Step 4.6.9: Calculate the unbiased estimate of the second-order central moment If the input is a position component, the robust correction of the a priori initial value is adopted Otherwise, use the deinitialization to completely correct

[0041] Step 4.6.10, Output required variables: If the input is position component θ t,i , then the output is the posterior standard deviation estimate of the corresponding dimension parameter Otherwise, output the mean and standard deviation estimates of the potential energy U(θ) and

[0042] Furthermore, the step 4.8 is specifically as follows:

[0043] The discrete dynamics simulation process in step 4.8 uses an improved forward Euler discretization to simulate the Diffusion process; the simulation process under the control of the meta-sampling strategy is specifically as follows:

[0044] Step 4.8.1: Use the sampling strategy learned by the neural network and input the current sample information. Pt,i, and Cate i , both are z t =(θ t , p t ) function, calculate the matrix Q(z t ) and D(z t ), that is, The elements are It is calculated from the output of the neural network, where c1 and c2 are two positive constants, ensuring that each diagonal element is always positive;

[0045] Step 4.8.2: Update particle momentum Where η is the sampling algorithm step size; represents a normal distribution with mean μ and covariance ∑; for any vector z and matrix A(z), define

[0046] Step 4.8.3, input the updated sample information of particle momentum p t+1，i and Cate i , both Function, calculate the matrix The diagonal elements of The elements are

[0047] Step 4.8.4: Update particle position Thus we get a new sample z t+1 =(θ t+1 , p t+1 ).

[0048] The present invention proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the structural system identification method based on Bayesian updating and adaptive meta-learning sampling method are implemented.

[0049] The present invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the structural system identification method based on Bayesian updating and adaptive meta-learning sampling methods.

[0050] Beneficial effects of the present invention:

[0051] 1. The present invention is a structural system identification method based on Bayesian updating. Compared with non-probabilistic methods, the identification result of the present invention is the posterior probability distribution of parameters, which is more detailed. The shape and scale of the obtained posterior distribution in each direction can be used for the subsequent quantitative identification result. The confidence and uncertainty have a good reference value in practical applications;

[0052] 2. The present invention adopts a sampling method based on a neural network, which can fine-tune the sampling strategy for specific problems and significantly improve the sampling efficiency;

[0053] 3. The present invention innovatively designs an adaptive meta-learning sampling method, which adaptively adjusts the sampling strategy according to the obtained sample information in the sampling warm-up stage, which can ensure that the sampling efficiency is scale-invariant to the posterior distribution when the sampling meta-strategy learned by the neural network remains unchanged, significantly improving the generalization ability of the sampling method after training and saving a lot of training time;

[0054] 4. In the adaptive meta-learning sampling method, the present invention innovatively improves the design of the loss function and its back-propagation gradient flow for its Markov chain environment, which can ensure the stability and efficiency of the algorithm training process. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] 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 embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0056] Figure 1 A flowchart of the structural system identification method based on Bayesian updating and adaptive meta-learning sampling method according to the present invention;

[0057] Figure 2 A flowchart of the adaptive meta-learning sampling process based on the Bayesian updating method involved in the present invention;

[0058] Figure 3 It is an overall implementation plan diagram for executing three similar structural system identification tasks in an embodiment of the present invention;

[0059] Figure 4 The acceleration measurement data time course curve diagrams of the three structural system identification tasks in the embodiment of the present invention: (a) is the acceleration measurement data of a 5-story building, (b) is the acceleration measurement data of a 2-story building, and (c) is the acceleration measurement data of a 10-story building;

[0060] Figure 5 2D projection scatter plots of the sampling results of the three tasks in the embodiment of the present invention in several pairs of parameter directions. The colors of the scatter points are the two-dimensional marginal probability density function values ​​estimated based on the sample projections in the figure: (a) is the sampling result of the 5-story building task, (b) is the sampling result of the 2-story building task, and (c) is the sampling result of the 10-story building task. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] The recognition results of the structural system identification method based on Bayesian updating are more detailed, but when the sampling method is used to simulate the posterior distribution, the practicality of the system identification method for complex structures will be limited by the sampling efficiency. In order to improve the sampling efficiency of the structural system identification method, the present invention designs an adaptive meta-learning sampling method. First, the present invention adopts a sampling method enhanced by a neural network to finely adjust the sampling strategy for specific problems and significantly improve the sampling efficiency. Secondly, according to the characteristics of various posterior probability distributions in the Bayesian updating problem of the structural dynamics model, an adaptive meta-learning architecture is designed to save a lot of neural network training time. Specifically, an input / output processing method considering parameter types is proposed to ensure the scale invariance of the posterior probability distribution of model parameters. Since the scale of the posterior probability distribution is unknown in advance, the present invention extracts key information such as the distribution scale according to the obtained sample information in the sampling preheating stage, and adaptively adjusts the sampling strategy. This architecture can improve the generalization ability of the sampler after training, because the scale difference of the posterior probability distribution is the most important difference between different system identification problems, and the overall shape of the conditional posterior probability distribution of the same parameters will be relatively similar. Finally, the design of the loss function and its back-propagation gradient flow is optimized to make it more suitable for network training in a Markov chain environment, ensuring the stability and efficiency of the algorithm training process.

[0063] Combination Figure 1-Figure 5 The present invention proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling method, the method comprising the following steps:

[0064] Step 1: Arrange vibration sensors on the target structure to obtain the measurement data of vibration indicators (acceleration, velocity, displacement, strain, etc.) at each measuring point over a period of time;

[0065] Step 2: Find out whether there is a saved adaptive meta-learning sampler trained for the same structure. If yes, go to step 5, otherwise go to step 3.

[0066] Step 3: According to the parameter types of the target structure, a similar training structure of a suitable scale with similar parameters is modeled, and the vibration response measurement data of multiple measuring points of the similar structure simplified by the target structure is obtained by using numerical simulation or scaled experiment and other methods;

[0067] Step 4: Based on the measured data of the training structure and the Bayesian update method, run the adaptive meta-learning sampling method, start the training mode, obtain and save the trained adaptive meta-learning sampler;

[0068] Step 5: Based on the measurement data of the target structure and the Bayesian update method, run the adaptive meta-learning sampling method, use the trained adaptive meta-learning sampler, turn off the training mode, obtain samples that obey the joint posterior distribution of the structural parameters, and characterize the joint probability distribution of each parameter, thereby realizing structural system identification.

[0069] The adaptive meta-learning sampling process based on the Bayesian updating method in step 4 and step 5 is based on the Bayesian theorem, according to the structural parameter prior probability distribution p(θ) obtained from the known information and the measured data The likelihood function obtained The Markov chain is used to simulate the process of multiple parameter sample points that obey the posterior probability distribution of structural parameters, where is a structural model parameter, and its dimension D is the number of parameters. K Markov chains can be selected to be run in parallel according to the computational efficiency requirements and the performance limitations of the computing equipment. The simulation process of the sampling method is specifically as follows:

[0070] Step 4.1. Define potential energy Where c* is an arbitrary constant for easy calculation;

[0071] Step 4.2: If there is a trained adaptive meta-learning sampler, use the neural network directly Otherwise, two small artificial neural networks with constant positive output are selected. Used to construct the curl matrix sub-block in the adaptive meta-learning sampler in the subsequent steps and diffusion matrix sub-blocks The network parameterization architecture is constructed and its network parameters are randomly initialized, where the non-diagonal elements of the two sub-block matrices Q(z) and D(z) are zero, and the diagonal elements are calculated and determined according to the output of the neural network in subsequent steps;

[0072] Step 4.3: Each chain randomly generates an initial sample z0 = (θ0, p0) according to the prior distribution p(θ), where the model parameter θ is regarded as the position of a particle in the D-dimensional space in the subsequent simulation, and the auxiliary variable is regarded as the particle momentum and follows a standard normal distribution, thus augmenting the vector is called the state variable of the particle, let t = 0, t0 = 0;

[0073] Step 4.4: When t<N, repeat steps 4.5 to 4.11. Each repetition will be based on the current sample z. t =(θ t , p t ) simulates a new sample z t+1 =(θ t+1 , p t+1 ), the total number of simulation steps N can be taken as N = 9000;

[0074] Step 4.5: Get the current sample information, including potential energy U(θ t ), position θ t , momentum p t and potential energy gradient The position component, momentum component, potential energy gradient component and corresponding parameter category of the particle in the i-th dimension are denoted as θ t，i 、p t，i , and Cate i , i=1,…,D;

[0075] Step 4.6: If the sampling process is in the adaptive adjustment stage, the potential energy U(θ t ) and each position component θ t，i , i = 1, ..., D, respectively update the first two moments μ of the potential energy U(θ) U and σ U Adaptive estimation of and standard deviation of each dimension of the posterior distribution of parameters i , i = 1, ..., adaptive estimation of D. The adaptive adjustment stage here should be in the warm-up stage of the sampling process. The warm-up stage can be set to t < 3000 and the adaptive adjustment stage to 500 <t<2800;

[0076] Step 4.7: Calculate the normalized potential energy and each normalized potential energy gradient component

[0077] Step 4.8: Enter the current sample information and Cate i ), calling the neural network The learned meta-sampling strategy, under the control of this strategy The diffusion process is simulated by discrete dynamics to obtain a new sample z t+1 =(θ t+1 , p t+1 );

[0078] Step 4.9, let t = t + 1;

[0079] Step 4.10: If it is training mode, create z t A new copy of is used for subsequent computations to stop the gradient flow;

[0080] Step 4.11: If it is training mode and t can be T T Divide and calculate the loss function And back propagate to update the neural network parameters, let t0 = t, in this step, you can set T T =15, M=3, where For sample Approximate estimated sample probability density function;

[0081] Step 4.12: If it is training mode, save the adaptive meta-learning sampler, otherwise output all samples after the warm-up phase.

[0082] The adaptive estimation method in step 4.6 is specifically as follows:

[0083] The potential energy U(θ t ) or any position component θ t，i Unified as y t,k , k=1,…,K,where k represents the kth Markov chain; the following adaptive estimators are established for the above D+1 variables (1 potential variable and D position components), and the exponential decay rates β1, β2∈[0,1) of the estimation process are set, which can be set to (β1, β2)=(0.99,0.998); the call count variable t′ with an initial value of 0 is built-in; the initial values ​​of the estimated results of the first two moments are m0=0, in When the input is potential energy, When the input is a position component, it is acceptable Or roughly estimate based on the training estimate, test structure difference and test data volume difference; then the adaptive estimation method in step 4.6 is specifically:

[0084] Step 4.6.1, update the number of calls t′=t′+1;

[0085] Step 4.6.2. Calculate the mean input

[0086] Step 4.6.3: Update the first-order moment estimate

[0087] Step 4.6.4. Calculate the unbiased estimate of the first moment If it is training mode and the input is position component, the robust correction of the prior initial value is adopted Otherwise, use the deinitialization to completely correct

[0088] Step 4.6.5: If t′=1, let

[0089] Step 4.6.6. Calculate the variance attenuation term

[0090] Step 4.6.7. Calculate the variance input

[0091] Step 4.6.8: Update the second-order central moment estimate

[0092] Step 4.6.9: Calculate the unbiased estimate of the second-order central moment If the input is a position component, the robust correction of the a priori initial value is adopted Otherwise, use the deinitialization to completely correct

[0093] Step 4.6.10, Output required variables: If the input is position component θ t,i , then the output is the posterior standard deviation estimate of the corresponding dimension parameter Otherwise, output the mean and standard deviation estimates of the potential energy U(θ) and

[0094] The step 4.8 is specifically as follows:

[0095] The discrete dynamics simulation process in step 4.8 can be simulated by using the improved forward Euler discretization method. Diffusion process; the simulation process under the control of the meta-sampling strategy is specifically as follows:

[0096] Step 4.8.1: Use the sampling strategy learned by the neural network to input the current sample information and Cate i , both are z t =(θ t , p t ) function), calculate the matrix Q(z t ) and D(z t ), that is, The elements are Calculated from the output of the neural network, where c1 and c2 are two small positive numbers, the default value is 10 -5 , ensuring that all diagonal elements are always positive;

[0097] Step 4.8.2: Update particle momentum Where η is the sampling algorithm step size, which is taken by default as represents a normal distribution with mean μ and covariance ∑; for any vector z and matrix A(z), define

[0098] Step 4.8.3, input the updated sample information of particle momentum ( p t+1，i and Cate i , both function), calculates the matrix The diagonal elements of The elements are

[0099] Step 4.8.4: Update particle position Thus we get a new sample z t+1 =(θ t+1 , p t+1 ).

[0100] The structural system identification method based on Bayesian updating and adaptive meta-learning sampling method proposed in the present invention, by proposing an adaptive meta-learning sampling method, on the basis of the detailed probability distribution identification result of Bayesian updating, utilizes the refined strategy learning ability of neural network to improve sampling efficiency, and utilizes adaptive meta-learning design to save neural network training time, so that the method is applicable to more complex structural system identification problems, thereby better serving the field of structural health detection.

[0101] Example

[0102] Combination Figure 3-Figure 5 , for the acceleration response of three multi-story shear structures with different numbers of floors under earthquake excitation, the structural system identification method based on Bayesian updating and adaptive meta-learning sampling method of the present invention is used to identify the structural system. The number of floors of the three multi-story buildings is 5, 2 and 10 respectively. Each building provides a working condition to form three tasks. The structural system identification of the present invention is carried out in turn. The overall implementation plan is as follows: Figure 3 shown.

[0103] The structural system identification method based on Bayesian updating and adaptive meta-learning sampling method in the present invention is used to perform structural system identification:

[0104] The step 1 is specifically as follows: acceleration sensors are arranged on the ground layer, first floor slab and roof of three multi-layer shear structures with 5 floors, 2 floors and 10 floors, and acceleration data of 3 seconds, 1 second and 10 seconds are collected from the 5-story, 2-story and 10-story buildings respectively to form three working conditions, with a sampling frequency of 100 Hz. The measured data are as follows: Figure 4 As shown;

[0105] The step 2 is specifically as follows: when executing the first working condition task, if there is no saved adaptive meta-learning sampler trained for the same structure, then the step 3 is entered; when executing the next two working condition tasks, if there is a saved adaptive meta-learning sampler trained for the same structure, then the step 5 is entered directly;

[0106] Specifically, Step 3 is as follows: After comprehensively considering computing power, time consumption, and structural representativeness, a 5-layer shear structure is modeled as the training structure. Using the numerical simulation method, the acceleration measurement data of 3 measuring points, namely the ground layer, the first-floor slab, and the roof, within 3 seconds under ground motion excitation are obtained from the training structure;

[0107] Specifically, Step 4 is as follows: Based on the measurement data of the training structure and the Bayesian update method, the adaptive meta-learning sampling method is run, the training mode is enabled, and 64 Markov chains are run in parallel. An artificial neural network with 10 units in each of the 3 hidden layers is selected. After each layer and the output, the ReLU activation function is used to make the network output non-negative. The total number of simulation steps is taken as N = 90000, and the adaptive adjustment stage is 500 < t < 45000. In the loss function, T T = 15, M = 3, the adaptive estimation exponential decay rate is set to (β1, β2) = (0.99, 0.998), and the initial value of the adaptive estimation of the second-order central moment of the position component takes the variance of the corresponding dimension of the prior distribution p(θ), and finally the trained adaptive meta-learning sampler is obtained and saved.

[0108] Specifically, Step 5 is as follows: Based on the measurement data of the target structure and the Bayesian update method, the adaptive meta-learning sampling method is run. Using the trained adaptive meta-learning sampler, the training mode is turned off, and 32 Markov chains are run in parallel. The total number of simulation steps is taken as N = 9000, the warm-up stage is set to t < 3000, the adaptive adjustment stage is 300 < t < 2800, the adaptive estimation exponential decay rate is set to (β1, β2) = (0.99, 0.998), and the initial value of the adaptive estimation of the second-order central moment of the position component is roughly estimated according to the training estimated value and the differences in the test structure and data volume. Finally, samples that follow the joint posterior distribution of the structural parameters are obtained, which represent the joint probability distribution of each parameter, that is, structural system identification is achieved. The two-dimensional projections of the samples in some parameter directions are as shown in Figure 5 the rightmost column.

[0109] Using the classical Hamiltonian Monte Carlo (HMC) sampling method to replace the adaptive meta-learning sampling method in the present invention as a control, the above three tasks are performed on the same computing device. The two-dimensional projections of the obtained samples in the corresponding directions are as shown in Figure 5 the leftmost column. It can be seen that the sample distributions obtained by the two methods are basically the same.

[0110] In the above embodiments, the number of valid samples obtained for each task can be counted according to the autocorrelation function of the obtained samples, thereby calculating the sampling efficiency. In the above-mentioned 5-story, 2-story and 10-story building system identification tasks, the average number of valid samples obtained per chain per hour by the method proposed in the present invention is 602.4, 1932.6 and 201.1, respectively, while under the same computing equipment, the sampling efficiencies of the HMC sampling method are 184.4, 793.3 and 43.0, respectively. Therefore, the sampling efficiency of the structural system identification method proposed in the present invention is 3.2, 2.4 and 4.6 times that of the HMC method in the three tasks, respectively, and only one training is required for the three tasks with different numbers of floors and different data volumes, or even more subsequent similar tasks, which effectively improves the practicability of the structural system identification method and is suitable for actual engineering applications.

[0111] The present invention proposes a structural system identification method based on Bayesian updating and adaptive meta-learning sampling method. The method first determines whether there is an adaptive meta-learning sampler adapted to the specific structural system identification task based on task data. If not, an adaptive meta-learning sampler adapted to the task is trained. Finally, the trained sampler is used to execute the adaptive meta-learning sampling method based on Bayesian updating to achieve efficient sampling and complete the structural system identification task. The adaptive meta-learning sampling method first adopts a neural network enhanced sampling method to finely adjust the sampling strategy for specific problems and significantly improve the sampling efficiency; secondly, according to the characteristics of various posterior probability distributions in the Bayesian updating problem of the structural dynamics model, an adaptive meta-learning architecture is designed to save a lot of neural network training time; finally, the loss function and its back-propagation gradient flow design are optimized to make it more suitable for network training in the Markov chain environment, ensuring the stability and efficiency of the algorithm training process. By proposing an adaptive meta-learning sampling method, the present invention uses the refined strategy learning ability of the neural network to improve the sampling efficiency on the basis of the detailed probability distribution identification results of Bayesian updating, and uses the adaptive meta-learning design to save the neural network training time, so that the method is applicable to more complex structural system identification problems, thereby better serving the field of structural health detection.

[0112] The present invention proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the structural system identification method based on Bayesian updating and adaptive meta-learning sampling method are implemented.

[0113] The present invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the structural system identification method based on Bayesian updating and adaptive meta-learning sampling methods.

[0114] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0115] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0116] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in conjunction with the embodiment of the present application can be directly embodied as a hardware processor for execution, or a combination of hardware and software modules in a processor for execution. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it is not described in detail here.

[0117] It should be noted that the processor in the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiment can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor can be combined and performed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0118] The above is a detailed introduction to the structural system identification method based on Bayesian updating and adaptive meta-learning sampling method proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A structural system identification method based on Bayesian updating and adaptive meta-learning sampling method, characterized in that: The method comprises the following steps: Step 1: Arrange vibration sensors on the target structure to obtain the measurement data of the vibration index of each measuring point over a period of time; Step 2: Find out whether there is a saved adaptive meta-learning sampler trained for the same structure. If yes, go to step 5, otherwise go to step 3. Step 3: According to the parameter types of the target structure, a training structure of the same scale with similar parameters is modeled, and the vibration response measurement data of multiple measuring points of the similar structure simplified by the target structure is obtained by numerical simulation or scaled experimental method; Step 4: Based on the measured data of the training structure and the Bayesian update method, run the adaptive meta-learning sampling method, start the training mode, obtain and save the trained adaptive meta-learning sampler; Step 5: Based on the measurement data of the target structure and the Bayesian update method, run the adaptive meta-learning sampling method, use the trained adaptive meta-learning sampler, turn off the training mode, obtain samples that obey the joint posterior distribution of the structural parameters, and characterize the joint probability distribution of each parameter, that is, realize structural system identification; The adaptive meta-learning sampling process based on the Bayesian updating method in step 4 and step 5 is specifically as follows: The adaptive meta-learning sampling process based on the Bayesian updating method in step 4 and step 5 is based on the Bayesian theorem, according to the structural parameter prior probability distribution p(θ) obtained from the known information and the measured data The likelihood function obtained The Markov chain is used to simulate the process of multiple parameter sample points that obey the posterior probability distribution of structural parameters, where is the structural model parameter, and its dimension D is the number of parameters. K Markov chains can be selected to run in parallel according to the computational efficiency requirements and the performance limitations of the computing equipment. The simulation process of the sampling method is specifically as follows: Step 4.

1. Define potential energy where c * An arbitrary constant for ease of calculation; Step 4.2: If there is a trained adaptive meta-learning sampler, use the neural network directly Otherwise, two artificial neural networks with positive outputs are selected. Used to construct the curl matrix sub-block in the adaptive meta-learning sampler in the subsequent steps and diffusion matrix sub-blocks The network parameterization architecture is constructed and its network parameters are randomly initialized, where the non-diagonal elements of the two sub-block matrices Q(z) and D(z) are zero, and the diagonal elements are calculated and determined according to the output of the neural network in subsequent steps; Step 4.3: Each chain randomly generates an initial sample z0 = (θ0, p0) according to the prior distribution p(θ), where the model parameter θ is regarded as the position of a particle in the D-dimensional space in the subsequent simulation, and the auxiliary variable is regarded as the momentum of the particle and follows a standard normal distribution, thus augmenting the vector is called the state variable of the particle, let t = 0, t0 = 0; Step 4.4: When t < N, repeat Steps 4.5 to 4.

11. Each repetition will simulate a new sample z t =(θ t , p t ), and the total number of simulation steps N is taken as N = 9000; t+1 =(θ t+1 , p t+1 ). Step 4.5: Get the current sample information, including potential energy U(θ t ), position θ t , momentum p t and potential energy gradient The position component, momentum component, potential energy gradient component and corresponding parameter category of the particle in the i-th dimension are denoted as θ t,i 、p t,i , and Catei, i=1,…,D; Step 4.6: If the sampling process is in the adaptive adjustment stage, according to the potential energy U(θ t ) and each position component θ t,i ,i=1,…,D, respectively update the first two moments μ of the potential energy U(θ) U and σ U Adaptive estimation of and the standard deviation of each dimension of the posterior distribution of parameters σ i ,i=1,…,adaptive estimation of D; Step 4.7: Calculate the normalized potential energy and each normalized potential energy gradient component Step 4.8: Enter the current sample information. p t,i , and Cate i , calling the neural network The learned meta-sampling strategy, under the control of this strategy The diffusion process is simulated by discrete dynamics to obtain a new sample z t+1 =(θ t+1 ,p t+1 ); Step 4.9, order t = t +1; Step 4.10: If it is training mode, create z t A new copy of is used for subsequent computations to stop the gradient flow; Step 4.11: If it is training mode and t can be T T Divide and calculate the loss function And back propagate to update the neural network parameters, let t0 = t, set T T =15, M=3, where For sample Approximate estimated sample probability density function; Step 4.12: If it is training mode, save the adaptive meta-learning sampler, otherwise output all samples after the warm-up phase.

2. The method according to claim 1, characterized in that The vibration indicators include acceleration, velocity, displacement and strain.

3. The method according to claim 1, characterized in that The adaptive adjustment stage in step 4.6 should be in the warm-up stage of the sampling process, and the warm-up stage is set to t<3000, and the adaptive adjustment stage is set to 500. <t<2800。 4. The method according to claim 3, characterized in that The potential energy U(θ t ) or any position component θ t,i Unified as y t,k ,k=1,…,K, where k represents the kth Markov chain; adaptive estimators are established for the above 1 potential variable and D position components, i.e., D+1 variables, and the exponential decay rates β1,β2∈[0,1) of the estimation process are set; the call count variable t' with an initial value of 0 is built-in; the initial values ​​of the estimated results of the first two moments are m0=0, in When the input is potential energy, When the input is a position component, it is acceptable Or a rough estimate based on training estimates, test structure differences, and test data size differences.

5. The method according to claim 4, characterized in that The adaptive estimation method in step 4.6 is specifically as follows: Step 4.6.1, update the number of calls t'=t'+1; Step 4.6.

2. Calculate the mean input Step 4.6.3: Update the first-order moment estimate Step 4.6.

4. Calculate the unbiased estimate of the first moment If it is training mode and the input is position component, the robust correction of the prior initial value is adopted Otherwise, use the deinitialization to completely correct Step 4.6.5: If t' = 1, then let Step 4.6.

6. Calculate the variance attenuation term Step 4.6.

7. Calculate the variance input Step 4.6.8: Update the second-order central moment estimate Step 4.6.9: Calculate the unbiased estimate of the second-order central moment If the input is a position component, the robust correction of the priori initial value is adopted Otherwise, use the deinitialization to completely correct Step 4.6.10, Output required variables: If the input is position component θ t,i , then the output is the posterior standard deviation estimate of the corresponding dimension parameter Otherwise, output the mean and standard deviation estimates of the potential energy U(θ) and 6. The method according to claim 5, characterized in that The step 4.8 is specifically as follows: The discrete dynamics simulation process in step 4.8 uses an improved forward Euler discretization to simulate the Diffusion process; the simulation process under the control of the meta-sampling strategy is specifically as follows: Step 4.8.1: Use the sampling strategy learned by the neural network and input the current sample information. p t,i , and Cate i , both are z t =(θ t ,p t ) function, calculate the matrix Q(z t ) and D(z t ), that is, The elements are It is calculated from the output of the neural network, where c1 and c2 are two positive constants, ensuring that each diagonal element is always positive; Step 4.8.2: Update particle momentum Where η is the sampling algorithm step size; represents a normal distribution with mean μ and covariance ∑; for any vector z and matrix A(z), define Step 4.8.3, input the updated sample information of particle momentum p t+1,i and Cate i , both Function, calculate the matrix The diagonal elements of The elements are Step 4.8.4: Update particle position Thus we get a new sample z t+1 =(θ t+1 ,p t+1 ).

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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