Structural damage system identification method based on physical consistent neural network

Abstract

The invention relates to a structural damage system identification method based on a physical consistent neural network, and solves the problems that a current system identification method based on physics is limited in generalization performance and insensitive to local loss. The method comprises the following steps: 1, collecting target building information and monitoring data; 2, establishing a physical consistent neural network; 3, constructing a network training data set; 4, carrying out physical consistent neural network training; and 5, obtaining structure parameters of inversion. According to the method, the similarity between the Timoshenko beam theory and the neural network principle is utilized, the physical consistent neural network is established, each parameter in the network has strict physical significance, and the interpretability and generalization performance of the network are greatly enhanced; and meanwhile, priori knowledge constraints are added in a loss function, so that the uncertainty and difficulty of inversion are obviously reduced.

Description

Technical Field

[0001] The invention relates to the field of earthquake engineering, and in particular to a structural damage system identification method based on a physical consistent neural network. Background Art

[0002] Structural health monitoring (SHM) typically involves deploying multiple sensors on a structure to measure its response in real time. By analyzing the recorded waveforms, the dynamic characteristics of the structure can be identified, enabling early detection of potential damage and rapid assessment of structural damage after natural or man-made disasters such as earthquakes and explosions. However, accurately identifying dynamic characteristics from the measured response data is a challenging task. Missing identification may lead to an erroneous assessment of the structural health status, failure to detect and repair damage in a timely manner, and thus endangering the safety of the structure. Conversely, false positives about structural damage may lead to unnecessary repairs, increased costs, and construction risks. Therefore, it is crucial to develop a reliable, damage-sensitive and accurate system identification method.

[0003] Numerous system identification methods have been developed and can be broadly classified into two categories: vibration-based methods and wave propagation methods. The vibration-based methods are the most widely studied and involve extracting the modal properties of the structure, such as natural frequencies, damping ratios, and mode shapes, from the measured acceleration records using various modal analysis techniques. By identifying the changes in these modal properties due to damage, the structural health can be monitored. While these methods are very effective in identifying damage that affects the overall stiffness of the structure, they may not detect localized damage because such damage has no significant effect on global properties such as natural frequencies and mode shapes. Wave propagation methods address this issue well because waves are very sensitive to localized damage during propagation. Localized damage can significantly change the velocity, attenuation, reflection, and scattering characteristics of the wave. By finely analyzing these changes in the wave propagation characteristics, localized damage can be accurately located and assessed. Another significant advantage of wave propagation methods is their insensitivity to soil-structure interaction effects, which holds true even in the case of more extensive foundation sway and coupled horizontal and sway responses.

[0004] Wave propagation methods consider the seismic response of a structure as a superposition of waves propagating in the structure, which reflect from the boundaries of the structure and interfere with each other. These methods, also known as seismic interferometry, usually assume that the structure is a shear beam and use wave velocity to characterize the structure. Wave velocity can be identified by deconvolution, a key step of which is to monitor the peaks of the impulse response function (IRF) between the signals recorded by different sensors. However, some scholars have confirmed that the accuracy of identification by monitoring these peaks alone is limited. Therefore, they proposed an identification algorithm based on least squares fitting of the IRF, which significantly improved the accuracy of identification. In addition, considering that the shear beam assumption ignores the contribution of bending deformation to the response, they first proposed a wave propagation method based on Timoshenko beam theory for identifying high-rise buildings, which further improved the identification accuracy.

[0005] In recent years, deep learning has been widely used in the field of system identification due to its excellent nonlinear fitting and feature extraction capabilities. These deep learning methods can be divided into two categories: data-driven methods and physics-based methods. The former assumes that the mechanism model is unknown and aims to use neural network models to approximate the input-output relationship of the structural system without involving the actual physical parameters of the system. These methods avoid the high computational cost and numerical problems caused by building and verifying structural numerical models. In addition, they can automatically adapt to the uncertainties caused by measurements. However, data-driven methods face two major challenges: (1) a large amount of data is required for network training, and insufficient data increases the possibility of overfitting, thereby reducing the generalization performance of the model; (2) the trained network model is a "black box" and lacks sufficient physical interpretability. To address these problems, scholars have proposed various physics-based methods. These methods involve establishing a representative physical model of the structure and introducing a physics-guided loss function during the network training process. The loss function is in the form of the residual of the governing equation corresponding to the physical model. The parameters of the physical model can be updated by minimizing the difference between the network prediction and the measured data. However, the network model itself still lacks physical interpretability and still faces the challenge of limited generalization performance. Furthermore, these physics-based approaches typically consider the seismic response of the structure as a vibration problem rather than a wave propagation problem and thus face the same challenge of being insensitive to local losses. Summary of the invention

[0006] The purpose of the present invention is to solve the problems of limited generalization performance and insensitivity to local losses in current physics-based system identification methods, and propose a physically consistent neural network to achieve system identification more efficiently and reliably.

[0007] The embodiment of the present application provides a method for identifying a structural damage system based on a physically consistent neural network. The method for identifying a structural damage system based on a physically consistent neural network is characterized by comprising the following steps:

[0008] Step 1: Collect target building information and monitoring data:

[0009] Collect detailed geometric dimensions and spatial layout information of the target building and historical acceleration responses recorded by acceleration monitors arranged in the target building;

[0010] Step 2: Establish a physically consistent neural network:

[0011] The physically consistent neural network is consistent with the cantilever layered Timoshenko beam theory, and is composed of an input layer, an output layer, and n hidden layers, wherein n corresponds to the number of layers in the cantilever layered Timoshenko beam model; the parameters of the physically consistent neural network are related to the parameters of the Timoshenko model, and the input and output of the physically consistent neural network are the Fourier spectra corresponding to the horizontal acceleration responses of the top and bottom floors of the building, respectively;

[0012] Step 3: Build a network training data set:

[0013] The amplitude of each frequency component is calculated by using discrete Fourier transform for the historical acceleration response recorded by the acceleration monitor arranged in the target building collected in step 1;

[0014] Step 4: Conduct physically consistent neural network training:

[0015] The loss function used to guide network training consists of data loss and physical constraint loss; data loss is defined as follows:

[0016]

[0017] in, and denote the sth element in the observed and predicted non-top acceleration response Fourier spectra, respectively; M denotes the total number of elements in these Fourier spectra; R(·) and Ι(·) denote real and imaginary part operations, respectively;

[0018] The physical constraint loss is defined as follows:

[0019]

[0020] in, and are the shear wave velocity V S,j and modulus ratio R j The lower bound of the search space; ReLU(·) represents the rectified linear unit function;

[0021] The final loss function is:

[0022] L all =λ1 ×L PC +λ 2 ×L data Formula (29)

[0023] Among them, λ 1 and λ 2 is the weight factor;

[0024] Step 5: Obtain the inverted structural parameters:

[0025] Since the parameter weights of the physically consistent neural network PCNN are related to the shear wave velocity V S Related to the modulus ratio R, when the PCNN training is completed, the shear wave velocity V of each layer of the Timoshenko beam model is obtained through the network parameters S and modulus ratio R.

[0026] 2. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that the specific method of establishing the physically consistent neural network in step 2 is:

[0027] The building is modeled as a cantilevered layered Timoshenko beam with its base subjected to horizontal earthquake motion u g The model contains n layers, the number of which is equal to the number of horizontal acceleration monitors arranged on the building minus one; each layer of the model is assumed to be uniform and isotropic, and adjacent layers are fully bonded; the layers of the model are numbered from top to bottom, and their geometric properties are determined by the cross-sectional area A j , second-order moment of inertia I j , height H j , Width W j and the shear correction factor k G,j Characterization, where j = 1, ..., n represents the index of each layer; the shear correction factor k G The non-uniform distribution of shear stress on the cross section is taken into account; the material properties of each layer are determined by the mass density ρ j , Young's modulus E j and shear modulus G j Characterized by mass density ρ j , longitudinal wave velocity V L,j and shear wave velocity V S,j characterization; the relationship between modulus and wave velocity is defined as and The damping adopts the Kelvin-Voigt material model and assumes that the bending and shear deformations have the same viscosity constant μ j ;

[0028] The cross section of the beam is perpendicular to the neutral axis before deformation and remains in a plane after deformation; however, due to shear deformation, the deformed cross section is no longer perpendicular to the deformation axis; the neutral axis of the beam is assumed to undergo only horizontal displacement, represented by u(z, t); the total rotation of the beam consists of two components: the rotation θ(z, t) caused by bending deformation and the rotation γ(z, t) caused by shear deformation; M(z, t) and V(z, t) represent bending moment and shear force, respectively;

[0029] Under the small deformation assumption, any layer in the above layered model is applicable to formula (1):

[0030]

[0031] Substituting the Kelvin-Voigt material model into formula (1) yields formula (2):

[0032]

[0033] According to the force, the dynamic equation shown in formula (3) can be obtained:

[0034]

[0035] By combining formula (2) and formula (3), the following results can be derived, as shown in formula (4)-formula (7):

[0036]

[0037]

[0038]

[0039]

[0040] Assuming that the load is simple harmonic excitation, the displacement u(z, t), angle θ(z, t), bending moment M(z, t) and shear force V(z, t) can be expressed by formula (8) and formula (9):

[0041] u(z,t)=U(z)e -iωt , θ(z,t)=θ(z)e -iωt Formula (8)

[0042]

[0043] Where ω is the circular frequency. Substituting formula (8) and formula (9) into formula (4)-formula (7), we obtain formula (10):

[0044]

[0045] in, represents the state vector, and the matrix B is defined as:

[0046]

[0047] According to the propagation matrix theory, if the matrix B is a continuous function of z (which is true in each layer), then the state vector f(z) at a specific point in the same layer can be calculated using formula (11). 0 ) Calculate the state vector f(z) at any point:

[0048] f(z)=P(z,z 0 )f(z 0 ) Formula (11)

[0049] Among them, P(z,z 0 ) is from z 0 The propagation matrix from z to z; According to the general solution form of the ordinary differential equation given in formula (10), the form of the propagation matrix can be defined as shown in formula (12):

[0050]

[0051] Among them, e (·) represents the matrix exponential function; given that the state vector must be continuous between adjacent layers, any interface z starting from the top j The state vector at can be determined as formula (13):

[0052]

[0053] For a cantilever beam, the free end (top) must satisfy the condition of zero stress, which means that the shear force and bending moment are both zero at this point; the bottom of the beam is the fixed end, so the rotation angle must be zero; Based on these conditions, the following formula can be derived:

[0054] f(z 0 )=[U 0 ,Θ 0 ,0,0] T Formula (14)

[0055]

[0056] Five of the physical quantities are non-zero; assuming that U 0 is a known quantity, and this assumption is applicable to the system identification task; then, the other four quantities can be calculated according to formula (13); the solution process is divided into two main steps, first determining the rotation angle Θ0 of the top; let us assume that:

[0057]

[0058] It can be deduced that:

[0059]

[0060] in, Representation Matrix The element in the pth row and qth column of 0 It can be deduced as:

[0061]

[0062] According to formula (18), the state vector f(z 0 ); Then, according to formula (13), the state vector at any interface can be obtained starting from the top;

[0063] Let u(z ref ,t) represents the reference point z ref The motion at the coordinate point z and the reference point z ref The transfer function between can be expressed as:

[0064]

[0065] To improve numerical stability and avoid division by very small numbers, the transfer function is often regularized as follows:

[0066]

[0067] Among them, the horizontal bar represents the complex conjugate, and η represents the regularization parameter;

[0068] For a neural network with L+1 layers, the relationship between the lth layer and the (l+1)th layer can be expressed as formula (21):

[0069] z l =σ l (W l ·z l-1 +b l ), l=1,...,L Formula (21)

[0070] Among them, z 0 and z L Represent the input and output of the network respectively, W l and b l Respectively represent the trainable weight matrix and bias vector of the lth layer; function σ l (·) is the nonlinear activation function of layer l;

[0071] A physically consistent neural network is established, which consists of an input layer, an output layer and n hidden layers, where n corresponds to the number of layers in the cantilever layered Timoshenko beam model; each hidden layer contains 4 neurons, which is equal to the number of elements in each state vector; the output of the lth hidden layer corresponds to the state vector at the top of the lth layer in the Timoshenko beam model; a post-processing layer is added after the output layer to connect the displacement output U(zj) of each network layer starting from the second hidden layer in order to calculate the subsequent loss function;

[0072] According to formula (18), the weight matrix of the first hidden layer of the physically consistent neural network can be derived as:

[0073]

[0074] The weight matrices of other hidden layers can be derived according to formula (16) as follows:

[0075] W j =P(z j-1 ,z j-2 ) Formula (23)

[0076] Among them, the value range of j is 2 to n; similarly, the weight matrix of the output layer can be derived as follows:

[0077] W n+1 =p 1 (z n ,z n-1 ) T Formula (24)

[0078] Among them, p 1 (z n ,z n-1 ) represents the propagation matrix P(z n ,z n-1 ), the superscript T indicates the transpose operation.

[0079] 3. The structural damage system identification method based on physically consistent neural network according to claim 2 is characterized in that the specific method of constructing the network training data set in step 3 is:

[0080] For a (digitized) acceleration record containing m equally spaced element values, the decomposition is as follows:

[0081]

[0082] Among them, ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ωs The complex Fourier amplitude of the acceleration response of the top floor of the building is used to construct the input data set, and the amplitude of the corresponding frequency components of the acceleration response of the remaining floors is used to construct the label data set.

[0083] 4. The structural damage system identification method based on physically consistent neural network according to claim 3 is characterized in that a in formula (25) s and b s Calculated by formula (30) and formula (31) respectively:

[0084]

[0085]

[0086] 5. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that in step 4, in the actual physical scene, the shear wave velocity V of each layer S,j and modulus ratio R j The following relationship must be satisfied:

[0087] V S,j >0, R j >0 Formula (27)

[0088] The value of j ranges from 1 to n.

[0089] 6. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that in step 4, the Adam optimizer and the learning rate decay strategy are used for training, and the shear wave velocity V S The initial learning rates of and modulus ratio R are set to 100 and 10-5 respectively. The learning rate decays to 0.1 times of the original every 50 training rounds, and the total number of training rounds is 150.

[0090] The beneficial effects of the present invention are as follows: the present invention utilizes the similarities between Timoshenko beam theory and neural network principles to build a physically consistent neural network, in which each parameter has a strict physical meaning, greatly enhancing the interpretability and generalization performance of the network; at the same time, prior knowledge constraints are added to the loss function, which significantly reduces the uncertainty and difficulty of inversion, and provides strong technical support for system identification.

[0091] Compared with the current physics-based system identification method, the system identification method based on the physically consistent neural network of the present invention has clear physical meaning and strong generalization performance, and at the same time has the advantage of being sensitive to local losses. Therefore, it is better in usability and more convenient and quick in actual use. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Schematic diagrams related to Timoshenko beams: (A) cantilever layered Timoshenko beam model representing a building; (B) geometric shape of the deformed micro-beam unit; (C) force diagram of the micro-beam unit.

[0093] Figure 2 The structure of the proposed PCNN. The orange circles represent input neurons, the green circles represent output neurons, and the other blue circles represent hidden neurons. The symbol inside each circle represents the output value of the corresponding neuron. The post-processing layer generates the final output by connecting the displacement output U(zj) from each network layer, starting from the second hidden layer.

[0094] Figure 3 54-story office building in downtown Los Angeles, California: (A) photo, (B) west-east elevation, (C) floor plan with speed monitoring equipment.

[0095] Figure 4 The location of the 54-story office building (marked by a triangle with coordinates 61.21528°N and 149.89296°W) and the epicenters of the five selected earthquakes (marked by circles).

[0096] Figure 5 are the shear wave velocity VS of each layer identified from the five earthquake events, and the corresponding bending stiffness EI and shear stiffness GA.

[0097] Figure 6 Figure 2. (a) Mean values ​​of shear wave velocity VS, bending stiffness EI and shear stiffness GA identified from five earthquake events, and (b) distribution diagram of the corresponding coefficient of variation (CV).

[0098] Figure 7 Comparison of the transfer functions (between roof and ground response) of the identified Timoshenko beam model with the observed transfer functions for five earthquake events. DETAILED DESCRIPTION

[0099] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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.

[0100] A structural damage system identification method based on physically consistent neural network is implemented in the following steps:

[0101] Step 1: Collect target building information and monitoring data:

[0102] Collect detailed geometric dimensions and spatial layout information of the target building, as well as the historical acceleration responses recorded by acceleration monitors arranged in the target building.

[0103] In this embodiment, the target building selected is a 54-story office building located in downtown Los Angeles, California. Figure 3 As shown, the building has 54 above-ground floors (210.2 meters) and 4 basement floors (14.0 meters). Its plan shape is rectangular with two rounded corners. The dimensions of the building are 196 feet × 121 feet (59.7 meters × 36.9 meters) before the 36th floor, 176 feet × 121 feet (53.6 meters × 36.9 meters) between the 36th and 46th floors, and 156 feet × 121 feet (47.5 meters × 36.9 meters) above the 46th floor to the top floor. The horizontal acceleration responses in the south-north direction of each floor of the building were collected during five earthquake events with magnitudes between 6.4 and 7.3 from 1992 to 2010. The epicenters are shown in Figure 1. Figure 4 shown.

[0104] Step 2: Establish a physically consistent neural network:

[0105] The physically consistent neural network is consistent with the theory of cantilever layered Timoshenko beam (hereinafter referred to as Timoshenko beam), and consists of an input layer, an output layer and n hidden layers, where n corresponds to the number of layers in the cantilever layered Timoshenko beam model. The parameters of the physically consistent neural network are related to the parameters of the Timoshenko model, and its input and output are the Fourier spectra corresponding to the horizontal acceleration responses of the top and bottom floors of the building, respectively.

[0106] (1) Cantilever layered Timoshenko beam model

[0107] The building is modeled as a cantilevered layered Timoshenko beam with its base subjected to horizontal earthquake motion u g ,like Figure 1 The model consists of n layers, which is equal to the number of horizontal acceleration monitors arranged on the building minus one. Each layer of the model is assumed to be uniform and isotropic, and adjacent layers are fully bonded. The layers of the model are numbered from top to bottom, and their geometric properties are determined by the cross-sectional area A. j , second-order moment of inertia I j , height H j , Width W j and the shear correction factor kG,j Here, j = 1, ..., n represents the index of each layer. Shear correction factor k G The non-uniform distribution of shear stress on the cross section is taken into account. The material properties of each layer are given by the mass density ρ j , Young's modulus E j and shear modulus G j Characterized by mass density ρ j , longitudinal wave velocity V L,j and shear wave velocity V S,j The relationship between modulus and wave velocity is defined as and The damping adopts the Kelvin-Voigt material model and assumes that the bending and shear deformations have the same viscosity constant μ j .

[0108] The Timoshenko beam theory takes into account not only bending deformation but also rotational inertia and shear deformation. Figure 1 (B) shows the geometry of a deformed tiny beam element at coordinate z. The cross section of the beam is perpendicular to the neutral axis before deformation and remains flat after deformation. However, due to shear deformation, the deformed cross section is no longer perpendicular to the deformation axis. The neutral axis of the beam is assumed to be only horizontally displaced, denoted by u(z,t). The total rotation of the beam consists of two components: the rotation θ(z,t) due to bending deformation and the rotation γ(z,t) due to shear deformation. Figure 1 (C) in the figure depicts the force diagram of the micro-beam unit at coordinate z, and the dotted line represents the inertia force. In this figure, M(z,t) and V(z,t) represent the bending moment and shear force respectively.

[0109] (2) Control equations and their analytical solutions

[0110] Under the small deformation assumption, any layer in the above layered model is applicable to formula (1):

[0111]

[0112] The layer index j is omitted here for simplicity. Substituting the Kelvin-Voigt material model into formula (1) yields formula (2):

[0113]

[0114] according to Figure 1 From the force diagram in (C), we can get the dynamic equation shown in formula (3):

[0115]

[0116] By combining formula (2) and formula (3), the following results can be derived, as shown in formula (4)-formula (7):

[0117]

[0118]

[0119]

[0120]

[0121] Assuming that the load is simple harmonic excitation, the displacement u(z, t), angle θ(z, t), bending moment M(z, t) and shear force V(z, t) can be expressed by formula (8) and formula (9):

[0122] u(z,t)=U(z)e -iωt , θ(z,t)=θ(z)e -iωt Formula (8)

[0123]

[0124] Where ω is the circular frequency. Substituting formula (8) and formula (9) into formula (4)-formula (7), we get formula (10):

[0125]

[0126] in, represents the state vector, and the matrix B is defined as:

[0127]

[0128] According to the propagation matrix theory, if the matrix B is a continuous function of z (which is true in each layer), then the state vector f(z) at a specific point in the same layer can be calculated using formula (11). 0 ) Calculate the state vector f(z) at any point:

[0129] f(z)=P(z,z 0 )f(z 0 ) Formula (11)

[0130] Among them, P(z,z 0 ) is from z 0 According to the general solution form of ordinary differential equations given in formula (10), the form of the propagation matrix can be defined as shown in formula (12):

[0131]

[0132] Among them, e(·) represents the matrix exponential function. Given that the state vector must be continuous between adjacent layers, any interface z starting from the top j The state vector at can be determined as formula (13):

[0133]

[0134] For a cantilever beam, the free end (top) must satisfy the condition of zero stress, which means that the shear force and bending moment are both zero at this point. The bottom of the beam is the fixed end, so the rotation angle must be zero. From these conditions, the following formula can be derived:

[0135] f(z 0 )=[U 0 ,Θ 0 ,0,0] T Formula (14)

[0136]

[0137] Five of the physical quantities are non-zero. Assume that U 0 is a known quantity, and this assumption is applicable to the system identification task. Then, the other four quantities can be calculated according to formula (13). The solution process is divided into two main steps. First, the rotation angle Θ0 of the top is determined. Let's assume that:

[0138]

[0139] It can be deduced that:

[0140]

[0141] in, Representation Matrix The element in the pth row and qth column of . Therefore, Θ 0 It can be deduced as:

[0142]

[0143] According to formula (18), the state vector f(z 0 ). Then, according to formula (13), the state vector at any interface can be obtained starting from the top.

[0144] (3) Transfer function

[0145] The transfer function (TF) is a mathematical representation of the relationship between the input and output of a linear time-invariant system in the frequency domain. Let u(z ref ,t) represents the reference point z ref The motion at coordinate point z is different from the motion at reference point z. refThe transfer function between can be expressed as:

[0146]

[0147] To improve numerical stability and avoid division by very small numbers, the transfer function is often regularized as follows:

[0148]

[0149] The horizontal bar represents the complex conjugate and η represents the regularization parameter. The regularization parameter η is taken as U(z ref ,ω) is 0.1%.

[0150] (4) Construction of physically consistent neural networks

[0151] For a neural network with L+1 layers, the relationship between the lth layer and the (l+1)th layer can be expressed as formula (21):

[0152] z l =σ l (W l ·z l-1 +b l ), l=1,...,L Formula (21)

[0153] Among them, z 0 and z L Represent the input and output of the network respectively, W l and b l Represent the trainable weight matrix and bias vector of the lth layer respectively. Function σ l (·) is the nonlinear activation function of layer l, which is crucial for the network to be able to learn complex mappings from input to output.

[0154] Based on the traditional neural network, a physically consistent neural network (PCNN) consistent with the Timoshenko beam theory is proposed. Its structure is as follows: Figure 2 As shown in Figure 2. The network consists of an input layer, an output layer, and n hidden layers, where n corresponds to the number of layers in the cantilever layered Timoshenko beam model. Each hidden layer contains 4 neurons, which is equal to the number of elements in each state vector. The output of the lth hidden layer corresponds to the state vector at the top of the lth layer in the Timoshenko beam model. A post-processing layer is added after the output layer to connect the displacement output U(zj) of each network layer starting from the second hidden layer in order to calculate the subsequent loss function. It should be noted that the activation functions of all layers are set to linear functions, and the bias vectors are fixed to non-trainable zero vectors.

[0155] According to formula (18), the weight matrix of the first hidden layer of the PCNN can be derived as:

[0156]

[0157] The weight matrices of other hidden layers can be derived according to formula (16) as follows:

[0158] W j =P(z j-1 ,z j-2 ) Formula (23)

[0159] Among them, the value range of j is 2 to n. Similarly, the weight matrix of the output layer can be derived as follows:

[0160] W n+1 =p 1 (z n ,z n-1 ) T Formula (24)

[0161] Among them, p 1 (z n ,z n-1 ) represents the propagation matrix P(z n ,z n-1 ), the superscript T indicates the transposition operation. As mentioned above, each parameter in the PCNN has a clear physical interpretation and is related to the structural parameters of the Timoshenko beam model. Therefore, the parameter optimization in network training actually corresponds to the process of inverting the structural parameters. By minimizing the difference between the network output and the target value, PCNN is able to identify the optimal structural parameters.

[0162] Step 3: Build a network training data set:

[0163] The historical acceleration response recorded by the acceleration monitor arranged in the target building collected in step 1 is used to obtain the amplitude of each frequency component by discrete Fourier transform. For the (digital) acceleration record containing m equidistant element values, it is decomposed into the following form:

[0164]

[0165] Among them, ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier amplitude of s and b s Calculated by formula (30) and formula (31) respectively:

[0166]

[0167]

[0168] The input data set is constructed based on the amplitude of each frequency component of the acceleration response of the top floor of the building, and the label data set is constructed using the amplitude of the corresponding frequency components of the acceleration response of the remaining floors.

[0169] Step 4: Conduct physically consistent neural network training:

[0170] The loss function used to guide network training consists of data loss and physical constraint loss. Data loss is defined as follows:

[0171]

[0172] in, and denote the sth element in the observed and predicted non-top acceleration response Fourier spectra, respectively. M denotes the total number of elements in these Fourier spectra. R(·) and Ι(·) denote real and imaginary part operations, respectively.

[0173] In actual physical scenarios, the shear wave velocity V of each layer S,j and modulus ratio R j The following relationship must be satisfied:

[0174] V S,j >0, R j >0 Formula (27)

[0175] Among them, the value range of j is 1 to n. In order to ensure that the identified parameters meet these constraints, in addition to the data loss, a physical constraint loss is introduced to enhance the reliability of the recognition results. The formula is as follows:

[0176]

[0177] in, and R min are the shear wave velocity V S,j and modulus ratio R j The lower limit of the search space is set to 0 in this embodiment. ReLU(·) represents the rectified linear unit function.

[0178] The final loss function of the PCNN is:

[0179] L all =λ 1 ×L PC +λ 2 ×L data Formula (29)

[0180] Among them, λ1 and λ 2 are weight factors, which are set to 1 and 0.001 respectively. By minimizing the final loss function, PCNN can effectively identify structural parameters. The shear wave velocity V of each layer of the Timoshenko beam model during training S The initial values ​​of the modulus ratio R are set to 100 m / s and 0.01 respectively, and the remaining parameters including the density ρ and the viscosity constant μ are assumed to be 300 kg / m 3 Only data in the 0.1-1.7 Hz frequency band is used for training, and the Adam optimizer and learning rate decay strategy are used for training. The shear wave speed V S The initial learning rates of and modulus ratio R are set to 100 and 10-5 respectively. The learning rate decays to 0.1 times of the original every 50 training rounds, and the total number of training rounds is 150.

[0181] Step 5: Obtain the inverted structural parameters:

[0182] Since the PCNN parameter weights are related to the shear wave velocity V S Related to the modulus ratio R, when the PCNN training is completed, the shear wave velocity V of each layer of the Timoshenko beam model is obtained through the network parameters S and modulus ratio R.

[0183] Table 1 summarizes the identification results, showing a high degree of consistency between different earthquake events. S Observation of the cross section shows that V S It does not increase monotonically from the top. Instead, there is an inversion between the second and third layers, that is, V S More than the third layer. In addition, the analysis of the modulus ratio profile shows that the modulus ratio of the first layer is significantly higher than that of other layers. The last two columns of Table 1 show the statistical characteristics of the recognition parameters. It can be seen that the coefficient of variation (CV) of all recognition parameters is less than 6%, indicating that the variability of the recognition results is low. This confirms that the proposed PCNN has excellent robustness.

[0184] Table 1. Parameters identified using the North-South (NS) direction acceleration waveforms (frequency range 0.1-1.7 Hz) of five earthquakes recorded in a 54-story office building.

[0185]

[0186] Figure 5 The shear wave velocity V of each layer is graphically shown. S, bending stiffness EI, and shear stiffness GA, where the histograms are arranged from the bottom to the top in the chronological order of the earthquake events. It can be observed that the VS profile identified from the BigBear earthquake shows a significant decrease compared to the Landers earthquake, indicating that the graphs are arranged from the bottom to the top in the chronological order of the earthquake events. It can be observed that the Big Bear earthquake may have caused a permanent decrease in stiffness compared to the Landers earthquake, which is reflected in both the EI and GA profiles. A similar decrease in VS was also observed after the Northridge earthquake, indicating that this event may have also caused a permanent decrease in stiffness. In contrast, no significant decrease in VS was observed during the last two earthquake events. Further analysis of the EI and GA profiles showed similar trends. In addition, during the Hectormine earthquake, the VS of the third floor was found to be lower than that of the second floor, while the GA of the third floor was higher than that of the second floor. This difference is due to the gradual decrease in the cross-sectional area of ​​the building from the base to the top, resulting in a larger cross-sectional area on the third floor than on the second floor.

[0187] Figure 6 The mean and CV of the shear wave velocity VS profiles identified in five earthquake events are shown, as well as the corresponding bending stiffness EI and shear stiffness GA profiles. It is worth noting that the VS inversion phenomenon between the second and third layers discussed previously also appears in the EI and GA profiles, although the cross-sectional area of ​​the second layer is smaller. A possible explanation for this phenomenon is the unique structural configuration between the 36th and 46th floors, which corresponds to the second layer in the Timoshenko beam model. In addition, by comparing the CV values ​​of the three profiles, it can be found that the CV values ​​of the EI and GA profiles are higher than those of the VS profile, and the variability decreases from top to bottom in general. In addition, the CV values ​​of both stiffness profiles are less than 10%, further verifying the robustness of the proposed PCNN model.

[0188] The dominant frequency of a building can be determined by analyzing the transfer function between the roof and ground responses, as this function will have a peak at the dominant frequency of the building. Figure 7 The transfer functions of the Timoshenko beam model identified from five earthquake events were compared with the transfer functions in the 0.1–1.7 Hz band obtained from the observed responses. It can be seen that the observed transfer functions also show significant peaks at non-dominant frequencies due to the influence of noise. For example, the transfer function of the Calexico earthquake shows a large peak in the 0.25–0.45 Hz band. However, the identified transfer functions still match the observations as a whole, and the identified dominant frequencies are very close to the observations, especially in the Northridge earthquake event.

[0189] Table 2 shows a quantitative comparative analysis of the first two main frequencies identified in the five earthquake events. Since the third to fifth main frequencies are difficult to distinguish in most earthquake events, the analysis was not extended to these frequencies. From the analysis, it can be observed that the first two main frequencies identified in the Northridge earthquake are significantly lower than those in the Lander-Big Bear earthquake sequence, indicating that the Northridge earthquake may have caused damage to the buildings. In contrast, the first two main frequencies identified in the Calexico earthquake are slightly higher than those in the Hector Mine earthquake, which may be attributed to measurement errors or repair work performed before the Calexico event. Table 2 also shows the relative errors between the observed and identified first two main frequencies in the five earthquakes. The maximum relative error does not exceed 7%, further verifying the reliability of the proposed PCNN model.

[0190] Table 2. Observed and identified dominant frequencies in the five earthquake events.

[0191]

[0192] The relative error is defined as the absolute difference between the observed dominant frequency and the identified dominant frequency divided by the observed dominant frequency.

Claims

1. A structural damage system identification method based on physically consistent neural network, characterized in that: The following steps are involved: Step 1: Collect target building information and monitoring data: Collect detailed geometric dimensions and spatial layout information of the target building and historical acceleration responses recorded by acceleration monitors arranged in the target building; Step 2: Establish a physically consistent neural network: The physically consistent neural network is consistent with the cantilever layered Timoshenko beam theory, and is composed of an input layer, an output layer, and n hidden layers, wherein n corresponds to the number of layers in the cantilever layered Timoshenko beam model; the parameters of the physically consistent neural network are related to the parameters of the Timoshenko model, and the input and output of the physically consistent neural network are the Fourier spectra corresponding to the horizontal acceleration responses of the top and bottom floors of the building, respectively; Step 3: Build a network training data set: The amplitude of each frequency component is calculated by using discrete Fourier transform for the historical acceleration response recorded by the acceleration monitor arranged in the target building collected in step 1; Step 4: Conduct physically consistent neural network training: The loss function used to guide network training consists of data loss and physical constraint loss; data loss is defined as follows: in, and denote the sth element in the observed and predicted non-top acceleration response Fourier spectra, respectively; M denotes the total number of elements in these Fourier spectra; R(·) and Ι(·) denote real and imaginary part operations, respectively; The physical constraint loss is defined as follows: in, and R min are the shear wave velocity V S,j and modulus ratio R j The lower bound of the search space; ReLU(·) represents the rectified linear unit function; The final loss function is: L all =λ1×L PC +λ2×L data Formula (29) Among them, λ1 and λ2 are weight factors; Step 5: Obtain the inverted structural parameters: Since the parameter weights of the physically consistent neural network PCNN are related to the shear wave velocity V S Related to the modulus ratio R, when the PCNN training is completed, the shear wave velocity V of each layer of the Timoshenko beam model is obtained through the network parameters S and modulus ratio R.

2. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that: The specific method of establishing a physically consistent neural network in step 2 is: The building is modeled as a cantilevered layered Timoshenko beam with its base subjected to horizontal earthquake motion u g , the model contains n layers, the number of which is equal to the number of horizontal acceleration monitors arranged on the building minus one; each layer of the model is assumed to be uniform and isotropic, and adjacent layers are fully bonded; The layers of the model are numbered from top to bottom, and their geometric properties are determined by the cross-sectional area A j , second-order moment of inertia I j , height H j , Width W j and the shear correction factor k G,j Characterization, where j = 1, ..., n represents the index of each layer; the shear correction factor k G The non-uniform distribution of shear stress on the cross section is taken into account; the material properties of each layer are determined by the mass density ρ j , Young's modulus E j and shear modulus G j Characterized by mass density ρ j , longitudinal wave velocity V L,j and shear wave velocity V S,j characterization; the relationship between modulus and wave velocity is defined as and The damping adopts the Kelvin-Voigt material model and assumes that the bending and shear deformations have the same viscosity constant μ j ; The cross section of the beam is perpendicular to the neutral axis before deformation and remains plane after deformation; however, due to shear deformation, the cross section after deformation is no longer perpendicular to the deformation axis; the neutral axis of the beam is assumed to undergo only horizontal displacement, represented by u(z,t); The total rotation of the beam consists of two components: the rotation θ(z,t) due to bending deformation and the rotation γ(z,t) due to shear deformation; M(z,t) and V(z,t) represent the bending moment and shear force, respectively; Under the small deformation assumption, any layer in the above layered model is applicable to formula (1): Substituting the Kelvin-Voigt material model into formula (1) yields formula (2): According to the force, the dynamic equation shown in formula (3) can be obtained: By combining formula (2) and formula (3), the following results can be derived, as shown in formula (4)-formula (7): Assuming that the load is simple harmonic excitation, the displacement u(z, t), angle θ(z, t), bending moment M(z, t) and shear force V(z, t) can be expressed by formula (8) and formula (9): u(z,t) = U(z)e -iωt , θ(z,t) = Θ(z)e -iωt Equation (8) Where ω is the circular frequency. Substituting formula (8) and formula (9) into formula (4)-formula (7), we obtain formula (10): in, represents the state vector, and the matrix B is defined as: According to propagation matrix theory, if the matrix B is a continuous function of z (which is true in each layer), the state vector f(z) at any point can be calculated from the state vector f(z0) at a specific point in the same layer using formula (11): f(z)=P(z,z0)f(z0) Formula (11) Where P(z,z0) is the propagation matrix from z0 to z. According to the general solution form of ordinary differential equations given in formula (10), the form of the propagation matrix can be defined as shown in formula (12): Among them, e (·) represents the matrix exponential function; given that the state vector must be continuous between adjacent layers, any interface z starting from the top j The state vector at can be determined as formula (13): For a cantilever beam, the free end (top) must satisfy the condition of zero stress, which means that the shear force and bending moment are both zero at this point; the bottom of the beam is the fixed end, so the rotation angle must be zero; Based on these conditions, the following formula can be derived: f(z0)=[U0,Θ0,0,0] T Official(14) Five of the physical quantities are non-zero; assume that U0 is a known quantity, which is applicable to the system identification task; then, the other four quantities can be calculated according to formula (13); the solution process is divided into two main steps, first determining the rotation angle Θ0 of the top; let us assume that: It can be deduced that: in, Representation Matrix The element in the p-th row and q-th column of ; therefore, Θ0 can be derived as: According to formula (18), the state vector f(z0) at the top can be completely determined; then according to formula (13), the state vector at any interface can be obtained starting from the top; Let u(z ref ,t) represents the reference point z ref The motion at the coordinate point z and the reference point z ref The transfer function between can be expressed as: To improve numerical stability and avoid division by very small numbers, the transfer function is often regularized as follows: Among them, the horizontal bar represents the complex conjugate, and η represents the regularization parameter; For a neural network with L+1 layers, the relationship between the lth layer and the (l+1)th layer can be expressed as formula (21): z l = σ l (W l · z l-1 + b l ), l = 1, ..., L Equation (21) Among them, z 0 and z L Represent the input and output of the network respectively, W l and b l Respectively represent the trainable weight matrix and bias vector of the lth layer; function σ l (·) is the nonlinear activation function of layer l; A physically consistent neural network is established, which consists of an input layer, an output layer and n hidden layers, where n corresponds to the number of layers in the cantilever layered Timoshenko beam model; each hidden layer contains 4 neurons, which is equal to the number of elements in each state vector; the output of the lth hidden layer corresponds to the state vector at the top of the lth layer in the Timoshenko beam model; a post-processing layer is added after the output layer to connect the displacement output U(zj) of each network layer starting from the second hidden layer in order to calculate the subsequent loss function; According to formula (18), the weight matrix of the first hidden layer of the physically consistent neural network can be derived as: The weight matrices of other hidden layers can be derived according to formula (16) as follows: W j =P(z j-1 ,z j-2 ) Formula (23) Among them, the value range of j is 2 to n; similarly, the weight matrix of the output layer can be derived as follows: W n+1 = p1(z n ,z n-1 ) T Formula (24) Among them, p1(z n ,z n-1 ) represents the propagation matrix P(z n ,z n-1 ), the superscript T indicates the transpose operation.

3. The structural damage system identification method based on physically consistent neural network according to claim 2 is characterized in that: The specific method for constructing the network training data set in step three is: For a (digitized) acceleration record containing m equally spaced element values, the decomposition is as follows: Among them, ω s is the sth equidistant frequency, a s and b s Respectively represent the frequency corresponding to ω s and -ω s The complex Fourier amplitude of the acceleration response of the top floor of the building is used to construct the input data set, and the amplitude of the corresponding frequency components of the acceleration response of the remaining floors is used to construct the label data set.

4. The structural damage system identification method based on physically consistent neural network according to claim 3 is characterized in that: In formula (25), a s and b s Calculated by formula (30) and formula (31) respectively:

5. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that: In step 4, in the actual physical scene, the shear wave velocity V of each layer S,j and modulus ratio R j The following relationship must be satisfied: V S,j >0, R j >0 Formula (27) The value of j ranges from 1 to n.

6. The structural damage system identification method based on physically consistent neural network according to claim 1 is characterized in that: In step 4, the Adam optimizer and learning rate decay strategy are used for training, and the shear wave velocity V S The initial learning rates of and modulus ratio R are set to 100 and 10-5 respectively. The learning rate decays to 0.1 times of the original every 50 training rounds, and the total number of training rounds is 150.

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