Structural modal parameter automatic identification method and device, electronic equipment and storage medium

Abstract

The present disclosure provides a structural modal parameter automatic identification method, comprising: dividing a structural response signal into blocks using a set time window to obtain a plurality of data blocks arranged in time sequence; identifying modal parameters of a first data block by an SSI algorithm to obtain a first modal parameter identification result of the structure; analyzing the first modal parameter identification result by a clustering algorithm to determine a stable mode of the structure; analyzing subsequent data blocks of the structure by a BSS algorithm according to the stable mode of the structure to obtain modal coordinates of each order of the subsequent data blocks, and obtaining free decay vibrations of each order of the modes using the modal coordinates; and identifying modal parameters of the free decay vibrations of each order of the modes by an HT algorithm to obtain a final modal parameter identification result. The method has good noise robustness and can significantly improve the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The embodiment of the present disclosure belongs to the technical field of modal parameter identification of engineering structures, and particularly relates to a structural modal parameter automatic identification method and device, an electronic device and a storage medium. BACKGROUND

[0002] With the development of society, the infrastructure is increasingly improved, such as super-large bridges, super-high buildings, dams and the like. Most of these buildings are concrete structures, and with the increase of service time of the buildings and the influence of environmental factors, the concrete of the buildings will age, and once the buildings fail, serious consequences will occur and adverse social impacts will be brought. The modal parameters of a structure represent the dynamic characteristics of the structure and are an evaluation index of the health state of the structure. However, the modal parameters identified by a single identification cannot reveal the evolution process of the performance of the structure, and it is difficult to reasonably evaluate the health state of the structure. Therefore, it is necessary to carry out long-term continuous vibration monitoring on the structure, automatically identify and track the changes of the modal parameters, eliminate the influence of environmental factors on the structure, and thus reflect the health state of the dam structure through only the frequency changes related to the material properties. Therefore, developing a modal parameter automatic identification algorithm has become a research focus.

[0003] However, the commonly used modal parameter automatic identification algorithms at present mainly include SSI (stochastic subspace identification) algorithm and FDD (frequency domain decomposition) algorithm. However, these algorithms have low computational efficiency, are greatly influenced by the given parameters, and need the assistance of other additional algorithms. Therefore, for long-term continuous health monitoring of a structure, it is necessary to develop a modal parameter automatic identification algorithm with high computational efficiency. SUMMARY

[0004] The present disclosure aims to at least solve one of the technical problems existing in the prior art.

[0005] To this end, a structural modal parameter automatic identification method with high computational efficiency is provided in the first aspect of the present disclosure, which combines SSI, BSS and HT algorithms, and proposes an SSI-BSS-HT modal parameter automatic identification method, and specifically includes the following steps.

[0006] S1, dividing a structural response signal into blocks by using a set time window to obtain a plurality of data blocks arranged in time sequence;

[0007] S2, identifying modal parameters of a first data block by using an SSI algorithm to obtain a first modal parameter identification result of the structure;

[0008] S3, analyzing the first modal parameter identification result by using a clustering algorithm to determine a stable mode of the structure;

[0009] S4, using the BSS algorithm to analyze the subsequent data blocks of the structure according to the stable modal of the structure, obtaining the modal coordinates of each order of the subsequent data blocks, and using the modal coordinates of each order to obtain the free decay vibration of each order of the modal;

[0010] S5, using the HT algorithm to identify the modal parameters of the free decay vibration of each order of the modal, and obtaining the final modal parameter identification result.

[0011] Optionally, before the structure response signal is blocked, the original result response signal is also preprocessed, and the preprocessing method includes removing drift, filtering and / or resampling.

[0012] Optionally, the first modal parameter identification result of the structure includes the frequency, damping ratio and mode shape of the structure.

[0013] Optionally, S2 specifically includes the following steps:

[0014] S21, constructing a discrete state model of an n-degree-of-freedom system excited by white noise, the expression being as follows:

[0015] x k+1 =A d x k +w k

[0016] y k =C d x k +v k

[0017] wherein x k ∈R 2n×1 、 are the state vector and the measured structure response vector at k time, respectively, A d ∈R 2n ×2n and are the state matrix and the output matrix, respectively, w k ∈R n×1 and are white noise with zero mean, and n0 is the number of output measuring points;

[0018] Using the measured structure response vector y k at discrete k time, a Hankel matrix H is constructed, the expression being as follows:

[0019]

[0020] wherein Y p and Y f are the past output matrix and the future output matrix, respectively,

[0021] S22. Based on the property that white noise has zero mean and is uncorrelated, calculate the covariance matrix of the output signal at time i using the following formula.

[0022]

[0023] Where E[·] represents the expected value of the computational mathematics, and A d i-1 In this context, the superscript i-1 represents the power of i-1; G is the covariance matrix of the output signal in the next state.

[0024] S23. Construct the first Toeplitz matrix using the covariance matrix. For the first Toeplitz matrix Θ 1i The observable matrix O at time i is obtained by decomposition. i and controllable matrix Γ i :

[0025]

[0026]

[0027]

[0028] Similarly, the second Toeplitz matrix is ​​constructed using the covariance matrix.

[0029]

[0030] The second Toeplitz matrix Θ 2i+1 It can be expressed in the following form:

[0031] Θ 2i+1 =O i A d Γ i =O i ΨΛΨ -1 Γ i =LΛR

[0032] Where L and R are the first and second construction matrices, respectively. Ψ∈R 2n×2n It is the state matrix A d The singular vector matrix, Λ∈R 2n×2n It is the state matrix A d The singular value matrix, specifically containing discrete-time complex eigenvalues ​​μ ii A diagonal matrix, Λ=L -1 Θ 2i+1 R -1 ;

[0033] S24, the state matrix A is calculated according to the following formula d and the output matrix C d :

[0034]

[0035]

[0036] wherein, O i-g represents the observable matrix O missing the last row i-g , represents the observable matrix O missing the first row i-g , represents the first row of the observable matrix O i-g ; the symbol represents the pseudo-inverse;

[0037] the state matrix A is subjected to eigenvalue decomposition to obtain: d

[0038] A d = ΨΛΨ -1

[0039] S25, based on the discrete-time complex eigenvalue μ ii , the complex eigenvalue λ ii and λ ii * of the structure are expressed as:

[0040]

[0041] wherein, ω ii and ξ ii are the ii-order frequency and damping ratio of the structure, respectively;

[0042] the ii-order modal parameters of the structure, including the frequency, damping ratio and mode shape, are obtained according to the following formula, which are taken as the first modal parameter identification results of the structure:

[0043]

[0044]

[0045] Φ = C d Ψ = L(1:n0,1:2n)

[0046] wherein, is the complex mode shape vector, and is the observable part of the singular vector matrix Ψ of the state matrix A d , and the superscripts I and R represent the imaginary part and the real part, respectively.

[0047] ​Optionally, the clustering algorithm is a DBSCAN clustering algorithm.

[0048] Optionally, S4 specifically comprises the following steps:

[0049] According to the modal expansion theory, the following expression is obtained:

[0050] q k+1 = Λq k + Ψ -1 w k

[0051] y k = C d Ψq k + v k = Φq k + v k

[0052] wherein q k ∈ R 2n×1 is each order modal coordinate at time k;

[0053] The following expression is obtained through matrix transformation:

[0054]

[0055]

[0056] wherein, is white noise; is a constructed measured matrix; is a generalized separation matrix of the BSS algorithm.

[0057] Through the above formula, each order modal coordinate q k is extracted, and the free decay vibration of each order modal is obtained using the random decrement method for each order modal coordinate.

[0058] Optionally, S5 specifically comprises the following steps:

[0059] For the extracted free decay vibration of each order modal, Hilbert transform is performed to obtain:

[0060]

[0061] wherein HT is a Hilbert transform operator; q(t) is a longitudinal coordinate of the free decay vibration of each order modal at time t, is a longitudinal coordinate of the free decay vibration of each order modal at time t obtained through Hilbert transform; u is an amplitude operator, which is a constant determined by an initial condition; ξ is a damping ratio of the free decay vibration of each order modal of the structure, ω n is a natural frequency of the nth order modal of the structure, and ω Dto damp the natural frequency, to be an initial phase;

[0062] An analytic signal z(t) of q(t) is constructed by using the following formula:

[0063]

[0064]

[0065]

[0066] wherein A(t) is an amplitude at time t, θ(t) is a phase at time t,

[0067] The logarithmic operation and the difference operation are respectively performed on the above formula to obtain:

[0068] ln[A(t)] = -ξω n t + ln u

[0069]

[0070]

[0071] wherein ω(t) is an angular velocity at time t.

[0072] The second aspect embodiment of the present disclosure provides a structure modal parameter automatic identification device, comprising:

[0073] A first module configured to block the structure response signal by using a set time window to obtain a plurality of data blocks arranged in time sequence;

[0074] A second module configured to identify the modal parameters of the first data block by using the SSI algorithm to obtain the first modal parameter identification result of the structure;

[0075] A third module configured to analyze the first modal parameter identification result by using a clustering algorithm to determine the stable mode of the structure;

[0076] A fourth module configured to analyze the subsequent data blocks of the structure by using the BSS algorithm according to the stable mode of the structure to obtain the modal coordinates of the subsequent data blocks, and obtain the free decay vibration of each order mode by using the modal coordinates;

[0077] A fifth module configured to identify the modal parameters of the free decay vibration of each order mode by using the HT algorithm to obtain the final modal parameter identification result.

[0078] The third aspect embodiment of the present disclosure provides an electronic device, comprising:

[0079] at least one processor, and a memory connected with the at least one processor in communication;

[0080] The memory stores instructions executable by the at least one processor, and the instructions are configured to execute the structural modal parameter automatic identification method in any one of claims 1-7.

[0081] The fourth aspect embodiment of the present disclosure provides a computer readable storage medium, which stores computer instructions for causing the computer to execute the structural modal parameter automatic identification method in any one of the first aspect embodiments of the present disclosure.

[0082] Compared with the prior art, the present disclosure has the following characteristics and beneficial effects:

[0083] The structural modal parameter automatic identification method provided by the embodiments of the present disclosure, for long-term continuous vibration monitoring, does not need to calculate the mode shape of each data set, but only needs to use the SSI algorithm to extract the modal parameters such as mode shape, frequency and damping ratio of the first data block; the mode shape extracted from the first data block is used to construct the mixing matrix of the BSS algorithm, so that the modal coordinates of each order can be quickly extracted, avoiding the time-consuming joint approximate diagonalization process in BSS, and therefore the method can significantly improve the calculation efficiency without reducing the identification accuracy; finally, the free decay vibration is extracted from the modal coordinates of each order, and the HT is used to automatically identify the modal parameters. The method of the present disclosure unifies the SSI algorithm and the BSS algorithm, and overcomes the use of the SSI algorithm for each data and the joint diagonalization solving process of the BSS algorithm in the traditional automatic identification algorithm, thereby significantly improving the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 is the overall flowchart of the structural modal parameter automatic identification method provided by the first aspect embodiment of the present disclosure.

[0085] Figure 2 is the structural response signal of the arch dam obtained in the method provided by the first aspect embodiment of the present disclosure.

[0086] Figure 3 is the stable figure of the first data block obtained by using the SSI and DBSCAN clustering algorithms in the method provided by the first aspect embodiment of the present disclosure.

[0087] Figure 4a 、 Figure 4b are the amplitude and frequency of the free decay vibration of the remaining data blocks obtained by using the BSS algorithm to extract the modal coordinates of each order in the method provided by the first aspect embodiment of the present disclosure.

[0088] Figure 4c , Figure 4d are the amplitude and frequency of the remaining data blocks automatically identified by the HT algorithm in the method provided by Embodiment 1 of the present disclosure, respectively.

[0089] Figure 5 is the automatic identification result finally obtained by the method provided by Embodiment 1 of the present disclosure.

[0090] Figure 6a is the result of five-order frequency identification of the 100 data blocks of the arch dam structure obtained by the method, BSS algorithm and SSI algorithm provided by the present disclosure 1; Figure 6b is the result of five-order damping identification of the 100 data blocks of the arch dam structure obtained by the method, BSS algorithm and SSI algorithm provided by the present disclosure 1.

[0091] Figure 7a , Figure 7b respectively show the identification error of frequency and damping ratio of the method provided by Embodiment 1 of the present disclosure under different noise levels.

[0092] Figure 8a , Figure 8b are the calculation efficiency diagrams of the algorithm embodiments of the present disclosure, respectively.

[0093] Figure 9 is the identification result of Embodiment 1 of the present disclosure under long-term continuous monitoring conditions and time-varying stiffness conditions.

[0094] Figure 10 is the automatic identification result of the modal parameters of the Baixo Sabor arch dam by Embodiment 1 of the present disclosure.

[0095] Figure 11 is a structural schematic diagram of an electronic device provided by the third aspect embodiment of the present disclosure. DETAILED DESCRIPTION

[0096] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0097] On the contrary, the present application covers any alternative, modification, equivalent method and scheme defined by the claims on the essence and scope of the present application. Further, in order to make the public better understand the present application, in the following detailed description of the present application, some specific details are described in detail. The present application can also be completely understood without the description of these details by those skilled in the art.

[0098] Referring to Figure 1The method for automatically identifying structural modal parameters provided by the first aspect of the present disclosure comprises the following steps:

[0099] S1, the structure response signal is divided into blocks by using a set time window, and a plurality of data blocks arranged in time sequence are obtained;

[0100] S2, the first data block is identified by using an SSI (stochastic subspace identification) algorithm, and a first modal parameter identification result of the structure is obtained;

[0101] S3, the first modal parameter identification result is analyzed by using a clustering algorithm, and a stable mode of the structure is determined;

[0102] S4, the subsequent data blocks of the structure are analyzed by using a BSS (blind source separation) algorithm and the stable mode of the structure, and modal coordinates of each order of the subsequent data blocks are obtained, and free decay vibrations of each order of the modal coordinates are obtained;

[0103] S5, the free decay vibrations of each order of the modal coordinates are identified by using an HT (Hilbert transform) algorithm, and a final modal parameter identification result is obtained.

[0104] In some embodiments, in step S1, a high-precision vibration sensor is installed on the structure to capture the original response signal (such as acceleration data) of the structure, and in the operation process, the vibration sensor can be fixed by gypsum or other methods, and GPS is used to ensure the synchronization of each measuring point. The original response signal is preprocessed, and the preprocessing methods include drift elimination, filtering, resampling, etc., so as to filter out unnecessary vibration information and obtain the structure response signal. The structure response signal is divided into blocks by using a set length of time window (such as one group of data is intercepted every 10-30 minutes), and a plurality of data blocks arranged in time sequence are obtained, and each data block represents the time history response signal of a measuring point of the structure in different time periods.

[0105] In some embodiments, step S2 is to identify the first data block by using the SSI algorithm, and the modal parameters of the first data block are obtained, that is, the first modal parameter identification result of the structure. Specifically, the following steps are included:

[0106] S21, a discrete state model of an n-degree-of-freedom system excited by white noise is constructed, and the expression is as follows:

[0107] x k+1 =A d x k +w k

[0108] y k =C d xk +v k

[0109] Where, x k ∈R 2n×1 , These are the state vector at time k and the measured structural response vector, A. d ∈R 2n ×2n and These are the state matrix and the output matrix, w k ∈R n×1 and , where n0 is the number of output measurement points, and R is the set of real numbers;

[0110] Using the measured structural response vector y at discrete time k k Construct the Hankel matrix H, as shown in the following expression:

[0111]

[0112] Among them, Y p and Y f These are the past output matrix and the future output matrix, respectively. Past output matrix Y p The number of rows and columns are g and j respectively, and the output matrix Y will be... f The number of rows and columns of y are (i-g) and j, respectively, and the number of rows and columns of the Hankel matrix are i and j, respectively; g It is an n0×1 dimensional column vector, representing the measured structural response vector at time g (composed of the responses of all measurement points at time g);

[0113] S22. Based on the property that white noise has zero mean and is uncorrelated, calculate the covariance matrix of the output signal at time i.

[0114]

[0115] Where E[·] represents the expected value of computation, T is the transpose operator, and A d i-1 In this context, the superscript i-1 represents the power of i-1; G is the covariance matrix of the output signal in the next state. x k+1 It is the state vector at time k+1;

[0116] S23. Construct the first Toeplitz matrix using the covariance matrix. For the first Toeplitz matrix Θ 1i The observable matrix O at time i is obtained by decomposition. i and controllable matrix Γi :

[0117]

[0118]

[0119]

[0120] Similarly, the second Toeplitz matrix Θ

[0121]

[0122] is constructed from the covariance matrix 2i+1 and expressed as follows:

[0123] Θ 2i+1 = O i A d Γ i = O i ΨΛΨ -1 Γ i = LΛR

[0124] where L and R are the first and second construction matrices, respectively, Ψ∈R 2n×2n is the singular vector matrix of the state matrix A d , Λ∈R 2n×2n is the singular value matrix of the state matrix A d , specifically a diagonal matrix containing the discrete-time complex eigenvalues μ ii , Λ = L -1 Θ 2i+1 R -1 , and once the singular value matrix Λ is obtained, the frequency and damping ratio of the structure can be identified therefrom;

[0125] S24, the state matrix A d and the output matrix C d are calculated as follows:

[0126]

[0127]

[0128] where O i-g denotes the observable matrix O i-g without the last row, denotes the observable matrix O i-g without the first row, denotes the first row of the observable matrix O i-g ; and the symbol Indicates a false reversal;

[0129] For state matrix A d Eigenvalue decomposition yields:

[0130] A d =ΨΛΨ -1

[0131] Where Ψ∈R 2n×2n It is a singular vector matrix, Λ∈R 2n×2n It contains discrete-time complex eigenvalues ​​μ ii A diagonal matrix.

[0132] S25, Based on discrete-time complex eigenvalues ​​μ ii The complex eigenvalues ​​λ of the structure ii and λ ii * Represented as:

[0133]

[0134] Where, ω ii and ξ ii These are the i-th order frequency and damping ratio of the structure, respectively.

[0135] The i-th modal parameters of the structure can be obtained from the above formula, including frequency, damping ratio and mode shape, which can be used as the identification result of the first modal parameters of the structure:

[0136]

[0137]

[0138] Φ=C d Ψ=L(1:n0,1:2n)

[0139] in, It is the complex mode vector, and it is the state matrix A. d The observable part of the singular vector matrix Ψ, where the superscripts I and R represent the imaginary and real parts respectively, and the first mode parameter identification result obtained in step S2 is used as a reference value for subsequent steps.

[0140] Based on the above, it can be understood that the SSI algorithm can be viewed as a process of diagonalizing the Toeplitz matrix.

[0141] In some embodiments, step S3 involves using the DBSCAN clustering algorithm to perform cluster analysis on the first modal parameter identification results of the structure to determine the stable modes of the structure, specifically including the following steps:

[0142] S31, determine a neighborhood radius and a density threshold value, and take the first modal parameter identification result of the structure as a stable point;

[0143] S32, for the stable point, determine a neighborhood range according to the neighborhood radius with the stable point as the center, and obtain the number of stable points in the neighborhood range to obtain a neighborhood sample capacity of the stable point;

[0144] S33, analyze the neighborhood sample capacity of the stable point according to the density threshold value, if the neighborhood sample capacity of the stable point is not less than the density threshold value, the stable point is a core point;

[0145] S34, analyze all core points according to the density reachable rule, determine whether there is a density reachable relationship between the core points, and connect the core points with the density reachable relationship to form a clustering cluster, which is taken as a stable mode of the structure.

[0146] In some embodiments, in step S4, the separation matrix of the BSS algorithm is constructed by using the mode shape obtained in step S2, and the stable mode of the structure obtained in step S3 is used to obtain the modal coordinates of each order of the subsequent data block, and the free decay vibration of each order of mode is obtained by using the modal coordinates of each order, which specifically includes the following steps:

[0147] According to the modal expansion theory, x k is expressed as the following form:

[0148] x k = Ψq k

[0149] Thus, the following expression is obtained:

[0150] q k+1 = Λq k + Ψ -1 w k

[0151] y k = C d Ψq k +v k = Φq k +v k

[0152] Wherein, q k ∈R 2n×1 is the modal coordinate of each order at time k, w k ∈R n×1 and v k ∈R n0×1 are white noise with zero mean;

[0153] The following expression is obtained by matrix transformation:

[0154]

[0155]

[0156] wherein, is white noise; is a constructed measured matrix; is a generalized separation matrix of the BSS algorithm.

[0157] Through the above formula, each order modal coordinate q k The random decrement method is used to obtain the free decay vibration of each order modal for each order modal coordinate.

[0158] In some embodiments, step S5 specifically comprises the following steps:

[0159] For the extracted free decay vibration of each order modal, a Hilbert transform is performed to obtain:

[0160]

[0161] wherein, HT is a Hilbert transform operator; q(t) is a longitudinal coordinate of the free decay vibration of each order modal at time t, is a longitudinal coordinate of the free decay vibration of each order modal at time t obtained by the Hilbert transform; u is an amplitude operator, which is a constant determined by the initial condition; e is a natural exponent; ξ is a damping ratio of the free decay vibration of each order modal of the structure, ω n is the natural frequency of the nth order modal of the structure, ω D is the damped natural frequency, is the initial phase.

[0162] An analytical signal z(t) of q(t) is constructed by using the following formula:

[0163]

[0164]

[0165]

[0166] wherein, A(t) is an amplitude at time t, θ(t) is a phase at time t,

[0167] The logarithmic operation and the difference operation are respectively performed on the above formula to obtain:

[0168] ln[A(t)] = -ξω n t + ln u

[0169]

[0170]

[0171] wherein ω(t) is the angular velocity at time t.

[0172] Further, in order to reduce the error, the obtained discrete points are linearly fitted (such as using the least square method), and the fitted ω D and -ξω n , and finally the automatic identification of the structural modal parameters is realized.

[0173] The following is a specific embodiment 1 of the method of the present disclosure. The method of this embodiment aims to identify the modal parameters of a six-degree-of-freedom model of an arch dam under environmental excitation, and uses the SSI-BSS-HT algorithm to realize fast identification and modal tracking. The specific implementation steps are as follows:

[0174] (1) Obtain the structural response signal of the arch dam (in this implementation, the acceleration of the arch dam is used), refer to Figure 2 , and use the set time window to block the structural response signal to obtain a plurality of data blocks arranged in time sequence.

[0175] (2) Identify and extract the modal parameters of the first data block by using the SSI algorithm and the DBSCAN clustering algorithm, determine the stable modes of the arch dam, and obtain the stable diagram as shown in Figure 3 .

[0176] (3) According to the modal shape extracted in the above step, use the BSS algorithm to extract the modal coordinates of each order, and extract the free decay vibration, as shown in Figure 4a , Figure 4b .

[0177] (4) According to the extracted free decay vibration, use the HT algorithm to identify the modal parameters, as shown in Figure 4c , Figure 4d .

[0178] (5) Repeat (3)-(4) for the subsequent data to realize the modal parameter identification and tracking of the subsequent data blocks, as shown in Figure 5 .

[0179] Effectiveness verification of embodiment 1 of the present disclosure:

[0180] Use the method provided by embodiment 1 of the present disclosure, the BSS algorithm and the SSI algorithm to identify the five-order modal parameters of 100 data blocks of the obtained arch dam structure, and the identification results are shown in Figure 6a , Figure 6b . From the five-order frequency identification results shown in Figure 6a , it can be seen that the identification frequencies of the three algorithms are basically the same, but the BSS algorithm will identify some false modes, i.e. irregular scatter points in the figure; from Figure 6bIt can be seen from the five-order damping ratio identification results shown that the three algorithms have great differences in identifying the damping ratio. Overall, the identification results of SSI algorithm and SSI-BSS-HT algorithm are relatively close.

[0181] Figure 7a 、 Figure 7b The identification errors of frequency and damping ratio of SSI-BSS-HT algorithm under different noise levels are shown respectively. It can be seen from the figure that the identification errors of six-order frequency are 0.53%~0.69%, 0.21%~0.24%, 0.23%~0.26%, 0.07%~0.12%, 0.14%~0.15% and 0.10%~0.12% respectively. This means that the differences of SSI-BSS-HT algorithm in identifying frequency under different noise levels are small, indicating that the identification results of SSI-BSS-HT algorithm are relatively stable with the increase of noise level, which shows that SSI-BSS-HT algorithm has good noise robustness. The identification error of damping ratio is relatively small, and the error of each order is 1.15%~2.00%, 1.27%~2.59%, 1.69%~2.78%, 2.52%~4.85%, 4.82%~5.56% and 2.26%~6.10% respectively. It is worth noting that there is no obvious correlation between the identification error of modal parameters and the noise level.

[0182] The calculation time of different algorithms under 20% noise level is shown in Figure 8a It can be seen from the figure that the calculation time of SSI-BSS-HT algorithm is significantly less than that of BSS and SSI algorithms, indicating that the calculation efficiency of SSI-BSS-HT algorithm is higher than that of the other two methods. In addition, referring to Figure 8b , with the increase of the number of sensors, the calculation time of BSS algorithm and SSI algorithm increases rapidly, while the calculation time of SSI-BSS-HT algorithm remains stable, indicating that the calculation efficiency of SSI-BSS-HT algorithm will not decrease with the increase of the number of sensors, which means that SSI-BSS-HT algorithm has great advantages in dealing with actual structures equipped with a large number of sensors.

[0183] During long-term continuous monitoring, environmental factors such as temperature or water level affect the structural frequency, and the material properties of concrete change over time, which also causes the change of frequency, and these changes in frequency can be explained as changes in stiffness, so it is necessary to study the effectiveness of the SSI-BSS-HT algorithm when the structural stiffness changes. In this study, the original working condition is marked as Case 0, K1 = 0.95K (Case 1), K2 = 1.05K (Case 2), K3 = 1.02K (Case 3) and K4 = 0.98K (Case 4) are used to simulate the increase and decrease of overall stiffness. For each working condition, 50 groups of white noise are randomly generated to excite the structure. The frequencies identified by the SSI-BSS-HT algorithm and the corresponding theoretical frequencies (pentagram) are shown in Figure 9 As can be seen from the figure, the identified frequencies of the SSI-BSS-HT algorithm and the corresponding theoretical frequencies are in good agreement under all working conditions.

[0184] The modal frequencies automatically identified by the SSI-BSS-HT algorithm from the continuous monitoring data are shown in Figure 10 As can be seen from the figure, the algorithm can successfully track the six-order frequencies of 48 groups of data within a day, and the six-order frequencies remain stable within a day, which indicates that the SSI-BSS-HT automatic identification algorithm can achieve good application in actual engineering.

[0185] In summary, the SSI-BSS-HT algorithm provided by the embodiments of the present disclosure has good noise robustness, ultra-high computing efficiency, effectiveness of long-term continuous monitoring and time-varying stiffness, and good applicability in actual structural engineering.

[0186] The structural modal parameter automatic identification device provided by the second aspect of the embodiments of the present disclosure comprises:

[0187] The first module is configured to block the structural response signal by using a set time window to obtain a plurality of data blocks arranged in time sequence;

[0188] The second module is configured to identify the modal parameters of the first data block by using the SSI algorithm to obtain the first modal parameter identification result of the structure;

[0189] The third module is configured to analyze the first modal parameter identification result by using a clustering algorithm to determine the stable mode of the structure;

[0190] The fourth module is configured to analyze the subsequent data blocks of the structure by using the BSS algorithm according to the stable mode of the structure to obtain the modal coordinates of each order of the subsequent data blocks, and obtain the free decay vibration of each order of the modal by using the modal coordinates of each order;

[0191] A fifth module configured to utilize the HT algorithm to perform modal parameter identification on the free decay vibration of each order modal to obtain a final modal parameter identification result.

[0192] To achieve the above-mentioned embodiments, the present disclosure further provides a computer readable storage medium having a computer program stored thereon, which is executed by a processor to perform the structural modal parameter automatic identification method provided by the first aspect of the present disclosure.

[0193] Reference will now be made to Figure 11 which shows a structural diagram of an electronic device suitable for implementing the electronic device provided by the third aspect of the present disclosure. The electronic device in the present disclosure can include, but is not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablets), PMPs (portable multimedia players), vehicle terminals (such as vehicle navigation terminals), and the like, and fixed terminals such as digital TVs, desktop computers, servers, and the like. Figure 11 The electronic device shown is merely an example and should not impose any limitation on the functions and use range of the present disclosure.

[0194] As shown in Figure 11 , the electronic device can include a processing device (such as a central processing unit, a graphics processing unit, etc.) 101, which can perform various appropriate actions and processes according to programs stored in a read-only memory (ROM) 102 or loaded into a random access memory (RAM) 103 from a storage device 108. In the RAM 103, various programs and data required for the operation of the electronic device are also stored. The processing device 101, the ROM 102, and the RAM 103 are connected to each other through a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0195] Generally, the following devices can be connected to the I / O interface 105: input devices 106 including, for example, a touch screen, a touch pad, a keyboard, a mouse, a camera, a microphone, and the like; output devices 107 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, and the like; storage devices 108 including, for example, a magnetic tape, a hard disk, and the like; and communication devices 109. The communication devices 109 can allow the electronic device to communicate with other devices wirelessly or by wire to exchange data. Although Figure 11 An electronic device with various devices is shown, but it should be understood that it is not required to implement or have all the devices shown. More or fewer devices can be implemented or provided instead.

[0196] In particular, according to embodiments of the present disclosure, the processes described above with reference to the flowcharts can be implemented as a computer software program. For example, the present embodiments include a computer program product comprising a computer program carried on a computer readable medium, the computer program containing program code for executing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network by the communication device 109, or installed from the storage device 108, or installed from the ROM 102. When the computer program is executed by the processing device 101, the above-mentioned functions defined in the methods of the present disclosure are performed.

[0197] It should be noted that the computer readable medium described above in the present disclosure can be a computer readable signal medium or a computer readable storage medium or any combination thereof. The computer readable storage medium may, for example, be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or apparatus, or any suitable combination thereof. More specific examples of the computer readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present disclosure, the computer readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus or device. In the present disclosure, the computer readable signal medium can include a data signal carried in a baseband or as part of a carrier wave, in which the computer readable program code is carried. Such a propagated data signal can take a variety of forms, including, but not limited to, an electromagnetic signal, an optical signal, or any suitable combination thereof. The computer readable signal medium can also be any computer readable medium that is not a computer readable storage medium and that can be used to carry or transmit a program for use by or in connection with an instruction execution system, apparatus or device. The program code contained in the computer readable medium can be transmitted by any suitable medium, including, but not limited to, a wire, an optical fiber, an RF (radio frequency) or the like, or any suitable combination thereof.

[0198] The computer readable medium described above can be included in the electronic device described above; or can exist separately from the electronic device and be not assembled into the electronic device.

[0199] The computer readable medium described above carries one or more programs, when the one or more programs are executed by the electronic device, the electronic device:

[0200] The structural response signal is divided into blocks by using a set time window, and a plurality of data blocks arranged in time sequence are obtained; the first data block is subjected to modal parameter identification by using the SSI algorithm, and the first modal parameter identification result of the structure is obtained; the first modal parameter identification result is analyzed by using the clustering algorithm, and the stable mode of the structure is determined; the subsequent data blocks of the structure are subjected to data analysis by using the BSS algorithm according to the stable mode of the structure, and the modal coordinates of each order of the subsequent data blocks are obtained, and the free decay vibration of each order of the mode is obtained by using the modal coordinates; the free decay vibration of each order of the mode is subjected to modal parameter identification by using the HT algorithm, and the final modal parameter identification result is obtained.

[0201] Computer program code for carrying out operations of the present disclosure can be written in one or more programming languages or combinations of languages including object oriented programming languages such as Java, Smalltalk, C++, Python, conventional procedural programming languages such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0202] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0203] In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise explicitly specified.

[0204] Any processes or methods described in the flowcharts or otherwise described herein can be understood as representing code modules, segments, or portions of code which include one or more executable instructions for implementing specific logic functions (or steps) of the application, and alternate implementations are possible. The various steps or functions described in the flowcharts or otherwise described herein can be implemented as program instructions (i.e., as one or more modules of computer program code) in any of a variety of programming languages. The various steps or functions described in the flowcharts or otherwise described herein can be implemented as machine or computer readable code on a computer readable medium. Such program instructions can be utilized by or in combination with a suitable processor or processors to perform the steps or functions indicated in the block diagrams and / or flowcharts. The program instructions might take any number of forms, including complete program modules, routines, programs, objects, components, data structures, etc. that may, for example, be compiled for implementation by or in combination with one or more processors.

[0205] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For purposes of this specification, a "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system (or apparatus or device) including a computer readable storage medium. Examples (non-exhaustive list) of the computer-readable medium include the following: a semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable

[0206] It should be understood that aspects of the application can be implemented in hardware, software, firmware, or combinations thereof. In the above embodiments, various steps or methods can be implemented in software or firmware that is stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, and in another embodiment, any of the following techniques, which are well known in the art, can be used to implement the application: a hybrid of the techniques mentioned above; a combination of one or more of the techniques mentioned above; or one or more other techniques that are well known in the art; which have similar requirements to the techniques mentioned above.

[0207] Those skilled in the art of the present technology can understand that all or part of the steps carried out by the above-mentioned embodiment methods can be completed by programs instructing related hardware, and the developed programs can be stored in a computer readable storage medium. When the program is executed, it includes one of the steps of the method embodiment or a combination thereof.

[0208] In addition, each functional unit in each embodiment of the present application can be integrated into one processing module, or each unit can exist physically alone, or two or more units can be integrated into one module. The integrated module can be realized in the form of hardware or in the form of a software functional module. The integrated module, if realized in the form of a software functional module and sold or used as an independent product, can also be stored in a computer readable storage medium.

[0209] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments within the scope of the present application.

Claims

1. A structural modal parameter automatic identification method, characterized by, The method comprises the following steps: S1, dividing the structural response signal into blocks by using a set time window to obtain a plurality of data blocks arranged in time sequence; S2, identifying the modal parameters of the first data block by using the SSI algorithm to obtain the first modal parameter identification result of the structure; S3, analyzing the first modal parameter identification result by using a clustering algorithm to determine the stable mode of the structure; S4, analyzing the subsequent data blocks of the structure by using the BSS algorithm according to the stable mode of the structure to obtain the modal coordinates of each order of the subsequent data blocks, and obtaining the free decay vibration of each order of the modal by using the modal coordinates; S5, identifying the modal parameters of the free decay vibration of each order of the modal by using the HT algorithm to obtain the final modal parameter identification result.

2. The structural modal parameter automatic identification method according to claim 1, characterized by, Before the structural response signal is divided into blocks, the original result response signal is preprocessed, and the preprocessing methods include drift elimination, filtering and / or resampling.

3. The structural modal parameter automatic identification method according to claim 1, characterized by, The first modal parameter identification result of the structure includes the frequency, damping ratio and mode shape of the structure.

4. The structural modal parameter automatic identification method of claim 1, wherein S2 specifically comprises the following steps: S21, constructing a discrete state model of an n-degree-of-freedom system under white noise excitation, and the expression is as follows: x k+1 = A d x k + w k y k = C d x k + v k where x k ∈ R 2n×1 , are the state vector and the measured structural response vector at time k, respectively, A d ∈ R 2n×2n and are the state matrix and the output matrix, respectively, w k ∈ R n×1 and are white noises with zero mean, and n0is the number of output measurement points. The measured structural response vector y at discrete k time instants k A Hankel matrix H is constructed, expressed as follows: where Y p and Y f are past and future output matrices, respectively, S22, according to the property that the mean of white noise is zero and is not correlated with each other, the covariance matrix of output signal at i moment is calculated according to the following formula where E[•] represents the mathematical expectation, A d i-1 the superscript i-1 in the above equation represents the i-1th power; G is the covariance matrix of the next state output signal, S23, the first Toeplitz matrix is composed by the covariance matrix The first Toeplitz matrix Θ 1|i is decomposed to obtain the observable matrix O i and the controllable matrix Γ i : Likewise, the second Toeplitz matrix is formed using the covariance matrix The second Toeplitz matrix Θ 2|i+1 is expressed in the form Θ 2|i+1 = O i A d Gamma i = O i Psi Lambda Psi -1 Gamma i = L Lambda R wherein L and R are a first and a second configuration matrix, respectively, Ψ∈R 2n×2n is a singular vector matrix of the state matrix A d , Λ∈R 2n×2n is a singular value matrix of the state matrix A d , in particular a diagonal matrix containing the discrete-time complex eigenvalues μ ii of A, Λ = L -1 Θ 2|i+1 R -1 ; S24, the state matrix A is calculated according to the following formula d and the output matrix C d : where The ii-order modal parameters of the structure are obtained according to the following formula, including the frequency, damping ratio and mode shape, which are used as the first modal parameter identification result of the structure: i-g denotes the observable matrix O missing the last row i-g , denotes the observable matrix O missing the first row i-g , denotes the first row of the observable matrix O i-g ; the symbol denotes the pseudo-inverse; Eigenvalue decomposition of the state matrix A d yields: A d = ΨΛΨ -1 S25, based on the discrete-time complex eigenvalue μ ii the complex eigenvalue λ ii and λ ii * is represented as: where ω ii and ξ ii are the structure's second order frequency and damping ratio, respectively; The clustering algorithm is a DBSCAN clustering algorithm. Φ = C d Ψ = L(1:n0,1:2n) where is the complex vector of the complex eigenvector matrix Ψ of the state matrix A d is the observable part of the singular vector matrix Ψ of the state matrix A, the superscripts I and R represent the imaginary and real parts, respectively.

5. The structural modal parameter automatic identification method according to claim 1, characterized by, S4 specifically comprises the following steps:

6. The structural modal parameter automatic identification method according to claim 4, characterized by, According to the modal expansion theory, the following expression is obtained: The following expression is obtained through matrix transformation: q k+1 = Λq k + Ψ -1 w k y k = C d Ψq k + v k = Φq k + v k where q k ∈R 2n×1 are the modal coordinates of order k at time k. S5 specifically comprises the following steps: wherein is white noise; is the constructed measured matrix; is the generalized separation matrix of the BSS algorithm; By the above equation, the modal coordinates q of each order are extracted k The free decay vibration of each order mode is obtained by using the random decrement method for each order modal coordinate.

7. The structural modal parameter automatic identification method according to claim 1, characterized by, For the extracted free decay vibration of each order of the modal, the Hilbert transform is performed to obtain: The analytic signal z(t) of q(t) is constructed by using the following formula: wherein HT is a Hilbert transform operator; q(t) is the longitudinal coordinate of the free decay vibration of each order mode at time t, is the longitudinal coordinate of the free decay vibration of each order mode at time t obtained by Hilbert transform; u is an amplitude operator, which is a constant determined by initial conditions; ξ is the damping ratio of the free decay vibration of each order mode of the structure, ω n is the natural frequency of the nth order mode of the structure, ω D is the damped natural frequency, is the initial phase; The logarithmic operation and the difference operation are performed on the above formula respectively to obtain: where A(t) is the amplitude at time t, and θ(t) is the phase at time t, Wherein, ω(t) is the angular velocity at time t. ln[A(t)] = -ξω n t + ln u The method comprises the following steps:

8. A structural modal parameter automatic identification apparatus characterized by comprising: The first module is configured to divide the structural response signal into blocks by using a set time window to obtain a plurality of data blocks arranged in time sequence; The second module is configured to identify the modal parameters of the first data block by using the SSI algorithm to obtain the first modal parameter identification result of the structure; The third module is configured to analyze the first modal parameter identification result by using a clustering algorithm to determine the stable mode of the structure; The fourth module is configured to analyze the subsequent data blocks of the structure by using the BSS algorithm according to the stable mode of the structure to obtain the modal coordinates of each order of the subsequent data blocks, and obtain the free decay vibration of each order of the modal by using the modal coordinates; The fifth module is configured to identify the modal parameters of the free decay vibration of each order of the modal by using the HT algorithm to obtain the final modal parameter identification result. The method comprises the following steps:

9. An electronic device, comprising: At least one processor, and a memory connected in communication with the at least one processor; Wherein, the memory stores instructions executable by the at least one processor, and the instructions are configured to execute the structural modal parameter automatic identification method in any one of claims 1-7. ​ 10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer instructions for causing the computer to execute the structural modal parameter automatic identification method in any one of claims 1-7.

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