Underdetermined time-varying operational modal parameter identification method and device based on dynamic sliding window

Abstract

The application relates to a dynamic sliding window-based underdetermined time-varying operational modal parameter identification method and device, and relates to the field of operational modal parameter identification.The application obtains a linear structure vibration response signal of a sensor measuring point, calculates the mean value and variance of signal data in an initial setting window, and flexibly changes the size of a sliding window according to the mean value difference between a current window and a previous window and according to the mean value difference and the variance.Under a short-time hypothesis, the data in the sliding window can be regarded as time-invariant.Through three-dimensional data construction on the signal in the window and application of a proposed tensor decomposition method to modal parameter identification, the dynamic characteristics of the system can be effectively extracted.Along with the movement of the sliding window, new data is introduced, and old data is deleted, so that real-time identification of underdetermined time-varying structure operational modal parameters is realized.The method is particularly suitable for time-varying modal monitoring of large structures such as bridges, high-rise buildings and wind turbines, and has high practical application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of operational modal parameter identification, and particularly to an underdetermined time-varying operational modal parameter identification method and device based on a dynamic sliding window. BACKGROUND

[0002] In traditional modal parameter identification techniques, it is usually assumed that the modal parameters of a system remain constant throughout the observation process. This assumption is applicable to time-invariant systems. However, actual engineering systems (such as bridges, mechanical equipment, vehicle dynamics systems, etc.) often exhibit time-varying characteristics, and the modal parameters of the system change with time, environmental conditions, or working conditions. For example, under the action of traffic loads, the modal frequency of a bridge may change with the position of the train; in rotating machinery, changes in rotational speed will cause fluctuations in modal frequency and damping ratio. These time-varying characteristics make it impossible for traditional static modal analysis methods to adapt, posing new challenges: how to accurately identify and track the modal parameters of time-varying systems in real time.

[0003] In particular, under the underdetermined condition, how to accurately identify the modal parameters (such as modal frequency, modal damping ratio, and modal shape) of the system is a problem that needs to be solved urgently. Underdetermined condition refers to the case where the number of sensors is less than the number of modes, which is very common in many practical engineering applications, especially in cases where sensor placement is limited, system structure is complex, or cost is limited. In this case, traditional modal parameter identification methods often cannot provide sufficient accuracy or cannot respond to system dynamics in a timely manner, resulting in inaccurate or lagging estimates of modal parameters.

[0004] To address this challenge, many researchers have proposed methods based on sliding windows. This method can segmentally process and track changes in system modal parameters by analyzing time-varying signals locally. Although the traditional sliding window method can model time-varying systems to some extent, it has significant limitations. For example, a fixed-size sliding window may not be able to adjust in time when faced with rapid or drastic system changes, resulting in an inability to accurately capture instantaneous changes in the system. In addition, the selection of a fixed window often depends on prior knowledge and lacks adaptability, which may affect the identification accuracy and real-time performance. SUMMARY

[0005] The main purpose of the present application is to overcome the above-mentioned defects in the prior art, and to propose an underdetermined time-varying operational modal parameter identification method and device based on a dynamic sliding window, which adjusts the size of the sliding window according to the mean and variance of the signal data within the set window, and realizes the identification of time-varying structures.

[0006] The present application adopts the following technical solutions:

[0007] A dynamic sliding window-based underdetermined time-varying operational modal parameter identification method, comprising:

[0008] Obtaining a vibration response signal of a linear structure under a set environmental excitation of a selected sensor measuring point;

[0009] After the vibration response signal in a window of a set length is subjected to adaptive filtering denoising processing, a denoised signal is obtained, features are extracted from the denoised signal by a convolutional neural network, a three-order tensor is constructed using the extracted features, and modal shape matrix and modal response matrix are obtained by decomposing the three-order tensor; the length of the window is dynamically changed according to the mean and variance of the vibration response signal in each window, the window is slid, the modal shape matrix and the modal response matrix of the vibration response signal in the next window are identified, and the identification of all vibration response signals is completed;

[0010] According to the modal shape matrix and the modal response matrix of the identified vibration response signal, the modal shape and the natural frequency of the linear structure are obtained respectively, and the underdetermined time-varying operational modal parameter identification is realized.

[0011] The adaptive filter is adjusted by continuously adjusting its parameters, so that the noise component is minimized, thereby retaining the main features of the vibration response signal.

[0012] The convolutional neural network includes multiple convolutional layers and pooling layers, the features extracted by the convolutional neural network include time domain mode and frequency domain mode of the vibration response signal, and the output of the convolutional neural network is arranged into a matrix.

[0013] The extracted features and the denoised signal are used to construct a three-order tensor, specifically:

[0014] Initializing a three-order tensor X with dimensions of N t ×n m ×K, where N t is the number of time points, n m is the number of sensors, and K is the feature dimension, representing the number of features extracted from the convolutional neural network;

[0015] For each window i and each sensor j, features are extracted from the signal processed by the adaptive filter and the convolutional neural network and filled into the tensor X .

[0016] Further comprising CP decomposition of the constructed three-order tensor X :

[0017]

[0018] Φ r is a modal shape matrix, Q r is a modal response matrix, Θ r is the rth component of the weight matrix, r is 1 to R, corresponding to a mode, R is the rank in CP decomposition, that is, the total number of factors in the decomposition, N represents the total number of sampling points; wherein represents the outer product of vectors; the vectors in the modal response matrix are processed by Fourier transform to estimate the natural frequency corresponding to each mode.

[0019] The length of the window is dynamically changed according to the mean and variance of the vibration response signal in each window, specifically:

[0020] The mean of the vibration response signal in the ith window is calculated Assuming that at time t, the size of the current window is w, the w data points in the window are x(t), x(t+1),..., x(t-w+1), and the mean is:

[0021]

[0022] The variance σ of the vibration response signal in the window is calculated 2 (t):

[0023]

[0024] j is the index inside the sliding window, the degree of change of the data is judged by calculating the mean difference between the current window and the previous window, and the length of the window is adjusted according to the degree of change of the data and the variance.

[0025] The mean of the vibration response signal of the current window is defined as The mean of the vibration response signal of the previous window is The difference value between the two is is:

[0026]

[0027] According to the difference value and the preset threshold value ∈ is compared:

[0028]

[0029] If it is satisfied, it means that the data changes dramatically, and the length of the window needs to be increased; otherwise, it means that the data is stable, and the length of the window needs to be reduced; the adjustment method of the length of the window w(t) is:

[0030]

[0031] wherein, is the variance of the data within the current window, is the maximum possible variance within the window, a is an adjustment factor, w min is the minimum length of the set window, w max is the maximum length of the set window.

[0032] The weighted weight of the data point of the vibration response signal within the window is calculated by an exponential weighting mechanism, and a weighted vibration response signal is obtained for identification; at time t, the window length is w, the w vibration response signals within the window are x(t), x(t+1),..., x(t-w+1), and the calculation formula of the exponential weighting factor is as follows:

[0033] Γ(j, t) = a t-j

[0034] wherein, Γ(j, t) represents the weight of the vibration response signal x(j) at time t, a e (0, 1) is an exponential decay factor; j is the time index of the data point within the window;

[0035] For each time of the predicted value The weighted vibration signal response is calculated by weighted average:

[0036]

[0037] wherein, w(t) is the window size at the current time, and Γ(j, t) exponentially decays with the increase of t-j.

[0038] According to the variance difference of the window, the decay rate a of the weighting factor is dynamically adjusted:

[0039]

[0040] wherein, a0 is the initial weighting factor, s(t) is the variance of the current window, s max is the theoretical maximum variance.

[0041] A dynamic sliding window-based underdetermined time-varying operational modal parameter identification device, comprising

[0042] A vibration response signal acquisition unit is configured to acquire a vibration response signal of a linear structure under a set environmental excitation of a selected sensor measurement point.

[0043] A parameter identification unit is configured to obtain a de-noised signal by performing adaptive filtering de-noising processing on a vibration response signal in a window with a set length, extract features of the de-noised signal through a convolutional neural network, construct a three-order tensor by using the extracted features, and obtain a modal shape matrix and a modal response matrix by decomposing the three-order tensor; dynamically change the length of the window according to the mean and variance of the vibration response signal in each window, slide the window, identify the modal shape matrix and the modal response matrix of the vibration response signal in the next window, and repeat the above steps until all the vibration response signals are identified.

[0044] An output unit is configured to obtain a modal shape and a natural frequency of the linear structure respectively according to the identified modal shape matrix and the modal response matrix of the vibration response signal, and realize identification of underdetermined time-varying operational modal parameters.

[0045] As can be seen from the above description of the present application, compared with the prior art, the present application has the following beneficial effects:

[0046] The present application can respond to the change of the input signal in real time by dynamically adjusting the size of the sliding window, solves the problem that the traditional fixed window method cannot adapt to the non-stationarity of the system, and improves the identification accuracy and adaptability of the time-varying modal.

[0047] The method of the present application is particularly suitable for the case where the number of sensors is less than the number of modes to be identified, can accurately extract modal information under underdetermined conditions, and solves the problem that the traditional method cannot identify incomplete modal information due to insufficient sensors.

[0048] In addition, the present application provides a powerful tool for exploring and analyzing complex structures and dynamic characteristics in multi-dimensional time series data by integrating autocorrelation, PCA, dynamic sliding window, mean and variance calculation, exponential weighting mechanism and tensor decomposition. This method is particularly suitable for processing large, high-dimensional and time-dependent data sets, such as vehicle dynamics systems, bridges and other fields. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The figure is a main flowchart of the method of the present application.

[0050] Figure 2 The figure is a specific flowchart of the method of the present application.

[0051] Figure 3 The figure is a time-varying three-degree-of-freedom spring oscillator model provided by an embodiment of the present application.

[0052] Figure 4 The figure is a schematic diagram of the device of the present application.

[0053] Fig. 5(1), Fig. 5(2) are comparison diagrams of modal shapes identified by the experimental method of the embodiment of the present application.

[0054] Figure 6 Comparison of the natural frequency variation curve of the three-degree-of-freedom time-varying structure theory and the identified natural frequency variation curve by the experimental method of the embodiment of the present application.

[0055] Figure 7 MAC value variation curve of the three-degree-of-freedom time-varying system identified by the experimental method of the embodiment of the present application.

[0056] The present application will be further described in detail below in combination with the drawings and specific embodiments. DETAILED DESCRIPTION

[0057] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0058] Referring to Figure 1 and Figure 2 A dynamic sliding window-based underdetermined time-varying operational modal parameter identification method, comprising:

[0059] S1 obtains the vibration response signal of a linear structure under a set environmental excitation at selected sensor measurement points. The number of sensors is less than the number of degrees of freedom, and the vibration response signal is a displacement vibration response signal.

[0060] S2 obtains a denoised signal after adaptive filtering denoising processing of the vibration response signal in a window of a set length, extracts features from the denoised signal through a convolutional neural network, constructs a three-order tensor using the extracted features, decomposes the three-order tensor to obtain a modal shape matrix and a modal response matrix; dynamically changes the length of the window according to the mean and variance of the vibration response signal in each window, slides the window, identifies the modal shape matrix and the modal response matrix of the vibration response signal in the next window, and repeats the process until all the vibration response signals are identified.

[0061] The vibration response signal in each window is defined as where w represents the length of the window, i is the sequence number of the window, n m is the number of sensors, is a real number;

[0062] An adaptive filter is applied to the vibration response signal X w (t) in each window, so as to obtain a denoised signal X d (t). This process optimizes the weight coefficient so that the filter output is closest to the expected signal. The adaptive filter continuously adjusts its parameters (such as step size and window size) so that the noise component is minimized, thereby retaining the main features of the signal:

[0063] Xd (t) = Filter(X w (t));

[0064] Filter(.) represents an adaptive filter.

[0065] In the present application, a convolutional neural network is designed to process each time window of the signal, and the spatial and temporal features of the signal are extracted using the convolutional neural network. Specifically, the convolutional neural network includes multiple convolutional layers and pooling layers, and the convolutional neural network will automatically learn the local features of the input signal and generate a feature map.

[0066] Feature Map = CNN(X d (t));

[0067] where CNN(.) represents a convolutional neural network.

[0068] The features extracted by the convolutional neural network include the time domain patterns (abrupt points of vibration, periodic fluctuations, etc.) and the frequency domain patterns (energy distribution of different frequency bands) of the vibration response signal. The output of the convolutional neural network (i.e., the convolutional feature map) is arranged into a matrix where N t is the number of time points, and C is the number of channels (feature dimension) of the convolutional layer.

[0069] The extracted features and the denoised signal are used to construct a third-order tensor, specifically:

[0070] Initialize the tensor: initialize a third-order tensor X with dimensions N t ×n m ×K, where N t is the number of time points, n m is the number of sensors, and K is the feature dimension, representing the number of features extracted from the convolutional neural network.

[0071] Fill the tensor: for each window i and each sensor j, extract the features from the signal processed by the adaptive filter and the convolutional neural network and fill them into the tensor X :

[0072] X [j,i,k] = CNN(X d (j,i)) k ;

[0073] where X d (j,i) is the signal after denoising and filtering, and k represents the kth feature.

[0074] In this embodiment, the third-order tensor constructed is also subjected to a three-dimensional convolutionX CP decomposition is performed:

[0075]

[0076] After decomposition, three factor matrices Φ r , Q r , Θ r are obtained, Φ r is a modal shape matrix, Q r is a modal response matrix, Θ r is the rth component of the weight matrix, r is 1 to R, corresponding to a mode, R is the rank in CP decomposition, that is, the total number of factors in decomposition, N represents the total number of sampling points; wherein represents the outer product multiplication of vectors; the vectors in the modal response matrix are processed by Fourier transform to estimate the natural frequency w i corresponding to each mode.

[0077] Through the above steps, the modal shape matrix and the modal response matrix of the vibration response signal in the ith window are identified.

[0078] According to the mean and variance of the vibration response signal in each window, the length of the window is dynamically changed, specifically:

[0079] The mean of the vibration response signal in the ith window is calculated Assuming that at time t, the size of the current window is w, the w data points in the window are x(t), x(t+1),..., x(t-w+1), and the mean is:

[0080]

[0081] The variance σ 2 of the vibration response signal in the window is calculated (t):

[0082]

[0083] j is the index inside the sliding window, and this variance measures the fluctuation size of the data in the current window.

[0084] Further, the change degree of the data is judged by calculating the mean difference between the current window and the previous window, and the length of the window is adjusted according to the change degree of the data and in combination with the variance. Specifically as follows:

[0085] The mean of the vibration response signal of the current window is defined as The mean of the vibration response signal of the previous window is The difference value between the two is:

[0086]

[0087] The difference value represents the change between the current window and the previous window. According to the difference value is compared with a preset threshold value ∈:

[0088]

[0089] If the above conditions are met, it indicates that the data changes dramatically, that is, the difference is significant, and the length of the window needs to be increased; otherwise, it indicates that the data is stable, and the length of the window needs to be reduced; the adjustment method of the length of the window w(t) is:

[0090]

[0091] wherein, is the variance of the data in the current window, is the maximum possible variance in the window (indicating the maximum fluctuation range of the data), and α is an adjustment factor for controlling the influence of the variance on the adjustment of the window size; w min is the minimum length of the set window, and w max is the maximum length of the set window.

[0092] In the present application, the weighted weight of the data points of the vibration response signal in the window is also calculated through an exponential weighting mechanism to obtain a weighted vibration response signal for recognition; at time t, the window length is w, and the w vibration response signals in the window are x(t), x(t+1),..., x(t-w+1), and the calculation formula of the exponential weighting factor is as follows:

[0093] Γ(j, t) = α t-j

[0094] wherein, Γ(j, t) represents the weight of the vibration response signal x(j) at time t, α ∈ (0, 1) is an exponential decay factor for controlling the influence degree of the long-term data on the model; j is the time index of the data points in the window, and the closer to the current time t, the greater the weight.

[0095] For each time prediction value The weighted vibration signal response is calculated by weighted average:

[0096]

[0097] Wherein, w(t) is the window size at the current time, and Γ(j, t) exponentially decays with the increase of t-j. Since Γ(j, t) exponentially decays with the increase of t-j, the data points far from the current time have less influence on the final prediction result.

[0098] The exponential weighting factor α determines the decay rate of the weighting. Smaller α makes the past data points have less influence on the prediction value, and larger α makes the past data have more significant influence. The selection of α is determined by cross-validation. In this embodiment, the decay rate α of the weighting factor is dynamically adjusted according to the variance difference of the window:

[0099]

[0100] Wherein, α0 is the initial weighting factor, σ(t) is the variance of the current window, σ max is the theoretical maximum variance, representing the maximum fluctuation range of the data in the window, so that when the data fluctuation is large (i.e. the variance is large), the weighting factor decay rate of the data in the window is small, so that the past data still has a greater influence on the prediction result; and when the data fluctuation is small, the decay rate increases, and the influence of the long-term data gradually decreases.

[0101] In this step, after the window length adjustment is completed, the window is slid forward to the i+1 window, and the modal parameters in the new window are calculated through the above steps until i is greater than or equal to T-w+1, and the process is ended.

[0102] S3, according to the modal shape matrix and the modal response matrix of the identified vibration response signal, obtains the modal shape and the natural frequency of the linear structure respectively, and realizes the identification of the underdetermined time-varying operational modal parameters.

[0103] In another preferred embodiment of the present application, a linear time-varying three-degree-of-freedom spring oscillator system is used to verify the modal parameter identification method proposed in the present application. As shown in the linear time-varying three-degree-of-freedom spring oscillator system. Figure 3

[0104] It is assumed that the sampling frequency f is 40 Hz, the sampling interval Δt is 0.025 s, and the sampling time t is 2000 s. It is assumed that the initial conditions of the three-degree-of-freedom displacement of the system are all zero, a Gaussian white noise excitation is applied to the mass 1, and the mass is set to:

[0105]

[0106] m2=m3=1kg, stiffness k1=1000N / m, k2=1000N / m, k3=1000N / m; damping c1=0.01N.s / m, c2=0.01N.s / m, c3=0.01N.s / m.

[0107] ​Then the three-degree-of-freedom spring oscillator is tested. The response signal is obtained by MATLAB / Newmark-β simulation, the sampling frequency of the signal is 40Hz, the sampling time is t=2000s, and the sampling interval is 0.025s. The Gaussian white noise excitation applied by the object m1 and the simulated response signal are as shown in Figure 3

[0108] This embodiment compares and evaluates the operating modal parameter identification method of the linear time-varying structure by modal assurance criterion (MAC) and modal natural frequency relative error.

[0109] The formula of the modal assurance criterion is as follows:

[0110]

[0111] wherein, and respectively represent the i-th estimated modal shape vector and the real modal shape vector, and the MAC value changes between 0 and 1. The greater (closer to 1) the MAC value is, the better the modal shape is.

[0112] The natural frequency relative error ζ i The formula of the evaluation method is as follows:

[0113]

[0114] wherein, ω i and ω i-theory respectively represent the i-th estimated modal natural frequency and the theoretical natural frequency, and the value of ζ i closer to 0, the more accurate the identified natural frequency is.

[0115] The MAC value identification results of the three-degree-of-freedom spring oscillator obtained in this experiment at the instant time of 260s and 640s are as follows, Table 1 is the modal assurance criterion degree of each order at the time of 260s, Table 2 is the modal assurance criterion degree of each order at the time of 640s, and Table 3 is the natural frequency error.

[0116] Table 1

[0117] Order MAC 1 1.0000 2 0.9287 3 0.8515

[0118]

[0119] Order MAC 1 1.0000 2 0.8742 3 0.7861

[0120] Table 3

[0121] Order Theoretical natural frequency Identified natural frequency Natural frequency error 1 2.2399 2.2430 0.1384％ 2 6.2760 7.2870 16.1090％ 3 9.0690 9.6700 6.6270％

[0122] ​Fig. 5(1), Fig. 5(2) are three degrees of freedom time-varying system inherent mode shapes at different time of 280.930s, 580.15s and comparison of the method provided by the embodiment of the application with the method for identifying instantaneous mode shapes.

[0123] As can be seen from Table 1, Table 2 and Fig. 5, the method provided by the application can well realize identification of modal parameters under underdetermined time-varying conditions.

[0124] Based on this, the application further provides an underdetermined time-varying operating modal parameter identification device based on a dynamic sliding window, which adopts the underdetermined time-varying operating modal parameter identification method based on a dynamic sliding window, and comprises:

[0125] A vibration response signal acquisition unit is configured to acquire vibration response signals of a linear structure of selected sensor measuring points under a set environmental excitation. The vibration response signal acquisition unit is configured to execute step S1 of the method.

[0126] A parameter identification unit is configured to obtain a de-noised signal by performing adaptive filtering de-noising processing on vibration response signals in a window of a set length, extract features of the de-noised signal by using a convolutional neural network, construct a three-order tensor by using the extracted features and the de-noised signal, and decompose the three-order tensor to obtain a modal shape matrix and a modal response matrix. The length of the window is dynamically changed according to the mean and variance of the vibration response signals in each window, the window is slid, the modal shape matrix and the modal response matrix of the vibration response signals in the next window are identified, and the identification of all the vibration response signals is completed. The vibration response signal unit is configured to execute step S2 of the method.

[0127] An output unit is configured to obtain modal shapes and natural frequencies of the linear structure according to the identified modal shape matrix and the modal response matrix of the vibration response signals, and realize identification of underdetermined time-varying operating modal parameters. The operating modal parameter identification unit is configured to execute step S3 of the method.

[0128] The application acquires vibration response signals of a linear structure of sensor measuring points, calculates mean and variance of signal data in an initially set window, dynamically changes the size of a sliding window according to the mean difference between the current window and the previous window and the variance, and under a short-time assumption, the data in the sliding window can be regarded as time-invariant. The method can effectively extract dynamic characteristics of a system by constructing three-dimensional data of the signals in the window and applying the proposed tensor decomposition method for modal parameter identification. With the movement of the sliding window, new data is introduced and old data is deleted, so that real-time identification of underdetermined time-varying operating modal parameters of a structure is realized. The method is particularly suitable for time-varying modal monitoring of large structures such as bridges, high-rise buildings and wind turbines, and has high practical application value.

[0129] The application also provides a computer readable medium, which can be included in the electronic device described in the above embodiments, or can exist independently without being assembled into the electronic device.

[0130] The computer readable medium described above carries one or more programs, which, when executed by the electronic device, enable the electronic device to implement the method in the above embodiments.

[0131] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, the division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into several modules or units.

[0132] From the above description of the embodiments, those skilled in the art can easily understand that the example embodiments described herein can be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, U disk, mobile hard disk, etc.) or network, and includes several instructions to make a computing device (which can be a personal computer, server, touch terminal, or network device, etc.) execute the method according to the embodiments of the present disclosure.

[0133] Other embodiments of the present disclosure will be apparent to those skilled in the art with the disclosure herein. The present disclosure is intended to cover any variations, uses, or adaptations of the present disclosure following the general principles thereof and including other non-disclosed features and concepts within the scope of the present disclosure.

[0134] The above is merely specific embodiments of the present application, but the design concept of the present application is not limited thereto, and any non-essential changes made to the present application using this concept shall be deemed to infringe the protection scope of the present application.

Claims

1. A dynamic sliding window based underdetermined time-varying operational modal parameter identification method, characterized in that: The method comprises: obtaining vibration response signals of a linear structure under a set environmental excitation at selected sensor measuring points; after adaptive filtering and denoising processing of the vibration response signals in a window of a set length, a denoised signal is obtained, a convolutional neural network is used to extract features from the denoised signal, a third-order tensor is constructed using the extracted features, and a modal shape matrix and a modal response matrix are obtained by decomposing the third-order tensor; the length of the window is dynamically changed according to the mean and variance of the vibration response signals in each window, the window is slid, the modal shape matrix and the modal response matrix of the vibration response signals in the next window are identified, and the identification of all vibration response signals is completed; the modal shape and the natural frequency of the linear structure are obtained according to the identified modal shape matrix and the modal response matrix of the vibration response signals, and the identification of underdetermined time-varying operational modal parameters is realized; the length of the window is dynamically changed according to the mean and variance of the vibration response signals in each window, and specifically: calculating a mean value of the vibration response signal within the i-th window , assuming that at time t, the size of the current window is w, the w data points within the window are , ,..., , the mean value of which is : ； computing a variance of the vibration response signal within the window : ； is an index inside the sliding window, the degree of change of data is judged by calculating the mean difference between the current window and the previous window, and the length of the window is adjusted according to the degree of change of data and in combination with the variance; The difference between the mean value of the vibration response signal of the current window and the mean value of the vibration response signal of the previous window is defined as ​ ； According to the difference value compared with a preset threshold value comparison: ； If yes, it means that the data changes dramatically, and the length of the window should be increased; otherwise, it means that the data is stable, and the length of the window should be decreased; the length of the window is adjusted as follows The adjustment mode is as follows: ； wherein, is the variance of the data within the current window, is the maximum variance within the window, is a tuning factor, is the minimum length of the set window, is the maximum length of the set window.

2. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method according to claim 1, characterized in that: by optimizing the weight coefficient to make the output of the adaptive filter closest to the expected signal, the adaptive filter continuously adjusts its parameters to minimize the noise component, thereby retaining the main features of the vibration response signals.

3. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method of claim 1, wherein: The convolutional neural network includes multiple convolutional layers and pooling layers, and the features extracted by the convolutional neural network include time-domain patterns and frequency-domain patterns of the vibration response signals. The output of the convolutional neural network is arranged into a matrix.

4. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method of claim 1, wherein: The extracted features and the denoised signal are used to construct a third-order tensor, and specifically: initializing a third-order tensor with dimensions wherein is the number of time points, is the number of sensors, K is the feature dimension, representing the number of features extracted from the convolutional neural network; For each window i and each sensor j, features are extracted from the signal after processing by the adaptive filter and convolutional neural network and padded to a tensor in the middle.

5. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method of claim 4, wherein: Also included is performing CP decomposition on the constructed third order tensor CP decomposition: ； is a modal shape matrix, ; is a modal response matrix, , is the rth component of the weight matrix, r is valued from 1 to R, corresponding to a mode, R is the rank in CP decomposition, i.e. the total number of factors in the decomposition, N represents the total number of sampling points; wherein denotes the outer product multiplication of vectors; the vectors in the modal response matrix are processed by Fourier transform to estimate the natural frequency corresponding to each mode.

6. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method of claim 1, wherein: The weighted weights of the data points of the vibration response signals in the window are calculated through an exponential weighting mechanism to obtain a weighted vibration response signal for identification; at a time t, the window size is , the w vibration response signals in the window are , ,..., , and a calculation formula of the exponential weighting factor is as follows: ; wherein, represents the vibration response signal at time t, the weight of the vibration response signal at time t, is a tuning factor; is a time index of the data points within the window. For each time instant the predicted value The weighted vibration signal response is calculated by a weighted average: ; where, is the window size at the current time instant, exponentially decays as t- increases.

7. The dynamic sliding window based underdetermined time-varying operational modal parameter identification method of claim 6, wherein: Adjustment factor for dynamically adjusting weighting factor according to variance difference of window : ; wherein, is an initial weighting factor, is a variance of a current window, is a theoretical maximum variance.

8. A dynamic sliding window based underdetermined time-varying operational modal parameter identification apparatus, characterized by: The method for identifying underdetermined time-varying operational modal parameters based on a dynamic sliding window according to any one of claims 1 to 7 comprises a vibration response signal acquisition unit for obtaining vibration response signals of a linear structure under a set environmental excitation at selected sensor measuring points; a parameter identification unit for obtaining a denoised signal after adaptive filtering and denoising processing of the vibration response signals in a window of a set length, extracting features from the denoised signal by a convolutional neural network, constructing a third-order tensor using the extracted features, and obtaining a modal shape matrix and a modal response matrix by decomposing the third-order tensor; the length of the window is dynamically changed according to the mean and variance of the vibration response signals in each window, the window is slid, the modal shape matrix and the modal response matrix of the vibration response signals in the next window are identified, and the identification of all vibration response signals is completed; an output unit for obtaining the modal shape and the natural frequency of the linear structure according to the identified modal shape matrix and the modal response matrix of the vibration response signals, and realizing the identification of underdetermined time-varying operational modal parameters.

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