Dynamic sliding window-based under-timing variable working mode parameter identification method and device

Abstract

The invention discloses an under-timing variable working mode parameter identification method and device based on a dynamic sliding window, and relates to the field of working mode parameter identification. According to the method, the mean value and the variance of the signal data in the initial set window are calculated by acquiring the linear structure vibration response signal of the sensor measuring point, and the size of the sliding window is flexibly changed according to the mean value difference and the variance by calculating the mean value difference between the current window and the previous window. Under a short-time hypothesis, data in the sliding window can be considered to be time-invariant. Three-dimensional data construction is carried out on signals in a window, modal parameter identification is carried out by applying a proposed tensor decomposition method, and the dynamic characteristics of the system can be effectively extracted. And along with the movement of the sliding window, new data is introduced, and old data is deleted, so that the real-time identification of the working modal parameters of the under-timing variable 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.

Description

Technical Field

[0001] The present invention relates to the field of working modal parameter identification, and in particular to a method and device for identifying under-timed variable working modal parameters based on a dynamic sliding window. Background Art

[0002] In traditional modal parameter identification technology, it is usually assumed that the modal parameters of the system remain unchanged 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 vary with the position of the train; in rotating machinery, changes in speed will cause fluctuations in modal frequency and damping ratio. These time-varying characteristics make traditional static modal analysis methods unable to adapt, and pose a new challenge: how to accurately identify and track the modal parameters of time-varying systems in real time.

[0003] Especially under underdetermined conditions, how to accurately identify the modal parameters of the system (such as modal frequency, modal damping ratio and modal vibration shape, etc.) is an urgent problem to be solved. Underdetermined conditions refer to the number of sensors being less than the number of modes, which is very common in many practical engineering applications, especially when the sensor layout is limited, the system structure is complex or the cost is limited. In this case, traditional modal parameter identification methods often cannot provide sufficient accuracy or cannot respond to the dynamic changes of the system in a timely manner, resulting in inaccurate or delayed estimation of modal parameters.

[0004] To address this challenge, many researchers have proposed a sliding window-based method. This method can process and track the changes in the system's modal parameters in segments by performing local analysis on the time-varying signal. Although the traditional sliding window method can model time-varying systems to a certain extent, it has significant limitations. For example, a sliding window of fixed size may not be able to adjust in time when faced with rapid or drastic system changes, resulting in an inability to accurately capture the instantaneous changes of the system. In addition, the selection of fixed windows often relies on prior knowledge and lacks adaptive capabilities, which may affect recognition accuracy and real-time performance. Summary of the invention

[0005] The main purpose of the present invention is to overcome the above-mentioned defects in the prior art and to propose a method and device for identifying under-time-varying working modal parameters based on a dynamic sliding window. The method and device calculate the mean and variance of the signal data in a set window and adjust the size of the sliding window according to these statistics to realize the identification of time-varying structures.

[0006] The present invention adopts the following technical solution:

[0007] A method for identifying under-timed variable working modal parameters based on a dynamic sliding window, comprising:

[0008] Obtain the vibration response signal of the linear structure at the selected sensor measurement point under the set environmental excitation;

[0009] A denoised signal is obtained by performing adaptive filtering and denoising on a vibration response signal in a window of a set length, extracting features from the denoised signal through a convolutional neural network, constructing a third-order tensor using the extracted features, and decomposing the third-order tensor to obtain a modal vibration shape matrix and a modal response matrix; dynamically changing the length of the window according to the mean and variance of the vibration response signal in each window, sliding the window, and identifying the modal vibration shape matrix and the modal response matrix of the vibration response signal in the next window until all vibration response signals are identified;

[0010] According to the modal vibration shape matrix and the modal response matrix of the identified vibration response signal, the modal vibration shape and the natural frequency of the linear structure are respectively obtained to realize the identification of under-time variable working modal parameters.

[0011] The adaptive filter output is made closest to the expected signal by optimizing the weight coefficient, and the adaptive filter minimizes the noise component by continuously adjusting its parameters, thereby retaining the main features of the vibration response signal.

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

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

[0014] Initialize a third-order tensor X , whose dimension is N t ×n m ×K, where N t is the number of time points, n m is the number of sensors, K is the feature dimension, which represents the number of features extracted from the convolutional neural network;

[0015] For each window i and each sensor j, extract features from the signal processed by the adaptive filter and convolutional neural network and fill it into the tensor X middle.

[0016] It also includes the third-order tensor constructed X Perform CP decomposition:

[0017]

[0018] Φ r is the mode shape matrix, Q r is the modal response matrix, Θ r is the rth component of the weight matrix, r ranges from 1 to R, corresponding to a mode, R is the rank in the CP decomposition, that is, the total number of factors in the decomposition, and N represents the total number of sampling points; Represents the outer product multiplication of the 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] Calculate the mean value of the vibration response signal in the i-th window Assume that at time t, the current window size is w, and the w data points in the window are x(t), x(t+1), ..., x(t-w+1), and their mean for:

[0021]

[0022] Calculate the variance σ of the vibration response signal within the window 2 (t):

[0023]

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

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

[0026]

[0027] According to the difference value Compare with the preset threshold ∈:

[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 window length w(t) is:

[0030]

[0031] in, is the variance of the data in the current window, is the maximum possible variance within the window, α is the adjustment factor, and w min is the minimum length of the window to be set, w max It is the maximum length of the window to be set.

[0032] The weighted weights of the data points of the vibration response signal in the window are calculated by an exponential weighting mechanism to obtain a weighted vibration response signal for identification; 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:

[0033] Γ(j,t)=α t-j

[0034] Where Γ(j,t) represents the weight of the vibration response signal x(j) at time t, α∈(0,1) is the exponential decay factor; j is the time index of the data point in the window;

[0035] The predicted value for each moment The weighted vibration signal response is calculated by weighted averaging:

[0036]

[0037] Among them, w(t) is the window size at the current moment, and Γ(j,t) decays exponentially as tj increases.

[0038] The decay rate α of the weighting factor is dynamically adjusted according to the variance difference of the window:

[0039]

[0040] Among them, α0 is the initial weighting factor, σ(t) is the variance of the current window, and σ max is the theoretical maximum variance.

[0041] A device for identifying under-timed variable working modal parameters based on a dynamic sliding window, comprising:

[0042] A vibration response signal acquisition unit, used to acquire a vibration response signal of a linear structure at a selected sensor measurement point under a set environmental excitation;

[0043] A parameter identification unit is used to obtain a denoised signal after performing adaptive filtering denoising processing on the vibration response signal in a window of a set length, extract features from the denoised signal through a convolutional neural network, construct a third-order tensor using the extracted features, and decompose the third-order tensor to obtain a modal vibration shape matrix and a modal response matrix; dynamically change the length of the window according to the mean and variance of the vibration response signal in each window, slide the window, and identify the modal vibration shape matrix and modal response matrix of the vibration response signal in the next window until all vibration response signals are identified;

[0044] The output unit is used to obtain the modal vibration shape and natural frequency of the linear structure according to the modal vibration shape matrix and the modal response matrix of the identified vibration response signal, so as to realize the identification of the under-time variable working modal parameters.

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

[0046] The present invention can respond to input signal changes in real time by dynamically adjusting the size of the sliding window, thereby solving the problem that the traditional fixed window method cannot adapt to the non-stationarity of the system and improving the recognition accuracy and adaptability to time-varying modes.

[0047] The method of the present invention is particularly aimed at the situation where the number of sensors is less than the number of modes to be identified. It can accurately extract modal information under underdetermined conditions, solving the problem of incomplete identification of modal information due to insufficient sensors in traditional methods.

[0048] In addition, the present invention provides a powerful tool for exploring and analyzing the complex structure and dynamic characteristics in multidimensional time series data by integrating autocorrelation, PCA, dynamic sliding window, calculation of mean, variance, 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 THE DRAWINGS

[0049] Figure 1 It is the main flow chart of the method of the present invention.

[0050] Figure 2 The figure is a specific flow chart of the method of the present invention.

[0051] Figure 3 A diagram of a time-varying three-degree-of-freedom spring oscillator model provided in an embodiment of the present invention.

[0052] Figure 4 It is a schematic diagram of the device of the present invention.

[0053] FIG. 5( 1 ) and FIG. 5( 2 ) are comparison diagrams of modal vibration shapes identified by the experimental method of an embodiment of the present invention.

[0054] Figure 6 The experimental method of the embodiment of the present invention is used to compare the identification of the theoretical natural frequency of the three-degree-of-freedom time-varying structure with the identification of the natural frequency variation curve.

[0055] Figure 7 The experimental method of the embodiment of the present invention identifies the MAC value variation curve of the three-degree-of-freedom time-varying system.

[0056] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. DETAILED DESCRIPTION

[0057] The present invention is further described below through specific implementation modes.

[0058] See also Figure 1 and Figure 2 , a method for identifying under-timed variable working modal parameters based on dynamic sliding window, comprising:

[0059] S1 obtains the vibration response signal of the linear structure at the selected sensor measurement point under the set environmental excitation. Among them, 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 and denoising of the vibration response signal in a window of set length, extracts features from the denoised signal through a convolutional neural network, constructs a third-order tensor using the extracted features, and decomposes the third-order tensor to obtain the modal vibration shape matrix and 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, and identifies the modal vibration shape matrix and modal response matrix of the vibration response signal in the next window until all vibration response signals are identified.

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

[0062] For each window, the vibration response signal X w (t) Apply the adaptive filter to obtain the denoised signal X d (t), this process optimizes the weight coefficients so that the filter output is closest to the expected signal. The adaptive filter minimizes the noise component by continuously adjusting its parameters (such as step size and window size), thereby retaining the main characteristics of the signal:

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

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

[0065] In the present invention, a convolutional neural network is designed to process each time window of the signal, and the convolutional neural network is used to extract the spatial and temporal features of the signal. Specifically, the convolutional neural network includes multiple convolutional layers and pooling layers. 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] Among them, CNN(.) stands for convolutional neural network.

[0068] The features extracted by the convolutional neural network include the time domain pattern (vibration mutation points, periodic fluctuations, etc.) and frequency domain pattern (energy distribution in different frequency bands) of the vibration response signal. The output of the convolutional neural network (i.e., the convolution feature map) is organized 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 denoised signals are used to construct a third-order tensor, specifically:

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

[0071] Filling tensor: For each window i and each sensor j, extract features from the signal processed by the adaptive filter and convolutional neural network and fill it into the tensor X middle:

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

[0073] Among them, 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 includedX Perform CP decomposition:

[0075]

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

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

[0078] The present invention dynamically changes the length of the window according to the mean and variance of the vibration response signal in each window, specifically:

[0079] Calculate the mean of the vibration response signal in the i-th window Assume that at time t, the current window size is w, and the w data points in the window are x(t), x(t+1), ..., x(t-w+1), and their mean for:

[0080]

[0081] Calculate the variance σ of the vibration response signal within the window 2 (t):

[0082]

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

[0084] Furthermore, the degree of change of the data is determined 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. The details are as follows:

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

[0086]

[0087] Difference It indicates the change between the current window and the previous window. Compare with the preset threshold ∈:

[0088]

[0089] If the above conditions are met, it means that the data changes dramatically, that is, the difference is significant, 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 window length w(t) is:

[0090]

[0091] in, is the variance of the data in the current window, is the maximum possible variance within the window (indicating the maximum fluctuation range of the data), and α is an adjustment factor used to control the impact of variance on window size adjustment; w min is the minimum length of the window to be set, w max It is the maximum length of the window to be set.

[0092] In the present invention, the weighted weights of the data points of the vibration response signal in the window are calculated by an exponential weighting mechanism to obtain a weighted vibration response signal for identification; 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] Among them, Γ(j,t) represents the weight of the vibration response signal x(j) at time t, α∈(0,1) is the exponential decay factor, which controls the influence of long-term data on the model; j is the time index of the data point in the window, and the closer the data is to the current time t, the greater its weight.

[0095] The predicted value for each moment The weighted vibration signal response is calculated by weighted averaging:

[0096]

[0097] Among them, w(t) is the window size at the current moment, and Γ(j,t) decays exponentially with the increase of tj. Since Γ(j,t) decays exponentially with the increase of tj, the data points far away from the current moment have little impact on the final prediction results.

[0098] The exponential weighting factor α determines the decay rate of the weighting. A smaller α will make the impact of past data points on the predicted value smaller, while a larger α will make the impact of past data more significant. The choice of α is determined by cross-validation. This embodiment dynamically adjusts the decay rate α of the weighting factor based on the variance difference of the window:

[0099]

[0100] Among them, α0 is the initial weighting factor, σ(t) is the variance of the current window, and σ max It is the theoretical maximum variance, which indicates the maximum fluctuation range of the data in the window. When the data fluctuates greatly (i.e. the variance is large), the decay rate of the weighting factor of the data in the window is small, so that the past data still has a greater impact on the prediction results; when the data fluctuates less, the decay rate increases, and the influence of the long-term data gradually decreases.

[0101] In this step, after the window length is adjusted, the window slides 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.

[0102] S3 obtains the modal vibration shape and natural frequency of the linear structure according to the modal vibration shape matrix and modal response matrix of the identified vibration response signal, thereby realizing the identification of the under-time variable working modal parameters.

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

[0104] Assume the sampling frequency f is 40 Hz, the sampling interval Δt is 0.025 s, and the sampling time is t = 2000 s. Assume that the initial conditions of the three degrees of freedom displacement of the system are all zero, apply Gaussian white noise excitation to block 1, and set the mass to:

[0105]

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

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

[0108] This embodiment compares and evaluates the working modal parameter identification methods of linear time-varying structures through the modal assurance criterion (MAC) and the relative error of the modal natural frequency.

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

[0110]

[0111] in, and They represent the estimated modal vibration shape vector and the true modal vibration shape vector of the i-th order, respectively, and the MAC value varies between 0 and 1. The larger the MAC value (close to 1), the better the vibration shape.

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

[0113]

[0114] Among them, ω i With ω i-theory denote the estimated modal natural frequency and theoretical natural frequency of the i-th order, ζ i The closer the value is 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 instantaneous moments of 260s and 640s are as follows. Table 1 is the confidence criterion of each order of mode at the moment of 260s, Table 2 is the confidence criterion of each order of mode at the moment of 640s, and Table 3 is the natural frequency error.

[0116] Table 1

[0117] Degree MAC 1 1.0000 2 0.9287 3 0.8515

[0118]

[0119] Degree MAC 1 1.0000 2 0.8742 3 0.7861

[0120] Table 3

[0121] Degree Theoretical natural frequency Identifying Natural Frequencies 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] FIG5(1) and FIG5(2) are comparisons of the natural vibration modes of the three-degree-of-freedom time-varying system at different times of 280.930s and 580.15s according to the experimental method provided in an embodiment of the present invention and the instantaneous vibration modes identified by the method of the present invention.

[0123] It can be seen from Table 1, Table 2 and FIG. 5 that the method proposed in the present invention can well realize the identification of modal parameters under under-time variation conditions.

[0124] Based on this, the present invention further proposes a device for identifying under-timed variable working modal parameters based on a dynamic sliding window. The device adopts the above-mentioned method for identifying under-timed variable working modal parameters based on a dynamic sliding window, including:

[0125] The vibration response signal acquisition unit is used to acquire the vibration response signal of the linear structure of the selected sensor measurement point under the set environmental excitation. The vibration response signal acquisition unit is used to execute step S1 of the above method.

[0126] The parameter identification unit is used to obtain a denoised signal after adaptive filtering and denoising the vibration response signal in a window of a set length, extract features from the denoised signal through a convolutional neural network, construct a third-order tensor using the extracted features and the denoised signal, and decompose the third-order tensor to obtain a modal vibration matrix and a modal response matrix; dynamically change the length of the window according to the mean and variance of the vibration response signal in each window, slide the window, and identify the modal vibration matrix and modal response matrix of the vibration response signal in the next window until all vibration response signals are identified. The vibration response signal unit is used to execute step S2 of the above method.

[0127] The output unit is used to obtain the modal vibration shape and natural frequency of the linear structure according to the modal vibration shape matrix and modal response matrix of the identified vibration response signal, so as to realize the identification of the under-time-dependent working modal parameters. The working modal parameter identification unit is used to execute step S3 of the above method.

[0128] The present invention obtains the linear structural vibration response signal of the sensor measuring point, calculates the mean and variance of the signal data in the initial setting window, and flexibly changes the size of the sliding window according to the mean difference and variance based on the calculated mean difference between the current window and the previous window. Under the short-time assumption, the data in the sliding window can be regarded as time-invariant. By constructing three-dimensional data of the signal in the window and applying the proposed tensor decomposition method to identify the modal parameters, the dynamic characteristics of the system can be effectively extracted. As the sliding window moves, new data will be introduced and old data will be deleted, thereby realizing real-time identification of the working modal parameters of the under-time variable structure. This 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 present invention further provides a computer-readable medium, which may be included in the electronic device described in the above embodiment; or may exist independently without being assembled into the electronic device.

[0130] The computer-readable medium carries one or more programs. When the one or more programs are executed by an electronic device, the electronic device implements the method in the above embodiment.

[0131] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this 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. On the contrary, the features and functions of one module or unit described above can be further divided into multiple modules or units to be embodied.

[0132] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the implementation 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, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to execute the method according to the implementation of the present disclosure.

[0133] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. The present disclosure is intended to cover any variations, uses or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary technical means in the art that are not disclosed in the present disclosure.

[0134] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited to this. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A method for identifying under-timed variable working modal parameters based on a dynamic sliding window, characterized in that: include: Obtain the vibration response signal of the linear structure at the selected sensor measurement point under the set environmental excitation; A denoised signal is obtained by performing adaptive filtering and denoising on a vibration response signal in a window of a set length, extracting features from the denoised signal through a convolutional neural network, constructing a third-order tensor using the extracted features, and decomposing the third-order tensor to obtain a modal vibration shape matrix and a modal response matrix; dynamically changing the length of the window according to the mean and variance of the vibration response signal in each window, sliding the window, and identifying the modal vibration shape matrix and the modal response matrix of the vibration response signal in the next window until all vibration response signals are identified; According to the modal vibration shape matrix and the modal response matrix of the identified vibration response signal, the modal vibration shape and the natural frequency of the linear structure are respectively obtained to realize the identification of under-time variable working modal parameters.

2. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 1, characterized in that: The adaptive filter output is made closest to the expected signal by optimizing the weight coefficient, and the adaptive filter minimizes the noise component by continuously adjusting its parameters, thereby retaining the main features of the vibration response signal.

3. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 1, characterized in that: The convolutional neural network includes multiple layers of convolutional layers and pooling layers. The features extracted by the convolutional neural network include the time domain pattern and the frequency domain pattern of the vibration response signal. The output of the convolutional neural network is organized into a matrix.

4. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 1, characterized in that: The extracted features and the denoised signal are used to construct a third-order tensor, specifically: Initialize a third-order tensor Its dimension is N t ×n m ×K, where N t is the number of time points, n m is the number of sensors, K is the feature dimension, which represents the number of features extracted from the convolutional neural network; For each window i and each sensor j, extract features from the signal processed by the adaptive filter and convolutional neural network and fill it into the tensor middle.

5. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window as claimed in claim 4, characterized in that: It also includes the third-order tensor constructed Perform CP decomposition: Φ r is the mode shape matrix, Q r is the modal response matrix, Θ r is the rth component of the weight matrix, r ranges from 1 to R, corresponding to a mode, R is the rank in the CP decomposition, that is, the total number of factors in the decomposition, and N represents the total number of sampling points; Represents the outer product multiplication of the vectors; the vectors in the modal response matrix are processed by Fourier transform to estimate the natural frequency corresponding to each mode.

6. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 1, characterized in that: The length of the window is dynamically changed according to the mean and variance of the vibration response signal in each window, specifically: Calculate the mean value of the vibration response signal in the i-th window Assume that at time t, the current window size is w, and the w data points in the window are x(t), x(t+1), ..., x(t-w+1), and their mean for: Calculate the variance σ of the vibration response signal within the window 2 (t): j is the index inside the sliding window. The degree of change of the data is determined by calculating the mean difference between the current window and the previous window. The length of the window is adjusted according to the degree of change of the data and in combination with the variance.

7. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 6, characterized in that: The mean value of the vibration response signal in the current window is defined as The mean value of the vibration response signal in the previous window is The difference between the two for: According to the difference value Compare with the preset threshold ∈: 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 window length w(t) is: in, is the variance of the data in the current window, is the maximum possible variance within the window, α is the adjustment factor, and w min is the minimum length of the window to be set, w max It is the maximum length of the window to be set.

8. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window according to claim 6, characterized in that: The weighted weights of the data points of the vibration response signal in the window are calculated by an exponential weighting mechanism to obtain a weighted vibration response signal for identification; 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: Γ(j,t)=α t-j Where Γ(j,t) represents the weight of the vibration response signal x(j) at time t, α∈(0,1) is the exponential decay factor; j is the time index of the data point in the window; The predicted value for each moment The weighted vibration signal response is calculated by weighted averaging: Among them, w(t) is the window size at the current moment, and Γ(j,t) decays exponentially as tj increases.

9. The method for identifying under-timed variable working modal parameters based on a dynamic sliding window as claimed in claim 8, characterized in that: The decay rate α of the weighting factor is dynamically adjusted according to the variance difference of the window: Among them, α0 is the initial weighting factor, σ(t) is the variance of the current window, and σ max is the theoretical maximum variance.

10. A device for identifying under-timed variable working modal parameters based on a dynamic sliding window, characterized in that: include A vibration response signal acquisition unit, used to acquire a vibration response signal of a linear structure at a selected sensor measurement point under a set environmental excitation; A parameter identification unit is used to obtain a denoised signal after performing adaptive filtering denoising processing on the vibration response signal in a window of a set length, extract features from the denoised signal through a convolutional neural network, construct a third-order tensor using the extracted features, and decompose the third-order tensor to obtain a modal vibration shape matrix and a modal response matrix; dynamically change the length of the window according to the mean and variance of the vibration response signal in each window, slide the window, and identify the modal vibration shape matrix and modal response matrix of the vibration response signal in the next window until all vibration response signals are identified; The output unit is used to obtain the modal vibration shape and natural frequency of the linear structure according to the modal vibration shape matrix and the modal response matrix of the identified vibration response signal, so as to realize the identification of the under-time variable working modal parameters.

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