Underdetermined working mode parameter identification method and system based on signal change sliding window

Abstract

The invention discloses an underdetermined working mode parameter identification method and system based on a signal change sliding window. The method comprises the following steps: acquiring a structure vibration response signal; the number of the sensor measuring points is less than the number of degrees of freedom; relevant parameters are set, and the current sliding window serial number i is made to be equal to 1; performing modal parameter identification on the vibration response signal in the current window; the change rate of the vibration response signal in the current window is calculated, the window length of the sliding window is changed according to the change rate, the sliding window is moved to the next window, and the sequence number i of the current sliding window is made to be equal to i + 1; repeating the step until all the vibration response signals are identified; and all identification results are connected and output, and time-varying working modal parameter identification under the underdetermined condition is realized. The invention provides a tool for exploring and analyzing a complex structure and dynamic characteristics in multi-dimensional time series data, and is suitable for processing a large amount of high-dimensional data with time-dependent characteristics, such as data of a vehicle dynamics system, a bridge system and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of modal parameter identification, and in particular to an underdetermined operating modal parameter identification method and system based on a signal change sliding window. Background Art

[0002] Traditional modal parameter identification technology is mainly aimed at time-invariant systems, assuming that the modal parameters of the system remain unchanged throughout the observation process. However, actual engineering systems (such as bridges, mechanical equipment, vehicle dynamics systems, etc.) often exhibit time-varying characteristics as time or working conditions change. For example, when a train passes over a bridge, the dynamic characteristics of the bridge will change as the position of the train changes; in rotating machinery, changes in speed will cause changes in modal frequency and damping ratio. Such time-varying characteristics pose new challenges to modal parameter identification: the modal parameters of the system change over time, making traditional static modal analysis methods inapplicable; in practical applications, the identification of the system's time-varying modal parameters often needs to be performed in real time to cope with rapid changes in system status.

[0003] The identification of time-varying operating modal parameters under underdetermined conditions involves how to accurately identify the modal parameters of the system in a dynamic system, such as modal frequency, modal damping ratio, and modal vibration shape, when the number of sensors is less than the number of modes. This identification problem is very common in practical engineering applications, especially when the sensor layout is limited, the structure is complex, or the cost is limited.

[0004] Under underdetermined conditions and time-varying systems, traditional modal analysis methods have many limitations, such as the fixed sliding window method: This method deals with time-varying systems by processing data in segments, but the selection of the sliding window size is static and difficult to adapt to rapid or drastic changes in the system. In addition, the fixed window size may cause the recognition results to lag or lack precision. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide an underdetermined working modal parameter identification method based on a signal change sliding window, comprising the following steps:

[0007] A collection step, obtaining a structural vibration response signal of a selected sensor measuring point under a set environmental excitation; the number of the sensor measuring points is less than the number of degrees of freedom;

[0008] Initialization step, setting relevant parameters and setting the current sliding window number i=1;

[0009] Identification step, performing modal parameter identification on the vibration response signal in the current window; calculating the change rate of the vibration response signal in the current window, changing the window length of the sliding window according to the change rate and moving to the next window, setting the current sliding window sequence number i=i+1; repeating the identification step until all vibration response signals are identified;

[0010] The output step connects the identification results of all windows and outputs them to achieve online identification of the time-varying structural modal parameters and realize the identification of the time-varying working modal parameters under underdetermined conditions.

[0011] Preferably, the setting of the relevant parameters is specifically as follows: setting the initial sliding window length L=L init ; Set the minimum window length L min and the maximum window length L max , and set the initial value of the forgetting factor λ(0).

[0012] Preferably, the step of performing modal parameter identification on the vibration response signal in the window comprises the following steps:

[0013] Perform empirical mode decomposition on the vibration response signal within the window to obtain a series of decomposition components X j , the sum of the decomposed components X is expressed as:

[0014]

[0015] Among them, k represents the frequency domain index, IMF j is the jth eigenmode parameter, r is the residual trend term;

[0016] Calculate each X j The frequency domain signal F j , expressed as:

[0017] F j =FFT(X j );

[0018] Wherein, FFT means Fourier transform;

[0019] Using X j The autocorrelation function analysis is used to detect the periodic characteristics of the signal and determine the lag period τ j , expressed as:

[0020]

[0021] τ j = arg max l (ACF j (l));

[0022] in, is the signal variance, μj is the signal mean, ACF j represents the autocorrelation function, l represents the time delay step; N represents the data length;

[0023] A tensor is constructed based on the frequency domain signal and CP decomposition is performed to achieve mode identification.

[0024] Preferably, constructing a tensor based on a frequency domain signal and performing CP decomposition comprises the following steps:

[0025] Initialize a third-order tensor X , whose dimension is n m ×K×τ, K is the feature dimension, τ is the maximum lag period, n m is the number of sensors;

[0026] For each l, fill the corresponding frequency domain and time domain features into the third dimension of the tensor:

[0027] X [:,:,l]=F·diag(τ j )

[0028] Where diag(τ) is the diagonal matrix of lag period, which is used to associate features with lag period; F refers to frequency domain features;

[0029] Perform CP decomposition on the constructed tensor:

[0030]

[0031] in, Represents the outer product multiplication of vectors; is the mode shape matrix; is the modal response matrix; Θ r represents the rth component of the weight matrix;

[0032] The modal vibration shape is obtained through the modal vibration shape matrix, and the natural frequency w corresponding to the modal vibration shape is estimated by Fourier transform processing of the vectors in the modal response matrix. i , as the recognition result within the window.

[0033] Preferably, the frequency domain feature F includes the main frequency f peak , spectrum energy E and band energy ratio B, respectively, are expressed as:

[0034] f peak = argmax(|F j |);

[0035]

[0036] Among them, f lowRefers to the lower frequency part of the signal spectrum, f high Refers to the higher frequency portion of a signal's spectrum; K is the feature dimension.

[0037] Preferably, calculating the change rate of the vibration response signal in the current window, changing the window length of the sliding window according to the change rate and moving to the next window comprises the following steps:

[0038] Calculate the signal change rate within the i-th window, expressed as:

[0039] Δx(t)=x(t)-x(t-1);

[0040] Where t represents the time step, and Δx(t) represents the rate of change of the signal at the t time step.

[0041] The forgetting factor is updated by the change rate Δx(t), which is expressed as:

[0042] λ(t)=λ(t-1)e -β·|Δx(t)| ;

[0043] Among them, β is a tuning parameter used to control the decay speed of the forgetting factor, and the specific value is set in the initialization step; λ(t) represents the forgetting factor of time step t;

[0044] The size of the sliding window is adjusted according to the value of the forgetting factor λ(t), which is expressed as:

[0045] L(t)=L min +(λ(t)·(L max -L min ));

[0046] Among them, L(t) represents the window length of t time step, L min is the minimum window length, L max is the maximum window length;

[0047] After the window length is adjusted, the sliding window slides forward to the i+1 window.

[0048] The present invention also provides an underdetermined operating modal parameter identification system based on a signal change sliding window, comprising:

[0049] An acquisition module is used to obtain structural vibration response signals of selected sensor measuring points under set environmental excitation; the number of the sensor measuring points is less than the number of degrees of freedom;

[0050] Initialize the module, set relevant parameters, and set the current sliding window number i=1;

[0051] The recognition module recognizes the modal parameters of the vibration response signal in the current window; calculates the change rate of the vibration response signal in the current window, changes the window length of the sliding window according to the change rate and moves to the next window, and sets the current sliding window sequence number i=i+1; repeats the recognition steps until all vibration response signals are recognized;

[0052] The output module connects the identification results of all windows and outputs them, so as to achieve the online identification of the time-varying structural modal parameters and realize the identification of the time-varying working modal parameters under underdetermined conditions.

[0053] The present invention has the following beneficial effects:

[0054] (1) The present invention adjusts the size of the sliding window and the forgetting factor to make it more sensitive to the sudden change and non-stationarity of the signal, and can respond to the changes in the input signal in real time and adjust the window length, 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 of time-varying modes. The method is particularly suitable for the case where the number of sensors is less than the number of modes to be identified, and can accurately extract modal information under underdetermined conditions. It is particularly suitable for complex scenarios such as non-stationary signals and multi-modal signals, and solves the problem that the traditional method has incomplete recognition of modal information due to insufficient sensors.

[0055] (2) The present invention provides a powerful tool for exploring and analyzing the complex structures and dynamic characteristics in multidimensional time series data by integrating autocorrelation, PCA, dynamic sliding windows, forgetting factors, 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.

[0056] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A method step diagram of an embodiment of the present invention;

[0058] Figure 2 Detailed flowchart of an embodiment of the present invention.

[0059] Figure 3 A diagram of a time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention;

[0060] Figure 4 A comparison diagram of the recognition results (modal vibration shapes) of a time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention;

[0061] Figure 5 This is a comparison diagram of the recognition results (natural frequency) of the time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention;

[0062] Figure 6 The MAC value variation curve of the recognition result of the time-varying three-degree-of-freedom spring oscillator model according to the embodiment of the present invention;

[0063] Figure 7 4 is a system structure diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0064] See also Figure 1 and Figure 2 The method step diagram and detailed flow chart of the embodiment of the present invention are shown, which include the following steps:

[0065] S101, a collection step of obtaining structural vibration response signals of selected sensor measuring points under a set environmental excitation; the number of the sensor measuring points is less than the number of degrees of freedom;

[0066] S102, initialization step, setting relevant parameters, and setting the current sliding window sequence number i=1;

[0067] S103, identification step, performing modal parameter identification on the vibration response signal in the current window; calculating the change rate of the vibration response signal in the current window, changing the window length of the sliding window according to the change rate and moving to the next window, setting the current sliding window sequence number i=i+1; repeating the identification step until all vibration response signals are identified;

[0068] S104, output step, connects and outputs the identification results of all windows to achieve online identification of time-varying structural modal parameters and realize identification of time-varying operating modal parameters under underdetermined conditions.

[0069] See also Figure 3 As shown, a linear time-varying three-degree-of-freedom spring oscillator system is used to perform a modal identification experiment on the system using the embodiment of the present invention. The experimental conditions are: the sampling frequency f is 40Hz, the sampling interval Δt is 0.025s, and the sampling time is t=2000s. Assume that the initial conditions of the three-degree-of-freedom displacement of the system are all zero, apply Gaussian white noise excitation to the object, and set the masses to be:

[0070]

[0071] m2=m3=1kg;

[0072] In addition, stiffness k1 = 1000 N / m, k2 = 1000 N / m, k3 = 1000 N / m; damping c1 = 0.01 Ns / m, c2 = 0.01 Ns / m, c3 = 0.01 Ns / m.

[0073] Experiments were conducted on a three-degree-of-freedom spring oscillator. The response signal was simulated using MATLAB / Newmark-β, with a sampling frequency of 40 Hz, a sampling duration of t=2000s, and a sampling interval of 0.025s. This embodiment compares and evaluates the underdetermined working modal parameter identification method of a linear time-varying structure by using the modal assurance criterion (MAC) and the relative error of the modal natural frequency. The formula of the modal assurance criterion is as follows:

[0074]

[0075] 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.

[0076] The formula for the natural frequency relative error evaluation method is as follows:

[0077]

[0078] 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.

[0079] The MAC value identification results of the three-degree-of-freedom spring oscillator obtained in this experiment at the instant of 850s and 1500s are shown in Tables 1 and 2, and the natural frequency error is shown in Table 3; Figure 4 A comparison diagram of the recognition results (modal vibration shapes) of a time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention; Figure 5 This is a comparison diagram of the recognition results (natural frequency) of the time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention; Figure 6 This is a curve showing the change in MAC value of the recognition result of the time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present invention.

[0080] Table 1 Confidence criteria of each modal at 850s

[0081] Degree MAC 1 1.0000 2 0.9937 3 0.9816

[0082] Table 2 Confidence criteria of each modal at 1500s

[0083] Degree MAC 1 1.0000 2 0.9713 3 0.9518

[0084] Table 3 Natural frequency errors of each order

[0085] Degree Theoretical natural frequency Identifying Natural Frequencies Natural frequency error 1 2.2399 2.2870 2.1027％ 2 6.2760 6.5700 4.6850％ 3 9.0690 9.5430 5.2266％

[0086] From Table 1 to Table 3 and Figures 4 to 6 It can be seen that the method proposed in the present invention can well realize the identification of modal parameters under under-time variation conditions.

[0087] For details, see Figure 7 FIG. 1 is a system structure diagram of an embodiment of the present invention, including:

[0088] The acquisition module 701 acquires the structural vibration response signal of the selected sensor measurement points under the set environmental excitation; the number of the sensor measurement points is less than the number of degrees of freedom;

[0089] Initialization module 702, setting relevant parameters and setting the current sliding window sequence number i=1;

[0090] The identification module 703 performs modal parameter identification on the vibration response signal in the current window; calculates the change rate of the vibration response signal in the current window, changes the window length of the sliding window according to the change rate and moves to the next window, and sets the current sliding window sequence number i=i+1; repeats the identification steps until all vibration response signals are identified;

[0091] The output module 704 connects the identification results of all windows and outputs them, so as to achieve online identification of the time-varying structural modal parameters and realize the identification of the time-varying operating modal parameters under underdetermined conditions.

[0092] It can be seen that the present invention provides an underdetermined working modal parameter identification method based on a signal change rate sliding window. The size of the forgetting factor is changed by calculating the change rate of the input signal, and then the size of the sliding window is changed. According to the short-term time-invariant assumption, the data in the window can be considered to be time-invariant; then, the sliding window moves, new data is added and old data is deleted, and the recognition of the time-varying structure is realized through the sliding window.

[0093] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying underdetermined operating modal parameters based on a signal change sliding window, characterized in that: The following steps are involved: The acquisition step is to obtain the structural vibration response signal of the selected sensor measuring points under the set environmental excitation; the number of the sensor measuring points is less than the number of degrees of freedom; Initialization step, setting relevant parameters and setting the current sliding window number i=1; Identification step, performing modal parameter identification on the vibration response signal in the current window; calculating the change rate of the vibration response signal in the current window, changing the window length of the sliding window according to the change rate and moving to the next window, setting the current sliding window sequence number i=i+1; repeating the identification step until all vibration response signals are identified; The output step connects the identification results of all windows and outputs them to achieve online identification of the time-varying structural modal parameters and realize the identification of the time-varying working modal parameters under underdetermined conditions.

2. The underdetermined operating modal parameter identification method based on signal change sliding window according to claim 1 is characterized in that: The setting of the relevant parameters is specifically as follows: setting the initial sliding window length L = L init ; Set the minimum window length L min and the maximum window length L max , and set the initial value of the forgetting factor λ(0).

3. The underdetermined operating modal parameter identification method based on signal change sliding window according to claim 1 is characterized in that: The modal parameter identification of the vibration response signal in the window comprises the following steps: Perform empirical mode decomposition on the vibration response signal within the window to obtain a series of decomposition components X j , the sum of the decomposed components X is expressed as: Among them, k represents the frequency domain index, IMF j is the jth eigenmode parameter, r is the residual trend term; Calculate each X j The frequency domain signal F j , expressed as: F j =FFT(X j ); Wherein, FFT means Fourier transform; Using X j The autocorrelation function analysis is used to detect the periodic characteristics of the signal and determine the lag period τ j , expressed as: t j =argmax l (ACF j (l)); in, is the signal variance, μ j is the signal mean, ACF j represents the autocorrelation function, l represents the time delay step; N represents the data length; A tensor is constructed based on the frequency domain signal and CP decomposition is performed to achieve mode identification.

4. The underdetermined operating modal parameter identification method based on signal change sliding window according to claim 3 is characterized in that: The method of constructing a tensor based on a frequency domain signal and performing CP decomposition comprises the following steps: Initialize a third-order tensor Its dimension is n m ×K×τ, K is the feature dimension, τ is the maximum lag period, n m is the number of sensors; For each l, fill the corresponding frequency domain and time domain features into the third dimension of the tensor: Where diag(τ) is the diagonal matrix of lag period, which is used to associate features with lag period; F refers to frequency domain features; Perform CP decomposition on the constructed tensor: Among them, ° represents the outer product multiplication of vectors; is the mode shape matrix; is the modal response matrix; Θ r represents the rth component of the weight matrix; The modal vibration shape is obtained through the modal vibration shape matrix, and the natural frequency w corresponding to the modal vibration shape is estimated by Fourier transform processing of the vectors in the modal response matrix. i , as the recognition result within the window.

5. The underdetermined operating modal parameter identification method based on signal change sliding window according to claim 4 is characterized in that: The frequency domain feature F includes the main frequency f peak , spectrum energy E and band energy ratio B, respectively, are expressed as: f peak =argmax(|F j |); Among them, f low Refers to the lower frequency part of the signal spectrum, f high Refers to the higher frequency portion of a signal's spectrum; K is the feature dimension.

6. The underdetermined operating modal parameter identification method based on signal change sliding window according to claim 1, characterized in that: The step of calculating the change rate of the vibration response signal in the current window, changing the window length of the sliding window according to the change rate and moving to the next window comprises the following steps: Calculate the signal change rate within the i-th window, expressed as: Δx(t)=x(t)-x(t-1); Where t represents the time step, and Δx(t) represents the rate of change of the signal at the t time step. The forgetting factor is updated by the change rate Δx(t), which is expressed as: λ(t)=λ(t-1)e -β·|Δx(t)| ; Among them, β is a tuning parameter used to control the decay speed of the forgetting factor, and the specific value is set in the initialization step; λ(t) represents the forgetting factor of time step t; The size of the sliding window is adjusted according to the value of the forgetting factor λ(t), which is expressed as: L(t)=L min +(λ(t)·(L max -L min )); Among them, L(t) represents the window length of t time step, L min is the minimum window length, L max is the maximum window length; After the window length is adjusted, the sliding window slides forward to the i+1 window.

7. An underdetermined operating modal parameter identification system based on a signal change sliding window, characterized in that: include: The acquisition module obtains the structural vibration response signal of the selected sensor measurement point under the set environmental excitation; The number of sensor measurement points is less than the number of degrees of freedom; Initialize the module, set relevant parameters, and set the current sliding window number i=1; The recognition module recognizes the modal parameters of the vibration response signal in the current window; calculates the change rate of the vibration response signal in the current window, changes the window length of the sliding window according to the change rate and moves to the next window, and sets the current sliding window sequence number i=i+1; repeats the recognition steps until all vibration response signals are recognized; The output module connects the identification results of all windows and outputs them, so as to achieve online identification of the time-varying structural modal parameters and realize the identification of the time-varying working modal parameters under underdetermined conditions.

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