Underdetermined operational modal parameter identification method and system based on signal change sliding window

Abstract

The application discloses a method and system for underdetermined operational modal parameter identification based on signal change sliding window, which comprises the following steps: obtaining a structure vibration response signal; the number of sensor measuring points is less than the number of degrees of freedom; setting relevant parameters and letting the current sliding window serial number; 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, letting the current sliding window serial number; repeating the step until all the vibration response signals are identified; connecting all the identification results and outputting, and realizing underdetermined time-varying operational modal parameter identification. The application provides a tool for exploring and analyzing complex structures and dynamic characteristics in multi-dimensional time series data, which is suitable for processing a large amount of high-dimensional data with time-dependent characteristics, such as vehicle dynamics system, bridge system and the like.

Description

Technical Field

[0001] This invention relates to the field of modal parameter identification technology, and in particular to a method and system for identifying underdetermined operating modal parameters based on a sliding window for signal changes. Background Technology

[0002] Traditional modal parameter identification techniques primarily target time-invariant systems, assuming that the system's modal parameters remain constant throughout the observation process. However, real-world engineering systems (such as bridges, mechanical equipment, and vehicle dynamics systems) often exhibit time-varying characteristics as time or operating conditions change. For example, the dynamic characteristics of a bridge change with the train's position when it crosses; in rotating machinery, changes in rotational speed lead to variations in modal frequencies and damping ratios. These time-varying characteristics present new challenges to modal parameter identification: the system's modal parameters change over time, rendering traditional static modal analysis methods inapplicable; and in practical applications, identifying the system's time-varying modal parameters often requires real-time analysis to address rapid changes in the system's state.

[0003] Identification of time-varying modal parameters under underdetermined conditions involves accurately identifying modal parameters, such as modal frequencies, modal damping ratios, and mode shapes, in dynamic systems when the number of sensors is less than the number of modes. This identification problem is very common in practical engineering applications, especially when sensor placement is limited, the structure is complex, or cost is a constraint.

[0004] Traditional modal analysis methods have many limitations under underdetermined conditions and time-varying systems. For example, the fixed sliding window method addresses time-varying systems by segmenting the data, but the window size is static and cannot adapt to rapid or drastic changes in the system. Furthermore, a fixed window size may lead to delayed recognition results or insufficient accuracy. Summary of the Invention

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

[0006] The technical solution adopted by this invention to solve its technical problem is: to provide a method for identifying underdetermined operating mode parameters based on a sliding window of signal changes, comprising the following steps:

[0007] The data acquisition step involves obtaining the structural vibration response signal from the selected sensor measurement points under a set environmental excitation; the number of sensor measurement points is less than the number of degrees of freedom.

[0008] The initialization steps involve setting relevant parameters and assigning the current sliding window number. ;

[0009] The identification step is to identify the modal parameters of 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 and moved to the next window according to the change rate, and the current sliding window number is ; the identification step is repeated until all the vibration response signals are identified;

[0010] The output step is to connect the identification results of all the windows and output, so as to realize the online identification of the modal parameters of the time-varying structure and realize the identification of the time-varying working modal parameters under the underdetermined condition.

[0011] Preferably, the setting of the related parameters is specifically: the initial sliding window length is set to ; the minimum window length and the maximum window length are set to specific values, and the initial value of the forgetting factor is set.

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

[0013] The vibration response signal in the window is subjected to empirical mode decomposition to obtain a series of decomposition components , and the sum X of the decomposition components is represented as:

[0014] ;

[0015] wherein k represents the frequency domain index, is the th intrinsic modal parameter, is the residual trend item;

[0016] The frequency domain signal of each is calculated , and is represented as:

[0017] ;

[0018] wherein represents the Fourier transform;

[0019] The autocorrelation function analysis of is used to detect the periodic characteristics of the signal and determine the lag period , and is represented as:

[0020] ;

[0021] ;

[0022] wherein is the signal variance, is the signal mean, denotes the autocorrelation function, denotes the step size of time delay; N denotes the data length;

[0023] The frequency domain signal is used to construct a tensor and perform CP decomposition to realize modal identification.

[0024] Preferably, the frequency domain signal is used to construct a tensor and perform CP decomposition, including the following steps:

[0025] Initialize a third-order tensor with dimensions K , K is the feature dimension, is the maximum lag period, is the number of sensors;

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

[0027]

[0028] wherein, is a diagonal matrix of the lag period, used to associate the features with the lag period; denotes the frequency domain feature;

[0029] CP decomposition is performed on the constructed tensor:

[0030] ;

[0031] wherein, denotes the outer product multiplication of vectors; is the modal shape matrix; is the modal response matrix; denotes the rth component of the weight matrix;

[0032] The modal shape is obtained through the modal shape matrix, and the Fourier transform processing is performed on the vectors in the modal response matrix to estimate the natural frequency corresponding to the modal shape , which is the identification result in this window.

[0033] Preferably, the frequency domain feature includes the main frequency , the spectral energy , and the frequency band energy ratio , which are respectively represented as:

[0034] ;

[0035] ;

[0036] ;

[0037] wherein, refers to the lower frequency part of the signal spectrum, refers to the higher frequency part of the signal spectrum; , is the feature dimension.

[0038] Preferably, the change rate of the vibration response signal in the current window is calculated, the window length of the sliding window is changed and the next window is moved according to the change rate, including the following steps:

[0039] The signal change rate in the first window is calculated, expressed as:

[0040] ;

[0041] wherein, t represents a time step, represents the signal change rate at t time step

[0042] The forgetting factor is updated by the change rate , expressed as:

[0043] ;

[0044] wherein, is an adjustment parameter for controlling the decay rate of the forgetting factor, and a specific value is set in the initialization step; represents the forgetting factor at t time step;

[0045] The size of the sliding window is adjusted according to the value of the forgetting factor , expressed as:

[0046] ;

[0047] wherein, represents the window length at t time step, is the minimum window length, is the maximum window length;

[0048] After the window length size is adjusted, the sliding window is slid forward to the window.

[0049] The application also provides an underdetermined operational modal parameter identification system based on signal change sliding window, comprising:

[0050] A collection module acquires the structural vibration response signal of the selected sensor measuring point under the set environmental excitation; the number of the sensor measuring point is less than the number of degrees of freedom;

[0051] Initialization module, set relevant parameters, and let the current sliding window sequence number ;

[0052] Identification module, modal parameter identification is carried out 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, and the next window is moved to, the current sliding window sequence number ; repeat the identification step until all vibration response signals are identified;

[0053] Output module, connect the identification results of all windows and output, achieve online identification of time-varying structure modal parameters, realize time-varying working modal parameter identification under underdetermined condition.

[0054] The present application has the following beneficial effects:

[0055] (1) The present application adjusts the size of the sliding window and the forgetting factor, so that it is more sensitive to the mutation and non-stationarity of the signal, can respond to the change of the input signal in real time, adjust the window length, solve the problem that the traditional fixed window method cannot adapt to the non-stationarity of the system, improve the identification accuracy and adaptability of the time-varying modal; this method is especially suitable for the case that the number of sensors is less than the number of modal to be identified, can accurately extract modal information under underdetermined condition, especially suitable for complex scenes such as non-stationary signal and multi-modal signal, solves the problem that the identification modal information is incomplete due to insufficient sensors in traditional method.

[0056] (2) The present application integrates autocorrelation, PCA, dynamic sliding window, forgetting factor and tensor decomposition, provides a powerful tool for exploring and analyzing complex structures and dynamic characteristics in multi-dimensional time series data; this method is especially suitable for processing large, high-dimensional and time-dependent data sets, such as vehicle dynamics system, bridge and other fields.

[0057] The present application will be further described in detail in combination with the drawings and examples, but the present application is not limited to the examples. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 The method step diagram of the embodiment of the present application;

[0059] Figure 2 The detailed flow chart of the embodiment of the present application.

[0060] Figure 3 The time-varying three-degree-of-freedom spring oscillator model diagram of the embodiment of the present application;

[0061] Figure 4 The identification result (modal shape) comparison diagram of the time-varying three-degree-of-freedom spring oscillator model of the embodiment of the present application;

[0062] Figure 5 Figure 4 is a comparison chart of the identification results (natural frequency) of the time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present application;

[0063] Figure 6 Figure 5 is a MAC value change curve of the identification results of the time-varying three-degree-of-freedom spring oscillator model according to an embodiment of the present application;

[0064] Figure 7 Figure 6 is a system structure diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0065] Referring to Figure 7, which is a method step diagram and a detailed flowchart of an embodiment of the present application, including the following steps: Figure 1 and Figure 2 Referring to Figure 7, which is a method step diagram and a detailed flowchart of an embodiment of the present application, including the following steps:

[0066] S101, a collection step, obtaining structural vibration response signals of selected sensor measurement points under a set environmental excitation; the number of the sensor measurement points is less than the number of degrees of freedom;

[0067] S102, an initialization step, setting relevant parameters, and setting the current sliding window serial number ;

[0068] S103, an identification step, performing modal parameter identification on the vibration response signals in the current window; calculating the rate of change of the vibration response signals in the current window, changing the window length of the sliding window according to the rate of change, and moving to the next window, setting the current sliding window serial number ; repeating the identification step until all vibration response signals are identified;

[0069] S104, an output step, connecting and outputting the identification results of all windows, achieving online identification of time-varying structural modal parameters, and realizing time-varying working modal parameter identification under underdetermined conditions.

[0070] Referring to Figure 8, which is a linear time-varying three-degree-of-freedom spring oscillator system, an experiment is performed on the system using an embodiment of the present application. The experimental conditions are as follows: the sampling frequency is 40 Hz, the sampling interval is 0.025 s, and the sampling time is t=2000 s. The initial conditions of the three degrees of freedom displacement of the system are all zero, a Gaussian white noise excitation is applied to the mass, and the masses are set as follows: Figure 3 ;

[0071] ;

[0072] 1 kg;

[0073] ​​In addition, the stiffness k1=1000N / m, k2=1000N / m, k3=1000N / m; the damping c1=0.01N.s / m, c2=0.01N.s / m, c3=0.01N.s / m.

[0074] The three-degree-of-freedom spring oscillator is experimented. The response signal is obtained by simulation simulation, the sampling frequency of the signal is 40Hz, the sampling time is t=2000s, and the sampling interval is 0.025s. The underdetermined operating modal parameter identification method of the linear time-varying structure is compared and evaluated by the modal confidence criterion (MAC) and the relative error of the modal natural frequency. The formula of the modal confidence criterion is as follows:

[0075]

[0076] Wherein, and respectively represent the estimated modal shape vector and the real modal shape vector of the first order, and the MAC value changes between 0 and 1. The larger the MAC value (close to 1), the better the mode.

[0077] The formula of the relative error evaluation method of the natural frequency is as follows:

[0078] 00%

[0079] Wherein, and respectively represent the estimated modal natural frequency and the theoretical natural frequency of the first order, The closer the value of to 0, the more accurate the identified natural frequency.

[0080] The MAC value identification results of the three-degree-of-freedom spring oscillator obtained in the experiment at 850s and 1500s are shown in Tables 1 and 2, and the natural frequency error is shown in Table 3; Figure 4 It is the comparison chart of the identification results (modal shape) of the time-varying three-degree-of-freedom spring oscillator model of the embodiment of the application; Figure 5 It is the comparison chart of the identification results (natural frequency) of the time-varying three-degree-of-freedom spring oscillator model of the embodiment of the application; Figure 6 It is the MAC value change curve of the identification results of the time-varying three-degree-of-freedom spring oscillator model of the embodiment of the application.

[0081] Table 1: Modal confidence criterion degree of each order at 850s

[0082] Order MAC 1 1.0000 2 0.9937 3 0.9816

[0083] Table 2: Modal confidence criterion degree of each order at 1500s

[0084] Order MAC 1 1.0000 2 0.9713 3 0.9518

[0085] Table 3 Inherent frequency error of each order

[0086] Order Theoretical natural frequency Identified natural frequency Natural frequency error 1 2.2399 2.2870 2.1027% 2 6.2760 6.5700 4.6850% 3 9.0690 9.5430 5.2266%

[0087] From Table 1 to Table 3 and Figures 4 to 6 It can be seen that the method provided by the present application can well realize identification of modal parameters under underdetermined time-varying conditions.

[0088] Specifically, referring to Figure 7 , it is a system structure diagram of the embodiment of the present application, which comprises:

[0089] The acquisition module 701 acquires the structural vibration response signal of the selected sensor measuring point under the set environmental excitation; the number of the sensor measuring points is less than the number of degrees of freedom;

[0090] The initialization module 702 sets the related parameters and lets the current sliding window serial number ;

[0091] The identification module 703 identifies the modal parameters of 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 and the sliding window is moved to the next window, the current sliding window serial number is let; the identification step is repeated until all the vibration response signals are identified;

[0092] The output module 704 connects the identification results of all the windows and outputs, so as to realize online identification of the modal parameters of the time-varying structure and realize identification of the working modal parameters under underdetermined conditions.

[0093] It can be seen that the present application 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 to change the size of the sliding window, according to the short-time time-invariant assumption, the data in the window can be considered as time-invariant; then, the sliding window is moved, new data is added and old data is deleted, and through the sliding window, identification of the time-varying structure is realized.

[0094] The above is only the preferred embodiment of the present application, and is not used to limit the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for identifying underdetermined operating mode parameters based on a sliding window for signal variation, characterized in that, Includes the following steps: The data acquisition step involves obtaining the structural vibration response signal from the selected sensor measurement points under a set environmental excitation; the number of sensor measurement points is less than the number of degrees of freedom. The initialization steps involve setting relevant parameters and assigning the current sliding window number. ; The identification steps involve: identifying modal parameters of the vibration response signal within the current window; calculating the rate of change of the vibration response signal within the current window; adjusting the window length of the sliding window based on the rate of change and moving to the next window; and assigning the current sliding window number to... ; Repeat the identification process until all vibration response signals have been identified; The output steps connect and output the recognition results of all windows to achieve online recognition of time-varying structural modal parameters and realize the recognition of time-varying working modal parameters under underdetermined conditions. The modal parameter identification of the vibration response signal within the current window includes the following steps: Empirical mode decomposition was performed on the vibration response signal within the window to obtain a series of decomposed components. The sum of the decomposed components, X, is expressed as: ； Where k represents the frequency domain index, It is the first One intrinsic modal parameter, It is the residual trend term; Calculate each frequency domain signal , represented as: ； in, Indicates Fourier transform; use Autocorrelation function analysis is used to detect the periodicity of signals and determine the lag period. , represented as: ； ； in, For signal variance, The mean of the signal. Represents the autocorrelation function. The step size represents the time delay; N represents the data length. Modality recognition is achieved by constructing a tensor based on the frequency domain signal and performing CP decomposition. The process of calculating the rate of change of the vibration response signal within the current window, changing the window length of the sliding window based on the rate of change, and moving to the next window includes the following steps: Calculate the first The rate of change of the signal within each window is expressed as: ； Where t represents the time step, This represents the rate of change of the signal at time step t; By signal change rate The updated forgetting factor is represented as: ； in, This is an adjustment parameter used to control the decay rate of the forgetting factor; its specific value is set during the initialization step. The forgetting factor represents the time step t. According to the forgetting factor The value adjusts the size of the sliding window, represented as: ； in, This represents the window length at time step t. It is the minimum window length. It is the maximum window length; After adjusting the window size, slide the sliding window forward to... window.

2. The underdetermined operating mode parameter identification method based on a signal variation sliding window according to claim 1, characterized in that, The specific parameters to be set are: Setting the initial sliding window length. Set minimum window length and maximum window length The specific value, setting the initial value of the forgetting factor. .

3. The underdetermined operating mode parameter identification method based on a signal variation sliding window according to claim 1, characterized in that, The process of constructing a tensor based on a frequency domain signal and performing CP decomposition includes the following steps: Initialize a third-order tensor Its dimensions are K K is the feature dimension. The maximum lag period, Number of sensors; For each Fill the third dimension of the tensor with the corresponding frequency domain and time domain features: ； in, It is a diagonal matrix of lag periods, used to associate features with lag periods; Frequency domain characteristics; Perform CP decomposition on the constructed tensor: ； in, This represents the outer product of vectors; It is the modal shape matrix; It is the modal response matrix; This represents the r-th component of the weight matrix; The mode shapes are obtained through the mode shape matrix, and the natural frequencies corresponding to the mode shapes are estimated by performing Fourier transform on the vectors in the modal response matrix. This serves as the recognition result within that window.

4. The underdetermined operating mode parameter identification method based on a signal variation sliding window according to claim 3, characterized in that, The frequency domain features Including clock speed Spectral energy and frequency band energy ratio , respectively represented as: ； ； ； in, This refers to the lower frequency portion of the signal spectrum. This refers to the higher frequency portion of the signal spectrum; , It is the feature dimension.

5. A system for identifying underdetermined operating mode parameters based on a sliding window for signal changes, characterized in that, include: The acquisition module acquires the structural vibration response signal of the selected sensor measurement points under a 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 assign the current sliding window number. ; The identification module performs modal parameter identification on the vibration response signal within the current window; it calculates the rate of change of the vibration response signal within the current window, adjusts the window length of the sliding window according to the rate of change, and moves to the next window, setting the current sliding window index... ; Repeat the identification process until all vibration response signals have been identified; The output module connects and outputs the recognition results of all windows, achieving online recognition of time-varying structural modal parameters and realizing the recognition of time-varying working modal parameters under underdetermined conditions. The modal parameter identification of the vibration response signal within the current window includes the following steps: Empirical mode decomposition was performed on the vibration response signal within the window to obtain a series of decomposed components. The sum of the decomposed components, X, is expressed as: ； Where k represents the frequency domain index, It is the first One intrinsic modal parameter, It is the residual trend term; Calculate each frequency domain signal , represented as: ； in, Indicates Fourier transform; use Autocorrelation function analysis is used to detect the periodicity of signals and determine the lag period. , represented as: ； ； in, For signal variance, The mean of the signal. Represents the autocorrelation function. The step size represents the time delay; N represents the data length. Modality recognition is achieved by constructing a tensor based on the frequency domain signal and performing CP decomposition. The process of calculating the rate of change of the vibration response signal within the current window, changing the window length of the sliding window based on the rate of change, and moving to the next window includes the following steps: Calculate the first The rate of change of the signal within each window is expressed as: ； Where t represents the time step, This represents the rate of change of the signal at time step t; By signal change rate The updated forgetting factor is represented as: ； in, This is an adjustment parameter used to control the decay rate of the forgetting factor; its specific value is set during the initialization step. The forgetting factor represents the time step t. According to the forgetting factor The value adjusts the size of the sliding window, represented as: ； in, This represents the window length at time step t. It is the minimum window length. It is the maximum window length; After adjusting the window size, slide the sliding window forward to... window.

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