Automatic extraction method of non-stationary segments of time series signals of wind-induced vibration of structures

Abstract

The present invention discloses a method for automatically extracting non-stationary segments of a structural wind-induced vibration time series signal, comprising: using a method of cubic spline interpolation of the maximum value of a data segment of a given length to calculate the upper envelope of the vibration time series signal, using a Gaussian mixture model to fit the probability density distribution of the upper envelope data, defining the first-order single Gaussian distribution fitting parameter with the smallest mean in the Gaussian mixture model as a statistical characteristic parameter of the vibration signal stationary data, and calculating the critical value of the vibration stationary data when the cumulative distribution function is close to 1, intercepting the corresponding time data segment when the upper envelope data is continuously greater than the critical value from the vibration time series signal, and selecting the data segment with a length greater than a preset length and a maximum value greater than a preset value in the intercepted data segment as the effective result of the wind-induced vibration non-stationary segment. The method of the present invention realizes the automatic and rapid extraction of non-stationary segments of structural wind-induced vibration time series signals that is less dependent on the professional knowledge of relevant practitioners.

Description

Technical Field

[0001] The invention belongs to the field of digital monitoring, detection and evaluation of structures, and in particular relates to a method for automatically extracting non-stationary segments of a time series signal of wind-induced vibration of a structure. Background Art

[0002] Structures and their components have been subjected to continuous wind loads since their construction. The random action of wind loads will produce random non-stationary segments in the vibration signals of structures or components. Accurately and effectively extracting non-stationary segments from the wind-induced vibration time series signals of structures is a prerequisite for analyzing the vibration performance of structures under wind loads. With the development of testing and transmission technology, it is not difficult to obtain the vibration time series signals of structures in real wind environments in real time and accurately. However, there is no clear and quantifiable boundary between the stationary and non-stationary segments in the wind-induced vibration time series signals. It is difficult for people who lack professional knowledge to accurately distinguish and automatically extract them through computer programs, which restricts the real-time nature of data analysis.

[0003] At present, there are few methods for automatically extracting non-stationary segments of wind-induced vibration time series signals in the fields of civil engineering and mechanics. The commonly used methods are as follows: (1) Professionals with professional knowledge use their experience to manually identify and extract non-stationary segments of the vibration time series signals that have been drawn. This method is simple and clear, but it is very dependent on the subjective judgment of the implementers, and because it needs to be completed manually, the timeliness of the method is extremely poor; (2) Professionals with professional knowledge set an empirical threshold, and then use a computer to automatically extract the signal that exceeds the threshold. However, due to the particularity of the vibration signal, the non-stationary segment is a signal with a mean value close to zero and oscillating up and down. The empirical threshold cannot completely extract the part of the non-stationary segment that is smaller than the threshold. In summary, the existing technologies cannot achieve the automatic extraction of the complete wind-induced vibration non-stationary segment by computer while relying as little on structural dynamics experience as possible.

[0004] Therefore, it is necessary to develop an automated method for extracting non-stationary segments of structural wind-induced vibration time series signals that is less dependent on the professional knowledge of relevant practitioners, so as to achieve rapid perception of the non-stationary characteristics of structural wind-induced vibration. Summary of the invention

[0005] In view of the above problems, the present invention proposes a method for automatically extracting non-stationary segments of structural wind-induced vibration time series signals, which can help non-related professional practitioners to quickly extract non-stationary segments of structural wind-induced vibration time series signals by computer.

[0006] To achieve the purpose of the present invention, the technical solution adopted by the present invention is:

[0007] A method for automatically extracting non-stationary segments of a structural wind-induced vibration time series signal specifically comprises the following steps:

[0008] Step 1, extracting the time series signal of wind-induced vibration of the structure, calculating the maximum value of the time series signal of wind-induced vibration in each predetermined length segment, using the cubic spline interpolation method to interpolate the coordinate positions of the remaining sampling points outside the maximum value position based on the maximum value of each predetermined length segment, and using the obtained interpolation curve result as the upper envelope data of the vibration time series signal;

[0009] Step 2, use the Gaussian mixture model to fit the probability density distribution of the upper envelope data;

[0010] Step 3, define the first-order single Gaussian distribution fitting parameter with the minimum mean in the Gaussian mixture model as the statistical characteristic parameter of the stationary data of the wind-induced vibration signal, normalize the integral value of the single Gaussian distribution curve of the stationary data to 1 on [0,∞], and obtain the Gaussian distribution probability density curve of the stationary data;

[0011] Step 4, integrating the Gaussian distribution probability density curve of the stationary data to obtain its cumulative distribution function curve, making the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α have a guarantee rate of β, and calculating the α value when the given β is close to 1; wherein α is the critical value of the stationary data and the non-stationary data;

[0012] Step 5, intercepting the corresponding data segments whose upper envelope data is continuously greater than α from the time series signal of wind-induced vibration, and selecting the data segments whose time length is greater than a preset length and whose maximum value of the wind-induced vibration signal is greater than a preset value as the effective results of the non-stationary segments of wind-induced vibration.

[0013] Furthermore, in said step 1, a time series signal of wind-induced vibration is extracted from a vibration sensor such as acceleration, velocity or dynamic displacement installed on the structure;

[0014] Furthermore, in step 1, a predetermined length segment is set to be an integer multiple (generally more than 10 times) of the sensor sampling frequency.

[0015] Furthermore, the calculation formula for fitting the probability density distribution of the upper envelope data using the Gaussian mixture model in step 2 is as follows:

[0016]

[0017] Where f(x) is the probability density distribution of the upper envelope data, x is the upper envelope data, μ i , σ i and φ i are the mean, standard deviation and weight fitting parameters of the i-th order single Gaussian distribution, and K is the total order of the Gaussian mixture model.

[0018] Furthermore, the method of step 4 is specifically as follows:

[0019] Step 4.1, integrate the Gaussian distribution probability density curve of the stationary data to obtain its cumulative distribution function curve, so that the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α has a guarantee rate of β as follows:

[0020]

[0021] In the formula, f 1 (x) is the Gaussian distribution probability density curve of stationary data, φ 1 is the weight fitting parameter of the first-order single Gaussian distribution, F 1 (x≤α) is the cumulative distribution function value of the stationary data when the quantile value is less than or equal to α, and P(x≤α) is the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α;

[0022] Step 4.2, given a guaranteed rate β that is close to 1 in engineering (such as making β equal to 0.999), inversely calculate the α value corresponding to β in step 4.1.

[0023] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0024] (1) The method has strict logic. In view of the fact that the amplitude of the non-stationary response data of wind-induced vibration of structures is higher than that of the stationary response data, the present invention proposes a method for locating the position of non-stationary segment data based on the Gaussian mixture model of the envelope of wind-induced vibration time series signals. The method uses the first-order single Gaussian model in the Gaussian mixture model to describe the amplitude characteristics of the stationary segment data, obeys the principle of structural dynamics, and can effectively distinguish the amplitude characteristics of the stationary segment and the non-stationary segment based on the statistical characteristic parameters of the envelope data. The inventive method has clear logic and conforms to the basic principles of mechanics.

[0025] (2) Comprehensive consideration of factors. The present invention takes into account the characteristic that the mean of the structural vibration time series signal is approximately zero, and proposes a strategy of first calculating the envelope of the time series signal, then describing the amplitude characteristics of the stable and non-stable segments in the vibration time series signal with the statistical characteristics of the envelope data, and finally extracting the non-stable segment of the vibration time series signal at the same position according to the statistical characteristics of the envelope data, thereby effectively retaining all the data and features in the non-stable segment of the wind-induced vibration. The inventive method takes comprehensive considerations, and the results obtained are more in line with engineering practice than traditional methods.

[0026] (3) Implementation has rules to follow. The implementation process of the present invention is basically based on the processing and calculation of sensor test data, with few empirical factors. Any technician with a certain foundation in mechanics, mathematics, and computers can realize the automatic extraction of non-stationary segments of structural wind-induced vibration time series signals according to this patent. The inventive method is highly reproducible and easy to apply and promote. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the method of the present invention;

[0028] Figure 2 It is a schematic diagram of the vibration acceleration time series signal and its upper envelope in the application example;

[0029] Figure 3 A schematic diagram of the upper envelope Gaussian mixture model and the determination of the critical value α of stationary / non-stationary data in the application example;

[0030] Figure 4 Schematic diagram of the effective extraction results of the non-stationary segment of wind-induced vibration in the application example. DETAILED DESCRIPTION

[0031] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0032] like Figure 1 As shown, the method for automatically extracting non-stationary segments of a structural wind-induced vibration time series signal of the present invention mainly comprises the following steps:

[0033] Step 1: Extract the vibration time series signal from the vibration sensor such as acceleration, velocity or dynamic displacement installed on the structure; set a given length value that is an integer multiple (generally more than 10 times) of the sensor sampling frequency, and calculate the maximum value of the vibration time series signal in each given length segment; use the cubic spline interpolation method to interpolate the coordinate positions of the remaining sampling points outside the maximum value position based on the maximum value of each given length segment, and use the obtained interpolation curve as the upper envelope of the vibration time series signal.

[0034] Step 2: Use the Gaussian mixture model to fit the probability density distribution of the upper envelope data as follows:

[0035]

[0036] In the formula, μ i , σ i and φ i are the fitting parameters of the i-th order single Gaussian distribution, and K is the total order of the Gaussian mixture model.

[0037] Step 3: Select the first-order single Gaussian distribution fitting parameter μ with the smallest mean in the Gaussian mixture model 1 , σ 1 and φ 1 , and define it as the statistical characteristic parameter of the stationary data of the vibration signal; normalize the integral value of the single Gaussian distribution curve of the stationary data on [0,∞] to 1, and use it as the Gaussian distribution probability density curve of the stationary data.

[0038] Step 4: Integrate the Gaussian distribution probability density curve of the stationary data to obtain its cumulative distribution function curve, and let the probability that the vibration data is less than or equal to α have a guarantee rate of β as follows:

[0039]

[0040] Given a guaranteed rate β that is close to 1 in engineering (such as making β equal to 0.999), inversely calculate the α value in the above formula that satisfies the guaranteed rate β.

[0041] Step 5: Taking α as the critical value for stationary data and non-stationary data, extract the corresponding data segments whose upper envelope data is continuously greater than the critical value α from the vibration time series signal; select the data segments whose time length is greater than the preset length and whose maximum value of the wind-induced vibration signal is greater than the preset value as the effective results of the non-stationary segments of wind-induced vibration.

[0042] Embodiment 1:

[0043] The following takes the vibration acceleration monitoring data of a certain cable of a certain long-span cable-stayed bridge in Jiangsu Province as an example to illustrate the specific implementation process of the present invention.

[0044] (1) Extract the acceleration time series signal from the acceleration sensor installed on the cable of the cable-stayed bridge. The sampling frequency of the acceleration signal is 50 Hz, and the unit is mm / s 2 ; Set a given length value of 10 times the sensor sampling frequency, calculate the maximum value of the acceleration time series signal in each given length segment (i.e., take a maximum value every 500 data intervals); use the cubic spline interpolation method to interpolate the coordinate positions of the remaining sampling points outside the maximum value position based on the maximum value of each given length segment, and use the obtained interpolation curve as the upper envelope of the acceleration time series signal (such as Figure 2 shown).

[0045] (2) Figure 3 As shown, a third-order Gaussian mixture model is used to fit the probability density distribution of the upper envelope data.

[0046] (3) Select the fitting parameters of the first-order single Gaussian distribution with the smallest mean in the Gaussian mixture model and define it as the statistical characteristic parameter of the stationary data of the vibration signal; normalize the integral value of the single Gaussian distribution curve of the stationary data on [0,∞] to 1, and use it as the Gaussian distribution probability density curve of the stationary data.

[0047] (4) The cumulative distribution function curve is obtained by integrating the Gaussian distribution probability density curve of the stationary data, and the probability that the vibration data is less than or equal to α has a guarantee rate of β; assuming that the probability that the acceleration data is less than or equal to α when the guarantee rate β is equal to 0.999 can be approximated to 1, and the α value that satisfies the guarantee rate in the above formula is calculated to be 39.695 (such as Figure 3shown).

[0048] (5) Taking α as the critical value between stationary data and non-stationary data, the corresponding time segment of the upper envelope data continuously greater than the critical value α is intercepted from the vibration time series signal; the preset effective length value is 27000 and the effective height value is 120. The data segment with a length greater than the preset effective length and a maximum value greater than the preset effective height value is selected from the intercepted data segment and is taken as the effective result of the non-stationary segment of wind-induced vibration (such as Figure 4 As shown in the figure, the dotted line is the time series signal, and the solid line is the effective non-stationary segment of the time series signal).

[0049] The above embodiments are only further specific descriptions of the scheme of the present invention. After reading the embodiments of the present invention, ordinary technicians in this field may make various equivalent modifications and substitutions to the present invention, which all belong to the scope of protection defined by the claims of the present invention.

Claims

1. A method for automatically extracting non-stationary segments of a time series signal of wind-induced vibration of a structure, characterized in that: The specific steps include: Step 1, extracting the time series signal of wind-induced vibration of the structure, calculating the maximum value of the time series signal of wind-induced vibration in each predetermined length segment, using the cubic spline interpolation method to interpolate the coordinate positions of the remaining sampling points outside the maximum value position based on the maximum value of each predetermined length segment, and using the obtained interpolation curve result as the upper envelope data of the vibration time series signal; Step 2, use the Gaussian mixture model to fit the probability density distribution of the upper envelope data; Step 3, define the first-order single Gaussian distribution fitting parameter with the minimum mean in the Gaussian mixture model as the statistical characteristic parameter of the stationary data of the wind-induced vibration signal, normalize the integral value of the single Gaussian distribution curve of the stationary data to 1 on [0,∞], and obtain the Gaussian distribution probability density curve of the stationary data; Step 4, integrating the Gaussian distribution probability density curve of the stationary data to obtain its cumulative distribution function curve, making the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α have a guarantee rate of β, and calculating the α value when the given β is close to 1; wherein α is the critical value of the stationary data and the non-stationary data; Step 5, intercepting the corresponding data segments whose upper envelope data is continuously greater than α from the time series signal of wind-induced vibration, and selecting the data segments whose time length is greater than a preset length and whose maximum value of the wind-induced vibration signal is greater than a preset value as the effective results of the non-stationary segments of wind-induced vibration.

2. The method for automatically extracting non-stationary segments of structural wind-induced vibration time series signals according to claim 1 is characterized in that: In the step 1, a time series signal of wind-induced vibration is extracted from a vibration sensor installed on the structure.

3. The method for automatically extracting non-stationary segments of structural wind-induced vibration time series signals according to claim 1 is characterized in that: In the step 1, the length is set to a predetermined length segment which is an integer multiple of the sampling frequency of the vibration sensor.

4. The method for automatically extracting non-stationary segments of structural wind-induced vibration time series signals according to claim 1 is characterized in that: The calculation formula for fitting the probability density distribution of the upper envelope data using the Gaussian mixture model in step 2 is as follows: Where f(x) is the probability density distribution of the upper envelope data, x is the upper envelope data, μ i , σ i and φ i are the mean, standard deviation and weight fitting parameters of the i-th order single Gaussian distribution, and K is the total order of the Gaussian mixture model.

5. The method for automatically extracting non-stationary segments of structural wind-induced vibration time series signals according to claim 1, characterized in that: In step 4, the Gaussian distribution probability density curve of the stationary data is integrated to obtain its cumulative distribution function curve, so that the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α has a guarantee rate of β as follows: Where f1(x) is the Gaussian distribution probability density curve of stationary data, φ1 is the weight fitting parameter of the first-order single Gaussian distribution, F1(x≤α) is the cumulative distribution function value of stationary data when the quantile value is less than or equal to α, and P(x≤α) is the probability that the vibration amplitude in the wind-induced vibration signal is less than or equal to α.

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