A method for identifying structural damping ratio based on non-stationary response of wind-induced vibration

Abstract

The present invention discloses a method for identifying the structural damping ratio based on the non-stationary response of wind-induced vibration, comprising: extracting the non-stationary response of wind-induced vibration and performing spectrum analysis, identifying the frequency result with the largest energy in the non-stationary vibration power spectrum and filtering the non-stationary vibration data with a bandpass filter within a certain positive and negative range, calculating the upper envelope of the non-stationary vibration response data after filtering, searching for multiple local maxima of the upper envelope and determining the position of the last descending segment with an upper envelope of a certain length starting from the last local maximum, calculating the Fourier inverse transform of the conjugate spectrum cross-spectral density of the last descending segment data of the non-stationary vibration after filtering, thereby constructing an impulse response function, using the exponential decay function of an underdamped single-degree-of-freedom system to fit the normalized constructed impulse response function, and the damping ratio fitting value in the fitting parameter is the identification result. The method of the present invention realizes online intelligent identification of structural damping ratio with high standardization and great automation potential.

Description

Technical Field

[0001] The invention relates to a structural damping ratio identification method based on non-stationary response of wind-induced vibration, and belongs to the field of structural intelligent monitoring, detection and evaluation. Background Art

[0002] Damping is an important property of engineering structures to resist vibration, and damping ratio is an important parameter that describes the damping properties of structures in vibration engineering. The identification of damping ratio is a widely concerned issue in the industry. However, due to harsh test conditions, strong variability in identification results, and low degree of automation in identification, accurate and rapid identification of structural damping ratios has not been well achieved. With the development of testing, transmission, and computer technology, the wind-induced vibration response of structures throughout their life cycle can be measured and processed in real time. The non-stationary vibration of structures in service wind environments has become a natural data source for identifying damping ratios. Effectively using the non-stationary response of wind-induced vibrations obtained through real-time measurements to identify the damping ratio of structures not only enables test data to be effectively utilized, but also helps engineers grasp the current dynamic performance of the structure in real time, providing an effective reference for performance evaluation, vibration control, and reinforcement and reconstruction of structures.

[0003] At present, there are few methods for identifying the damping ratio of structures based on wind-induced vibration response in the field of structural engineering, and there are even fewer methods for automatically identifying the damping ratio of structures based on online wind-induced vibration non-stationary response data. Commonly used methods for identifying the damping ratio of structures are as follows: (1) Using the excitation method, the structure is pulse-excited by a hammer (for small structures) or a heavy vehicle (for large structures), and the frequency response function is estimated based on the excitation data and the response data of the structure after excitation, and the damping ratio is identified. This method needs to eliminate the influence of the surrounding environment on the vibration of the structure, and it is necessary to measure the excitation data and the response data at the same time, and the application conditions are harsh; (2) Using the natural excitation method, based on the response data of the structure under natural excitation such as environmental wind or vehicle service loads, an estimated pulse response function is constructed and the damping ratio is identified. Although this method eliminates the measurement step of the excitation load, the natural excitation has a strong variability, and there is continuous external energy input in the rising section of the vibration amplitude in the natural excitation response, resulting in inaccurate identification of the damping ratio and large variability. A relatively stable automatic identification method is needed. In summary, although the existing technology can effectively identify the structural damping ratio in theory, in actual operation it has harsh conditions, low accuracy, high variability and insufficient automation potential.

[0004] Therefore, it is necessary to develop a convenient, stable, highly standardized and automated method for identifying the structural damping ratio, so as to realize the online intelligent identification of the damping ratio throughout the life cycle of the structure. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a structural damping ratio identification method based on the non-stationary response of wind-induced vibration, which can realize automatic online identification of the damping ratio during the entire life cycle of the structure.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for identifying structural damping ratio based on non-stationary response of wind-induced vibration includes the following steps:

[0008] Step 1, extracting the non-stationary response of each wind-induced vibration from the sensor installed on the structure, performing frequency domain power spectrum analysis on the extracted non-stationary vibration response data to obtain the non-stationary vibration power spectrum, identifying the frequency result with the largest energy in the non-stationary vibration power spectrum, and filtering the non-stationary vibration response data using a bandpass filter within a certain range of the maximum energy frequency;

[0009] Step 2, using a method of cubic spline interpolation of the maximum value of a given length segment area to calculate the upper envelope of the non-stationary vibration response data after filtering, searching for multiple local maximum values ​​of a fixed number of equal segments of the upper envelope that are greater than a fixed proportion of the maximum value of the entire upper envelope, and taking the upper envelope data from the last local maximum value to the end point after a certain length as the last descending segment of the upper envelope;

[0010] Step 3, determining the last descending segment data of the non-stationary vibration after filtering at the corresponding position according to the last descending segment position of the upper envelope, calculating the fast Fourier transform result of the last descending segment data of the non-stationary vibration after filtering and finding its conjugate complex number, constructing an impulse response function with the fixed-length data in the first half of the fast Fourier inverse transform result of the product of the two, and normalizing the constructed impulse response function;

[0011] Step 4: Use the exponential decay function of the underdamped single-degree-of-freedom system to fit the normalized impulse response function. The damping ratio fitting value in the fitting parameters is the damping ratio identification result of the non-stationary response of the wind-induced vibration.

[0012] As a preferred embodiment of the present invention, the method of step 1 is specifically as follows:

[0013] Step 1.1, extracting the non-stationary response of each wind-induced vibration from the time-series monitoring data of the acceleration, velocity or dynamic displacement sensor installed on the structure;

[0014] Step 1.2, perform frequency domain power spectrum analysis on the extracted non-stationary vibration response data to obtain the non-stationary vibration power spectrum, and use the peak method to identify the frequency result Fr with the largest energy in the non-stationary vibration power spectrum;

[0015] Step 1.3, use a bandpass filter with a certain range of positive and negative maximum energy frequency to filter the non-stationary vibration response data, and the certain range is any value between 0.45 and 0.5 times the minimum difference between the natural frequencies of each order of the structure.

[0016] As a preferred embodiment of the present invention, the method of step 2 is as follows:

[0017] Step 2.1, set the integer multiple of the sensor sampling frequency as a given length segment, calculate the maximum value of the non-stationary vibration response data after filtering 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 non-stationary vibration response data after filtering;

[0018] Step 2.2, divide the upper envelope into a fixed number of equal parts, search for multiple local maxima that are greater than a fixed proportion of the maximum value of the entire upper envelope among the maximum values ​​of each equal segment of the upper envelope, and use the upper envelope data from the last local maximum value to the end point after a certain length as the last descending segment of the upper envelope.

[0019] As a preferred solution of the present invention, the integer multiple is 1, the fixed number of portions is 20, the fixed ratio is 9 / 10, and the length from the last local maximum to the end point after a certain length is specifically 8 / 10 of the length from the last local maximum to the last point of the upper envelope.

[0020] As a preferred embodiment of the present invention, the method of step 3 is as follows:

[0021] Step 3.1, determining the last descending segment data of the non-stationary vibration after filtering at the corresponding position according to the last descending segment position of the upper envelope;

[0022] Step 3.2, calculate the fast Fourier transform result of the last descending segment of the non-stationary vibration after filtering and find its conjugate complex number, and find the inverse fast Fourier transform result of the product of the two, intercept a fixed length of data from the first half of the inverse fast Fourier transform result to construct an impulse response function, and normalize the constructed impulse response function by dividing all the intercepted data by the maximum value.

[0023] As a preferred solution of the present invention, the fixed length is a fixed multiple of the result obtained by multiplying 1 / Fr by the sampling frequency of the sensor, and Fr is the frequency result with the maximum energy in the non-stationary vibration power spectrum.

[0024] As a preferred solution of the present invention, in step 4, the exponential decay function of the underdamped single degree of freedom system is used to fit the normalized impulse response function, and the calculation formula is as follows:

[0025]

[0026] Where y(t) is the fitting curve when the impulse response function is fitted using the exponential decay function of the underdamped single-degree-of-freedom system, A = 1, ζ is the structural damping ratio, and f n is the frequency of vibration, take f n =Fr, t is the time independent variable of vibration, is the initial phase of vibration.

[0027] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0028] 1. The present invention firstly proposes to use the response under natural excitation of ambient wind as the data source for damping ratio identification, which does not require special testing for damping ratio identification and saves costs; then extracts the non-stationary segment of wind-induced vibration that is most similar to the characteristics of the impulse response, and uses a bandpass filter to eliminate interference, meeting the basic conditions for damping ratio identification; finally, the last descending segment of the non-stationary segment of wind-induced vibration after filtering is used to identify the attenuation characteristics of structural vibration, which conforms to the classic definition of damping ratio. The method has clear logic and conforms to the basic principles of mechanics.

[0029] 2. The present invention proposes to identify the damping ratio of the structure based on the last descending segment of the non-stationary response of wind-induced vibration after filtering. The extraction operation of the non-stationary segment of vibration eliminates the white noise interference of the stationary segment, and the filtering operation eliminates the interference of other vibration modes in the same non-stationary segment. The use of the last descending segment eliminates the input energy interference brought by the natural excitation of the ambient wind during the rising period of the structural vibration amplitude, so that the damping ratio identified by the method of the present invention is closer to the actual damping properties of the structure. The method is relatively comprehensive and the results obtained are more practical than the traditional method.

[0030] 3. The implementation process of the present invention is basically based on the processing and calculation of sensor test data, with few empirical factors. Any professional technician with a certain foundation in mathematics, computer science, and dynamics can implement the identification of structural damping ratio based on the non-stationary response of wind-induced vibration according to the present invention. The method is highly reproducible and has great automation potential, which is easy to apply and promote. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of the method of the present invention;

[0032] Figure 2 It is a schematic diagram of acceleration time series monitoring data and a certain section of wind-induced vibration non-stationary response in an embodiment of the present invention;

[0033] Figure 3 1 is a schematic diagram of the spectrum analysis result of non-stationary vibration and the passband range of bandpass filtering in an embodiment of the present invention;

[0034] Figure 4 Schematic diagram of the process of determining the last descending segment of the non-stationary vibration after filtering based on the upper envelope in an embodiment of the present invention;

[0035] Figure 5 It is a schematic diagram of normalized structural impulse response function fitting and structural damping ratio identification in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0037] like Figure 1 As shown, the structural damping ratio identification method based on the non-stationary response of wind-induced vibration described in the present invention mainly includes the following steps:

[0038] Step 1: Extract the non-stationary responses of each wind-induced vibration from the time-series monitoring data of acceleration, velocity or dynamic displacement sensors installed on the structure; perform frequency domain power spectrum analysis on the extracted non-stationary vibration response data, and use the peak method to identify the frequency result Fr with the largest energy in the non-stationary vibration power spectrum; use a bandpass filter with a certain range of positive and negative maximum energy frequency to filter the non-stationary vibration data. The recommended range is any value between 0.45 and 0.5 times the minimum difference between the natural frequencies of each order of the structure.

[0039] Step 2: Set a given length value that is an integer multiple (generally 1) of the sensor sampling frequency, calculate the maximum value of the non-stationary vibration response data after filtering 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 non-stationary vibration response data after filtering;

[0040] The upper envelope is divided into a fixed number of equal parts (for example, 20 parts), and multiple local maxima that are greater than a fixed fraction (generally 9 / 10) of the maximum value of the entire upper envelope are searched for among the maximum values ​​of each equally divided segment of the upper envelope. The upper envelope data from the last local maximum value to the end point after a certain length (such as 8 / 10 of the length from the last local maximum value to the last point of the upper envelope, rounded to the nearest integer) is the last descending segment of the upper envelope.

[0041] Step 3: Determine the last descending segment data of the non-stationary vibration after filtering at the corresponding position according to the last descending segment position of the upper envelope; calculate the fast Fourier transform result of the last descending segment data of the non-stationary vibration after filtering and find its conjugate complex number, and find the inverse fast Fourier transform result of the product of the two (the so-called conjugate spectrum cross-spectral density), and construct an impulse response function by intercepting data of a fixed length (generally a fixed multiple multiplied by 1 / Fr and then multiplied by the sensor sampling frequency) from the first half of the data of the inverse fast Fourier transform result. The constructed impulse response function must be normalized by dividing all the intercepted data by the maximum value thereof.

[0042] Step 4: Use the classical exponential decay function of the underdamped single-degree-of-freedom system to fit the normalized constructed impulse response function. The fitting formula is as follows:

[0043]

[0044] Where ζ is the structural damping ratio, t is the time independent variable of vibration, is the initial phase of vibration, f n is the frequency of vibration (usually f n =Fr), Since the impulse response function has been normalized, A=1 is directly set.

[0045] The damping ratio fitting value in the fitting parameters is the damping ratio identification result of the non-stationary response of the wind-induced vibration.

[0046] Example

[0047] 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.

[0048] (1) Extract the non-stationary response of wind-induced vibration from the time-series monitoring data of the acceleration sensor installed on the structure (such as Figure 2 As shown in the figure, taking a section of wind-induced vibration non-stationary response as an example), the sampling frequency of the acceleration signal is 50Hz, and the unit is mm / s 2 ;like Figure 3 As shown, the extracted non-stationary vibration response data is subjected to frequency domain power spectrum analysis, and the peak method is used to identify the frequency with the largest energy in the non-stationary vibration power spectrum, and the result is Fr=8.4950Hz; a bandpass filter with a maximum energy frequency range of plus or minus 0.088Hz is used to filter the non-stationary vibration data.

[0049] (2) Figure 4As shown in the figure, a predetermined length value of 1 times the sampling frequency of the sensor is set, the maximum value of the non-stationary vibration response data after filtering in each predetermined length segment is calculated, and the coordinate positions of the remaining sampling points outside the maximum value position are interpolated based on the maximum value of each predetermined length segment using the cubic spline interpolation method, and the obtained interpolation curve is used as the upper envelope of the non-stationary vibration response data after filtering; the upper envelope is divided into 20 parts, and multiple local maxima that are greater than 9 / 10 of the maximum value of the entire upper envelope are searched in the maximum value of each equally divided segment of the upper envelope, and the upper envelope data at the end point of 65 / 100 of the length from the last local maximum value to the last point of the upper envelope is taken as the last descending segment of the upper envelope.

[0050] (3) According to the last descending segment position of the upper envelope, determine the last descending segment data of the non-stationary vibration after filtering at the corresponding position (such as Figure 4 Calculate the fast Fourier transform result of the last descending segment of the non-stationary vibration after filtering and find its conjugate complex number, and find the inverse fast Fourier transform result of the product of the two. From the first half of the data of the inverse fast Fourier transform result, extract data with a length of 180 times 1 / Fr multiplied by the sampling frequency of the sensor to construct an impulse response function. The constructed impulse response function must be normalized by dividing all the intercepted data by the maximum value thereof.

[0051] (4) The normalized constructed impulse response function is fitted using the classical exponential decay function of the underdamped single degree of freedom system, and f n = Fr, the fitting result of the damping ratio parameter ζ is equal to 0.0271% (such as Figure 5 The damping ratio fitting value in the fitting parameters is the damping ratio identification result of the non-stationary response of the wind-induced vibration.

[0052] The above embodiments are only for illustrating the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A structural damping ratio identification method based on non-stationary response of wind-induced vibration, characterized in that: The steps include: Step 1, extracting the non-stationary response of each wind-induced vibration from the sensor installed on the structure, performing frequency domain power spectrum analysis on the extracted non-stationary vibration response data to obtain the non-stationary vibration power spectrum, identifying the frequency result with the largest energy in the non-stationary vibration power spectrum, and filtering the non-stationary vibration response data using a bandpass filter within a certain range of the maximum energy frequency; Step 2, using a method of cubic spline interpolation of the maximum value of a given length segment area to calculate the upper envelope of the non-stationary vibration response data after filtering, searching for multiple local maximum values ​​of a fixed number of equal segments of the upper envelope that are greater than a fixed proportion of the maximum value of the entire upper envelope, and taking the upper envelope data from the last local maximum value to the end point after a certain length as the last descending segment of the upper envelope; Step 3, determining the last descending segment data of the non-stationary vibration after filtering at the corresponding position according to the last descending segment position of the upper envelope, calculating the fast Fourier transform result of the last descending segment data of the non-stationary vibration after filtering and finding its conjugate complex number, constructing an impulse response function with the fixed-length data in the first half of the fast Fourier inverse transform result of the product of the two, and normalizing the constructed impulse response function; Step 4, using the exponential decay function of the underdamped single degree of freedom system to fit the normalized impulse response function, the damping ratio fitting value in the fitting parameter is the damping ratio identification result of the non-stationary response of the wind-induced vibration; The exponential decay function of the underdamped single degree of freedom system is used to fit the normalized impulse response function, and the calculation formula is as follows: Where y(t) is the fitting curve when the impulse response function is fitted using the exponential decay function of the underdamped single-degree-of-freedom system, A = 1, ζ is the structural damping ratio, and f n is the frequency of vibration, take f n =Fr, t is the time independent variable of vibration, is the initial phase of vibration.

2. The structural damping ratio identification method based on the non-stationary response of wind-induced vibration according to claim 1 is characterized in that: The method of step 1 is as follows: Step 1.1, extracting the non-stationary response of each wind-induced vibration from the time-series monitoring data of the acceleration, velocity or dynamic displacement sensor installed on the structure; Step 1.2, perform frequency domain power spectrum analysis on the extracted non-stationary vibration response data to obtain the non-stationary vibration power spectrum, and use the peak method to identify the frequency result Fr with the largest energy in the non-stationary vibration power spectrum; Step 1.3, use a bandpass filter with a certain range of positive and negative maximum energy frequency to filter the non-stationary vibration response data, and the certain range is any value between 0.45 and 0.5 times the minimum difference between the natural frequencies of each order of the structure.

3. The structural damping ratio identification method based on the non-stationary response of wind-induced vibration according to claim 1 is characterized in that: The method of step 2 is as follows: Step 2.1, set the integer multiple of the sensor sampling frequency as a given length segment, calculate the maximum value of the non-stationary vibration response data after filtering 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 non-stationary vibration response data after filtering; Step 2.2, divide the upper envelope into a fixed number of equal parts, search for multiple local maxima that are greater than a fixed proportion of the maximum value of the entire upper envelope among the maximum values ​​of each equal segment of the upper envelope, and use the upper envelope data from the last local maximum value to the end point after a certain length as the last descending segment of the upper envelope.

4. The structural damping ratio identification method based on the non-stationary response of wind-induced vibration according to claim 3 is characterized in that: The integer multiple is 1, the fixed number of portions is 20, the fixed ratio is 9 / 10, and the end point from the last local maximum to a certain length is specifically 8 / 10 of the length from the last local maximum to the last point of the upper envelope.

5. The structural damping ratio identification method based on the non-stationary response of wind-induced vibration according to claim 1 is characterized in that: The method of step 3 is as follows: Step 3.1, determining the last descending segment data of the non-stationary vibration after filtering at the corresponding position according to the last descending segment position of the upper envelope; Step 3.2, calculate the fast Fourier transform result of the last descending segment of the non-stationary vibration after filtering and find its conjugate complex number, and find the inverse fast Fourier transform result of the product of the two, intercept a fixed length of data from the first half of the inverse fast Fourier transform result to construct an impulse response function, and normalize the constructed impulse response function by dividing all the intercepted data by the maximum value.

6. The structural damping ratio identification method based on the non-stationary response of wind-induced vibration according to claim 5 is characterized in that: The fixed length is a fixed multiple of the result obtained by multiplying 1 / Fr by the sampling frequency of the sensor, and Fr is the frequency result with the maximum energy in the non-stationary vibration power spectrum.

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