Axial force identification method of steel column based on sound signal

Abstract

The present invention discloses a method for identifying the axial force of a column based on a sound signal, comprising: a sound acquisition system acquires and stores the original sound signal, and obtains the natural frequencies ω1 and ω2 before and after the column applies the axial force by analyzing the spectrum of the sound signal. 1P ; The natural frequencies ω1 and ω before and after the axial force is applied to the column 1P Substitute it into the derived column axial force identification numerical model to calculate the axial force of the column. The present invention solves the measurement error caused by the additional mass through a non-contact measurement method. In addition, the test method has the advantages of fast speed, high accuracy and low cost, and is a column non-destructive testing method worthy of promotion.

Description

Technical Field

[0001] The invention relates to the technical field of sound signals, and in particular to a method for identifying the axial force of a steel column based on sound signals. Background Art

[0002] In recent years, the test methods of natural frequency have received extensive attention. Generally, the existing test methods can be divided into two types: contact method and non-contact method. The contact method requires the installation of accelerometers or displacement sensors in the component, which often produces inevitable errors due to the mass influence of the sensor. As an alternative, non-contact methods (such as laser-based test methods) have better performance because it does not require the installation of sensors in the structure. But the cost of laser-based test methods is usually very expensive. Summary of the invention

[0003] In order to solve the deficiencies and shortcomings of the traditional methods, the present invention provides a cheap and high-precision method for identifying the axial force of a steel column.

[0004] To achieve the above object, the present invention provides the following technical solution: a method for identifying the axial force of a steel column based on sound signals, comprising the following steps:

[0005] S1. Use a standard round hammer to artificially excite the same point of the steel column before and after the axial force is applied, and use a sound signal acquisition system to record the sound signals emitted by the steel column before and after the axial force is applied under artificial excitation;

[0006] S2. The sound signal is intercepted for signal processing, imported into MATLAB and analyzed by periodogram method, the power spectrum density curve is obtained and the 50-200Hz part is intercepted to obtain the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column. 1P ;

[0007] S3, the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column 1P Substitute it into the constructed axial force identification numerical model to identify the axial force of the steel column.

[0008] Preferably, in step S1:

[0009] The artificial excitation point is the relative midpoint of the steel column.

[0010] The location of the sound signal acquisition system is 0.1 m away from the excitation point.

[0011] The weight of the standard ball hammer is 500g.

[0012] The sound signal acquisition system is a mobile phone or a microphone; the sampling frequency of the sound signal acquisition system is 48000 Hz, and the sound signal format is m4a.

[0013] The duration of the sound signal collection is 3 seconds, and the number of collection times is 3 times.

[0014] Preferably, in step S2:

[0015] The number of intercepted sound signal data points N is 2 17 .

[0016] The power spectral density curve is intercepted at 75-135 Hz.

[0017] The calculation process of the power spectral density curve is as follows:

[0018] The power spectral density is calculated using the fast Fourier transform as shown below

[0019]

[0020] The discrete power spectral density is obtained as follows

[0021]

[0022] where F S is the sound sampling frequency;

[0023] For easy display, the power spectral density PSD curve is converted as follows

[0024] PSD = 10 × log 10 (P XX ) (3)

[0025] Preferably, in step S3, the component process of the axial force identification numerical model is as follows:

[0026] The finite element model is used to analyze the theoretical natural vibration mode of the component. The component is divided into several beam units of equal length along the length direction. The unit mass matrix can be expressed as:

[0027]

[0028] ρ represents the linear density of the component, A is the cross-sectional area of ​​the component, and L is the length of the unit in the finite element model;

[0029] The corresponding element bending stiffness matrix can be expressed as:

[0030]

[0031] Where E is the elastic modulus of the specimen, and I is the section moment of inertia of the specimen;

[0032] The geometric stiffness matrix of the steel column under axial force is:

[0033]

[0034] Where P is the axial force of the steel column; Assuming S is the constant term in equation (6), it can be expressed as:

[0035]

[0036] Then formula (6) can be rewritten as:

[0037] K P =P·S (8)

[0038] The natural modes of the steel column with boundary conditions are obtained using the assembled global mass and stiffness matrix; the characteristic equation of the column can be expressed as:

[0039] K0φ1=λ1Mφ1 (9)

[0040] Where K0 is the overall stiffness matrix, M is the overall stiffness matrix and mass matrix, λ1 is the first-order eigenvalue corresponding to the natural frequency, φ1 is the first-order modal vibration shape of the steel column; the characteristic equation of the axial force on the column can be expressed as:

[0041] (K0-K G )(φ1+△φ1)=(λ1-△λ1)M(φ1+△φ1) (10)where K G is the overall geometric stiffness corresponding to the axial force. Relative to formula (7), Δλ1 and Δφ1 are the changes of the characteristic value λ1 and the first-order modal vibration shape φ1 of the steel column, respectively. From equation (10), it can be seen that λ1 and φ1 are associated with the axial force. Under normal circumstances, the steel column is in an elastic working state, then Δφ1=0. Therefore, equation (10) can be expressed as:

[0042] (K0-P·S G )φ1=(λ1-△λ1)Mφ1 (11)

[0043] Where S G is the overall geometric stiffness matrix corresponding to the axial force equal to 1; transpose both sides of the equation (11) by multiplying φ1 on the left, and we can get:

[0044]

[0045] Considering the modal equation and The property of , equation (10) can be written as:

[0046]

[0047] According to formula (13), the axial force P of the steel column can be expressed as:

[0048]

[0049] Assume that the natural frequencies before and after the axial force is applied to the steel column are ω1 and ω 1P , then formula (14) can be rewritten as:

[0050]

[0051] The axial force P can be determined by equation (15) with the basic assumption that Δφ1=0.

[0052] Compared with the prior art, the present invention has the following beneficial effects: by collecting sound signals through a non-contact device and performing spectrum analysis, the natural frequencies ω1 and ω2 of the steel column before and after the axial force is applied are obtained respectively. 1P ; Bring it into the constructed axial force identification numerical model to identify the axial force of the steel column. By adopting the non-contact steel column axial force identification method, there will be no measurement error due to the additional mass, and it has the advantages of fast speed, high accuracy and low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the method for identifying the axial force of a steel column based on sound signals provided by the present invention.

[0054] Figure 2 It is a finite element model of a steel column under axial force in an embodiment of the present invention.

[0055] Figure 3 It is the natural frequency of the sound signal test of the column in the state without axial force in the embodiment of the present invention: (a)-(c) time relationship curve of the sound signal; (d)-(f) PSD estimation of the sound signal.

[0056] Figure 4 The natural frequency of the sound signal test of the steel column under P = 110KN in the embodiment of the present invention: (a)-(c) time relationship curve of the sound signal; (d)-(f) PSD estimation of the sound signal.

[0057] Figure 5 The natural frequency of the sound signal test of the steel column under P = 230KN in the embodiment of the present invention: (a)-(c) time relationship curve of the sound signal; (d)-(f) PSD estimation of the sound signal. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further specifically described below through embodiments.

[0059] Example

[0060] This embodiment provides a method for identifying the axial force of a steel column based on sound signals, such as Figure 1 As shown, the following steps are included:

[0061] Step 1: artificially excite the same point of the steel column of the steel member before and after the axial force is applied using a standard round hammer, and use a sound signal acquisition system to record the sound signals emitted by the steel column before and after the axial force under artificial excitation. The sound signal acquisition lasts for 3 seconds, and the sound acquisition operation is performed 3 times as a baseline;

[0062] Step 2: The number of data points N intercepted from the sound collection device is 2^17 for signal processing, and then they are imported into MATLAB and analyzed by periodogram method to obtain the power spectrum density (PSD) curve and intercept the 50Hz to 200Hz part to obtain the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column. 1P ;

[0063] Step 3: The natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column 1P Substitute it into the constructed axial force identification numerical model to identify the axial force of the steel column.

[0064] In step one,

[0065] Position and method of striking: artificial excitation is carried out at the midpoint of the steel member;

[0066] The location of the sound collection system: 0.1m away from the excitation point of the steel column;

[0067] Specifications of a standard round-peen hammer: The weight of a standard round-peen hammer is approximately 500g;

[0068] Sound signal acquisition system: simple devices such as mobile phones and microphones; the sampling frequency is 48000Hz, and the sound signal format is m4a.

[0069] In step 2, the number of data points N intercepted from the sound collection device is 2^17 for signal processing, and then they are imported into MATLAB and spectral analyzed by periodogram method to obtain power spectrum density (PSD) curve, which also includes:

[0070] The power spectral density (PSD) is calculated using the Fast Fourier Transform (FFT) as shown below

[0071]

[0072] The discrete power spectral density (PSD) is obtained as follows

[0073]

[0074] Where Fs is the sound sampling frequency;

[0075] For easy display, the power spectral density PSD curve is converted as follows

[0076] PSD = 10 × log 10 (P XX ) (3)

[0077] In step 3, the principle of the axial force identification numerical model is as follows:

[0078] The finite element model is used to analyze the theoretical natural vibration mode of the component. The component is divided into several beam units of equal length along the length direction. The unit mass matrix can be expressed as:

[0079]

[0080] ρ represents the linear density of the component, A is the cross-sectional area of ​​the component, and L is the length of the unit in the finite element model;

[0081] The corresponding element bending stiffness matrix can be expressed as:

[0082]

[0083] Where e is the elastic modulus of the sample, and I is the section moment of inertia of the sample.

[0084] The geometric stiffness matrix of the steel column under axial force is:

[0085]

[0086] Where P is the axial force of the steel column. Assuming S is the constant term in equation (6), it can be expressed as:

[0087]

[0088] Then formula (6) can be rewritten as:

[0089] K P =P·S (8)

[0090] The natural modes of the steel column with boundary conditions are obtained using the assembled global mass and stiffness matrix. The characteristic equation of the column can be expressed as:

[0091] K0φ1=λ1Mφ1 (9)

[0092] Where K0 is the overall stiffness matrix, M is the overall mass matrix, λ1 is the first-order eigenvalue corresponding to the natural frequency, and φ1 is the first-order vibration mode. The characteristic equation of the axial force on the column can be expressed as:

[0093] (K0-K G )(φ1+△φ1)=(λ1-△λ1)M(φ1+△φ1) (10)

[0094] Where K G is the overall geometric stiffness corresponding to the axial force. Relative to formula (7), Δλ1 and Δφ1 are the changes of the characteristic value λ1 and the modal shape φ1, respectively. From equation (10), it can be seen that λ1 and φ1 are associated with the axial force. Usually, the steel column is in an elastic working state, then Δφ1 = 0. Therefore, equation (10) can be expressed as:

[0095] (K0-P·S G )φ1=(λ1-△λ1)Mφ1 (11)

[0096] Where S G is the overall geometric stiffness matrix corresponding to the axial force equal to 1. By transposing both sides of the equation (11) by multiplying them by φ1, we can obtain:

[0097]

[0098] Considering the modal equation and The property of , equation (10) can be written as:

[0099]

[0100] According to formula (13), the axial force P of the steel column can be expressed as:

[0101]

[0102] Assume that the natural frequencies before and after the axial force is applied to the steel column are ω1 and ω 1P , then formula (14) can be rewritten as:

[0103]

[0104] The axial force P can be determined by equation (15) with the basic assumption that Δφ1=0.

[0105] Case Analysis

[0106] Figure 2This is the finite element model of the steel column under axial force. The length of the steel column is 1150mm. The model is divided into 23 units, and the unit length is 50mm. The initial parameters of the steel column are shown in Table 1. The axial force of the steel column is identified based on the sound signal. (The axial force is applied by hydraulic loading in the axial direction. In order to verify the calculation results, a dynamometer is installed to measure the axial force.)

[0107] Table 1 Initial parameters of the test steel column

[0108]

[0109] First, a standard round hammer was used to artificially excite the same point of the steel column before and after the axial force was applied. The sound signal acquisition system was used to record the sound signals of the steel column before and after the axial force under artificial excitation. The sound signal acquisition lasted for 3 seconds. We performed the sound acquisition operation 3 times as the baseline.

[0110] Secondly, the number of data points N intercepted from the sound collection device is 2 17 After signal processing, they are imported into MATLAB and spectral analyzed by periodogram method to obtain the power spectral density (PSD) curve and intercept the 75Hz to 130Hz part, as shown in Figure 3-5 As shown;

[0111] in Figure 3 (a)-(c) show Figure 2 The time course of the sound signal obtained by the experimental device in the experiment. We collected the sound three times as a baseline. No axial load was applied to the column. The corresponding PSD curve is Figure 3 As shown in (d)-(f), the stable natural frequency of the steel column ω1=107.7Hz is obtained.

[0112] Figure 4 (a)-(c) show the three time histories of the sound signal recorded when the axial force P = 110 kN. Figure 4 (d)-(f) show the PSD results obtained from the corresponding sound analysis. Figure 4 From the PSD curve, it can be seen that when P is 110KN, the natural frequency is 100.8Hz twice and 100.7Hz only once. This result is consistent with the natural frequency calculated by the finite element model, and the natural frequency ω can be determined. 1P =100.8Hz.

[0113] Figure 5 (a)-(c) reflect the three time histories of the sound signal recorded when the axial force P = 230KN. Figure 5From the PSD curves (d)-(f), it can be seen that with the increase of axial force, the natural frequency drops to 94.3 Hz, that is, ω 1P =94.3Hz.

[0114] Finally, the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column are 1P Substitute it into the constructed axial force identification numerical model to identify the axial force of the steel column and compare it with the actual force, as shown in the following table:

[0115] Table 2 Test column AF detection

[0116]

[0117] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying the axial force of a steel column based on sound signals, characterized in that: The steps include: S1. Use a standard round hammer to artificially excite the same point of the steel column before and after the axial force is applied, and use a sound signal acquisition system to record the sound signals emitted by the steel column before and after the axial force is applied under artificial excitation; S2. The sound signal is intercepted for signal processing, imported into MATLAB and analyzed by periodogram method, the power spectrum density curve is obtained and the 50-200Hz part is intercepted to obtain the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column. 1P ; S3, the natural frequencies ω1 and ω2 before and after the axial force is applied to the steel column 1P Substitute it into the constructed axial force identification numerical model to identify the axial force of the steel column; In step S3, the component process of the axial force identification numerical model is as follows: The finite element model is used to analyze the theoretical natural vibration mode of the component. The component is divided into several beam units of equal length along the length direction. The unit mass matrix can be expressed as: ρ represents the linear density of the component, A is the cross-sectional area of ​​the component, and L is the length of the unit in the finite element model; The corresponding element bending stiffness matrix can be expressed as: Where E is the elastic modulus of the specimen, and I is the section moment of inertia of the specimen; The geometric stiffness matrix of the steel column under axial force is: Where P is the axial force of the steel column; Assuming S is the constant term in equation (6), it can be expressed as: Then formula (6) can be rewritten as: K P =P·S (8) The natural modes of the steel column with boundary conditions are obtained using the assembled global mass and stiffness matrix; the characteristic equation of the column can be expressed as: Where K0 is the overall stiffness matrix, M is the overall mass matrix, λ1 is the first-order eigenvalue corresponding to the natural frequency, is the first-order modal vibration shape of the steel column; the characteristic equation of the axial force on the column can be expressed as: Where K G is the overall geometric stiffness corresponding to the axial force. Relative to formula (7), Δλ1 and They are the eigenvalue λ1 and the first-order mode vibration shape of the steel column. The change in λ1 and Associated with the axial force; usually, the steel column is in an elastic working state. Therefore, equation (10) can be expressed as: Where S G is the overall geometric stiffness matrix corresponding to the axial force equal to 1; multiply both sides of the equal sign in equation (11) by The transpose of , we get: Considering the modal equation and The property of , equation (10) can be written as: According to formula (13), the axial force P of the steel column can be expressed as: Assume that the natural frequencies before and after the axial force is applied to the steel column are ω1 and ω 1P , then formula (14) can be rewritten as: The axial force P can be obtained by equation (15) with the basic assumption Carry out determination.

2. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S1, the artificial excitation point is the relative midpoint of the steel column.

3. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S1, the position of the sound signal acquisition system is 0.1 m away from the excitation point.

4. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S1, the weight of the standard round hammer is 500g.

5. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S1, the sound signal acquisition system is a mobile phone or a microphone; the sampling frequency of the sound signal acquisition system is 48000 Hz, and the sound signal format is m4a.

6. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S1, the duration of the sound signal collection is 3 seconds.

7. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S2, the number of intercepted sound signal data points N is 2 17 .

8. The method for identifying the axial force of a steel column based on sound signals according to claim 1 is characterized in that: In step S2, the 75-135 Hz portion of the power spectrum density curve is intercepted.

9. The method for identifying the axial force of a steel column based on sound signals according to claim 7 or 8, characterized in that: In step S2, the calculation process of the power spectrum density curve is as follows: The power spectral density is calculated using the fast Fourier transform as shown below The discrete power spectral density is obtained as follows Where Fs is the sound sampling frequency; For easy display, the power spectral density PSD curve is converted as follows PSD=10×log 10 (P XX ) (3)。

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