A modal parameter identification method for long-span spatial structures

Abstract

The application provides a large-span space structure modal parameter identification method, and aims to solve the technical problem of mode aliasing in the current modal identification method for processing non-stationary nonlinear signals.The displacement signal is expressed as a combination of multiple sinusoidal functions, and an analytical signal of the displacement signal subjected to interference is obtained; the frequency of each component in the analytical signal is judged to select a reference frequency; the analytical signal is right-shifted according to the reference frequency to obtain an improved signal, and the improved signal is subjected to standard empirical mode decomposition to obtain each intrinsic function; each intrinsic function is subjected to Hilbert transformation to obtain the analytical signal, and each order modal function of the displacement signal is obtained; and the structure modal parameters are obtained according to each order modal function.The application can effectively solve the problem that the traditional EMD method cannot be used due to mode aliasing, has good adaptability and robustness, can well process signals with poor signal-to-noise ratio, nonlinearity and non-stationarity, and has strong operability and can be applied to engineering sites.

Description

Technical Field

[0001] This invention relates to the technical field of large-span spatial structures, and in particular to a method for identifying modal parameters of large-span spatial structures. Background Technology

[0002] Current modal identification methods for large-span structures, such as wavelet decomposition based on Fourier transform, are not effective in handling nonlinear and non-stationary structural vibration data. This is because Fourier transform has a fixed window size, while wavelet transform requires a defined wavelet basis and lacks adaptability. Empirical Mode Decomposition (EMD), on the other hand, exhibits excellent adaptability and robustness. Theoretically, any signal can be processed using this method, especially for nonlinear and non-stationary signals, where it demonstrates significant advantages and can effectively handle such problems. Furthermore, compared to some newly proposed methods, this approach offers greater operability.

[0003] This method applies EMD and Hilbert transform to structural modal identification. Empirical Mode Decomposition (EMD) decomposes the signal into a series of intrinsic mode function (EMF) components. The isolated EMFs are then transformed using the Hilbert transform, and finally, the results are fitted using the least squares method. However, this approach has drawbacks. EMD requires a high signal-to-noise ratio for impact signals and is not ideal for modal identification of complex structures, often resulting in mode aliasing. While similar methods, such as "data extension based on neural networks," have been proposed to address this issue, they are not readily applicable in practical engineering.

[0004] Patent application number 201610101215.1 discloses a method for identifying modal parameters of ultra-tall structures. Based on the discrete synchronous squeezed wavelet transform, it effectively analyzes non-stationary, nonlinear, and strong noise signals, accurately reconstructing the characteristics of modal components of complex synthetic signals in the form of resonant components. Combined with the Hilbert transform, it effectively analyzes the resonant components, obtaining the instantaneous amplitude and frequency characteristics, thereby achieving the purpose of identifying the main frequencies and damping ratios of ultra-tall structures. To ensure the accuracy of modal parameter identification, a least-squares linear fitting method is introduced to smooth the prediction results. The final processing results of the aforementioned invention clearly show modal aliasing, while the method proposed in this application can effectively avoid this problem. Summary of the Invention

[0005] To address the technical problem of mode aliasing in current modal identification methods for nonstationary and nonlinear signals, this invention proposes a modal parameter identification method for large-span spatial structures. This method is based on an improved Empirical Mode Decomposition (EMD) method and Hilbert transform, solving the problem that traditional EMD methods cannot handle signals with poor signal-to-noise ratios. Furthermore, it is applicable not only to modal parameter identification of large-span structures but also to the identification of structural modal frequencies, damping, and array configurations in civil engineering, mechanical engineering, and other fields.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a method for identifying modal parameters of a large-span spatial structure, comprising the following steps:

[0007] Step 1: Express the displacement signal x(t) as a combination of multiple sine functions, and find the analytic signal z(t) = x(t) + jH(x(t)) of the displacement signal x(t) when disturbed, where H(x(t)) is the Hilbert transform function of the displacement signal x(t), and j represents the imaginary part;

[0008] Step 2: Determine whether the frequencies of each component in the analytic signal z(t) satisfy the following conditions. And f i >f i+1 If the conditions are met, then select a reference frequency f0 such that... Among them, f i To analyze the frequency values ​​of each component in the real part x(t) of the signal z(t), proceed to step three; if the conditions are not met... Directly perform standard empirical mode calculations on the analytic signal z(t);

[0009] Step 3: Obtain the frequency f i =f i -f0 is substituted into the analytic signal z(t) and converted to a time-domain expression, then multiplied by... The improved signal x is obtained f0 (t), for the improved signal x f0 (t) Perform standard empirical mode decomposition to obtain each eigenfunction IMFx f0i , where x f0i These are the improved signal mode functions decomposed by the EMD method.

[0010] Step 4: Convert each eigenfunction IMFx f0i The analytic signal is obtained by using the Hilbert transform, and then multiplied by... Taking the real part yields the modal functions x of the displacement signal x(t). fi ;

[0011] Step 5: Based on the mode functions x of each orderfi Solve for the structural modal parameters.

[0012] The Hilbert transform function of the displacement signal x(t) Where PV is the Cauchy principal value.

[0013] The method for solving the structural modal parameters in step five is as follows:

[0014] Find the modal functions x of each order. fi Analytical signal: z fi =x fi +jH(x fi )=a(t)e jθ(t) ;

[0015] In the formula, amplitude phase

[0016] Modal function x fi The corresponding impulse response function is

[0017] Where A is the amplitude, ω n Let ξ be the system angular frequency and ξ be the system damping ratio.

[0018] The result of the impulse response function after Hilbert transform is:

[0019] H(x) fi Substituting the impulse response function into the phase θ(t), we obtain the phase. This equation is a straight line equation, ω d The slope of the straight line is also the damping frequency. The constant is the result of the differential calculation.

[0020] H(x) fi Substituting the amplitude a(t) into the impulse response function, the instantaneous amplitude of the signal is... Taking the logarithm of both sides, we have ln(a(t))=-ξω n t+ln(A), which is a linear equation with a slope k=-ξω n Thus, a fixed angular frequency is obtained. Damping ratio

[0021] The improved signal x f0 (t) Perform empirical mode decomposition to fit the upper and lower envelopes e max With e min Find the average envelope of the upper and lower envelopes.

[0022] Take the sequence h i(t)=x f0 (t)-m i Determine the sequence h i (t) Whether the eigenfunction mode condition is satisfied; if not, then take the sequence h. i Let (t) be the new input signal. If the condition is met, then denote the signal c. j (t)=h i (t), at which time the signal c j (t) represents an IMF component;

[0023] Signal c j (t) is separated from the original signal: the remainder term is r(t), and r1(t) = x f0 (t)c j (t), the subsequent remainder r j+1 (t)=r j (t)-c j+1 (t), and finally the remainder r is obtained. n (t), when the remainder r n The iteration stops when (t) is a monotonic function; where n represents the final number of IMF functions obtained, i.e., the order of the structural mode; i represents the index of the number of iterations for IMF function determination; and j represents the number of IMF functions obtained.

[0024] Improved signal after computation Among them, c j (t) represents the characteristic mode function (IMF) for each order, r n (t) represents the final remainder.

[0025] The intrinsic function mode conditions are: 1) The number of extreme points of the signal is equal to the number of times the signal crosses zero, or differs by at most 1; 2) At any given moment, the average value of the upper envelope formed by the local maxima and the lower envelope formed by the local minima of the signal is zero.

[0026] The resulting improved signal x f0 (t) multiplied by After taking the real part, we obtain the decomposed signal x(t) from the original signal. Then, we perform a Hilbert transform on signal x(t): Therefore, the inherent circle flatness ratio can be obtained. With damping ratio

[0027] The final obtained signal is directly fitted, and the amplitude logarithm function ln(a(t))-t is fitted according to the linear least squares method. Then the slope is calculated to obtain the modal parameters of the structure.

[0028] The beneficial effects of this invention: The key point of this invention lies in the use of an improved empirical mode decomposition method based on the characteristics of Hilbert transform, which compares the signal x(t) in the EMD method with the signal x after spectral shifting. f0 Based on the displacement relationship between (t), this invention proposes a method to effectively solve the problem of mode aliasing in traditional EMD methods, which renders the algorithm unusable. This invention also addresses the issue that empirical mode decomposition methods cannot handle signals with poor signal-to-noise ratios and are unsuitable for large-span structures. Compared to other mode identification methods that do not employ Hilbert transform, the method of this invention exhibits better adaptability and robustness, and can effectively handle signals with poor signal-to-noise ratios, nonlinearity, and non-stationary signals. Compared to other similar mode identification methods that employ Hilbert transform, it has stronger operability and can be applied to engineering field use. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of the process of the present invention.

[0031] Figure 2 This is a line graph of the structural displacement signal.

[0032] Figure 3 This is a schematic diagram of the results of the original empirical mode decomposition method.

[0033] Figure 4 This is a diagram showing the recognition results of the method of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] like Figure 1 As shown, this invention aims to propose a modal parameter identification method for large-span spatial structures. It is an improved empirical mode decomposition and mode aliasing decoupling method based on the displacement properties of Fourier transform. Based on this method, and combined with Hilbert transform, an improved modal identification method is proposed. Specifically, this invention adopts the following technical solution:

[0036] Step 1: Currently, the structural detection only obtains acceleration signals. Integrating the acceleration signals yields the displacement signal x(t) of the structure. Representing the displacement signal x(t) as a combination of multiple sine functions, we obtain... Among them, a i f represents the magnitude of the i-th term, n represents the number of terms, and f i This is the frequency value of the i-th term. For long-span structures, monitoring signals are often subject to interference, resulting in mode aliasing in the derived frequency expression, making the result unusable for calculating the structure's modal parameters. The method in application number 201610101215.1 suffers from this problem. Any signal can be represented by a superposition of a series of sinusoidal signals.

[0037] Step 2: Find the analytic signal z(t) of the displacement signal x(t) affected by the disturbance signal, z(t) = x(t) + jH(x(t)), where, Here, PV represents the Hilbert transform formula, i.e., the Hilbert transform coefficients of the displacement signal x(t), where PV denotes the Cauchy principal value and j denotes the imaginary part. An analytic signal is a complex-valued function without negative frequency components; the real and imaginary parts of an analytic signal are real-valued functions associated with the Hilbert transform.

[0038] Step 3: For the frequencies f of each component in the analytic signal z(t) i (f i >f i+1 Due to mode aliasing, each frequency order satisfies This relationship, when chosen as the reference frequency f0, makes Among them, f i To analyze the frequency values ​​of each component in the real part x(t) of the signal z(t), the reference frequency f0 is a frequency value that satisfies the above formula, found through trial and error. If it does not satisfy... This relationship proves that there is no mode aliasing between the two modes, and modal calculations can be performed directly.

[0039] Step 4: Obtain the frequency f i =f i -f0 is substituted into the analytic signal z(t) and converted to a time-domain expression, then multiplied by... The improved signal x is obtained. f0 (t). The improved signal is equivalent to shifting the spectrum of the analytic signal z(t) to the right by f0 units.

[0040] Step 5: Improve signal x f0 (t) Perform standard empirical mode decomposition to obtain each eigenfunction IMFx f0i x f0iThese are the modal functions of the improved signal decomposed by the EMD method.

[0041] For empirical mode methods, mode identification is impossible when the signal-to-noise ratio is poor. This patent introduces a reference frequency f0, reduces the signal-to-noise ratio through displacement relationship, and then restores it, thus solving the problem that traditional EMD methods cannot solve.

[0042] Step 6: Combine the above eigenfunctions IMFx f0i The analytic signal is obtained by using the Hilbert transform, and then multiplied by... Taking the real part yields the mode functions x(t) of the original signal x(t) based on the improved empirical mode decomposition method. fi .

[0043] The analytic signal of each eigenfunction is solved using the Hilbert transform. This is because the transform in step 4 involves multiplying by a certain factor. Analytical signal multiplied The time domain can be converted to the frequency domain. Compared with the results of direct empirical mode decomposition, the traditional method suffers from mode aliasing, and its results are unreliable. The method of this invention solves this problem.

[0044] Step 7: Solve for the structural modal parameters.

[0045] First calculation of the modal functions x of each order fi Analyzed signal:

[0046] z fi =x fi +jH(x fi )=a(t)e jθ(t) (1)

[0047] In the formula, the amplitude

[0048] phase

[0049] Modal function x fi The corresponding impulse response function expression is:

[0050] Where A is the amplitude, ω n Let ξ be the system angular frequency and ξ be the system damping ratio.

[0051] The result of equation (4) after Hilbert transformation is:

[0052] Solving for the damping frequency data: Substituting equations (4) and (5) into equation (3) yields phase. This equation is a straight line equation, ω d The slope of the straight line is also the damping frequency. The constant is the result of the differential calculation.

[0053] Solving for the amplitude data: Substituting equations (4) and (5) into equation (2), the instantaneous amplitude of the signal is... Taking the logarithm of both sides, we have ln(a(t))=-ξω n t+ln(A), this equation is also a linear equation, and its slope k=-ξω n ,and but Thus, the damping ratio and the fixed circular frequency can be obtained.

[0054] Specific examples:

[0055] The specific process of the invention will be further illustrated by a practical example:

[0056] 1. Firstly, regarding Figure 2 The given signal, i.e., the displacement curve, is analyzed using the signal z(t) = x(t) + jH(x(t)) to solve for the displacement amount f0 = 167Hz, and the improved signal x is obtained by processing it according to the method of this invention. f0 (t).

[0057] Figure 2 The displacement data is obtained by integrating the acceleration data of an actual structure subjected to impact twice. The sampling frequency is 256Hz and the sampling time is 10 seconds, which is 35 to 45 seconds. The impact excitation is excluded. The response can be fully understood to occur under the pure environmental excitation and can reflect the modal parameters of the structure well.

[0058] 2. Improve signal x f0 (t) Perform empirical mode decomposition to fit the upper and lower envelopes e max With e min Find the average envelope of the upper and lower envelopes.

[0059] 3. Take the sequence h i (t)=x f0 (t)-m i At this point, it is necessary to determine the sequence h. i (t) Whether the eigenfunction mode conditions are satisfied: First, the number of extreme points of the signal is equal to the number of times the signal crosses zero, or differs by at most 1; second, at any given time, the average of the upper envelope formed by the local maxima and the lower envelope formed by the local minima of the signal is zero; if not satisfied, then take the sequence h. i(t) represents the new input signal. Repeat steps 1 to 3. If the condition is met, then denote the signal c. j (t)=h i (t), at which time the signal c j (t) is an IMF component.

[0060] 4. Transfer signal c j (t) is separated from the original signal, and the remainder term is taken as r(t), r1(t) = x f0 (t)c j (t), for the subsequent remainder r j+1 (t)=r j (t)-c j+1 (t), the final remainder r n (t), when r n The iteration stops when (t) is a monotonic function. n represents the final number of IMF functions obtained, i.e., the order of the structural modes. i represents the subscript of the number of iterations for IMF function determination, and j represents the number of IMF functions obtained. For the sake of the method's universality, numerical subscripts are not used to directly indicate this; see the flowchart for details.

[0061] 5. Improved signal after calculation and processing Among them, c j (t) represents the characteristic mode function (IMF) for each order, r n (t) represents the final remainder, indicating the mean or stationary trend of the signal.

[0062] The above are the basic methods for improving empirical modes. The signal obtained after this processing is quite different from the original signal in the frequency domain after being shifted by the reference frequency f0 and decomposed by EMD, and the IMF mode function at this time does not have mode aliasing.

[0063] 6. The obtained improved signal x f0 (t) multiplied by After taking the real part, we obtain the decomposed signal x(t) from the original signal. Then, we perform a Hilbert transform on signal x(t): At this time, Taking the real part again is equivalent to returning the reference frequency f0 of the previous displacement. The natural circularity can be solved from step 7. With damping ratio

[0064] 7. Since the obtained damping frequency and amplitude data do not perfectly satisfy the straight pipeline, the final obtained signal is directly fitted. Therefore, ln(a(t))-t is fitted using the linear least squares method, and the slope is then calculated to obtain the modal parameter data of the structure. See the comparison results below. Figure 2-4 See Table 1-2.

[0065] Figure 3 To follow the traditional method Figure 2 After processing the signal, it can be seen that the second and third order modes are no longer recognizable, meaning that traditional methods cannot effectively process this displacement signal. Figure 4 The method of the present invention is for Figure 2 The processing of the signal shows that the method of the present invention effectively separates the first three levels of data of the signal.

[0066] Tables 1 and 2 show the comparison results between the frequency and damping ratio calculated by the present invention and the traditional method, respectively.

[0067] Table 1 Frequency Identification Values

[0068]

[0069] Table 2 Damping Ratio Identification Values

[0070]

[0071] Depend on Figure 3 , Figure 4 As shown in Tables 1 and 2, the method of the present invention effectively handles the situation where the signal-to-noise ratio is poor, and performs modal decoupling and parameter identification based on the structural displacement response signal using improved empirical mode decomposition and Hilbert transform. The method of the present invention can accomplish this task well and obtain relatively accurate modal parameters.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modal parameter identification of long-span spatial structures, characterized in that, The steps are as follows: Step one: express the displacement signal x(t) as a combination of multiple sinusoidal functions, and solve the analytic signal z(t) of the displacement signal x(t) disturbed by the interference, wherein H(x(t)) is the Hilbert transform function of the displacement signal x(t), and j represents the imaginary part; Step two: judge whether the frequency of each component in the analytic signal z(t) satisfies and f i i+1 , if yes, select the reference frequency f0 so that where f i is the frequency value of each component in the real part x(t) of the analytic signal z(t), enter step three; if not directly perform standard empirical mode calculation on the analytic signal z(t);​ Step three: take the frequency f i = f i -f0 into the analytical signal z(t) and convert to time domain expression multiplied by Get the improved signal x f0 (t), the standard empirical mode decomposition is carried out on the improved signal x f0 (t), and each intrinsic function IMFx f0i is obtained, wherein x f0i is the mode function of each order of the improved signal decomposed by the EMD method; Step four: each eigenfunction IMFx f0i The analytical signal is solved by Hilbert transform, and then multiplied by The real part is taken to obtain each order modal function x fi ; Step five: The modal functions x fi Solving the modal parameters of the structure.

2. The method of claim 1, wherein, The Hilbert transform function of the displacement signal x(t) where PV is the Cauchy principal value.

3. The method of claim 1, wherein, The method for solving the structural modal parameters in the step five is: Find the analytical signal z of the mode function x of order n: fi z = x + jH(x) fi = a(t)e fi fi jθ(t) ;​​ wherein the amplitude phase Modal function x fi The corresponding impulse response function is where A is the amplitude, ω is the system circular frequency, and ξ is the system damping ratio. n where A is the amplitude, ω is the system circular frequency, and ξ is the system damping ratio. The result of the impulse response function after the Hilbert transform is H(x fi ) and the impulse response function into the phase θ(t), the phase This equation is a straight line equation, ω d is the slope of the straight line and also the damping frequency, is a constant after the differential calculation; H(x fi ) and the impulse response function into the amplitude a(t), the instantaneous amplitude of the signal is Taking logarithm on both sides simultaneously, ln(a(t)) = -ξω n t + ln(A), which is a linear equation, and the slope k = -ξω n , so as to get the fixed circular frequency Damping ratio 4. The method of claim 1 or 3, wherein, the improved signal x f0 (t) performing empirical mode decomposition to fit upper and lower envelopes e max with e min finding an average envelope of the upper and lower envelopes h i (t) = x f0 (t) - m i h i (t) is an IMF component. i (t) is a new input signal. l (t) = h i (t) is an IMF component. l (t) is an IMF component. The signal c l (t) is separated from the original signal: the remainder is r(t), and r1(t)=x f0 (t)c l (t), the subsequent remainder r l+1 (t) = r l (t)-c l+1 (t), and finally the remainder r n (t) is obtained, and the iteration stops when the remainder r n (t) is a monotonic function; wherein n represents the number of IMFs finally obtained, i.e. the order of the structural mode; i represents the subscript of the number of iterations for IMF judgment, and l represents the number of IMFs obtained. Improved signal after computation Among them, c l (t) represents the characteristic mode function (IMF) for each order, r n (t) represents the final remainder.

5. The method of claim 4, wherein, The intrinsic function modal condition is: 1) the number of signal extreme points is equal to the number of times that the signal passes through zero, or at most differs by 1; 2) at any time, the average value of the upper envelope line composed of local maximum values and the lower envelope line composed of local minimum values of the signal is zero.

6. The modal parameter identification method of a long-span space structure according to claim 3 or 5, characterized in that, Directly fitting the finally obtained signal, fitting the amplitude logarithmic function ln(a(t))-t according to the linear least square method, and then solving the slope to obtain the modal parameters of the structure.

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