Structure vibration displacement frequency domain integration method based on low-frequency truncation

Abstract

The invention discloses a structure vibration displacement frequency domain integration method based on low-frequency truncation, and belongs to the field of structure engineering. The method comprises the following steps: firstly, removing a direct current component based on a mean value elimination baseline correction method, and preprocessing through a least square fitting method to obtain a corrected acceleration signal; fourier transform is carried out on the corrected acceleration signal, a proper frequency is selected as a cutoff frequency according to spectral characteristics, and an initial phase is corrected in a low-frequency zero clearing mode to solve the problem that an initial value is unknown; and removing high-frequency noise by adopting a low-pass filter, and performing primary frequency domain integration on the processed acceleration signal to obtain a displacement signal. The method is verified through numerical simulation and a vibration table test, the result shows that the displacement accuracy obtained through integration of the method can reach 82.90%, high precision is achieved, and technical support can be provided for structural state evaluation.

Description

Technical Field

[0001] The invention relates to a structural vibration displacement frequency domain integration method based on low-frequency truncation, and belongs to the field of structural engineering. Background Art

[0002] Vibration displacement refers to the maximum distance an object moves from its equilibrium position when vibrating. In the field of structural engineering, vibration displacement is a crucial parameter. It reflects the vibration of the structure under external force or excitation, and is closely related to the stability, safety and durability of the structure. Therefore, monitoring vibration displacement is of great significance to ensure the safety and reliability of the structure.

[0003] There are different methods for monitoring structural vibration displacement. Common contact displacement sensors have high accuracy, but the monitoring equipment is expensive and is limited by the sensor installation location and space. Typical non-contact methods such as laser displacement sensors have a wide measurement range and high accuracy, but there are disadvantages such as multiple maintenance and calibration during use. Acceleration signals are easier to measure and there is an integral operation relationship between acceleration and displacement. Therefore, the vibration displacement of the structure can be measured by installing an acceleration sensor to measure the acceleration signal, and the vibration displacement time history of the structure can be obtained by integration.

[0004] At present, the traditional integration methods used for acceleration signals include time domain integration (Simpson integration method, second-order central difference method) and frequency domain integration. Zhou Xiaoxiang et al. obtained displacement through time domain integration and used the least squares method to eliminate the trend term that is easy to generate in the process, but the waveform correction method will submerge the effective signal. Lee et al. proposed an acceleration integral displacement scheme suitable for low-frequency dominant structures. The scheme introduced overlapping time windows to improve the accuracy of reconstructed displacement and suppress low-frequency noise. However, when the target frequency is set relatively low, oscillation is prone to occur in the frequency domain. Lee HS et al. proposed an FDM-FIR filter. Unlike traditional integration methods, they use ridge regression to solve the rank deficiency problem. The FDM-FIR filter only performs integration operations in the time domain, reducing the time-frequency domain conversion process of traditional filters and improving computational efficiency. However, the determination of the regularization coefficient only relies on empirical formulas and lacks sufficient theoretical basis. Park et al. studied the influence of initial velocity and initial displacement on acceleration integral displacement, used a high-pass filter to reduce the integral error, and performed segmented integration on the acceleration signal, but required more knowledge of the displacement waveform of the measured system and was difficult to apply to systems with unknown displacement. In the theoretical deduction of various integration methods, Zhou Yingjie proposed theoretical demonstrations of various algorithms and analyzed the influence of the selection of integral control parameters on the integral results. Among them, the "low-frequency attenuation integral algorithm" did not correct the acceleration signal throughout the process but only corrected the acceleration peak error. It did not correct the acceleration signal throughout the process, resulting in a large acceleration error and a large error in the displacement signal obtained after integration. Guo Xiangying and others combined the least squares moving average method with a filter to reduce the influence of random errors through multiple smoothing, filtering and integration for the integration problem of noisy acceleration signals. Compared with the standard signal, the obtained integral displacement signal has a large initial value error and still has amplitude differences. The above methods cannot solve the influence of low-frequency interference signals on the displacement time course well. The integration of low-frequency signals will obviously show a "drift" phenomenon. Effective preprocessing of acceleration signal data becomes the key.

[0005] From the above analysis, we can see that the actual monitored acceleration signal is interfered by noise, and as time accumulates, the integrated displacement shows a significant "drift" phenomenon. Therefore, how to reduce the errors caused by trend terms and low-frequency interference signals in structural engineering has always been a major problem for scholars at home and abroad.

[0006] In view of this, the present invention is proposed. Summary of the invention

[0007] The present invention provides a structural vibration displacement frequency domain integration method based on low-frequency truncation, which is used to solve the technical problem of large trend term error caused by noise interference and unknown initial value.

[0008] The technical solution of the present invention is:

[0009] According to a first aspect of the present invention, a method for frequency domain integration of structural vibration displacement based on low-frequency truncation is provided, comprising the following steps:

[0010] S1. Preprocessing the acceleration signal to obtain a corrected acceleration signal;

[0011] S2, performing Fourier transform on the corrected acceleration signal, presetting the low-frequency zeroing cutoff frequency according to the spectrum characteristics, and correcting the initial phase of the low-frequency interference signal by low-frequency zeroing;

[0012] S3. Use a low-pass filter to remove high-frequency noise, and perform a frequency domain integration of the processed acceleration signal to obtain a displacement signal.

[0013] Furthermore, S1 is specifically as follows: for the acceleration signal, a baseline correction method based on eliminating the mean is used to remove the DC component, and random signal interference in the acceleration signal is eliminated by trend term fitting of the least square method to obtain a corrected acceleration signal.

[0014] Furthermore, the S2 is specifically:

[0015] The Fourier transform FFT is used on the corrected acceleration signal; after Fourier transform and inverse Fourier fast transform, the accumulated vibration displacement is expressed as:

[0016]

[0017] In the formula, F -1 represents the symbol of the Fourier fast inverse transform function, F(a(t)) is the frequency domain signal of the acceleration signal after Fourier transform;

[0018] The function H(w k ), the expression is:

[0019]

[0020] In the formula, w k is the angular frequency.

[0021] Furthermore, the function H(w k ) is defined as:

[0022]

[0023] In the formula, f T Zero the cutoff frequency for low frequencies.

[0024] Furthermore, the low-pass filter is used to remove high-frequency noise, and the displacement signal after filtering satisfies the following relationship:

[0025]

[0026] In the formula, f s is the upper cutoff frequency, w k is the angular frequency; F -1 represents the symbol of the Fourier fast inverse transform function, and F(a(t)) is the frequency domain signal of the acceleration signal after Fourier transform.

[0027] According to a second aspect of the present invention, a terminal is provided, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor is configured to execute the steps of any one of the above-mentioned structural vibration displacement frequency domain integration methods based on low-frequency truncation.

[0028] The beneficial effects of the present invention are as follows: the present invention first removes the DC component based on the baseline correction method of eliminating the mean, and pre-processes the modified acceleration signal by the least squares fitting method; the modified acceleration signal is Fourier transformed, and a suitable frequency is selected as the cutoff frequency according to the spectrum characteristics, and the initial phase is corrected by low-frequency zeroing to solve the problem of unknown initial value; a low-pass filter is used to remove high-frequency noise, and the pre-processed acceleration signal is integrated in the frequency domain once to obtain a displacement signal. The method proposed by the present invention is verified by numerical simulation and vibration table test, and the results show that the displacement accuracy obtained by the proposed method can reach 82.90%, which has high accuracy and can provide technical support for structural state assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is the algorithm flow chart;

[0030] Figure 2 This is the principle diagram of bandpass filtering;

[0031] Figure 3 It is a single sinusoidal acceleration signal diagram;

[0032] Figure 4 This is a comparison chart of single sinusoidal displacement signals;

[0033] Figure 5 It is a local diagram of the middle segment signal of a single sine wave;

[0034] Figure 6 This is a comparison diagram of the single sine wave displacement signal after tail end correction;

[0035] Figure 7 This is the peak recognition result of the single sine wave displacement signal;

[0036] Figure 8 This is a comparison diagram of multi-wave superposition displacement signals;

[0037] Fig. 9 This is a comparison diagram of multi-wave superposition displacement signals after tail end correction;

[0038] Fig.10 This is a diagram of the vibration table simulation device;

[0039] Fig.11 It is the loading condition sequence diagram;

[0040] Fig.12 This is the acceleration signal diagram of working condition 1 (1200gal);

[0041] Fig.13 This is the amplitude-frequency characteristic diagram of the acceleration signal of working condition 1 (1200gal);

[0042] Fig.14 This is the displacement time history diagram without processing;

[0043] Fig.15 This is the displacement comparison chart of working condition 1 (1200gal);

[0044] Fig.16 This is a partial enlarged view of the middle section signal (1200gal);

[0045] Fig.17 This is the displacement comparison chart of working condition 2 (1500gal);

[0046] Fig.18 This is the displacement comparison diagram of working condition 3 (2000gal);

[0047] Fig.19 is the positive displacement peak identification result;

[0048] Fig. 20 This is the negative displacement peak identification result. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0050] In view of the "integral drift" phenomenon existing in traditional time domain integration and the problem of large errors caused by the uncertain initial value of frequency domain integration, the present invention analyzes the time domain algorithm, studies the source of errors, and uses the least squares method to preprocess the data of the trend item in the time domain stage; uses the frequency domain algorithm in the frequency domain stage to solve the problem of unknown initial phase, and proposes a method of clearing the low-frequency part and setting a low-pass filter to control the error of the frequency domain integration method; finally, through numerical simulation and vibration table experiments, and introducing accuracy value evaluation indicators, the effectiveness and accuracy of the method disclosed in the present invention are quantitatively analyzed.

[0051] According to a first aspect of an embodiment of the present invention, a frequency domain integration method for structural vibration displacement based on low-frequency truncation is provided, which is specifically described as follows:

[0052] In the actual measurement process, the acceleration signal obtained has random interference and DC components. The expression of the acceleration signal can be expressed as:

[0053] a(t)=a s (t)+a n (t)+ε;

[0054] The velocity signal expression obtained by integrating the acceleration signal is:

[0055] v(t)=∫a(t)dt=∫a s (t)dt+∫a n (t)dt+εt+c;

[0056] The displacement signal expression obtained by integrating the velocity signal is:

[0057]

[0058] In the formula, a s (t) is the measured acceleration signal, a n (t) is the random interference part of the measured acceleration signal, a(t) is the real acceleration sequence; v(t) is the velocity signal, s(t) is the displacement signal; ε is the coefficient of the quadratic term in the trend term, that is, the DC component; c is the coefficient of the linear term in the trend term, and e is the coefficient of the constant term in the trend term.

[0059] Due to the interference of DC components and random signals in the acceleration signal, random interference terms, a first-order trend term (ct+e), and a second-order trend term 0.5εt are introduced into the acceleration signal during the time domain integration process. 2 +ct+e, in order to eliminate the trend term from the integral signal, the present invention first removes the mean value of the acceleration signal to remove the DC component, and then eliminates the random signal interference in the acceleration signal by fitting the trend term using the least squares method.

[0060] Since the sampled signal is in discrete form in practice, the frequency domain integration generally uses Fast Fourier Transform (FFT), and the discrete algorithm expression is:

[0061]

[0062] Where N is the number of sampling points, x(r) is a time signal sequence with N sampling points (r = 0, 1, 2, LN-1), X(k) is its discrete spectrum (k = 0, 1, 2, LN-1), and j is an imaginary unit.

[0063] In the frequency domain, the integration operation of the acceleration signal is equivalent to a simple phase adjustment of the spectrum. Therefore, FFT is used to avoid error accumulation and amplification by replacing time domain integration with frequency domain integration. The spectrum of the acceleration time series FFT can be expressed as:

[0064]

[0065] Among them, a k is the real part of the acceleration signal sequence, b k is the imaginary part of the acceleration signal sequence, a(r) is the acceleration signal sequence with N sampling points, that is, the corrected acceleration signal; a(k) is the discrete acceleration time series with N sampling data. The amplitude, angular frequency and initial phase angle of the corresponding simple harmonic wave can be calculated by the following formula, where A k is the amplitude of the discrete acceleration time series a(k), f k is the frequency of the discrete acceleration time series a(k), Q k is the initial phase angle of the discrete acceleration time series a(k), w k is the angular frequency of the discrete acceleration time series a(k), and the expression of the simple harmonic wave it represents is:

[0066]

[0067] Then a(k) and vibration displacement can be cumulatively expressed as:

[0068] a(k)=A k cos(2πf k t+Q k );

[0069]

[0070] The above relationship is expressed using FFT and Inverse Fast Fourier Transform (IFFT) as follows:

[0071]

[0072] In the formula, F -1 represents the symbol of the fast inverse Fourier transform function, and F(a(t)) is the frequency domain signal after FFT of the acceleration signal.

[0073] Frequency domain integration is to convert the acceleration signal from the time domain to the frequency domain, then perform Fourier transform on the acceleration signal, integrate it once to get the time course of the displacement signal in the frequency domain, and finally convert the displacement signal in the frequency domain into a time domain signal through inverse Fourier transform.

[0074] In the actual test process of acceleration signal, due to the existence of test error, the amplitude below the cutoff frequency (low-frequency part) in the amplitude spectrum is not zero. In the frequency domain integration process, the Fourier coefficient of the displacement signal in the frequency domain is inversely proportional to the square of the frequency. k The closer it is to 0, the greater the Fourier coefficient deviation is, so the low-frequency cutoff frequency plays a key role in filtering, while the high-frequency cutoff frequency plays a smaller role in filtering. Improper selection of the low-frequency cutoff frequency will lead to a larger error in the displacement signal after frequency domain integration. If a bandpass filter is used to remove the trend term, in the stopband region Figure 2 The existence of the transition band has a great impact on the frequency domain integration. Therefore, the present invention converts the acceleration signal into the frequency domain, clears the low-frequency interference signal, and uses a low-pass filter to remove the high-frequency noise part, thereby improving the displacement recognition accuracy.

[0075] The low-frequency truncation algorithm introduces the function H(w k ), the expression is:

[0076]

[0077] In the low-frequency cutoff algorithm, a low-frequency clearing cutoff frequency f needs to be selected. T , where f T is the low frequency zero cutoff frequency. Its function H(w k ) is defined as:

[0078]

[0079] In the process of frequency domain integration of acceleration signal to displacement, in order to reduce the influence of high-frequency noise on the result, it is usually necessary to introduce a low-pass filter for signal processing. There are many types of low-pass filters, and common low-pass filters include: Gaussian low-pass filter, Butterworth low-pass filter and trapezoidal low-pass filter. Compared with other filters, Butterworth low-pass filter has a stable amplitude-frequency characteristic both inside and outside the passband. Therefore, the present invention adopts Butterworth low-pass filter to reduce the interference to the trend term, where f sThe upper cutoff frequency is used to preprocess the acceleration data through the above method to reduce the error caused by the high-frequency part. The displacement time history after filtering satisfies the following relationship:

[0080]

[0081] In the frequency domain integration process, signals of different frequencies will introduce different degrees of phase delay during the integration process, resulting in phase differences between components of different frequencies. To address this problem, the present invention adopts a method of setting the displacement signal to zero at the initial moment to reduce the interference caused by the phase difference.

[0082] The acceleration signal is preprocessed by eliminating the DC component and removing the random signal, and then the acceleration signal is converted to the frequency domain. The low-frequency interference signal is cleared to correct the problem of unknown initial phase, and a Butterworth low-pass filter is added to remove high-frequency noise. Finally, the displacement signal is obtained by integrating once in the frequency domain. The flow chart is as follows: Figure 1 shown.

[0083] To verify the effectiveness of the algorithm, the present invention selects a single sine wave and a sine wave superimposed by multiple waves as the superimposed displacement signal, performs a derivative on it to obtain an acceleration signal, processes the acceleration signal using the above-mentioned method to obtain a displacement signal, and compares it with the real displacement signal.

[0084] The obtained acceleration signal is a sinusoidal signal with a frequency of 2 Hz and an amplitude of 1 m / s 2 , the initial phase is 0, and the sampling frequency is 200Hz. To verify the robustness of the algorithm, the influence of different degrees of interference on the acceleration integral is simulated, and Gaussian white noise of 10% and 20% root mean square (RMS) is added to the acceleration signal respectively. Figure 3 The final displacement signal is compared with the real displacement signal. The single sine wave verification satisfies the following relationship:

[0085]

[0086] a(t)=sin(2π×2t);

[0087] The acceleration signal obtained by derivation is integrated once from the time domain and the method proposed by the present invention to obtain the displacement time history ((RMS) 0% is the displacement time history without adding Gaussian white noise, (RMS) 10% and (RMS) 20% are the displacement time history obtained by adding 10% and 20% Gaussian white noise). The displacement time history obtained by the present invention is compared with the original true displacement signal, as shown in FIG. Figure 4 As shown in the figure, the displacement signal obtained by integration has a relatively large error at the end of the time period, while the displacement obtained by frequency domain integration in the initial value and the middle time period is consistent with the true theoretical displacement signal. Figure 5As shown in , the displacement signal obtained by frequency domain integration has the same frequency as the real signal. Even when the root mean square error reaches 20%, the displacement matching effect is still good, indicating that the method proposed in this paper has high accuracy and robustness. Further quantitative recognition results are shown in Figure 7 As shown in the figure, the peak error is generally controlled between 7% and 9%. Through the error analysis and comparison of the displacement integration effect under different root mean square errors, adding Gaussian white noise will cause some interference to the integration effect, but the amplitude change is still small and has little impact on the overall result.

[0088] The problem of relatively large error in the displacement signal obtained by integration at the end of the time period Figure 4 The main reason is that the frequency domain integration usually requires the number of sampling points of the input signal to be a power of 2. Therefore, the present invention fills zeros at the end of the acceleration signal through a low-pass filter to make the number of sampling points reach 1024 points. The displacement time history diagram is as follows: Figure 6 As shown, the error in the final segment is reduced and the accuracy is improved.

[0089] The sinusoidal signal is superimposed as the initial acceleration signal. The simulated sinusoidal signal is composed of frequency components of 2 Hz and 4 Hz, and the acceleration amplitudes are 1 and 2 m / s respectively. 2 , the sampling frequency is 200Hz, the acceleration signal and the accumulated displacement signal expression are:

[0090] a(t)=sin(4πt)+2sin(8πt);

[0091]

[0092] The above acceleration signal is used to obtain the accumulated displacement signal using the method proposed in this paper, such as Figure 8 It shows that the proposed method is consistent with the theoretical displacement signal in the middle section, but there are errors in the initial and final time periods. After the acceleration is low-frequency truncated and the tail is filled with zeros, the displacement time history diagram is as follows: Fig. 9 As shown in the figure, the consistency of the last segment is improved and the overall recognition effect is good.

[0093] The present invention uses a two-story reinforced concrete frame shaking table test with a scale ratio of 1:3 for verification. Accelerometers and displacement meters are installed on each layer of the frame and the shaking table surface. Fig.10 ), sampling frequency 200Hz, loading is divided into 3 working conditions such as Fig.11 , the same seismic wave time history is used for different working conditions, and only the peak value is scaled. Therefore, the acceleration under different working conditions is as follows: Fig.12 The frequency components are the same, only the amplitude is different, and its amplitude-frequency characteristics are as follows Fig.13 shown.

[0094] If the acceleration signal of working condition 1 is not preprocessed, the displacement time history diagram is as follows Fig.14 As shown in the figure, the displacement of time domain integration and frequency domain integration is poorly matched, and there is low-frequency noise interference.

[0095] Acceleration time domain signal conversion to frequency domain Fig.13 , its frequency components are mainly distributed in the range of 0:20Hz, and the high-frequency signal contains fewer components. T = 0.05Hz as the low-frequency zeroing cutoff frequency, zero the low-frequency part, reduce the error amplified by the frequency domain integration, and then add the Butterworth low-pass filter to reduce the interference to the trend term, and the baseline drift is significantly improved. After the above operation, the corrected time domain integral and the corrected displacement time history of the present invention are as follows Fig.15 As shown in FIG. 1 , the time domain integration and the method proposed in the present invention are compared with those before data preprocessing, and the displacement time history is more consistent. The method proposed in the present invention is more consistent with the real displacement signal. The displacement within 42.5:43.5 seconds is amplified, as shown in FIG. Fig.16 As shown, the integral displacement value has little difference in amplitude compared with the true value, so the method proposed in the present invention has good accuracy.

[0096] The accuracy value evaluation index is introduced to evaluate the acceleration signal integration result, and the accuracy value Δ is used to measure the overall consistency of s(t) relative to s′(t). The two methods are quantitatively analyzed by this index. The accuracy value of the corrected time domain integration is 57.81%, and the accuracy value of the integration method proposed in the present invention is 82.90%. Compared with the existing literature methods, the accuracy value of the existing acceleration signal integral displacement value is 73.32%. The accuracy of the method proposed in the present invention has been improved, which verifies that the method of using a low-pass filter and clearing the low-frequency part in the present invention can improve the displacement accuracy value, and the overall consistency is high. Where s(t) is the true displacement signal, s′(t) is the accumulated vibration displacement, and Δ is the accuracy value after integration. Its expression is as follows:

[0097]

[0098] In addition, the acceleration signal of working condition 2 is scaled by the acceleration signal of working condition 1. Its frequency components are the same, but the amplitudes are different. Therefore, the same cutoff frequency (f T =0.05Hz) to clear the low-frequency part and obtain the displacement time history by frequency domain integration Fig.17 The overall recognition effect is good. There is no large error at the initial and terminal moments. The waveforms fit well and there are small differences in amplitude.

[0099] The acceleration signal of working condition 3 is preprocessed by the same method, and the method proposed by the present invention is used to select f T=0.05Hz as the cutoff frequency, clear the low-frequency part, and obtain the displacement time history by frequency domain integration Fig.18 , the overall agreement is good, and the error is small at the peak.

[0100] By comparing the displacement peak signals under different working conditions, the identification results are further quantified. Fig.19 , Fig. 20 The minimum positive displacement peak error is -8.89%, the average is 13.00%, the minimum negative displacement peak error is -8.33%, the average is 10.55%, and the overall error fluctuation is small. The algorithm can effectively identify the displacement peak response.

[0101] According to a second aspect of an embodiment of the present invention, a terminal is provided, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor is configured to execute the steps of any one of the above-mentioned structural vibration displacement frequency domain integration methods based on low-frequency truncation.

[0102] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A structural vibration displacement frequency domain integration method based on low-frequency truncation, characterized in that: The following steps are involved: S1. Preprocessing the acceleration signal to obtain a corrected acceleration signal; S2, performing Fourier transform on the corrected acceleration signal, presetting the low-frequency zeroing cutoff frequency according to the spectrum characteristics, and correcting the initial phase of the low-frequency interference signal by low-frequency zeroing; S3. Use a low-pass filter to remove high-frequency noise, and perform a frequency domain integration of the processed acceleration signal to obtain a displacement signal.

2. The structural vibration displacement frequency domain integration method based on low-frequency truncation according to claim 1 is characterized in that: The S1 is specifically as follows: for the acceleration signal, a baseline correction method based on eliminating the mean is used to remove the DC component, and random signal interference in the acceleration signal is eliminated by trend term fitting of the least square method to obtain a corrected acceleration signal.

3. The structural vibration displacement frequency domain integration method based on low-frequency truncation according to claim 1 is characterized in that: The S2 is specifically: The Fourier transform FFT is used on the corrected acceleration signal; after Fourier transform and inverse Fourier fast transform, the accumulated vibration displacement is expressed as: In the formula, F -1 represents the symbol of the Fourier fast inverse transform function, F(a(t)) is the frequency domain signal of the acceleration signal after Fourier transform; The function H(w k ), the expression is: In the formula, w k is the angular frequency.

4. The structural vibration displacement frequency domain integration method based on low-frequency truncation according to claim 3 is characterized in that: The function H(w k ) is defined as: In the formula, f T Zero the cutoff frequency for low frequencies.

5. The structural vibration displacement frequency domain integration method based on low-frequency truncation according to claim 1 is characterized in that: The low-pass filter is used to remove high-frequency noise, and the displacement signal after filtering satisfies the following relationship: In the formula, f s is the upper cutoff frequency, w k is the angular frequency; F -1 represents the symbol of the Fourier fast inverse transform function, and F(a(t)) is the frequency domain signal of the acceleration signal after Fourier transform.

6. A terminal, characterized in that: The invention comprises a processor, a memory and a computer program stored in the memory and executable on the processor, wherein the processor is configured to execute the steps of the structural vibration displacement frequency domain integration method based on low-frequency truncation according to any one of claims 1 to 8.

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