Acceleration, speed and displacement conversion method based on frequency-time domain processing combination

Abstract

The application relates to the technical field of civil structure monitoring, in particular to an acceleration, speed and displacement conversion method based on frequency-time domain processing combination, wherein only acceleration sensors are installed, three groups of acceleration, speed and displacement data can be obtained, the multifunctionalization of the acceleration sensors is realized, the method is convenient and low in cost; the obtained acceleration signals are processed through the method to obtain speed and displacement which are relatively close to theoretical values or measured values, the conversion accuracy is high, the conversion result is reliable, and the required precision of engineering can be met; in addition, the signals are decomposed into two parts, i.e. a direct current component and a zero-mean signal, and the time domain and frequency domain methods are respectively used for analysis, so that the method is not only suitable for vibration signals with initial and final speeds and initial and final displacements of 0, but also suitable for working conditions with residual speed or residual displacement.

Description

Technical Field

[0001] This invention relates to the field of civil structure monitoring technology, and more specifically, to a method for converting acceleration, velocity, and displacement based on a combination of frequency and time domain processing. Background Technology

[0002] For civil engineering structures, acceleration, velocity, and displacement are all important monitoring variables. Compared to accelerometers, displacement sensors are more complex and difficult to install, especially for large structures in practical engineering projects. It is often difficult to find a stationary reference point to fix the displacement gauge, which limits the accuracy of displacement measurement and greatly increases the cost and workload. Accurately converting acceleration signals into displacement signals is a more convenient and cost-effective method, but research in this area still has certain limitations. Currently, frequency domain integration or time domain integration methods are commonly used to convert acceleration and displacement signals. However, frequency domain integration methods are difficult to consider the influence of DC components in the signal and are only suitable for vibration signals with zero initial and final velocities and displacements. They are not suitable for vibration conditions with residual velocities or displacements. Civil structures often have residual displacements when undergoing plastic deformation under load, such as after an earthquake. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for converting acceleration, velocity, and displacement based on a combination of frequency and time domain processing. This method is applicable to signals with initial acceleration, velocity, and displacement values ​​of 0, and can also process and convert signals with residual velocity or residual displacement.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for converting acceleration, velocity, and displacement based on a combination of frequency and time domain processing is provided, including the following steps: S10. An acceleration vibration signal is sampled at a sampling frequency of sf to obtain a time sequence t=[t(0) t(1)t(2) t(3) ... t(N-1)] and an acceleration sequence a(t)=[a(0) a(1) a(2) a(3) ... a(N-1)], where N is the length of the sequence and is an even number; S20. Perform a Fourier transform on the acceleration sequence a(t) from step S10 to obtain the complex sequence F1; S30. In the frequency domain, the complex sequence F1 described in step S20 is subjected to noise filtering to obtain the complex sequence F3, and the mean value A of the acceleration sequence a(t) is determined; S40. Integrate the complex sequence F3 from which noise has been filtered out in step S30 once in the frequency domain and perform an inverse Fourier transform to obtain sequence F5. Take the real part of sequence F5 to obtain sequence v1. S50. Summing the sequence v1 from step S40 with the integral of the mean A in the time domain yields sequence v2. Based on the condition that the initial velocity is 0, the initial value of v2 is shifted to 0, thus obtaining the velocity sequence v3. S60. Perform a Fourier transform on the velocity sequence v3 in step S50 to obtain a complex sequence F6, and determine the mean V of the velocity sequence v3; S70. Integrate the complex sequence F6 from step S60 once in the frequency domain and perform an inverse Fourier transform to obtain the sequence F8; S80. Take the real part of sequence F8 from step S70 to obtain sequence s1; S90. Summing the sequence s1 from step S80 with the integral of the mean V in the time domain yields the sequence s2. Based on the condition that the initial displacement is 0, the initial value of s2 is shifted to 0, thus obtaining the displacement sequence s3.

[0005] The acceleration, velocity, and displacement conversion method of this invention, which combines frequency and time domain processing, can obtain three sets of data—acceleration, velocity, and displacement—by installing only an acceleration sensor, thus realizing the multi-functionality of the acceleration sensor. In addition, this invention decomposes the signal into two parts, namely the DC component and the zero-mean signal, and analyzes them respectively through time domain and frequency domain methods. It is applicable not only to vibration signals with initial and final velocities and initial and final displacements of 0, but also to working conditions with residual velocity or residual displacement.

[0006] Preferably, in step S10, the acceleration sequence a(t) is divided into a difference sequence between the acceleration sequence a(t) and the mean A. f az ( t The two parts are () and the mean A, where f az ( t The mean of ) is 0, and A is the mean of the acceleration sequence a; in step S60, sequence v3 is divided into the difference sequence between sequence v3 and the mean V. f vz ( t The two parts are () and the mean V, where, f vz ( t The mean of ) is 0, and V is the mean of sequence v3.

[0007] Preferably, in step S40, the initial value of the complex sequence F3 with the noise filtered out is set to 0 before integration in the frequency domain; in step S70, the initial value of the complex sequence F6 is set to 0 before integration in the frequency domain.

[0008] Preferably, in step S20, the complex sequence F1 is expressed as follows:

[0009] Represents the complex sequence F1 with the th element. Each parameter, the frequency sequence corresponding to F1 ω =2π[0 sf / N 2sf / N3sf / N ... sf / 2 -(sf / 2-sf / N) -(sf / 2-2sf / N) -(sf / 2-3sf / N) ...-sf / N], Let represent the m-th parameter in the acceleration sequence a(t), where k is an integer and i represents the imaginary unit.

[0010] Preferably, step S30 is performed as follows: S31. Based on complex sequence F1 and ω Plot the amplitude spectrum F12 of a, as follows:

[0011] Among them, the frequency sequence corresponding to F12 ω 2=2π[0 sf / N 2sf / N 3sf / N ... sf / 2]; S32. Determine the filter parameter c based on the amplitude spectrum F12: ;

[0012] The elements in the complex sequence F1 that satisfy the above two formulas are assigned the value 0 to obtain the sequence F2, where c is the upper limit of the noise amplitude; S33. Determine the bandpass parameters min and max for the frequency sequence. ω 2 The number in F2 corresponding to the parameter is assigned to 0; the first number F2(1) in the F2 sequence is assigned to 0, and the sequence F3 is obtained. F3 is the Fourier transform sequence of the acceleration sequence a after removing the mean A and filtering out noise. The mean A is obtained using the following formula: .

[0013] Preferably, step S40 is performed according to the following steps: S41. Integrate the sequence F3 once in the frequency domain, that is, divide F3(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part. The imaginary part is replaced by the original real part with a negative sign, to obtain the sequence F4. S42. Perform an inverse Fourier transform on sequence F4 to obtain sequence F5, that is:

[0014] Let f(x) represent the m-th parameter in the complex sequence F5. Take the real part of sequence F5 to get sequence v1.

[0015] Preferably, step S50 is performed according to the following steps: S51. Summing the integral of sequence v1 with the mean A in the time domain yields sequence v2: v2=v1+A×t S52. Based on the condition that the initial velocity is 0, shift the initial value of v2 to 0 to obtain the velocity sequence v3; that is: v3 = v2 - v2(1) In the formula, v2(1) represents the first value of sequence v2.

[0016] Preferably, step S60 is performed according to the following steps: S61. Perform a Fourier transform on the velocity sequence v3 to obtain the complex sequence F6:

[0017] Represents the complex sequence F6, the first... There are several parameters, and the frequency sequence corresponding to the complex sequence F6 is... ω =2π[0 sf / N2sf / N 3sf / N ... sf / 2 -(sf / 2-sf / N) -(sf / 2-2sf / N) -(sf / 2-3sf / N) ...-sf / N]; S62. The mean V of the velocity sequence v3 is obtained by the following formula: .

[0018] Preferably, step S70 is performed according to the following steps: S71. Integrate the complex sequence F6 once in the frequency domain, that is: divide F6(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part. The imaginary part is replaced by the original real part with a negative sign, to obtain the sequence F7. S72. Perform an inverse Fourier transform on sequence F7 to obtain sequence F8, i.e. .

[0019] This represents the m-th parameter in the complex sequence F8.

[0020] Preferably, step S90 is performed according to the following steps: S91. Summing the integral of sequence s1 with the mean V in the time domain yields sequence s2: s2=s1+V×t S92. Based on the condition that the initial displacement is 0, shift the initial value of s2 to 0 to obtain the displacement sequence s3: s3=s2-s2(1) In the formula, s2(1) represents the first value of the sequence s2.

[0021] Compared with the prior art, the beneficial effects of the present invention are: This invention is based on a method for converting acceleration, velocity, and displacement by combining frequency and time domain processing. It can obtain three sets of data, namely acceleration, velocity, and displacement, by installing only an acceleration sensor, thus realizing the multi-functionality of the acceleration sensor, which is convenient and low in cost. The acceleration, velocity, and displacement conversion method based on the combination of frequency and time domain processing of the present invention decomposes the signal into two parts, namely the DC component and the zero-mean signal, and analyzes them respectively through time domain and frequency domain methods. It is not only applicable to vibration signals with initial and final velocities and initial and final displacements of 0, but also applicable to working conditions with residual velocity or residual displacement, and can meet various engineering needs. This invention is based on a method for converting acceleration, velocity, and displacement using a combination of frequency and time domain processing. Based on acceleration signals, it can obtain accurate and reliable velocity and displacement signals, meeting the accuracy requirements of various engineering projects. Attached Figure Description

[0022] Figure 1 This is a schematic diagram illustrating the steps of a method for converting acceleration, velocity, and displacement based on a combination of frequency and time domain processing. Figure 2 This is a schematic diagram of the acceleration curve with noise in the time history of Example 1; Figure 3 This is a schematic diagram of the amplitude spectrum before filtering in Example 1; Figure 4 This is a schematic diagram of the amplitude spectrum after filtering in Example 1; Figure 5 This is a schematic diagram of the velocity time history curve obtained by acceleration conversion in Example 1 and the velocity time history curve obtained by theoretical calculation; Figure 6 This is a schematic diagram of the displacement-time history curve obtained by acceleration conversion and the displacement-time history curve obtained by theoretical calculation in Example 1; Figure 7 This is a schematic diagram of the acceleration time history curve in Example 2; Figure 8 This is a schematic diagram of the amplitude spectrum before filtering in Example 2; Figure 9 This is a schematic diagram of the amplitude spectrum after filtering in Example 2; Figure 10 A schematic diagram of the velocity-time history curve obtained from acceleration conversion; Figure 11 This is a schematic diagram of the displacement-time history curve obtained by acceleration conversion and the measured displacement-time history curve in Example 2; Figure 12 This is the acceleration time history curve from Example 3; Figure 13 This is a schematic diagram of the amplitude spectrum after filtering in Example 3; Figure 14 This is a schematic diagram of the velocity time history curve obtained by acceleration conversion and the measured velocity time history curve in Example 3; Figure 15 This is a schematic diagram of the displacement-time history curve obtained by acceleration conversion and the measured displacement-time history curve in Example 3. Detailed Implementation

[0023] The present invention will be further described below with reference to specific embodiments.

[0024] Example 1 like Figure 1 The figure shown is a specific embodiment of the acceleration, velocity, and displacement conversion method based on frequency-time domain processing of the present invention, which includes the following steps: S10. In a set of analog signals, an analog acceleration signal is used to form acceleration data, forming an acceleration sampling frame with a sampling frequency of 200Hz, resulting in a time series t=[t(0) t(1) t(2) t(3) ... t(N-1)] and an acceleration sequence a(t)=[a(0) a(1) a(2) a(3) ... a(N-1)], where N is the length of the sequence and is an even number. The analog signal N=1604. Assuming the initial acceleration is not 0, and the velocity and displacement are both 0, the acceleration curve graph with noise is shown below. Figure 2 As shown; S20. Perform a Fourier transform on the acceleration sequence a(t) from step S10 to obtain the complex sequence F1; S30. In F1, the sequence values ​​(noise signals) below a certain value on the amplitude spectrum are assigned a value of 0, and c is set to 0.005 to obtain sequence F2; if F2(1) is positive, then let A = / N; otherwise, A = - / N; the amplitude spectrum before filtering is as follows Figure 3 As shown, the amplitude spectrum after filtering is as follows: Figure 4 As shown; S40. The corresponding frequency points in F2 that are lower or higher than a certain value are assigned a value of 0, and F2(1) is assigned a value of 0 to obtain sequence F3; the complex sequence F3 with noise filtered out in step S30 is integrated once in the frequency domain, that is: F3(2:n) is divided by its corresponding frequency respectively. The imaginary part is transformed into the real part, and the original real part is negativeed to become the imaginary part, resulting in sequence F4. The inverse Fourier transform of sequence F4 is performed to obtain sequence F5, and the real part of sequence F5 is taken to obtain sequence v1. S50. Summing the integral of sequence v1 and mean A in the time domain in step S40 yields sequence v2, v2 = v1 + A × t; and according to the condition that the initial velocity is 0, shifting the initial value of v2 to 0, thus obtaining velocity sequence v3, v3 = v2 - v2(1); In this embodiment, the velocity sequence v3 obtained by acceleration conversion and the velocity sequence obtained by theoretical calculation are as follows Figure 5 As shown; S60. Perform a Fourier transform on the velocity sequence v3 from step S50 to obtain the complex sequence F6. If F6(1) is positive, then let V = / N, otherwise V=- / N, and determine the mean value of velocity sequence v3 as V = -3.6442; S70. Integrate the complex sequence F6 in step S60 once in the frequency domain, that is: divide F6(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part, and replace the imaginary part with the original real part by adding a negative sign to obtain the sequence F7; and perform an inverse Fourier transform on the sequence F7 to obtain the sequence F8. S80. Take the real part of sequence F8 from step S70 to obtain sequence s1; S90. Summing the integral of the sequence s1 and the mean V in the time domain in step S80, we get the sequence s2, s2 = s1 + V × t; and according to the condition that the initial displacement is 0, we shift the initial value of s2 to 0, thus obtaining the displacement sequence s3, s3 = s2 - s2(1). In this embodiment, the displacement sequence s3 obtained by acceleration conversion and the displacement sequence obtained by theoretical calculation are as follows: Figure 6 As shown.

[0025] After implementing the above steps, the conversion between acceleration, velocity, and displacement can be achieved. Through multiple combinations of filtering and integration, the calculated velocity and theoretical velocity, as well as the calculated displacement and theoretical displacement, are very close, and the results are reliable and can meet the accuracy requirements of engineering projects.

[0026] Example 2 This embodiment demonstrates the application of the acceleration, velocity, and displacement conversion method based on frequency-time domain processing of the present invention to a suspension bridge model. An acceleration sensor is vertically installed on the bridge deck at mid-span, and the process includes the following steps: S10. A rubber mallet is used to strike the suspension bridge deck to retrieve acceleration data of the vertical vibration at mid-span. The sampling frequency is 1000Hz, resulting in a time series t=[t(0) t(1) t(2) t(3) ... t(N-1)] and an acceleration series a=[a(0) a(1) a(2) a(3) ... a(N-1)], where N is the length of the sequence and is an even number. In this embodiment, N=6870. The obtained acceleration time history curve is shown below. Figure 7 As shown; S20. Perform a Fourier transform on the acceleration sequence a(t) from step S10 to obtain the complex sequence F1; S30. In F1, the sequence values ​​(noise signals) below a certain value on the amplitude spectrum are assigned a value of 0, and c=0.003 is set to obtain sequence F2; if F1(1) is positive, then let A= / N; otherwise, A = - / N; In this embodiment, A=0, and the amplitude spectrum before filtering is as follows: Figure 8 As shown, the amplitude spectrum after filtering is as follows: Figure 9 As shown; S40. The corresponding frequency points in F2 that are lower or higher than a certain value are assigned a value of 0, and F2(1) is assigned a value of 0 to obtain sequence F3; the complex sequence F3 with noise filtered out in step S30 is integrated once in the frequency domain, that is: F3(2:n) is divided by its corresponding frequency respectively. The imaginary part is transformed into the real part, and the original real part is negativeed to become the imaginary part, resulting in sequence F4. The inverse Fourier transform of sequence F4 is performed to obtain sequence F5, and the real part of sequence F5 is taken to obtain sequence v1. S50. Summing the integral of sequence v1 and mean A in the time domain from step S40, we get sequence v2, v2 = v1 + A × t; and according to the condition that the initial velocity is 0, we shift the initial value of v2 to 0, thus obtaining velocity sequence v3, v3 = v2 - v2(1); The velocity sequence v3 obtained by acceleration conversion in this embodiment is shown in the figure. Figure 10 As shown; S60. Perform a Fourier transform on the velocity sequence v3 from step S50 to obtain the complex sequence F6. If F6(1) is positive, then let V = / N, otherwise V=- / N, and determine the mean value of velocity sequence v3 as V = -6.070431937872909e-06; S70. F6(1) is assigned the value 0. The complex sequence F6 in step S60 is integrated once in the frequency domain, that is: F6(2:N) is divided by its corresponding frequency ω(2:N) respectively, and the real part is replaced by the imaginary part. The imaginary part is replaced by the original real part with a negative sign to obtain the sequence F7; and the inverse Fourier transform of the sequence F7 is performed to obtain the sequence F8. S80. Take the real part of sequence F8 from step S70 to obtain sequence s1; S90. Summing the integral of the sequence s1 and the mean V in the time domain in step S80, we get the sequence s2, s2 = s1 + V × t; and according to the condition that the initial displacement is 0, we shift the initial value of s2 to 0, thus obtaining the displacement sequence s3, s3 = s2 - s2(1). In this embodiment, the displacement sequence s3 obtained by acceleration conversion and the displacement sequence obtained by actual measurement are shown in the figure. Figure 11 As shown.

[0027] After implementing the above steps, the conversion between acceleration, velocity, and displacement can be achieved. Through multiple combinations of filtering and integration, the calculated velocity and the measured velocity, as well as the calculated displacement and the measured displacement, are very close, and the results are reliable and can meet the accuracy requirements of engineering projects.

[0028] Example 3 This embodiment illustrates the application of the acceleration, velocity, and displacement conversion method based on frequency-time domain processing of the present invention in seismic wave processing, including the following steps: S10. In a set of seismic wave acceleration signals, with a sampling frequency of 200Hz, a time series t=[t(0) t(1) t(2) t(3) ... t(N-1)] and an acceleration series a=[a(0) a(1) a(2) a(3) ... a(N-1)] are obtained, where N is the length of the sequence and is an even number; in this embodiment, N=18000. Assuming the initial acceleration is not zero, and the velocity and displacement are both zero, the acceleration curve graph of the noisy time history is shown below. Figure 12 As shown; S20. Perform a Fourier transform on the acceleration sequence a(t) from step S10 to obtain the complex sequence F1; S30. In the complex sequence F1, the sequence values ​​(noise signals) with amplitude spectra below a certain value are assigned a value of 0, and c=0.005 is set to obtain sequence F2; if F1(1) is positive, then let A= / N; otherwise, A = - / N; the filtered amplitude spectrum is as follows Figure 13 As shown; S40. The corresponding frequency points in F2 that are lower or higher than a certain value are assigned a value of 0, and F2(1) is assigned a value of 0 to obtain sequence F3; the complex sequence F3 with noise filtered out in step S30 is integrated once in the frequency domain, that is: F3(2:n) is divided by its corresponding frequency respectively. The imaginary part is transformed into the real part, and the original real part is negativeed to become the imaginary part, resulting in sequence F4. The inverse Fourier transform of sequence F4 is performed to obtain sequence F5, and the real part of sequence F5 is taken to obtain sequence v1. S50. Summing the integral of sequence v1 and mean A in the time domain in step S40 yields sequence v2, v2 = v1 + A × t; and according to the condition that the initial velocity is 0, shifting the initial value of v2 to 0, thus obtaining velocity sequence v3, v3 = v2 - v2(1); In this embodiment, the velocity sequence v3 obtained by acceleration conversion and the measured velocity sequence are as follows Figure 14 As shown; S60. Perform a Fourier transform on the velocity sequence v3 from step S50 to obtain the complex sequence F6. If F6(1) is positive, then let V = / N, otherwise V=- / N, and determine the mean value of velocity sequence v3 as V = -3.6442; S70. Integrate the complex sequence F6 in step S60 once in the frequency domain, that is: divide F6(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part, and replace the imaginary part with the original real part by adding a negative sign to obtain the sequence F7; and perform an inverse Fourier transform on the sequence F7 to obtain the sequence F8. S80. Take the real part of sequence F8 from step S70 to obtain sequence s1; S90. Summing the integral of the sequence s1 and the mean V in the time domain in step S80, we get the sequence s2, s2 = s1 + V × t; and according to the condition that the initial displacement is 0, we shift the initial value of s2 to 0, thus obtaining the displacement sequence s3, s3 = s2 - s2(1). In this embodiment, the displacement sequence s3 obtained by acceleration conversion and the displacement sequence obtained by actual measurement are shown in the figure. Figure 15 As shown.

[0029] After implementing the above steps, the conversion between acceleration, velocity, and displacement can be achieved. Through multiple combinations of filtering and integration, the calculated velocity and the measured velocity, as well as the calculated displacement and the measured displacement, are very close, indicating reliable results that meet the accuracy requirements of engineering projects. Therefore, this embodiment demonstrates accurate conversion precision in post-earthquake acceleration conversion and is also suitable for scenarios where structures undergo plastic deformation under load and exhibit residual displacement.

[0030] In the specific implementation of the above embodiments, the technical features can be combined in any non-contradictory way. For the sake of brevity, not all possible combinations of the above technical features are described. However, as long as the combination of these technical features is not contradictory, it should be considered to be within the scope of this specification.

[0031] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for converting acceleration, velocity, and displacement based on a combination of frequency and time domain processing, characterized in that: Includes the following steps: S10. Sample an acceleration vibration signal at a sampling frequency of sf to obtain a time sequence t=[t(0) t(1) t(2) t(3) ... t(N-1)] and an acceleration sequence a(t)=[a(0) a(1) a(2) a(3) ... a(N-1)], where N is the length of the sequence and is an even number; S20. Perform a Fourier transform on the acceleration sequence a(t) from step S10 to obtain the complex sequence F1; S30. In the frequency domain, the complex sequence F1 described in step S20 is subjected to noise filtering to obtain the complex sequence F3, and the mean value A of the acceleration sequence a(t) is determined; S40. Integrate the complex sequence F3 from which noise has been filtered out in step S30 once in the frequency domain and perform an inverse Fourier transform to obtain sequence F5. Take the real part of sequence F5 to obtain sequence v1. S50. Summing the integral of the sequence v1 from step S40 with the mean A in the time domain yields the sequence v2. Based on the condition that the initial velocity is 0, the initial value of v2 is shifted to 0, thus obtaining the velocity sequence v3. S60. Perform a Fourier transform on the velocity sequence v3 in step S50 to obtain a complex sequence F6, and determine the mean V of the velocity sequence v3; S70. Integrate the complex sequence F6 from step S60 once in the frequency domain and perform an inverse Fourier transform to obtain the sequence F8; S80. Take the real part of sequence F8 from step S70 to obtain sequence s1; S90. Summing the sequence s1 from step S80 with the integral of the mean V in the time domain to obtain sequence s2, and shifting the initial value of s2 to 0 according to the condition that the initial displacement is 0, thus obtaining the displacement sequence s3. In step S10, the acceleration sequence a(t) is divided into a difference sequence between the acceleration sequence a(t) and the mean A. f az ( t The two parts are () and the mean A, where f az ( t The mean of ) is 0, and A is the mean of the acceleration sequence a(t); in step S60, the sequence v3 is divided into the difference sequence between the sequence v3 and the mean V. f vz ( t The two parts are () and the mean V, where, f vz ( t The mean of ) is 0, and V is the mean of sequence v3.

2. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, In step S40, the initial value of the complex sequence F3 with the noise filtered out is set to 0 before integration in the frequency domain; in step S70, the initial value of the complex sequence F6 is set to 0 before integration in the frequency domain.

3. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, In step S20, the complex sequence F1 is expressed as follows: Represents the complex sequence F1 with the th element. Each parameter, the frequency sequence corresponding to F1 ω =2π[0 sf / N 2sf / N 3sf / N... sf / 2 -(sf / 2-sf / N) -(sf / 2-2sf / N) -(sf / 2-3sf / N) ...-sf / N], This represents the m-th parameter in the acceleration sequence a(t), where k is an integer. , where i represents the imaginary unit.

4. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 3, characterized in that, Step S30 is performed as follows: S31. Based on complex sequence F1 and ω Plot the amplitude spectrum F12 of a, as follows: Among them, the frequency sequence corresponding to F12 ω 2=2π[0 sf / N 2sf / N 3sf / N ... sf / 2]; S32. Determine the filter parameter c based on the amplitude spectrum F12: when hour, ; when hour, The elements in the complex sequence F1 that satisfy the above two formulas are assigned the value 0 to obtain the sequence F2, where c is the upper limit of the noise amplitude; S33. Determine the bandpass parameters min and max for the frequency sequence. ω 2 The number in F2 corresponding to the parameter is assigned to 0; the first number F2(1) in the F2 sequence is assigned to 0, and the sequence F3 is obtained. F3 is the Fourier transform sequence of the acceleration sequence a(t) minus the mean A and after filtering out noise. The mean A is obtained using the following formula: 。 5. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, Step S40 is performed as follows: S41. Integrate the sequence F3 once in the frequency domain, that is, divide F3(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part. The imaginary part is replaced by the original real part with a negative sign, to obtain the sequence F4. S42. Perform an inverse Fourier transform on sequence F4 to obtain sequence F5, that is: Let f(x) represent the m-th parameter in the complex sequence F5. Taking the real part of sequence F5 yields sequence v1. .

6. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, Step S50 is performed as follows: S51. Summing the integral of sequence v1 with the mean A in the time domain yields sequence v2: v2=v1+A×t S52. Based on the condition that the initial velocity is 0, shift the initial value of v2 to 0 to obtain the velocity sequence v3; that is: v3 = v2 - v2(1) In the formula, v2(1) represents the first value of sequence v2.

7. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, Step S60 is performed as follows: S61. Perform a Fourier transform on the velocity sequence v3 to obtain the complex sequence F6: Represents the complex sequence F6, the first... There are several parameters, and the frequency sequence corresponding to the complex sequence F6 is... ω =2π[0 sf / N2sf / N 3sf / N ... sf / 2 -(sf / 2-sf / N) -(sf / 2-2sf / N) -(sf / 2-3sf / N) ...-sf / N], ; S62. The mean V of the velocity sequence v3 is obtained by the following formula: 。 8. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, Step S70 is performed as follows: S71. Integrate the complex sequence F6 once in the frequency domain, that is: divide F6(2:N) by its corresponding frequency ω(2:N) respectively, and replace the real part with the imaginary part. The imaginary part is replaced by the original real part with a negative sign, to obtain the sequence F7. S72. Perform an inverse Fourier transform on sequence F7 to obtain sequence F8, i.e. This represents the m-th parameter in the complex sequence F8. .

9. The acceleration, velocity, and displacement conversion method based on frequency-time domain processing according to claim 1, characterized in that, Step S90 is performed as follows: S91. Summing the integral of sequence s1 with the mean V in the time domain yields sequence s2: s2=s1+V×t S92. Based on the condition that the initial displacement is 0, shift the initial value of s2 to 0 to obtain the displacement sequence s3: s3=s2-s2(1) In the formula, s2(1) represents the first value of the sequence s2.

Images