Baseline shift correction method for near-fault ground motion acceleration record based on continuous wavelet transform

Abstract

The application relates to a near-fault ground motion acceleration record baseline offset correction method based on continuous wavelet transformation, and belongs to the technical field of ground motion data processing, which comprises the following steps: S1, removing the average value before the occurrence of an earthquake in an original acceleration record; S2, performing low-pass filtering on the initial acceleration record; S3, determining a ground permanent displacement estimation value; S4, performing continuous wavelet transformation on the low-pass filtered acceleration record; S5, extracting a pulse possibly containing the permanent ground displacement; S6, determining the pulse signal containing the permanent ground displacement; S7, obtaining a non-pulse signal; S8, performing high-pass filtering on the non-pulse signal; and S9, obtaining the corrected near-fault ground motion acceleration record. The application can retain the permanent ground deformation characteristics in the near-fault ground motion, and the obtained ground motion record can more accurately reflect the influence of the earthquake on a structure.

Description

Technical Field

[0001] This invention belongs to the field of seismic motion data processing technology, and relates to a method for baseline offset correction of near-fault seismic acceleration records based on continuous wavelet transform. Background Technology

[0002] Digital strong-motion accelerometers (DFAs) are effective instruments for acquiring ground motion patterns, providing high-resolution acceleration records that capture the complete ground motion. However, due to instrumental errors, baseline shifts occur in the acceleration records, and the velocity and displacement records obtained by integrating the unprocessed acceleration records exhibit even greater deviations. Common baseline correction methods generally assume that the acceleration baseline shift lies within the low-frequency signal and that the velocity and displacement records converge to zero at their ends. Typically, a high-pass filter is applied to the original acceleration record to obtain a corrected acceleration record. Integrating this corrected acceleration record yields corrected velocity and displacement records, which in turn converge to zero at their ends.

[0003] However, in near-fault regions, ground deformation caused by fault rupture often results in permanent ground displacement in seismic motions, meaning the displacement records do not converge to zero at the end. Existing high-pass filtering baseline correction methods eliminate permanent ground displacement in seismic motion records and are not suitable for baseline offset correction of near-fault ground motion acceleration records. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a baseline offset correction method for near-fault ground motion acceleration records based on continuous wavelet transform. This method uses continuous wavelet transform to extract pulse signals containing permanent ground displacement from the original record, performs high-pass filtering on the remaining ground motion record (i.e., non-pulse signals) to eliminate baseline offset, and finally reconstructs the two signals to obtain the corrected ground motion acceleration record. This method effectively solves the problem of the inability to retain permanent ground displacement in near-fault ground motion baseline offset correction, making the corrected ground motion record more consistent with the actual motion state of the near-fault region.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A baseline migration correction method for near-fault ground motion acceleration records based on continuous wavelet transform includes the following steps:

[0007] S1: Remove the average value from the original acceleration record prior to the earthquake;

[0008] S2: Perform low-pass filtering on the initial acceleration record;

[0009] S3: Determine the estimated value of permanent ground displacement;

[0010] S4: Perform continuous wavelet transform on the low-pass filtered acceleration record;

[0011] S5: Extract pulses that may contain permanent ground displacement;

[0012] S6: Identify the pulse signal containing permanent ground displacement;

[0013] S7: Obtain the non-pulse signal;

[0014] S8: High-pass filtering of non-pulse signals;

[0015] S9: Obtain the corrected near-fault ground motion acceleration record.

[0016] Further, in step S1, the average value of the first n seconds of the original acceleration record a0(t) is calculated, and then the average value of the first n seconds is subtracted from the entire original acceleration record a0(t) to obtain the initial acceleration record a1(t).

[0017] Furthermore, in step S2, a low-pass filter is used to perform low-pass filtering on the initial acceleration record a1(t). The acceleration record after low-pass filtering is defined as a 11 (t).

[0018] Furthermore, in step S3, the acceleration record a 11 Integrate (t) to obtain the corresponding displacement record d. 11 (t); Identify displacement record d 11 At the moment T when the slope is last zero in (t), the displacement value d at time T is... 11 (T) is determined as the estimated value of the permanent ground displacement, D.

[0019] Furthermore, in step S4, the acceleration record a after low-pass filtering is... 11 (t) Perform continuous wavelet transform to calculate the acceleration record a after low-pass filtering. 11 wavelet coefficients of (t) The calculation formula is:

[0020]

[0021] In the formula, a is the scale parameter; b is the position parameter; ψ (a,b) For a wavelet function, it is necessary to ensure that the value of the wavelet function after double integration does not converge to zero.

[0022] Furthermore, in step S5, wavelet coefficients are identified. The scale parameter a corresponding to the maximum absolute value in the middle k With position parameter b k Then calculate the pulse signal P extracted in the kth iteration. k (t), the calculation formula is:

[0023]

[0024] Where P0(t) is the zero vector;

[0025] Acceleration record a after low-pass filtering 11 (t) Subtract the extracted pulse signal P k (t) Obtain the residual acceleration record R of the kth iteration. k (t), then record the residual acceleration R. k (t) Perform continuous wavelet transform to calculate the (k+1)th wavelet coefficients. The calculation formula is

[0026]

[0027] Furthermore, step S6 specifically includes:

[0028] Repeat step S5 to obtain m pulse signals P1(t), P2(t), ..., P m (t), integrate these m pulses to the displacement to obtain their respective displacement record end values ​​D1(end), D2(end), ..., D m (end), select the pulse signal whose end value of the displacement record is closest to the estimated value of permanent ground displacement D as the pulse signal P(t) containing permanent ground displacement.

[0029] Furthermore, the calculation formula for the non-pulse signal in step S7 is as follows:

[0030] NonP(t) = a1(t) - P(t).

[0031] Further, in step S9, the pulse signal P(t) is combined with the corrected non-pulse signal CorrNonP(t) to obtain the corrected near-fault ground motion acceleration record a(t), calculated using the following formula:

[0032] a(t)=P(t)+CorrNonP(t).

[0033] The beneficial effects of this invention are as follows: This invention uses continuous wavelet transform to extract pulse signals containing permanent ground displacement, thus preserving the permanent ground deformation characteristics present in near-fault ground motions and avoiding the problem of previous filtering methods eliminating permanent ground displacement in the records. Furthermore, because this invention preserves the permanent displacement in ground motion near the fault, ground motion records obtained using the method proposed in this invention can more accurately reflect the impact of earthquakes on structures crossing faults during seismic design.

[0034] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0036] Figure 1 This is a schematic diagram showing the acceleration, velocity, and displacement of the original ground motion in a certain earthquake dataset.

[0037] Figure 2 This is a schematic diagram of the initial ground motion, the ground motion after low-pass filtering, and the acceleration, velocity, and displacement of the pulse signal in an embodiment of the present invention.

[0038] Figure 3 These are the corrected acceleration, velocity, and displacement records obtained according to the baseline offset correction method in this embodiment of the invention.

[0039] Figure 4 This is a schematic diagram of the baseline offset correction method for near-fault ground motion acceleration records based on continuous wavelet transform as described in this invention. Detailed Implementation

[0040] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0041] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0042] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0043] This invention is mainly applied to seismic ground motion in areas near faults. Figure 1 , Figure 2 and Figure 3 This is a case study based on the present invention, from Figure 3 The effectiveness of the baseline offset correction method based on continuous wavelet transform in this invention can be seen, which can effectively preserve the permanent ground displacement in near-fault ground motion.

[0044] Based on the east-west acceleration records of station TCU052 during the 1999 Chi-Chi earthquake in Taiwan, the specific application of the method described in this invention is shown below, with the flowchart provided. Figure 4 :

[0045] Step 1: Remove the average value from the original acceleration record prior to the earthquake.

[0046] The original ground motion record is an unprocessed ground motion acceleration record. The average value of the first 5 seconds of the original acceleration record a0(t) is calculated, and then the average value of the first 5 seconds is subtracted from the entire original acceleration record a0(t) to obtain the initial acceleration record a1(t).

[0047] Step 2: Perform low-pass filtering on the initial acceleration record.

[0048] The initial acceleration record a1(t) is low-pass filtered using, for example, a Butterworth fourth-order low-pass filter function. The cutoff frequency can be selected as 0.15Hz, and different cutoff frequencies can be selected for different ground motions. The acceleration record after low-pass filtering is defined as a1(t). 11 (t);

[0049] Step 3: Determine the estimated value of permanent ground displacement

[0050] Acceleration record a after low-pass filtering 11 (t) is used for double integration to obtain the corresponding displacement record d. 11 (t). Identify displacement record d 11At the moment T when the slope is last zero in (t), the displacement value d at time T is... 11 (T) is determined as the estimated value of the permanent ground displacement, D;

[0051] Step 4: Perform continuous wavelet transform on the low-pass filtered acceleration records.

[0052] Acceleration record a after low-pass filtering 11 (t) Perform continuous wavelet transform to calculate the acceleration record a after low-pass filtering. 11 wavelet coefficients of (t) The calculation formula is:

[0053]

[0054] In the formula: a is the scale parameter; b is the position parameter; ψ (a,b) The wavelet function must be guaranteed to not converge to zero after double integration. The wavelet function can be a first-order Gaussian wavelet or a Haar wavelet.

[0055] Step 5: Extract pulses that may contain permanent ground displacement.

[0056] Identifying wavelet coefficients The scale parameter a corresponding to the maximum absolute value in the middle k With position parameter b k Scale parameter a k With position parameter b k The selection range can be further limited to obtain different pulse signals. The pulse signal P extracted in the kth iteration is calculated. k (t), the calculation formula is:

[0057]

[0058] Where: P0(t) is the zero vector.

[0059] Acceleration record a after low-pass filtering 11 (t) Subtract the extracted pulse signal P k (t) Obtain the residual acceleration record R of the kth iteration. k (t), then record the residual acceleration R. k (t) Perform continuous wavelet transform to calculate the (k+1)th wavelet coefficients. The calculation formula is

[0060]

[0061] Step 6: Identify the pulse signal containing permanent ground displacement.

[0062] Repeat step five 10 times to calculate 10 pulse signals P1(t), P2(t), ..., P 10 (t). Integrating these 10 pulses into displacement yields their respective displacement record end values ​​D1(end), D2(end), ..., D. 10 (end), select the pulse signal whose end value of the displacement record is closest to the estimated value of permanent ground displacement D as the pulse signal P(t) containing permanent ground displacement.

[0063] Step 7: Obtain the non-pulse signal

[0064] The non-pulse signal NonP(t) is obtained by recording the initial acceleration a1(t) and decreasing the pulse signal P(t).

[0065] Step 8: Perform high-pass filtering on non-pulse signals.

[0066] The non-pulse signal NonP(t) is high-pass filtered using a filter such as a fourth-order Butterworth high-pass filter function with a cutoff frequency of 0.1Hz to obtain the corrected non-pulse signal CorrNonP(t). This step will eliminate low-frequency noise in the signal.

[0067] Step 9: Obtain the corrected near-fault ground motion acceleration records

[0068] By combining the pulse signal P(t) with the corrected non-pulse signal CorrNonP(t), the corrected near-fault ground motion acceleration record a(t) is obtained, and the calculation formula is as follows:

[0069] a(t)=P(t)+CorrNonP(t) (4)

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform, characterized in that: Includes the following steps: S1: Calculate the original acceleration record a 0( t The average value of the first n seconds, then from the entire original acceleration record. a 0( t Subtract the average value of the first n seconds from the initial acceleration data to obtain the initial acceleration record. a 1( t ); S2: Perform low-pass filtering on the initial acceleration record; S3: Determine the estimated value of permanent ground displacement; S4: Perform continuous wavelet transform on the low-pass filtered acceleration record; S5: Extract pulses that may contain permanent ground displacement; S6: Identify the pulse signal containing permanent ground displacement; S7: Obtain the non-pulse signal; S8: High-pass filtering of non-pulse signals; S9: Obtain the corrected near-fault ground motion acceleration record.

2. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 1, characterized in that: In step S2, a low-pass filter is used to record the initial acceleration. a 1( t The acceleration record after low-pass filtering is defined as follows: a 11 ( t ).

3. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 2, characterized in that: In step S3, the acceleration is recorded. a 11 ( t Integrate to obtain the corresponding displacement record. d 11 ( t ); Identify displacement records d 11 ( t The moment when the slope is 0 for the last time T ,Will T Displacement value at time d 11 ( T The estimated value of the permanent ground displacement was determined. D .

4. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 3, characterized in that: In step S4, the acceleration record after low-pass filtering is processed. a 11 ( t Perform continuous wavelet transform to calculate the acceleration record after low-pass filtering. a 11 ( t wavelet coefficients The calculation formula is: In the formula a For scale parameters; b For position parameters; ψ (a,b) For a wavelet function, it is necessary to ensure that the value of the wavelet function after double integration does not converge to zero.

5. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 4, characterized in that: In step S5, wavelet coefficients are identified. The scale parameter corresponding to the maximum absolute value in the middle a k With position parameters b k ， Then calculate the first k The extracted pulse signal P k (t) The calculation formula is: in P 0 (t) It is a zero vector; Accelerometer recording after low-pass filtering a 11 ( t Subtract the extracted pulse signal P k ( t ) obtained the k Secondary residual acceleration record R k (t) Then, the residual acceleration was recorded. R k (t) Perform continuous wavelet transform to calculate the th k+ First wavelet coefficients The calculation formula is: 。 6. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 5, characterized in that: Step S6 specifically includes: Repeat step S5 to obtain m pulse signals. P 1 (t) , P 2 (t) … P m (t) Integrate these m pulses into displacement to obtain the end value of each displacement record. D 1 (end) , D 2 (end) … D m (end) Select the displacement record end value that is closest to the estimated permanent ground displacement value. D The pulse signal is a pulse signal that includes permanent ground displacement. P ( t ).

7. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 6, characterized in that: The formula for calculating the non-pulse signal in step S7 is as follows: NonP ( t ) =a 1( t )- P ( t )。 8. The method for baseline offset correction of near-fault ground motion acceleration records based on continuous wavelet transform according to claim 7, characterized in that: In step S9, the combined pulse signal P ( t ) and the corrected non-pulse signal CorrNonP ( t Corrected near-fault ground motion acceleration records were obtained. a ( t The calculation formula is: 。

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