K value self-pickup method based on MK trend detection

Abstract

The invention relates to the technical field of seismology, and particularly discloses a K value self-pickup method based on MK trend detection, which comprises the following steps of: preprocessing seismic oscillation data; performing curve feature recognition on the seismic oscillation Fourier spectrum by using an MK trend detection algorithm; picking up starting and ending frequencies of a seismic oscillation high-frequency descending section according to the Fourier spectrum ascending and descending characteristic curve; and extracting a descending frequency band according to the start-stop frequency, and performing fitting calculation to obtain a K value. According to the method, the value of the seismic oscillation high-frequency attenuation parameter K is calculated by extracting the curve rising and falling characteristics of the seismic oscillation Fourier spectrum and then identifying the starting and ending frequencies, so that the precision of picking up the starting and ending frequencies of the descending section of the Fourier spectrum can be remarkably improved, and batch calculation of the seismic oscillation high-frequency attenuation parameters is realized; the method has the characteristics of high flexibility, high accuracy, high efficiency, simplicity in operation and the like.

Description

Technical Field

[0001] The invention relates to the technical field of seismology, and in particular to a K value self-picking method based on MK trend detection. Background Art

[0002] The tectonic activities in the southwest are intense, and the risk of triggering strong earthquakes is high. Research on disasters caused by strong earthquakes is an urgent need for the deepening of development and construction in the west. The ground motion in the near-field area of ​​strong earthquakes is highly destructive and rich in high-frequency components. It is significantly controlled by the earthquake source and is more complicated under the influence of near-fault effects. The high-frequency attenuation parameter controls the shape of the high-frequency descending section of the ground motion Fourier spectrum and is a key parameter for ground motion simulation under different site conditions. Therefore, it is widely used in ground motion simulation to provide input for earthquake design, especially in the construction of important infrastructure such as nuclear power plants and dams in areas where ground motion records are lacking.

[0003] At present, there are three main methods for calculating the high-frequency attenuation parameters of earthquake motion: the first is visual selection, that is, first select the point where the amplitude decreases significantly under the logarithmic coordinates of the earthquake motion Fourier spectrum, set it as the starting frequency, and then select the point where the slope of the decline changes significantly as the cutoff frequency. Visual selection can flexibly select the start and end frequencies according to the curve characteristics of different earthquake motion Fourier spectra, effectively avoiding the influence of abnormal values ​​and small rises or horizontal segments in the decline segment on the identification, and has good anti-interference ability for factors such as mutation values, so that the decline segment can be selected more accurately according to the decline characteristics of different acceleration spectra. However, the visual selection process will be affected by the subjective factors of the selector, and the efficiency is low when processing a large amount of data. The second is the fixed frequency band method, that is, by observing a large amount of data and summarizing and statistics, the distribution characteristics of most earthquake motion high-frequency decline segments are determined, so as to determine them as the high-frequency decline segments of all earthquake data. The fixed frequency band method can achieve simple automation and has high calculation efficiency. However, the selected fixed frequency is not suitable for all earthquake motion Fourier spectra, and the data needs to be observed and counted first, which still has a certain degree of subjectivity. The third is a simple automatic identification method, which constructs a ratio function of the root mean square error and the bandwidth, and selects the best combination by judging the value of the ratio function at different start and end frequencies. Before using this method, it is necessary to observe the data characteristics and impose certain restrictions on the range of the start and end frequencies.

[0004] At present, the calculation of the high-frequency attenuation parameter K of seismic motion requires the seismic motion to be Fourier transformed first, and then the descending section of the curve is found by human observation, and then the data of the descending section is linearly fitted. This traditional method has low computational efficiency and requires a lot of manpower and material resources when the amount of data is large. In addition, the existing automatic algorithm needs to observe a large amount of data before the calculation begins to obtain the value range of a specific parameter, and input the value range into the algorithm before the calculation can begin. Once the value range is exceeded, the accuracy of the calculation result will be affected.

[0005] In view of the shortcomings of the current calculation method of high-frequency attenuation parameters of earthquake motion, such as subjectivity, low calculation efficiency, and poor accuracy, the present invention proposes a kappa (K) self-picking method based on Mann-Kendall (MK) trend detection, which automatically picks the start and end frequencies by identifying the rising and falling characteristics of the earthquake motion Fourier spectrum, and then obtains the high-frequency attenuation parameters of earthquake motion. This method is suitable for the calculation of high-frequency attenuation parameters of earthquake motion Fourier spectrum in different regions, sites and magnitudes, and provides a certain reference for the parameters required for earthquake motion simulation of important infrastructure such as nuclear power plants and dams in areas lacking earthquake motion records. Summary of the invention

[0006] In order to solve the problems existing in the prior art, the present invention provides a K value self-picking method based on MK trend detection, which is a method for calculating the seismic motion high-frequency attenuation parameter K value by extracting the curve rising and falling characteristics of the seismic motion Fourier spectrum and then identifying the start and end frequencies. The method can significantly improve the accuracy of picking up the start and end frequencies of the descending section of the Fourier spectrum; realize batch calculation of the seismic motion high-frequency attenuation parameters; and has the characteristics of strong flexibility, high accuracy, high efficiency and simple operation, and solves the problems mentioned in the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solution: a K value self-picking method based on MK trend detection, comprising the following steps:

[0008] S1, ground motion data preprocessing;

[0009] S2, using MK (Mann-Kendall) trend detection algorithm to identify curve features of the seismic Fourier spectrum;

[0010] S3, picking up the start and end frequencies of the high-frequency descending section of the earthquake motion according to the Fourier spectrum rise and fall characteristic curve;

[0011] S4. Extract the descending frequency band according to the start and end frequencies, and obtain the K (kappa) value by fitting calculation.

[0012] Preferably, in step S1, the following is specifically included:

[0013] S11. Baseline correction is performed on the seismic data using the following formula:

[0014]

[0015] In the formula, A 0 is the baseline corrected data, N r is the number of sampling points of acceleration time history, a(t) is the acceleration at time t, i is the number of sampling points of different acceleration time history, and a(1) is the acceleration at the first moment;

[0016] S12, filtering the seismic data;

[0017] S13, performing Fourier transform;

[0018] S14. Use the Pazen window to smooth the Fourier spectrum to obtain a smoothed ground motion Fourier spectrum.

[0019] Preferably, in step S2, the method specifically includes: first, the smoothed ground motion Fourier spectrum is segmented as data input in the form of a sliding window, wherein the window width of the sliding window used is 3 Hz, and the length of each sliding is 1 Hz, until the Fourier spectrum ends; then, the key parameters S, Z for identifying curve features under different sliding windows are calculated by the MK trend detection algorithm. mk , V(S) and β, and after integration, we get the rising and falling characteristic values ​​H of the entire Fourier spectrum curve.

[0020] Preferably, the parameters S, Z mk The calculation process of , V(S) and β is as follows:

[0021] ① Construct a statistical variable S to calculate the sum of the rank values ​​of each data point, that is, subtract each data point from all the previous data points. If the difference is greater than 0, S increases by 1, and if the difference is less than 0, S decreases by 1. The expression of S value is as follows:

[0022]

[0023] Where n is the total number of data, all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and j-th value in the data respectively;

[0024] When the total number of data input into the MK trend detection algorithm is greater than 8, the statistical variable S roughly follows a normal distribution with a mean of 0;

[0025] ② Transform the S value into the standard normal distribution value Z through the following formula mk ;

[0026]

[0027] Where V(S) is the variance of S, and Z mkThe value determines the rising and falling characteristics of the input segment. mk When the absolute value is greater than or equal to 1.96, it means that the 95% confidence level significance test has been passed, that is, there is a significant upward or downward trend;

[0028] ③ The β value is an indicator of the speed of the upward and downward trend, which is calculated by the following formula:

[0029]

[0030] In the formula, Median() is the median, 1 <j<i<n。

[0031] Preferably, the rising and falling characteristic values ​​H of the entire curve are represented by Z mk The value and β value are calculated, and the specific process is as follows:

[0032] (1) Set Z greater than 1.96 mk The value is assigned to 1, which is less than -1.96 Z mk The value is assigned to -1, and the rest are assigned to 0;

[0033] (2) Based on the calculated β value, divide its positive and negative values ​​by the absolute values ​​of the maximum positive value and the minimum negative value respectively, assign 0 to the part of the β value whose absolute value is less than 0.1, and assign 1 to the rest;

[0034] (3) Z mk Multiplying it by the β value gives the Fourier spectrum characteristic curve H. H will only have three values, 1, -1, and 0, representing a significant increase, a significant decrease, and a level, respectively.

[0035] Preferably, in step S3, the following steps are specifically included:

[0036] S31, judging whether the first H value in the Fourier spectrum rise and fall characteristic curve is -1, that is, whether it is a descending section; if it is not -1, continue to judge the second value until the first H value appears to be -1;

[0037] S32. When the first H value is -1, three picking methods need to be used in sequence for judgment. If any one of them is satisfied, the sequence value of the H value is the value to be found, and this sequence value contains the information of the starting frequency. If none of the three picking methods are satisfied, the next H value needs to be extracted in sequence for judgment until a point that meets the requirements is found. The three picking methods are:

[0038] 1) The first picking method: It is necessary to determine whether the H values ​​of the four points after this point show an overall downward trend, that is, whether the sum of these five values ​​is less than or equal to -4; this indicates that only one horizontal segment is allowed to appear in these five sliding windows, and the rest are significantly decreasing segments, and the horizontal segment can appear at any position; if the first picking method is satisfied, it ends; if not, it enters the second picking method;

[0039] 2) The second picking method: It is necessary to determine whether the H values ​​of the 6 points after this point show an overall downward trend, that is, whether the sum of these 7 values ​​is less than or equal to -4; this indicates that at most one rising segment and one horizontal segment are allowed to appear in these 7 sliding windows, and the rest are significant falling segments, and the rising segment and horizontal segment can appear at any position; if the second picking method is satisfied, it ends; if not, it enters the third picking method;

[0040] 3) The third picking method: It is necessary to determine whether the H values ​​of the 8 points after this point show an overall downward trend, that is, whether the sum of these 9 values ​​is less than or equal to -5; this indicates that at most 2 rising segments are allowed to appear in these 9 sliding windows, and the rest are significant falling segments;

[0041] S33. After finding the H value that meets the requirements, record the point number, which indicates the sliding window number. The starting frequency f is obtained by calculating the average of the last two frequencies of the sliding window. l ;

[0042] S34, the identified starting frequency f l Input to F(f U ) to calculate different f U When the function value is small, select f that minimizes the function value. U , which is the cut-off frequency, the formula is as follows:

[0043]

[0044] In the formula, f l is the starting frequency, f U is the cut-off frequency, A(f) is the Fourier spectrum, a and b are the linear fitting parameters within the selected start and end frequency range, and f i Indicates that the Fourier spectrum is in f l and f U other frequencies in between.

[0045] Preferably, in step S4, according to the start and end frequencies of the high-frequency descending segment of the earthquake motion obtained in step S3, the earthquake motion Fourier spectrum of the corresponding frequency band is extracted, and a least square method is used for linear fitting to obtain the slope and intercept of the fitting curve, and the slope is converted to obtain the earthquake motion high-frequency attenuation parameter K value, and the K value calculation formula is as follows:

[0046]

[0047] Where A(f) is the Fourier amplitude spectrum of acceleration, f l is the starting frequency, f U is the cut-off frequency, d is the change, and f is the frequency.

[0048] The beneficial effects of the present invention are:

[0049] 1) The K value of the high-frequency attenuation parameter of earthquake motion calculated in the present invention has a high accuracy rate, and the MK curve characteristic trend detection used can avoid the influence of mutation values ​​in the data, and has a high accuracy rate in identifying curve features. The earthquake motion Fourier spectrum curve is accompanied by violent oscillations during the rise and fall process, and there are many "sharps". The MK curve characteristic trend detection can reduce the influence of mutation values ​​on the overall curve rise and fall feature recognition. The accurate rise and fall characteristics of the Fourier spectrum curve provide a basis for picking up the starting frequency of the earthquake motion Fourier spectrum, and then calculating the accurate K value.

[0050] (2) The high-frequency attenuation segment of the Fourier spectrum of earthquake motion in the present invention can be automatically picked up, which greatly reduces the time and economic cost of manual selection. The present invention does not rely on visual observation data to provide parameter ranges, has strong batch processing capabilities for data, and is simple and fast to operate. The existing method of selecting the high-frequency attenuation drop segment of earthquake motion mostly adopts the visual recognition method, which requires manual observation of data one by one to determine the starting frequency and cutoff frequency of the high-frequency drop segment of the Fourier spectrum, and the calculation efficiency is low.

[0051] (3) The present invention is highly applicable to different seismic motion data. Seismic motion has strong randomness. Different magnitudes, epicenter distances and site conditions will affect the range of the high-frequency drop segment of the seismic motion. The existing batch calculation of seismic motion high-frequency attenuation parameters by fixing the start and end frequencies only considers the distribution characteristics of the high-frequency drop segment of most data, and is not applicable to all data, thus affecting the calculation accuracy. The present invention picks up the start and end frequencies according to the rising and falling characteristics of the curve itself, and has a wider applicability.

[0052] (4) The start and end frequency picking of the present invention is more objective and less affected by human factors. The existing calculation method of the ground motion high-frequency attenuation parameter K value requires advance observation of data to provide the value range of the corresponding parameter, which has a certain degree of subjectivity. The present invention unifies the standards in the process of picking the start and end frequencies, which is more objective. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a schematic flow chart of a K value self-picking method based on MK trend detection in an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of an example of seismic data in an embodiment of the present invention;

[0055] Figure 3a In the embodiment of the present invention, Z mk Schematic diagram of value examples;

[0056] Figure 3b This is a schematic diagram of an example of β value in an embodiment of the present invention;

[0057] Figure 3c This is a schematic diagram of an example of H value in an embodiment of the present invention;

[0058] Figure 3d This is a schematic diagram of an example of the F value in an embodiment of the present invention;

[0059] Figure 4 Schematic diagram of an example of K value in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] The present invention provides a technical solution: a K value self-picking method based on MK trend detection, such as Figure 1 As shown, the following steps are included:

[0062] S1. Earthquake motion data preprocessing.

[0063] Further, the specifics include the following:

[0064] S11. The original seismic data can be downloaded from the National Strong Motion Network Center. Examples of seismic data are as follows: Figure 2 As shown. Baseline correction is performed on the seismic data using the following formula:

[0065]

[0066] In the formula, A 0 is the baseline corrected data, N r is the number of sampling points of acceleration time history, a(t) is the acceleration at time t, i is the number of sampling points of different acceleration time history, and a(1) is the acceleration at the first moment;

[0067] S12, filtering the seismic data; using a 4th-order bandpass Butterworth filter with a cutoff frequency range of 0.01 to 30 Hz;

[0068] S13, performing Fourier transform;

[0069] S14. Use a Pazen window to smooth the Fourier spectrum. The smoothing uses a Pazen window with a window width of 0.4 Hz to obtain a smoothed ground motion Fourier spectrum.

[0070] Specifically, the smoothed seismic Fourier spectrum is segmented as data input in the form of a sliding window, where the window width of the sliding window is 3 Hz and the length of each sliding is 1 Hz until the Fourier spectrum ends; then, the key parameters S and Z for curve feature identification under different sliding windows are calculated by the MK trend detection algorithm. mk , V(S) and β, and after integration, we get the rising and falling characteristic values ​​H of the entire Fourier spectrum curve.

[0071] The data input into the algorithm in sequence is n independent data (x 1 ,x 2 …), the rising and falling characteristics of the curve are judged by the null hypothesis and the alternative hypothesis, where the null hypothesis is that there is no obvious trend in the selected data, and the alternative hypothesis is that the data has an obvious upward or downward trend.

[0072] Parameters S, Z mk The calculation process of , V(S) and β is as follows:

[0073] ① Construct a statistical variable S to calculate the sum of the rank values ​​of each data point, that is, subtract each data point from all the previous data points. If the difference is greater than 0, S increases by 1, and if the difference is less than 0, S decreases by 1. The expression of S value is as follows:

[0074]

[0075] Where n is the total number of data, all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and j-th value in the data respectively;

[0076] When the total number of data input into the MK trend detection algorithm is greater than 8, the statistical variable S roughly follows a normal distribution with a mean of 0;

[0077] ② Transform the S value into the standard normal distribution value Z through the following formula mk ;

[0078]

[0079] Where V(S) is the variance of S, and Z mk The value determines the rising and falling characteristics of the input segment. mk When the absolute value is greater than or equal to 1.96, it means that the 95% confidence level significance test has been passed, that is, there is a significant upward or downward trend;

[0080] ③ The β value is an indicator of the speed of the upward and downward trend, which is calculated by the following formula:

[0081]

[0082] In the formula, Median() is the median, 1 <j<i<n。

[0083] The calculated Z mk The values ​​are shown in the example Figure 3(a), where each point represents the Z value calculated by each sliding window. mk Each point on the graph is represented by the midpoint of the sliding window. For example, the abscissa of the first point is the midpoint of the first sliding window 0-3Hz, i.e. 1.5Hz. A ordinate greater than 1.96 indicates a significant increase. The calculated β value is shown in Figure 3(b).

[0084] The rising and falling characteristic values ​​H of the entire curve are given by Z mk The value and β value are calculated, as shown in Figure 3(c). The specific process is as follows:

[0085] (1) Set Z greater than 1.96 mk The value is assigned to 1, which is less than -1.96 Z mk The value is assigned to -1, and the rest are assigned to 0;

[0086] (2) Based on the calculated β value, divide its positive and negative values ​​by the absolute values ​​of the maximum positive value and the minimum negative value respectively, assign 0 to the part of the β value whose absolute value is less than 0.1, and assign 1 to the rest;

[0087] (3) Z mk Multiplying it by the β value gives the Fourier spectrum characteristic curve H. H will only have three values, 1, -1, and 0, representing a significant increase, a significant decrease, and a level, respectively.

[0088] S3. According to the Fourier spectrum rise and fall characteristic curve, pick up the start and end frequencies of the high-frequency descending section of the earthquake motion.

[0089] In step S3, the following steps are specifically included:

[0090] S31. Determine whether the first H value in the Fourier spectrum rising and falling characteristic curve is -1, that is, whether it is a descending segment; if it is not -1, continue to determine the second value until the first H value is -1; this is because when the H value is 1, it indicates that the curve in the sliding window is an ascending segment, not the required descending segment.

[0091] S32. When the first H value is -1, three picking methods need to be used in sequence for judgment. If any one of them is satisfied, the sequence value of the H value is the value to be found, and this sequence value contains the information of the starting frequency. If none of the three picking methods are satisfied, the next H value needs to be extracted in sequence for judgment until a point that meets the requirements is found. The three picking methods are:

[0092] 1) The first picking method: It is necessary to determine whether the H values ​​of the four points after this point show an overall downward trend, that is, whether the sum of these five values ​​is less than or equal to -4; this indicates that only one horizontal segment is allowed to appear in these five sliding windows, and the rest are significantly decreasing segments, and the horizontal segment can appear at any position; if the first picking method is satisfied, it ends; if not, it enters the second picking method;

[0093] 2) The second picking method: It is necessary to determine whether the H values ​​of the 6 points after this point show an overall downward trend, that is, whether the sum of these 7 values ​​is less than or equal to -4; this indicates that at most one rising segment and one horizontal segment are allowed to appear in these 7 sliding windows, and the rest are significant falling segments, and the rising segment and horizontal segment can appear at any position; if the second picking method is satisfied, it ends; if not, it enters the third picking method;

[0094] 3) The third picking method: It is necessary to determine whether the H values ​​of the 8 points after this point show an overall downward trend, that is, whether the sum of these 9 values ​​is less than or equal to -5; this indicates that at most 2 rising segments are allowed to appear in these 9 sliding windows, and the rest are significant falling segments;

[0095] S33. After finding the H value that meets the requirements, record the point number. This point represents the sliding window number. The starting frequency f is obtained by calculating the average of the last two frequencies of the sliding window. l .

[0096] As can be seen from Figure 3(c), the second point meets the requirements, indicating that the starting frequency is within the second sliding window, that is, 1-4Hz. Since the sliding window slides 1Hz each time, the first 2Hz will contain the data of the previous rising segment, so the midpoint of the last 1Hz is used as the starting frequency, that is, 3.5Hz.

[0097] S34, the identified starting frequency f l Input to F(f U ) to calculate different f U When the function value is small, select f that minimizes the function value. U , which is the cut-off frequency, as shown in the example of Figure 3(d). The formula is as follows:

[0098]

[0099] In the formula, f l is the starting frequency, f U is the cut-off frequency, A(f) is the Fourier spectrum, a and b are the linear fitting parameters within the selected start and end frequency range, and f i Indicates that the Fourier spectrum is in f l and f U other frequencies in between.

[0100] S4. Extract the descending frequency band according to the start and end frequencies, and obtain the K value by fitting calculation.

[0101] In step S4, according to the start and end frequencies of the high-frequency descending segment of the earthquake motion obtained in step S3, the Fourier spectrum of the earthquake motion of the corresponding frequency band is extracted, and a linear fit is performed using the least squares method to obtain the slope and intercept of the fitting curve. The slope is converted to obtain the high-frequency attenuation parameter K value of the earthquake motion, such as Figure 4 As shown, the K value calculation formula is as follows:

[0102]

[0103] Where A(f) is the Fourier amplitude spectrum of acceleration, f l is the starting frequency, f U is the cut-off frequency, d is the change, and f is the frequency.

[0104] The start and end frequency picking of the present invention is more objective and less affected by human factors. The existing calculation method of the ground motion high-frequency attenuation parameter K value requires observation of data in advance to provide the value range of the corresponding parameter, which has a certain degree of subjectivity. The present invention unifies the standards in the process of picking the start and end frequencies, which is more objective. And it can be picked automatically, greatly reducing the time and economic cost of manual selection.

[0105] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0106] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The singular forms "a", "said" and "the" used in the embodiments of the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings.

[0107] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0108] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0109] The "first\second" mentioned in the embodiments is only to distinguish similar objects, and does not represent a specific order for the objects. It is understandable that the "first\second" can be interchanged with the specific order or sequence where permitted. It should be understood that the objects distinguished by "first\second" can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0110] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A K value self-picking method based on MK trend detection, characterized in that: The steps include: S1, ground motion data preprocessing; S2, using MK trend detection algorithm to identify curve features of the seismic Fourier spectrum; S3, picking up the start and end frequencies of the high-frequency descending section of the earthquake motion according to the Fourier spectrum rise and fall characteristic curve; S4. Extract the descending frequency band according to the start and end frequencies, and obtain the K value by fitting calculation.

2. The K value self-picking method based on MK trend detection according to claim 1, characterized in that: In step S1, the specific steps include: S11. Baseline correction is performed on the seismic data using the following formula: In the formula, A0 is the baseline corrected data, N r is the number of sampling points of acceleration time history, a(t) is the acceleration at time t, i is the number of sampling points of different acceleration time history, and a(1) is the acceleration at the first moment; S12, filtering the seismic data; S13, performing Fourier transform; S14. Use the Pazen window to smooth the Fourier spectrum to obtain a smoothed ground motion Fourier spectrum.

3. The K value self-picking method based on MK trend detection according to claim 1, characterized in that: In step S2, the following steps are specifically performed: first, the smoothed seismic Fourier spectrum is segmented as data input in the form of a sliding window, wherein the window width of the sliding window used is 3 Hz, and the length of each sliding is 1 Hz, until the Fourier spectrum ends; then, the key parameters S and Z for identifying curve features under different sliding windows are calculated by the MK trend detection algorithm. mk , V(S) and β, and after integration, we get the rising and falling characteristic values ​​H of the entire Fourier spectrum curve.

4. The K value self-picking method based on MK trend detection according to claim 3 is characterized in that: The parameters S, Z mk The calculation process of , V(S) and β is as follows: ① Construct a statistical variable S to calculate the sum of the rank values ​​of each data point, that is, subtract each data point from all the previous data points. If the difference is greater than 0, S increases by 1, and if the difference is less than 0, S decreases by 1. The expression of S value is as follows: Where n is the total number of data, all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and j-th value in the data respectively; When the total number of data input into the MK trend detection algorithm is greater than 8, the statistical variable S roughly follows a normal distribution with a mean of 0; ② Transform the S value into the standard normal distribution value Z through the following formula mk ; Where V(S) is the variance of S, and Z mk The value determines the rising and falling characteristics of the input segment. mk When the absolute value is greater than or equal to 1.96, it means that the 95% confidence level significance test has been passed, that is, there is a significant upward or downward trend; ③ The β value is an indicator of the speed of the upward and downward trend, which is calculated by the following formula: In the formula, Median() is the median, 1 <j<i<n。 5. The K value self-picking method based on MK trend detection according to claim 3 is characterized in that: The rising and falling characteristic values ​​H of the entire curve are given by Z mk The value and β value are calculated, and the specific process is as follows: (1) Set Z greater than 1.96 mk The value is assigned to 1, which is less than -1.96 Z mk The value is assigned to -1, and the rest are assigned to 0; (2) Based on the calculated β value, divide its positive and negative values ​​by the absolute values ​​of the maximum positive value and the minimum negative value respectively, assign 0 to the part of the β value whose absolute value is less than 0.1, and assign 1 to the rest; (3) Z mk Multiplying it by the β value gives the Fourier spectrum characteristic curve H. H will only have three values, 1, -1, and 0, representing a significant increase, a significant decrease, and a level, respectively.

6. The K value self-picking method based on MK trend detection according to claim 1 is characterized in that: In step S3, the following steps are specifically included: S31, judging whether the first H value in the Fourier spectrum rise and fall characteristic curve is -1, that is, whether it is a descending section; if it is not -1, continue to judge the second value until the first H value appears to be -1; S32. When the first H value is -1, three picking methods need to be used in sequence for judgment. If any one of them is satisfied, the sequence value of the H value is the value to be found, and this sequence value contains the information of the starting frequency. If none of the three picking methods are satisfied, the next H value needs to be extracted in sequence for judgment until a point that meets the requirements is found. The three picking methods are: 1) The first picking method: It is necessary to determine whether the H values ​​of the four points after this point show an overall downward trend, that is, whether the sum of these five values ​​is less than or equal to -4; this indicates that only one horizontal segment is allowed to appear in these five sliding windows, and the rest are significantly decreasing segments, and the horizontal segment can appear at any position; if the first picking method is satisfied, it ends; if not, it enters the second picking method; 2) The second picking method: It is necessary to determine whether the H values ​​of the 6 points after this point show an overall downward trend, that is, whether the sum of these 7 values ​​is less than or equal to -4; this indicates that at most one rising segment and one horizontal segment are allowed to appear in these 7 sliding windows, and the rest are significant falling segments, and the rising segment and horizontal segment can appear at any position; if the second picking method is satisfied, it ends; if not, it enters the third picking method; 3) The third picking method: It is necessary to determine whether the H values ​​of the 8 points after this point show an overall downward trend, that is, whether the sum of these 9 values ​​is less than or equal to -5; this indicates that at most 2 rising segments are allowed to appear in these 9 sliding windows, and the rest are significant falling segments; S33. After finding the H value that meets the requirements, record the point number. This point represents the sliding window number. The starting frequency f is obtained by calculating the average of the last two frequencies of the sliding window. l ; S34, the identified starting frequency f l Input to F(f U ) to calculate different f U When the function value is small, select f that minimizes the function value. U , which is the cut-off frequency, the formula is as follows: In the formula, f l is the starting frequency, f U is the cut-off frequency, A(f) is the Fourier spectrum, a and b are the linear fitting parameters within the selected start and end frequency range, and f i Indicates that the Fourier spectrum is in f l and f U other frequencies in between.

7. The K value self-picking method based on MK trend detection according to claim 1 is characterized in that: In step S4, according to the start and end frequencies of the high-frequency descending segment of the earthquake motion obtained in step S3, the earthquake motion Fourier spectrum of the corresponding frequency band is extracted and linear fitting is performed using the least squares method to obtain the slope and intercept of the fitting curve. The slope is converted to obtain the earthquake motion high-frequency attenuation parameter K value. The calculation formula of K value is as follows: Where A(f) is the Fourier amplitude spectrum of acceleration, f l is the starting frequency, f U is the cut-off frequency, d is the change, and f is the frequency.

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