A K-value self-picking method based on MK trend detection

Abstract

The present invention relates to the technical field of seismology, and specifically discloses a K-value self-picking method based on MK trend detection, which includes the following steps: preprocessing of ground motion data; using the MK trend detection algorithm to identify the curve characteristics of the ground motion Fourier spectrum; picking up the start and end frequencies of the high-frequency descending section of the ground motion according to the ascending and descending characteristic curves of the Fourier spectrum; extracting the descending frequency band according to the start and end frequencies, and fitting and calculating to obtain the K value. By extracting the ascending and descending characteristics of the Fourier spectrum curve of the ground motion to identify the start and end frequencies and calculate the high-frequency attenuation parameter K value of the ground motion, the present invention can significantly improve the accuracy of picking up the start and end frequencies of the descending section of the Fourier spectrum, realize the batch calculation of the high-frequency attenuation parameters of the ground motion, and has the characteristics of strong flexibility, high accuracy, high efficiency and simple operation.

Description

Technical Field

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

[0002] In the southwestern region, tectonic activities are intense and the risk of strong earthquake triggering is high. Studying the disasters caused by strong earthquakes is an urgent need for the in-depth development and construction of the western region. The ground motion in the near field of a strong earthquake has strong destructiveness and rich high-frequency components, which are significantly controlled by the seismic source and are more complex under the influence of the near-fault effect. 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 seismic design, especially for the construction of important infrastructure such as nuclear power plants and dams in areas lacking ground motion records.

[0003] Currently, there are mainly three methods for calculating the high-frequency attenuation parameter of ground motion: The first is visual selection. That is, under the logarithmic coordinates of the ground motion Fourier spectrum, first select the points where the amplitude significantly decreases as the starting frequency, and then select the points where the descending slope significantly changes as the cut-off frequency. Visual selection can flexibly select the start and end frequencies according to the curve characteristics of different ground motion Fourier spectra, effectively avoiding the influence of outliers and small upward or horizontal segments in the descending section on the recognition, and having good anti-interference ability for factors such as mutation values, and thus accurately selecting the descending section according to the descending characteristics of different acceleration spectra. However, the visual selection process is affected by the subjective factors of the selector, and the efficiency is low when dealing with a large amount of data. The second is the fixed frequency band method, that is, after observing a large amount of data and conducting inductive statistics, determine the distribution characteristics of the high-frequency descending sections of most ground motions, and use this as the high-frequency descending section of all seismic data. The fixed frequency band method can achieve simple automation and has a high calculation efficiency. However, the selected fixed frequency does not fit all ground motion Fourier spectra, and a certain amount of observation and statistics of the data are required first, and there is still a certain degree of subjectivity. The third is a simple automatic recognition method, that is, by constructing a ratio function of the root mean square error and the frequency band width, and by judging the size of the ratio function values at different start and end frequencies, select the best combination. This method requires observing the data characteristics first and imposing certain restrictions on the range of the start and end frequencies.

[0004] At present, to calculate the high-frequency attenuation parameter K value of ground motion, it is necessary to first perform a Fourier transform on the ground motion, then use the method of human eye observation to find the descending section of the curve, and then perform a linear fit on the data of this descending section. The calculation efficiency of this traditional method is relatively low, and it requires a large amount of manpower and material resources when the data volume is large. In addition, existing automatic algorithms need to obtain the value range of specific parameters through a large number of observed data before the calculation starts, and input this value range into the algorithm to start the calculation. Once it exceeds the value range, it will affect the accuracy of the calculation results.

[0005] Aiming at the deficiencies in the current calculation method of the high-frequency attenuation parameter of ground 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. By identifying the rising and falling characteristics of the Fourier spectrum of ground motion, the start and end frequencies are automatically picked up, and then the high-frequency attenuation parameter of ground motion is obtained. This method is applicable to the calculation of the high-frequency attenuation parameter of the Fourier spectrum of ground motion in different regions, sites, and magnitudes, and provides a certain reference for the parameters required for the ground motion simulation of important infrastructure such as nuclear power plants and dams in areas lacking ground motion records. Summary of the Invention

[0006] 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 high-frequency attenuation parameter K value of ground motion by extracting the rising and falling characteristics of the curve of the Fourier spectrum of ground motion and then identifying the start and end frequencies. It can significantly improve the picking accuracy of the start and end frequencies of the descending section of the Fourier spectrum; realize the batch calculation of the high-frequency attenuation parameter of ground motion; has the characteristics of strong flexibility, high accuracy, high efficiency, and simple operation, and solves the problems mentioned in the above 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, including the following steps:

[0008] S1. Pretreatment of ground motion data;

[0009] S2. Use the MK (Mann-Kendall) trend detection algorithm to identify the curve characteristics of the Fourier spectrum of ground motion;

[0010] S3. According to the rising and falling characteristic curve of the Fourier spectrum, pick up the start and end frequencies of the high-frequency descending section of ground motion;

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

[0012] Preferably, in step S1, it specifically includes the following:

[0013] S11. Perform baseline correction on the ground motion data, and the formula is as follows:

[0014]

[0015] Wherein, A0 is the data after baseline correction, N r is the number of sampling points of the acceleration time history, a(t) is the acceleration at time t, i is the number of sampling points of different acceleration time histories, and a(1) is the acceleration at the first moment;

[0016] S12. Filter the ground motion data;

[0017] S13. Perform Fourier transform;

[0018] S14. Smooth the Fourier spectrum using the Parzen window to obtain the smoothed ground motion Fourier spectrum.

[0019] Preferably, in step S2, it specifically includes: First, segment the smoothed ground motion Fourier spectrum in the form of a sliding window as data input, where the window width of the sliding window used is 3 Hz, and the length of each slide is 1 Hz until the Fourier spectrum ends; Then, calculate the key parameters S, Z mk , V(S) and β of the curve feature recognition under different sliding windows through the MK trend detection algorithm, and integrate to obtain the rising and falling eigenvalue H value of the entire curve of the Fourier spectrum.

[0020] Preferably, the calculation processes of the parameters S, Z mk , V(S) and β are 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 data points before it. 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 the S value is as follows:

[0022]

[0023] Wherein, n is the total number of data, for all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and the 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 approximately follows a normal distribution, and its mean is 0;

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

[0026]

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

[0028] ③ The β value is an index of the speed of the rising and falling trend, and 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 value H value of the whole curve is calculated from the Z mk value and the β value. The specific process is as follows:

[0032] (1) Assign a value of 1 to the Z mk value greater than 1.96, assign a value of -1 to the Z mk value less than -1.96, and assign a value of 0 to the rest;

[0033] (2) According to 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, and assign the part where the absolute value of the processed β value is less than 0.1 to 0, and assign the rest to 1;

[0034] (3) Multiply the Z mk value and the β value to obtain the Fourier spectrum characteristic curve H. H can only have three values, 1, -1, and 0, representing significant rise, significant fall, and horizontal respectively.

[0035] Preferably, in step S3, it specifically includes the following steps:

[0036] S31. Judge whether the first H value in the Fourier spectrum rising and falling characteristic curve is -1, that is, whether it is a falling segment; if it is not -1, continue to judge the second value until the first H value is -1;

[0037] S32. When the first H value is -1, three picking methods need to be used in sequence for judgment. If any one is satisfied, the sequence value of this 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 respectively:

[0038] 1) The first picking method: It is necessary to determine whether the H values of the 4 points after this point show an overall downward trend, that is, whether the sum of these 5 values is less than or equal to -4; this indicates that only one horizontal segment is allowed to appear within these 5 sliding windows, and the rest are significant downward segments, and this horizontal segment can appear at any position; if the first picking method is satisfied, it ends, and 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 1 rising segment and one horizontal segment are allowed to appear within these 7 sliding windows, and the rest are significant downward segments, and this rising segment and horizontal segment can appear at any position; if the second picking method is satisfied, it ends, and 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 within these 9 sliding windows, and the rest are significant downward segments;

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

[0042] S34. Input the identified starting frequency f l into F(f U ) to calculate the magnitudes of the function values at different f U , and select the f U when the function value is the smallest, which is the cut-off frequency. The formula is expressed 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 starting and ending frequency ranges, and f i represents other frequencies between f l and f U .

[0045] Preferably, in step S4, according to the starting and ending frequencies of the high-frequency descending segment of the ground motion obtained in step S3, the Fourier spectrum of the ground motion in the corresponding frequency band is extracted and linearly fitted by the least squares method to obtain the slope and intercept of the fitting curve. The slope is transformed to obtain the high-frequency attenuation parameter K value of the ground motion. The calculation formula of the K value is as follows:

[0046]

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

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

[0049] 1) The accuracy of the K value of the high-frequency attenuation parameter of the ground motion calculated in the present invention is high. The MK curve feature trend detection used can avoid the influence of mutation values in the data, and has a high accuracy in identifying curve features. During the rising and falling processes of the ground motion Fourier spectrum curve, there are violent oscillations and many "cusps". The MK curve feature trend detection can reduce the influence of mutation values on the recognition of the rising and falling features of the overall curve. The accurate rising and falling features of the Fourier spectrum curve provide a basis for picking up the starting frequency of the ground motion Fourier spectrum, and then calculating the accurate K value.

[0050] (2) In the present invention, the high-frequency attenuation section of the ground motion Fourier spectrum can be automatically picked up, greatly reducing the time and economic costs of manual selection. The present invention does not rely on visual observation data to provide parameter ranges, has strong batch processing ability for data, and is simple and fast to operate. The selection of the high-frequency attenuation descending section of the existing ground motion mostly uses the method of visual recognition, which requires manual observation of data one by one to judge the starting frequency and cut-off frequency of the high-frequency descending section of the Fourier spectrum, and the calculation efficiency is low.

[0051] (3) The present invention has strong applicability to different ground motion data. Ground motion has strong randomness, and different magnitudes, epicentral distances, and site conditions, etc. will all affect the range of the high-frequency descending section of the ground motion. The existing method of batch calculating the high-frequency attenuation parameter of the ground motion by fixing the starting and ending frequencies only considers the distribution characteristics of the high-frequency descending sections of most data, and is not applicable to all data, thus affecting the calculation accuracy. However, the present invention picks up the starting and ending frequencies according to the rising and falling characteristics of the curve itself, and has a wider applicability.

[0052] (4) The picking of the starting and ending frequencies in the present invention is more objective and less affected by human factors. The existing calculation method of the K value of the high-frequency attenuation parameter of the ground motion requires observing data in advance to provide the value range of corresponding parameters, which has a certain subjectivity. However, the present invention has a unified standard in the process of picking up the starting and ending frequencies, which is more objective. Description of the Drawings

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

[0054] Figure 2 is a schematic diagram of the ground motion data example in the embodiment of the present invention;

[0055] Figure 3a Schematic diagram of Z value example in the embodiment of the present invention mk value example schematic diagram;

[0056] Figure 3b Schematic diagram of β value example in the embodiment of the present invention;

[0057] Figure 3c Schematic diagram of H value example in the embodiment of the present invention;

[0058] Figure 3d Schematic diagram of F value example in the embodiment of the present invention;

[0059] Figure 4 Schematic diagram of K value example in the embodiment of the present invention. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

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

[0062] S1. Pretreatment of ground motion data.

[0063] Further, specifically, it includes the following:

[0064] S11. The original ground motion data can be downloaded from the National Strong Motion Network Center, and the ground motion data example is as Figure 2 shown. Perform baseline correction on the ground motion data, and the formula is as follows:

[0065]

[0066] In the formula, A0 is the data after baseline correction, N r is the number of acceleration time history sampling points, a(t) is the acceleration at time t, i is the number of different acceleration time history sampling points, and a(1) is the acceleration at the first moment;

[0067] S12. Filter the ground motion data; use a 4th-order band-pass Butterworth filter, and the cut-off frequency range is 0.01 - 30 Hz;

[0068] S13. Perform Fourier transform;

[0069] S14. Smooth the Fourier spectrum using a Parzen window with a window width of 0.4 Hz to obtain the smoothed Fourier spectrum of the ground motion.

[0070] Specifically, it includes: First, segment the smoothed Fourier spectrum of the ground motion in the form of a sliding window as data input. The window width of the sliding window used is 3 Hz, and the length of each slide is 1 Hz until the end of the Fourier spectrum. Then, calculate the key parameters S, Z mk , V(S), and β of the curve features under different sliding windows through the MK trend detection algorithm, and integrate them to obtain the rise and fall eigenvalue H of the entire curve of the Fourier spectrum.

[0071] The data input into the algorithm in sequential segments is n independent data (x1, x2,...) arranged in order. Determine the rise and fall characteristics of the curve through the null hypothesis and the alternative hypothesis. The null hypothesis is that there is no obvious trend in the selected data, and the alternative hypothesis is that there is an obvious upward or downward trend in the data.

[0072] Parameters S, Z mk , V(S), and β are calculated as follows:

[0073] ① Construct the statistical variable S to calculate the sum of the rank values of each data point, that is, subtract each data point from all the data points before it. If the difference is greater than 0, S is incremented by 1; if the difference is less than 0, S is decremented by 1. The expression for the S value is as follows:

[0074]

[0075] In the formula, n is the total number of data, for all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and the 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 approximately follows a normal distribution with a mean of 0;

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

[0078]

[0079] In the formula, V(S) is the variance of S. Judge the rise and fall characteristics of the input segment through the Z mk value. When the absolute value of Z mk is greater than or equal to 1.96, it means that the significance test with a confidence level of 95% has passed, that is, there is a significant upward or downward trend;

[0080] ③ The β value is an indicator of the speed of the rise and fall trend and is calculated through the following formula:

[0081]

[0082] Where Median() is the median, and 1 < j < i < n.

[0083] The calculated Z mk value is shown in Example Figure 3(a). Each point in the figure represents the Z value calculated for each sliding window. mk value. Each point on the graph is represented by the midpoint value of the sliding window. For example, the abscissa of the first point is the midpoint of the first sliding window from 0 - 3 Hz, which is 1.5 Hz. If the ordinate is greater than 1.96, it indicates a significant increase. The calculated β value is shown in Figure 3(b).

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

[0085] (1) Assign a value of 1 to the Z mk value greater than 1.96, a value of -1 to the Z mk value less than -1.96, and a value of 0 to the rest.

[0086] (2) According to 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 a value of 0 to the part where the absolute value of the processed β value is less than 0.1, and a value of 1 to the rest.

[0087] (3) Multiply the Z mk and β values to obtain the Fourier spectrum characteristic curve H. H can only have three values, 1, -1, and 0, representing significant increase, significant decrease, and horizontal respectively.

[0088] S3. According to the Fourier spectrum rising and falling characteristic curve, pick up the start and end frequencies of the high - frequency decreasing section of the ground motion.

[0089] In step S3, it specifically includes the following steps:

[0090] S31. Judge whether the first H value in the Fourier spectrum rising and falling characteristic curve is -1, that is, whether it is a decreasing section; if it is not -1, continue to judge the second value until the first H value of -1 appears; this is because when the H value is 1, it means the curve in the sliding window is an increasing section, not the required decreasing section.

[0091] S32. When the first H value of -1 appears, it is necessary to judge successively using three picking methods. If any one is satisfied, the sequence value of this H value is the value to be found, and this sequence value contains information about the start frequency; if none of the three picking methods are satisfied, it is necessary to extract the next H value in sequence for judgment until a point that meets the requirements is found; the three picking methods are respectively:

[0092] 1) The first picking method: It is necessary to determine whether the H values of the 4 points after this point show an overall downward trend, that is, whether the sum of these 5 values is less than or equal to -4; this indicates that only one horizontal segment is allowed to appear within these 5 sliding windows, and the rest are significant downward segments. This 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 1 rising segment and one horizontal segment are allowed to appear within these 7 sliding windows, and the rest are significant downward segments. This 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 within these 9 sliding windows, and the rest are significant downward segments;

[0095] S33. After finding the H value that meets the requirements, record which point this is. This point represents which sliding window it is. Calculate the average value of the last two frequencies of the sliding window to obtain the starting frequency f l 。

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

[0097] S34. Input the identified starting frequency f l into F(f U ) to calculate the magnitudes of the function values at different f U . Select the f U when the function value is the smallest as the cut-off frequency, as shown in the example of Figure 3(d). The formula is expressed 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 starting and ending frequency ranges, and f i represents other frequencies between f l and f U .

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

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

[0102]

[0103] In the formula, A(f) is the acceleration Fourier amplitude spectrum, f l is the start frequency, f U is the cut-off frequency, d represents the change amount, and f represents the frequency.

[0104] The picking of the start and end frequencies in the present invention is more objective and less affected by human factors. The existing calculation methods for the high-frequency attenuation parameter K value of ground motion need to observe data in advance to provide the value range of corresponding parameters, which has certain subjectivity. While in the present invention, the standard is unified during 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 costs of manual selection.

[0105] It should be noted that in this article, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or device including the said 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 of "a", "the" and "said" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

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

[0108] Depending on the context, as used herein, the word "if" can be interpreted as "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detecting (stated condition or event)" can be interpreted as "when determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)".

[0109] The "first / second" mentioned in the embodiments is only used to distinguish similar objects and does not represent a specific order for the objects. It can be understood that the "first / second" can be interchanged in a specific order or sequence when permitted. It should be understood that the objects distinguished by the "first / second" can be interchanged as 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 foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for self-picking K value based on MK trend detection, characterized in that, It includes the following steps: S1. Pretreatment of ground motion data; S2. Use the MK trend detection algorithm to identify the curve characteristics of the ground motion Fourier spectrum; specifically, it includes: First, segment the smoothed ground motion Fourier spectrum in the form of a sliding window as the data input. The window width of the sliding window used is 3 Hz, and the length of each slide is 1 Hz until the Fourier spectrum ends. Then, calculate the key parameter statistical variables S, the standard normal distribution value Z, the variance V(S) of the statistical variable, and the index β of the rising and falling trend speed through the MK trend detection algorithm, and integrate them to obtain the rising and falling characteristic values H of the entire Fourier spectrum curve. The rising and falling characteristic values H of the entire curve are calculated from the Z mk value and the β value, and the specific process is as follows: mk value and the β value, and the specific process is as follows: (1) Assign a value of 1 to Z greater than 1.96 mk and a value of -1 to Z less than -1.96, mk while assigning a value of 0 to the rest; (2) According to 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 the part with the absolute value of the processed β value less than 0.1 to 0, and the rest to 1; (3) Multiply Z mk by the β value to obtain the Fourier spectrum feature curve H. H will only have three values, 1, -1, and 0, representing significant increase, significant decrease, and horizontal respectively; S3. Pick up the start and end frequencies of the high-frequency descending section of the ground motion according to the rising and falling characteristic curve of the Fourier spectrum; specifically, it includes the following steps: S31. Judge whether the first H value in the rising and falling characteristic curve of the Fourier spectrum 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 of -1 appears; S32. When the first H value of -1 appears, three picking methods need to be used for judgment in turn. If any one is satisfied, the sequence value of this H value is the value to be found, and this sequence value contains the information of the start 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 as follows: 1) The first picking method: It is necessary to judge whether the H values of the 4 points after this point show an overall downward trend, that is, whether the sum of these 5 values is less than or equal to -4; this indicates that only one horizontal section is allowed to appear within these 5 sliding windows, and the rest are significant descending sections, and this horizontal section can appear at any position; if the first picking method is satisfied, it ends, and if not, it enters the second picking method; 2) The second picking method: It is necessary to judge 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 1 rising section and one horizontal section are allowed to appear within these 7 sliding windows, and the rest are significant descending sections, and this rising section and horizontal section can appear at any position; if the second picking method is satisfied, it ends, and if not, it enters the third picking method; 3) The third picking method: It is necessary to judge 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 sections are allowed to appear within these 9 sliding windows, and the rest are significant descending sections; S33. After finding the H value that meets the requirements, record which point this is. This point represents which sliding window. Calculate the average value of the last two frequencies of the sliding window to obtain the starting frequency f l ; S34. Input the recognized starting frequency f l into F(f U ) to calculate the magnitudes of function values at different f U . Select the f U at which the function value is minimized as the cut-off frequency. The formula is expressed as follows: where 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 starting and ending frequency ranges, and f i represents other frequencies of the Fourier spectrum between f l and f U ; S4. Extract the descending frequency band according to the start and end frequencies, and fit and calculate to obtain the K value.

2. The K-value self-picking method based on MK trend detection according to claim 1, characterized in that: In step S1, it specifically includes the following: S11. Perform baseline correction on the ground motion data, and the formula is as follows: where A0 is the data after baseline correction, N r is the number of sampling points of the acceleration time history, a(t) is the acceleration at time t, i is the number of sampling points of different acceleration time histories, and a(1) is the acceleration at the first moment; S12. Filter the ground motion data; S13. Perform Fourier transform; S14. Smooth the Fourier spectrum using the Parzen window to obtain the smoothed ground motion Fourier spectrum.

3. The K-value self-picking method based on MK trend detection according to claim 1, characterized in that: The parameters S and Z mk , the calculation processes of V(S) and β are as follows: ①Construct 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 data points before it. If the difference is greater than 0, S is increased by 1, and if the difference is less than 0, S is decreased by 1; the expression of the S value is as follows: where n is the total number of data, for all i, j ≤ n, and i ≠ j, x i and x j are the i-th value and the 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 approximately follows a normal distribution with a mean of 0; ② Transform the S value into a standard normal distribution value Z through the following formula mk ; Where, V(S) is the variance of S, and the rising and falling characteristics of the input segment are judged by the Z mk value. When the absolute value of Z mk is greater than or equal to 1.96, it indicates that the significance test with a confidence level of 95% is passed, that is, there is a significant upward or downward trend; ③The β value is an index of the speed of the rising and falling trend, and is calculated by the following formula: In the formula, Median() is the median, 1 < j < i < n.

4. The K-value self-picking method based on MK trend detection according to claim 1, wherein: In step S4, according to the start and end frequencies of the high-frequency decreasing section of the ground motion obtained in step S3, the Fourier spectrum of the ground motion in the corresponding frequency band is extracted and linearly fitted by the least square method to obtain the slope and intercept of the fitting curve. The slope is transformed to obtain the high-frequency attenuation parameter K value of the ground motion. The calculation formula of the K value is as follows: where \(A(f)\) is the acceleration Fourier amplitude spectrum, \(f\) l is the starting frequency, \(f\) U is the cut-off frequency, \(d\) represents the change amount, and \(f\) represents the frequency.

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