A site characteristics analysis method based on HVSR dynamic clustering

Abstract

This paper proposes a site characteristic analysis method based on HVSR dynamic clustering. This method uses a dynamic clustering algorithm to process HVSR sequences. Specifically, it solves a regularized objective function optimization problem under conditional constraints. The first term of the regularized objective function minimizes the weighted total distance within all classes, and the second term smoothes the weights between adjacent classes, thereby enhancing the distinction between classes. The technical solution of the present invention uses a dynamic clustering learning method to assign unbiased centers and response spectrum means, demonstrating good clustering performance and robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of earthquake motion spectrum characteristic analysis, and in particular relates to a site characteristic analysis method based on HVSR dynamic clustering. Background Art

[0002] Currently, some stations in my country's strong motion network lack borehole survey data, resulting in a relatively simplified classification of station sites. Therefore, classifying station sites based on the shape of spectral ratio curves can be an effective approach to address this problem. However, using strong motion records to study site effects requires minimizing the influence of the earthquake source and propagation path. The earliest approach employed selected bedrock outcrops near the soil layer or the bedrock surface at the bottom of the borehole as reference points. The Fourier spectrum of observations recorded at various points in the soil layer was compared with the reference point to produce a curve showing the site amplification factor varying with frequency. However, this reference point spectral ratio method, limited by the selection of suitable reference points, cannot be applied to site classification over large areas and is generally only used to study site effects at specific stations. When the site is hard, the impedance ratio between the topsoil and underlying bedrock is relatively small, significantly reducing the site amplification. Generally, the average spectral ratio curve for rock and hard soil is much flatter than that for soft soil sites, making it likely that the classification based solely on the dominant period will be ineffective. Existing classification criteria based on the shape of the H / V spectral ratio curve require further improvement in clustering performance and robustness. Summary of the Invention

[0003] In view of the above technical problems, the present invention proposes a site characteristic analysis method based on HVSR dynamic clustering. The method uses a dynamic clustering algorithm to process HVSR sequences. The dynamic clustering algorithm is specifically an optimization problem of the regularized objective function (1) under the constraint of condition (2).

[0004]

[0005]

[0006] The regularized objective function (1) includes a distance function P and a regularization term Qw, where C is the cluster center; U is a binary matrix, λ ip is the element in U; ​​W is the weight matrix, w pj is an element in W; m0 is the minimum number of HVSR sequences assigned to each class, and i, j, p, m, n, k are all integers.

[0007] Another aspect of the present invention provides a computer system comprising a plurality of computers, each of which executes all instructions for implementing the above method.

[0008] Compared with the prior art, the technical solution of the present invention adopts a dynamic clustering learning method to allocate centers and response spectrum means without deviation, showing good clustering performance and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 : Some embodiments provide a before-and-after comparison of baseline correction and filtering of strong ground motion data;

[0010] Figure 2 : Processing results of the dynamic clustering algorithm of some implementation methods; HVSR clustering results: (a) first category, (b) second category, (c) third category, (d) cluster center; the number of categories is 3. DETAILED DESCRIPTION

[0011] First, some terms in the present invention are explained and illustrated as necessary. HVSR: Horizontal-to-vertical spectral ratio; Dynamic clustering: includes a class of optimization problems, wherein the optimization problem is defined as having a regularized objective function; Seismic motion data: seismic motion data collected by the station, wherein the S band is the seismic shear wave (the S wave in the seismic signal is the main energy affecting the site), wherein EW is the east-west direction, wherein NS is the north-south direction, wherein UD is the up-down direction, and seismic motion data can be obtained from some public databases, such as the PEER NGA seismic motion database and the Japanese DONET1 sea area seismic motion data.

[0012] The technical solution of the present invention is described by the following embodiments, but should not be construed as limiting the present invention. Without departing from the spirit and essence of the present invention, modifications or replacements made to the methods, steps or conditions of the present invention are within the scope of the present invention.

[0013] In some embodiments, a dynamic clustering algorithm is used to process HVSR sequences, wherein the dynamic clustering algorithm comprises:

[0014] Under the constraint of condition (2), the solution of the regularized objective function (1) is calculated as follows:

[0015]

[0016]

[0017] The regularized objective function (1) includes a distance function P and a regularization term Qw, where C is the cluster center; U is a binary matrix, λ ip is the element in U; ​​W is the weight matrix, w pjis an element in W; m0 is the minimum number of HVSR sequences assigned to each class, and i, j, p, m, n, k are all integers. Preferably, m0 = 6; to ensure that the results of each class are statistically significant, each class is set to have at least 6 groups of HVSR sequences.

[0018] Preferably, each HVSR sequence is configured to be labeled with one or more information including number, magnitude, epicenter distance, station, etc. By adding labels, it is possible to know which group of earthquake records the clustering result corresponds to, facilitating the summary of classification characteristics from earthquake-related parameters.

[0019] Some more specific embodiments of the distance function P include a distance function P as shown in formula (3):

[0020]

[0021] C is the cluster center, where c pj are p cluster centers; U is a binary matrix, λ ip is the element in U; ​​W is the weight matrix, w pj is an element in W; z ij is the HVSR sequence; i, j, p, m, n, and k are all integers; the optimal number of classifications k is 3. As the number of classifications increases, the sum of squared errors tends to be stable. Combined with the elbow rule, the optimal number of classifications k is determined to be 3.

[0022] In some more specific embodiments, the regularization term Q W Specifically, it includes a regularization term Q as follows: W :

[0023]

[0024] Among them, α is the smoothing parameter, W is the weight matrix, and w pj is an element in W. Specifically, the method for calculating α is as follows:

[0025]

[0026] Some embodiments also include a dynamic clustering learning process, which includes taking two variables in the cluster center C, weight matrix W, and binary matrix U of the regularized objective function (1) as known quantities and optimizing the third variable using an information updating method.

[0027] A more specific embodiment involves the dynamic clustering learning process including iterating steps S1-S3:

[0028] S1 Given a hypothetical weight matrix W and cluster center C, the HVSR sequence is assigned to the class of the hypothetical cluster center C when the conditions (5) are met:

[0029]

[0030] Among them, λ ip is an element in U; ​​m0 is the minimum number of HVSR sequences assigned to each class, preferably, m0 = 6; to ensure that the results of each class are statistically significant, set each class to have at least 6 groups of HVSR sequences; i, p, m, k are all integers; where k is the optimal number of classifications, preferably k is 3;

[0031] S2: After the weight matrix W and the binary matrix U are determined, the new cluster center after the information update is solved by setting the derivative of the regularized objective function (1) to 0;

[0032] S3 determines the binary matrix U and cluster center C through S1 and S2, and calculates the weight matrix W when the conditions (6) are met:

[0033]

[0034] where w pj is an element in the weight matrix W.

[0035] It should be noted that the dynamic clustering learning process aims to minimize the regularized objective function (1), and the original problem is transformed into a quadratic programming problem to calculate the weight matrix W.

[0036] S2 specifically includes the calculation according to the following formula:

[0037]

[0038]

[0039] Among them, λ ip is the element of the binary matrix U, z ij is the HVSR sequence, w pj is the element in the weight matrix W, c pj are p cluster centers.

[0040] In S3, the Frank-Wolfe optimization method is used to solve the quadratic programming problem. The calculation steps are described in the literature: Frank M, Wolfe P. An algorithm for quadratic programming [J]. Naval research logistics quarterly, 1956, 3(1-2): 95-110. The program written in C language can be downloaded from the following website: https: / / www.ymcn.org / d-c2Li.html

[0041] Some embodiments further include the following strong earthquake data processing steps:

[0042] Obtain earthquake observation record data from the PEER NGA earthquake motion database;

[0043] Extracting strong ground motion data from the earthquake observation record data, where the extraction conditions include: magnitude greater than 4 and PGA < 20 cm / s2;

[0044] Baseline correction and filtering are performed on the strong earthquake motion data to eliminate signal deviations including baseline drift, instrument noise and environmental noise. The comparison results of the strong earthquake motion data before and after processing are shown in Figure 1 .

[0045] The segmented baseline proposed by Boore is used to perform baseline correction on strong earthquake data. For details, please refer to the literature: Boore DM, Bommer JJ. Processing of strong-motion accelerograms: needs, options and consequences [J]. Soil Dynamics and Earthquake Engineering, 2005, 25(2): 93-115. Based on the method in this literature, some specific implementation methods use the detrend function of Matlab.

[0046] In some implementations, based on the above implementations, a 4th-order Butterworth bandpass filter with a cutoff frequency of 0.1 Hz to 20 Hz is used to filter the strong earthquake data.

[0047] In some embodiments, the calculation of the HVSR sequence comprises the following steps:

[0048] Intercept the strong ground motion data of the S band;

[0049] Performing a fast Fourier transform on the S-band strong earthquake motion data to obtain a Fourier amplitude spectrum;

[0050] Smoothing the 0.2-20 Hz frequency band in the Fourier amplitude spectrum using the Konno smoothing method;

[0051] The EW and NS directions of the smoothed S-band strong ground motion data are synthesized into the horizontal direction using the geometric mean, and then divided by the corresponding UD-direction smoothed Fourier amplitude spectrum to obtain the strong ground motion HVSR;

[0052] Discretizing the strong earthquake motion HVSR to obtain an HVSR sequence;

[0053] Each of the HVSR sequences was tagged.

[0054] Some more specific implementation methods are obtained based on the sea-area seismic data from 6 submarine stations of Japan's K-net network from 2000 to 2018. Figure 2 The HVSR clustering results are used to characterize the characteristics of sea area sites (sea area site classification).

[0055] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output.

[0056] Although the present invention has been described in detail above using general explanations, specific embodiments, and experiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the present invention. Therefore, such modifications and improvements, which do not depart from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

[0057] Certain embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the activities recited in the claims can be performed in a different order and still achieve the desired results. As an example, the processes depicted in the accompanying figures do not necessarily require the particular order or sequential sequence shown to achieve the desired results. In certain implementations, multitasking and parallel processing may be advantageous.

Claims

1. A site characteristics analysis method based on HVSR dynamic clustering, characterized in that: The method uses a dynamic clustering algorithm to process HVSR sequences. The dynamic clustering algorithm is specifically an optimization problem of the regularized objective function (1) under the constraint of condition (2). The regularized objective function (1) includes a distance function P and a regularization term Qw, where C is the cluster center; U is a binary matrix, λ ip is the element in U; ​​W is the weight matrix, w pj is an element in W; m0 is the number of HVSR sequences allocated in each class, i, j, p, m, n, k are all integers; the calculation of the HVSR sequence includes the following steps: Intercept the strong ground motion data of the S band; Performing a fast Fourier transform on the S-band strong earthquake motion data to obtain a Fourier amplitude spectrum; Smoothing the 0.2-20 Hz frequency band in the Fourier amplitude spectrum using the Konno smoothing method; The EW and NS directions of the smoothed S-band strong ground motion data are synthesized into the horizontal direction using the geometric mean, and then divided by the corresponding UD-direction smoothed Fourier amplitude spectrum to obtain the strong ground motion HVSR; Discretizing the strong earthquake motion HVSR to obtain the HVSR sequence; The distance function P specifically includes a distance function P as shown in the following formula (3): C is the cluster center, where c pj are p cluster centers; U is a binary matrix, λ ip is the element in U; ​​W is the weight matrix, w pj is an element in W; z ij is the HVSR sequence; i, j, p, m, n, k are all integers, where k is the optimal classification number, which is 3; The regularization term Q W Specifically, it includes a regularization term Q as follows: W : Among them, α is the smoothing parameter, W is the weight matrix, and w pj are elements in W, j, p, n, k are all integers.

2. The method according to claim 1, wherein The invention also includes a dynamic clustering learning process, which includes the steps of taking two variables of the cluster center C, the weight matrix W, and the binary matrix U of the regularized objective function (1) as known quantities and optimizing the third variable by using an information updating method.

3. The method according to claim 2, wherein The dynamic clustering learning process specifically includes: S1 Given a hypothetical weight matrix W and cluster center C, the HVSR sequence is assigned to the class of the cluster center C when the conditions (5) are met: Where λip is an element in the binary matrix U; m0 is the number of HVSR sequences assigned to each class, and m0 is 6; i, p, m, k are all integers; k is the optimal number of classifications, and k is 3; S2: After the weight matrix W and the binary matrix U are determined, the new cluster center C after the information update is solved by setting the derivative of the regularized objective function (1) to 0; S3 determines the binary matrix U and cluster center C through S1 and S2, and calculates the weight matrix W when the conditions (6) are met: where w pj is an element in the weight matrix W.

4. The method according to claim 3, wherein The S3 further includes calculating the weight matrix W using the Frank-Wolfe optimization method.

5. The method according to claim 1, wherein The method further includes a strong earthquake data processing step, wherein the strong earthquake data processing step includes: Obtain earthquake observation record data; Extract strong ground motion data from the earthquake observation record data. The extraction conditions include: magnitude greater than 4 and PGA < 20cm / s 2 ; Baseline correction and filtering are performed on the strong earthquake motion data to eliminate signal deviations including baseline drift, instrument noise and environmental noise.

6. The method according to claim 5, wherein The strong earthquake data were baseline corrected using the segmented baseline proposed by Boore.

7. The method according to claim 5, wherein The strong earthquake data is filtered using a 4th-order Butterworth bandpass filter with a cutoff frequency of 0.1 Hz to 20 Hz.

8. A computer system, characterized in that: The system comprises a plurality of computers, each of which executes instructions of any one of the methods as claimed in claims 1-7.

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