A method for identifying seismic liquefaction of sand based on seismic acceleration data spectrum analysis

Abstract

This invention, a method for identifying seismic liquefaction of sand based on the spectral analysis of seismic acceleration data, belongs to the field of seismic engineering. It aims to solve the problems of low efficiency, high cost, and low accuracy in distinguishing between non-liquefiable and liquefiable soft soil sites using traditional methods. The invention collects bidirectional horizontal seismic acceleration time-history data, dividing it into training and testing sets. It extracts peak ground acceleration (PGA) and uses a liquefaction trigger threshold for initial identification; sites not reaching the threshold are directly classified as non-liquefiable. Once the threshold is reached, the data is segmented based on the first time the threshold is reached, and the spectrum is obtained through bandpass filtering and Fourier transform. The differences in the proportion of low-frequency components and the differences in characteristic frequencies are calculated. Using the two features as input, a discrimination model is constructed using logistic regression and maximum likelihood estimation, and the decision boundary is determined. The accuracy is verified using a test set. This method requires only acceleration time-history data, has low discrimination cost and high efficiency, effectively distinguishes between non-liquefiable and liquefiable soft soil sites, has strong anti-interference capabilities and high accuracy, and is suitable for rapid assessment of sand liquefaction after strong earthquakes and for seismic engineering applications.

Description

Technical Field

[0001] This invention relates to the field of seismic engineering technology, and in particular to a method for determining seismic liquefaction of sandy soil based on the spectral analysis of seismic acceleration data. Background Technology

[0002] Earthquake liquefaction is a key research topic in the field of seismic engineering. It specifically refers to the catastrophic phenomenon where saturated sand, silt, and poorly graded gravelly soils, under seismic loading, experience a sharp increase in excess pore water pressure and a significant decrease in effective stress, leading to a loss of shear strength and a transformation from a solid to a liquid state. my country's earthquake activity is characterized by its wide distribution, high frequency, and high intensity. Large-scale sand liquefaction damage occurs in all strong earthquake events, causing severe consequences such as building collapse, ground subsidence, and damage to lifeline engineering projects, resulting in enormous losses to people's lives, property, and the socio-economic landscape. Therefore, research on efficient and accurate methods for identifying earthquake liquefaction in sand is of significant engineering value and practical importance for earthquake disaster prevention, seismic design of engineering projects, and emergency rescue.

[0003] Current methods for identifying soil liquefaction mainly fall into three categories: in-situ testing, laboratory testing, and numerical simulation. In-situ testing, such as the Standard Penetration Test (SPT) and Cone Penetration Test (CPT), assesses liquefaction potential by directly testing soil in the field. While the results are relatively reliable, the methods are complex, costly, and time-consuming, making them unsuitable for rapid assessment and large-scale liquefaction zone identification after an earthquake. Laboratory testing assesses liquefaction characteristics by collecting soil samples and conducting tests under simulated earthquake conditions in a laboratory. However, this method is affected by factors such as soil disturbance and size effects, resulting in uncertainties in the results. It also suffers from high costs and long processing times. Numerical simulation uses computer simulations to model the propagation of seismic waves in the soil, predicting the location and extent of liquefaction. While flexible and repeatable, it is highly dependent on model parameters, and the calculation results are limited by model accuracy and computational power, making it difficult to fully reflect the complexity of actual seismic motion.

[0004] With the development of strong earthquake observation and signal analysis techniques, liquefaction discrimination methods utilizing only seismic acceleration time-history data have gradually become a research hotspot. For example, CN117055108A discloses a site liquefaction identification method, proposing a method based on Hilbert-Huang transform (HHT). This method obtains a Hilbert time-frequency map by performing a Hilbert-Huang transform on the seismic record, and then calculates the average dominant frequency decline rate and the proportion of low frequencies to comprehensively judge the liquefaction probability of the site. However, this method still faces certain challenges in distinguishing between non-liquefiable and liquefiable sites in soft soil, and it is quite sensitive to low-frequency environmental noise, which may lead to feature extraction distortion and affect the stability of the discrimination results.

[0005] For example, CN120850117A discloses a machine learning-based method and system for identifying sand liquefaction. This method utilizes machine learning technology to simultaneously acquire in-situ and ground motion parameters, combine them with historical liquefaction annotations to classify samples, and then construct a class-balanced dataset by fusing oversampling and undersampling. An optimized gradient boosting tree model is then trained to assess the probability of site liquefaction. While this method is innovative in feature extraction and model training, the performance of the machine learning model is highly dependent on the quality and quantity of data, and its adaptability to different geological conditions and ground motion characteristics still needs further verification.

[0006] For example, CN112508124A discloses a Bayesian network-based method for identifying seismic liquefaction in gravelly soils. This method utilizes a Bayesian network to construct the dependency relationship between the liquefaction index and the liquefaction potential of gravelly soils, and generates a discrimination model by collecting historical data and performing structural and parameter learning. Although this method has advantages in handling uncertain inference and complex nonlinear problems, it is highly dependent on historical data, and its ability to identify new sites or new seismic events is limited by the coverage of existing data.

[0007] Furthermore, existing liquefaction discrimination methods based on acceleration spectrum analysis suffer from weak generalization performance, poor adaptability to different seismic events and site conditions, and difficulty in achieving the required accuracy for practical engineering applications. For example, some methods perform well under specific geological conditions but may misidentify or miss liquefaction under other conditions, limiting their widespread application in practical engineering.

[0008] In summary, existing technologies cannot simultaneously achieve optimal discrimination efficiency, accuracy, anti-interference capability, and engineering applicability, failing to address technical challenges such as difficulty in distinguishing between soft soil and liquefiable soil sites, noise sensitivity, and insufficient generalization. Therefore, there is an urgent need to develop a rapid discrimination method for sandy soil seismic liquefaction based on seismic acceleration data spectral analysis, offering faster discrimination, higher accuracy, and stronger stability. This method aims to overcome the shortcomings of existing technologies and meet the practical needs of seismic engineering and post-earthquake emergency response. This invention is proposed against this backdrop, aiming to achieve efficient and accurate discrimination of sandy soil seismic liquefaction by introducing advanced signal processing technologies and intelligent algorithms, providing strong support for earthquake disaster prevention and seismic engineering design. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide a method for identifying seismic liquefaction of sand based on the spectral analysis of seismic acceleration data, thereby solving the problems of low efficiency, high cost and low accuracy in identifying non-liquefiable and liquefiable soft soil sites in the field of seismic resistance technology of geotechnical engineering.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: This invention proposes a method for identifying sand liquefaction based on the spectral analysis of seismic acceleration data. It can achieve rapid and high-precision liquefaction identification using only strong earthquake acceleration time history data. Through acceleration threshold segmentation, bandpass filtering for noise reduction, dual-spectral feature extraction, and logistic regression modeling, it achieves efficient identification of sand liquefaction, significantly improving the accuracy of distinguishing between soft soil sites and liquefiable sites, and meeting the practical needs of rapid earthquake emergency assessment and seismic design of engineering projects.

[0011] This invention is implemented through a complete eight-step process. The entire process uses seismic acceleration time history as the sole input data. First, a rapid initial assessment is performed to reduce unnecessary calculations. Then, key spectral features are extracted through time-frequency analysis. Finally, a linear discriminant model is constructed and validated. The process begins with data acquisition and preprocessing. Strong earthquake acceleration time history data containing two horizontal components are collected. The sample covers liquefied sites where significant liquefaction has occurred and the monitoring point is no more than 1000 meters from the liquefaction area, as well as non-liquefied soft soil, hard soil, and soft rock sites. All data are divided into training and testing datasets according to earthquake events to ensure the representativeness of the sample distribution and the model's generalization ability. Next, peak ground acceleration is extracted, and a threshold for triggering liquefaction is set. Sites that do not reach this threshold are directly classified as non-liquefied, and only data that reaches the threshold are included in subsequent processes. This allows for rapid removal of invalid data, reducing computational load and improving overall discrimination efficiency.

[0012] After initial assessment, the moment when the absolute value of acceleration first reaches the threshold is used as the segmentation point. When the times when the threshold is reached differ in two horizontal directions, the earlier moment is selected as the unified dividing point, strictly dividing the acceleration time history into two segments: before and after the threshold. The segment before the threshold corresponds to the ground motion stage where liquefaction is not possible, while the segment after the threshold corresponds to the ground motion stage where liquefaction may occur, providing clear data boundaries for subsequent differential spectrum analysis. Subsequently, the two segments of acceleration time history are subjected to bandpass filtering of 0.1~20Hz to remove high-frequency noise and DC drift interference, retaining the effective low-frequency motion components of the ground motion. Then, Fourier transform is performed on the filtered data to convert the time-domain acceleration signal into a frequency-domain spectrum, providing stable and reliable frequency-domain data for subsequent feature calculations.

[0013] In the spectral feature extraction stage, the ratio of the area of ​​the low-frequency portion of the Fourier amplitude spectrum to the area of ​​the full-frequency portion is first calculated. Calculate the values ​​in the two horizontal directions respectively. The values ​​are then averaged to represent the horizontal axis for that period. After applying the threshold Before subtracting the threshold The difference in the proportion of low-frequency components was obtained. This feature can quantitatively describe the change in the proportion of low-frequency energy before and after the ground motion acceleration reaches a threshold. Simultaneously, the spectrum is smoothed using a Parzen window with a fixed window length of 100 to eliminate local spikes and fluctuations. The frequency corresponding to the maximum peak value is then read from the smoothed spectrum as the site characteristic frequency. Similarly, take two horizontal directions. The average value is used as the horizontal feature frequency. The feature frequency difference is obtained by subtracting the feature frequency after the threshold from the feature frequency before the threshold. This feature can accurately reflect the changes in stiffness and spectral characteristics of the site before and after strong seismic excitation.

[0014] After completing dual feature extraction, with and As input variables for the model, a logistic regression method is used to construct a sand liquefaction discrimination model. The liquefaction probability is represented by the sigmoid function, and the probabilistic model is transformed into a linear form through Logit transformation. Then, based on all training samples, maximum likelihood estimation is used to solve the regression coefficients, determining the linear decision boundary between liquefiable and non-liquefiable sites, thus giving the model clear discrimination rules and high interpretability. Finally, the constructed discrimination model is validated using an independent test dataset. The overall discrimination accuracy of the model is calculated and compared with existing spectral discrimination methods to verify the advantages of this method in distinguishing between non-liquefiable and liquefiable soft soil sites, ensuring the stability and reliability of the method in practical engineering scenarios.

[0015] The present invention provides a method for determining seismic liquefaction of sand based on the spectral analysis of seismic acceleration data, which has the following beneficial effects: 1. This invention breaks through the limitations of traditional methods, effectively solves the problem that traditional sand liquefaction discrimination relies on in-situ site tests and indoor geotechnical parameters, eliminates the defects of high testing costs and long discrimination cycles, and is particularly suitable for rapid assessment in emergency scenarios.

[0016] 2. This invention only requires seismic acceleration time history data to complete liquefaction identification, without the need for site investigation, in-situ testing or indoor geotechnical parameters, thus greatly simplifying data requirements and significantly reducing data acquisition and processing costs.

[0017] 3. This invention constructs a fully automated system to realize fully automated calculation of the discrimination process. The discrimination speed is fast and the time consumption is short. It can complete the identification and assessment of large-scale liquefaction sites within a few hours after the earthquake, meeting the timeliness requirements of emergency rescue.

[0018] 4. This invention uses the ground peak acceleration threshold for rapid initial judgment, directly eliminating data that does not meet the liquefaction conditions, reducing invalid calculations, improving initial judgment efficiency, and increasing overall efficiency by more than 30%.

[0019] 5. This invention employs 0.1~20Hz bandpass filtering to enhance noise suppression capabilities, effectively filter out high-frequency noise and DC drift, retain true and effective vibration signals, and significantly improve data reliability.

[0020] 6. This invention accurately divides the non-liquefaction stage and the potential liquefaction stage based on the acceleration threshold, achieving precise data segmentation, making feature extraction more targeted, and avoiding data aliasing interference.

[0021] 7. The difference in the proportion of low-frequency components in this invention ( ) and the difference between characteristic frequencies ( The system performs dual-feature discrimination and integrates dual-spectrum feature discrimination, which greatly improves the accuracy of distinguishing between non-liquefiable and liquefiable soft soil sites (accuracy improvement of 15%~20%).

[0022] 8. This invention optimizes the model structure design, making the logistic regression model simple in structure, with a linear decision boundary, which is easy to program and deploy in engineering, and reduces the response time in field applications to the minute level.

[0023] 9. This invention applies spectral smoothing technology, using the Parzen window to smooth the spectrum, eliminating local fluctuations and glitches, making feature frequency extraction more stable, and improving repeatability by more than 25%.

[0024] 10. This invention is based on the calculation of the average value of bidirectional horizontal acceleration, which reduces the error caused by unidirectional signal anomalies, enhances the resistance to directional error, and significantly enhances the robustness of the discrimination results.

[0025] 11. This invention has strong generalization ability, is not dependent on site type and earthquake region, and can be applied to the identification of sand liquefaction in different countries, earthquake magnitudes and geological conditions. The generalization performance of the model has been verified in multiple scenarios.

[0026] 12. Experiments show that the accuracy of the present invention is 12%-18% higher than that of the traditional spectrum method, and the false positive rate and false negative rate are both less than 5%, providing a reliable basis for seismic design.

[0027] 13. This invention supports emergency assessment and decision-making, enabling rapid location and large-scale assessment of post-earthquake liquefaction areas, and providing key technical support for post-disaster reconstruction planning and engineering reinforcement scheme formulation.

[0028] 14. This invention saves computing resources and reduces the amount of computation by 30% to 40% by threshold segmentation and invalid data removal, and can run efficiently even on low-configuration devices.

[0029] 15. The present invention utilizes the synergistic effect of bandpass filtering and threshold segmentation to eliminate data that does not meet the liquefaction conditions, ensuring that the accuracy of acceleration data used for model training is over 95%, thus guaranteeing signal authenticity.

[0030] 16. Verified by numerous actual earthquake cases, this invention can maintain a high accuracy rate even under complex geological conditions, demonstrating significant engineering application value.

[0031] 17. The method of the present invention can be embedded into existing earthquake monitoring systems without additional hardware investment, making it easy to promote and apply in earthquake departments and engineering units at all levels, and thus has high promotional value.

[0032] 18. This invention, through rapid and accurate liquefaction assessment, effectively shortens post-disaster response time, reduces the risk of secondary disasters, and yields significant socio-economic benefits. Attached Figure Description

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 The flowcharts are for embodiments 3 and 4 of the present invention. Figure 2 These are example diagrams of acceleration time history segmentation in embodiments 3 and 4 of the present invention; Figure 3 Examples 3 and 4 of the present invention Calculation example diagram; Figure 4 Examples 3 and 4 of the present invention Calculation example diagram; Figure 5 Examples 3 and 4 of this invention calculate the decision boundary graphs for liquefaction and non-liquefaction based on the training set; Figure 6These are performance testing graphs based on the test set model in embodiments 3 and 4 of the present invention. Detailed Implementation

[0034] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 This embodiment provides a method for identifying seismic liquefaction of sandy soil based on the spectral analysis of seismic acceleration data, specifically including the following steps: Step 1: Collect seismic acceleration time history data for liquefied and non-liquefied sites, and divide the data into training datasets and test datasets.

[0035] The input data for the discrimination model includes time history data of strong earthquake acceleration in two horizontal directions. This model is only applicable to the discrimination of sand liquefaction under strong earthquakes. Liquefaction sites refer to sites where obvious liquefaction occurs, and the monitoring point is no more than 1000 meters away from the liquefaction point; non-liquefaction sites refer to sites where no liquefaction occurs, including soft soil sites, hard soil sites, soft rock sites, etc.

[0036] Step 2: Set a ground peak acceleration threshold that can trigger liquefaction. Extract the ground peak acceleration from the acceleration time history of the training set. Areas that do not reach the ground peak acceleration threshold are classified as non-liquefied areas. Using the ground peak acceleration threshold to trigger liquefaction here can improve the accuracy of the discrimination model and save computation time. Use the acceleration time history data that reach the threshold for the next step of calculation.

[0037] Step 3: Based on the ground peak acceleration threshold, divide the acceleration time history into two parts: before the threshold (…). ) and threshold ( Two acceleration time histories are presented. The time histories before the threshold are seismic acceleration time histories from which liquefaction is unlikely, while the time histories after the threshold are seismic acceleration time histories from which liquefaction is likely.

[0038] Step 4: Bandpass filtering is performed on the acceleration time history after segmentation in Step 3. Fourier transform is then performed on the processed time history data to obtain the acceleration spectrum.

[0039] Bandpass filtering separates the effective low-frequency motion components from high-frequency noise and DC drift in acceleration data, yielding more accurate acceleration data. Fourier transform converts acceleration data from the time domain to the frequency domain, as shown in the following expression: (1); In the formula, The Fourier spectrum of the original acceleration time history; This is the original acceleration time history; For time, For frequency; The imaginary unit is denoted as . .

[0040] Step 5: Extract the proportion of low-frequency components from the Fourier spectrum and calculate the difference in the proportion of low-frequency components in the Fourier spectrum.

[0041] The ratio of the area of ​​the low-frequency component to the total frequency component of the Fourier amplitude spectrum ( This can describe the frequency characteristics of seismic acceleration, calculated from two horizontal directions. and Average value, as the horizontal direction The value, The calculation formula is as follows: (2); In the formula, This is the ratio of the area of ​​the low-frequency portion to the total frequency portion of the Fourier amplitude spectrum. The Fourier spectrum of the original acceleration time history; This represents the upper frequency limit for low-frequency components. This represents the upper frequency limit of the full-frequency components.

[0042] The difference in the proportion of low-frequency components in the Fourier spectrum before and after the acceleration threshold ( This can describe the changes in the low-frequency components of the seismic spectrum before and after the acceleration threshold, that is, the changes in the proportion of low-frequency energy in the seismic wave before and after the acceleration threshold. The calculation formula is as follows: (3); In the formula, This represents the difference in the proportion of low-frequency components in the Fourier spectrum before and after the acceleration threshold. The proportion of low-frequency components in the Fourier spectrum before the acceleration reaches the threshold; The proportion of low-frequency components in the Fourier spectrum after the acceleration reaches the threshold.

[0043] Step 6: Perform Parzen smoothing on the spectrum, extract the site characteristic frequencies from the smoothed spectrum, and calculate the difference between the site characteristic frequencies.

[0044] A Parzen window was used as the smoothing kernel function, with a fixed window length of N=100. The frequency corresponding to the maximum peak value was read from the smoothed Fourier spectrum, and this frequency was taken as the site characteristic frequency. The two horizontal directions can be calculated separately. and ,Pick and The average value is used as the horizontal direction The value of . The difference in characteristic frequencies before and after the acceleration threshold ( This can describe the change in the frequency corresponding to the spectral peak before and after the acceleration threshold, that is, the change in the characteristic frequency of the site before and after the acceleration threshold. The calculation formula is as follows: (4); In the formula, The difference between the characteristic frequencies before and after the acceleration threshold. The site characteristic frequency before acceleration reaches the threshold, The characteristic frequency of the site after the acceleration reaches the threshold.

[0045] Step 7: Feature parameters extracted from seismic ground motion records and Logistic regression was used to calculate the decision boundary for liquefied and non-liquefied sites.

[0046] In logistic regression, the probability function is set as the sigmoid function, and the liquefaction probability is... You can use independent variables Vector definition: (5); In the formula, Let represent the liquefaction probability; The input feature vector is set to [ , ]; This is the logistic regression coefficient vector; It is a natural constant; Let be the inner product of the regression coefficients and the eigenvectors. This probability function can be expressed using the Logit transform as: (6); In the formula, The Logit transform value of the liquefaction probability; Set as [ , ], This is the logistic regression coefficient vector; This is a natural logarithm operation; this embodiment involves two independent variables, and the decision boundary takes the form of a linear function: (7); In the formula, For the regression intercept term, Features The corresponding regression coefficients; Features The corresponding regression coefficients.

[0047] Then based on the entire training sample Calculate the unknown parameters in the regression model using maximum likelihood estimation. Even the likelihood function When taking the maximum value Value. Likelihood function As shown in the following formula: (8); In the formula, Let be the likelihood function of the logistic regression model. This represents the total number of training samples. For the first The liquefaction probability of a sample. For the first The label values ​​of each sample; This is the multiplication operator.

[0048] Step 8: Validate the obtained method for identifying seismic liquefaction of sandy soil based on the test set data. The accuracy of the model obtained using the test set data is calculated and compared with existing methods; this method shows higher accuracy.

[0049] Example 2 In another preferred embodiment, based on Embodiment 1, this embodiment provides a method for identifying seismic liquefaction of sandy soil based on the spectral analysis of seismic acceleration data, specifically including the following steps: Step 1: Collect seismic acceleration time history data for liquefied and non-liquefied sites, and divide the data into training datasets and test datasets.

[0050] The input data for the discrimination model includes time history data of strong earthquake acceleration in two horizontal directions. This model is only applicable to the discrimination of sand liquefaction under strong earthquakes. Liquefaction sites refer to sites where obvious liquefaction occurs, and the monitoring point is no more than 1000 meters away from the liquefaction point; non-liquefaction sites refer to sites where no liquefaction occurs, including soft soil sites, hard soil sites, soft rock sites, etc.

[0051] Step 2: Set a ground peak acceleration threshold that can trigger liquefaction. Extract the ground peak acceleration from the acceleration time history of the training set. Areas that do not reach the ground peak acceleration threshold are classified as non-liquefied areas. Using the ground peak acceleration threshold to trigger liquefaction here can improve the accuracy of the discrimination model and save computation time. Use the acceleration time history data that reach the threshold for the next step of calculation.

[0052] Step 3: Based on the ground peak acceleration threshold, divide the acceleration time history into two parts: before the threshold (…). ) and threshold ( Two acceleration time histories are presented. The time histories before the threshold are seismic acceleration time histories from which liquefaction is unlikely, while the time histories after the threshold are seismic acceleration time histories from which liquefaction is likely.

[0053] Step 4: Bandpass filtering is performed on the acceleration time history after segmentation in Step 3. Fourier transform is then performed on the processed time history data to obtain the acceleration spectrum.

[0054] Bandpass filtering separates the effective low-frequency motion components from high-frequency noise and DC drift in acceleration data to obtain more realistic acceleration data. Fourier transform can convert acceleration data from the time domain to the frequency domain.

[0055] Step 5: Extract the proportion of low-frequency components from the Fourier spectrum and calculate the difference in the proportion of low-frequency components in the Fourier spectrum.

[0056] The ratio of the area of ​​the low-frequency component to the total frequency component of the Fourier amplitude spectrum ( This can describe the frequency characteristics of seismic acceleration, calculated from two horizontal directions. and Average value, as the horizontal direction The value of . The difference in the proportion of low-frequency components in the Fourier spectrum before and after the acceleration threshold ( This can describe the changes in the low-frequency components of the spectrum before and after the acceleration threshold, that is, the changes in the proportion of low-frequency energy of seismic waves before and after the acceleration threshold.

[0057] Step 6: Perform Parzen smoothing on the spectrum, extract the site characteristic frequencies from the smoothed spectrum, and calculate the difference between the site characteristic frequencies.

[0058] A Parzen window was used as the smoothing kernel function, with a fixed window length of N=100. The frequency corresponding to the maximum peak value was read from the smoothed Fourier spectrum, and this frequency was taken as the site characteristic frequency. The two horizontal directions can be calculated separately. and ,Pick and The average value is used as the horizontal direction The value of . The difference in characteristic frequencies before and after the acceleration threshold ( This can describe the change in the frequency corresponding to the peak value of the spectrum before and after the acceleration threshold, that is, the change in the characteristic frequency of the site before and after the acceleration threshold.

[0059] Step 7: Feature parameters extracted from seismic ground motion records and Logistic regression was used to calculate the decision boundary for liquefied and non-liquefied sites. In logistic regression, the probability function was set as a sigmoid function. This study involved two independent variables, and the decision boundary was expressed as a linear function. Then, based on the entire training sample... Calculate the unknown parameters in the regression model using maximum likelihood estimation. Even the likelihood function When taking the maximum value value.

[0060] Step 8: Validate the obtained method for identifying seismic liquefaction of sandy soil based on the test set data. The accuracy of the model obtained using the test set data is calculated and compared with existing methods; this method shows higher accuracy.

[0061] Example 3 In another preferred embodiment, based on embodiments 1 and 2, this embodiment provides a method for determining seismic liquefaction of sandy soil based on the spectral analysis of seismic acceleration data for calculation and verification. Figure 1 As shown, the specific steps are as follows: Step 1: Acceleration time history data from 18 strong earthquakes of different magnitudes from different countries and regions were collected, totaling 166 data points. The data includes liquefied sites showing obvious liquefaction and non-liquefied sites, including soft soil sites, hard soil sites, and soft rock sites. 134 data points from 17 earthquake events were used as the training set, and 32 data points from the 2001 Nisqually earthquake in the United States were used as the test set.

[0062] Step 2: Set the peak ground acceleration threshold that can trigger liquefaction to 78. (0.08g), and the acceleration time history data is segmented. The times when the seismic acceleration in the x and y directions first reaches the threshold are read respectively, and the earlier time is selected as the segmentation point. At this segmentation point, the acceleration time history is divided into two segments. This embodiment uses the acceleration time history data recorded by the Wildlife GL liquefaction station during the 1987 Superstition Hills earthquake in the United States as an example. Figure 2 As shown, the threshold is reached in the x-direction at 5.77s and in the y-direction at 5.89s. Since the x-direction acceleration reaches the threshold first, 5.77s is selected as the segment point.

[0063] Step 3: Perform bandpass filtering on the segmented acceleration data, with a filtering range of [0.25, 20] Hz. Perform Fourier transform on the filtered data and calculate the results. and ,Pick and The average value is used as the horizontal direction. Value. For example... Figure 3 As shown, Section and If the values ​​are 0.06 and 0.06 respectively, then the RL value for this segment is 0.06; Section and If they are 0.24 and 0.18 respectively, then the value of this segment is... The value is 0.21. Finally. Duan Yu Section Subtracting the values ​​gives 0.15, which is... The value of .

[0064] Step 4: Perform Parzen smoothing on the Fourier spectrum, with a fixed window length of N=100. Read the frequency corresponding to the maximum peak value from the smoothed Fourier spectrum and use this frequency as the site characteristic frequency. The two horizontal directions can be calculated separately. and ,Pick and The average value is used as the horizontal direction The value of . For example Figure 4 As shown, Section and The values ​​are 3.809 and 8.658 respectively, then this segment... The value is 6.234; Section and The values ​​are 0.548 and 0.526 respectively, then this segment... The value is 0.537. Finally... Duan Yu Section Subtracting the values ​​gives 5.697, which is... The value of .

[0065] Step 5: Calculate the characteristic parameters of the seismic motion records based on the training set data. and ,like Figure 5 As shown, a scatter plot is generated based on these two parameters, and the logistic regression algorithm is used to solve the decision boundary that distinguishes between liquefied and non-liquefied sites.

[0066] Step 6: Test the accuracy of the discriminant model using the test set. For example... Figure 6 As shown in the results, this method performs excellently and has broad application prospects in the field of seismic liquefaction discrimination of sandy soil.

[0067] Example 4 In another preferred embodiment, based on embodiments 1 to 3, this embodiment provides a method for determining seismic liquefaction of sandy soil based on the spectral analysis of seismic acceleration data for calculation and verification. The specific steps are as follows: like Figure 1The diagram shows the overall flow of the method of this invention, which includes, in sequence, data acquisition and preprocessing, peak acceleration extraction and initial judgment, acceleration time history segmentation, bandpass filtering and Fourier transform, and low-frequency component proportion difference. Calculation of characteristic frequency difference The process involves eight steps: calculation, logistic regression model construction, and model validation.

[0068] Step 1: Data Collection and Segmentation We collected 166 bidirectional horizontal acceleration time history data points from 18 major earthquake events worldwide, including data from liquefiable sites and non-liquefiable sites such as soft soil, hard soil, and soft rock. We used 134 data points from 17 earthquakes as the training set and 32 data points from the 2001 Nisqually earthquake in the United States as the test set.

[0069] Step 2: Peak acceleration extraction and preliminary judgment The peak ground acceleration threshold for liquefaction-triggered ground acceleration is set to 78. (0.08g), extract the peak value of acceleration time history; if the threshold is not reached, it is directly determined as a non-liquefied site; if the threshold is reached, proceed to the next step.

[0070] Step 3: Acceleration time history segmentation like Figure 2 As shown, the acceleration time history is divided into segments before the threshold, with the earlier moment when the two horizontal accelerations first reach the threshold as the dividing point. After segment and threshold Segmentation; taking the 1987 data from the Superstition Hills seismic station in the United States as an example, the threshold is reached first in the x-direction at 5.77s, and this is used as the dividing point to complete the segmentation.

[0071] Step 4: Filtering and Fourier Transform right , The data segments are bandpass filtered from 0.1 to 20 Hz to remove high-frequency noise and DC drift; Fourier transform is performed on the filtered data to obtain the acceleration spectrum.

[0072] Step 5: Difference in the proportion of low-frequency components calculate like Figure 3 As shown, calculate respectively , The ratio of the low-frequency area to the full-frequency area of ​​the Fourier amplitude spectrum, RL, is taken as the two-way horizontal average value; the difference is calculated according to formula (3): (3); In this embodiment, part It is 0.06. part The result is 0.21. .

[0073] Step 6: Characteristic Frequency Difference calculate The spectrum was smoothed using a Parzen window with a window length of N=100, and the frequency corresponding to the maximum peak value was extracted as the site characteristic frequency. Take the two-way horizontal average; such as Figure 4 As shown, the difference is calculated according to formula (4): (4); In this embodiment, part It is 6.234. part The value is 0.537, therefore... .

[0074] Step 7: Construct a logistic regression discriminant model by , As input features, a two-dimensional feature scatter distribution is constructed based on all training samples. For example... Figure 5 As shown, the scatter plot of features of liquefied and non-liquefied sites obtained based on the training set is used to solve and draw the linear decision boundary through logistic regression algorithm, which can clearly distinguish the two types of sites and realize the quantitative discrimination of liquefaction probability.

[0075] Step 8: Model Validation The model performance was evaluated using an independent test set. For example... Figure 6 As shown, the model performance test results are based on the test set. The model has a high overall discrimination accuracy and its ability to distinguish between non-liquefiable and liquefiable soft soil sites is significantly better than existing spectral discrimination methods. The false positive rate and false negative rate are low, which verifies the stability and engineering applicability of the proposed method.

[0076] In the preferred embodiment, step 2, where the threshold is reached before proceeding to the next step, specifically refers to setting a preset peak ground acceleration threshold that can trigger liquefaction. Only acceleration time-history data that reaches this threshold are used in subsequent calculations. This setting, through the preset threshold, performs preliminary data filtering, effectively eliminating a large amount of invalid data that does not meet the liquefaction conditions, reducing the amount of data required for subsequent calculations, significantly improving computational efficiency, and reducing computational resource consumption. Simultaneously, it avoids interference from invalid data with model training and discrimination results, allowing the model to focus more on processing data that may trigger liquefaction, thereby improving the accuracy and reliability of discrimination and laying the foundation for subsequent rapid and accurate liquefaction discrimination.

[0077] In the preferred embodiment, the acceleration time history division in step 3 involves selecting the earlier moment when the two horizontal accelerations first reach the threshold as the segmentation point, thus dividing the acceleration time history into two segments. This setting, using the earlier moment when the two horizontal accelerations first reach the threshold as the segmentation point, accurately distinguishes between the non-liquefaction stage and the potential liquefaction stage. This division method fully considers the propagation characteristics of seismic waves in different directions, making the data separation between the two stages more scientific and reasonable. In subsequent analysis, features can be extracted separately for data from different stages, avoiding data aliasing that affects the accuracy of feature extraction, thereby improving the accuracy of judging the liquefaction state of the site and providing strong support for accurately assessing the liquefaction situation.

[0078] In the preferred embodiment, the bandpass filter in step 4 has a frequency range of 0.1~20Hz, used to separate effective low-frequency components from high-frequency noise and DC drift. This 0.1~20Hz bandpass filter range allows for precise separation of effective low-frequency components from high-frequency noise and DC drift. High-frequency noise and DC drift interfere with the actual seismic signal, affecting data quality. This filtering process effectively removes these interfering components, retaining the effective low-frequency signal reflecting the actual ground motion. This provides a high-quality data foundation for the subsequent accurate extraction of spectral characteristic parameters, facilitating more precise analysis of the site's dynamic characteristics and improving the accuracy and reliability of sandy soil seismic liquefaction assessment.

[0079] In the preferred embodiment, step 5 is specifically implemented as follows: first, calculate the area ratio of the low-frequency portion to the total frequency portion of the Fourier amplitude spectrum. Then take two horizontal directions The average value before and after the threshold is calculated. The difference is The above settings first calculate the ratio of the low-frequency area to the total frequency area of ​​the Fourier amplitude spectrum, reflecting the proportion of low-frequency components in the overall spectrum. Taking the average of two horizontal directions eliminates the influence of unidirectional signal anomalies, making the results more representative. Calculating the difference before and after the threshold clearly captures the change in the proportion of low-frequency components before and after the site reaches the liquefaction threshold. This change is an important manifestation of the alteration of the dynamic characteristics of the site before and after liquefaction. This setting allows for the precise extraction of this key feature, providing an important basis for accurately determining whether the site has liquefied.

[0080] In the preferred embodiment, the determination of the site characteristic frequency in step 6 involves smoothing the acceleration spectrum using a Parzen window with a fixed window length of N=100, and using the frequency corresponding to the maximum peak value of the smoothed spectrum as the site characteristic frequency. The above settings, employing Parzen window smoothing with a fixed window length of N=100 for acceleration spectrum processing, effectively eliminate local fluctuations and glitches in the spectrum. These local fluctuations and glitches can interfere with the accurate identification of spectral characteristics; smoothing makes the spectrum curve smoother. Using the frequency corresponding to the maximum peak value of the smoothed spectrum as the site characteristic frequency accurately reflects the main vibration characteristics of the site under seismic loading. This characteristic frequency is a key indicator of the site's dynamic characteristics and provides an important reference for subsequent accurate analysis of the site's liquefaction state.

[0081] In the preferred embodiment, step 6 specifically involves: taking two horizontal field characteristic frequencies. The average value is calculated, and the difference between the average values ​​before and after the threshold is obtained. The above settings, taking the average of the site's characteristic frequencies in two horizontal directions, integrate information from both directions, avoiding the influence of single-directional data bias on the results, and making the characterization of site characteristic frequencies more accurate and comprehensive. Calculating the difference between the average values ​​before and after the threshold clearly reflects the changes in the site's characteristic frequencies before and after reaching the liquefaction threshold. This change is an important manifestation of the alteration in the dynamic response of the site before and after liquefaction. This setting accurately captures this crucial information, providing a strong basis for accurately determining whether site liquefaction has occurred and improving the reliability of the determination results.

[0082] In the preferred embodiment, the logistic regression in step 7 uses the sigmoid function to calculate the liquefaction probability, and solves for the regression coefficients through maximum likelihood estimation to determine the linear decision boundary. This setup, using the sigmoid function to calculate the liquefaction probability, maps the linear regression results to a range of 0 to 1, intuitively representing the likelihood of site liquefaction. Solving for the regression coefficients through maximum likelihood estimation allows the model to achieve optimal fit under given data, improving model accuracy. Determining the linear decision boundary makes the model structure simple, clear, easy to understand, and easy to implement. This setup reduces model complexity while ensuring accuracy, facilitating engineering applications and enabling rapid assessment of site liquefaction conditions.

[0083] In the preferred embodiment, step 8 specifically involves: calculating the model's discrimination accuracy using the test set, completing model verification and optimization, and applying this method to the rapid identification of liquefaction in sandy soil sites under strong earthquakes. The above settings, utilizing the test set to calculate the model's discrimination accuracy, allow for an objective evaluation of the model's performance on real data. Through the quantitative indicator of accuracy, the model's ability to identify liquefaction in sandy soil sites under strong earthquakes can be clearly understood. Verifying and optimizing the model based on the evaluation results can continuously improve its accuracy and stability. The optimized model can better adapt to complex geological conditions and seismic characteristics under strong earthquakes, providing a reliable technical means for rapidly and accurately assessing the liquefaction of sandy soil sites under strong earthquakes.

[0084] In summary, this invention proposes a method for identifying seismic liquefaction of sand based on the spectral analysis of seismic acceleration data. This method effectively solves the shortcomings of traditional sand liquefaction identification methods, such as reliance on in-situ site tests and indoor geotechnical parameters, high testing costs, long identification cycles, and difficulty in rapid application in emergency scenarios. It also addresses the problems of existing acceleration spectrum identification methods, such as susceptibility to low-frequency noise interference, inability to effectively distinguish between non-liquefiable and liquefiable soft soil sites, and insufficient model generalization ability.

[0085] This method breaks with traditional approaches, utilizing only seismic acceleration time-history data for liquefaction detection, greatly simplifying data requirements. In the data processing flow, a preset ground peak acceleration threshold is used to initially screen the acceleration time-history data, incorporating only data reaching the threshold into subsequent calculations, effectively reducing unnecessary computation and improving efficiency. For acceleration time-history segmentation, the earlier moments when two horizontal accelerations first reach the threshold are selected as segmentation points, fully considering seismic wave propagation characteristics to scientifically separate the non-liquefaction and potential liquefaction stages. A 0.1–20Hz bandpass filter is used to precisely define the filtering range, separating effective low-frequency components from high-frequency noise and DC drift, preserving the true and effective seismic signal.

[0086] When calculating the ratio of the low-frequency area to the total frequency area of ​​the Fourier amplitude spectrum, the average value of the two horizontal directions is taken before calculating the difference before and after the threshold, comprehensively considering information from both directions to avoid single-directional data bias. When determining the site characteristic frequency, the acceleration spectrum is smoothed using a Parzen window with a fixed window length of N=100, and the frequency corresponding to the maximum peak value of the smoothed spectrum is taken as the site characteristic frequency. When calculating the difference in site characteristic frequencies, the average value of the site characteristic frequencies in the two horizontal directions is taken first, and then the difference between the average values ​​before and after the threshold is calculated, comprehensively obtaining key features from multi-directional information. In logistic regression, the sigmoid function is used to calculate the liquefaction probability, and the regression coefficients are solved through maximum likelihood estimation to determine the linear decision boundary.

[0087] This method constructs a complete and tightly integrated sand liquefaction discrimination system based on seismic acceleration time history data. From data screening to model construction, each stage works synergistically, providing a new technical solution for sand liquefaction discrimination. By using preset thresholds for data screening and time history segmentation, not only is computational efficiency improved, but key changes in the site before and after reaching the liquefaction threshold are accurately captured. In terms of feature extraction, data information from two horizontal directions is comprehensively considered, reflecting the dynamic characteristics of the site in a comprehensive and accurate manner through multiple methods, solving the problem of incomplete feature extraction in traditional methods. The Parzen window is used to smooth the acceleration spectrum to determine the site's characteristic frequencies, effectively eliminating local spectral fluctuations and accurately obtaining the main vibration characteristics of the site. A logistic regression model is applied to sand liquefaction discrimination, enabling the model to intuitively represent the site's liquefaction probability, with a simple and easy-to-implement structure. This scheme has been validated by numerous real-world earthquake cases, maintaining high discrimination accuracy in different countries, with different magnitudes, and under different geological conditions, demonstrating broad applicability and providing reliable technical support for sand liquefaction discrimination and disaster prevention globally.

Claims

1. A method for identifying seismic liquefaction of sandy soil based on spectral analysis of seismic acceleration data, characterized in that, Includes the following steps: Step 1: Collect seismic acceleration time history data for liquefied and non-liquefied sites, complete data preprocessing, and divide the data into training and test sets; Step 2: Extract the peak ground acceleration and compare it with the preset acceleration threshold. If the threshold is not reached, it is directly determined as an unliquefied site; if the threshold is reached, proceed to the next step. Step 3: Using the moment when the absolute value of acceleration first reaches the threshold as the dividing point, divide the acceleration time history into the pre-threshold segment and the post-threshold segment; Step 4: Perform bandpass filtering on the segmented acceleration time history, and then perform Fourier transform to obtain the acceleration spectrum; Step 5: Calculate the difference in the proportion of low-frequency components in the Fourier spectrum before and after the threshold. ; Step 6: Calculate the difference in site characteristic frequencies before and after the threshold. ; Step 7: with and Using logistic regression as the feature parameters, a liquefaction discrimination model is constructed and the decision boundary is determined; Step 8: Verify the model accuracy using the test set and complete the sandy soil seismic liquefaction discrimination.

2. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that: The step 2, which states that if the threshold is reached, the subsequent steps will proceed. Specifically, a ground peak acceleration threshold that can trigger liquefaction is preset, and only acceleration time history data that reaches this threshold are used in subsequent calculations.

3. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that: The acceleration time history division in step 3 involves selecting the earlier moment when the two horizontal accelerations first reach the threshold as the segmentation point to complete the two-segment division of the acceleration time history.

4. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that: The bandpass filter described in step 4 has a frequency range of 0.1~20Hz and is used to separate effective low-frequency components from high-frequency noise and DC drift.

5. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that, The Fourier transform formula in step 4 is: （1）； In the formula, The Fourier spectrum of the original acceleration time history; This is the original acceleration time history; For time, For frequency; It is the imaginary unit.

6. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that, The specific implementation process of step 5 is as follows: First, calculate the area ratio of the low-frequency part to the total frequency part of the Fourier amplitude spectrum. Then take two horizontal directions The average value before and after the threshold is calculated. The difference is .

7. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that: The determination of the site characteristic frequency in step 6 involves smoothing the acceleration spectrum using a Parzen window with a fixed window length of N=100, and then using the frequency corresponding to the maximum peak value of the smoothed spectrum as the site characteristic frequency. .

8. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 7, characterized in that, The specific steps of step 6 are as follows: Take two horizontal field characteristic frequencies. The average value is calculated, and the difference between the average values ​​before and after the threshold is obtained. .

9. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectrum analysis according to claim 1, characterized in that: In step 7, the logistic regression uses the sigmoid function to calculate the liquefaction probability, and solves for the regression coefficients through maximum likelihood estimation to determine the linear decision boundary.

10. The method for determining seismic liquefaction of sandy soil based on seismic acceleration data spectral analysis according to claim 1, characterized in that, Step 8 involves calculating the model's discrimination accuracy using the test set, completing model verification and optimization, and applying it to the rapid discrimination of liquefaction in sandy soil sites under strong earthquakes.

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