A recursive method for online automatic identification of seismic events
By combining recursive graphs with quantitative indicators, the problem of real-time identification and early warning of seismic events in bridge health monitoring is solved, realizing rapid and accurate seismic event monitoring and early warning, which is applicable to bridge health monitoring systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGAN UNIV
- Filing Date
- 2024-12-12
- Publication Date
- 2026-05-12
AI Technical Summary
Existing methods for real-time monitoring and early warning of earthquake events in bridge health monitoring suffer from poor real-time processing, low automation, and difficulty in timely identification and alarm.
By employing recursive graphs and improved recursive quantification indicators, and through phase space reconstruction, recursive graph drawing, and quantitative analysis, automatic identification and real-time early warning of seismic events can be achieved.
It enables rapid and accurate identification and real-time early warning of earthquake events, adapts to noisy random signals, reduces human intervention, and meets the real-time online requirements for bridge health monitoring.
Smart Images
Figure CN119716967B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of earthquake event identification and early warning in bridge health monitoring, and relates to an automatic earthquake event identification and early warning method. Background Technology
[0002] Real-time online monitoring and early warning of earthquake events is a crucial aspect of bridge health monitoring. Existing research methods mainly include the long-short window ratio method, the Akaike information criterion, machine learning, and integrated analysis algorithms combining various methods. However, existing methods suffer from poor real-time processing and low automation, making real-time monitoring and early warning of seismic events challenging and unable to provide timely decision-making recommendations for bridge maintenance. Summary of the Invention
[0003] To address the shortcomings of existing technologies, the present invention aims to provide a recursive method for online automatic identification of earthquake events. This method introduces a recursive graph and improved recursive quantification indicators to solve the problems of low accuracy, unintuitive results, and low timeliness in earthquake event identification, thereby enabling graphical display and real-time early warning of earthquake events.
[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0005] A recursive method for online automatic identification of earthquake events includes the following steps:
[0006] Step 1, Phase Space Reconstruction: The phase space of the seismic event time series is reconstructed using the delayed coordinate method, and the optimal embedding dimension and optimal delay time required for phase space reconstruction are determined.
[0007] Step 2, Draw the recursion graph: Draw the recursion graph of the phase space reconstruction results and determine the parameters required for drawing the recursion graph;
[0008] Step 3, Determine the recursive quantification index: Perform quantitative analysis on the recursive graph to obtain the earthquake identification quantification index;
[0009] Step 4: Based on the distribution patterns of earthquake identification and quantitative indicators, issue early warnings for earthquake events.
[0010] The present invention also includes the following technical features:
[0011] Specifically, in step 1, the phase space reconstruction of the time series is performed as follows:
[0012] X(i)={x(i),x(i+τ),...,x(i+(m-1)τ)}
[0013] In the formula, X(i) is the time series matrix after phase space reconstruction, i represents time; x(i+(m-1)τ) represents the time series at time i+(m-1)τ; m is the embedding dimension, and τ is the delay time.
[0014] Specifically, in step 1, the process of determining the optimal embedding dimension includes: determining the embedding dimension m using the false neighbor method: defining the time series x(t) as a series of phase point vectors in the m-dimensional phase space, solving for its false neighbor points, calculating the proportion of false neighbor points corresponding to different embedding dimensions to determine the optimal embedding dimension, and when the proportion of false neighbor points is less than 5% or the false neighbor points no longer decrease with the increase of m, the corresponding dimension is the optimal embedding dimension.
[0015] Specifically, in step 1, the process of determining the optimal delay time includes: determining the delay time τ using the mutual information method: defining the time series x(t) and the time series x(t+τ) with delay time τ as two discrete sequences, and calculating the mutual information I(τ) between the two sequences based on the principle of information theory; if I(τ) = 0, then x(t+τ) and x(t) are uncorrelated; the minimum value of I(τ) indicates that x(t+τ) and x(t) are most likely uncorrelated; the first minimum point in I(τ) is the optimal delay time.
[0016] Specifically, in step 2, the recursive graph is a graph composed of 0-1 matrices described by different colors and two time axes. The distance between any two vectors is defined as follows:
[0017]
[0018] In the formula: R i,j It is a two-dimensional square matrix of order N-(m-1)·τ, where i,j represent the time moments i and j, and N is the state vector. The number of elements, m is the embedding dimension, τ is the delay time, ε is the cutoff threshold, ||·|| represents the Euclidean norm, Θ(·) represents the Heaviside function, Θ(x≤0)=0; Θ(x>0)=1; in the recursion graph, different R i,j The values are represented using two easily distinguishable colors.
[0019] Specifically, the cutoff threshold ε is selected using a dynamic threshold method, with the selection criterion being 20% of the maximum phase space diameter r. m ;
[0020] When ε≥r m When ε < r, all points are recursive points, and the recursion graph is pure black; when ε < r m At this time, the signal will be divided into recursive points and non-recursive points, and the recursion graph is composed of intersecting black and white lines.
[0021] Specifically, in step 3, the earthquake identification quantification index T R :
[0022]
[0023] In the formula: N represents the number of sampling points in the recursion graph; TT is the average vertical line in the recursion graph; RR is the recursion rate; the value range of TT is [0, N / 2], and the value range of RR is [0, 1].
[0024] Specifically, the formula for calculating TT is as follows:
[0025]
[0026] In the formula, N represents the number of sampling points in the recursion graph, v represents the length of the vertical line in the recursion graph, and v min Let v represent the minimum vertical line length, and P(v) be the probability distribution of the vertical line of length ν in the recursive graph.
[0027] Specifically, the RR calculation formula is as follows:
[0028]
[0029] In the formula, N represents the number of sampling points in the recursion graph, i,j represents the time step i,j, and R... i,j (ε) is the recursive value.
[0030] Specifically, in step 4, when the earthquake identification quantification index T... R If the distribution is near 0, it is a random signal; when the earthquake identification quantification index T... R If the value approaches 1 and the distribution range is (0.8, 1], then it is an earthquake signal, and an earthquake early warning can be issued.
[0031] Compared with the prior art, the present invention has the following technical effects:
[0032] This invention uses recursive graphs to visualize phase space reconstruction results to analyze the characteristics of dynamic systems. Recursive graphs provide a more intuitive way to observe and understand the nonlinear characteristics of dynamic systems. Seismic event signal identification is based on improved recursive quantization indices, which are simple to calculate with low computational cost and enable fast seismic event identification. Recursive graphs are highly adaptable to noisy random signal data, and the indices are stable. Using the improved recursive quantization indices, real-time online seismic event identification can be achieved without any manual intervention.
[0033] The method of this invention is a seismic motion signal identification method based on recursive graphs. It combines recursive quantification indicators to provide early warning of earthquakes and proposes new alarm indicators based on the relationship between earthquake intensity and acceleration.
[0034] This invention utilizes seismic time-history signals acquired from accelerometers placed at locations such as bridge abutments and anchorages. During an earthquake, the time-history signals exhibit significant abrupt changes, resulting in distinct black and white stripes on the recurrence relation. In contrast, the structural response under random environmental excitation is non-stationary, time-varying, and random, exhibiting multimodal random vibration. These differences are used as distinguishing factors for the monitoring and identification of seismic events.
[0035] Faced with massive amounts of earthquake monitoring data, this invention can automatically, quickly, and accurately identify earthquake signals, meeting the basic requirements for real-time online bridge health monitoring. Attached Figure Description
[0036] Figure 1 This is a schematic diagram of the principle framework of the method of the present invention.
[0037] Figure 2 The spurious nearest neighbor method is used to determine the dimension of the embedded phase space.
[0038] Figure 3 The mutual information method is used to determine the delay time map.
[0039] Figure 4 It is a recursive graph of a random signal.
[0040] Figure 5 This is a recursive diagram of earthquake signals.
[0041] Figure 6 This is a comparison chart of the maximum acceleration amplitude of an earthquake and recursive quantification indicators.
[0042] Figure 7 This is a cloud map showing the results of 21 earthquakes in the bridge site area from 2020 to 2023.
[0043] Figure 8 This is an image from a multi-channel earthquake sensor. Detailed Implementation
[0044] This invention provides a recursive method for online automatic identification of earthquake events. First, phase space reconstruction is performed on the time series of earthquake events, and the parameters required for phase space reconstruction are determined. Then, a recursive graph is plotted on the phase space reconstruction results, and the parameters required for plotting the recursive graph are determined. Next, a recursive quantification index for earthquake events is determined based on the characteristics of the recursive graph, and the warning threshold is determined by comparing the recursive quantification index with the earthquake signal time history curve. Finally, an early warning is issued for earthquake events based on the set warning threshold. Figure 1 Specifically, it includes the following steps:
[0045] Step 1, Phase Space Reconstruction
[0046] The phase space of the chaotic time series is reconstructed using the delayed coordinate method to extract more information from the time series. The following formula represents the reconstruction of the time series:
[0047] X(i)={x(i),x(i+τ),...,x(i+(m-1)τ)}
[0048] In the above formula, X(i) is the time series matrix after phase space reconstruction, i represents time; x(i+(m-1)τ) represents the time series at time i+(m-1)τ, m is the embedding dimension, and τ is the delay time. Therefore, the parameters required for the above phase space reconstruction are the embedding dimension m and the delay time τ.
[0049] As can be seen from the coordinate delay method formula, phase space reconstruction requires determining two parameters: the delay time τ and the embedded phase space dimension m. The embedding dimension and time delay must be selected based on the actual situation; otherwise, the quality of the phase space reconstruction will be affected. The specific selection method is as follows:
[0050] The spurious neighbor method is used to determine the embedding dimension m. In this embodiment, the optimal embedding dimension m = 4. The time series x(t) is defined as a series of phase point vectors in an m-dimensional phase space, and its spurious neighbor points are calculated. The spurious neighbor method determines the optimal embedding dimension by calculating the proportion of spurious neighbor points corresponding to different embedding dimensions. It can be considered that when the proportion of spurious neighbor points is less than 5% or when the number of spurious neighbor points no longer decreases with increasing m, the corresponding dimension is the optimal embedding dimension. (See Appendix) Figure 2 .
[0051] The mutual information method is used to determine the delay time τ. In this embodiment, the optimal delay time τ = 4. The response evolution of a complex system like a bridge structure is inevitably a nonlinear process, and the mutual information method is precisely used to determine the correlation of nonlinear systems. The time series x(t) and the time series x(t+τ) with delay time τ are defined as two discrete sequences. Based on the principles of information theory, the mutual information I(τ) between the two sequences is calculated. Given x(t), if the magnitude of I(τ) is also known, the deterministic magnitude of x(t+τ) can be calculated. If I(τ) = 0, then x(t+τ) and x(t) are uncorrelated. The minimum value of I(τ) indicates that x(t+τ) and x(t) are most likely uncorrelated. The first minimum point in I(τ) is the optimal delay time τ, as shown in the appendix. Figure 3 .
[0052] Step 2, draw the recursion graph
[0053] Phase space reconstruction is a prerequisite for drawing a recursive graph, which is a visual representation of the reconstructed phase space. After step 1, the optimal embedding dimension and optimal delay time were determined, and phase space reconstruction was performed. The recursive graph is then drawn. The recursive graph is a graph composed of 0-1 matrices described by different colors and two time axes. The distance between any two vectors is defined as follows:
[0054]
[0055] In the formula: R i,j It is a two-dimensional square matrix of order N-(m-1)·τ, where i,j represent the time moments i and j, and N is the state vector. The number of elements, m is the embedding dimension, τ is the delay time, ε is the cutoff threshold, ||·|| represents the Euclidean norm, Θ(·) represents the Heaviside function, Θ(x≤0)=0; Θ(x>0)=1.
[0056] In the recursion graph, different R i,j The values are represented using two easily distinguishable colors.
[0057] The cutoff threshold ε is an empirical value, and different values can significantly affect the plotting and quantitative analysis of the recursive graph. The recursive threshold selection method for seismic signal identification is the dynamic threshold method, with the selection criterion being 20% of the maximum phase space diameter (r). m To prevent interference from abrupt noise, for signals with an amplitude less than 0.1, a maximum phase space diameter of 1% (r) is selected. m That's all.
[0058] The aforementioned maximum phase space diameter r m This describes the maximum distance between orbits i and j within a system, i.e.:
[0059] r m =max|x i -x j |
[0060] When ε≥r m When ε < r, all points are recursive points, and the recursion graph is pure black. m At this time, the signal will be divided into recursive points and non-recursive points, and the recursion graph is composed of intersecting black and white lines.
[0061] Step 3, Determine the recursive quantitative indicators
[0062] Recurrence graphs are tools for qualitative signal analysis; quantitative analysis of recurrence graphs can quantify seismic signals, laying the foundation for automatic seismic event identification. This study selects the average vertical line length (Trapping time, TT) for analysis, and combines it with the recurrence rate (RR) to reduce it, resulting in the seismic identification quantification index T. R :
[0063]
[0064] In the formula: N represents the number of sampling points in the recursion graph; TT is the average vertical line in the recursion graph, indicating that some states of this signal change slowly or not at all at certain times, i.e., stagnant states. This index is calculated by ensuring that all values reach the minimum length ν. min The average length of the vertical lines is used to estimate the average dwell time of the signal under certain conditions. The calculation formula is as follows:
[0065]
[0066] In the formula, N represents the number of sampling points in the recursion graph, v represents the length of the vertical line in the recursion graph, and v min This represents the minimum vertical line length, which is 2. P(v) is the probability distribution of a vertical line of length ν in the recursive graph. R i,j The value is the recursive value, and k is a natural number.
[0067] RR is the recursion rate, which is calculated by taking the percentage of black points in the entire recursion graph. It represents the degree of clustering of phase points in phase space and the recursion frequency. The formula is as follows:
[0068]
[0069] In the formula, N represents the number of sampling points in the recursion graph, i,j represents the time step i,j, and R... i,j (ε) is the recursive value.
[0070] TT has a value range of [0, N / 2], and RR has a value range of [0, 1].
[0071] For random signals, the vertical line length distribution range is narrow and mainly concentrated in the short vertical line region. The average vertical line length and the maximum vertical line length are both small, and the recurrence rate RR approaches 0.
[0072] For seismic signals, the vertical line length distribution is relatively wide and uniform, with the average vertical line length TT approaching [a certain value]. The maximum vertical line value is close to N, and the recursion rate RR approaches 1.
[0073] In summary, the quantization index T of a random signal R The value tends towards 0, while for seismic signals, the value tends towards 1.
[0074] Step 4, determine and issue an early warning:
[0075] Based on the distribution pattern of the above-mentioned quantitative indicators, when a random signal occurs, the overall acceleration signal shows a relatively small degree of abrupt change, and this quantitative indicator T... RIt is distributed around 0; when an earthquake occurs, the degree of abrupt change in the acceleration signal intensifies, and the greater the degree of change, the higher the quantitative index T becomes. R The larger the value, the greater the earthquake alarm T. R The range is (0.8, 1).
[0076] The following are specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments. All equivalent modifications made based on the technical solutions of this application fall within the protection scope of the present invention.
[0077] Example:
[0078] Using actual earthquake monitoring data from multiple earthquakes in the vicinity of a cross-sea bridge site from 2020 to 2023, an identification test was conducted to verify the accuracy of the identification method. The earthquake information statistics for this period are shown in the table below:
[0079] Table 1. Earthquake statistics of a cross-sea bridge site area from 2020 to 2023.
[0080]
[0081]
[0082] Note 1: Except for the epicentral distance, all the above data are from seismic networks; the epicentral distance is an approximate estimate.
[0083] Note 2: Criteria for event selection: earthquakes within 300 km of the bridge site area with a magnitude of 2.0 or higher.
[0084] Note 3: Seismic intensity estimation formula: I = 4.493 + 1.454M - 1.792Ln(R + 16.0).
[0085] Note 4: The seismic station is some distance from the bridge site, and the monitoring data of the strong motion instrument at the bridge site has a certain lag, with the identification time lagging behind the seismic network by 1-2 minutes.
[0086] The identification results using the method of this invention are as follows: Figure 5 As shown. Because earthquake signals occur at a fixed time and propagate over a wide area, they can be detected by multiple sensors; while noise signals at different times are random, propagate over a limited area, and are generally detected by only a single sensor. For example... Figure 6 As shown, comparative analysis can be performed using multi-channel sensors. When the multi-channel verification conditions are met, an alarm is triggered, which can further improve the recognition accuracy.
[0087] e = sum([0 / 1]) 1×N ) / N
[0088]
[0089] In the formula: N represents the number of sensors, and multi-channel verification is triggered only when 3 sensors are present; 0 / 1 represents the earthquake criterion, where 1 indicates that an earthquake signal has been detected; e represents the proportion of multiple sensors that trigger an alarm. This indicates the results of multi-sensor verification, with 1 indicating that an earthquake alarm was ultimately triggered.
[0090] This invention combines recursive graphs and recursive quantization indices for the automatic identification of special seismic events. The false nearest neighbor method is used to determine the optimal embedding dimension *m*, and mutual information is used to determine the time delay *τ*. For seismic signal identification, a new quantization index *T* is proposed, combining the average vertical line length and the recursion rate. R The accuracy of this indicator was verified by measuring earthquakes at the bridge site of a cross-sea bridge from 2020 to 2023. The accuracy will be further improved when multiple strong-motion seismometers are used for joint identification and calibration.
[0091] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.
[0092] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.
[0093] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.
Claims
1. A recursive method for online automatic identification of earthquake events, characterized in that, Includes the following steps: Step 1, Phase Space Reconstruction: The phase space of the seismic event time series is reconstructed using the delayed coordinate method, and the optimal embedding dimension and optimal delay time required for phase space reconstruction are determined. Step 2, Draw the recursion graph: Draw the recursion graph of the phase space reconstruction results and determine the parameters required for drawing the recursion graph; Step 3, Determine the recursive quantification index: Perform quantitative analysis on the recursive graph to obtain the earthquake identification quantification index; Step 4: Based on the distribution patterns of earthquake identification and quantitative indicators, issue early warnings for earthquake events; In step 1, the phase space reconstruction of the time series is performed as follows: In the formula, The time series matrix after phase space reconstruction. Indicates time; Indicates the first Time series of moments; For the embedding dimension, For delay time; In step 1, the process of determining the optimal embedding dimension includes: determining the embedding dimension using the spurious nearest neighbor method. Define time series for Given a series of phase point vectors in a phase space, find their spurious neighbors. Calculate the proportion of spurious neighbors for different embedding dimensions to determine the optimal embedding dimension. The optimal embedding dimension is determined when the proportion of spurious neighbors is less than 5% or when spurious neighbors no longer follow the embedding. When the dimension increases and decreases, the corresponding dimension is the optimal embedding dimension; In step 1, the process of determining the optimal delay time includes: determining the delay time using the mutual information method. Define time series With delay time time series Given two discrete sequences, calculate their mutual information based on information theory principles. ;like ,but and Irrelevant; The minimum value of represents and It is the most likely to be unrelated; The first local minimum point in the time interval is the optimal delay time. In step 2, the recursive graph is a graph composed of 0-1 matrices described by different colors and two time axes. The distance between any two vectors is defined as follows: In the formula: It is A two-dimensional square matrix of order 1. Indicates the first time, It is a state vector Quantity, It is the embedding dimension. It is a delay time. It is the cutoff threshold. Denotes the Euclidean norm. express function, In a recursive graph, different The values are represented using two easily distinguishable colors; In step 3, earthquake identification quantification indicators : In the formula: N represents the number of sampling points in the recursion graph; TT is the average vertical line in the recursion graph; and RR is the recursion rate. The value range is [0, N / 2]. The value range is [0,1]; The cutoff threshold The selection method is the dynamic threshold method, and the selection criterion is 20% of the maximum phase space diameter. ; when When all points are recursive points, the recursion graph is pure black; when At this time, the signal will be divided into recursive points and non-recursive points, and the recursion graph is composed of intersecting black and white lines; The formula for calculating TT is as follows: In the formula, N represents the number of sampling points in the recursion graph. This represents the length of the vertical line in the recursion graph. Indicates the minimum vertical line length. For a recursive graph of length The probability distribution of vertical lines; In step 4, when the earthquake identification quantification index If the distribution is near 0, it is a random signal; when the earthquake identification quantification index If the value approaches 1 and the distribution range is (0.8, 1], then it is an earthquake signal, and an earthquake early warning can be issued.
2. The recursive method for online automatic identification of earthquake events as described in claim 1, characterized in that, The formula for calculating RR is as follows: In the formula, N represents the number of sampling points in the recursion graph. Indicates the first time, This is a recursive value.