CN113009553A - Interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values - Google Patents
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Abstract
The invention discloses an interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values, which relates to the technical field of seismic engineering and comprises the following steps: step 1, determining a research area, collecting seismic event waveform and metadata information in the research area, analyzing and processing the seismic event waveform and the metadata information, and establishing a strong vibration database; step 2, carrying out data cleaning on the strong vibration data, and selecting data for machine learning model training; step 3, training a machine learning model for predicting the probability density distribution of earthquake motion parameters by using the selected strong vibration record and a natural gradient lifting algorithm; step 4, SHAP values of all characteristics of all samples are calculated, importance of each characteristic is analyzed according to the SHAP values, how earthquake motion parameter prediction is influenced is achieved, and a machine learning model is explained; and 5, predicting the probability density distribution of the earthquake motion parameters of the newly generated or supposed earthquake by using the trained machine learning model.
Description
Technical Field
The invention relates to the technical field of seismic engineering, in particular to an interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values.
Background
Casualties and property loss caused by earthquakes are mainly caused by the damage and collapse of building structures caused by strong ground movement. Strong ground movement is also a direct cause of secondary disasters such as landslides. After an earthquake, the rapid estimation of strong ground motion parameters (peak acceleration (PGA), peak velocity (PGV), peak displacement (PGD) and acceleration response Spectrum (SA)) can be used for judging the loss caused after the earthquake and guiding emergency rescue work. The method can be used for earthquake risk probability analysis and guiding city planning and design and construction of major projects (such as nuclear power stations, reservoir dams, sea-crossing bridges and the like) before earthquake, and can be used for predicting earthquake motion generated by imaginary earthquakes possibly occurring on dangerous faults.
There are three main methods for calculating or predicting seismic motion parameters: numerical simulation, seismic motion prediction equations (also commonly referred to as seismic motion attenuation relationships), and machine learning. Numerical simulation methods based on finite differences, finite elements, spectral elements or finite volumes, etc., have clear physical significance, but the simulation of high frequency seismic wavefields requires huge computational effort, as well as accurate seismic source and subsurface velocity structural models. The earthquake motion prediction equation has definite form and high calculation speed, and the method is generally used in earthquake motion graphs and probability earthquake risk analysis. However, the modern earthquake motion prediction equation is complex in form, the selection of the function form and the characteristic variable has no unified standard, the subjectivity is high, and the nonlinear coupling effect before each item cannot be considered.
With the development of artificial intelligence technology, more and more attention is paid to the earthquake motion parameter prediction by using a data-driven machine learning algorithm. The existing method for predicting earthquake motion parameters by utilizing machine learning can be mainly divided into two types. One is to obtain a function equation which can predict earthquake motion parameters by methods such as evolution modeling and the like. Unlike seismic motion prediction equations, such machine learning algorithms do not require a functional form to be assumed in advance, and functional equations are obtained by learning. Another type of machine learning method is seismic motion parameter prediction by training models such as decision trees, neural networks and the like. However, at present, the two types of algorithms have some problems: for example, a method for learning a seismic motion parameter prediction function equation limits the complexity of the equation to ensure the reasonableness of the equation, and the prediction accuracy is generally low. The method based on the decision tree and the neural network (especially the deep learning) has the disadvantages of complex model, high prediction precision and poor interpretability. In addition, the current machine learning method for earthquake motion parameter prediction cannot give uncertainty of a prediction result, and the method is more important for subsequent post-earthquake damage evaluation and probability earthquake risk analysis.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values, and provides a natural gradient boost (NGboost) algorithm for solving the uncertainty problem of seismic motion parameter prediction results. In order to solve the interpretability problem of the seismic motion parameter prediction machine learning model, the method provides a SHAP (Shapley Additive explantations) value for research on the importance of each characteristic and how to influence the prediction result, and carries out machine learning model interpretation.
The purpose of the invention is realized by the following technical scheme:
the interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values comprises the following steps:
and 5, predicting the probability density distribution of the earthquake motion parameters of the newly generated or supposed earthquake by using the trained machine learning model.
Preferably, the metadata information includes moment magnitude MwDistance of earthquake Rjb30m average S-wave velocity undergroundDegree VS30Fault top depth ZTORSliding angle Rake, fault Dip Dip and VSDepth Z up to 2.5km/s2.5。
Preferably, the seismic motion parameters include peak acceleration, peak velocity and peak displacement.
Preferably, the classification and regression tree is used as a basic learner for training the machine learning model in the step 3, and the logarithmic score is used as a scoring rule.
Preferably, the best hyper-parameters trained by the machine learning model are searched by adopting K-fold cross validation and grid search.
Preferably, the step 4 further comprises the following steps:
for each sample, the SHAP value φ for each feature i is calculatedi：
Wherein M represents the number of input features;
a set of all permutations representing the M features;
representing a set of all feature components preceding feature i in rank R; f. ofx(S)＝E[f(X)|Xs＝xS]And expressing the condition expectation under the condition of the known feature subset S, researching how each feature influences the earthquake motion parameter prediction according to the calculated SHAP value, judging the reasonability of the machine learning model if the earthquake motion parameter prediction conforms to the physical law.
The invention has the beneficial effects that:
1. the prediction of the probability density distribution of the seismic motion parameters is realized by introducing a natural gradient (NGboost) algorithm. Compared with the predicted value, the probability density distribution of the earthquake motion parameter is more important for the follow-up earthquake risk analysis.
2. The machine learning model interpretation is realized by calculating the SHAP value, how each characteristic influences the earthquake motion parameter prediction can be researched by using the SHAP value, and the rationality of the machine learning model is evaluated.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a comparison of the actual observed peak acceleration (PGA) to the predicted values of the machine learning model for the test set data;
FIG. 3 is a comparison of actual observed peak velocity (PGV) versus predicted values for a machine learning model for test set data;
FIG. 4 is a comparison of the actual observed peak displacement (PGD) versus the predicted values for the machine learning model for the test set data;
FIG. 5 is a once M for the California region of the United states in 2009wPredicting the probability density distribution of peak acceleration (PGA) given by a 4.45-level earthquake and machine learning model;
FIG. 6 is a once M for the California region of the United states in 2009wPredicting the probability density distribution of peak velocity (PGV) given by a 4.45-level earthquake and machine learning model;
FIG. 7 is a once M for the California region of the United states in 2009wPredicting the probability density distribution of peak displacement (PGD) given by a 4.45-level earthquake and machine learning model;
FIG. 8 is a SHAP summary of a peak acceleration (PGA) predictive machine learning model;
FIG. 9 is a SHAP summary of a peak velocity (PGV) predictive machine learning model;
FIG. 10 is a SHAP summary of a peak shift (PGD) predictive machine learning model;
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, the interpretable seismic motion parameter probability density distribution prediction method based on NGBoost and SHAP values in the embodiment is implemented according to the following steps:
the method comprises the following steps: determining a research area, collecting seismic event waveform and metadata information in the research area, analyzing and processing the seismic event waveform and the metadata information, and establishing a strong vibration database;
and selecting a research area according to requirements, and intercepting the waveform of the seismic event by using a seismic catalog provided by a seismic table network in the research area. If the research area is domestic, the earthquake catalog can adopt 'China Taiwan official earthquake catalog', and the earthquake event waveform can be obtained from the national earthquake scientific data center according to the earthquake catalog. If the area of study is foreign, an International Seismic Center (ISC) or the us geological survey (USGS) may be used to provide seismic catalogs, and seismic event waveforms may be downloaded from the american seismic research association (IRIS) or a local seismic grid website. For seismic event waveform data, only the east-west and north-south components are selected. Performing instrument response removing, mean removing, trend removing, baseline correction and band-pass filtering (0.1-30 Hz) on the seismic waveform data, rotating two orthogonal horizontal components to obtain a non-geometric average form (RotD50) irrelevant to the arrangement direction of an observation instrument, and measuring to obtain peak acceleration (PGA), peak velocity (PGV) and peak displacement (PGD). And collecting relevant literature data, and analyzing to obtain the seismic source, the propagation path and the field information metadata corresponding to the strong vibration record. The source information includes at least a moment magnitude (M)w) Fault top depth (Z)TOR) Sliding angle (Rake) and fault Dip angle (Dip). The propagation path information includes at least the epicenter distance (R)jb). The site information at least comprises the average S-wave velocity (V) of 30m undergroundS30) And VSDepth (Z) up to 2.5km/s2.5). If a better high-vibration database exists in the research area, the method can be directly used, such as the NGA-WEST2 high-vibration database in the United states and the ESM high-vibration database in the European-Mediterranean region.
Step two: cleaning data, and selecting strong vibration data for machine learning model training from a strong vibration database;
a jolt record is selected that occurs in the study area at a moment magnitude of 3.5 or greater and contains the necessary metadata information. And removing the incomplete or abnormal strong vibration record of the waveform. Remove strong shock recordings with large epicenter distances (greater than 350km) that may have systematic errors. And removing strong vibration records which cannot reflect the free field effect underground and above two-storey buildings. And removing the aftershock record.
Step three: training a machine learning model for predicting the probability density distribution of earthquake motion parameters by using the selected strong vibration record and a natural gradient boost (NGboost) algorithm;
the machine learning algorithm employs a Boosting algorithm based on natural gradients, which enhances a set of weak learners (base learners) to strong learners by the Boosting algorithm. The basic learner employs classification and regression trees. The scoring rules employ logarithmic scores. The selected strong vibration data are randomly divided into a training set (80%) and a testing set (20%), wherein the training set data are used for machine learning model training, and the testing set data are used for machine learning model evaluation. The input features include moment magnitude (M)w) Distance between earthquakes (R)jb) 30m average S-wave velocity (V) undergroundS30) Fault top depth (Z)TOR) Sliding angle (Rake), fault Dip angle (Dip) and VSDepth (Z) up to 2.5km/s2.5). And searching the optimal hyper-parameters (the maximum depth of the basic learner, the learning rate and the number of the basic learners) trained by the machine learning model by adopting K-fold cross validation and grid search.
Step four: and calculating SHAP values of all characteristics of all samples, analyzing the importance of each characteristic according to the SHAP values, and explaining a machine learning model on how to influence the earthquake motion parameter prediction.
For each sample, the SHAP value φ for each feature i is calculatedi：
Wherein M represents the number of input features;
a set of all permutations representing the M features;
representing a set of all feature components preceding feature i in rank R; f. ofx(S)＝E[f(X)|Xs＝xS]Indicating the conditional expectation for the case of a known feature subset S. The SHAP value represents the contribution of the feature i to the average case when taken to a particular value. According to the calculated SHAP value, the importance of each characteristic is researched, how the characteristics influence the earthquake motion parameter prediction is analyzed, whether the characteristics accord with the physical law or not is analyzed, and the rationality of the machine learning model is evaluated.
Step five: predicting the probability density distribution of the earthquake motion parameters of the newly generated or supposed earthquake by using the machine learning model trained in the third step;
when an earthquake occurs in a research area, characteristic parameters are input, and the peak acceleration (PGA), the peak speed (PGV) and the peak displacement (PGD) of the earthquake caused by the new earthquake can be obtained by using the machine learning model to guide emergency rescue work. When the future earthquake risk of the research area is analyzed, the earthquake motion condition caused by the earthquake once occurring in the dangerous fault in the area can be researched by using the machine learning model.
Example (b): in the embodiment, the method for constructing the interpretable seismic motion parameter probability density distribution prediction method based on the NGA-WEST2 strong vibration database by utilizing the NGBoost and the SHAP values is implemented according to the following steps:
the method comprises the following steps: determining a research area, collecting seismic event waveform and metadata information in the research area, analyzing and processing the seismic event waveform and the metadata information, and establishing a strong vibration database;
the NGA-WEST2 strong vibration database is a database which is established by the Pacific seismic engineering research center for developing the next generation seismic motion prediction equation. It is the most complete strong vibration database at present. In order to train a seismic motion parameter prediction machine learning model suitable for shallow crust earthquake, an NGA-WEST2 strong vibration database is selected. It contains 21529 seismic records of 599 earthquakes, along with corresponding metadata information.
Step two: cleaning data, and selecting data for machine learning model training from a strong vibration database;
for the NGA-WEST2 high vibration database, the data was further cleaned using the following criteria: (1) removing the strong vibration record lacking the necessary metadata information; (2) removing the strong vibration record with incomplete or abnormal waveform; (3) removing strong vibration records with system errors possibly existing when the epicenter distance is too large (more than 350 km); (4) removing strong vibration records which cannot reflect the free field effect underground and above two-storey buildings; (5) and removing the aftershock record. Finally, 12107 recordings of 282 earthquakes were used for training of the machine learning model.
Step three: training a machine learning model for predicting the probability density distribution of earthquake motion parameters by using the selected strong vibration record and a natural gradient boost (NGboost) algorithm;
the selected NGA-WEST2 strong vibration data are randomly divided into a training set (80%) and a testing set (20%), wherein the training set data are used for machine learning model training, and the testing set data are used for machine learning model evaluation. Using moment-magnitude (M) simultaneouslyw) Distance between earthquakes (R)jb) 30m average S-wave velocity (V) undergroundS30) Fault top depth (Z)TOR) Sliding angle (Rake), fault Dip angle (Dip) and VSDepth (Z) up to 2.5km/s2.5) As an input feature. And training the machine learning model by adopting a natural gradient boost (NGboost) algorithm. The basic learner adopts classification and regression trees, and the scoring rule adopts logarithmic score. And searching for the optimal hyper-parameters (the maximum depth of the basic learner, the learning rate and the number of the basic learners) by adopting K-fold cross validation and grid search. For the PGA, PGV and PGD prediction machine learning models in this example, the maximum depths of the basic learners are respectively 7, 6 and 6, the learning rates are respectively 0.01, the numbers of the basic learners are respectively 233, 284 and 302, and the performance of the corresponding machine learning models is optimal.
Step four: and calculating SHAP values of all characteristics of all samples, analyzing the importance of each characteristic according to the SHAP values, and explaining a machine learning model on how to influence the earthquake motion parameter prediction.
For the peak acceleration (PGA), peak velocity (PGV) and peak displacement (PGD) predictive machine learning model, the SHAP value of each feature of each sample is calculated. From the calculated SHAP values, SHAP summary maps of the peak acceleration (PGA), peak velocity (PGV), and peak displacement (PGD) predictive machine learning models are plotted (FIGS. 8, 9, and 10). In the SHAP abstract diagram, the features are arranged from top to bottom according to the importance, and each point representsIn one example, the X-axis represents the magnitude of the characteristic SHAP value, and the color scale represents the magnitude of the characteristic value. The SHAP abstract diagram shows the importance of each feature and the effect on seismic motion. As can be seen in FIGS. 8, 9 and 10, the moment magnitude (M)w) Distance between earthquakes (R)jb) And 30m mean S-wave velocity (V) undergroundS30) The prediction of seismic motion parameters is most important. Predicting a machine learning model for peak acceleration (PGA), peak velocity (PGV), and peak displacement (PGD), MwThe SHAP values of all follow MwIncrease in value, RjbThe SHAP value of each depends on RjbIncrease and decrease in value, VS30All SHAP values ofS30The increase and decrease of the value are consistent with the existing research, which shows that the trained machine learning model is reasonable and reliable.
Step five: predicting the probability density distribution of the earthquake motion parameters of the newly generated or supposed earthquake by using the machine learning model trained in the third step;
for the test set data, we predicted peak acceleration (PGA), peak velocity (PGV) and peak displacement (PGD) using machine learning models. The comparison of the predicted values and actual observed values for the machine learning model is shown in fig. 2, 3, and 4. All points in fig. 2, 3 and 4 are located near the dashed line with a slope of 1, which illustrates that the trained machine learning model can give an accurate prediction. For the peak acceleration (PGA), the peak velocity (PGV) and the peak displacement (PGD) prediction machine learning models, the correlation coefficients of the predicted value and the true value are 0.972, 0.984 and 0.990, which are higher than all currently known earthquake motion parameter prediction machine learning models based on the NGA-WEST2 strong vibration database. For first time M in the California region of 2009 USAw4.45-level earthquakes, probability density distributions of peak acceleration (PGA), peak velocity (PGV) and peak displacement (PGD) were predicted using machine learning models (fig. 5, 6 and 7). About 84% of the points in fig. 5, 6 and 7 are located within the 85% confidence interval, which illustrates that the trained machine learning model can predict the probability density distribution of peak acceleration (PGA), peak velocity (PGV) and peak displacement (PGD) well.
The foregoing is merely a preferred embodiment of the invention, it being understood that the embodiments described are part of the invention, and not all of it. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. The invention is not intended to be limited to the forms disclosed herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (6)
1. The interpretable seismic motion parameter probability density distribution prediction method based on NGboost and SHAP values is characterized by comprising the following steps of:
step 1, determining a research area, collecting seismic event waveform and metadata information in the research area, analyzing and processing the seismic event waveform and the metadata information, and establishing a strong vibration database;
step 2, carrying out data cleaning on the strong vibration data, and selecting data for machine learning model training;
step 3, training a machine learning model for predicting the probability density distribution of earthquake motion parameters by using the selected strong vibration record and a natural gradient lifting algorithm;
step 4, SHAP values of all characteristics of all samples are calculated, importance of each characteristic is analyzed according to the SHAP values, how earthquake motion parameter prediction is influenced is achieved, and a machine learning model is explained;
and 5, predicting the probability density distribution of the earthquake motion parameters of the newly generated or supposed earthquake by using the trained machine learning model.
2. The method of predicting NGBoost and SHAP value-based interpretable seismic motion parameter probability density distribution according to claim 1, wherein the metadata information includes moment magnitude MwDistance of earthquake RjbUnderground 30m average S-wave velocity VS30Fault top depth ZTORSliding angle Rake, fault Dip Dip and VSDepth Z up to 2.5km/s2.5。
3. The method of predicting NGBoost and SHAP value-based interpretable seismic motion parameter probability density distribution according to claim 1, wherein the seismic motion parameters include peak acceleration, peak velocity, and peak displacement.
4. The method for predicting the probability density distribution of the interpretable seismic motion parameter based on the NGboost and the SHAP values as claimed in claim 1, wherein the classification and regression tree is adopted by a basic learner for training the machine learning model in the step 3, and the logarithmic score is adopted by a scoring rule.
5. The method of predicting the probability density distribution of interpretable seismic motion parameters based on NGBoost and SHAP values of claim 3, wherein K-fold cross validation and grid search are employed to search for the best hyperparameters trained by machine learning models.
6. The method of predicting the probability density distribution of interpretable seismic motion parameters based on NGBoost and SHAP values of claim 1, wherein the step 4 further comprises:
for each sample, the SHAP value φ for each feature i is calculatedi：
Wherein M represents the number of input features;
a set of all permutations representing the M features;
representing all preceding features i in the arrangement RA set of feature components; f. ofx(S)＝E[f(X)|Xs＝xS]And expressing the condition expectation under the condition of the known feature subset S, researching how each feature influences the earthquake motion parameter prediction according to the calculated SHAP value, judging the reasonability of the machine learning model if the earthquake motion parameter prediction conforms to the physical law.
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