CN117075192B - Multi-parameter-based method for establishing earthquake slope permanent displacement prediction model - Google Patents
Multi-parameter-based method for establishing earthquake slope permanent displacement prediction model Download PDFInfo
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Abstract
The invention relates to a multi-parameter-based method for establishing a permanent displacement prediction model of a seismic slope, which selects high-correlation seismic vibration parameters by comprehensively considering correlation between a plurality of parameters recorded by seismic vibration and permanent displacement of the slope, screens permanent displacement model parameters based on variation rate and growth rate, establishes a multi-type permanent displacement prediction model, and adopts indexes such as fitting goodness, standard deviation and the like to select an optimal displacement model. The invention has important significance for preventing and relieving the earthquake disasters, can provide scientific basis and technical support for preventing and relieving the earthquake disasters, and contributes to the construction of a safe, stable and sustainable society.
Description
Technical Field
The invention relates to the technical field of seismic monitoring, in particular to a method for establishing a seismic slope permanent displacement prediction model based on multiple parameters.
Background
Earthquake is a common natural disaster, and the earthquake has very remarkable influence on the surface topography and the topography. Under the action of strong earthquake, the earth surface can generate severe vibration and deformation, and the deformation often causes geological disasters such as landslide, mud-rock flow and the like. Earthquake landslide hazard is a common geological hazard and is extremely dangerous. Earthquake landslide disasters are often caused by geological disasters such as landslide, collapse or rock mass sliding caused by earthquakes, and soil and stone bodies can slide downwards or move forwards to cause serious casualties and property loss.
The earthquake slope permanent displacement prediction model is one of important methods for researching earthquake disasters, the earthquake slope permanent displacement is generally used for measuring the stability of an earthquake slope, the larger the permanent displacement is, the worse the slope stability is, and the magnitude of the earthquake slope permanent displacement is related to factors such as earthquake vibration, the geometrical shape of the slope, the physical and mechanical parameters of a rock-soil body and the like. Therefore, how to implement the prediction of the seismic slope displacement by the seismic slope permanent displacement prediction model is a problem to be considered at present.
It should be noted that the information disclosed in the above background section is only for enhancing understanding of the background of the present disclosure and thus may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for establishing a seismic slope permanent displacement prediction model based on multiple parameters, which can realize seismic slope risk evaluation through the seismic slope permanent displacement prediction model.
The aim of the invention is achieved by the following technical scheme: a method for establishing a prediction model of a permanent displacement of a seismic slope based on multiple parameters comprises the following steps:
establishing a seismic vibration database, classifying and calculating seismic vibration parameters, and calculating permanent displacement of the movable slide block;
carrying out correlation analysis on the earthquake motion parameters and the calculated permanent displacement through weighted average correlation coefficients, selecting the earthquake motion parameters with the weighted average correlation coefficients exceeding a first preset value to carry out linear correlation analysis on the earthquake motion parameters and the parameters, calculating to obtain Pearson correlation coefficients, and taking the earthquake motion parameters with the Pearson correlation coefficients meeting a second preset value as selection items in the construction of a displacement model;
evaluating the difference of the strongly related parameters on the model prediction effect by adopting the growth rate and the variation rate, selecting the earthquake motion parameters according to the model parameter selection principle, inputting the earthquake motion parameters into each type of model, and establishing a permanent displacement prediction model;
and comparing and analyzing the prediction effect among various models and the influence of the number of the earthquake parameters in the models on the model prediction effect through the fitting goodness and the standard deviation, selecting a permanent displacement prediction model with high fitting goodness and small standard deviation, comparing the number of the parameters in the model, and selecting a model with few parameters as an optimal permanent displacement prediction model.
The calculation formula of the Pearson correlation coefficient is as follows:
wherein IM i A parameter indicating the ith seismic effort,mean value of earthquake motion parameters, D Ni Representing the permanent displacement corresponding to the ith earthquake motion, < ->The average value of permanent displacement corresponding to all earthquake motions is shown, and the PCC absolute value ranges from 0.8 to 1, the two variables show extremely strong correlation, the strong correlation ranges from 0.6 to 0.8, the medium correlation ranges from 0.4 to 0.6, the weak correlation ranges from 0.2 to 0.4, and the extremely weak correlation or the uncorrelation ranges from 0 to 0.2.
The calculation formula of the weighted average correlation coefficient is as follows:
wherein, representing the weighted average correlation coefficient between the seismic parameters and the permanent displacement, N i Indicating the number of permanent displacements, N, meeting the condition at the ith critical acceleration total Sum of critical acceleration amounts, PCC, representing compliance at all critical accelerations i Representing Pearson correlation coefficients between eligible permanent displacements and the seismic parameters at the ith critical acceleration.
The calculation formula of the growth rate is as followsAnd->The calculation formula of the mutation rate is ∈>Wherein R is g(IM1) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM1 to the permanent displacement prediction model, R g(IM2) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM2 to the permanent displacement prediction model, R v Representing the variability of the parameters to the permanent displacement prediction model between IM1 and IM2, R 2 (IM1,IM2) Representing the goodness of fit of the model when parameters IM1 and IM2 are applied simultaneously in the predictive model, R 2 (IM1) Representing the goodness of fit of the model when only parameter IM1 is applied in the predictive model, R 2 (IM2) Representing the goodness of fit of the model when only parameter IM2 is applied in the predictive model, IM1 and IM2 representing different seismic parameters.
The model parameter selection principle comprises the following steps:
when R is g(IM1) ＝R g(IM2) ＝R v When the parameter is=0, the two parameters are considered to be equivalent in the permanent displacement prediction model, only one of the parameters is selected at the moment, and only one of the parameters is considered when the parameter pair correlation analysis is carried out;
when R is g(IM1) And R is g(IM2) When the predictive effect of the two parameters in each model is equal to that of the model, only the earthquake motion parameters with high comprehensive relevance to the permanent displacement are selected at the moment;
when R is g(IM1) Less than 3% in each type of predictive model, R g(IM2) When more than 3% of the 5-type prediction model exists, the lifting effect of the parameter IM2 on the IM1 is considered to be poor, and the lifting effect of the parameter IM1 on the IM2 is considered to be good, which indicates that the IM1 can replace the condition that two parameters exist simultaneously, so that only the IM1 is selected during parameter screening; similarly, when R g(IM2) Less than 3% in each type of predictive model, R g(IM1) When more than 3% of the prediction models exist, only IM2 is selected during parameter screening;
when R is g(IM1) And R is g(IM2) When more than 3% of all the prediction models exist, the two parameters are considered to have good fitting effect on the permanent displacement prediction model compared with one parameter, and at the moment, the situation that one parameter is not used for replacing the two parameters exists at the same time cannot be replaced, so that the two parameters are not discarded and are selected as the alternative parameters of the permanent displacement prediction model.
The calculation formulas of the goodness of fit and the standard deviation are respectively as follows:
wherein,D Ni representing the permanent displacement corresponding to the ith earthquake motion, < ->Mean value representing the permanent displacement corresponding to all seismic vibrations, < >>Representing the predicted permanent displacement corresponding to the ith earthquake motion, SS tot Representing the sum of the squares of the permanent displacements, SS res Representing the sum of squares of the residuals of the permanent shifts, when R 2 >At 0.8, the correlation between the two variables is high.
The following 5 types of permanent displacement prediction models are obtained through arrangement and analysis of the earthquake slope permanent displacement prediction model:
logD N ＝A1+A2loga c +A3logIM1+A4logIM2+A5logIM3+A6logIM4+A7logIM5+A8logIM6
logD N ＝B1+B2log[(1-a c /PGA) B3 (a c /PGA) B4 ]+B5logIM1+B6logIM2+B7logIM3+B8logIM4+B9logIM5+B10logIM6
logD N ＝C1+C2loga c +C3log 2 a c +C4loga c logIM1+C5logIM1+C6log 2 IM1+C7logIM2+C8logIM3+C9logIM4+C10logIM5+C11logIM6
logD N ＝C1+C2loga c +C3log 2 a c +C4loga c logIM1+C5logIM1+C6log 2 IM1+C7loga c logIM2+C8logIM2+C9log 2 IM2+C10logIM3+C11logIM4+C12logIM5+C13logIM6
logD N ＝D1+D2(a c /PGA)+D3(a c /PGA) 2 +D4(a c /PGA) 3 +D5(a c /PGA) 4 +D6logIM1+D7logIM2+D8logIM3+D9logIM4+D10logIM5+D11logIM6
wherein A1, A2, A3 … …, B1, B2, B3 … …, C1, C2, C3 … …, and D1, D2, D3 … … each represent coefficients of a permanent displacement prediction model, and IM1, IM2, IM3 … … represent different earthquake motion parameters.
The establishing the earthquake motion database comprises the following steps: based on the NGA database, record data which simultaneously contain two horizontal earthquake motions and one vertical earthquake motion are selected, the earthquake motion record data are identified by utilizing a multi-component impulse classification algorithm, and an impulse earthquake motion database is established.
The classification and calculation of the earthquake motion parameters comprise: the earthquake motion parameters are divided into five categories of earthquake motion parameters including time duration, peak value, reaction spectrum, energy and pulse according to the physical meaning of the earthquake motion parameter representation, the five categories of earthquake motion parameters comprise 73 parameter indexes, and the parameter value of each earthquake motion record is calculated according to the calculation formula of each parameter index.
The invention has the following advantages: the method for establishing the earthquake slope permanent displacement prediction model based on multiple parameters has important significance for preventing and relieving earthquake disasters, can provide scientific basis and technical support for preventing and relieving the earthquake disasters, and contributes to the construction of a safe, stable and sustainable society.
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FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, which are generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Accordingly, the following detailed description of the embodiments of the present application, provided in connection with the accompanying drawings, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, are intended to be within the scope of the present application. The invention is further described below with reference to the accompanying drawings.
The invention particularly relates to a multi-parameter-based method for establishing a permanent displacement prediction model of an earthquake slope, which can be used for establishing the permanent displacement prediction model of the earthquake slope, further can be applied to regional earthquake landslide hazard research, and is characterized in that the earthquake vibration parameters with high correlation are selected by comprehensively considering the correlation between a plurality of parameters recorded by earthquake vibration and the permanent displacement of the slope, the permanent displacement model parameter screening is carried out based on the mutation rate and the growth rate, the establishment of the multi-type permanent displacement prediction model is carried out, and the optimal displacement model is selected by adopting the indexes such as fitting goodness, standard deviation and the like.
As shown in fig. 1, the following are specifically included:
s1, establishing a earthquake motion database: the portion of the seismic record that contains both 3 directions (2 horizontal directions seismic and 1 vertical direction seismic) is selected based on the NGA database. And identifying the earthquake motion records by utilizing a multi-component pulse classification algorithm, and establishing a pulse earthquake motion database.
S2, classifying and calculating earthquake motion parameters: the earthquake motion parameters are divided into 73 indexes such as duration type, peak value type, reaction spectrum type, energy type and pulse type according to the physical meaning expressed by the earthquake motion parameters, and the parameter value of each earthquake motion record is obtained according to various parameter calculation modes.
Wherein, hold the time class and include: time duration (Duration of the record, T), period of superiority (Predominant period, tp), period of average (Mean period, tm), period of spectrum of superiority of smoothing (Smoothed spectral predominant period, T0), moment of center of square acceleration (Tc), moment of energy (Td), moment of energy k, energy distribution characteristic parameter mu k Time of importance (Significant duration, D) s5-75 ) Time of importance (Significant duration, D) s5-95 ) Cycle of seismic characteristics (Characteristic period, T) g ) Strong vibration(s) 0 ) Main period of the earthquake (Predominant period of the ground motion, T) 1 ) Sub-period of earthquake motion (T 2 ) Zero point number (v) 0 ) Average zero point number) 16 parameters;
the peak classes include: peak ground acceleration (Peak ground acceleration, PGA), sustained maximum acceleration (Sustained Maximum Acceleration, SMA), peak ground speed (Peak ground velocity, PGV), sustained maximum speed (Sustained Maximum Velocity, SMV), peak ground displacement (Peak ground displacement, PGD), peak ground displacement to acceleration ratio (PGD/PGA), peak ground speed to acceleration ratio (PGV/PGA), composite acceleration correlation index (Compound acc.— related intensity measure, I a ) Compound speed related index (Compound level-related intensity measure, I) v ) Compound displacement related index (Compound acc. -related intensity measure, I) d ) 12 parameters such as Fajfar Index (FI);
the reaction profile classes include: acceleration response spectrum intensity (Acceleration spectrum intensity, ASI), effective peak acceleration (Effective peak acceleration, EPA), peak acceleration response spectrum (Peak acceleration of response spectrum, PSA), effective design acceleration (Effective design acceleration, EDA), acceleration response spectrum with period of 0.2s (Acceleration of response spectrum at 0.2.2 s, s) a,T＝0.2 ) Acceleration response spectrum with period of 1s (Acceleration of response spectrum at s, S a,T＝1 ) Velocity response spectrum intensity (Velocity spectrum intensity, VSI), peak velocity response spectrum (Peak velocity of response spectrum, PSV), housner intensity (Housner Intensity, I) H ) Effective peak velocity (Effective peak velocity, EPV), peak shift response spectrum (Peak displacement of response spectrum, PSD), shift response spectrum with period 1s (5784 s, S) d,T＝1 ) Shift response spectrum with period of 2s (Displacement of response spectrum at s, S d,T＝2 ) Shift response spectrum with period 3s (Displacement of response spectrum at s, S d,T＝3 ) Shift response spectrum with period 4s (Displacement of response spectrum at s, S d,T＝4 ) 15 parameters;
the energy classes include: ariiasi intensity (Ar)ias Intensity,I A ) Acceleration index (Acceleration parameter, A) 95 ) Square Root of acceleration (Root-square of acceleration, A) rs ) Root mean square (Root-mean-square of acceleration, A) RMS ) Characacteristic intensity (Characteristic Intensity, I) C ) Destructive potential factors (Destructiveness Potential Factor, P D ) Integrated absolute velocity (Cumulative absolute velocity, CAV), seismic power (Power of the seismic excitation, P) a5-75 ) Ground vibration power (Power of the seismic excitation, P) a5-95 ) Specific energy density (Specific energy density, SED), square Root of velocity (Root-square of velocity, V) rs ) Root mean square (Root-mean-square of velocity, V) RMS ) Cumulative absolute displacement (Cumulative absolute displacement, CAD), seismic power (Power of the seismic excitation, P) v5-95 ) Square Root of displacement (Root-square of displacement, D rs ) Root mean square (Root-mean-square of displacement, D) RMS ) Ground vibration power (Power of the seismic excitation, P) d5-95 ) Square of peak ground displacement to root mean square of displacement (PGD) 2 /D RMS ) A specific reference energy index (Specific referential energy, r (t)), a seismic energy index (I D ) 20 parameters;
the pulse class parameters include: pulse period (T) pulse ) Peak ground velocity Pulse (PGV) p ) Peak ground speed ratio (PGV radio), pulse energy (SED) p ) Pulse residual Energy ratio (Energy ratio), baker pulse index (Pulse indicator of Baker, PI) B ) Energy pulse index (E) p ) Pulse index (Pulse indicator of Mukhopadhyay, PI) M ) Shahi pulse index (Pulse indicator of Shahi, PI) S ) Kardoutsou pulse index (Pulse indicator of Kardoutsou, PI) K ) Etc. 10 parameters.
S3, calculating permanent displacement of the movable sliding block:
the invention adopts a coupling power sliding block method to calculate the permanent displacement, and the calculation mode is as follows:
wherein u (y, t) represents the displacement of the sliding block in the forward slope direction in the dynamic sliding block model,representing the ith order mode function, Y i (t) represents an ith order generalized modal coordinate, y represents a height from a column top, t represents time, and H represents a height of a side slope.
To simplify the calculation, the method considers only the 1 st order mode shape function, i.e., the mode shape number n is 1. Thereby obtaining the equation of motion of the system as follows:
wherein lambda is the damping ratio of viscous material, M 1 Is a generalized mass, representing the mass distributed along the height of the system, L 1 Is the earthquake accelerationM (y) represents a landslide system unit with respect to a parameter of a system height and a vibration mode functionHigh quality, V s Is the shear wave velocity, omega of the material 1 Representing the first order circular frequency of the landslide system. In a distributed mass system, the force exerted by the seismic vibrations is +.>And in the total mass system +.>
For a landslide body motion system, when the ground vibration input load at the bottom of the system exceeds the friction strength between the sliding block and the landslide base, the sliding block generates speed relative to the base, so that displacement is generated. When considering only the case of downward movement of the slider along a slope, the system is in a transitional state on the shear plane between the slider and the base, and the equilibrium equation in this state is:
in the method, in the process of the invention,force generated for seismic loading ∈ ->For the internal force of the material, μ is the coefficient of friction at the bottom of the structure, which is the value corresponding to the critical acceleration a of the system c The same applies.
After the system state breaks through the critical condition and generates permanent displacement, the motion equation of the sliding block is as follows:
wherein s represents the difference between the displacement of the slider and the displacement of the base,representing the sliding inertial force.
The equilibrium equation on the shear plane between the slider and the base also changes:
equations (8) and (9) define the equilibrium conditions for a sliding, deformable system. Substituting equation (9) into equation (8) yields:
the above formula represents the system balance equation of the slider in the motion process, and when the speed of the slider becomes 0 again, the control equation of the system becomes formula (3) again. And continuously repeating the process under the action of the earthquake load, and finally calculating the permanent displacement under the condition of the flexible side slope.
S4, correlation analysis between earthquake motion parameters and displacement and correlation analysis between parameters:
the correlation between the seismic parameters and the permanent displacements (obtained in step S3) calculated by the bi-directional-coupling model was analyzed by Pearson correlation coefficient (Pearson correlation coefficient, PCC) as follows:
in IM i A parameter indicating the ith seismic effort,representing an average value of the seismic parameters; d (D) Ni Representing the permanent displacement corresponding to the ith earthquake motion, < ->The average of all seismic vibrations corresponding to permanent displacements is shown. Wherein the PCC exhibits extremely strong correlation between two variables in the range of 0.8 to 1, strong correlation in the range of 0.6 to 0.8, medium correlation in the range of 0.4 to 0.6, weak correlation in the range of 0.2 to 0.4, and extremely weak or no correlation in the range of 0 to 0.2.
In order to better analyze the correlation between the seismic parameters and the permanent displacement, the invention provides a weighted average correlation coefficient between the seismic parameters and the permanent displacement, and the calculation formula is as follows:
in the method, in the process of the invention,representing the weighted average correlation coefficient between the seismic parameters and the permanent displacement, N i Indicating the number of permanent displacements, N, meeting the condition at the ith critical acceleration total Sum of critical acceleration amounts, PCC, representing compliance at all critical accelerations i Representing Pearson correlation coefficients between eligible permanent displacements and the seismic parameters at the ith critical acceleration.
Selecting based on the weighted average correlation coefficient calculated by equation (14)Seismic parameters exceeding 0.7, performing linear correlation analysis between the seismic parameters and the parameters, and calculatingThe Pearson correlation coefficient is obtained. When the correlation coefficient is close to 12, the representative parameters are almost completely correlated, and 1 is selected when the displacement model is built.
S5, classifying permanent displacement prediction models:
the following 5 types of permanent displacement prediction models are obtained through arrangement and analysis of the earthquake slope permanent displacement prediction models:
where A1, A2, A3 … … and B1, B2, B3 … … and C1, C2, C3 … … and D1, D2, D3 … … represent coefficients of a permanent displacement prediction model, and IM1, IM2, IM3 … … represent different seismic parameters.
S6, establishing a permanent displacement prediction model:
according to the analysis of the step S4, the earthquake motion parameters with the comprehensive correlation coefficient exceeding 0.7 between the permanent displacement are selected as the alternative parameters under the whole earthquake motion database. In order to study the influence of strong correlation between earthquake and vibration parameters on the fitting effect of a permanent displacement prediction model, two indexes of an increase rate and a variation rate are provided for evaluating the difference of the strong correlation parameters on the model prediction effect. Wherein the growth rate represents the degree of improvement of the fitting effect of the prediction model by simultaneously applying two earthquake motion parameters compared with the use of only one parameter, and the calculation expression is shown in the formula (21) and the formula (22); the variation rate represents the degree of difference of the fitting effect of the permanent displacement prediction model between two earthquake motion parameters, and the calculation expression is shown in the formula (23):
wherein R is g(IM1) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM1 to the permanent displacement prediction model, R g(IM2) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM2 to the permanent displacement prediction model, R v Representing the variability of the parameters to the permanent displacement prediction model between IM1 and IM2, R 2 (IM1,IM2) Representing the goodness of fit of the model when parameters IM1 and IM2 are applied simultaneously in the predictive model, R 2 (IM1) Representing the goodness of fit of the model when only parameter IM1 is applied in the predictive model, R 2 (IM2) The goodness of fit of the model when only parameter IM2 is applied in the predictive model is represented.
Further, the model parameter selection principle is as follows:
(1) For all 5 types of permanent displacement prediction models, when R g(IM1) ＝R g(IM2) ＝R v When the value is=0, the two parameters are considered to be equivalent in the permanent displacement prediction model, so that only one of the parameters is selected, and only one of the parameters is considered when the correlation analysis is performed;
(2) When R is g(IM1) And R is g(IM2) When less than 3% of all 5-class predictive models, then both parameters are considered to be at 5The prediction effect in the class model is almost equivalent, so that only the earthquake motion parameters with higher comprehensive correlation with permanent displacement are selected;
(3) When R is g(IM1) Less than 3% in all class 5 predictive models, and R g(IM2) When more than 3% of the 5-type prediction model exists, the lifting effect of the parameter IM2 on the IM1 is considered to be poor, and the lifting effect of the parameter IM1 on the IM2 is considered to be good, which indicates that the IM1 can replace the condition that two parameters exist simultaneously, so that only the IM1 is selected during parameter screening; similarly, when R g(IM2) Less than 3% in all class 5 predictive models, and R g(IM1) When more than 3% of the 5-class prediction model exists, only selecting IM2 during parameter screening;
(4) When R is g(IM1) And R is g(IM2) When more than 3% of the 5-class prediction model exists, the fitting effect of the two parameters on the permanent displacement prediction model is considered to be obviously improved compared with that of one parameter, and one parameter cannot be used for replacing the condition that the two parameters exist at the same time, so that the two parameters are not discarded and are selected as the alternative parameters of the permanent displacement prediction model.
And (5) carrying the selected earthquake motion parameters into each model type, and establishing a permanent displacement prediction model.
S7, model comparison analysis:
by fitting goodness (R 2 ) And standard deviation (sigma) to analyze the effect of prediction between 5 models, the influence of the number of earthquake motion parameters in the model on the effect of prediction on the model, and the goodness of fit R 2 The calculation formula of (2) is shown as formula (27), and the calculation formula is as follows:
wherein D is Ni Representing the permanent displacement corresponding to the ith seismic event,the average of all seismic vibrations corresponding to permanent displacements is shown. />Representing the predicted permanent displacement corresponding to the ith seismic motion. SS (support System) tot Total sum of squares (Total sum of square) representing permanent displacement, SS res Representing the sum of squares of the residuals of the permanent displacement (Residual sum of square). Goodness of fit (Goodless of fit, R 2 ) Also called a decision coefficient (Coefficient of determination) which indicates the correlation strength between two parameters, R 2 The larger the value, the higher the interpretation degree of the independent variable to the dependent variable, and the larger the influence degree of the variation of the independent variable to the dependent variable, the more the scatter diagram is gathered near the fitted regression curve, and R is generally considered 2 >At 0.8, the correlation between the two variables is high.
The calculation formula of the standard deviation is shown in formula (28):
in the formula, the parameter meanings are as shown in formulas (24) to (27). The standard deviation sigma, also called the mean square error, is the arithmetic square root of the variance, and can reflect the degree of dispersion of data, and is a non-negative value. The larger the standard deviation of a set of data, the larger the difference between the data value and the majority of the predicted values; conversely, the smaller the standard deviation of the data, the closer the representative majority of the predicted value is to the data value.
According to the calculation result, selecting the goodness of fitR 2 And finally, selecting a model with good fitting effect and few model parameters as an optimal model by comparing the quantity of parameters in the model.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and environments and is capable of modifications within the scope of the inventive concept, either as taught or as a matter of routine skill or knowledge in the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (7)
1. A method for establishing a seismic slope permanent displacement prediction model based on multiple parameters is characterized by comprising the following steps: the prediction model building method comprises the following steps:
establishing a seismic vibration database, classifying and calculating seismic vibration parameters, and calculating permanent displacement of the movable slide block;
carrying out correlation analysis on the earthquake motion parameters and the calculated permanent displacement through weighted average correlation coefficients, selecting the earthquake motion parameters with the weighted average correlation coefficients exceeding a first preset value to carry out linear correlation analysis on the earthquake motion parameters and the parameters, calculating to obtain Pearson correlation coefficients, and taking the earthquake motion parameters with the Pearson correlation coefficients meeting a second preset value as selection items in the construction of a displacement model;
evaluating the difference of the strongly related parameters on the model prediction effect by adopting the growth rate and the variation rate, selecting the earthquake motion parameters according to the model parameter selection principle, inputting the earthquake motion parameters into each type of model, and establishing a permanent displacement prediction model;
analyzing the prediction effect among various models and the influence of the number of earthquake parameters in the models on the model prediction effect through comparison of the fitting goodness and the standard deviation, selecting a permanent displacement prediction model with high fitting goodness and small standard deviation, comparing the number of parameters in the model, and selecting a model with few parameters as an optimal permanent displacement prediction model;
the calculation formula of the growth rate is as followsAnd->The calculation formula of the mutation rate is ∈>Wherein R is g(IM1) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM1 to the permanent displacement prediction model, R g(IM2) Representing the growth rate of the parameter pair IM1 and IM2 relative to the single parameter IM2 to the permanent displacement prediction model, R v Representing the variability of the parameters to the permanent displacement prediction model between IM1 and IM2, R 2 (IM1,IM2) Representing the goodness of fit of the model when parameters IM1 and IM2 are applied simultaneously in the predictive model, R 2 (IM1) Representing the goodness of fit of the model when only parameter IM1 is applied in the predictive model, R 2 (IM2) Representing the goodness of fit of the model when only parameter IM2 is applied in the predictive model, IM1 and IM2 representing different seismic parameters;
the model parameter selection principle comprises the following steps:
when R is g(IM1) ＝R g(IM2) ＝R v When the parameter is=0, the two parameters are considered to be equivalent in the permanent displacement prediction model, only one of the parameters is selected at the moment, and only one of the parameters is considered when the parameter pair correlation analysis is carried out;
when R is g(IM1) And R is g(IM2) When the predictive effect of the two parameters in each model is equal to that of the model, only the earthquake motion parameters with high comprehensive relevance to the permanent displacement are selected at the moment;
when R is g(IM1) Less than 3% in each type of predictive model, R g(IM2) When more than 3% of the prediction models exist, the improvement effect of the parameter IM2 on the IM1 is considered to be poor, and the improvement effect of the parameter IM1 on the IM2 is considered to be good, which indicates that the IM1 canTo replace the simultaneous existence of two parameters, so only IM1 is selected during parameter screening; similarly, when R g(IM2) Less than 3% in each type of predictive model, R g(IM1) When more than 3% of the prediction models exist, only IM2 is selected during parameter screening;
when R is g(IM1) And R is g(IM2) When more than 3% of all the prediction models exist, the two parameters are considered to have good fitting effect on the permanent displacement prediction model compared with one parameter, and at the moment, the situation that one parameter is not used for replacing the two parameters exists at the same time cannot be replaced, so that the two parameters are not discarded and are selected as the alternative parameters of the permanent displacement prediction model.
2. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 1, wherein the method comprises the following steps: the calculation formula of the Pearson correlation coefficient is as follows:
wherein IM i A parameter indicating the ith seismic effort,mean value of earthquake motion parameters, D Ni Representing the permanent displacement corresponding to the ith earthquake motion, < ->The average value of permanent displacement corresponding to all earthquake motions is shown, and the PCC absolute value ranges from 0.8 to 1, the two variables show extremely strong correlation, the strong correlation ranges from 0.6 to 0.8, the medium correlation ranges from 0.4 to 0.6, the weak correlation ranges from 0.2 to 0.4, and the extremely weak correlation or the uncorrelation ranges from 0 to 0.2.
3. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 2, wherein the method comprises the following steps: the calculation formula of the weighted average correlation coefficient is as follows:
wherein, representing the weighted average correlation coefficient between the seismic parameters and the permanent displacement, N i Indicating the number of permanent displacements, N, meeting the condition at the ith critical acceleration total Sum of critical acceleration amounts, PCC, representing compliance at all critical accelerations i Representing Pearson correlation coefficients between eligible permanent displacements and the seismic parameters at the ith critical acceleration.
4. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 1, wherein the method comprises the following steps: the calculation formulas of the goodness of fit and the standard deviation are respectively as follows:
wherein,D Ni representing the permanent displacement corresponding to the ith earthquake motion, < ->Mean value representing the permanent displacement corresponding to all seismic vibrations, < >>Representing the predicted permanent displacement corresponding to the ith earthquake motion, SS tot Representing the sum of the squares of the permanent displacements, SS res Representing the sum of squares of the residuals of the permanent shifts, when R 2 >At 0.8, the correlation between the two variables is high.
5. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 1, wherein the method comprises the following steps: the following 5 types of permanent displacement prediction models are obtained through arrangement and analysis of the earthquake slope permanent displacement prediction model:
log D N ＝A1+A2log a c +A3log IM1+A4log IM2+A5log IM3+A6log IM4+A7log IM5+A8log IM6
logD N ＝B1+B2log[(1-a c /PGA) B3 (a c /PGA) B4 ]+B5log IM1+B6log IM2+B7log IM3+B8log IM4+B9log IM5+B10log IM6
logD N ＝C1+C2loga c +C3log 2 a c +C4loga c log IM1+C5log IM1+C6log 2 IM1+C7log IM2+C8log IM3+C9log IM4+C10log IM5+C11log IM6
logD N ＝C1+C2loga c +C3log 2 a c +C4loga c log IM1+C5log IM1+C6log 2 IM1+C7loga c log IM2+C8log IM2+C9log 2 IM2+C10log IM3+C11log IM4+C12log IM5+C13log IM6
logD N ＝D1+D2(a c /PGA)+D3(a c /PGA) 2 +D4(a c /PGA) 3 +D5(a c /PGA) 4 +D6log IM1+D7log IM2+D8log IM3+D9log IM4+D10log IM5+D11log IM6
wherein A1, A2, A3 … …, B1, B2, B3 … …, C1, C2, C3 … …, and D1, D2, D3 … … each represent coefficients of a permanent displacement prediction model, and IM1, IM2, IM3 … … represent different earthquake motion parameters.
6. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 1, wherein the method comprises the following steps: the establishing the earthquake motion database comprises the following steps: based on the NGA database, record data which simultaneously contain two horizontal earthquake motions and one vertical earthquake motion are selected, the earthquake motion record data are identified by utilizing a multi-component impulse classification algorithm, and an impulse earthquake motion database is established.
7. The multi-parameter-based seismic slope permanent displacement prediction model building method according to claim 1, wherein the method comprises the following steps: the classification and calculation of the earthquake motion parameters comprise: the earthquake motion parameters are divided into five categories of earthquake motion parameters including time duration, peak value, reaction spectrum, energy and pulse according to the physical meaning of the earthquake motion parameter representation, the five categories of earthquake motion parameters comprise 73 parameter indexes, and the parameter value of each earthquake motion record is calculated according to the calculation formula of each parameter index.
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