CN112488197A - Side slope stability influence factor sensitivity analysis method based on PSO-SVM prediction model - Google Patents

Side slope stability influence factor sensitivity analysis method based on PSO-SVM prediction model Download PDF

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CN112488197A
CN112488197A CN202011374746.0A CN202011374746A CN112488197A CN 112488197 A CN112488197 A CN 112488197A CN 202011374746 A CN202011374746 A CN 202011374746A CN 112488197 A CN112488197 A CN 112488197A
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孙广存
李宁
王开华
徐乐
尚强
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Beijing Zhongguancun Zhilian Safety Science Research Institute Co ltd
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Abstract

The invention provides a slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model, which comprises the following steps: analyzing and determining main factors influencing the slope stability, carrying out normalization processing on the influencing factors, and establishing a PSO-SVM prediction model; adopting a single variable principle, removing one influence factor from each PSO-SVM prediction model, and establishing a plurality of PSO-SVM prediction models to research the influence degree of each influence factor, namely the sensitivity analysis of the influence factors; calculating mean square error MSE and square correlation coefficient R2Two evaluation indexes; and comprehensively analyzing the two evaluation indexes to obtain the influence degree of each influence factor on the slope stability.

Description

Side slope stability influence factor sensitivity analysis method based on PSO-SVM prediction model
Technical Field
The invention relates to the field of slope safety coefficient prediction, in particular to a slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model.
Background
Slope stability is one of hot research subjects in geotechnical engineering, relates to the engineering fields of mines, water conservancy and hydropower, roads, railways and the like, and is related to the economic benefit of enterprises and the life and property safety of people. However, due to the characteristics of complexity, uncertainty, data imperfection, nonlinearity and the like of slope engineering, the stability of the slope engineering is difficult to evaluate and make accurate and effective prediction and forecast, so that the slope case subjected to engineering practice inspection is analyzed and researched, and the method has very important practical significance, and the relation between the slope stability and the parameters is discussed.
Disclosure of Invention
The invention aims to provide a slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model, and provides a new method for analyzing the slope stability influence factor sensitivity.
In order to solve the problems, the invention provides a slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model, and the slope stability influence factor sensitivity analysis method based on the PSO-SVM prediction model comprises the following steps:
analyzing and determining main factors influencing the slope stability, carrying out normalization processing on the influencing factors, and establishing a PSO-SVM prediction model;
adopting a single variable principle, removing one influence factor from each PSO-SVM prediction model, and establishing a plurality of PSO-SVM prediction models to research the influence degree of each influence factor, namely the sensitivity analysis of the influence factors;
calculating mean square error MSE and square correlation coefficient R2Two evaluation indexes;
and comprehensively analyzing the two evaluation indexes to obtain the influence degree of each influence factor on the slope stability.
Further, the influencing factors include: cohesion c, internal friction angle
Figure BDA0002806345330000011
Length of slide-resistant pile lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstr。
Further, aiming at n influencing factors, n +1 PSO-SVM prediction models are established, wherein one PSO-SVM prediction model comprises n influencing factors, and the rest n PSO-SVM prediction models comprise n-1 different influencing factors.
Further, the kernel function of the PSO-SVM prediction model is a Gaussian BRF kernel function. (ii) a
Further, the mean square error MSE is calculated as follows:
Figure BDA0002806345330000021
wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample.
Further, the more the mean square error MSE is close to 0, which indicates that the more the predicted value is close to the actual value, the better the prediction effect is.
Further, the square correlation coefficient R2The calculation method of (2) is as follows:
Figure BDA0002806345330000022
wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample.
Further, the square correlation coefficient R2The closer to 1, the closer to the actual value the predicted value is, the better the prediction effect is.
Further, the two evaluation indexes were calculated using a PSO-SVM program written in MATLAB.
Compared with the prior art, the invention has the following characteristics and beneficial effects:
1. and (3) establishing a PSO-SVM prediction model by using the PSO optimizing SVM parameter, analyzing and predicting the slope stability, and finding out the factor which has the greatest influence on the slope stability. By adopting the evaluation method, the sensitivity factors influencing the slope stability are analyzed and sequenced, and a new analysis method is provided for field engineers.
2. The invention adopts mean square error MSE and square correlation coefficient R2These two indices are used to evaluate susceptibility to the influencing factor. Wherein, the closer the MSE is to 0, the closer the predicted value is to the actual value, and the better the prediction effect is; r2The closer to 1, the higher the correlation degree between the two, i.e. the closer the predicted value and the actual value are, the better the prediction effect is. And the two evaluation indexes are comprehensively analyzed, so that the influence degree of each influence factor on the slope stability can be obtained.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 shows the discrimination results of 9 PSO-SVM models.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Pso (particle Swarm optimization) is an english abbreviation for particle Swarm optimization algorithm, proposed by j.kennedy and r.c. eberhart in 1995.
SVM (support Vector machine) is the English abbreviation for support Vector machine, first proposed by Corinna Cortes and Vladimir Vapnik in 1995.
RBF (radial Basis function) is an English abbreviation for radial Basis function, proposed by Michael James David Powell in 1985.
The invention provides a slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model, which comprises the following steps:
step S1: and analyzing and determining main factors influencing the slope stability, carrying out normalization processing on the influencing factors, and establishing a PSO-SVM prediction model.
Aiming at a specific side slope, analyzing and determining influence factors influencing the stability of the side slope, and being particularly suitable for the side slope with a mode of supporting an anti-slide pile and a rib belt layer, wherein the side slope mainly comprises a soil side slope and 8 influence factors, namely cohesive force c and an internal friction angle
Figure BDA0002806345330000041
Length of slide-resistant pile lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstr8 parameters; for the side slope without the slide-resistant pile supporting form, the related influence factor, namely the length l of the slide-resistant pile can be determinedpStrength p of anti-slide pilestrThe method is also applicable when only the other 6 factors are considered; for the side slope without the supporting form of the band layer, the related influence factor, namely the length l of the band layergInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstrThe method is equally applicable, except that only the remaining 4 factors are taken into account.
In this embodiment, taking a high fill slope with a support form of an anti-slide pile and a rib belt layer as an example, the influence factors influencing the slope stability are analyzed and determined to include cohesive force c and internal friction angle
Figure BDA0002806345330000042
Length of slide-resistant pile lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstr8 parameters, in the actual engineering design, design optimization and slope management, the influence factor with the largest slope stability influence needs to be found, so that the slope stability can be more effectively developedAnd (5) beginning management work, namely carrying out sensitivity analysis on all the influence factors of the slope stability.
Collecting cohesive force c and internal friction angle
Figure BDA0002806345330000043
Length of slide-resistant pile lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstrAnd the data of 8 influencing factors are normalized, so that the influence on the prediction result due to different units and different magnitude of the influencing factors is avoided.
The SVM has a solid theoretical basis, is based on the Structure Risk Minimization Principle (SRMP), has strong generalization capability, and can effectively solve the problems of small samples, high dimension, nonlinearity and the like; the PSO algorithm is an evolutionary algorithm based on group intelligence and proposed by Kenne-dy and Eberhart, and is widely applied to selection and optimization of model parameters, the two algorithms are coupled, the established PSO-SVM prediction model has higher classification accuracy, higher precision of the slope safety coefficient prediction and stronger popularization generalization capability, the research result has certain theoretical and practical significance on analysis and prediction of slope stability, the slope stability is analyzed and predicted, and the factor which has the greatest influence on the slope stability is found.
The performance of the PSO-SVM prediction model is reduced due to the fact that the number of the influencing factors participating in the PSO-SVM prediction model training is too small, and prediction is failed, therefore, the kernel function of the PSO-SVM prediction model in the invention is a Gaussian BRF kernel function, and the number of the influencing factors participating in the model training is 8.
Step S2: and (3) adopting a single variable principle, removing one influence factor from each PSO-SVM prediction model, and establishing a plurality of PSO-SVM prediction models so as to research the influence degree of each influence factor, namely the sensitivity analysis of the influence factor.
The original PSO-SVM prediction model established by the invention comprises cohesive force c and internal friction angle
Figure BDA0002806345330000051
Length of anti-slide pileDegree lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstr8 influencing factors, and predicting the slope safety factor under the 8 influencing factors. Under the condition of only one influence factor, the model prediction performance is very poor, and no obvious distinction degree exists among different groups of prediction experiments. Therefore, in order to research the influence degree of each factor on the stability of the high fill slope, the experiment adopts a single variable principle, each prediction model excludes a certain influence factor, and 9 PSO-SVM models are re-established to research the influence degree of each influence factor, namely influence factor sensitivity analysis, wherein:
the first PSO-SVM prediction model contains all 8 influencing factors;
the second PSO-SVM prediction model comprises 7 influence factors, the influence factor of soil mass cohesion c is eliminated, and the experimental sample is predicted again so as to research the influence degree of the soil mass cohesion c on the stability of the high fill slope;
the third PSO-SVM prediction model comprises 7 influence factors and eliminates the internal friction angle of the soil body
Figure BDA0002806345330000052
Influence factors, and predicting the experimental sample again to research the internal friction angle of the soil body
Figure BDA0002806345330000053
Influence degree on stability of the high fill side slope;
the fourth PSO-SVM prediction model comprises 7 influencing factors, and the length l of the slide-resistant pile is eliminatedpInfluence factors, and predicting the experimental sample again to research the length l of the slide-resistant pilepInfluence degree on stability of the high fill side slope;
the fifth PSO-SVM prediction model comprises 7 influence factors, and the anti-slide pile strength p is eliminatedstrInfluence factors, and predicting the experimental sample again to research the strength p of the slide-resistant pilestrInfluence degree on stability of the high fill side slope;
sixth PSO-SThe VM prediction model comprises 7 influence factors, and the length l of the tendon band is eliminatedgInfluence factors, and predicting the experimental sample again to research the length l of the tendongInfluence degree on stability of the high fill side slope;
the seventh PSO-SVM prediction model comprises 7 influencing factors, and the interval d of the tendon and band layers is eliminatedgInfluence factors, and predicting the experimental sample again to research the interval d between the tendon and the belt layersgInfluence degree on stability of the high fill side slope;
the eighth PSO-SVM prediction model comprises 7 influence factors, eliminates the influence factor of the reinforced soil friction coefficient R, and predicts the experimental sample again to research the influence degree of the reinforced soil friction coefficient R on the stability of the high fill slope;
the ninth PSO-SVM prediction model comprises 7 influencing factors, and the strength g of the tendon belt is eliminatedstrInfluence factors, and predicting the experimental sample again to research the strength g of the tendon and the beltstrInfluence degree on the stability of the high fill side slope.
The influence of the influence factors on the slope stability can be reflected by the prediction result of the PSO-SVM prediction model, and the lower the prediction accuracy of the PSO-SVM prediction model is, the higher the sensitivity of the influence factors excluded by the prediction model is. Based on the PSO-SVM algorithm, the excellent performance is realized in the slope safety coefficient prediction, the relative sensitivity of 8 influence factors is obtained through the established 9 PSO-SVM prediction models relating to different influence factor parameters, and the experimental scheme has high discrimination while ensuring high prediction precision.
Table 1 shows the influencing factor sensitivity analysis experimental scheme, showing the influencing factor parameters involved in the 9 models in the scheme, wherein v represents the influencing factors contained in the models, and x represents the eliminated influencing factors in the models.
Figure BDA0002806345330000071
TABLE 1
Step S3: calculating mean square error MSE and square correlation coefficient R2Two evaluationsAnd (4) indexes.
The mean square error MSE can be calculated according to the following equation:
Figure BDA0002806345330000072
wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample. The closer the MSE is to 0, the closer the predicted value is to the actual value, and the better the prediction effect is.
The squared correlation coefficient R can be calculated according to the following formula2：
Figure BDA0002806345330000073
Wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample. R2The closer to 1, the higher the correlation degree between the two, i.e. the closer the predicted value and the actual value are, the better the prediction effect is.
Sensitivity analysis can be carried out on the slope stability influence factors according to the theoretical formula.
The PSO-SVM calculation program can be written by MATLAB according to the theoretical formula, and the calculation program can also be written separately to calculate the mean square error MSE and the square correlation coefficient R2Two evaluation indexes.
Step S4: and comprehensively analyzing the two evaluation indexes to obtain the influence degree of each influence factor on the slope stability.
For the same sample set, the slope safety coefficient prediction performance evaluation indexes of the 9 groups of PSO-SVM models comprise mean square error MSE and square correlation coefficient R2Are listed in table 2.
Figure BDA0002806345330000081
TABLE 2
Model predictiveIn the evaluation index, the more the mean square error MSE is close to 0, R2The closer to 1, the better the prediction performance is, that is, the closer to the original value, the model prediction value is, and from the viewpoint of the prediction result, the prediction effect of the model 1 is the best, the influence of 8 influencing factors on the stability of the slope is shown, and the more comprehensive the influencing factors are, the better the prediction performance of the model is.
One influence factor is removed from each of the remaining 8 models, and the model with the better prediction effect in the 8 prediction models indicates that the influence factor removed by the model correspondingly has little influence on the prediction performance of the model, namely the removed influence factor has little influence on the stability of the slope and belongs to a secondary factor; on the contrary, the worse the prediction effect is, the larger the influence of the influence factor removed by the model on the model prediction performance is, that is, the influence factor removed has a large influence on the slope stability, and belongs to the main factor.
The prediction results of the 9 groups of PSO-SVM prediction models show that all the influencing factors are more or less sensitive to slope stability analysis. The invention aims to research the slope stability prediction and find scientific and reasonable measures to prevent or reduce the damage of the slope and improve the slope design and treatment efficiency, and the analysis of the sensitivity sequence of the influencing factors is the premise of providing the targeted measures. The sensitivity of 8 influencing factors can be realized by calculating the mean square error MSE and the square correlation coefficient R of 9 PSO-SVM prediction models2And comparing the evaluation indexes.
By comprehensively analyzing the prediction results in table 2 and the relationship curve in fig. 2, the order of the influence degrees of the 8 influence factors on the slope stability can be finally obtained, and the influence degrees are sequentially from large to small: internal friction angle
Figure BDA0002806345330000091
Length of slide-resistant pile lpInter-layer distance d of rib beltgLength of tendon bandgStrength p of anti-slide pilestrThe friction coefficient R, cohesive force c and the strength g of the rib belt of the reinforced soilstr。
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A slope stability influence factor sensitivity analysis method based on a PSO-SVM prediction model is characterized by comprising the following steps:
analyzing and determining main factors influencing the slope stability, carrying out normalization processing on the influencing factors, and establishing a PSO-SVM prediction model;
adopting a single variable principle, removing one influence factor from each PSO-SVM prediction model, and establishing a plurality of PSO-SVM prediction models to research the influence degree of each influence factor, namely the sensitivity analysis of the influence factors;
calculating mean square error MSE and square correlation coefficient R2Two evaluation indexes;
and comprehensively analyzing the two evaluation indexes to obtain the influence degree of each influence factor on the slope stability.
2. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM predictive model as recited in claim 1, wherein the influence factors comprise: cohesion c, internal friction angle
Figure FDA0002806345320000012
Length of slide-resistant pile lpStrength p of anti-slide pilestrLength of tendon bandgInter-layer distance d of rib beltgCoefficient of friction R of rib soil and strength g of rib beltstr。
3. The slope stability influence factor sensitivity analysis method based on the PSO-SVM prediction model as claimed in claim 2, characterized in that n +1 PSO-SVM prediction models are established for n influence factors, wherein one PSO-SVM prediction model comprises n influence factors, and the remaining n PSO-SVM prediction models comprise n-1 different influence factors.
4. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM predictive model as recited in claim 1, wherein the kernel function of the PSO-SVM predictive model is a Gaussian BRF kernel function.
5. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM prediction model as claimed in claim 1, wherein the mean square error MSE is calculated as follows:
Figure FDA0002806345320000011
wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample.
6. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM prediction model as recited in claim 5, wherein the mean square error MSE is closer to 0, which indicates that the prediction effect is better as the predicted value is closer to the actual value.
7. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM prediction model as claimed in claim 1, wherein the square correlation coefficient R2The calculation method of (2) is as follows:
Figure FDA0002806345320000021
wherein n is the number of training samples, yiTo train the actual value of the sample, yi' is a predicted value output by the training sample.
8. The method for analyzing sensitivity of influence factors of slope stability based on PSO-SVM prediction model as recited in claim 7, wherein the square correlation coefficient R2The closer to 1, the closer to the actual value the predicted value is, the better the prediction effect is.
9. The method for analyzing the sensitivity of the influence factors of the slope stability based on the PSO-SVM predictive model according to claim 1, characterized in that the two evaluation indexes are calculated by using a PSO-SVM program written by MATLAB.
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Application publication date: 20210312