CN116305434A - Method for predicting earthquake vulnerability of nuclear power plant based on machine learning and MSA - Google Patents

Method for predicting earthquake vulnerability of nuclear power plant based on machine learning and MSA Download PDF

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CN116305434A
CN116305434A CN202310165782.3A CN202310165782A CN116305434A CN 116305434 A CN116305434 A CN 116305434A CN 202310165782 A CN202310165782 A CN 202310165782A CN 116305434 A CN116305434 A CN 116305434A
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郑志
王勇
潘晓兰
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Taiyuan University of Technology
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Abstract

The invention discloses a method for predicting earthquake vulnerability of a nuclear power plant based on machine learning and MSA, which comprises the steps of establishing an earthquake response model of the nuclear power plant; calculating the structural earthquake median capability value of the containment and secondary system of the nuclear power plant; scaling the near-field pulse wave, selecting a seismic vibration parameter IM, and performing dynamic time-course response analysis to form a data set; using machine learning to perform feature selection and model selection, and determining optimal earthquake motion parameters for predicting earthquake demand response; establishing a probabilistic earthquake demand model PSDM with structural response based on machine learning, realizing earthquake demand parameter EDP response prediction, and verifying a prediction model effect; and (3) carrying out multi-stripe analysis MSA by using a prediction model, and determining the median value and standard deviation of the failure of the safety shell and the secondary system according to a least square method, thereby establishing a vulnerability curve of the safety shell and the secondary system of the nuclear power plant. The method can realize the evaluation of the earthquake damage risk and the earthquake resistance of the nuclear power plant structure under strong earthquake.

Description

Method for predicting earthquake vulnerability of nuclear power plant based on machine learning and MSA
Technical Field
The invention relates to a method for predicting earthquake vulnerability of a nuclear power plant based on machine learning and MSA, belonging to the field of earthquake resistance and disaster reduction of the nuclear power plant.
Background
As a last line of defense against nuclear leakage, the containment vessel of a nuclear power plant should be capable of withstanding the threat of natural disasters such as earthquakes. In recent years, the capability of nuclear power stations to defend against earthquakes is becoming more and more important in the world, and once a concrete containment is damaged, the capability of preventing nuclear leakage is lost. It is worth noting that the structure and equipment of the nuclear power station may be seriously threatened by strong earthquakes, so that in the earthquake-resistant design of the nuclear power station, not only the containment structure should not be damaged, but also secondary systems such as internal instruments and equipment should be safe. Within the framework of a behavior-based seismic engineering, the relationship between EDP and IM needs to be properly established in PSDM. An important aspect of the PSDM of a nuclear power plant is the accurate prediction of the response to seismic demand, with respect to a nuclear power plant, the uncertainty and randomness associated with the seismic vibrations far exceeds any other uncertainty associated with the structure of the nuclear power plant.
Traditional methods of establishing PSDM for nuclear power plants are based on linear regression, taking into account the correlation of IM and seismic demand response, using scalar IM or vector IMs to predict the seismic demand response. However, scalar IM or vector IMs cannot account for all relevant features of ground motion, while due to the lack of flexibility of conventional linear functions in incorporating various sources of uncertainty, demand estimation may be affected, particularly in the construction of nuclear power plants, this limitation being particularly critical because nuclear power plant containment and secondary systems tend to exhibit inelastic behavior in view of stiffness degradation under over-design base earthquakes. In many prior published documents, the procedure for deriving vulnerability curves comes from nonlinear dynamic time course analysis, including cloud methods (C.A.Cornell, F.Jalayer, R.O.Hamburger, D.A.Foutch, probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines,J.Struct.Eng.128 (4) (2002) 526-533; F.Jalayer, direct probabilistic seismic analysis: imaging non-linear dynamic dynamics analysis (2003)), incremental dynamic analysis IDA (D.Vamvatsikos, C.A.Cornell, incremental dynamic analysis, earthquake Eng. Strut. Dyn.31 (3) (2002) 491-514), and multi-stripe analysis MSA (F.Jalayer, J.Beck, effects of two Alternative representations of ground-motion uncertainty on probabilistic seismic demand assessment of structures, earthquake Eng. Dyn.37 (1) (2008) 61-79; F.Jalayer, C.A.Cornell, alternatin-linear demand estimation methods for probability-based seismic assessments, earthquake Eng Struct Dyn,38 (8) (2009), 951-972. The cloud approach is accomplished by analyzing a set of unscaled seismic acceleration sequences assuming that the IM-EDP relationship exists in a proper log-log linear relationship. The limitations of cloud analysis are mainly due to the potential regression assumption that under over-design reference earthquakes, linear regression based scalar IM cannot capture inelastic behavior, resulting in bias in the mapping process. Thus, cloud methods are not strictly applicable to nuclear power plants with tri-linear shear behavior. While the IDA method uses a specific seismic input, by setting a series of monotonically increasing IMs, and performing structural nonlinear time-course analysis on the seismic input under each seismic intensity index, the MSA method uses a seismic record scaled to a specific target intensity as the structural input, covering the whole reaction process from elasticity to elastoplasticity to structural dynamic instability, and simultaneously being capable of reflecting the seismic demand capacity and the overall collapse resistance capacity of the structure under different intensity classes of earthquake, the time-course analysis is computationally laborious. Machine learning has facilitated application in different engineering fields due to its advantages in analyzing complex and uncertain problems. The application of existing machine learning methods in vulnerability analysis of nuclear power plants has been rarely studied in the past, and the current application is also focused on selecting the most relevant IM using neural networks and quantifying vulnerability curve uncertainty, however, the probability of structural failure is still calculated by cloud methods, and it is difficult to capture the nonlinear behavior of the structure under over-design reference earthquakes (Z.Wang, N.Pedroni, I.Zentner, E.Zio, seismic fragility analysis with artificial neural networks: applicationto nuclearpowerplantequipment, eng.struct,162, (2018) 213-225).
Therefore, the complex relation between strong earthquake and structural demand response is captured by utilizing machine learning, the constraint of prior assumptions of the traditional linear function form and parameter distribution is avoided, a reliable PSDM framework driven by machine learning can be established and applied to vulnerability research, so that the rigidity degradation of a nuclear power plant under the over-design reference earthquake is effectively and accurately considered, the inelastic behavior under the strong earthquake is captured, the calculation cost of the traditional IDA and MSA is greatly reduced, and the method has important theoretical significance and application value for promoting the development and expansion of vulnerability evaluation work of the vulnerability research.
Disclosure of Invention
The invention aims to provide a method for predicting the earthquake vulnerability of a nuclear power plant based on machine learning and MSA, which is used for establishing PSDM by forming model data so as to efficiently and accurately predict the earthquake demand response of a structure and deduce a vulnerability curve by combining with MSA.
The technical conception of the invention is as follows: 1) Firstly, efficient and accurate earthquake demand response prediction of a nuclear power plant is realized by using multiple IMs based on machine learning, and PSDM is constructed on the basis. The number of seismic parameters and how the machine learning regression algorithm affects the prediction performance are further known by using feature selection and model selection methods based on iterative elimination of random forest RRF. The optimal machine learning regression model is determined through ten-fold cross validation and compared with the traditional linear regression model based on scalar IM and vector IMs in generalization capability, so that the method has absolute advantages in PSDM construction, can overcome the limitations of the traditional linear model and capture complex nonlinear relations between earthquake IM and EDP, and provides a certain basis for improving PSDM in a nuclear power plant structure by using the machine learning to consider multiple IMs. 2) Secondly, a reliable vulnerability curve deducing method is provided based on machine learning and MSA. The vulnerability curve is generally applied to seismic vulnerability assessment, uncertainty of ground movement is considered, probability exceeding structural capacity is related to the seismic vibration parameter through PSDM with multiple IMs constructed based on machine learning and MSA, so that nonlinear time-course analysis cost is reduced, compared with the traditional IDA and MSA methods, efficiency is greatly improved, meanwhile, stiffness degradation of the nuclear power plant under over-designed earthquake can be considered, nonlinear behavior of the nuclear power plant under strong earthquake is captured, and the method has important significance for seismic probability safety assessment of the nuclear power plant exceeding design basis.
The technical scheme of the invention is as follows:
a method for predicting seismic vulnerability of a nuclear power plant based on machine learning and MSA, comprising the steps of:
s1, establishing a nuclear power plant earthquake response model;
s2, calculating structural earthquake median capability values of the containment and the secondary system;
s3, scaling the near-field pulse wave, selecting earthquake motion parameters, and performing random dynamic time-course analysis to form a data set;
s4, performing feature selection and model selection by using machine learning, and determining an optimal machine learning prediction model;
s5, establishing a PSDM based on machine learning, realizing earthquake demand response prediction, and verifying a prediction model effect;
s6, MSA is carried out by using a prediction model, and the median value and standard deviation of the failure of the containment and the secondary system of the nuclear power plant are determined according to a least square method, so that a vulnerability curve of the containment and the secondary system of the nuclear power plant is established.
The above method is further described as follows:
the step S1 specifically comprises the following steps: and determining the calculation parameters of the nuclear power plant containment seismic response model, selecting original unscaled near-field pulse seismic waves, and calculating the seismic demand response.
The calculated parameters of the nuclear power plant containment seismic response model comprise: structural distribution of the containment and secondary systems, material parameters, floor mass and moment of inertia of the structure, geometric area, shear area and moment of inertia of the floor, wherein the material parameters comprise dynamic elastic modulus, shear modulus, poisson ratio and damping ratio of the concrete.
And the original unscaled near-field pulse seismic waves are selected by utilizing response spectrum matching, and seismic wave preprocessing including filtering and baseline zeroing is carried out in a PEER strong earthquake database, so that the average frequency spectrum of the input seismic waves is consistent with the RG1.60 design frequency spectrum.
The earthquake demand response is obtained by inputting random vibration into an established nuclear power plant earthquake response model, a nuclear power plant dynamic response calculation model can be formed, dynamic time interval analysis is carried out, dynamic response results of a containment and a secondary system of the nuclear power plant under different earthquakes are obtained, wherein the containment takes the maximum value (Dmax) of peak displacement as an earthquake demand parameter, and the secondary system takes the average floor acceleration response spectrum value (AFSA) of 5-33Hz as the earthquake demand parameter.
The step S2 specifically comprises the following steps: loading in a uniform distribution mode, and performing pushing and covering analysis to obtain a vertex displacement-substrate shear curve, wherein the displacement corresponding to the tail end of the linear section is the structural earthquake median capability of the containment; and (3) performing dynamic time-course analysis on the selected near-field pulse wave, zooming and amplitude-modulating to the spectrum acceleration of the nuclear power plant consistent risk spectrum at the first self-vibration period of the structure by 0.95g, and selecting the secondary system AFSA in S1 as an index to obtain the corresponding secondary system and the structure earthquake median capability, wherein the specific expression is as follows:
Figure BDA0004095889160000031
wherein y is i Is the AFSA value of the secondary system obtained by dynamic time-course analysis, and the logarithmic standard deviation beta r Representing the randomness of the earthquake motion, the logarithmic standard deviation beta u Representing the uncertainty of the structural material, beta according to Kennedy and Ravindra (J.W.Reed, R.P.Kennedy, methodology for Developing Seismic Fragilities, TR-103959.Electric Power Research Institute,Palo Alto,California, (1994)) results of extensive statistical studies r And beta u The values of (2) are determined to be 0.26 and 0.34, respectively.
The step S3 specifically comprises the following steps: scaling of the near-field pulse wave refers to adjusting the original seismic wave to a set of discrete intensity level seismic waves according to the magnitude of the ground peak acceleration PGA to include a sufficient number of over-designed reference seismic waves to account for inelastic behavior exhibited by the structure in the higher intensity range, expanding the range of machine learning training samples. The seismic parameters include 33 usual seismic parameters such as PGA and the like which are directly obtained from seismic vibrations and parameters such as Sa (T1) and the like which are obtained from structural elastic reactions.
The step S4 specifically comprises the following steps: the dataset was then set to 7: and 3, randomly dividing to be respectively used as a training set and a testing set, wherein the feature in feature selection is IM, the feature selection is realized based on the importance of the radix by using an iterative random forest elimination algorithm RRF, and the mean square error change of each variable prediction caused by splitting in the regression tree growth is compared to be used as a variable exclusion standard. The most important IMs of 3/4 are retained to reconstruct the model. 1/4 of the least significant IMs are recursively deleted and a new forest is built using the remaining IMs until only one IM remains. The model includes 14 selected machine learning regression algorithms, including: (i) a linear regression-based method: including Linear Regression (LR), bayesian Regression (BR), auto-correlation determination regression (ARD), and Huber Regression (HR); (ii) kernel ridge regression (KR) based on kernel; (iii) a decision boundary based method: including support vector machine regression (SVR) and nu support vector machine regression (NuSVR); (iv) distance-based K Nearest Neighbor (KNN); (v) gaussian process kernel (GK) based on gaussian process; (vi) a tree-based enhancement method: including Decision Tree (DT), random Forest (RF), gradient enhancement (GB), adaptive enhancement (ADAB), and extreme gradient boosting (XGB), in R 2 MAE, MSE, RMSE are evaluation indexes, and the performance of the machine learning model is evaluated by using 10-fold cross validation, and the optimal machine learning prediction model is selected.
The step S6 specifically comprises the following steps: and (3) scaling the original earthquake motion selected in the step (S1) to a specific target intensity level as the input of a prediction model according to the nuclear power plant earthquake demand response prediction model obtained in the step (S5), obtaining corresponding structural earthquake demand response output, calculating the failure probability of the structure under the specific IM by using the structural earthquake median capability proposed in the step (S2) as the failure threshold value, fitting by using a least square method, quantifying the median and the uncertainty, and obtaining the vulnerability curves of the containment and secondary systems of the nuclear power plant.
The specific expression of the failure probability is as follows:
F(im)＝P(EDP＞edp j |IM＝im)
in edp j Is the failure threshold of EDP; IM is a particular value for IM.
The invention has the beneficial effects that:
(1) The method adopts machine learning, and can determine proper multi-element earthquake motion parameters and a machine learning regression algorithm to efficiently and accurately predict the demand response of the containment and secondary system of the nuclear power plant under strong earthquake, and meanwhile, the traditional PSDM is improved, so that the method has important significance for earthquake-resistant design and evaluation, post-earthquake reinforcement and decision-making of the nuclear power plant.
(2) The method can effectively and accurately consider the rigidity degradation of the nuclear power plant under the over-design reference earthquake, capture the inelastic behavior under the strong earthquake, and has important significance for reasonable evaluation of the engineering performance of the actual nuclear power plant.
(3) The method and the device can be directly applied to predicting the earthquake damage state of the nuclear power plant structure, are high in applicability, and are convenient to operate, and only the model dataset is required to be widely trained.
(4) Through MSA, a least square method is adopted to draw a vulnerability curve, the calculation cost is low on the premise of not reducing the precision, the calculation efficiency is remarkably improved, and the seismic damage risk and the seismic performance evaluation of the nuclear power plant structure under strong earthquake are realized.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a seismic response model of a nuclear power plant in an embodiment; (a) A cross-sectional view of a nuclear power plant, (b) a simplified model of the nuclear power plant;
FIG. 3 is a verification set performance map selected based on RRF features in an embodiment;
FIG. 4 is a diagram of predictive performance of different machine learning algorithms in an embodiment;
FIG. 5 is a graph showing the comparison of the predicted structural demand response and the conventional model predicted structural demand response in an embodiment;
FIG. 6 is a graph comparing MSA predicted structural demand response with traditional model MSA predicted structural demand response in an embodiment;
FIG. 7 is a graph comparing predicted vulnerability curves with conventional model vulnerability curves in an example.
Detailed Description
The present invention is further illustrated by, but not limited to, the following examples.
Example 1:
as shown in fig. 1-7, the embodiment provides a method for predicting the earthquake vulnerability of a nuclear power plant based on machine learning and MSA, which is specifically applied as follows:
(1) A typical nuclear power plant structure model is determined, and comprises a containment vessel and a secondary system, wherein the structural distribution of the established nuclear power plant earthquake response model is shown in fig. 2, and the model consists of a bottom plate, a containment vessel structure and the secondary system. The material parameters are specifically as follows: dynamic elastic modulus of 4X 10 10 N·m -2 Shear modulus of 1.6X10 10 N·m -2 The Poisson ratio is 0.2, the damping ratio is 0.07, and the bending moment curvature of the nonlinear beam column unit is in linear elastic relation. In order to represent the crack resistance of the concrete, a tri-linear skeleton curve is adopted to represent the shear characteristic, and the unloading rigidity degradation characteristic based on displacement ductility is considered in a hysteresis rule. For cyclic response under seismic load, a maximum point orientation model is used as the basis of a time hysteresis criterion in the loading and unloading process. The mass and the structural moment of inertia of the floor in the model are concentrated at the node positions, and the nonlinear beam column units among the nodes only have geometric properties and mechanical properties, such as the geometric area, the shearing area and the moment of inertia among the nodes.
According to the condition characteristics of the nuclear power plant construction site, 100 near-field pulse seismic waves are selected from the PEER strong earthquake database by using a reaction spectrum matching method, and filtering and baseline zeroing are performed.
The method comprises the steps of inputting random earthquake vibration into an established nuclear power plant earthquake response model, forming a nuclear power plant dynamic response calculation model, carrying out dynamic response time-course analysis, and obtaining demand response results of a nuclear power plant containment and a secondary system under different earthquake vibration intensities, wherein for a containment structure, an earthquake demand parameter is a maximum value Dmax8 of peak 8 node displacement, and for a secondary system, because frequencies of main equipment in the nuclear power plant are almost concentrated in 5-33HZ, AFSA between 5-33HZ is used as an earthquake demand parameter of the secondary system. Considering the distribution positions of several major components, the seismic demand parameters of the secondary system are represented by average floor acceleration response spectrum values AFSA2, AFSA10 and AFSA12 at 5-33Hz for nodes 2, 10 and 12.
(2) And calculating the structural earthquake median capability value of the containment and the secondary system, wherein the damage state of the concrete containment structure of the nuclear power plant is mainly determined by the displacement level, and when the maximum displacement of the top point of the containment reaches a specified value, the concrete is considered to crack. In order to determine the capacity of the concrete containment, a pushing and covering analysis is carried out under a uniformly distributed mode load, and the displacement corresponding to the tail end of the line segment of the displacement curve of the shear force and the vertex of the substrate is taken as the anti-cracking and anti-seismic capacity of the containment, namely a failure threshold value. The displacement corresponding to the end of the segment of the shear curve of the substrate from the vertex displacement obtained in the example is 18.8mm, which is the vertex displacement capacity value of the containment fracture. In order to calculate the median earthquake capability value of the secondary system structure, the selected earthquake record is scaled and amplitude-modulated to the spectrum acceleration of 0.95g of the nuclear power plant consistent risk spectrum at the first self-vibration period of the structure, which is the spectrum ordinate of the target design spectrum at the first self-vibration period of the structure. The structural earthquake median capability of the secondary system adopts an earthquake capability value of the secondary system with a 50% guarantee rate level, and the calculation formula is as follows:
Figure BDA0004095889160000061
wherein y is i Is the AFSA value, beta of the secondary system obtained by dynamic time-course analysis r And beta u The values of (2) are 0.26 and 0.34, respectively.
The median structural seismic capacities for nodes 2, 10 and 12 were found in the examples to be 0.067g, 3.530g and 5.960g, respectively.
(3) And scaling the near-field pulse wave, and scaling the original seismic wave intensity by 1, 2, 3, 4, 5 and 6 times according to the magnitude of the ground peak acceleration PGA so as to consider the stiffness degradation effect of the nuclear power plant under the over-design reference seismic to form 600 random seismic waves. And selecting the earthquake motion parameters, and carrying out random dynamic response analysis to form a data set. Among them, the earthquake motion parameters include 33 usual earthquake motion parameters such as PGA and the like which are directly obtained from earthquake motion and parameters such as Sa (T1) and the like which are obtained from structural elastic reaction. The earthquake motion parameters are shown in table 1.
TABLE 1 details of seismic parameters
Figure BDA0004095889160000062
Figure BDA0004095889160000071
(4) The 30% dataset was retained and used as the test set for evaluation based on the demand response and selected seismic parameters from the time course analysis. The data set partitioning process is random, training and validation using 10-fold cross validation for the remainder.
Feature selection is based on the RRF algorithm, implemented using random forest basis Yu Jini importance, by comparing the predicted mean square error change for each variable caused by splitting in the regression tree growth as a criterion for variable exclusion. In the recursive process, the most important IMs of 3/4 are preserved to reconstruct the model according to the importance of the variables. The 1/4 least significant earthquake motion parameters are recursively deleted and a new forest is built using the remaining IM until only one IM remains.
Further, in an embodiment, 14 machine learning regression algorithms are selected, including: (i) Linear regression-based methods including linear regression LR, bayesian regression BR, auto-correlation determination regression ARD and Huber regression HR; (ii) kernel-based kernel ridge regression KR; (iii) The decision boundary-based method comprises the steps of enabling a support vector machine to return SVR and enabling a nu support vector machine to return NuSVR; (iv) a K nearest neighbor KNN based on distance; (v) gaussian process kernel GK based on gaussian process; (vi) Tree enhancement-based methods, including decision tree DT, random forest RF, gradient enhancement GB, adaptive enhancement ADAB, and extreme gradient boost XGB.
The machine learning performance evaluation index is determined, and in the embodiment, four performance indexes of a decision coefficient (R2), an average absolute error (MAE), a Mean Square Error (MSE) and a Root Mean Square Error (RMSE) are specifically adopted. The specific formula is as follows:
Figure BDA0004095889160000081
Figure BDA0004095889160000082
Figure BDA0004095889160000083
Figure BDA0004095889160000084
in the middle of
Figure BDA0004095889160000085
As predicted value, y i Representing the target value obtained by the ith time course analysis, and y is the average value of the target values.
For performance indexes MAE, MSE and RMSE, the value interval is 0 to + -infinity, the larger the value is, the larger the overall error of the model is, the value interval of R2 is 0-1, and the closer the value is to 1, the better the overall performance of the model is. The use of RRF-based feature selection to determine optimal seismic parameters based on the above-described evaluation criteria, see fig. 3, does not significantly improve overall accuracy before the peak point, but cannot be ignored, demonstrating the benefit of EDP response prediction in combination with higher performance multiple IMs. However, it is not beneficial to add more IMs after a certain number, but rather, redundancy of IM can affect the performance of ML. The performance of the EDP response is predicted by model selection and comparison of various ML regression algorithms, see fig. 4, GK and GB regression respectively generate the most accurate prediction results for the containment and secondary systems, and therefore the optimal machine learning prediction model of each seismic demand parameter is selected, and is specifically shown in table 2.
TABLE 2 optimal ML model for EDPs
Figure BDA0004095889160000086
Figure BDA0004095889160000091
(5) And selecting an optimal machine learning prediction model, adopting a test set to verify the effect of the prediction model, and simultaneously comparing the effect with a linear prediction model formed by scalar or vector IMs with highest correlation. Through correlation studies of nuclear power plant containment and secondary systems EDPs and 33 IMs, sa (T1) correlated highest for Dmax8 and AFSA2, followed by Sd (T1), ASI correlated highest for AFSA10 and AFSA12, followed by Sa (T1). The same training set was used to determine a conventional linear regression model as shown in table 3. The performance of the model on the test set is used as an index of the unknown data performance, namely the generalization capability of the model, EDP response prediction is carried out on the test set in the embodiment according to the model of the table 3, and the optimal multi-element IMs model based on machine learning is compared with the predicted EDP response of the traditional scalar IM and vector IMs linear model, and the model is shown in figure 5. The dashed line in the figure represents the contour line of the predicted value and the target value, the abscissa of each discrete point is the target value based on time-course analysis, the ordinate is the predicted value based on ML multiple IMs, traditional scalar IM and vector IMs models, it can be seen that the predicted output point based on ML multiple IMs models is more close to the vicinity of the dashed line of the 'prediction-target', the accuracy of the predicted EDP response of each component of the nuclear power plant is compared, the model based on machine learning multiple IMs can be found, the prediction accuracy of the containment is 92.0%, the traditional scalar-based model is 85.4%, and the model based on vector IMs is 85.3%. It can be seen that EDP and IM of the concrete containment have strong linear correlation, and there is little change from scalar IM input to vector IMs, and the use of ML multivariate IMs predictive model is a significant improvement. For a secondary system, the prediction accuracy based on scalar IM is 76.8, 80.1% and 74.4%, the model accuracy based on vector IMs is 77.3%, 82.1% and 76.9%, respectively, while the prediction accuracy based on machine learning is remarkably improved by 10.1-10.6%, 9.3-11.3% and 11.6-14.1%, respectively, and the prediction accuracy can reach 87.4%, 91.4% and 88.5% respectively. The present results find that machine learning models that consider multiple IMs and capture nonlinear behavior are more suitable than models that consider scalar or vector IMs using linear regression, particularly on secondary systems. Therefore, having a ML-based multivariate IMs prediction model has great potential to improve PSDM.
TABLE 3 Linear prediction model form based on traditional scalar IM and vector IMs
Figure BDA0004095889160000092
Figure BDA0004095889160000101
(6) In an embodiment, sa (T1) is selected as the earthquake motion intensity index, MSA is performed on Sa (T1) and earthquake requirement response of the sample, and Sa (T1) of earthquake motion in each test data set is scaled to 0.5g-5.0g with an interval of 0.5g. Further performing time-course analysis on the 10 earthquake intensity levels to obtain structural earthquake demand response under specific IM, and comparing the demand response of MSA based on the optimal ML model and MSA based on the traditional scalar IM and vector IMs model, as shown in figure 6. FIG. 6 shows the EDP response distribution of a nuclear plant for 10 target intensities in a near field pulse seismic event. The dashed line represents the average of the EDP responses from different earthquakes and the dashed line represents the EDP failure threshold for each component of the nuclear power plant. The fringe distribution based on the traditional scalar IM, vector IMs model is close to the target output based on nonlinear time-course analysis at low intensities. However, based on nonlinear time-course analysis results, stripe distribution based on the traditional scalar IM and vector IMs models has high prediction bias under strong seismic intensity, and the ML model can more accurately capture inelastic behaviors caused by stiffness degradation under over-design reference earthquakes, in particular EDP response distribution reflected at Dmax 8. Therefore, in the low Sa (T1) range, the vulnerability can be well estimated by the linear regression (cloud) based method, and the calculation amount is small. However, it does not give an accurate output over a higher intensity range, while ML-based multivariate IMs can capture well the nonlinearity of IM-EDP relations.
Using the median seismic capability of the containment structure and secondary system structure as a failure threshold, the probability of exceeding the threshold for a given seismic intensity is calculated. The specific expression of the failure probability is as follows:
F(im)＝P(EDP＞edp j |IM＝im)
in edp j Is the failure threshold of EDP; IM is a particular value for IM.
And determining corresponding median and logarithmic standard deviation under the damage states of the containment and the secondary system according to a least square method to obtain a vulnerability curve. In the embodiment, a comparison graph of an MSA predicted vulnerability curve based on an ML multi-element IMs model and a vulnerability curve established based on a scalar or vector IMs model is shown in fig. 7, the reliability of the MSA based on the ML multi-element IMs model on the vulnerability of a containment and a secondary system is obviously larger than that of the MSA based on a scalar IM or vector IMs model, the vulnerability curve caused by the traditional method is steeper, and the MSA based on the ML multi-element IMs model generates a vulnerability curve which is more approximate to that of the MSA method using time-course analysis data. Compared with the traditional linear regression model based on scalar IM and vector IMs, the multi-element IMs prediction model based on ML can capture more accurate median and logarithmic standard deviation when applied to MSA, effectively and accurately considers the rigidity degradation of the nuclear power plant under the over-design reference earthquake, and captures the inelastic behavior under the strong earthquake. It can be seen that the vulnerability profile of the containment is steeper relative to the secondary system, which also indicates that the EDP of the containment has a strong linear relationship with Sa (T1). Notably, the predicted vulnerability curves based on machine learning multiple IMs, vector IMs and scalar IM model Dmax8 and AFSA2 deviate from the time-course analysis derived reference curves, the latter being steeper than the former. This is because the correlation between these two EDPs and Sa (T1) is strongest, sa (T1) is the dominant factor in the regression model formed by training, and especially in scalar IM-based predictions, sa (T1) is the only factor, and the fringes formed in MSA based on Sa (T1) become discrete points, which increases the deviation of the vulnerability curve. MSA based on ML multiple IMs is not accurate in MSA based on nonlinear time-course analysis data, however, the vulnerability curve precision is superior to that of the traditional linear regression model based on scalar IM or vector IMs, and the calculation level approaches to cloud, so that the time of nonlinear time-course analysis is greatly reduced, and the risk assessment efficiency of a nuclear power plant is improved.
Taken together, the methods presented herein are shown to be effective.
The present invention has been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present invention.

Claims (8)

1. The method for predicting the earthquake vulnerability of the nuclear power plant based on machine learning and MSA is characterized by comprising the following steps:
s1, establishing a nuclear power plant earthquake response model;
s2, calculating structural earthquake median capability values of the containment and the secondary system;
s3, scaling the near-field pulse wave, selecting earthquake motion parameters, and performing random dynamic time-course analysis to form a data set;
s4, performing feature selection and model selection by using machine learning, and determining an optimal machine learning prediction model;
s5, establishing a PSDM based on machine learning, realizing earthquake demand response prediction, and verifying a prediction model effect;
s6, MSA is carried out by using a prediction model, and the median value and standard deviation of the failure of the containment and the secondary system of the nuclear power plant are determined according to a least square method, so that a vulnerability curve of the containment and the secondary system of the nuclear power plant is established.
2. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 1, wherein: the step S1 specifically comprises the following steps: determining calculation parameters of a nuclear power plant containment seismic response model, selecting original unscaled near-field pulse seismic waves, and calculating seismic demand response;
the calculated parameters of the nuclear power plant containment seismic response model comprise: structural distribution of the containment and secondary systems, material parameters, floor mass and rotational inertia of the structure, geometric area, shear area and moment of inertia of the floor, wherein the material parameters comprise dynamic elastic modulus, shear modulus, poisson ratio and damping ratio of the concrete;
and the original unscaled near-field pulse seismic waves are selected by utilizing response spectrum matching, and seismic wave preprocessing including filtering and baseline zeroing is carried out in a PEER strong earthquake database, so that the average frequency spectrum of the input seismic waves is consistent with the RG1.60 design frequency spectrum.
3. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 2, wherein: the earthquake demand response is obtained by inputting random vibration into an established nuclear power plant earthquake response model, a nuclear power plant power response calculation model can be formed, power time course analysis is carried out, and power response results of a containment and a secondary system of the nuclear power plant under different earthquakes are obtained, wherein the containment takes a maximum value Dmax of peak displacement as an earthquake demand parameter, and the secondary system takes an average floor acceleration response spectrum value AFSA of 5-33Hz as an earthquake demand parameter.
4. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 1, wherein: the step S2 specifically comprises the following steps: loading in a uniform distribution mode, and performing pushing and covering analysis to obtain a vertex displacement-substrate shear curve, wherein the displacement corresponding to the tail end of the linear section is the structural earthquake median capability of the containment; and (3) performing dynamic time-course analysis on the selected near-field pulse wave, zooming and amplitude-modulating to the spectrum acceleration of the nuclear power plant consistent risk spectrum at the first self-vibration period of the structure by 0.95g, and selecting the secondary system AFSA in S1 as an index to obtain the corresponding secondary system and the structure earthquake median capability, wherein the specific expression is as follows:
Figure FDA0004095889150000011
wherein y is i Is the secondary system AF obtained by dynamic time course analysisSA value, logarithmic standard deviation beta r Representing the randomness of the earthquake motion, the logarithmic standard deviation beta u Representing uncertainty of structural material, beta r And beta u The values of (2) are 0.26 and 0.34, respectively.
5. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 1, wherein: the step S3 specifically comprises the following steps: the near-field pulse wave scaling refers to adjusting the original seismic wave into a set of seismic waves with discrete intensity levels according to the magnitude of the ground peak acceleration PGA so as to comprise a sufficient number of over-designed reference seismic waves to consider the inelastic behavior of the structure in a higher intensity range and expand the range of machine learning training samples; the earthquake motion parameters comprise parameters obtained directly from earthquake motion and parameters obtained from structural elastic reaction.
6. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 1, wherein: the step S4 specifically comprises the following steps: the dataset was then set to 7:3, randomly dividing, namely, taking the random division as a training set and a testing set respectively, wherein the characteristics in characteristic selection are IM, the characteristic selection is realized by using an iterative elimination random forest algorithm RRF based on the importance of the radix, and the mean square error change of each variable prediction caused by splitting in the growth of a regression tree is compared to be taken as a variable elimination standard; 3/4 of the most important IMs are reserved to reconstruct the model; recursively deleting 1/4 least significant IMs, and constructing a new forest by using the rest IMs until only one IM is left; the model includes 14 selected machine learning regression algorithms, including: (i) a linear regression-based method: including linear regression LR, bayesian regression BR, auto-correlation determination regression ARD and Huber regression HR; (ii) kernel-based kernel ridge regression KR; (iii) a decision boundary based method: the method comprises the steps of supporting a vector machine regression SVR and nu supporting a vector machine regression NuSVR; (iv) a K nearest neighbor KNN based on distance; (v) gaussian process kernel GK based on gaussian process; (vi) a tree-based enhancement method: comprises decision tree DT, random forest RF, gradient enhancement GB, adaptive enhancement ADAB and extreme gradient boost XGB, R 2 MAE, MSE, RMSE are evaluation indexes, and the performance of the machine learning model is evaluated by using 10-fold cross validation, and the optimal machine learning prediction model is selected.
7. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 1, wherein: the step S6 specifically comprises the following steps: and (3) scaling the original earthquake motion selected in the step (S1) to a specific target intensity level as the input of a prediction model according to the nuclear power plant earthquake demand response prediction model obtained in the step (S5), obtaining corresponding structural earthquake demand response output, calculating the failure probability of the structure under the specific IM by using the structural earthquake median capability proposed in the step (S2) as the failure threshold value, fitting by using a least square method, quantifying the median and the uncertainty, and obtaining the vulnerability curves of the containment and secondary systems of the nuclear power plant.
8. The method for predicting seismic vulnerability of nuclear power plant based on machine learning and MSA of claim 7, wherein: the specific expression of the failure probability is as follows:
F(im)＝P(EDP＞edp j IM＝im)
in edp j Is the failure threshold of EDP; IM is a particular value for IM.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117271964A (en) * 2023-09-01 2023-12-22 南昌航空大学 Probability earthquake analysis model optimization method in subway station structure based on probability earthquake demand analysis model

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