Ground motion intensity index selection method based on kernel density estimation and related equipment

Abstract

The application discloses a kind of based on kernel density estimation seismic intensity index selection method and related equipment, the method includes: the finite element model of high-pile wharf is constructed;Based on finite element model, obtain the maximum horizontal displacement of high-pile wharf under the action of seismic ground motion, get engineering demand parameter;By kernel density estimation, construct probability seismic demand model;Based on probability seismic demand model, construct the evaluation criteria of candidate seismic intensity index;Based on fuzzy analytic hierarchy process, obtain the target weight of evaluation criteria;According to target weight, obtain the comprehensive score of each candidate seismic intensity index;The candidate seismic intensity index corresponding to the maximum comprehensive score is obtained, and the target seismic intensity index of high-pile wharf is obtained.The application can improve the engineering applicability and decision reliability of index selection result, and can be widely applied in the field of earthquake engineering technology.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering technology, and in particular to a method and related equipment for selecting seismic motion intensity indices based on kernel density estimation. Background Technology

[0002] In the field of earthquake engineering, seismic vulnerability analysis of structures is a crucial method for evaluating their seismic performance. For high-pile wharves, earthquake damage surveys indicate that damage during earthquakes can lead to substantial economic losses. Within the framework of probabilistic seismic demand analysis (PSDA), it is necessary to establish the probabilistic relationship between the intensity index (IM) and the engineering demand parameter (EDP) of the high-pile wharf, thereby calculating the probability that the wharf will reach or exceed a certain limit state under different seismic intensities. The appropriate selection of the IM directly determines the accuracy and reliability of the vulnerability analysis results. An ideal IM should possess characteristics such as high efficiency (i.e., low dispersion of the EDP given the IM), sufficiency (independent of other characteristics of the seismic motion), and monotonicity (the EDP changes monotonically with the IM). However, in reality, dozens of candidate IMs exist, requiring the selection of one or a few IMs with optimal overall performance.

[0003] Traditional methods for optimizing IM (Instantaneous Mobility) are mostly based on the assumption of log-linear regression, which assumes that IM and EDP (Effective Dependent Product) have a linear relationship in logarithmic space and that the residuals have homogeneity of variance. However, when actual wharf structures enter the nonlinear stage under strong earthquakes, the IM-EDP relationship often exhibits significant nonlinearity and heteroscedasticity, making traditional linear regression methods prone to systematic bias. Furthermore, existing evaluation indicators are mostly single-dimensional (such as focusing only on efficiency or sufficiency), lacking a comprehensive, multi-criteria evaluation system, making it difficult to fully reflect the merits of IM. Summary of the Invention

[0004] In view of this, the main objective of this invention is to provide a method and related equipment for selecting seismic intensity indicators based on kernel density estimation, in order to solve at least one of the problems in the prior art. This invention can improve the engineering applicability and decision-making reliability of the indicator selection results.

[0005] To achieve the above objectives, one aspect of the present invention provides a method for selecting seismic intensity indices based on kernel density estimation, the method comprising: Construct a finite element model of the high-pile wharf; Based on the finite element model, the maximum horizontal displacement of the wharf panel under seismic motion is obtained, and the engineering requirement parameters are obtained. A probabilistic earthquake demand model is constructed using kernel density estimation. Based on the probabilistic earthquake demand model, an evaluation criterion for the seismic motion intensity index is constructed. The target weights of the evaluation criteria are obtained based on the fuzzy hierarchical analysis method. Based on the target weights, obtain the comprehensive score for each of the seismic motion intensity indicators; The seismic intensity index corresponding to the highest comprehensive score is obtained to obtain the target seismic intensity index of the high-pile wharf.

[0006] In some embodiments, constructing the finite element model of the high-pile wharf includes the following steps: Piles are simulated using nonlinear beam-column elements and fiber sections; The soil was simulated using a four-node plane strain element. The contact surface between the pile and the soil is simulated using thin-layer elements after reducing the shear parameters; The hydrostatic pressure and dynamic inertia of water bodies are simulated using the equivalent load-mass method. A finite element model is established based on the pile, the soil, the contact surface, and the effects of hydrostatic pressure and hydrodynamic inertia, and free field boundaries are set on both sides of the finite element model.

[0007] In some embodiments, obtaining the maximum horizontal displacement of the wharf deck under seismic motion based on the finite element model to obtain the engineering requirement parameters includes the following steps: Select batch of ground motion samples; The seismic motion is input into the finite element model, and the maximum horizontal displacement of the wharf panel under the action of seismic motion is obtained through nonlinear dynamic time history analysis. The maximum horizontal displacement of the wharf panel is used as the engineering requirement parameter.

[0008] In some embodiments, constructing a probabilistic seismic demand model through kernel density estimation includes the following steps: The seismic intensity index is logarithmically transformed to obtain the logarithmic domain intensity index; Perform a logarithmic transformation on the engineering requirement parameters to obtain logarithmic domain requirement parameters; Obtain a one-dimensional kernel density estimate of the logarithmic field strength index; Two-dimensional data is obtained based on the logarithmic domain strength index and the logarithmic domain requirement parameters; Obtain a two-dimensional kernel density estimate of the two-dimensional data; Dividing the two-dimensional kernel density estimate by the one-dimensional kernel density estimate yields the probabilistic earthquake demand model.

[0009] In some embodiments, obtaining the target weights of the evaluation criteria based on fuzzy hierarchical analysis includes the following steps: Based on the relative importance relationships among the various evaluation criteria, obtain the triangular fuzzy number; Based on the triangular fuzzy number, construct a fuzzy judgment matrix; Based on the fuzzy judgment matrix, the target weights corresponding to each of the evaluation criteria are obtained.

[0010] In some embodiments, obtaining the target weights corresponding to each evaluation criterion based on the fuzzy judgment matrix includes the following steps: Obtain the row and vector, and column and vector of the fuzzy judgment matrix; the row and vector include row and upper bound value, row and middle value, and row and lower bound value; the column and vector include column and upper bound value, column and middle value, and column and lower bound value. Divide the row and upper bound value by the column and lower bound value to obtain the comprehensive degree upper bound component; Divide the row and the median value by the column and the median value to obtain the comprehensiveness median component; Divide the row and lower bound by the column and upper bound to obtain the lower bound component of the comprehensive degree. The fuzzy comprehensiveness of the evaluation criterion is obtained based on the upper bound component of the comprehensiveness, the middle component of the comprehensiveness, and the lower bound component of the comprehensiveness. The sharpness coefficient of the evaluation criterion is obtained by arithmetically averaging the upper bound component, the middle component, and the lower bound component of the fuzzy comprehensive degree. The clarification coefficients of all the evaluation criteria are normalized to obtain the target weights corresponding to each evaluation criterion.

[0011] In some embodiments, obtaining a comprehensive score for each seismic intensity index based on the target weight includes the following steps: The efficiency index value of the efficiency criterion is reverse normalized to obtain the first normalized index. The distance correlation coefficient of the dependency criterion is positively normalized to obtain the second normalized index; The mutual information content of the mutual information criterion is positively normalized to obtain the third normalization index; The ridge slope index value of the monotonic sensitivity criterion is positively normalized to obtain the fourth normalized index. Based on the target weights corresponding to each of the evaluation criteria, the first normalized index, the second normalized index, the third normalized index, and the fourth normalized index are weighted and summed to obtain the comprehensive score of the seismic intensity index. The evaluation criteria include the efficiency criterion, the dependency criterion, the mutual information criterion, and the monotonic sensitivity criterion.

[0012] To achieve the above objectives, another aspect of the present invention proposes a seismic intensity index selection device based on kernel density estimation, the device comprising: The finite element model building module is used to build finite element models of high-pile wharves; The engineering requirement parameter acquisition module is used to obtain the maximum horizontal displacement of the wharf panel under seismic motion based on the finite element model, and thus obtain the engineering requirement parameters. The probabilistic earthquake demand model building module is used to construct a probabilistic earthquake demand model through kernel density estimation. The evaluation criteria construction module is used to construct evaluation criteria for ground motion intensity indicators based on the probabilistic earthquake demand model. The weight acquisition module is used to obtain the target weights of the evaluation criteria based on the fuzzy hierarchical analysis method. The comprehensive score acquisition module is used to acquire the comprehensive score of each of the seismic motion intensity indicators according to the target weight; The seismic intensity index selection module is used to obtain the seismic intensity index corresponding to the highest comprehensive score, and thus obtain the target seismic intensity index of the high-pile wharf.

[0013] To achieve the above objectives, another aspect of the present invention provides an electronic device, the electronic device including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method described above.

[0014] To achieve the above objectives, another aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0015] To achieve the above objectives, another aspect of the present invention provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions to cause the computer device to perform the aforementioned method.

[0016] The embodiments of the present invention include at least the following beneficial effects: The present invention provides a method and related equipment for selecting seismic intensity indicators based on kernel density estimation. This scheme accurately restores the dynamic characteristics between piles, soil, and water by constructing a finite element model of a high-pile wharf; based on the finite element model, the maximum horizontal displacement of the wharf panel under seismic action is obtained, and engineering requirement parameters are obtained, which can effectively characterize the overall deformation degree of the wharf and are directly related to the structural damage state; through kernel density estimation, a probabilistic earthquake requirement model is constructed without the need for preset distribution assumptions, improving the model's adaptability to rare earthquakes; based on the probabilistic earthquake requirement model, evaluation criteria for seismic intensity indicators are constructed, transforming the indicator selection problem into a quantifiable multi-attribute decision problem; based on fuzzy hierarchical analysis, the target weights of the evaluation criteria are obtained, effectively resolving the fuzziness and subjective preferences of qualitative judgments in expert experience, and enhancing the objectivity and engineering rationality of weight allocation; according to the target weights, the comprehensive score of each seismic intensity indicator is obtained, realizing the integrated quantification of multi-dimensional evaluation criteria; the seismic intensity indicator corresponding to the largest comprehensive score is obtained, and the target seismic intensity indicator of the high-pile wharf is obtained, selecting the optimal key input parameters for the seismic fortification and vulnerability analysis of the high-pile wharf. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the method for selecting seismic intensity indices based on kernel density estimation provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the hardware structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0020] It should be noted that although functional modules are divided in the system diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terms "first / S100" and "second / S200" in the specification, claims, and the foregoing drawings may be used herein to describe various concepts, but unless specifically stated otherwise, these concepts are not limited by these terms. These terms are used only to distinguish one concept from another. For example, first information may also be referred to as second information without departing from the scope of the embodiments of the invention, and similarly, second information may also be referred to as first information. Depending on the context, the words "if" or "when" as used herein may be interpreted as "when," "in response to a determination," or "in the event of a determination."

[0021] The terms “at least one,” “multiple,” “each,” “any,” etc., used in this invention, “at least one” includes one, two, or more than two; “multiple” includes two or more than two; “each” refers to each of the corresponding multiple; and “any” refers to any one of the multiple.

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0023] Before providing a detailed description of the embodiments of the present invention, some of the nouns and terms involved in the embodiments of the present invention will be explained first. The nouns and terms involved in the embodiments of the present invention are subject to the following interpretations.

[0024] Kernel density estimation (KDE): A nonparametric probability density estimation method that does not presuppose that the data follows a specific distribution (such as a normal distribution). Instead, it constructs a continuous density curve based on the sample data itself through a kernel function and smoothing bandwidth, which can flexibly capture the true distribution characteristics of the data.

[0025] Bandwidth: A parameter that controls the smoothness in kernel density estimation. Too little bandwidth will cause the estimated curve to fluctuate wildly (undersmooth), while too much bandwidth will mask the details of the data (oversmooth).

[0026] High-pile wharf: A wharf whose superstructure is supported by a series of piles driven into the ground, transferring the load of the wharf to the deep, solid bearing layer of the ground through the piles.

[0027] Intensity measure (IM) is a physical parameter used to quantitatively describe the intensity of ground motion during an earthquake. Common parameters include peak ground acceleration (PGA), peak velocity, spectral acceleration, Arias intensity, and cumulative absolute velocity.

[0028] Engineering demand parameter (EDP): Indicators describing the response of an engineering structure under seismic action, such as inter-story drift angle, pier top displacement, beam end rotation angle, and base shear force, are used to assess the degree of structural damage.

[0029] Probabilistic Seismic Demand Analysis (PSDA): An analytical method for establishing the probabilistic relationship between the Intensity Indicator (IM) and Engineering Demand Parameter (EDP). It aims to obtain the probability distribution of the EDP given the IM and is the basis for seismic vulnerability analysis and risk assessment.

[0030] Fuzzy Hierarchical Analysis (FAHP): A multi-criteria decision-making method that combines fuzzy mathematics with hierarchical analysis. It uses triangular fuzzy numbers to express the uncertainty of pairwise comparison judgments and is suitable for solving the problem of determining the weights of indicators with fuzziness and subjectivity.

[0031] In related technologies, traditional probabilistic seismic demand models typically assume a logarithmic linear relationship between ground motion intensity indices and engineering demand parameters in logarithmic space. However, this model implicitly contains two strong constraints: linear correlation and homogeneity of variance, resulting in the following limitations: when the IM-EDP relationship exhibits significant nonlinearity, a single logarithmic straight line cannot effectively fit the actual dependency; the homoscedasticity assumption assumes that different IM levels... EDP The conditional variance is always constant. However, actual data often exhibits heteroscedasticity; normality assumption: error term The assumption that the structure follows a normal distribution is not always true. In actual earthquake engineering, high-pile wharf structures are mostly complex nonlinear systems, and their seismic responses exhibit significant nonstationarity and state dependence. Traditional global log-linear regression methods are prone to causing systematic biases in the assessment of seismic intensity indices and subsequent assessments of the wharf's seismic vulnerability.

[0032] In view of this, this invention provides a method and related equipment for selecting seismic intensity indices based on kernel density estimation. This method utilizes the nonparametric modeling capabilities of kernel density estimation to adaptively capture the nonlinear relationship and heteroscedasticity characteristics between the engineering requirements parameters of high-pile wharf structures and seismic intensity indices, avoiding the assumption biases of traditional parametric models. Furthermore, it constructs a four-dimensional evaluation criterion system including efficiency, dependency, mutual information, and monotonic sensitivity, comprehensively quantifying the performance of seismic intensity indices from four perspectives: prediction accuracy, correlation strength, information content, and response sensitivity. Then, based on the fuzzy hierarchical analysis method (FAHP), the weights of each evaluation criterion are determined, and the relative importance relationship between the evaluation criteria is expressed using a triangular fuzzy number complementary scaling method, ensuring a scientific and reasonable weight allocation for each criterion. Finally, the comprehensive scoring and ranking of candidate seismic intensity indices for wharf structures provides optimal seismic intensity index recommendations for wharf seismic design and post-earthquake repair decisions.

[0033] The method for selecting seismic intensity indices based on kernel density estimation provided in this invention relates to the field of earthquake engineering technology. This method can be applied to terminals, servers, or software running on either. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle-mounted terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the method for selecting seismic intensity indices based on kernel density estimation, but is not limited to the above forms.

[0034] Figure 1 This is an optional flowchart of a method for selecting seismic intensity indices based on kernel density estimation, provided in an embodiment of the present invention. Figure 1 The method may include, but is not limited to, steps S100 to S700: Step S100: Construct the finite element model of the high-pile wharf; Step S200: Based on the finite element model, obtain the maximum horizontal displacement of the wharf panel under the action of seismic motion to obtain the engineering requirement parameters. Step S300: Construct a probabilistic earthquake demand model through kernel density estimation; Step S400: Based on the probabilistic earthquake demand model, construct the evaluation criteria for candidate ground motion intensity indices. Step S500: Based on fuzzy hierarchical analysis, obtain the target weights of the evaluation criteria; Step S600: Obtain the comprehensive score of each candidate ground motion intensity index according to the target weight; Step S700: Obtain the candidate ground motion intensity index corresponding to the highest comprehensive score, and obtain the target ground motion intensity index of the high-pile wharf.

[0035] In step S100 of some embodiments, a finite element model is established on the OpenSees platform for the high-pile wharf to accurately restore the dynamic characteristics of the piles, soil and water, and overcome the simulation deviation of traditional simplified algorithms in terms of spatial forces and boundary constraints.

[0036] In some embodiments, step S100 may include, but is not limited to, steps S110 to S150: Step S110: Simulate the pile using nonlinear beam-column elements and fiber sections; Step S120: Simulate the soil using a four-node plane strain element; Step S130: Simulate the contact surface between the pile and the soil using thin-layer elements after reducing shear parameters; Step S140: Simulate the hydrostatic pressure and dynamic inertia of the water body using the equivalent load-mass method; Step S150: Based on the pile, soil, contact surface, and the effects of hydrostatic pressure and hydrodynamic inertia, establish a finite element model and set free field boundaries on both sides of the finite element model.

[0037] In step S110 of some embodiments, the pile is simulated using nonlinear beam-column elements and fiber sections, and the fiber sections and constitutive materials used in the pile are selected according to the actual situation of the pile.

[0038] In step S120 of some embodiments, the soil is simulated using a four-node plane strain element based on Biot's pore medium theory. Optionally, a pressure-dependent multi-yield material constitutive model is used for cohesive soil, and a pressure-independent multi-yield material constitutive model is used for cohesive soil.

[0039] In step S130 of some embodiments, the contact surface between the pile and the soil is simulated by setting a thin layer unit with a thickness of 0.1m and reducing the shear parameters of the thin layer unit.

[0040] In step S140 of some embodiments, the equivalent load-mass method is used to consider the hydrostatic pressure and hydrodynamic inertia of the water body. The equivalent load-mass method simplifies the complex fluid-structure interaction of the water body on the high-pile wharf into statically distributed equivalent loads (simulating hydrostatic pressure) and an equivalent mass matrix attached to the structure (simulating hydrodynamic inertia). This allows for efficient and stable solutions to the dynamic response of the wharf-water system without considering the water body solid elements. The finite element model of the high-pile wharf can reflect both the initial stress state caused by hydrostatic pressure and achieve a refined simulation of the dynamic characteristics of the structure under the influence of water inertial forces during earthquakes, thus ensuring the reliability of subsequent earthquake demand analysis and strength index selection.

[0041] In step S150 of some embodiments, a finite element model of a high-pile wharf can be obtained based on the simulated piles, soil, contact surfaces, and hydrostatic pressure and hydrodynamic inertia. Free field boundaries are set on both sides of the finite element model to simulate the semi-infinite site radiation damping effect.

[0042] In step S200 of some embodiments, since the maximum horizontal displacement of the wharf panel can be quantitatively mapped to the peak strain of the pile body through pushover analysis, the maximum horizontal displacement of the wharf panel under seismic action is obtained as a core engineering requirement parameter. This engineering requirement parameter can effectively characterize the overall deformation degree of the wharf and is directly related to the structural damage state, providing an accurate and reliable data foundation for the subsequent construction of a probabilistic earthquake requirement model based on kernel density estimation and the selection of seismic intensity indicators.

[0043] In some embodiments, step S200 may include, but is not limited to, steps S210 to S230: Step S210: Select a batch of ground motions; Step S220: Input the seismic motion into the finite element model and obtain the maximum horizontal displacement of the wharf panel under the action of seismic motion through nonlinear dynamic time history analysis. Step S230: The maximum horizontal displacement of the wharf panel is used as the engineering requirement parameter.

[0044] In step S210 of some embodiments, based on the established finite element model of the high-pile wharf, a batch of ground motions are selected as a consistent excitation and input into the bottom of the finite element model. For each selected ground motion, various ground motion intensity indices IM can be calculated from the time history of that ground motion, including peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), velocity spectrum intensity (VSI), etc.

[0045] In steps S220 to S230 of some embodiments, after inputting the seismic motion into the finite element model, the maximum horizontal displacement of the wharf panel under seismic action can be obtained as a core engineering requirement parameter through nonlinear dynamic time history analysis.

[0046] In step S300 of some embodiments, kernel density estimation is used for completely nonparametric modeling. It does not require pre-setting the data distribution and can automatically capture arbitrarily complex nonlinear trends and heteroscedastic characteristics, thereby obtaining a conditional probability density estimate that better reflects the actual situation of high-pile wharves. This allows for the construction of a probabilistic seismic demand model and avoids systematic biases. Kernel density estimation is a nonparametric density estimation method that does not pre-set the data distribution but constructs a smooth probability density function based on the sample data itself.

[0047] In some embodiments, step S300 may include, but is not limited to, steps S310 to S360: Step S310: Perform a logarithmic transformation on the candidate ground motion intensity index to obtain the logarithmic domain intensity index; Step S320: Perform a logarithmic transformation on the engineering requirement parameters to obtain the logarithmic domain requirement parameters; Step S330: Obtain a one-dimensional kernel density estimate of the logarithmic field strength index; Step S340: Obtain two-dimensional data based on the logarithmic domain strength index and the logarithmic domain requirement parameters; Step S350: Obtain the two-dimensional kernel density estimate of the two-dimensional data; Step S360: Divide the two-dimensional kernel density estimate by the one-dimensional kernel density estimate to obtain the probabilistic earthquake demand model.

[0048] In steps S310 to S320 of some embodiments, in earthquake engineering, the seismic intensity index and engineering requirement parameters typically follow a log-normal distribution. Therefore, a logarithmic transformation is first performed on the candidate seismic intensity indices in all valid samples to obtain the logarithmic domain intensity index. Simultaneously, a logarithmic transformation is performed on the engineering requirement parameters in all valid samples to obtain the logarithmic domain requirement parameters. Valid samples refer to usable observational sample data obtained from the nonlinear time-history analysis of the same seismic motion, where the analysis converges and no collapse or numerical divergence occurs. For example, performing a logarithmic transformation on all valid samples yields the following expression: ; ; In the formula, Represents the strength index of the logarithmic field; Represents the intensity of ground motion; Represents the logarithmic field requirement parameter; Representative engineering requirement parameters; This represents a logarithmic transformation operation.

[0049] In step S330 of some embodiments, for a one-dimensional random variable Given 1 independent and identically distributed observation sample Then the kernel estimate of the probability density function of the random variable is: ; In the formula, Represents random variables The kernel estimate of the probability density function represents the value at the point to be measured. The density obtained from the above estimation; Represents the number of samples; Representing the One sample; Represents the sample index; Represents bandwidth, used to control the smoothness of the estimate; bandwidth It is the most critical parameter in kernel density estimation. Too small a value can lead to excessive fluctuations (unsmoothness). Excessive smoothing can obscure the true nature of the phenomenon. Representative of the points to be measured With sample points Distance, in bandwidth Dimensionless; The kernel function is typically the standard normal density function (Gaussian kernel): ; In the formula, The independent variable representing the kernel function is the dimensionless distance.

[0050] For the one-dimensional case, the asymptotically optimal bandwidth using a Gaussian kernel is: ; In the formula, The optimal bandwidth represents the one-dimensional kernel density estimation; This represents the sample standard deviation.

[0051] In some embodiments, the optimal bandwidth of the one-dimensional kernel density estimation is used for or Optionally, for the logarithmic domain strength index This one-dimensional continuous variable, Taking the logarithm of each valid sample of seismic intensity index yields a logarithmic domain intensity index sample. First, obtain samples of the logarithmic domain strength index. Standard deviation Based on standard deviation Calculate the optimal bandwidth for one-dimensional kernel density estimation of the logarithmic domain strength index. Then we have the following expression: ; Then the optimal bandwidth Substituting into the kernel density estimation formula, we obtain the kernel estimation expression for the probability density function of the logarithmic domain strength index as follows: ; In the formula, This represents a one-dimensional kernel density estimate of the logarithmic field strength index; Representative of the points to be measured With sample points Distance, in bandwidth Dimensionless.

[0052] Optionally, for logarithmic field required parameters This one-dimensional continuous variable, By taking the logarithm of each valid sample of engineering requirement parameters, we can obtain a sample of logarithmic domain requirement parameters. First, obtain a sample of the required parameters for the logarithmic field. Standard deviation Based on standard deviation Calculate the optimal bandwidth for a one-dimensional kernel density estimate of the logarithmic domain demand parameter. Then we have the following expression: ; Then the optimal bandwidth Substituting into the kernel density estimation formula, we obtain the kernel estimation expression for the probability density function of the logarithmic domain demand parameter: ; In the formula, This represents a one-dimensional kernel density estimate of the logarithmic domain requirement parameters; Representative of the points to be measured With sample points Distance, in bandwidth Dimensionless.

[0053] In step S340 of some embodiments, the logarithmic domain strength index and the logarithmic domain requirement parameter are combined to obtain two-dimensional data. .

[0054] In step S350 of some embodiments, for two-dimensional data Two-dimensional joint density estimation is performed using isotropic bandwidth, meaning that both dimensions use the same scalar bandwidth. The expression is: ; In the formula, Represents dimensions; The mean of the standard deviations of the two sample dimensions is represented by... and The mean of the sample standard deviation, ; This represents the number of samples, which can optionally be 1000.

[0055] For two-dimensional data The kernel estimation expression with joint probability density is:

[0056] In the formula, Two-dimensional kernel density estimation representing two-dimensional data.

[0057] In step S360 of some embodiments, according to the basic definition of probability theory, given hour conditional probability density The probability density can be determined by dividing the joint probability density by the marginal probability density, that is, dividing the two-dimensional kernel density estimate by the one-dimensional kernel density estimate. The probabilistic seismic demand model can then be expressed as: ; in, For two-dimensional data The two-dimensional joint kernel density estimation is obtained at point The density value; for A one-dimensional kernel density estimate is obtained at point The density value at that location was determined. Based on this, a probabilistic seismic demand model based on KDE was established. This probabilistic seismic demand model makes no assumptions about any parametric form, is entirely data-driven, and can adaptively capture... Nonlinear trends and heteroscedasticity characteristics in the relationship.

[0058] In some embodiments, conditional expectations can be calculated based on a probabilistic earthquake demand model. Conditional standard deviation : ; .

[0059] In step S400 of some embodiments, based on the KDE probabilistic earthquake demand model, four evaluation criteria for ground motion intensity indices are defined to comprehensively evaluate the performance of candidate ground motion intensity indices from four dimensions: efficiency, dependence, mutual information, and monotonic sensitivity. For example, the evaluation criteria include: (1) Efficiency Criterion ): Efficiency measure given (i.e., given IM) The conditional uncertainty is determined by the efficiency of the seismic demand model. Higher efficiency corresponds to a smaller conditional variance. Traditional methods use the standard deviation of linear regression residuals as a measure of efficiency, but this method is limited by the linear assumption. This invention directly estimates the conditional standard deviation based on the probabilistic seismic demand model estimated by KDE: it directly estimates the conditional probability density function of the EDP at a given IM level, then calculates the conditional standard deviation of this conditional probability density function, and finally... The mean of the conditional standard deviations of multiple points within the range is used as the final efficiency index. ; in, In order to be in Selected at equal intervals within the range of values One assessment point; The conditional standard deviation. Efficiency index value. The smaller the value, the stronger the predictive ability of IM for EDP, and the higher the efficiency of IM.

[0060] (2) Dependency criterion ): Traditional Pearson correlation coefficient can only capture linear correlations between variables, while distance correlation coefficient... Quantifiable nonlinear dependencies of any form among variables. Let... , These are valid sample pairs. The pairwise distance is calculated using the following formula: ; ; Therefore, we can obtain two. Distance matrix and .

[0061] In the formula, Representing the The sample and the first one sample Distance in direction; Representing the The sample and the first one sample Distance in a direction.

[0062] Then, for the distance matrix and The calculation formulas used for "dual-centering" include: ; ; In the formula, and This represents the matrix after bi-centering; Representation distance matrix No. The mean of all elements in a row. ; Representation distance matrix No. The mean of all elements in the column; Representation distance matrix The overall mean of all; Representation distance matrix No. The mean of all elements in a row; Representation distance matrix No. The mean of all elements in the column; Representation distance matrix The overall mean of all.

[0063] Then distance covariance Defined as: ; Distance variance , Defined as: ; ; Distance correlation coefficient The calculation formula is: ; The distance correlation coefficient ranges from [0,1], if and only if and When they are independent, Distance correlation coefficient The larger the value, the more likely it is to represent and The stronger the connection between them.

[0064] (3) Mutual information criterion ): Mutual Information (MI), originating from information theory, is a core indicator in information theory for measuring the degree of dependency between variables. It quantifies the amount of information gleaned from one variable about another; a higher MI value indicates a stronger dependency between MI and EDP, and thus better MI performance. For continuous random variables, mutual information... Defined as: ; With a finite number of samples, the mutual information can be approximated using the sample mean. : ; In the formula, Representing the Two-dimensional joint kernel density estimation of the locations of each valid sample point; Representing the One valid sample Density value at; Representing the One valid sample The density value at that location.

[0065] All density values ​​were estimated using the KDE method, and the density values ​​were truncated to the smallest positive number. This is to prevent logarithmic aberrations.

[0066] (4) Monotonicity sensitivity criterion ): The ridge line is defined as the conditional mode following The trajectory of change. The conditional mode refers to a given... When, make conditional density The largest Value, denoted as This represents the most likely EDP value for each IM value. The ridge slope measures the sensitivity of the EDP to changes in IM: the larger the absolute value of the slope, the more significant the change in EDP with IM, the more effectively IM reflects changes in structural response, and the better the performance. To avoid extreme values ​​affecting the robustness of the fit, a specific value is used in the calculation. The 25% to 75% quartile interval. For each point within this quartile interval... ,calculate The conditional probability density, taking the value corresponding to the maximum density. As the conditional mode; then for A univariate linear fit is performed between the grid points and their corresponding conditional modes, resulting in the following expression: ; In the formula, Represents the slope of the fit; Represents the intercept. The fitted slope... absolute value As an index value of ridge slope.

[0067] In step S500 of some embodiments, the selection of seismic intensity index is a multi-criteria decision problem. This embodiment of the invention introduces a fuzzy hierarchical analysis method based on a fuzzy complementary judgment matrix. It uses triangular fuzzy quantification to determine the judgment interval of the importance of the index, and uses a scale of 0.1 to 0.9 to construct a fuzzy complementary relationship, thereby solving for the weights of each evaluation criterion.

[0068] In some embodiments, step S500 may include, but is not limited to, steps S510 to S530: Step S510: Obtain the triangular fuzzy number based on the relative importance relationship between the various evaluation criteria; Step S520: Construct a fuzzy judgment matrix based on the triangular fuzzy number; Step S530: Obtain the target weights corresponding to each evaluation criterion based on the fuzzy judgment matrix.

[0069] In step S510 of some embodiments, the four seismic motion intensity evaluation criteria in the probabilistic earthquake demand model based on kernel density estimation (KDE) are as follows: (Efficiency, by) (Measurement, smaller values ​​are better) (Dependency, determined by the distance correlation coefficient) (Measurement, the larger the value, the better) (Mutual information, derived from mutual information content) (Measurement, the larger the value, the better) and (Monotonicity sensitivity, due to ridge slope) (Measurement, the larger the value, the better). Among them... Directly measuring the conditional dispersion of EDP under a given IM is the core factor in determining the sample size and confidence interval width required for vulnerability analysis, and it is of the highest importance. and Both are correlation metrics and are of comparable importance; they are relative to each other. Both are slightly more important; As an auxiliary sensitivity indicator, it has the lowest importance. A complementary scale of 0.1–0.9 triangular fuzzy numbers is used to describe the relative importance of the above criteria, with the core being the complementarity constraint: for two evaluation indicators… and There are triangular fuzzy numbers and satisfy , , ,Right now .in, They represent the evaluation indicators respectively. relative to evaluation indicators The lower limit, median, and upper limit of importance; They represent the evaluation indicators respectively. relative to evaluation indicators The lower limit, middle value, and upper limit of importance.

[0070] In step S520 of some embodiments, a fourth-order fuzzy judgment matrix is ​​constructed using triangular fuzzy numbers. The matrix elements are triangular fuzzy numbers. ,in, They represent the evaluation indicators respectively. relative to evaluation indicators The lower, middle, and upper limits of importance are shown in Table 1.

[0071] Table 1. Triangular fuzzy number judgment matrix established using a scale of 0.1 to 0.9

[0072]

[0073] In step S530 of some embodiments, the triangular fuzzy number judgment matrix shown in Table 1 is established. Then, the fuzzy weight vectors of each evaluation criterion need to be calculated and defuzzified to obtain clear target weights.

[0074] In some embodiments, step S530 may include, but is not limited to, steps S531 to S537: Step S531: Obtain the row and vector and column and vector of the fuzzy judgment matrix; the row and vector include the row and upper bound value, the row and middle value, and the row and lower bound value; the column and vector include the column and upper bound value, the column and middle value, and the column and lower bound value. Step S532: Divide the row and upper bound values ​​by the column and lower bound values ​​to obtain the comprehensive degree upper bound component; Step S533: Divide the row and median value by the column and median value to obtain the comprehensiveness median component; Step S534: Divide the row and lower bound values ​​by the column and upper bound values ​​to obtain the lower bound component of the comprehensive degree. Step S535: Based on the upper bound component, the middle component, and the lower bound component of the comprehensiveness, the fuzzy comprehensiveness of the evaluation criteria is obtained. Step S536: Perform an arithmetic mean on the upper bound component, the middle component, and the lower bound component of the fuzzy comprehensive degree to obtain the clarity coefficient of the evaluation criterion. Step S537: Normalize the clarification coefficients of all evaluation criteria to obtain the target weights corresponding to each evaluation criterion.

[0075] In step S531 of some embodiments, the fuzzy judgment matrix ,in For each evaluation criterion Obtain evaluation criteria rows and vectors Column and vector The calculation formula is: ; ; Where rows and vectors Including row and upper bound values Rows and median values and row and lower bound values ; Columns and vectors Including columns and upper bound values Columns and intermediate values And columns and lower bound values .

[0076] In step S532 of some embodiments, the row and upper bound values ​​are... Divide by column and lower bound value The upper bound component of the comprehensiveness can be obtained. .

[0077] In step S533 of some embodiments, rows and intermediate values ​​are... Divide by column and median This allows us to obtain the intermediate component of the overall degree. .

[0078] In step S534 of some embodiments, the row and lower bound values ​​are... Divide by column and upper bound value This allows us to obtain the lower bound component of the comprehensiveness. .

[0079] In step S535 of some embodiments, based on the synthesis degree upper bound component Comprehensiveness Intermediate Component and the lower bound component of the comprehensiveness Each evaluation criterion can be obtained. Fuzzy comprehensiveness The expression is: .

[0080] In step S536 of some embodiments, for each fuzzy synthesis degree The sharpening factor can be obtained by taking the arithmetic mean of the three components. The calculation formula used is: .

[0081] In step S537 of some embodiments, the clarification coefficients for all evaluation criteria are... By normalizing, we can obtain the various evaluation criteria. Corresponding target weight The calculation formulas used include: .

[0082] Finally, based on the constructed triangular fuzzy number judgment matrix, the target weights of the four evaluation indicators can be calculated as follows: .

[0083] In step S600 of some embodiments, the optimal candidate ground motion intensity index is determined as the target ground motion intensity index by calculating the comprehensive score of each candidate ground motion intensity index. For example, the target weights of each evaluation criterion are obtained. Then, the comprehensive score of each seismic intensity index (IM) can be calculated, thereby achieving optimal ranking. Since the original indexes of the four evaluation criteria have different dimensions and different optimization directions, they need to be normalized first. The first metric is for minima optimization, and the other three are for maxima optimization. To unify the weighting logic, all metrics are normalized so that larger normalized metrics are better, with a value range of [0,1].

[0084] In some embodiments, step S600 may include, but is not limited to, steps S610 to S650: Step S610: The efficiency index value of the efficiency criterion is reverse normalized to obtain the first normalized index. Step S620: The distance correlation coefficient of the dependency criterion is positively normalized to obtain the second normalized index. Step S630: Perform positive normalization on the mutual information quantity of the mutual information criterion to obtain the third normalization index. Step S640: The ridge slope index value of the monotonic sensitivity criterion is positively normalized to obtain the fourth normalized index. Step S650: Based on the target weights corresponding to each evaluation criterion, perform weighted summation on the first normalized index, the second normalized index, the third normalized index, and the fourth normalized index to obtain the comprehensive score of the candidate seismic intensity index. The evaluation criteria include efficiency criteria, dependency criteria, mutual information criteria, and monotonic sensitivity criteria.

[0085] In step S610 of some embodiments, for efficiency criteria The smaller the value, the higher the predictive efficiency of IM. Therefore, by back-normalizing the efficiency index value of the efficiency criterion, the expression for the first normalization index can be obtained as follows: ; In the formula, Representing the The first normalized index of the candidate vibration intensity indices; Representing the Efficiency criteria for candidate vibration intensity indices; Representing the Efficiency criteria for candidate vibration intensity indices , The total number of candidate vibration intensity indices; This represents a numerically stable term, which is a minimum value to ensure that the denominator is not zero.

[0086] In step S620 of some embodiments, for the distance correlation coefficient The larger the value, the better the candidate vibration intensity index. Therefore, by positively normalizing the distance correlation coefficient of the dependency criterion, the expression for the second normalization index can be obtained as follows: ; In the formula, Representing the The second normalized index of the candidate vibration intensity indices; Representing the Distance correlation coefficient of candidate vibration intensity indices; Representing the Distance correlation coefficients of candidate vibration intensity indices.

[0087] In step S630 of some embodiments, for mutual information The larger the value, the better the candidate vibration intensity index. Therefore, by positively normalizing the mutual information quantity of the mutual information criterion, the expression for the third normalization index can be obtained as follows: ; In the formula, Representing the The third normalized index of the candidate vibration intensity indices; Representing the Mutual information of candidate vibration intensity indices; Representing the The mutual information of each candidate vibration intensity index.

[0088] In step S640 of some embodiments, the ridge slope index is... The larger the value, the better the candidate vibration intensity index. Therefore, by positively normalizing the ridge slope index of the monotonic sensitivity criterion, the expression for the fourth normalized index can be obtained as follows: ; In the formula, Representing the The fourth normalized index of the candidate vibration intensity indices; Representing the Ridge slope index of candidate vibration intensity indices; Representing the The ridge slope index of the candidate vibration intensity index.

[0089] In step S650 of some embodiments, based on the target weights corresponding to each evaluation criterion, a weighted sum of the first normalized index, the second normalized index, the third normalized index, and the fourth normalized index is calculated to obtain the comprehensive score of the candidate seismic intensity index. For example, for the first... Each candidate vibration intensity index has a comprehensive score. The calculation formula is: ; Overall Score The larger the value, the better the overall performance of the candidate vibration intensity index.

[0090] In step S700 of some embodiments, based on the overall score By sorting all candidate ground motion intensity indices from largest to smallest, the optimal target ground motion intensity index for the high-pile wharf can be obtained by selecting the candidate ground motion intensity index corresponding to the highest comprehensive score.

[0091] In some optional embodiments, this invention employs a Gaussian kernel, but other kernel functions (such as the Epanechnikov kernel, triangular kernel, etc.) can also be used. Besides the Silverman rule, bandwidth selection methods can also employ cross-validation (CV) or plug-in methods to adaptively determine bandwidth, but this will increase computational complexity. This invention uses range normalization (min-max normalization), but Z-score standardization (subtracting the mean and dividing by the standard deviation) can also be used. This invention employs a weighted sum model (SAW), but a weighted product model (WP) or TOPSIS method can also be used for multi-criteria decision-making.

[0092] This invention also provides a seismic intensity index selection device based on kernel density estimation, which can implement the above-mentioned seismic intensity index selection method based on kernel density estimation. The device includes: The finite element model building module is used to build finite element models of high-pile wharves; The engineering requirement parameter acquisition module is used to obtain the maximum horizontal displacement of the wharf panel under seismic motion based on the finite element model, and thus obtain the engineering requirement parameters. The probabilistic earthquake demand model building module is used to construct a probabilistic earthquake demand model through kernel density estimation. The evaluation criteria construction module is used to construct evaluation criteria for candidate ground motion intensity indices based on the probabilistic earthquake demand model. The weight acquisition module is used to obtain the target weights of the evaluation criteria based on the fuzzy hierarchical analysis method. The comprehensive score acquisition module is used to obtain the comprehensive score of each candidate ground motion intensity index according to the target weight; The seismic intensity index selection module is used to obtain the candidate seismic intensity index corresponding to the highest comprehensive score, and thus obtain the target seismic intensity index of the high-pile wharf.

[0093] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0094] This invention also provides an electronic device, which includes a processor and a memory. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including a tablet computer, an in-vehicle computer, or similar device.

[0095] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0096] refer to Figure 2 , Figure 2 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 801 can be implemented using a general-purpose central processing unit (CPU), microprocessor, application specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention. The memory 802 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 802 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 802 and is called and executed by the processor 801. The 803 input / output interface is used to implement information input and output. The communication interface 804 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 805 transmits information between various components of the device (e.g., processor 801, memory 802, input / output interface 803, and communication interface 804); The processor 801, memory 802, input / output interface 803, and communication interface 804 are connected to each other within the device via bus 805.

[0097] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0098] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0099] This invention also provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions to cause the computer device to perform the aforementioned method.

[0100] In summary, the method and related equipment for selecting seismic intensity indices based on kernel density estimation according to embodiments of the present invention have the following advantages: 1. The embodiments of this invention have stronger data adaptability. Existing methods assume that ln(IM) and ln(EDP) satisfy a linear relationship and that the residual variances are homogeneous. However, the seismic response of actual high-pile wharves (especially after entering nonlinearity under strong earthquakes) often violates these assumptions. This invention uses kernel density estimation for completely nonparametric modeling, without the need for preset data distribution forms. It can automatically capture arbitrarily complex nonlinear trends and heteroscedastic characteristics, thereby obtaining a conditional probability density estimate that better reflects the actual situation of high-pile wharves and avoiding systematic bias.

[0101] 2. The embodiments of this invention offer a more comprehensive evaluation dimension. Traditional methods rely on the traditional logarithmic linear assumption for their evaluation dimensions, lacking consideration for the nonlinear trends of the data. This invention introduces four criteria to complementarily evaluate IM performance from different perspectives, providing a novel evaluation dimension system for the seismic intensity index of high-pile wharves.

[0102] 3. The embodiments of the present invention have a more scientific weight allocation mechanism. The present invention adopts the fuzzy hierarchical analysis method, quantifies the relative importance between the complementary scaling criteria of triangular fuzzy numbers, and solves the fuzzy weights using the row sum normalization method, which not only ensures the mathematical rigor of the weight calculation, but also fully incorporates the prior knowledge in the field of earthquake engineering.

[0103] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0104] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0105] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0106] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0107] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0108] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0109] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0110] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A method for selecting seismic motion intensity indices based on kernel density estimation, characterized in that, Includes the following steps: Construct a finite element model of the high-pile wharf; Based on the finite element model, the maximum horizontal displacement of the wharf panel under seismic motion is obtained, and the engineering requirements parameters are obtained. A probabilistic earthquake demand model is constructed using kernel density estimation. Based on the probabilistic earthquake demand model, an evaluation criterion for candidate ground motion intensity indices is constructed. The target weights of the evaluation criteria are obtained based on the fuzzy hierarchical analysis method. Based on the target weights, obtain the comprehensive score for each candidate ground motion intensity index; The candidate ground motion intensity index corresponding to the highest comprehensive score is obtained to obtain the target ground motion intensity index of the high-pile wharf.

2. The method according to claim 1, characterized in that, The construction of the finite element model for the high-pile wharf includes the following steps: Piles are simulated using nonlinear beam-column elements and fiber sections; The soil was simulated using a four-node plane strain element. The contact surface between the pile and the soil is simulated using thin-layer elements after reducing the shear parameters; The hydrostatic pressure and dynamic inertia of water bodies are simulated using the equivalent load-mass method. A finite element model is established based on the pile, the soil, the contact surface, and the effects of hydrostatic pressure and hydrodynamic inertia, and free field boundaries are set on both sides of the finite element model.

3. The method according to claim 1, characterized in that, Based on the finite element model, the maximum horizontal displacement of the wharf deck under seismic motion is obtained to acquire the engineering requirements parameters, including the following steps: Select batch of ground motion samples; The seismic motion is input into the finite element model, and the maximum horizontal displacement of the wharf panel under the action of seismic motion is obtained through nonlinear dynamic time history analysis. The maximum horizontal displacement of the wharf panel is used as the engineering requirement parameter.

4. The method according to claim 1, characterized in that, The process of constructing a probabilistic earthquake demand model through kernel density estimation includes the following steps: The candidate ground motion intensity indices are logarithmically transformed to obtain logarithmic domain intensity indices; Perform a logarithmic transformation on the engineering requirement parameters to obtain logarithmic domain requirement parameters; Obtain a one-dimensional kernel density estimate of the logarithmic field strength index; Two-dimensional data is obtained based on the logarithmic domain strength index and the logarithmic domain requirement parameters; Obtain a two-dimensional kernel density estimate of the two-dimensional data; Dividing the two-dimensional kernel density estimate by the one-dimensional kernel density estimate yields the probabilistic earthquake demand model.

5. The method according to claim 1, characterized in that, The method of obtaining the target weights of the evaluation criteria based on fuzzy hierarchical analysis includes the following steps: Based on the relative importance relationships among the various evaluation criteria, obtain the triangular fuzzy number; Based on the triangular fuzzy number, construct a fuzzy judgment matrix; Based on the fuzzy judgment matrix, the target weights corresponding to each of the evaluation criteria are obtained.

6. The method according to claim 5, characterized in that, The step of obtaining the target weights corresponding to each evaluation criterion based on the fuzzy judgment matrix includes the following steps: Obtain the row and vector, and column and vector of the fuzzy judgment matrix; the row and vector include row and upper bound value, row and middle value, and row and lower bound value; the column and vector include column and upper bound value, column and middle value, and column and lower bound value. Divide the row and upper bound value by the column and lower bound value to obtain the comprehensive degree upper bound component; Divide the row and the median value by the column and the median value to obtain the comprehensiveness median component; Divide the row and lower bound by the column and upper bound to obtain the lower bound component of the comprehensive degree. The fuzzy comprehensiveness of the evaluation criterion is obtained based on the upper bound component of the comprehensiveness, the middle component of the comprehensiveness, and the lower bound component of the comprehensiveness. The sharpness coefficient of the evaluation criterion is obtained by arithmetically averaging the upper bound component, the middle component, and the lower bound component of the fuzzy comprehensive degree. The clarification coefficients of all the evaluation criteria are normalized to obtain the target weights corresponding to each evaluation criterion.

7. The method according to claim 1, characterized in that, The step of obtaining a comprehensive score for each candidate seismic intensity index based on the target weight includes the following steps: The efficiency index value of the efficiency criterion is reverse normalized to obtain the first normalized index. The distance correlation coefficient of the dependency criterion is positively normalized to obtain the second normalized index; The mutual information content of the mutual information criterion is positively normalized to obtain the third normalization index; The ridge slope index value of the monotonic sensitivity criterion is positively normalized to obtain the fourth normalized index. Based on the target weights corresponding to each of the evaluation criteria, the first normalized index, the second normalized index, the third normalized index, and the fourth normalized index are weighted and summed to obtain the comprehensive score of the candidate ground motion intensity index. The evaluation criteria include the efficiency criterion, the dependency criterion, the mutual information criterion, and the monotonic sensitivity criterion.

8. A device for selecting seismic intensity indices based on kernel density estimation, characterized in that, include: The finite element model building module is used to build finite element models of high-pile wharves; The engineering requirement parameter acquisition module is used to obtain the maximum horizontal displacement of the wharf panel under seismic motion based on the finite element model, and thus obtain the engineering requirement parameters. The probabilistic earthquake demand model building module is used to construct a probabilistic earthquake demand model through kernel density estimation. The evaluation criteria construction module is used to construct evaluation criteria for candidate ground motion intensity indices based on the probabilistic earthquake demand model. The weight acquisition module is used to obtain the target weights of the evaluation criteria based on the fuzzy hierarchical analysis method. The comprehensive score acquisition module is used to acquire the comprehensive score of each candidate ground motion intensity index according to the target weight; The seismic intensity index selection module is used to obtain the candidate seismic intensity index corresponding to the highest comprehensive score, and to obtain the target seismic intensity index of the high-pile wharf.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

Images