A method for analyzing the importance of ground motion parameters based on Sobol method

Abstract

The present invention provides a method for analyzing the importance of earthquake parameters based on the Sobol method, comprising: training a Kriging model based on each group of earthquake parameters and corresponding structural response parameters obtained by elastic-plastic time history analysis; sampling to obtain earthquake parameter samples based on earthquake parameter distribution types and distribution parameters; inputting the earthquake parameter samples into the trained Kriging model to obtain corresponding structural response parameters to form importance analysis samples; and using the Sobol method to perform importance analysis on earthquake parameters based on the importance analysis samples. The method proposed by the present invention can be used for earthquake parameter importance analysis.

Description

Technical Field

[0001] The present invention relates to the field of earthquake motion parameter importance analysis, and more specifically, to an earthquake motion parameter importance analysis method based on the Sobol method. Background Art

[0002] In structural design, structures in high-intensity areas and structures with complex layouts require elastic time-history verification and elastoplastic time-history verification. The earthquake motion used in the verification directly determines the verification results. The results obtained by using different earthquake motion records are often very different, making the elastic and elastoplastic time-history verification become a formality and cannot provide an effective reference for the design. The importance analysis of earthquake motion parameters can clarify the characteristics of earthquake motion, so as to select appropriate earthquake records for elastic and elastoplastic time-history verification. Summary of the invention

[0003] Based on the requirements in the background technology, the present invention provides a method for analyzing the importance of earthquake parameters based on the Sobol method, comprising:

[0004] Performing elastoplastic time history analysis on a multi-story frame structure to obtain structural response parameters corresponding to each set of earthquake motion parameters, wherein each set of earthquake motion parameters includes multiple earthquake motion parameters, and the structural response parameters include base shear force and maximum inter-story displacement angle;

[0005] Based on each set of ground motion parameters and corresponding structural response parameters, the Kriging model is trained;

[0006] Acquire multiple ground motion records and determine ground motion parameter distribution types and distribution parameters;

[0007] Based on the seismic motion parameter distribution type and distribution parameter, each seismic motion parameter is sampled to form a seismic motion parameter sample;

[0008] Inputting the seismic parameter samples into the trained Kriging model to obtain corresponding structural response parameters, wherein the seismic parameter and the corresponding structural response parameter constitute importance analysis samples;

[0009] Based on the importance analysis sample, the Sobol method is used to perform importance analysis on the seismic parameters.

[0010] The present invention provides a method for analyzing the importance of seismic parameters based on the Sobol method, which can analyze the importance of each seismic parameter and can serve as a reference for the selection of seismic records in elastic and elastoplastic time history verification. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1A schematic flow chart of a method for analyzing the importance of ground motion parameters based on the Sobol method provided in an embodiment of the present invention;

[0012] Figure 2 A schematic diagram of a finite element model of a multi-layer frame structure according to an embodiment of the present invention;

[0013] Figure 3 It is a schematic diagram of the sensitivity results of ground motion parameters based on base shear force according to an embodiment of the present invention;

[0014] Figure 4 It is a schematic diagram of the sensitivity results of ground motion parameters based on the maximum inter-story displacement angle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention can be arbitrarily combined with each other to form a feasible technical solution. This combination is not subject to the constraints of the sequence of steps and / or the structural composition mode, but must be based on the ability of ordinary technicians in this field to achieve. When the combination of technical solutions is contradictory or cannot be achieved, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0016] Figure 1 A flow chart of a method for analyzing the importance of ground motion parameters based on the Sobol method provided by the present invention is shown in FIG. Figure 1 As shown, the method includes:

[0017] Step 1: perform elastic-plastic time history analysis on the multi-story frame structure to obtain structural response parameters corresponding to each set of seismic motion parameters, each set of seismic motion parameters includes multiple seismic motion parameters, and the structural response parameters include base shear and maximum inter-story displacement angle.

[0018] It is understandable that the Kriging model of earthquake response is first established. The main idea of ​​the proxy model is to approximate the structural analysis model with high computational cost with a numerical proxy model with low computational cost. When the proxy model method is applied to elastic-plastic time-history analysis, more structural seismic response samples can be obtained based on limited seismic motion records to achieve the purpose of improving calculation accuracy. As one of the proxy model methods, the Kriging model is a parameterized "input-output" system.

[0019] For multi-story frame structures, elastic-plastic time-history analysis is performed to obtain the structural response parameters corresponding to each set of seismic motion parameters. Each set of seismic motion parameters includes multiple seismic motion parameters, and the structural response parameters include base shear and maximum inter-story displacement angle. Multiple sets of seismic motion parameters and corresponding multiple sets of structural response parameters constitute a training data set.

[0020] Step 2: Based on each set of ground motion parameters and corresponding structural response parameters, train the Kriging model.

[0021] It is understandable that, based on the acquired training data set, the Kriging model is trained, and the trained Kriging model can replace the finite element model to obtain the structural response through the parameterized input of the earthquake motion.

[0022] Step 3: Obtain multiple earthquake motion records and determine the earthquake motion parameter distribution type and distribution parameters.

[0023] It is understandable that more than 300 ground motion records with a fault distance of no more than 60 km were selected from the Pacific Earthquake Engineering Research (PEER) groundmotion database for statistics, and ground motion parameters were extracted from each ground motion record. It was assumed that the ground motion parameters obeyed a uniform distribution. The 17 alternative ground motion parameters and their distribution ranges are shown in Table 1.

[0024] Table 1 Multivariate parameters and distribution ranges of ground motion

[0025]

[0026] Step 4: based on the seismic motion parameter distribution type and distribution parameter, sample each seismic motion parameter to form a seismic motion parameter sample.

[0027] It can be understood that, for each type of seismic motion parameter and its distribution range, Latin hypercube sampling (LHS) is performed on each seismic motion parameter according to the uniform distribution probability model of the seismic motion parameters in Table 1 to obtain a set of sampled seismic motion parameters as seismic motion parameter samples.

[0028] Step 5: Input the seismic parameter samples into the trained Kriging model to obtain corresponding structural response parameters. The seismic parameter and the corresponding structural response parameter constitute importance analysis samples.

[0029] It can be understood that the seismic parameter samples are input into the trained Kriging model to obtain the corresponding structural response parameters, and the sampled seismic parameter samples and the corresponding structural responses together constitute the importance analysis samples.

[0030] Step 6: Based on the importance analysis samples, the Sobol method is used to perform importance analysis on the seismic parameters.

[0031] It is understandable that the core idea of ​​the Sobol method is to decompose the model into a single parameter and a combination of parameters based on the decomposition of variance, and to perform importance analysis by calculating the influence of the variance of a single input parameter or a combination of input parameters on the variance of the total output variable. The Sobol method is an importance analysis method based on variance analysis, which has the following two characteristics: 1) It can analyze the influence of a single input variable as well as the interaction between different input variables; 2) The analysis results are not affected by the system model (the system model includes the finite element model and the Kriging model). In view of the complexity and correlation of the input seismic parameters, this paper uses the Sobol method to perform importance analysis of structural variables and seismic parameters.

[0032] In the Sobol method, the Sobol sensitivity index is a quantitative evaluation index of the sensitivity of the input variables. The input variables are defined as where x i is the ground motion parameter, the total number is n x , for example, a total of 17 ground motion parameters; output variables where y k (X) is the seismic response parameter of the structure, the total number is n y , for example, two structural response parameters, base shear and maximum inter-story displacement angle. For any input variable x i and any output variable y k (X), Sobol method uses conditional variance to quantify y k (X) for x i The conditional variance can be written as:

[0033]

[0034] In the formula, Does not contain x i Other input variables X -i The variance of .

[0035] According to formula (1), calculate the value of x i The variance of each input variable except x i The variance of each input variable other than is averaged and recorded in the input variable x i The randomness is:

[0036]

[0037] The smaller the value of formula (2), the smaller the input variable xi For the output variable y k The greater the impact of (X). According to the law of total variance, we can get:

[0038]

[0039] In the formula, Does not contain x i The input variable X -i The mathematical expectation of .

[0040] Formula (3) is equivalent to,

[0041]

[0042] The Sobol method takes the first term on the right side of equation (4) as the Sobol sensitivity index, then the Sobol sensitivity index S of the i-th input variable to the k-th output variable is k，i It can be expressed as:

[0043]

[0044] Where V k，i and V k are the variance of the kth output variable obtained based on the ith input variable and all input variables, respectively.

[0045] From formula (3), we can know that S k，i ≤1, and S k，i The smaller the value, the smaller the input variable x i For the output variable y k The smaller the impact of (X).

[0046] Sobol sensitivity index S k，i Normalization is performed and the normalized index is used as the importance index of the seismic parameters. According to the normalized importance index γ of the i-th input variable k，i It can be written as:

[0047]

[0048] In the formula, S k，max It is the maximum value of the Sobol sensitivity index of all input variables to the kth output variable.

[0049] According to formula (6), the normalized importance index γ of each input variable to the kth output variable is calculated: k，i , the importance index of each seismic parameter can be analyzed.

[0050] The following is a detailed description of the Sobol method-based earthquake motion parameter importance analysis method provided by the present invention based on a specific embodiment.

[0051] The present invention uses the multi-story frame structure of a museum in Moshi Town, Luding County as an example. The frame is located on the Moshi Terrace and was severely damaged in the Luding 6.8-magnitude earthquake that occurred on September 5, 2022. The multi-story building is a two-story frame structure, with the first and second floors being 4.8m and 4.2m high, respectively, and a typical column grid span of 7.8m. According to my country's latest earthquake zoning map, the location of the museum belongs to the 9-degree zone (0.4g), a Class II site, and the seismic motion group is the third group with a characteristic period of 0.45s. The present invention uses the general analysis software ANSYS to perform elastic time-history analysis on frame W2. According to the on-site rebound test and measurement results, the concrete strength of the frame column, frame beam and floor slab is C30, and the steel bar is HRB400, and the material strength values ​​are all standard values. Concrete and steel bars use multi-fold line and double-fold line ideal elastic-plastic constitutive relations, respectively, and both use isotropic strengthening models without considering the Bauschinger effect. The frame beam and the "imitation bracket" are modeled with 3D linear finite strain beam unit BEAM188; the floor slab is modeled with 3D finite strain shell unit SHELL181; in order to accurately take into account the influence of stirrups on the plastic development of frame columns, the 3D solid unit with reinforcement SOLID65 is used within the bottom 1.5m of the first-floor frame column, and the remaining frame columns are simulated with 3D secondary finite strain beam unit BEAM189; the longitudinal reinforcement of the components is dispersed in the entire cross section. The solid unit part at the lower end of the column is divided by hexahedron mapping, and the mesh is encrypted. The finite element mesh division is shown in Figure 2 According to the analysis results and the Code for Seismic Design of Buildings (GB 50011-2010), frame W2 has three irregularities: torsion irregularity, concave-convex irregularity, and discontinuity of vertical lateral force resisting members. It is a particularly irregular structure and requires elastic time-history analysis for supplementary calculations during design. Figure 3 , is a schematic diagram of the sensitivity results of ground motion parameters based on base shear, Figure 4 is the sensitivity result of ground motion parameters based on the maximum inter-story displacement angle, where: Figure 3 and Figure 4 The horizontal axis is the various seismic parameters. Figure 3 The vertical axis in represents the base shear force, Figure 4 The vertical axis represents the maximum inter-story displacement angle data.

[0052] The embodiment of the present invention provides a method for analyzing the importance of seismic parameters based on the Sobol method. The Kriging model is trained based on each set of seismic parameters and corresponding structural response parameters obtained through elastic-plastic time history analysis. Seismic parameter samples are sampled based on the seismic parameter distribution type and distribution parameters. The seismic parameter samples are input into the trained Kriging model to obtain corresponding structural response parameters to form importance analysis samples. Based on the importance analysis samples, the Sobol method is used to perform importance analysis on the seismic parameters. The method proposed by the present invention can realize the analysis of the importance of each seismic parameter, and can serve as a reference for the selection of earthquake records in elastic and elastic-plastic time history verification.

[0053] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and for parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0054] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0055] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0056] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0057] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0058] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0059] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for analyzing the importance of ground motion parameters based on the Sobol method, characterized in that: include: Performing elastoplastic time history analysis on a multi-story frame structure to obtain structural response parameters corresponding to each set of earthquake motion parameters, wherein each set of earthquake motion parameters includes multiple earthquake motion parameters, and the structural response parameters include base shear force and maximum inter-story displacement angle; Based on each set of ground motion parameters and corresponding structural response parameters, the Kriging model is trained; Acquire multiple ground motion records and determine ground motion parameter distribution types and distribution parameters; Based on the seismic motion parameter distribution type and distribution parameter, each seismic motion parameter is sampled to form a seismic motion parameter sample; Inputting the seismic parameter samples into the trained Kriging model to obtain corresponding structural response parameters, wherein the seismic parameter and the corresponding structural response parameter constitute importance analysis samples; Based on the importance analysis sample, the importance analysis of ground motion parameters is performed using the Sobol method; The importance analysis of the seismic parameters is performed based on the importance analysis sample using the Sobol method, including: Define the input variables as ,in is the ground motion parameter, the total number is , output variable ,in is the structural response parameter, the total number is ; For any input variable and any output variable , based on the Sobol method, the conditional variance is quantified right The sensitivity of the i-th input variable to the k-th output variable is calculated. ; Sobol sensitivity index Normalization is performed and the normalized index is used as the importance index of the seismic parameters. ; For any input variable and any output variable , based on the Sobol method, the conditional variance is quantified right The sensitivity of the i-th input variable to the k-th output variable is calculated. ,include: right The sensitivity is: （1）； In the formula, To not include Input variables The variance of According to formula (1), the The variance of each input variable except The average value of the variance of each input variable other than The randomness is: （2）； According to the total variance formula, we get: （3）； In the formula, To not include Input variables The mathematical expectation of Formula (3) is equivalent to: （4）； The first term on the right side of equation (4) is taken as the Sobol sensitivity index, then the Sobol sensitivity index of the i-th input variable to the k-th output variable is It is expressed as: （5）； In the formula, and are the variance of the kth output variable obtained based on the ith input variable and all input variables, respectively.

2. The method for analyzing the importance of ground motion parameters according to claim 1, characterized in that: The obtaining of multiple earthquake motion records and determining earthquake motion parameter distribution types and distribution parameters includes: More than 300 seismic motion records with a fault distance of no more than 60 km were selected for statistics. Assuming that the seismic motion parameters obey uniform distribution, 17 seismic motion parameters and the distribution range of each seismic motion parameter were obtained.

3. The method for analyzing the importance of ground motion parameters according to claim 2, characterized in that: The method of sampling each seismic parameter based on the seismic parameter distribution type and distribution parameter to form a seismic parameter sample includes: Based on the distribution probability model of the seismic motion parameters and the distribution interval of each seismic motion parameter, Latin hypercube sampling is performed on each seismic motion parameter to obtain a seismic motion parameter sample.

4. The method for analyzing the importance of ground motion parameters according to claim 1, characterized in that: Sobol sensitivity index Normalization is performed and the normalized index is used as the importance index of the seismic parameters. ,include: In the formula, It is the maximum value of the Sobol sensitivity index of all input variables to the kth output variable.

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