Quantitative analysis and prediction method and system for floor acceleration amplification coefficient

Abstract

The invention discloses a quantitative analysis and prediction method and system for a floor acceleration amplification coefficient. The method comprises the following steps: acquiring floor acceleration data of each station in a strong earthquake database; calculating a floor acceleration coefficient according to the floor acceleration data and acquiring factors of each station influencing a floor acceleration amplification coefficient; carrying out quantitative analysis on the factors through a variance analysis method, and determining the significance of each factor on the floor acceleration amplification coefficient; constructing a prediction model of the floor acceleration amplification coefficient by adopting a multiple linear regression method based on the significant factors determined by variance analysis; and accurately predicting acceleration responses under different building conditions according to the prediction model. According to the method, various factors and interaction effects thereof are comprehensively considered, and the prediction precision of the floor acceleration amplification coefficient is remarkably improved. The prediction model is suitable for seismic design of various buildings, and can provide a scientific basis for design optimization especially in the aspect of acceleration demand analysis of non-structural members.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake resistance of building structures, and in particular to a quantitative analysis and prediction method and system for a floor acceleration amplification factor. Background Art

[0002] The floor acceleration amplification factor is the ratio of the peak floor acceleration to the peak ground acceleration under earthquake conditions, reflecting the amplification effect of the building structure on the ground acceleration. This factor is an important parameter in the calculation of the seismic bearing capacity of non-structural components of buildings. However, current research on the floor acceleration amplification factor is mostly based on finite element simulation or statistical and computational analysis of a small number of floor earthquake records. These methods cannot fully reflect the actual distribution characteristics of the floor acceleration amplification factor in various building structures. Therefore, there is a significant difference between the calculated results and the actual structure's response under earthquake conditions, which affects the accuracy of the seismic design and, in turn, the seismic performance of non-structural components.

[0003] In addition, the existing research on the factors affecting the floor acceleration amplification factor is relatively scattered and lacks systematic analysis. The floor acceleration amplification factor is directly or indirectly affected by a variety of factors, and there may be complex interactions between these factors. Therefore, in the existing research, the selection of influencing factors and their interrelationships have not been fully and reasonably explained, resulting in greater uncertainty in the prediction results.

[0004] Therefore, a quantitative analysis and prediction method for the floor acceleration magnification factor is urgently needed to make up for the defect that the existing research fails to fully consider the interactive influence of various factors, so as to improve the accuracy and applicability of the floor acceleration magnification factor prediction, and then provide a more reliable basis for the seismic design and optimization of modern buildings. Summary of the invention

[0005] In order to solve the above technical problems, this application proposes the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a quantitative analysis and prediction method of a floor acceleration amplification factor, comprising:

[0007] Obtain the floor acceleration data of each station in the strong earthquake database;

[0008] Calculating the floor acceleration coefficient according to the floor acceleration data and obtaining factors affecting the floor acceleration amplification coefficient at each station;

[0009] The factors are quantitatively analyzed by variance analysis to determine the significance of each factor on the floor acceleration amplification factor;

[0010] Based on the significant factors determined by variance analysis, a prediction model for floor acceleration amplification coefficient was constructed using multiple linear regression method.

[0011] The acceleration response under different building conditions is accurately predicted based on the prediction model.

[0012] In a possible implementation, obtaining the floor acceleration data of each site in the strong earthquake database includes:

[0013] Obtain the floor acceleration time history curve in the strong earthquake database;

[0014] The floor acceleration peak value in the floor acceleration time history curve of each floor is obtained.

[0015] In a possible implementation, a formula for calculating the floor acceleration coefficient according to the floor acceleration data is:

[0016] FAA=PFA / PGA

[0017] Among them, FAA is the floor acceleration amplification factor, PFA is the floor acceleration peak, and PGA is the ground acceleration peak.

[0018] In a possible implementation, the obtaining of factors affecting the floor acceleration magnification coefficient at each site includes:

[0019] Determine the factors that affect the floor acceleration amplification factor;

[0020] The factors of different structure types, different structure heights, different site categories, different structure relative heights, different seismic intensity and different structure periods are obtained.

[0021] In a possible implementation, the quantitative analysis of the factors by variance analysis method to determine the significance of each factor on the floor acceleration magnification factor includes:

[0022] A variance analysis model is constructed, and the variance analysis model is expressed as:

[0023] Y ij =μ+α i +ε ij

[0024] Where i represents different factor levels or categories, j represents different floor acceleration magnification coefficient values ​​under each factor level, and Y ij is the floor acceleration magnification factor corresponding to the jth observation under the i-th factor level, μ is the average acceleration magnification factor under all factor levels, α i is the effect of the i-th group of factor levels, ε ij is the error term;

[0025] Calculate the F value in the variance analysis and obtain the P value through the F value;

[0026] The significance of each factor on the floor acceleration amplification factor is determined based on the P value.

[0027] In a possible implementation, the formula for calculating the F value in variance analysis is:

[0028]

[0029] The calculation formula for the between-group variance is:

[0030]

[0031] Where k is the number of levels of different factors that affect the floor acceleration amplification factor, n i is the number of samples at the i-th factor level, is the average value of the acceleration amplification factor of all samples in the i-th group, is the overall average value of all floor acceleration amplification factors;

[0032] The calculation formula of the within-group variance is:

[0033]

[0034] Among them, N is the total number of samples in all groups, Y ij is the floor acceleration amplification factor corresponding to the jth observation under the i-th factor level.

[0035] In a possible implementation, the prediction model of the floor acceleration amplification factor is constructed by using a multivariate linear regression method based on the significant factors determined by variance analysis, including:

[0036] Obtain multiple significant influencing factors after variance analysis;

[0037] A multiple linear regression model is constructed based on the multiple significant influencing factors, and the multiple linear regression model is expressed as:

[0038] Y=β0+β1X1+β2X2+.....+β p X p +ε;

[0039] Among them, Y is the floor acceleration magnification factor, X1, X2, X p is a significant factor, β0 is the intercept of the regression equation, β1, β2, β p is the regression coefficient and ε is the error term.

[0040] In a possible implementation, accurately predicting the acceleration response under different building conditions according to the prediction model includes:

[0041] A significance test is performed on each regression coefficient in the prediction model.

[0042] The calculation formula for the verification is:

[0043]

[0044] Among them, β j is the regression coefficient of the jth significant influencing factor; SE(β j ) is the regression coefficient β j The standard error of ; t is the test statistic, which represents the regression coefficient β j The relationship between the corresponding factors and the floor acceleration amplification factor;

[0045] The goodness of fit of the model is calculated, and the goodness of fit calculation formula is:

[0046]

[0047] Among them, R 2 is the goodness of fit of the regression model; i is the actual value of the acceleration magnification factor of the i-th floor; is the predicted value of the acceleration amplification factor of the i-th floor; is the overall average of all floor acceleration amplification factors; n is the total number of floor acceleration amplification factors.

[0048] In a second aspect, the embodiment of the present application provides a quantitative analysis and prediction system for floor acceleration amplification factor, including:

[0049] An acquisition module is used to obtain the floor acceleration data of each station in the strong earthquake database;

[0050] A calculation module, used to calculate the floor acceleration coefficient according to the floor acceleration data and obtain factors affecting the floor acceleration amplification coefficient at each station;

[0051] A quantitative analysis module, used to perform quantitative analysis on the factors by variance analysis method to determine the significance of each factor on the floor acceleration amplification factor;

[0052] The construction module uses the multivariate linear regression method to construct a prediction model for the floor acceleration amplification factor based on the significant factors determined by variance analysis;

[0053] The prediction module is used to accurately predict the acceleration response under different building conditions according to the prediction model.

[0054] Compared with the prior art, the beneficial effects of this application are:

[0055] This application conducts a systematic quantitative analysis of the factors that affect the floor acceleration amplification factor and combines it with a prediction model to accurately predict the floor acceleration response under different building conditions, optimize the seismic design of non-structural components, and improve the overall seismic performance of the building.

[0056] This application comprehensively considers multiple factors and their interactions, significantly improving the prediction accuracy of the floor acceleration amplification factor. The prediction model is suitable for the seismic design of various buildings, especially in the analysis of acceleration requirements of non-structural components. It can provide a scientific basis for design optimization, overcome the shortcomings of existing methods in insufficient analysis of multi-factor interactions, and more comprehensively reflect the acceleration response of buildings under earthquakes. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic flow chart of a quantitative analysis and prediction method of a floor acceleration amplification factor provided in an embodiment of the present application;

[0058] Figure 2 A schematic diagram of a quantitative analysis and prediction system for floor acceleration amplification factor provided in an embodiment of the present application. DETAILED DESCRIPTION

[0059] The present solution is described below in conjunction with the accompanying drawings and specific implementation methods.

[0060] Figure 1 A flow chart of a quantitative analysis and prediction method of a floor acceleration amplification factor provided in an embodiment of the present application is shown in FIG. Figure 1 In this embodiment, a quantitative analysis and prediction method of a floor acceleration amplification factor includes:

[0061] S101, obtaining the floor acceleration data of each station in the strong earthquake database.

[0062] In this embodiment, the historical data of floor acceleration in the strong earthquake database are used. These data cover the acceleration responses of different buildings in multiple earthquake events. The floor acceleration time history curve in the strong earthquake database is obtained, and the floor acceleration peak value in the floor acceleration time history curve of each floor is obtained.

[0063] S102, calculating the floor acceleration coefficient according to the floor acceleration data and obtaining factors affecting the floor acceleration amplification coefficient at each station.

[0064] In this embodiment, the formula for calculating the floor acceleration coefficient according to the floor acceleration data is:

[0065] FAA=PFA / PGA

[0066] Among them, FAA is the floor acceleration amplification factor, PFA is the floor acceleration peak, and PGA is the ground acceleration peak.

[0067] According to the availability of data, appropriate influencing factors are selected for analysis. In this embodiment, the factors affecting the floor acceleration amplification coefficient are determined, and the factors of different structural types, different structural heights, different site categories, different structural relative heights, different seismic intensities and different structural periods are obtained. Among them, the structural types of buildings include concrete structures, steel structures and steel-concrete composite structures. The structural heights include multi-story and high-rise. The site categories include Class I, Class II, Class III, and Class IV sites. The seismic intensity includes PGA <0.035g, 0.035g~0.1g, 0.1g~0.22g, PGA>0.2g.

[0068] In this embodiment, the building data equipped with control systems are excluded, and the floor acceleration response data of 153 buildings of various structural types are used, including 69 concrete structures, 49 steel structures, and 35 steel-concrete composite structures.

[0069] S103, quantitatively analyzing the factors by variance analysis method to determine the significance of each factor on the floor acceleration magnification coefficient.

[0070] In this embodiment, the influence of various factors on the floor acceleration magnification coefficient is statistically analyzed, and the above factors are quantitatively analyzed using variance analysis to obtain the relationship between each factor and the floor acceleration magnification coefficient. The specific method is:

[0071] Construct a variance analysis model, assuming that there are k different factor levels, each level represents an influencing factor. In this embodiment, relative height, structure height, structure type, site category, and earthquake intensity are all possible factors. Let the floor acceleration amplification factor be the dependent variable Y, and the influencing factors are X1, X2, ...X p The ANOVA model can be expressed as:

[0072] Y ij =μ+α i +ε ij

[0073] Where i represents different factor levels or categories, j represents different floor acceleration magnification coefficient values ​​under each factor level, and Y ij is the floor acceleration magnification factor corresponding to the jth observation under the i-th factor level, μ is the average acceleration magnification factor under all factor levels, α i is the effect of the i-th group of factor levels, ε ij is the error term.

[0074] The F value in the variance analysis is calculated and the P value is obtained by the F value. In this embodiment, the formula for calculating the F value is:

[0075] The calculation formula for the between-group variance is:

[0076] Where k is the number of levels of different factors that affect the floor acceleration amplification factor, n i is the number of samples at the i-th factor level, is the average value of the acceleration amplification factor of all samples in the i-th group, is the overall average value of all floor acceleration amplification factors.

[0077] The calculation formula for within-group variance is:

[0078] Among them, N is the total number of samples in all groups, Y ij is the floor acceleration amplification factor corresponding to the jth observation under the i-th factor level.

[0079] If the difference between groups is much greater than the difference within groups, the F value will be large, indicating that the factor has a significant effect on the acceleration magnification factor. The P value is calculated using the F distribution and represents the probability that the observed F value is more extreme than the current one if the null hypothesis (the factor has no effect on the floor acceleration magnification factor) is true. The significance of each factor on the floor acceleration magnification factor is determined based on the P value.

[0080] If the P value is less than the significance level, the null hypothesis is rejected, and it is considered that at least one factor significantly affects the floor acceleration amplification coefficient. If the P value is greater than the significance level, the null hypothesis cannot be rejected, and it is considered that the difference between the factor levels is not significant.

[0081] In this embodiment, the variance analysis of the floor acceleration magnification coefficient is performed by SAS software, which can evaluate the influence of multiple independent variables on the dependent variable, so as to clarify the significance and contribution of each factor to the floor acceleration magnification coefficient. Further, the following six factors are used as independent variables: relative height (X1), structure height (X2), structure type (X3), site category (X4), seismic intensity (X5) and structural period (X6), and the floor acceleration magnification coefficient is used as the dependent variable. The variance analysis method is used to evaluate the influence of each variable. The results of the variance analysis are shown in Table 1:

[0082] Table 1 Results of variance analysis

[0083]

[0084] The P value is used to determine the significance between the independent variable and the dependent variable. Among them, the items with a P value ≤ 0.01 have an extremely significant effect on the floor acceleration magnification factor, the items with a 0.01 < P value ≤ 0.05 have a significant effect on the floor acceleration magnification factor, and the items with a P value > 0.05 have no significant effect on the floor acceleration magnification factor.

[0085] According to the analysis results in Table 1, it can be seen that the relative height (X1) and structure height (X2) have the most significant impact on the floor acceleration magnification factor, with P values ​​less than 0.0001 and 0.0004 respectively. The structural type (X3) and site category (X4) are second, with P values ​​of 0.0010 and 0.0062 respectively. The P values ​​of ground motion intensity (X5) and structural period (X6) are greater than 0.05, indicating that their impact on the floor acceleration magnification factor is not significant.

[0086] Furthermore, it was determined that relative height (X1), structure height (X2), structure type (X3) and site category (X4) were significant factors affecting the floor acceleration amplification factor.

[0087] S104, based on the significant factors determined by variance analysis, a prediction model for the floor acceleration amplification factor was constructed using the multivariate linear regression method.

[0088] A multivariate linear regression analysis method is used to establish a floor acceleration amplification coefficient prediction model that can comprehensively consider multiple factors.

[0089] In this embodiment, multiple significant influencing factors after variance analysis are obtained, and a multiple linear regression model is constructed according to the multiple significant influencing factors. The multiple linear regression model is expressed as:

[0090] Y=β0+β1X1+β2X2+.....+β p X p +ε;

[0091] Among them, Y is the floor acceleration magnification factor, X1, X2, X p is a significant factor, β0 is the intercept of the regression equation, β1, β2, β p is the regression coefficient and ε is the error term.

[0092] Furthermore, in the process of regression analysis in this embodiment, the assignment of independent variables is shown in Table 2:

[0093] Table 2 Independent variable assignment

[0094]

[0095] Table 3 Results of multiple linear regression analysis of factors affecting floor acceleration amplification coefficient

[0096]

[0097] The statistical significance results of the regression analysis are shown in Table 3. According to the regression analysis results, the multivariate linear regression model of the floor acceleration amplification coefficient is obtained as follows:

[0098] FAA=0.93+0.94X1+0.25X2+(-0.43)X3+0.47X4

[0099] Where: X1 is the relative height of the structure (z / h), X2 is the height of the structure, X3 is the type of structure, and X4 is the site category, respectively, which are the independent variables of the regression model; 0.93 is the model constant; 0.25 is the unstandardized coefficient of the structure height, -0.43 is the unstandardized coefficient of the structure type, and 0.47 is the unstandardized coefficient of the site category.

[0100] Furthermore, according to Table 3, we can get:

[0101] 1. Significance analysis: The P values ​​of all independent variables X1 (relative height), X2 (structure height), X3 (structure type) and X4 (site category) are less than 0.05, indicating that these variables have a significant impact on the floor acceleration amplification factor.

[0102] 2. The direction of influence of variables:

[0103] X1 (relative height z / h) has a positive impact on the floor acceleration amplification factor, and its unstandardized coefficient is 0.94, indicating that for every unit increase in relative height, the floor acceleration amplification factor increases by 0.94 on average.

[0104] X3 (structural type) has a negative impact on the floor acceleration amplification factor, with a coefficient of -0.43.

[0105] X2 (structure height) and X4 (site category) have a positive impact on the floor acceleration amplification factor, with coefficients of 0.25 and 0.47 respectively.

[0106] S105: accurately predicting the acceleration response under different building conditions according to the prediction model.

[0107] In this embodiment, a significance test is performed on each regression coefficient in the prediction model, and the calculation formula for the test is:

[0108]

[0109] Among them, β j is the regression coefficient of the jth significant influencing factor; SE(β j ) is the regression coefficient β j The standard error of ; t is the test statistic, which represents the regression coefficient β jThe relationship between the corresponding factors and the floor acceleration amplification factor.

[0110] The goodness of fit of the model is calculated, and the goodness of fit calculation formula is:

[0111]

[0112] Among them, R 2 is the goodness of fit of the regression model; i is the actual value of the acceleration magnification factor of the i-th floor; is the predicted value of the acceleration amplification factor of the i-th floor, is the overall average of all floor acceleration amplification factors, and n is the total number of floor acceleration amplification factors.

[0113] The goodness of fit (R2) of the regression model in this embodiment is 0.836, indicating that the model has a high explanatory power for the changes in the floor acceleration amplification factor.

[0114] Corresponding to the quantitative analysis and prediction method of the floor acceleration amplification factor provided in the above embodiment, the present application also provides an embodiment of a quantitative analysis and prediction system of the floor acceleration amplification factor.

[0115] See also Figure 2 A quantitative analysis and prediction system 20 for floor acceleration amplification factor provided in an embodiment of the present application includes: an acquisition module 201 for acquiring floor acceleration data of each site in a strong earthquake database.

[0116] The calculation module 202 is used to calculate the floor acceleration coefficient according to the floor acceleration data and obtain the factors affecting the floor acceleration magnification coefficient at each station.

[0117] The quantitative analysis module 203 is used to perform quantitative analysis on the factors by using a variance analysis method to determine the significance of each factor on the floor acceleration magnification factor.

[0118] The construction module 204 constructs a prediction model of the floor acceleration amplification factor using a multivariate linear regression method based on the significant factors determined by the variance analysis.

[0119] The prediction module 205 is used to accurately predict the acceleration response under different building conditions according to the prediction model.

[0120] In the embodiments of the present application, "multiple" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the associated objects before and after are in an "or" relationship.

[0121] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0122] The above is only a specific implementation of the present application. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. The protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A quantitative analysis and prediction method for floor acceleration amplification factor, characterized in that: include: Obtain the floor acceleration data of each station in the strong earthquake database; Calculating the floor acceleration coefficient according to the floor acceleration data and obtaining factors affecting the floor acceleration amplification coefficient at each station; The factors are quantitatively analyzed by variance analysis to determine the significance of each factor on the floor acceleration amplification factor; Based on the significant factors determined by variance analysis, a prediction model for floor acceleration amplification coefficient was constructed using multiple linear regression method. The acceleration response under different building conditions is accurately predicted based on the prediction model.

2. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The obtaining of floor acceleration data of each station in the strong earthquake database includes: Obtain the floor acceleration time history curve in the strong earthquake database; The floor acceleration peak value in the floor acceleration time history curve of each floor is obtained.

3. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The formula for calculating the floor acceleration coefficient according to the floor acceleration data is: FAA=PFA / PGA Among them, FAA is the floor acceleration amplification factor, PFA is the floor acceleration peak, and PGA is the ground acceleration peak.

4. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The factors affecting the floor acceleration magnification coefficient at each station are obtained, including: Determine the factors that affect the floor acceleration amplification factor; The factors of different structure types, different structure heights, different site categories, different structure relative heights, different seismic intensity and different structure periods are obtained.

5. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The quantitative analysis of the factors by variance analysis method to determine the significance of each factor on the floor acceleration magnification factor includes: A variance analysis model is constructed, and the variance analysis model is expressed as: Y ij =μ+a i +e ij Where i represents different factor levels or categories, j represents different floor acceleration magnification coefficient values ​​under each factor level, and Y ij is the floor acceleration magnification factor corresponding to the jth observation under the i-th factor level, μ is the average acceleration magnification factor under all factor levels, α i is the effect of the i-th group of factor levels, ε ij is the error term; Calculate the F value in the variance analysis and obtain the P value through the F value; The significance of each factor on the floor acceleration amplification factor is determined based on the P value.

6. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 5, characterized in that: The formula for calculating the F value in the variance analysis is: The calculation formula of the between-group variance is: Where k is the number of levels of different factors that affect the floor acceleration amplification factor, n i is the number of samples at the i-th factor level, is the average value of the acceleration amplification factor of all samples in the i-th group, is the overall average value of all floor acceleration amplification factors; The calculation formula of the within-group variance is: Among them, N is the total number of samples in all groups, Y ij is the floor acceleration amplification factor corresponding to the jth observation under the i-th factor level.

7. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The prediction model of the floor acceleration amplification coefficient is constructed by using a multivariate linear regression method based on the significant factors determined by variance analysis, including: Obtain multiple significant influencing factors after variance analysis; A multiple linear regression model is constructed based on the multiple significant influencing factors, and the multiple linear regression model is expressed as: Y=β0+β1X1+β2X2+.....+β p X p +e; Among them, Y is the floor acceleration magnification factor, X1, X2, X p is a significant factor, β0 is the intercept of the regression equation, β1, β2, β p is the regression coefficient and ε is the error term.

8. The quantitative analysis and prediction method of floor acceleration amplification factor according to claim 1, characterized in that: The prediction model is used to accurately predict the acceleration response under different building conditions, including: A significance test is performed on each regression coefficient in the prediction model. The calculation formula for the verification is: Among them, β j is the regression coefficient of the jth significant influencing factor; SE(β j ) is the regression coefficient β j The standard error of ; t is the test statistic, which represents the regression coefficient β j The relationship between the corresponding factors and the floor acceleration amplification factor; The goodness of fit of the model is calculated, and the goodness of fit calculation formula is: Among them, R 2 is the goodness of fit of the regression model; i is the actual value of the acceleration magnification factor of the i-th floor; is the predicted value of the acceleration amplification factor of the i-th floor; is the overall average of all floor acceleration amplification factors; n is the total number of floor acceleration amplification factors.

9. A quantitative analysis and prediction system for floor acceleration amplification factor, characterized in that: include: An acquisition module is used to obtain the floor acceleration data of each station in the strong earthquake database; A calculation module, used to calculate the floor acceleration coefficient according to the floor acceleration data and obtain factors affecting the floor acceleration amplification coefficient at each station; A quantitative analysis module, used to perform quantitative analysis on the factors by variance analysis method to determine the significance of each factor on the floor acceleration amplification factor; The construction module uses the multivariate linear regression method to construct a prediction model for the floor acceleration amplification factor based on the significant factors determined by variance analysis; The prediction module is used to accurately predict the acceleration response under different building conditions according to the prediction model.

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